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The molecular-dynamics method is used to model the interaction processes of pulsed ion beams with metal targets. The main parameters of a pulsed ion beam interacting with a target are the ion energy, pulse duration, and charge density per unit area of the target. Using averaged values of these parameters of ion beams published for various types of accelerators, a numerical study of the dependence of the dynamics of thermal and structural processes in irradiated targets upon a change in the size and heterogeneity of the structure is performed. Simulation of the irradiation processes and estimates of the distribution of beam ions in the volume are carried out in the range of beam ion energies of 1–2 keV using the concept of a shock wave. The results are important for developing the model of a pulsed ion beam and classifying the types of structural changes in the irradiated material depending on the model parameters.

Molecular dynamics modeling of the long-range effect in a metal target irradiated with nanoclusters is performed. It is found that moving high-temperature regions merge in the bulk of the target when it is subjected to simultaneous irradiation with several nanoclusters having different areas of interaction with its surface. The temperature in the region of merger risse abruptly and goes past the melting temperature of the target. This can produce structural changes in the crystal lattice at depths inside the target exceeding that of nanocluster penetration, resulting in the long-range effect.

The evolution of the continuous-atomistic approach to the simulation of processes of the interaction between high-energy heavy ions and metals is presented in this paper. The continuous-atomistic model is described by two different classes of equations, namely, thermal-conductivity equations with a source in the thermal-spike model and equations of motion of material points irradiated with a beam in a model of molecular dynamics. A software package is developed for simulation within the framework of the continuous-atomistic model. The results of simulation of the processes of metal-target irradiation with high-energy heavy ions depending on the parameters of the source function and the electron–phonon interaction coefficient are obtained.

A model of structural changes in a copper target when irradiated with Cu(147) nanoclusters is studied by means of molecular dynamics, supplemented by the thermal spike model. The results from modeling structural changes include the density and depth of penetration of the nanocluster atoms into the bombarded target, depending on the energy of the nanoclusters. The shapes of the sources in the thermal spike model for describing the energy losses of nanoclusters in a target are determined.

To study the processes of irradiating metals with high-energy heavy ions, a thermal spike model is often used, i.e., a system of electron-gas thermal conductivity equations and a lattice. Upon the irradiation of materials with high-energy heavy ions, more than 90% of the energy is consumed in the excitation of the electronic subsystem of the irradiated material. Further, this energy is transferred to the lattice subsystem and there is high heating of the lattice in a small volume, which can cause melting (evaporation), resulting in a structural change (amorphization, formation of high pressure areas, tracks, etc.) in the irradiated material. This work is devoted to studying structural changes in the surface of nickel by irradiation with high-energy ions of uranium. The thermal spike model is used for the initial distribution of temperature conditions in the irradiated nickel, which imitates the action of radiation on a molecular-dynamic system. The further evolution of the system is studied by molecular dynamics. As part of this approach, the processes of structural changes on the surface of the irradiated target can be investigated in more detail.

When nanoclusters irradiate a metal target a large amount of energy is realized in a small volume which leads to structural changes in metal. These changes can be a consequence of thermal processes or of elastic repulsions of target atoms. The experimental studies fixe the results of these structural changes in the target. The application of methods of mathematical modeling allows to “see” the dynamics of the irradiation process, including thermal and structural changes. Therefore, the mathematical modeling remains an important tool for such studies. One of such methods for modeling thermal processes in metals irradiated by nanoclusters is the method of molecular dynamics.

A difference scheme of splitting with respect to physical processes for a model of heat and moisture transfer is proposed. The model involves three physical processes—heat, liquid and saturated vapor transfer in the porous material. The density of saturated vapor and the transfer coefficients of liquid and vapor moistures depend on the temperature. At the same time, the heat capacity and conductivity of the porous material depend on moisture. On the basis of the proposed scheme of the model, a numerical simulation of the heat and moisture transfer for a drying process has been performed.

Formation of hydrated electron states in water is investigated within the polaron model which is described by a system of nonlinear partial differential equations. This framework is shown to provide an agreement of numerical results with experimental data on absorbtion of the light by the hydrated electron. Mathematical formulation of problem and the numerical approach are described, results of numerical simulation are presented in comparison with experimental data.Formation of hydrated electron states in water is investigated within the polaron model which is described by a system of nonlinear partial differential equations. This framework is shown to provide an agreement of numerical results with experimental data on absorbtion of the light by the hydrated electron. Mathematical formulation of problem and the numerical approach are described, results of numerical simulation are presented in comparison with experimental data.

A method and a complex of computer programs are developed for the numerical simulation of the polaron states excitation process in condensed media. A numerical study of the polaron states formation in water under the action of the ultraviolet range laser irradiation is carried out. Our approach allows to reproduce the experimental data of the hydrated electrons formation. A numerical scheme is presented for the solution of the respective system of nonlinear partial differential equations. Parallel implementation is based on the MPI technique. The numerical results are given in comparison with the experimental data and theoretical estimations.

Phase transitions occur in materials under the action of high-current high-power beams of charged particles. As a rule, such problems are solved within the framework of the heat-conduction equation. In this paper, studies of phase transitions are carried out within the framework of the thermal spike model, and both models are analyzed and compared. It is established that taking the electron gas into account significantly affects the dynamics of the crystal-lattice temperature and the dynamics of the phase transition.

The thermal processes arising in InP and GaAs single crystals irradiated with high-energy heavy ions are investigated with the help of a thermal peak model. Numerical simulation is used to estimate the sizes of regions where the melting process can occur and the structural changes arising in the irradiated materials are observed.

In our previous papers, the processes of formation and evolution of thermoelastic waves produced in metals under the action of powerful pulsed beams of small-energy ions were studied using the system of thermoelasticity equations. In this paper, the detailed numerical study of thermoelasticity processes taking into account temperature effects in the electronic and lattice subsystems is carried out using a temperature model of the thermal peak and the system of thermoelasticity equations in the case of propagation of a heavy ion through a condensed medium. New data and dependences are obtained. An analysis involving the comparison between the obtained results and the results of previous papers is presented.

A modified thermal spike model is proposed. In contrast to the previous model, this scheme involves a source function dependent on ion energy losses determined by the penetration depth of a target and the characteristic time of ion penetration until comes to a complete stop. Such an approach is especially significant for confirming its applicability for track formation processes observed in materials because, as is shown, characteristic times appreciably exceed the periods of phonon oscillations with frequencies of 1013 Hz or more. The performed calculations make it possible to infer that the source function of the modified model describes thermal processes differently than does the commonly used source function. It is established that the temperature of a material exceeds the solid-liquid transition temperature in the cylindrical regions with sizes that are smaller than those calculated without allowance for ion motion.

The evolution of polarons in a homogeneous medium is studied depending on model parameters and initial conditions that are chosen in the form of various combinations of stationary polaron states. A computational scheme and results of numerical modeling are presented.

The temperature dependences of the specific heat capacity and thermal conductivity are introduced for a highly oriented pyrolytic graphite; i.e., the nonlinear model of a thermal spike is considered and a comparative analysis of the obtained results and those for the linear model of a thermal spike is performed. The temperature effects observed in the highly oriented pyrolytic graphite with a change in the electron-phonon interaction coefficient g are investigated in detail. It is shown that, under irradiation of the highly oriented pyrolytic graphite by bismuth ions with an energy of 710 MeV, the temperature on the surface of the target within the framework of the nonlinear model can exceed the sublimation temperature, whereas the temperature on the surface of the target under irradiation by krypton ions with an energy of 253 MeV does not exceed the sublimation temperature. The characteristic range of variations in the electron-phonon interaction coefficient g is evaluated. For values of g in this range, the thermal spike model explains the experimental data on the presence of structures in the form of hillocks with craters at their centers on the surface of the highly oriented pyrolytic graphite exposed to irradiation by 209Bi ions and on the absence of such structures in the case of irradiation by 86Kr ions.

Temperature effects in the highly oriented pyrolytic graphite (HOPG) under bombardment by 86Kr (253 MeV) and 209Bi (710 MeV) heavy ions are studied in the framework of a three-dimensional thermal spike model. It is shown that the surface temperature of an HOPG target under bombardment by bismuth ions can exceed the sublimation temperature at particular values of the electron-phonon interaction coefficient. At the same time, the temperature at the target surface during bombardment of HOPG by krypton ions does not exceed the sublimation temperature over a wide range of variations in the electron-phonon interaction belongs. The calculations allow the explanation of the observed changes in the surface structure of HOPG single crystal under bombardment by 209Bi and 86Kr ions.

For a set of the measured diffusion moisture proles a numerical method for determination of the moisture transfer coefcient D(w, t) is suggested. The transfer coefcient is found as a sum of the degree p0w p(t) and exponential A e μ(w−v0) functions of the moisture concentration w, as opposed to the previous works. The exponent p(t) of the power function depends on the time t. The exponential function describes proles for large times nearby the boundary of the sample, where evaporation of the moisture to the atmosphere takes place. A conservative difference scheme for numerical solution of the direct problem is suggested. An inverse problem for minimization of an error functional is solved by the Newton method. Thus, a more accurate coincidence of the calculated proles of the moisture concentration with the measured proles is gained. �·¥¤²μ|¥´ I¨¸²¥´´O° ³¥Eμ¤ μ¶·¥¤¥²¥´¨O ±μOEE¨I¨¥´E ¶¥·¥´μ¸ ¢² £¨ D(w, t) ¤²O ´ iμ· ¨§³¥·O¥³OI ¤¨EEE§¨μ´´OI ¶·μE¨²¥° ¢² |´μ¸E¨. SμOEE¨I¨¥´E ¶¥·¥´μ¸ ´ I줨E¸O ± ± ¸E³³ ¸E¥¶¥´´μ° p0w p(t) ¨ O±¸¶μ´¥´I¨ ²O´μ° A e μ(w−v0 ) EE´±I¨° ±μ´I¥´E· I¨¨ ¢² £¨ w ¢ μE²¨I¨¥ μE ¶·¥¤O¤EШI · iμE. �±¸¶μ´¥´E p(t) ¸E¥¶¥´´μ° EE´±I¨¨ § ¢¨¸¨E μE ¢·¥³¥´¨ t. �±¸¶μ´¥´I¨ ²O´ O EE´±I¨O 춨¸O¢ ¥E ¶·μE¨²¨ ¢² £¨ ¤²O iμ²OI¨I ¢·¥³¥´ ¢i²¨§¨ £· ´¨IO μi· §I , £¤¥ ¶·μ¨¸Iμ- ¤¨E ¨¸¶ ·¥´¨¥ ¢² £¨ ¢ E³μ¸E¥·E. �·¥¤²μ|¥´ ±μ´¸¥·¢ E¨¢´ O · §´μ¸E´ O ¸I¥³ ¤²O I¨¸²¥´´μ£μ ·¥I¥´¨O ¶·O³μ° § ¤ I¨. �i· E´ O § ¤ I ³¨´¨³¨§ I¨¨ EE´±I¨μ´ ² ¶μ£·¥I´μ¸E¨ ·¥I ¥E¸O ³¥- Eμ¤μ³ �OOEμ´ . '²¥¤μ¢ E¥²O´μ, μi¥¸¶¥I¨¢ ¥E¸O iμ²¥¥ EμI´μ¥ ¸μ¢¶ ¤¥´¨¥ ¢OI¨¸²O¥³OI ¶·μE¨²¥° ±μ´I¥´E· I¨¨ ¢² £¨ ¸ ¨§³¥·O¥³O³¨ ¶·μE¨²O³¨.

On the basis of the solution of a nonlinear diffusion equation with initial and boundary conditions, a transfer coefficient of moisture in a sample of a porous material is found by minimization of a functional, which expresses error of the calculated profile of moisture concentration in well defined time moments from their experimental values for the defined moisture transfer coefficient. In this case the transfer coefficient as opposed to previous studies is found as a sum of a power function and an exponential function of the moisture concentration. The exponent of the power function depends on time. Thus, a more accurate coincidence of the calculated profiles of the moisture concentration to their experimental profiles is gained in comparison to the investigations performed by other authors. The exponential term provides a good coincidence of the mentioned profiles for big times nearby the boundary of the sample, where the moisture evaporation to the atmosphere takes place.

Methods of computational physics developed at JINR for investigation of models of complex physical processes in different fields of theoretical physics are considered. A general mathematical formulation of equations for the models under study is given, numerical methods are described, and information on developed program packages is presented. Particular models of physical processes are discussed. Results of their numerical study are demonstrated.

A system of equations for the electron and lattice temperatures around and along the path of a 700-MeV heavy (uranium) ion in nickel (one-layer material) is solved numerically in the axially symmetric cylindrical coordinate system under the assumption of temperature-dependent specific heat and thermal conductivity. The obtained dependences of the lattice temperature on the radius (distance from the ion path) and depth suggest that the ionization energy loss of a 700-MeV uranium ion in nickel is sufficient to melt the material. A comparative analysis with the linear model is performed and the maximum radius and depth of the region where the target material can melt is estimated. Then, the initial system of equations is solved for the region around and along the path of a 710-MeV heavy (bismuth 209Bi) ion in the two-layer material Ni(2 μm)-W with constant thermophysical parameters. The obtained dependences of the lattice temperature on the radius and depth show that the ionization energy loss of a 710-MeV bismuth ion in this two-layer material is sufficient for melting. The maximum radius and depth of the regions in the target material where phase transitions may occur are estimated.

A system of equations for electron gas and lattice around and along the trajectory of a heavy uranium ion with an energy of 700 MeV in nickel at constant heat capacity and heat conduction taken at room temperature is solved numerically in an axially symmetric cylindrical coordinate system. On the basis of the lattice temperature obtained as a function of radius around the ion trajectory and depth, a conclusion is made that the ionization energy losses of a uranium ion in nickel are sufficient for melting and evaporating the material from the surface. The maximum radius and depth of the region in which melting and evaporation take place are estimated.

We consider the dynamic polaron model of the hydrated electron state on the basis of a system of three nonlinear partial differential equations with appropriate initial and boundary conditions. A parallel numerical algorithm for the numerical solution of this system has been developed. Its effectiveness has been tested on a few multi-processor systems. A numerical simulation of the polaron states formation in water under the action of the ultraviolet range laser irradiation has been performed. The numerical results are shown to be in a reasonable agreement with experimental data and theoretical predictions.

A computer simulation of the formation of photoexcited electrons in water is performed within the framework of a dynamic model. The obtained results are discussed in comparison with experimental data and theoretical estimates., Comment: 6 pages, 8 figures

Recent investigations of the meson spectroscopy often have been based on models considering mesons as quark–antiquark bound states. These models are described by three-dimensional relativistic equations with various generalizations of Coulomb and confining potentials in momentum space. Algorithms and codes are developed for numerical investigations of these equations. The modified Generalized Continuous analogue of the Newton method is used. The numerical results demonstrate the efficiency of the created software. The code allows obtaining a numerical solution with a required accuracy. The numerical results are compared with the same results obtained by other authors.

The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.

The iterative schemes based on the Continuous analogue of the Newton's method (CANM) have been applied to the solving a number of the QCD problems.

A numerical method for studying nonlinear problems arising in mathematical models of physics is systematically described in this review. The unified basis for the development of numerical schemes is a generalization of the continuous analog of Newton’s method, which represents a qualitatively new development of the Newtonian evolution process on the basis of the integration of concepts from perturbation theory and the theory of evolution in parameters. The results are presented of numerical studies of quantum-field models of the polaron, the solvated electron, the binucleon, and also QCD potential models for some commonly used potentials.

For the three-body problem with a Coulomb interaction (two positive charged particles with charges Za=Zb=1 and one negative charged particle with charge Zc=-1) the matrix elements of the momentum of the two-centre problem are calculated. The matrix elements connecting the two-centre states which correspond to the first three shells according to the separated-atom classification are presented in graphical form.