TY  - JOUR
AU  - Rymzhanov, R.A.
AU  - Ćosić, Marko
AU  - Medvedev, N.
AU  - Volkov, A.E.
PY  - 2024
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12567
AB  - Surface nanopatterning of CaF2 by swift heavy ions irradiation under oblique angles is studied with a combination of the event-by-event Monte Carlo particle transport model and molecular dynamics simulations. The model describes the electronic system excitation and energy transfer to the lattice followed by the atomic response. The approach allowed us to simulate the kinetics of the electronic ensemble excited by a grazing ion demonstrating that the presence of the surface does not reduce the energy of the lattice as expected. On the contrary, the track core temperature near the surface is slightly higher than in the bulk, because electrons reflected from the surface bring a part of the energy back to the core. The formation kinetics of entire grazing ion tracks is studied revealing the mechanisms of various surface nanostructures formation. Depending on the penetration depth, the ion produces a groove bordered by hillocks, a single chain of nanohillocks, a huge hillock at the end of the rift, and a single continuous structure afterward. The critical depth of the material expulsion from the surface equals approximately to the transient molten zone radius (∼4–4.5 nm). The simulated structures are in reasonable agreement with the available experimental data.
T2  - Applied Surface Science
T1  - From groove to hillocks – Atomic-scale simulations of swift heavy ion grazing impacts on CaF2
VL  - 652
SP  - 159310
DO  - 10.1016/j.apsusc.2024.159310
ER  - 

@article{
author = "Rymzhanov, R.A. and Ćosić, Marko and Medvedev, N. and Volkov, A.E.",
year = "2024",
abstract = "Surface nanopatterning of CaF2 by swift heavy ions irradiation under oblique angles is studied with a combination of the event-by-event Monte Carlo particle transport model and molecular dynamics simulations. The model describes the electronic system excitation and energy transfer to the lattice followed by the atomic response. The approach allowed us to simulate the kinetics of the electronic ensemble excited by a grazing ion demonstrating that the presence of the surface does not reduce the energy of the lattice as expected. On the contrary, the track core temperature near the surface is slightly higher than in the bulk, because electrons reflected from the surface bring a part of the energy back to the core. The formation kinetics of entire grazing ion tracks is studied revealing the mechanisms of various surface nanostructures formation. Depending on the penetration depth, the ion produces a groove bordered by hillocks, a single chain of nanohillocks, a huge hillock at the end of the rift, and a single continuous structure afterward. The critical depth of the material expulsion from the surface equals approximately to the transient molten zone radius (∼4–4.5 nm). The simulated structures are in reasonable agreement with the available experimental data.",
journal = "Applied Surface Science",
title = "From groove to hillocks – Atomic-scale simulations of swift heavy ion grazing impacts on CaF2",
volume = "652",
pages = "159310",
doi = "10.1016/j.apsusc.2024.159310"
}

Rymzhanov, R.A., Ćosić, M., Medvedev, N.,& Volkov, A.E.. (2024). From groove to hillocks – Atomic-scale simulations of swift heavy ion grazing impacts on CaF2. in Applied Surface Science, 652, 159310.
https://doi.org/10.1016/j.apsusc.2024.159310

Rymzhanov R, Ćosić M, Medvedev N, Volkov A. From groove to hillocks – Atomic-scale simulations of swift heavy ion grazing impacts on CaF2. in Applied Surface Science. 2024;652:159310.
doi:10.1016/j.apsusc.2024.159310 .

Rymzhanov, R.A., Ćosić, Marko, Medvedev, N., Volkov, A.E., "From groove to hillocks – Atomic-scale simulations of swift heavy ion grazing impacts on CaF2" in Applied Surface Science, 652 (2024):159310,
https://doi.org/10.1016/j.apsusc.2024.159310 . .

TY  - JOUR
AU  - Ćosić, Marko
PY  - 2024
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12286
AB  - It is well known that diffraction effects belong to the low-energy realm of wave physics, while the channeling effect resides in the high-energy realm of particle physics. The energy increase induces the transition between these two effects and is a well-understood singular semiclassical limiting process. In this paper, it will be shown that in the case of high-energy electron diffraction, the change of beam angular divergence can induce a continuous transition between the quantum planar channeling of electrons and Bragg’s electron diffraction at the constant energy. In the described settings, the appearance of the diffraction maxima in the angular distribution of the transmitted electrons will be connected with the appearance of the quasi- stationary quai-periodic waves in crystal channels.
T2  - Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
T1  - The continuous transition from quantum channeling to the Bragg diffraction at the constant energy
VL  - 1060
SP  - 169025
DO  - 10.1016/j.nima.2023.169025
ER  - 

@article{
author = "Ćosić, Marko",
year = "2024",
abstract = "It is well known that diffraction effects belong to the low-energy realm of wave physics, while the channeling effect resides in the high-energy realm of particle physics. The energy increase induces the transition between these two effects and is a well-understood singular semiclassical limiting process. In this paper, it will be shown that in the case of high-energy electron diffraction, the change of beam angular divergence can induce a continuous transition between the quantum planar channeling of electrons and Bragg’s electron diffraction at the constant energy. In the described settings, the appearance of the diffraction maxima in the angular distribution of the transmitted electrons will be connected with the appearance of the quasi- stationary quai-periodic waves in crystal channels.",
journal = "Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment",
title = "The continuous transition from quantum channeling to the Bragg diffraction at the constant energy",
volume = "1060",
pages = "169025",
doi = "10.1016/j.nima.2023.169025"
}

Ćosić, M.. (2024). The continuous transition from quantum channeling to the Bragg diffraction at the constant energy. in Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1060, 169025.
https://doi.org/10.1016/j.nima.2023.169025

Ćosić M. The continuous transition from quantum channeling to the Bragg diffraction at the constant energy. in Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 2024;1060:169025.
doi:10.1016/j.nima.2023.169025 .

Ćosić, Marko, "The continuous transition from quantum channeling to the Bragg diffraction at the constant energy" in Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1060 (2024):169025,
https://doi.org/10.1016/j.nima.2023.169025 . .

TY  - CONF
AU  - Hadžijojić, Milivoje
AU  - Ćosić, Marko
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12420
AB  - We present the results of our theoretical study of 5 keV proton transmission through two-dimensional crystals. Proton trajectories were obtained by numerical solving Newton's equations of motion. Obtained trajectories are subsequently used to construct the proton angular yield. Singularities of a function that maps initial proton positions to the set of scattering angles form lines in the scattering angle plane along which the angular yield is significantly larger. These lines are named rainbow lines in analogy with optical rainbow scattering. It is shown that the rainbow pattern determines the shape of the angular distribution of transmitted protons. Change in the interaction potential, due to reorientation of the crystal relative to the direction of the incident beam or by varying model parameters, induces nontrivial transformation of the rainbow pattern. We have conducted a thorough study of these transfigurations, which led to the development of the morphological analysis of rainbow scattering. The developed analysis technique is based on the study of shape, not the exact particle count or position of the rainbow line, which makes it insensitive to noise. An established morphological method was used for studying graphene thermal motion. The Debye theory and Molecular Dynamics were used to calculate the covariance matrix of atomic thermal vibrations. It was shown that the outer part of the rainbow pattern can be modeled by ellipses, whose parameters are dependent on the structure of the covariance matrix. A numerical procedure was developed to extract the covariance matrix from the corresponding outer rainbow lines. Furthermore, it was shown that the outer rainbows' size could be used to characterize the atomic composition of two-dimensional crystals. We have investigated the influence of a crystal structure on the rainbow pattern by studying the transmission of protons through graphene containing different point defects. It was shown that each defect type produces a distinctive rainbow pattern, which then could be used to determine the unknown densities of the different defect types present in the same sample.
C3  - SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts
T1  - Analysis of Two-Dimensional Crystals Via Rainbow Scattering
SP  - 60
EP  - 60
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12420
ER  - 

@conference{
author = "Hadžijojić, Milivoje and Ćosić, Marko",
year = "2023",
abstract = "We present the results of our theoretical study of 5 keV proton transmission through two-dimensional crystals. Proton trajectories were obtained by numerical solving Newton's equations of motion. Obtained trajectories are subsequently used to construct the proton angular yield. Singularities of a function that maps initial proton positions to the set of scattering angles form lines in the scattering angle plane along which the angular yield is significantly larger. These lines are named rainbow lines in analogy with optical rainbow scattering. It is shown that the rainbow pattern determines the shape of the angular distribution of transmitted protons. Change in the interaction potential, due to reorientation of the crystal relative to the direction of the incident beam or by varying model parameters, induces nontrivial transformation of the rainbow pattern. We have conducted a thorough study of these transfigurations, which led to the development of the morphological analysis of rainbow scattering. The developed analysis technique is based on the study of shape, not the exact particle count or position of the rainbow line, which makes it insensitive to noise. An established morphological method was used for studying graphene thermal motion. The Debye theory and Molecular Dynamics were used to calculate the covariance matrix of atomic thermal vibrations. It was shown that the outer part of the rainbow pattern can be modeled by ellipses, whose parameters are dependent on the structure of the covariance matrix. A numerical procedure was developed to extract the covariance matrix from the corresponding outer rainbow lines. Furthermore, it was shown that the outer rainbows' size could be used to characterize the atomic composition of two-dimensional crystals. We have investigated the influence of a crystal structure on the rainbow pattern by studying the transmission of protons through graphene containing different point defects. It was shown that each defect type produces a distinctive rainbow pattern, which then could be used to determine the unknown densities of the different defect types present in the same sample.",
journal = "SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts",
title = "Analysis of Two-Dimensional Crystals Via Rainbow Scattering",
pages = "60-60",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12420"
}

Hadžijojić, M.,& Ćosić, M.. (2023). Analysis of Two-Dimensional Crystals Via Rainbow Scattering. in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts, 60-60.
https://hdl.handle.net/21.15107/rcub_vinar_12420

Hadžijojić M, Ćosić M. Analysis of Two-Dimensional Crystals Via Rainbow Scattering. in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts. 2023;:60-60.
https://hdl.handle.net/21.15107/rcub_vinar_12420 .

Hadžijojić, Milivoje, Ćosić, Marko, "Analysis of Two-Dimensional Crystals Via Rainbow Scattering" in SFKM : 21. Simpozijum fizike kondenzovane materije = SCMP : the 21st symposium on condensed matter physics : book of abstracts (2023):60-60,
https://hdl.handle.net/21.15107/rcub_vinar_12420 .

TY  - CONF
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12349
AB  - The main goal of our analysis is to show that the shape of the angular distributions can be used to study 2D materials. For this kind of systems, angular distributions contain lines along which large yield dominantly determine their shape. We focus on the relationship between the reduced interaction potential and the shape of the rainbow pattern. Metamorphoses of the rainbow pattern in the impact parameter plane were investigated and attributed to the bifurcations of the critical points of the rainbow line curvature. It will be shown that the impact parameter rainbow vertices are connected with the corresponding cusps of rainbows in the scattering angle plane, and their bifurcations will be analyzed in detail.
C3  - ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings
T1  - The Morphological analysis of the rainbow scattering effect in proton transmission through graphene
SP  - 115
EP  - 120
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12349
ER  - 

@conference{
author = "Ćosić, Marko and Hadžijojić, Milivoje",
year = "2023",
abstract = "The main goal of our analysis is to show that the shape of the angular distributions can be used to study 2D materials. For this kind of systems, angular distributions contain lines along which large yield dominantly determine their shape. We focus on the relationship between the reduced interaction potential and the shape of the rainbow pattern. Metamorphoses of the rainbow pattern in the impact parameter plane were investigated and attributed to the bifurcations of the critical points of the rainbow line curvature. It will be shown that the impact parameter rainbow vertices are connected with the corresponding cusps of rainbows in the scattering angle plane, and their bifurcations will be analyzed in detail.",
journal = "ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings",
title = "The Morphological analysis of the rainbow scattering effect in proton transmission through graphene",
pages = "115-120",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12349"
}

Ćosić, M.,& Hadžijojić, M.. (2023). The Morphological analysis of the rainbow scattering effect in proton transmission through graphene. in ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings, 115-120.
https://hdl.handle.net/21.15107/rcub_vinar_12349

Ćosić M, Hadžijojić M. The Morphological analysis of the rainbow scattering effect in proton transmission through graphene. in ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings. 2023;:115-120.
https://hdl.handle.net/21.15107/rcub_vinar_12349 .

Ćosić, Marko, Hadžijojić, Milivoje, "The Morphological analysis of the rainbow scattering effect in proton transmission through graphene" in ISI-2023 : 26th International Conference Ion-Surface Interactions : Proceedings (2023):115-120,
https://hdl.handle.net/21.15107/rcub_vinar_12349 .

TY  - CONF
AU  - Ćosić, Marko
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12348
AB  - We are investigating the quantum dynamics of a well-collimated electron beam transmitting through planar channels of the Si crystal. Electron states were represented by wave packets, while the electron beam was treated as an ensemble of noninteracting wave packets. The evolution of electron states was obtained using the method of Chebyshev global propagation, specifically modified to give complex wave functions at arbitrarily chosen time instances without compromising the accuracy of the time propagation. The evolution of the ensemble in the configuration and the phase space was obtained by numerical simulation. We have analyzed how electron dynamics depend on the initial mean position and angular divergence. We have also investigated the relationship between the classical caustic pattern and the shape of the electron Wigner function. Obtained quantum probability densities have multiple maxima generated by an electron’s self-interference. Their sum, which represents an ensemble’s probability density, was found to depend strongly on the beam angular divergence. For small divergence, most peaks are aligned, causing the wavelike behavior of the ensemble. For moderate divergence, the maxima of some are aligned with the minima of others, resulting in the emergence of the classical caustic pattern.
C3  - GRID'2023 : 10th International Conference "Distributed Computing and Grid Technologies in Science and Education"
T1  - Classical patterns in the rainbow channeling of high energy electrons
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12348
ER  - 

@conference{
author = "Ćosić, Marko",
year = "2023",
abstract = "We are investigating the quantum dynamics of a well-collimated electron beam transmitting through planar channels of the Si crystal. Electron states were represented by wave packets, while the electron beam was treated as an ensemble of noninteracting wave packets. The evolution of electron states was obtained using the method of Chebyshev global propagation, specifically modified to give complex wave functions at arbitrarily chosen time instances without compromising the accuracy of the time propagation. The evolution of the ensemble in the configuration and the phase space was obtained by numerical simulation. We have analyzed how electron dynamics depend on the initial mean position and angular divergence. We have also investigated the relationship between the classical caustic pattern and the shape of the electron Wigner function. Obtained quantum probability densities have multiple maxima generated by an electron’s self-interference. Their sum, which represents an ensemble’s probability density, was found to depend strongly on the beam angular divergence. For small divergence, most peaks are aligned, causing the wavelike behavior of the ensemble. For moderate divergence, the maxima of some are aligned with the minima of others, resulting in the emergence of the classical caustic pattern.",
journal = "GRID'2023 : 10th International Conference "Distributed Computing and Grid Technologies in Science and Education"",
title = "Classical patterns in the rainbow channeling of high energy electrons",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12348"
}

Ćosić, M.. (2023). Classical patterns in the rainbow channeling of high energy electrons. in GRID'2023 : 10th International Conference "Distributed Computing and Grid Technologies in Science and Education".
https://hdl.handle.net/21.15107/rcub_vinar_12348

Ćosić M. Classical patterns in the rainbow channeling of high energy electrons. in GRID'2023 : 10th International Conference "Distributed Computing and Grid Technologies in Science and Education". 2023;.
https://hdl.handle.net/21.15107/rcub_vinar_12348 .

Ćosić, Marko, "Classical patterns in the rainbow channeling of high energy electrons" in GRID'2023 : 10th International Conference "Distributed Computing and Grid Technologies in Science and Education" (2023),
https://hdl.handle.net/21.15107/rcub_vinar_12348 .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10615
AB  - We have investigated long-time dynamics of the transverse resonant states occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. This was done by a detailed analysis of quantum carpet, generated by the interference of the resonant states. We found that structure of the carpet depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Close to every fractional revival additional repeated and inverted reconstructed patterns were observed which do not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately, and conclude that dynamics, in this case, is quasi-periodic. This peculiar behavior was traced back to the level of coordination between fluctuations of resonances amplitude and phase functions.
T2  - Chaos, Solitons and Fractals
T1  - Nonlinear dynamics of positron resonances in a carbon nanotube
VL  - 166
SP  - 112898
DO  - 10.1016/j.chaos.2022.112898
ER  - 

@article{
author = "Ćosić, Marko and Hadžijojić, Milivoje",
year = "2023",
abstract = "We have investigated long-time dynamics of the transverse resonant states occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. This was done by a detailed analysis of quantum carpet, generated by the interference of the resonant states. We found that structure of the carpet depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Close to every fractional revival additional repeated and inverted reconstructed patterns were observed which do not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately, and conclude that dynamics, in this case, is quasi-periodic. This peculiar behavior was traced back to the level of coordination between fluctuations of resonances amplitude and phase functions.",
journal = "Chaos, Solitons and Fractals",
title = "Nonlinear dynamics of positron resonances in a carbon nanotube",
volume = "166",
pages = "112898",
doi = "10.1016/j.chaos.2022.112898"
}

Ćosić, M.,& Hadžijojić, M.. (2023). Nonlinear dynamics of positron resonances in a carbon nanotube. in Chaos, Solitons and Fractals, 166, 112898.
https://doi.org/10.1016/j.chaos.2022.112898

Ćosić M, Hadžijojić M. Nonlinear dynamics of positron resonances in a carbon nanotube. in Chaos, Solitons and Fractals. 2023;166:112898.
doi:10.1016/j.chaos.2022.112898 .

Ćosić, Marko, Hadžijojić, Milivoje, "Nonlinear dynamics of positron resonances in a carbon nanotube" in Chaos, Solitons and Fractals, 166 (2023):112898,
https://doi.org/10.1016/j.chaos.2022.112898 . .

TY  - JOUR
AU  - Ćosić, Marko
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11077
AB  - This paper contains the results of the classical, uniform semiclassical, and quantum mechanical study of the channeling of 1 MeV positrons in a short (11, 9) chiral carbon nanotube. In the classical part of the study, we have analyzed the positron trajectories, which reveal the existence of the primary, secondary, and higher-order rainbow lines. The semiclassical part of the study has been performed with the incident positron represented as a plane wave, while in the fully quantum approach, by a wide Gaussian wave packet. In the former case, only the primary rainbow exists; in the latter, the higher-order rainbows also appear. The evolution of the semiclassical spatial distribution of channeled positrons reveals that rainbow and dislocation points are organized in lines. These points and lines are recognized in the evolution of the quantum spatial distribution of channeled positrons. In the quantum party of the study, special attention has been paid to the Bohm positron trajectories and their finite-time Lyapunov exponents. We demonstrate that the classical, semiclassical, and quantum rainbow effects are complex and catastrophic. These results explain entirely the rainbow effect in the positron transmission through the nanotube.
T2  - The European Physical Journal Plus
T1  - On the complexity of the positron’s dynamics in a short carbon nanotube: a full explanation of the rainbow effect
VL  - 138
IS  - 5
SP  - 464
DO  - 10.1140/epjp/s13360-023-04107-w
ER  - 

@article{
author = "Ćosić, Marko",
year = "2023",
abstract = "This paper contains the results of the classical, uniform semiclassical, and quantum mechanical study of the channeling of 1 MeV positrons in a short (11, 9) chiral carbon nanotube. In the classical part of the study, we have analyzed the positron trajectories, which reveal the existence of the primary, secondary, and higher-order rainbow lines. The semiclassical part of the study has been performed with the incident positron represented as a plane wave, while in the fully quantum approach, by a wide Gaussian wave packet. In the former case, only the primary rainbow exists; in the latter, the higher-order rainbows also appear. The evolution of the semiclassical spatial distribution of channeled positrons reveals that rainbow and dislocation points are organized in lines. These points and lines are recognized in the evolution of the quantum spatial distribution of channeled positrons. In the quantum party of the study, special attention has been paid to the Bohm positron trajectories and their finite-time Lyapunov exponents. We demonstrate that the classical, semiclassical, and quantum rainbow effects are complex and catastrophic. These results explain entirely the rainbow effect in the positron transmission through the nanotube.",
journal = "The European Physical Journal Plus",
title = "On the complexity of the positron’s dynamics in a short carbon nanotube: a full explanation of the rainbow effect",
volume = "138",
number = "5",
pages = "464",
doi = "10.1140/epjp/s13360-023-04107-w"
}

Ćosić, M.. (2023). On the complexity of the positron’s dynamics in a short carbon nanotube: a full explanation of the rainbow effect. in The European Physical Journal Plus, 138(5), 464.
https://doi.org/10.1140/epjp/s13360-023-04107-w

Ćosić M. On the complexity of the positron’s dynamics in a short carbon nanotube: a full explanation of the rainbow effect. in The European Physical Journal Plus. 2023;138(5):464.
doi:10.1140/epjp/s13360-023-04107-w .

Ćosić, Marko, "On the complexity of the positron’s dynamics in a short carbon nanotube: a full explanation of the rainbow effect" in The European Physical Journal Plus, 138, no. 5 (2023):464,
https://doi.org/10.1140/epjp/s13360-023-04107-w . .

TY  - JOUR
AU  - Hadžijojić, Milivoje
AU  - Ćosić, Marko
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11092
AB  - We have studied the transmission of 5 keV protons through graphene. Proton dynamics was modeled by classical theory. Proton trajectories define a mapping of the set of initial proton positions to the set of scattering angles. Singularities of the Jacobian associated with the introduced mapping form curves known as the rainbow lines. The differential cross section is infinite along the rainbow lines, making the proton count significantly larger along the rainbow pattern. Hence, rainbows dominantly determine the shape and size of the angular distribution of transmitted protons. It was found that reorientation of the graphene with respect to the incident beam direction and deformation of the graphene crystal lattice induce the transformation of the proton rainbow pattern. We thoroughly studied the morphological properties of the proton rainbow pattern. It was shown that angular distribution and the corresponding rainbow pattern could be used to determine the covariance matrix of atomic thermal displacements and to characterize point defects present in graphene. Graphical abstract: [Figure not available: see fulltext.] © 2023, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.
T2  - European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics
T1  - Study of graphene by proton rainbow scattering
VL  - 77
IS  - 5
SP  - 86
DO  - 10.1140/epjd/s10053-023-00664-y
ER  - 

@article{
author = "Hadžijojić, Milivoje and Ćosić, Marko",
year = "2023",
abstract = "We have studied the transmission of 5 keV protons through graphene. Proton dynamics was modeled by classical theory. Proton trajectories define a mapping of the set of initial proton positions to the set of scattering angles. Singularities of the Jacobian associated with the introduced mapping form curves known as the rainbow lines. The differential cross section is infinite along the rainbow lines, making the proton count significantly larger along the rainbow pattern. Hence, rainbows dominantly determine the shape and size of the angular distribution of transmitted protons. It was found that reorientation of the graphene with respect to the incident beam direction and deformation of the graphene crystal lattice induce the transformation of the proton rainbow pattern. We thoroughly studied the morphological properties of the proton rainbow pattern. It was shown that angular distribution and the corresponding rainbow pattern could be used to determine the covariance matrix of atomic thermal displacements and to characterize point defects present in graphene. Graphical abstract: [Figure not available: see fulltext.] © 2023, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.",
journal = "European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics",
title = "Study of graphene by proton rainbow scattering",
volume = "77",
number = "5",
pages = "86",
doi = "10.1140/epjd/s10053-023-00664-y"
}

Hadžijojić, M.,& Ćosić, M.. (2023). Study of graphene by proton rainbow scattering. in European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics, 77(5), 86.
https://doi.org/10.1140/epjd/s10053-023-00664-y

Hadžijojić M, Ćosić M. Study of graphene by proton rainbow scattering. in European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics. 2023;77(5):86.
doi:10.1140/epjd/s10053-023-00664-y .

Hadžijojić, Milivoje, Ćosić, Marko, "Study of graphene by proton rainbow scattering" in European Physical Journal D. Atoms, Molecules, Clusters and Optical Physics, 77, no. 5 (2023):86,
https://doi.org/10.1140/epjd/s10053-023-00664-y . .

TY  - CONF
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12285
AB  - We have investigated long-time dynamics of the quantum carpets occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. We found that the carpet structure depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Additional inverted revived patterns were observed close to fractional revival, which does not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately and conclude that dynamics, in this case, is quasi-periodic.
C3  - 9th International Conference "Charged & Neutral Particles Channeling Phenomena"
T1  - The structure of quantum carpets in a carbon nanotube
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12285
ER  - 

@conference{
author = "Ćosić, Marko and Hadžijojić, Milivoje",
year = "2023",
abstract = "We have investigated long-time dynamics of the quantum carpets occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. We found that the carpet structure depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Additional inverted revived patterns were observed close to fractional revival, which does not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately and conclude that dynamics, in this case, is quasi-periodic.",
journal = "9th International Conference "Charged & Neutral Particles Channeling Phenomena"",
title = "The structure of quantum carpets in a carbon nanotube",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12285"
}

Ćosić, M.,& Hadžijojić, M.. (2023). The structure of quantum carpets in a carbon nanotube. in 9th International Conference "Charged & Neutral Particles Channeling Phenomena".
https://hdl.handle.net/21.15107/rcub_vinar_12285

Ćosić M, Hadžijojić M. The structure of quantum carpets in a carbon nanotube. in 9th International Conference "Charged & Neutral Particles Channeling Phenomena". 2023;.
https://hdl.handle.net/21.15107/rcub_vinar_12285 .

Ćosić, Marko, Hadžijojić, Milivoje, "The structure of quantum carpets in a carbon nanotube" in 9th International Conference "Charged & Neutral Particles Channeling Phenomena" (2023),
https://hdl.handle.net/21.15107/rcub_vinar_12285 .

TY  - CONF
AU  - Rymzhanov, Ruslan
AU  - O’Connell, Jacques
AU  - Medvedev, Nikita
AU  - Ćosić, Marko
AU  - Skuratov, Vladimir
AU  - Janse van Vuuren, Arno
AU  - Gorbunov, Sergey
AU  - Volkov, Alexander
PY  - 2022
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/12378
AB  - A combined Monte Carlo (MC) and Molecular Dynamics (MD) approach enables us to study in detail effects of different stages of swift heavy ion (SHI) track formation. The MC model (TREKIS [1]) describes excitation of the electronic system and energy transfer to the lattice providing initial conditions for the MD simulations of subsequent lattice response. We discuss here the kinetics of individual track formation, tracks overlap and surface modifications in some amorphizable (YAG, Mg2SiO4) and non-amorphizable (Al2O3, MgO, CaF2) solids irradiated with SHIs. High-resolution transmission electron microscopy analysis of samples irradiated with Xe and Bi ions is used to validate the developed model and to investigate the link between the basic properties of the studied materials and the kinetics of structural changes of the targets. We demonstrate the following: 1) The size and morphology of individual latent tracks and tracks overlap at high fluences are strongly affected by recrystallization of the transiently disordered zone [2]. 2) Different spectra of electrons generated by ions of different energies result in a velocity effect of track formation and a mismatch between the position of the maximal damage and the Bragg peak of the projectile energy loss [3]. 3) Protrusion of molten material and a final structure of surface defects induced by an SHI are governed by mobility of target atoms, surface tensions and recrystallization of a material during the ultra-short cooling period [4]. 4) A target thickness affects formation of surface defects under SHI irradiation: the thinnest layers form a through hole, semispherical and spherical hillocks are created after an ion impact at medium thicknesses, whereas nanoparticle emission occurs from thick layers [5]. 5) Impact of an SHI under a grazing incidence results in formation of a groove-like structure vs. a chain of nanohillocks depending on material and irradiation properties. It can be concluded that hydrodynamic (Rayleigh) instability of molten material on the surface dominates in hillock chain formation over the effect of the dependence of ion energy loss on the impact parameter.
PB  - Helsinki, Finland : University of Helsinki
C3  - ICACS & SHIM 2022 : 29th International conference on atomic collisions in solids & 11th International symposium on swift heavy ions in matter : Book of abstracts
T1  - Comprehensive model of SHI impacts: from ion passage to track formation
SP  - 39
EP  - 39
UR  - https://hdl.handle.net/21.15107/rcub_vinar_12378
ER  - 

@conference{
author = "Rymzhanov, Ruslan and O’Connell, Jacques and Medvedev, Nikita and Ćosić, Marko and Skuratov, Vladimir and Janse van Vuuren, Arno and Gorbunov, Sergey and Volkov, Alexander",
year = "2022",
abstract = "A combined Monte Carlo (MC) and Molecular Dynamics (MD) approach enables us to study in detail effects of different stages of swift heavy ion (SHI) track formation. The MC model (TREKIS [1]) describes excitation of the electronic system and energy transfer to the lattice providing initial conditions for the MD simulations of subsequent lattice response. We discuss here the kinetics of individual track formation, tracks overlap and surface modifications in some amorphizable (YAG, Mg2SiO4) and non-amorphizable (Al2O3, MgO, CaF2) solids irradiated with SHIs. High-resolution transmission electron microscopy analysis of samples irradiated with Xe and Bi ions is used to validate the developed model and to investigate the link between the basic properties of the studied materials and the kinetics of structural changes of the targets. We demonstrate the following: 1) The size and morphology of individual latent tracks and tracks overlap at high fluences are strongly affected by recrystallization of the transiently disordered zone [2]. 2) Different spectra of electrons generated by ions of different energies result in a velocity effect of track formation and a mismatch between the position of the maximal damage and the Bragg peak of the projectile energy loss [3]. 3) Protrusion of molten material and a final structure of surface defects induced by an SHI are governed by mobility of target atoms, surface tensions and recrystallization of a material during the ultra-short cooling period [4]. 4) A target thickness affects formation of surface defects under SHI irradiation: the thinnest layers form a through hole, semispherical and spherical hillocks are created after an ion impact at medium thicknesses, whereas nanoparticle emission occurs from thick layers [5]. 5) Impact of an SHI under a grazing incidence results in formation of a groove-like structure vs. a chain of nanohillocks depending on material and irradiation properties. It can be concluded that hydrodynamic (Rayleigh) instability of molten material on the surface dominates in hillock chain formation over the effect of the dependence of ion energy loss on the impact parameter.",
publisher = "Helsinki, Finland : University of Helsinki",
journal = "ICACS & SHIM 2022 : 29th International conference on atomic collisions in solids & 11th International symposium on swift heavy ions in matter : Book of abstracts",
title = "Comprehensive model of SHI impacts: from ion passage to track formation",
pages = "39-39",
url = "https://hdl.handle.net/21.15107/rcub_vinar_12378"
}

Rymzhanov, R., O’Connell, J., Medvedev, N., Ćosić, M., Skuratov, V., Janse van Vuuren, A., Gorbunov, S.,& Volkov, A.. (2022). Comprehensive model of SHI impacts: from ion passage to track formation. in ICACS & SHIM 2022 : 29th International conference on atomic collisions in solids & 11th International symposium on swift heavy ions in matter : Book of abstracts
Helsinki, Finland : University of Helsinki., 39-39.
https://hdl.handle.net/21.15107/rcub_vinar_12378

Rymzhanov R, O’Connell J, Medvedev N, Ćosić M, Skuratov V, Janse van Vuuren A, Gorbunov S, Volkov A. Comprehensive model of SHI impacts: from ion passage to track formation. in ICACS & SHIM 2022 : 29th International conference on atomic collisions in solids & 11th International symposium on swift heavy ions in matter : Book of abstracts. 2022;:39-39.
https://hdl.handle.net/21.15107/rcub_vinar_12378 .

Rymzhanov, Ruslan, O’Connell, Jacques, Medvedev, Nikita, Ćosić, Marko, Skuratov, Vladimir, Janse van Vuuren, Arno, Gorbunov, Sergey, Volkov, Alexander, "Comprehensive model of SHI impacts: from ion passage to track formation" in ICACS & SHIM 2022 : 29th International conference on atomic collisions in solids & 11th International symposium on swift heavy ions in matter : Book of abstracts (2022):39-39,
https://hdl.handle.net/21.15107/rcub_vinar_12378 .

TY  - JOUR
AU  - Ćosić, Marko
PY  - 2022
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10255
AB  - The freedom to define branch cuts of the complex function is used to derive an integral representation of the quantum carpet, thus producing a generalization of the Poincaré recurrence theorem in the case of the continuous spectrum. This approach provides a different way to renormalize resonant states to be both space and time convergent. The coherence of quantum carpets was related to the properties of the Wigner function in the canonical time-frequency phase space. It has been shown that the distortion of the Wigner function shape is directly responsible for the lack of the ability of the dynamics to produce revivals equally as sharp as the initial wave packet.
T2  - Physical Review A
T1  - Quantum carpets in a leaky box: Poincaré's recurrences in the continuous spectrum
VL  - 105
IS  - 4
SP  - 042218
DO  - 10.1103/PhysRevA.105.042218
ER  - 

@article{
author = "Ćosić, Marko",
year = "2022",
abstract = "The freedom to define branch cuts of the complex function is used to derive an integral representation of the quantum carpet, thus producing a generalization of the Poincaré recurrence theorem in the case of the continuous spectrum. This approach provides a different way to renormalize resonant states to be both space and time convergent. The coherence of quantum carpets was related to the properties of the Wigner function in the canonical time-frequency phase space. It has been shown that the distortion of the Wigner function shape is directly responsible for the lack of the ability of the dynamics to produce revivals equally as sharp as the initial wave packet.",
journal = "Physical Review A",
title = "Quantum carpets in a leaky box: Poincaré's recurrences in the continuous spectrum",
volume = "105",
number = "4",
pages = "042218",
doi = "10.1103/PhysRevA.105.042218"
}

Ćosić, M.. (2022). Quantum carpets in a leaky box: Poincaré's recurrences in the continuous spectrum. in Physical Review A, 105(4), 042218.
https://doi.org/10.1103/PhysRevA.105.042218

Ćosić M. Quantum carpets in a leaky box: Poincaré's recurrences in the continuous spectrum. in Physical Review A. 2022;105(4):042218.
doi:10.1103/PhysRevA.105.042218 .

Ćosić, Marko, "Quantum carpets in a leaky box: Poincaré's recurrences in the continuous spectrum" in Physical Review A, 105, no. 4 (2022):042218,
https://doi.org/10.1103/PhysRevA.105.042218 . .

TY  - JOUR
AU  - Despotović, Sanja Z.
AU  - Ćosić, Marko
PY  - 2022
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10381
AB  - The morphological method—based on the topology and singularity theory and originally developed for the analysis of the scattering experiments—was extended to be applicable for the analysis of biological data. The usefulness of the topological viewpoint was demonstrated by quantification of the changes in collagen fiber straightness in the human colon mucosa (healthy mucosa, colorectal cancer, and uninvolved mucosa far from cancer). This has been done by modeling the distribution of collagen segment angles by the polymorphic beta-distribution. Its shapes were classified according to the number and type of critical points. We found that biologically relevant shapes could be classified as shapes without any preferable orientation (i.e. shapes without local extrema), transitional forms (i.e. forms with one broad local maximum), and highly oriented forms (i.e. forms with two minima at both ends and one very narrow maximum between them). Thus, changes in the fiber organization were linked to the metamorphoses of the beta-distribution forms. The obtained classification was used to define a new, shape-aware/based, measure of the collagen straightness, which revealed a slight and moderate increase of the straightness in mucosa samples taken 20 and 10 cm away from the tumor. The largest increase of collagen straightness was found in samples of cancer tissue. Samples of healthy individuals have a uniform distribution of beta-distribution forms. We found that this distribution has the maximal information entropy. At 20 cm and 10 cm away from cancer, the transition forms redistribute into unoriented and highly oriented forms. Closer to cancer the number of unoriented forms decreases rapidly leaving only highly oriented forms present in the samples of the cancer tissue, whose distribution has minimal information entropy. The polarization of the distribution was followed by a significant increase in the number of quasi-symmetrical forms in samples 20 cm away from cancer which decreases closer to cancer. This work shows that the evolution of the distribution of the beta-distribution forms—an abstract construction of the mind—follows the familiar laws of statistical mechanics. Additionally, the polarization of the beta-distribution forms together with the described change in the number of quasi-symmetrical forms, clearly visible in the parametric space of the beta-distribution and very difficult to notice in the observable space, can be a useful indicator of the early stages in the development of colorectal cancer.
T2  - Frontiers in Physics
T1  - The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer
VL  - 10
DO  - 10.3389/fphy.2022.915644
ER  - 

@article{
author = "Despotović, Sanja Z. and Ćosić, Marko",
year = "2022",
abstract = "The morphological method—based on the topology and singularity theory and originally developed for the analysis of the scattering experiments—was extended to be applicable for the analysis of biological data. The usefulness of the topological viewpoint was demonstrated by quantification of the changes in collagen fiber straightness in the human colon mucosa (healthy mucosa, colorectal cancer, and uninvolved mucosa far from cancer). This has been done by modeling the distribution of collagen segment angles by the polymorphic beta-distribution. Its shapes were classified according to the number and type of critical points. We found that biologically relevant shapes could be classified as shapes without any preferable orientation (i.e. shapes without local extrema), transitional forms (i.e. forms with one broad local maximum), and highly oriented forms (i.e. forms with two minima at both ends and one very narrow maximum between them). Thus, changes in the fiber organization were linked to the metamorphoses of the beta-distribution forms. The obtained classification was used to define a new, shape-aware/based, measure of the collagen straightness, which revealed a slight and moderate increase of the straightness in mucosa samples taken 20 and 10 cm away from the tumor. The largest increase of collagen straightness was found in samples of cancer tissue. Samples of healthy individuals have a uniform distribution of beta-distribution forms. We found that this distribution has the maximal information entropy. At 20 cm and 10 cm away from cancer, the transition forms redistribute into unoriented and highly oriented forms. Closer to cancer the number of unoriented forms decreases rapidly leaving only highly oriented forms present in the samples of the cancer tissue, whose distribution has minimal information entropy. The polarization of the distribution was followed by a significant increase in the number of quasi-symmetrical forms in samples 20 cm away from cancer which decreases closer to cancer. This work shows that the evolution of the distribution of the beta-distribution forms—an abstract construction of the mind—follows the familiar laws of statistical mechanics. Additionally, the polarization of the beta-distribution forms together with the described change in the number of quasi-symmetrical forms, clearly visible in the parametric space of the beta-distribution and very difficult to notice in the observable space, can be a useful indicator of the early stages in the development of colorectal cancer.",
journal = "Frontiers in Physics",
title = "The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer",
volume = "10",
doi = "10.3389/fphy.2022.915644"
}

Despotović, S. Z.,& Ćosić, M.. (2022). The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer. in Frontiers in Physics, 10.
https://doi.org/10.3389/fphy.2022.915644

Despotović SZ, Ćosić M. The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer. in Frontiers in Physics. 2022;10.
doi:10.3389/fphy.2022.915644 .

Despotović, Sanja Z., Ćosić, Marko, "The Morphological Analysis of the Collagen Fiber Straightness in the Healthy Uninvolved Human Colon Mucosa Away From the Cancer" in Frontiers in Physics, 10 (2022),
https://doi.org/10.3389/fphy.2022.915644 . .

TY  - CONF
AU  - Butenko, Yuri A.
AU  - Ćosić, Marko
AU  - Nechaevskiy, Andrey V.
AU  - Podgainy, Dmitriy V.
AU  - Rahmonov, Ilhom R.
AU  - Stadnik, Alexey V.
AU  - Streltsova, Oksana I.
AU  - Zuev, Maxim I.
PY  - 2022
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10564
AB  - The work presents the possibilities for using the ML/DL/HPC ecosystem deployed on the HybriLIT Heterogeneous Platform (Meshcheryakov Laboratory of Information Technologies JINR) on top of JupyterHub, which provides opportunities for solving tasks not only in the field of machine learning and deep learning, but also for the convenient organization of calculations and scientific visualization. The ecosystem allows one to develop and implement program modules in Python, as well as to carry out methodical computations. The relevance of deploying such an environment is primarily associated with the great demand for software modules that are provided to a group of researchers or the scientific community, when all stages of the study can be reproduced; the code has been modified and used by the scientific community. Using the example of solving a specific problem to study the dynamics of magnetization in a Phi-0 Josephson Junction (Superconductor-Ferromagnet-Superconductor structure), a methodology for developing software modules is presented; it enables not only to carry out calculations, but also to visualize the results of the study and accompany them with the necessary formulas and explanations. The possibility of parallel implementation of the algorithm for performing computations for various values of parameters of the model based on the Joblib Python library is shown, and the results of computational experiments demonstrating the efficiency of parallel data processing are presented.
C3  - Proceedings of Science
T1  - ML/DL/HPC Ecosystem of the HybriLIT Heterogeneous Platform (MLIT JINR): New Opportunities for Applied Research
VL  - 429
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10564
ER  - 

@conference{
author = "Butenko, Yuri A. and Ćosić, Marko and Nechaevskiy, Andrey V. and Podgainy, Dmitriy V. and Rahmonov, Ilhom R. and Stadnik, Alexey V. and Streltsova, Oksana I. and Zuev, Maxim I.",
year = "2022",
abstract = "The work presents the possibilities for using the ML/DL/HPC ecosystem deployed on the HybriLIT Heterogeneous Platform (Meshcheryakov Laboratory of Information Technologies JINR) on top of JupyterHub, which provides opportunities for solving tasks not only in the field of machine learning and deep learning, but also for the convenient organization of calculations and scientific visualization. The ecosystem allows one to develop and implement program modules in Python, as well as to carry out methodical computations. The relevance of deploying such an environment is primarily associated with the great demand for software modules that are provided to a group of researchers or the scientific community, when all stages of the study can be reproduced; the code has been modified and used by the scientific community. Using the example of solving a specific problem to study the dynamics of magnetization in a Phi-0 Josephson Junction (Superconductor-Ferromagnet-Superconductor structure), a methodology for developing software modules is presented; it enables not only to carry out calculations, but also to visualize the results of the study and accompany them with the necessary formulas and explanations. The possibility of parallel implementation of the algorithm for performing computations for various values of parameters of the model based on the Joblib Python library is shown, and the results of computational experiments demonstrating the efficiency of parallel data processing are presented.",
journal = "Proceedings of Science",
title = "ML/DL/HPC Ecosystem of the HybriLIT Heterogeneous Platform (MLIT JINR): New Opportunities for Applied Research",
volume = "429",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10564"
}

Butenko, Y. A., Ćosić, M., Nechaevskiy, A. V., Podgainy, D. V., Rahmonov, I. R., Stadnik, A. V., Streltsova, O. I.,& Zuev, M. I.. (2022). ML/DL/HPC Ecosystem of the HybriLIT Heterogeneous Platform (MLIT JINR): New Opportunities for Applied Research. in Proceedings of Science, 429.
https://hdl.handle.net/21.15107/rcub_vinar_10564

Butenko YA, Ćosić M, Nechaevskiy AV, Podgainy DV, Rahmonov IR, Stadnik AV, Streltsova OI, Zuev MI. ML/DL/HPC Ecosystem of the HybriLIT Heterogeneous Platform (MLIT JINR): New Opportunities for Applied Research. in Proceedings of Science. 2022;429.
https://hdl.handle.net/21.15107/rcub_vinar_10564 .

Butenko, Yuri A., Ćosić, Marko, Nechaevskiy, Andrey V., Podgainy, Dmitriy V., Rahmonov, Ilhom R., Stadnik, Alexey V., Streltsova, Oksana I., Zuev, Maxim I., "ML/DL/HPC Ecosystem of the HybriLIT Heterogeneous Platform (MLIT JINR): New Opportunities for Applied Research" in Proceedings of Science, 429 (2022),
https://hdl.handle.net/21.15107/rcub_vinar_10564 .

TY  - JOUR
AU  - Hadžijojić, Milivoje
AU  - Ćosić, Marko
AU  - Rymzhanov, Ruslan
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9968
AB  - We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.
T2  - Journal of Physical Chemistry C
T1  - Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene
VL  - 125
IS  - 38
SP  - 21030
EP  - 21043
DO  - 10.1021/acs.jpcc.1c05971
ER  - 

@article{
author = "Hadžijojić, Milivoje and Ćosić, Marko and Rymzhanov, Ruslan",
year = "2021",
abstract = "We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.",
journal = "Journal of Physical Chemistry C",
title = "Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene",
volume = "125",
number = "38",
pages = "21030-21043",
doi = "10.1021/acs.jpcc.1c05971"
}

Hadžijojić, M., Ćosić, M.,& Rymzhanov, R.. (2021). Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene. in Journal of Physical Chemistry C, 125(38), 21030-21043.
https://doi.org/10.1021/acs.jpcc.1c05971

Hadžijojić M, Ćosić M, Rymzhanov R. Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene. in Journal of Physical Chemistry C. 2021;125(38):21030-21043.
doi:10.1021/acs.jpcc.1c05971 .

Hadžijojić, Milivoje, Ćosić, Marko, Rymzhanov, Ruslan, "Morphological Analysis of the Rainbow Patterns Created by Point Defects of Graphene" in Journal of Physical Chemistry C, 125, no. 38 (2021):21030-21043,
https://doi.org/10.1021/acs.jpcc.1c05971 . .

TY  - CONF
AU  - Jovanović, Zoran
AU  - Balvanović, Roman V.
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
AU  - Telečki, Igor N.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10280
AB  - FAMA is a user facility for materials science with low-energy ion beams in the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. It includes a heavy ion source, a light ion source, two channels for modification of materials, and two channels for analysis of materials. Recently, the designing of a channel for transmission studies within FAMA has begun. The initial studies to be undertaken in this channel are related to the rainbow e ffects with very thin electrostatic lenses and two-dimensional materials.
C3  - 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi
T1  - Transmission Studies With Ion Beams Within FAMA
SP  - 127
EP  - 128
DO  - 10.18429/JACoW-RuPAC2021-FRB07
ER  - 

@conference{
author = "Jovanović, Zoran and Balvanović, Roman V. and Ćosić, Marko and Nešković, Nebojša B. and Telečki, Igor N.",
year = "2021",
abstract = "FAMA is a user facility for materials science with low-energy ion beams in the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. It includes a heavy ion source, a light ion source, two channels for modification of materials, and two channels for analysis of materials. Recently, the designing of a channel for transmission studies within FAMA has begun. The initial studies to be undertaken in this channel are related to the rainbow e ffects with very thin electrostatic lenses and two-dimensional materials.",
journal = "27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi",
title = "Transmission Studies With Ion Beams Within FAMA",
pages = "127-128",
doi = "10.18429/JACoW-RuPAC2021-FRB07"
}

Jovanović, Z., Balvanović, R. V., Ćosić, M., Nešković, N. B.,& Telečki, I. N.. (2021). Transmission Studies With Ion Beams Within FAMA. in 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi, 127-128.
https://doi.org/10.18429/JACoW-RuPAC2021-FRB07

Jovanović Z, Balvanović RV, Ćosić M, Nešković NB, Telečki IN. Transmission Studies With Ion Beams Within FAMA. in 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi. 2021;:127-128.
doi:10.18429/JACoW-RuPAC2021-FRB07 .

Jovanović, Zoran, Balvanović, Roman V., Ćosić, Marko, Nešković, Nebojša B., Telečki, Igor N., "Transmission Studies With Ion Beams Within FAMA" in 27th Russian Particle Accelerator Conference (RuPAC'21) : 27 September-01 October 2021, Alushta, Russi (2021):127-128,
https://doi.org/10.18429/JACoW-RuPAC2021-FRB07 . .

TY  - CHAP
AU  - Petrović, Srđan M.
AU  - Starčević, Nikola
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10309
AB  - This work shows how recent experimental results of angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction can be explained by the very accurate rainbow ion-atom interaction potential. The obtained results are compared with the ones applying universal ZBL interaction ion-atom potential, which is mainly used in the literature. © 2021 Walter de Gruyter GmbH, Berlin/Boston.
T2  - Advanced Ceramics and Applications
T1  - On the doughnut effect and the rainbow proton-silicon interaction potential
SP  - 271
EP  - 276
DO  - 10.1515/9783110627992-019
ER  - 

@inbook{
author = "Petrović, Srđan M. and Starčević, Nikola and Ćosić, Marko and Nešković, Nebojša B.",
year = "2021",
abstract = "This work shows how recent experimental results of angular distributions of 2 MeV protons channeled in a 55-nm-thick (001) silicon crystal tilted away from the [001] direction can be explained by the very accurate rainbow ion-atom interaction potential. The obtained results are compared with the ones applying universal ZBL interaction ion-atom potential, which is mainly used in the literature. © 2021 Walter de Gruyter GmbH, Berlin/Boston.",
journal = "Advanced Ceramics and Applications",
booktitle = "On the doughnut effect and the rainbow proton-silicon interaction potential",
pages = "271-276",
doi = "10.1515/9783110627992-019"
}

Petrović, S. M., Starčević, N., Ćosić, M.,& Nešković, N. B.. (2021). On the doughnut effect and the rainbow proton-silicon interaction potential. in Advanced Ceramics and Applications, 271-276.
https://doi.org/10.1515/9783110627992-019

Petrović SM, Starčević N, Ćosić M, Nešković NB. On the doughnut effect and the rainbow proton-silicon interaction potential. in Advanced Ceramics and Applications. 2021;:271-276.
doi:10.1515/9783110627992-019 .

Petrović, Srđan M., Starčević, Nikola, Ćosić, Marko, Nešković, Nebojša B., "On the doughnut effect and the rainbow proton-silicon interaction potential" in Advanced Ceramics and Applications (2021):271-276,
https://doi.org/10.1515/9783110627992-019 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Takabayashi, Yuichi
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9144
AB  - We are investigating the quantum dynamics of a well-collimated electron beam transmitting through planar channels of the Si crystal. Electron states were represented by wave packets while the electron beam is treated as an ensemble of noninteracting wave packets. We have investigated the relationship between classical caustic pattern and anharmonicity of the potential and analyzed how quantum dynamic depends on the wave packet impact parameter and beam's angular divergence. We found that the extrema of the electron trajectory period, considered as a function of the impact parameter, determine the shape of the caustic pattern. All wave packet probability densities have multiple maxima generated by a self-interference. Their sum, that represents probability density of an ensemble, was found to depends strongly on the beam angular divergence. For small divergence, most peaks of different wave packets are aligned causing wavelike behavior of the ensemble. For moderate angular divergence maxima of some wave packets, are aligned with minima of others, resulting in the emergence of the classical caustic pattern. We have shown and experimentally confirmed that the only indication that the observed caustic pattern is generated by the quantum dynamics is a slight systematic shift of the corresponding caustic maxima. © 2021 American Physical Society.
T2  - Physical Review A
T1  - Classical patterns in the quantum rainbow channeling of high energy electrons
VL  - 103
IS  - 2
SP  - 022818
DO  - 10.1103/PhysRevA.103.022818
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Takabayashi, Yuichi",
year = "2021",
abstract = "We are investigating the quantum dynamics of a well-collimated electron beam transmitting through planar channels of the Si crystal. Electron states were represented by wave packets while the electron beam is treated as an ensemble of noninteracting wave packets. We have investigated the relationship between classical caustic pattern and anharmonicity of the potential and analyzed how quantum dynamic depends on the wave packet impact parameter and beam's angular divergence. We found that the extrema of the electron trajectory period, considered as a function of the impact parameter, determine the shape of the caustic pattern. All wave packet probability densities have multiple maxima generated by a self-interference. Their sum, that represents probability density of an ensemble, was found to depends strongly on the beam angular divergence. For small divergence, most peaks of different wave packets are aligned causing wavelike behavior of the ensemble. For moderate angular divergence maxima of some wave packets, are aligned with minima of others, resulting in the emergence of the classical caustic pattern. We have shown and experimentally confirmed that the only indication that the observed caustic pattern is generated by the quantum dynamics is a slight systematic shift of the corresponding caustic maxima. © 2021 American Physical Society.",
journal = "Physical Review A",
title = "Classical patterns in the quantum rainbow channeling of high energy electrons",
volume = "103",
number = "2",
pages = "022818",
doi = "10.1103/PhysRevA.103.022818"
}

Ćosić, M., Petrović, S. M.,& Takabayashi, Y.. (2021). Classical patterns in the quantum rainbow channeling of high energy electrons. in Physical Review A, 103(2), 022818.
https://doi.org/10.1103/PhysRevA.103.022818

Ćosić M, Petrović SM, Takabayashi Y. Classical patterns in the quantum rainbow channeling of high energy electrons. in Physical Review A. 2021;103(2):022818.
doi:10.1103/PhysRevA.103.022818 .

Ćosić, Marko, Petrović, Srđan M., Takabayashi, Yuichi, "Classical patterns in the quantum rainbow channeling of high energy electrons" in Physical Review A, 103, no. 2 (2021):022818,
https://doi.org/10.1103/PhysRevA.103.022818 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Bellucci, Stefano
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9675
AB  - This is a study of proton transmission through planar channels of tungsten, where a proton beam is treated as an ensemble of noninteracting wave packets. For this system, the structural stability manifests in an appearance of caustic lines, and as an equivalence of self-interference produced waveforms with canonical diffraction patterns. We will show that coordination between particle self-interference is an additional manifestation of the structural stability existing only in ensembles. The main focus of the analysis was on the ability of the coordination to produce classical structures. We have found that the structures produced by the self-interference are organized in a very different manner. The coordination can enhance or suppress the quantum aspects of the dynamics. This behavior is explained by distributions of inflection, undulation, and singular points of the ensemble phase function, and their bifurcations. We have shown that the coordination has a topological origin which allows classical and quantum levels of reality to exist simultaneously. The classical behavior of the ensemble emerges out of the quantum dynamics without a need for reduction of the quantum to the classical laws of motion.
T2  - Scientific Reports
T1  - Coordinated self-interference of wave packets: a new route towards classicality for structurally stable systems
VL  - 10
IS  - 1
SP  - 16949
DO  - 10.1038/s41598-020-72965-w
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Bellucci, Stefano",
year = "2020",
abstract = "This is a study of proton transmission through planar channels of tungsten, where a proton beam is treated as an ensemble of noninteracting wave packets. For this system, the structural stability manifests in an appearance of caustic lines, and as an equivalence of self-interference produced waveforms with canonical diffraction patterns. We will show that coordination between particle self-interference is an additional manifestation of the structural stability existing only in ensembles. The main focus of the analysis was on the ability of the coordination to produce classical structures. We have found that the structures produced by the self-interference are organized in a very different manner. The coordination can enhance or suppress the quantum aspects of the dynamics. This behavior is explained by distributions of inflection, undulation, and singular points of the ensemble phase function, and their bifurcations. We have shown that the coordination has a topological origin which allows classical and quantum levels of reality to exist simultaneously. The classical behavior of the ensemble emerges out of the quantum dynamics without a need for reduction of the quantum to the classical laws of motion.",
journal = "Scientific Reports",
title = "Coordinated self-interference of wave packets: a new route towards classicality for structurally stable systems",
volume = "10",
number = "1",
pages = "16949",
doi = "10.1038/s41598-020-72965-w"
}

Ćosić, M., Petrović, S. M.,& Bellucci, S.. (2020). Coordinated self-interference of wave packets: a new route towards classicality for structurally stable systems. in Scientific Reports, 10(1), 16949.
https://doi.org/10.1038/s41598-020-72965-w

Ćosić M, Petrović SM, Bellucci S. Coordinated self-interference of wave packets: a new route towards classicality for structurally stable systems. in Scientific Reports. 2020;10(1):16949.
doi:10.1038/s41598-020-72965-w .

Ćosić, Marko, Petrović, Srđan M., Bellucci, Stefano, "Coordinated self-interference of wave packets: a new route towards classicality for structurally stable systems" in Scientific Reports, 10, no. 1 (2020):16949,
https://doi.org/10.1038/s41598-020-72965-w . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Bellucci, Stefano
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9680
AB  - We have investigated the dynamics of a quantum particle in the optical lattice potential. Initially, the quantum particle was represented by a Gaussian wave packet, located in the center of the well. The corresponding Schrödinger equation was solved explicitly by the method of the Chebyshev global propagation. Obtained solutions were also used for the construction of the Wigner functions. We found a great number of local abrupt changes of the solution shape. To explain this behavior, we used the fact that structurally stable systems, which form the largest class of the low dimensional dynamical systems, can be modeled and classified according to the catastrophe theory. All important features of the exact solution were explained on the basis of the mathematical properties of the catastrophic model. Such an approach enabled us to extract relevant information out of numerical solutions without employing any kind of approximations. We have investigated the influence of the Wigner catastrophes on the details of the quantum-classical correspondence breakdown. The wave packet was found to expand rapidly, filling the whole classically available area of the phase space. It was found that its self-interference pattern saturates quickly. A region of the phase space emerges in which the Wigner function oscillations transform into the singularity driven fluctuations. Once this region covers the whole area of the phase space, a wave packet dynamics enters into the new regime where its Wigner function fluctuates around the ergodic average. It will be shown that all mentioned processes are caused by the proliferation of the catastrophes and their mutual interactions
T2  - Chaos
T1  - On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential
VL  - 30
IS  - 10
SP  - 103107
DO  - 10.1063/1.5140528
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Bellucci, Stefano",
year = "2020",
abstract = "We have investigated the dynamics of a quantum particle in the optical lattice potential. Initially, the quantum particle was represented by a Gaussian wave packet, located in the center of the well. The corresponding Schrödinger equation was solved explicitly by the method of the Chebyshev global propagation. Obtained solutions were also used for the construction of the Wigner functions. We found a great number of local abrupt changes of the solution shape. To explain this behavior, we used the fact that structurally stable systems, which form the largest class of the low dimensional dynamical systems, can be modeled and classified according to the catastrophe theory. All important features of the exact solution were explained on the basis of the mathematical properties of the catastrophic model. Such an approach enabled us to extract relevant information out of numerical solutions without employing any kind of approximations. We have investigated the influence of the Wigner catastrophes on the details of the quantum-classical correspondence breakdown. The wave packet was found to expand rapidly, filling the whole classically available area of the phase space. It was found that its self-interference pattern saturates quickly. A region of the phase space emerges in which the Wigner function oscillations transform into the singularity driven fluctuations. Once this region covers the whole area of the phase space, a wave packet dynamics enters into the new regime where its Wigner function fluctuates around the ergodic average. It will be shown that all mentioned processes are caused by the proliferation of the catastrophes and their mutual interactions",
journal = "Chaos",
title = "On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential",
volume = "30",
number = "10",
pages = "103107",
doi = "10.1063/1.5140528"
}

Ćosić, M., Petrović, S. M.,& Bellucci, S.. (2020). On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential. in Chaos, 30(10), 103107.
https://doi.org/10.1063/1.5140528

Ćosić M, Petrović SM, Bellucci S. On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential. in Chaos. 2020;30(10):103107.
doi:10.1063/1.5140528 .

Ćosić, Marko, Petrović, Srđan M., Bellucci, Stefano, "On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential" in Chaos, 30, no. 10 (2020):103107,
https://doi.org/10.1063/1.5140528 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Nešković, Nebojša B.
AU  - Petrović, Srđan M.
PY  - 2019
UR  - https://linkinghub.elsevier.com/retrieve/pii/S0168583X19300758
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8049
AB  - This is a theoretical study of the superfocusing and zero-degree focusing effects appearing in channeling of protons of energy of 2 MeV in the {1 1 0} channel of a thin silicon crystal. We prove that the ultimate origin of these effects is the crystal rainbow effect, which has been discovered and explored in ion transmission through axial crystal channels, nanotubes and graphene. Moreover, the effect is the origin of the shapes of the whole spatial and angular distributions of channeled protons. The incident proton velocity vector is taken to be parallel to the channel midplane. We use the Molière's approximation of the Thomas-Fermi proton-atom interaction potential and the continuum approximation. The effect of thermal vibrations of the crystal's atoms is included. We solve numerically the proton equation of motion and analyze the spatial and angular proton transmission functions. The extrema of these functions are the spatial and angular rainbow points, respectively. When the whole proton beam is taken into account, a spatial rainbow pattern, composed of the lines emerging from the superfocusing points, and an angular rainbow pattern, consisting of the lines emerging from the origin and the zero-degree focusing points, appear along the channel. We consider the region of crystal thickness comprising the first, second and third superfocusing and zero-degree focusing points. When the effect of thermal vibrations is neglected, each of these rainbow lines look like the bifurcation set of the cusp catastrophe, and when the effect is included, the line resembles the bifurcation set of the butterfly catastrophe. We demonstrate that the spatial and angular distributions of transmitted protons are fully determined by the spatial and angular rainbow lines, respectively. The superfocusing and zero-degree focusing effects weaken with the increase of the crystal thickness. This is a consequence of the anharmonicity of the continuum proton-crystal interaction potential, which makes the proton beam propagation through the channel incoherent. We also explore the influence of the effect of proton collisions with the crystal's electrons on the beam dynamics in the channel. This effect additionally contributes to the incoherence of the beam motion along the channel. Our opinion is that the peaks of the spatial and angular distributions of ions transmitted through the planar channels lying off the origin registered before were in fact the rainbow peaks. © 2019 Elsevier B.V.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal
VL  - 444
SP  - 10
EP  - 22
DO  - 10.1016/j.nimb.2019.02.004
ER  - 

@article{
author = "Ćosić, Marko and Nešković, Nebojša B. and Petrović, Srđan M.",
year = "2019",
abstract = "This is a theoretical study of the superfocusing and zero-degree focusing effects appearing in channeling of protons of energy of 2 MeV in the {1 1 0} channel of a thin silicon crystal. We prove that the ultimate origin of these effects is the crystal rainbow effect, which has been discovered and explored in ion transmission through axial crystal channels, nanotubes and graphene. Moreover, the effect is the origin of the shapes of the whole spatial and angular distributions of channeled protons. The incident proton velocity vector is taken to be parallel to the channel midplane. We use the Molière's approximation of the Thomas-Fermi proton-atom interaction potential and the continuum approximation. The effect of thermal vibrations of the crystal's atoms is included. We solve numerically the proton equation of motion and analyze the spatial and angular proton transmission functions. The extrema of these functions are the spatial and angular rainbow points, respectively. When the whole proton beam is taken into account, a spatial rainbow pattern, composed of the lines emerging from the superfocusing points, and an angular rainbow pattern, consisting of the lines emerging from the origin and the zero-degree focusing points, appear along the channel. We consider the region of crystal thickness comprising the first, second and third superfocusing and zero-degree focusing points. When the effect of thermal vibrations is neglected, each of these rainbow lines look like the bifurcation set of the cusp catastrophe, and when the effect is included, the line resembles the bifurcation set of the butterfly catastrophe. We demonstrate that the spatial and angular distributions of transmitted protons are fully determined by the spatial and angular rainbow lines, respectively. The superfocusing and zero-degree focusing effects weaken with the increase of the crystal thickness. This is a consequence of the anharmonicity of the continuum proton-crystal interaction potential, which makes the proton beam propagation through the channel incoherent. We also explore the influence of the effect of proton collisions with the crystal's electrons on the beam dynamics in the channel. This effect additionally contributes to the incoherence of the beam motion along the channel. Our opinion is that the peaks of the spatial and angular distributions of ions transmitted through the planar channels lying off the origin registered before were in fact the rainbow peaks. © 2019 Elsevier B.V.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal",
volume = "444",
pages = "10-22",
doi = "10.1016/j.nimb.2019.02.004"
}

Ćosić, M., Nešković, N. B.,& Petrović, S. M.. (2019). Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 444, 10-22.
https://doi.org/10.1016/j.nimb.2019.02.004

Ćosić M, Nešković NB, Petrović SM. Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2019;444:10-22.
doi:10.1016/j.nimb.2019.02.004 .

Ćosić, Marko, Nešković, Nebojša B., Petrović, Srđan M., "Superfocusing and zero-degree focusing in planar channeling of protons in a thin silicon crystal" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 444 (2019):10-22,
https://doi.org/10.1016/j.nimb.2019.02.004 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8226
AB  - Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes.
T2  - Atoms
T1  - Quantum Rainbows in Positron Transmission through Carbon Nanotubes
VL  - 7
IS  - 1
SP  - 16
DO  - 10.3390/atoms7010016
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2019",
abstract = "Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes.",
journal = "Atoms",
title = "Quantum Rainbows in Positron Transmission through Carbon Nanotubes",
volume = "7",
number = "1",
pages = "16",
doi = "10.3390/atoms7010016"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2019). Quantum Rainbows in Positron Transmission through Carbon Nanotubes. in Atoms, 7(1), 16.
https://doi.org/10.3390/atoms7010016

Ćosić M, Petrović SM, Nešković NB. Quantum Rainbows in Positron Transmission through Carbon Nanotubes. in Atoms. 2019;7(1):16.
doi:10.3390/atoms7010016 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "Quantum Rainbows in Positron Transmission through Carbon Nanotubes" in Atoms, 7, no. 1 (2019):16,
https://doi.org/10.3390/atoms7010016 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
AU  - Rymzhanov, Ruslan
AU  - Petrović, Srđan M.
AU  - Bellucci, Stefano
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8022
AB  - The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.
T2  - Carbon
T1  - Investigation of the graphene thermal motion by rainbow scattering
VL  - 145
SP  - 161
EP  - 174
DO  - 10.1016/j.carbon.2019.01.020
ER  - 

@article{
author = "Ćosić, Marko and Hadžijojić, Milivoje and Rymzhanov, Ruslan and Petrović, Srđan M. and Bellucci, Stefano",
year = "2019",
abstract = "The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.",
journal = "Carbon",
title = "Investigation of the graphene thermal motion by rainbow scattering",
volume = "145",
pages = "161-174",
doi = "10.1016/j.carbon.2019.01.020"
}

Ćosić, M., Hadžijojić, M., Rymzhanov, R., Petrović, S. M.,& Bellucci, S.. (2019). Investigation of the graphene thermal motion by rainbow scattering. in Carbon, 145, 161-174.
https://doi.org/10.1016/j.carbon.2019.01.020

Ćosić M, Hadžijojić M, Rymzhanov R, Petrović SM, Bellucci S. Investigation of the graphene thermal motion by rainbow scattering. in Carbon. 2019;145:161-174.
doi:10.1016/j.carbon.2019.01.020 .

Ćosić, Marko, Hadžijojić, Milivoje, Rymzhanov, Ruslan, Petrović, Srđan M., Bellucci, Stefano, "Investigation of the graphene thermal motion by rainbow scattering" in Carbon, 145 (2019):161-174,
https://doi.org/10.1016/j.carbon.2019.01.020 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Hadžijojić, Milivoje
AU  - Rymzhanov, Ruslan
AU  - Petrović, Srđan M.
AU  - Bellucci, Stefano
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8031
AB  - The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.
T2  - Carbon
T1  - Investigation of the graphene thermal motion by rainbow scattering
VL  - 145
SP  - 161
EP  - 174
DO  - 10.1016/j.carbon.2019.01.020
ER  - 

@article{
author = "Ćosić, Marko and Hadžijojić, Milivoje and Rymzhanov, Ruslan and Petrović, Srđan M. and Bellucci, Stefano",
year = "2019",
abstract = "The thermal motion of graphene atoms was investigated using angular distributions of transmitted protons. The static proton-graphene interaction potential was constructed applying the Doyle-Turner's expression for the proton-carbon interaction potential. The effects of atom thermal motion were incorporated by averaging the static proton-graphene interaction potential over the distribution of atom displacements. The covariance matrix of graphene displacements was modeled according to the Debye theory, and calculated using Molecular Dynamics approach. Proton trajectories were used for construction of angular yields. We have found that there are lines, called rainbows, along which the angular yield is very large. Their evolution in respect to different sample orientation was examined in detail. Further we found that atom thermal motion has negligible influence on rainbows generated by protons experiencing distant collisions with the carbon atoms forming the graphene hexagon. On the other hand, rainbows generated by protons experiencing close collisions with the carbon atoms can be modeled by ellipses whose parameters are very sensitive to the structure of the covariance matrix. Numerical procedure was developed for extraction of the covariance matrix from the corresponding rainbow patterns in the general case, when atoms perform fully anisotropic and correlated motion.",
journal = "Carbon",
title = "Investigation of the graphene thermal motion by rainbow scattering",
volume = "145",
pages = "161-174",
doi = "10.1016/j.carbon.2019.01.020"
}

Ćosić, M., Hadžijojić, M., Rymzhanov, R., Petrović, S. M.,& Bellucci, S.. (2019). Investigation of the graphene thermal motion by rainbow scattering. in Carbon, 145, 161-174.
https://doi.org/10.1016/j.carbon.2019.01.020

Ćosić M, Hadžijojić M, Rymzhanov R, Petrović SM, Bellucci S. Investigation of the graphene thermal motion by rainbow scattering. in Carbon. 2019;145:161-174.
doi:10.1016/j.carbon.2019.01.020 .

Ćosić, Marko, Hadžijojić, Milivoje, Rymzhanov, Ruslan, Petrović, Srđan M., Bellucci, Stefano, "Investigation of the graphene thermal motion by rainbow scattering" in Carbon, 145 (2019):161-174,
https://doi.org/10.1016/j.carbon.2019.01.020 . .

TY  - JOUR
AU  - Petrović, Srđan M.
AU  - Starčević, Nikola
AU  - Ćosić, Marko
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8112
AB  - This work is devoted to the construction of the universal axial (0 0 1) rainbow channeling proton-crystal interaction potential. It has been done by modifying the Moliere's interaction potential. We show that for very thin crystals with the cubic crystallographic structure, in the (0 0 1) orientation with respect to 2 MeV proton beams, it is possible to obtain a universal proton-crystal interaction potential from the morphological analysis of the rainbows in the proton transmission angular plane.
T2  - Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
T1  - Universal axial (0 0 1) rainbow channeling interaction potential
VL  - 447
SP  - 79
EP  - 83
DO  - 10.1016/j.nimb.2019.03.050
ER  - 

@article{
author = "Petrović, Srđan M. and Starčević, Nikola and Ćosić, Marko",
year = "2019",
abstract = "This work is devoted to the construction of the universal axial (0 0 1) rainbow channeling proton-crystal interaction potential. It has been done by modifying the Moliere's interaction potential. We show that for very thin crystals with the cubic crystallographic structure, in the (0 0 1) orientation with respect to 2 MeV proton beams, it is possible to obtain a universal proton-crystal interaction potential from the morphological analysis of the rainbows in the proton transmission angular plane.",
journal = "Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms",
title = "Universal axial (0 0 1) rainbow channeling interaction potential",
volume = "447",
pages = "79-83",
doi = "10.1016/j.nimb.2019.03.050"
}

Petrović, S. M., Starčević, N.,& Ćosić, M.. (2019). Universal axial (0 0 1) rainbow channeling interaction potential. in Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 447, 79-83.
https://doi.org/10.1016/j.nimb.2019.03.050

Petrović SM, Starčević N, Ćosić M. Universal axial (0 0 1) rainbow channeling interaction potential. in Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 2019;447:79-83.
doi:10.1016/j.nimb.2019.03.050 .

Petrović, Srđan M., Starčević, Nikola, Ćosić, Marko, "Universal axial (0 0 1) rainbow channeling interaction potential" in Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 447 (2019):79-83,
https://doi.org/10.1016/j.nimb.2019.03.050 . .

TY  - JOUR
AU  - Ćosić, Marko
AU  - Petrović, Srđan M.
AU  - Nešković, Nebojša B.
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7640
AB  - This article studies the rainbow scattering of 5-key protons by the single sheet of free-standing graphene and its possible use as a tool for investigation of the ion-graphene interaction. The proton-graphene interaction potential was constructed by using the Doyle-Turner, ZBL, and Moliere proton-carbon interaction potentials. The thermal motion of carbon atoms was included by averaging the potentials according to the Debye model. Proton trajectories were obtained by numerical solution of the corresponding Newton equations of motion. They were used to obtain the mapping of the proton initial positions to their scattering angles. Morphological properties of the introduced mapping including its multiplicity and the rainbow singularities were used to explain important features of the obtained angular distributions of transmitted protons.
T2  - Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms
T1  - The forward rainbow scattering of low energy protons by a graphene sheet
VL  - 422
SP  - 54
EP  - 62
DO  - 10.1016/j.nimb.2018.02.028
ER  - 

@article{
author = "Ćosić, Marko and Petrović, Srđan M. and Nešković, Nebojša B.",
year = "2018",
abstract = "This article studies the rainbow scattering of 5-key protons by the single sheet of free-standing graphene and its possible use as a tool for investigation of the ion-graphene interaction. The proton-graphene interaction potential was constructed by using the Doyle-Turner, ZBL, and Moliere proton-carbon interaction potentials. The thermal motion of carbon atoms was included by averaging the potentials according to the Debye model. Proton trajectories were obtained by numerical solution of the corresponding Newton equations of motion. They were used to obtain the mapping of the proton initial positions to their scattering angles. Morphological properties of the introduced mapping including its multiplicity and the rainbow singularities were used to explain important features of the obtained angular distributions of transmitted protons.",
journal = "Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms",
title = "The forward rainbow scattering of low energy protons by a graphene sheet",
volume = "422",
pages = "54-62",
doi = "10.1016/j.nimb.2018.02.028"
}

Ćosić, M., Petrović, S. M.,& Nešković, N. B.. (2018). The forward rainbow scattering of low energy protons by a graphene sheet. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 422, 54-62.
https://doi.org/10.1016/j.nimb.2018.02.028

Ćosić M, Petrović SM, Nešković NB. The forward rainbow scattering of low energy protons by a graphene sheet. in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms. 2018;422:54-62.
doi:10.1016/j.nimb.2018.02.028 .

Ćosić, Marko, Petrović, Srđan M., Nešković, Nebojša B., "The forward rainbow scattering of low energy protons by a graphene sheet" in Nuclear Instruments and Methods in Physics Research. Section B: Beam Interactions with Materials and Atoms, 422 (2018):54-62,
https://doi.org/10.1016/j.nimb.2018.02.028 . .