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The MPI/C++ /Fortran package of computer codes has been developed for high-performance numerical analysis of experimental data on elastic nucleus-nucleus scattering within a microscopic model of optical potential. In the package, a modified DWUCK4 Fortran-code for calculating the physical characteristics of elastic scattering based on a numerical solution of the corresponding Schrödingerequation has been incorporated into the C++ framework, which is responsible for the input-output procedure and a comparison of numerical results with experimental data. MPI-based parallelism allows efficient calculations of the observables depending on a wide range of parameters of real and imaginary parts of the microscopic OP. The package has been used to analyze experimental data on differential cross sections of the 12,14Ве+12Сelastic scattering.

One of important tasks in a development of gas-condensate fields is to minimize hydrocarbons loss arising from the gas condensation in pores of the gas-bearing layer. The search for the optimal gas production regime is carried out both on the basis of laboratory experiments and on the base of computer simulation. In this regard, the relevant is the verification of the constructed mathematical models by means of comparison of numerical results with experimental data obtained on the laboratory models of a hydrocarbon reservoirs. Within the classical approach on the basis of the Darcy law and the law continuity for flows, the model is formulated that describes the passing a multicomponent gas-condensate mixture through a porous medium in the depletion mode. The numerical solution of the corresponding system of nonlinear partial differential equations is implemented on the basis of the combined use of the C++ programming language and the Maple software. Shown that the approach used provides an agreement of results of numerical simulations with experimental data on the dynamics of hydrocarbon recoverability depending on the pressure obtained at VNIIGAZ, Ukhta.

The dynamics of the magnetization under the action of a current pulse in a ϕ0 Josephson junction with the direct coupling between the magnetic moment and a superconducting current has been analyzed. Time dependences of the components of the magnetic moment at different parameters of the ϕ0 junction have been calculated. These dependences have been used to determine intervals of the parameters where the magnetic moment is reversed from mz = 1 to mz = −1. Periodicity has been revealed in the appearance of intervals of the reversal of the magnetic moment under the variation of the spin-orbit coupling, Gilbert damping parameter, and Josephson-to-magnetic energy ratio. The results obtained can be used in various fields of superconducting spintronics, in particular, to create a memory unit based on the Josephson ϕ0 junction.

Elastic cross sections are calculated and compared with the data on $\pi^{\pm}$ scattering on $^{28}$Si, $^{40}$Ca, $^{58}$Ni, $^{208}$Pb nuclei in the energy range from 130 to 290 MeV. To this end, both the folding optical potential (OP) and the local modified Kisslinger-type OP were calculated, and then the $\pi A$ cross sections were obtained by solving the Klein-Gordon equation to account for the relativization and distortion wave effects. In the folding OPs, the parameters of the elementary $\pi N$ amplitude were fitted when describing the $\pi A$ scattering data, and thus the essential in-medium effect on the parameters of the $\pi N$ amplitude was established since the pion is scattered not on a free but on a bound nuclear nucleon. Fairly good agreement with experimental data was obtained for both models of optical potentials and their forms turn out to be in coincidence in the region of their surfaces., Comment: 16 pages, 6 figures, 2 tables; accepted for publication in Nuclear Physics A

Small-angle X-ray scattering (SAXS) is used to characterize the vesicular structure of the phospholipid transport nanosystem (PTNS) at PTNS concentrations in water of 25, 31.25, and 37.5% (w/w). The average vesicle radius, size polydispersity, bilayer thickness, and internal structure are determined from the experiment using two models for the photon scattering density distribution. Two independent methods are used to calculate the SAXS spectra: the form factor of a heterogeneous spherical shell and the method of separated form factors. The two methods for calculating the spectra and two models for description of the internal structure of the lipid bilayer provide identical results, which demonstrate a decrease in the vesicle radius, thickness of the bilayer, and thickness of the hydrocarbon-chain region upon an increase in the maltose concentration in water. It is shown that a decrease in the lipid bilayer thickness upon an increase in the maltose concentration is caused by interdigitation of the hydrocarbon chains. The hydrophobic volume of one vesicle suitable for water-insoluble drugs is shown to have a maximum value of 14.55 × 106 A3 at a PTNS concentration in water of 25%. Increasing the PTNS concentration in water up to 37.5% leads to a decrease in the hydrophobic volume to 6.16 × 106 A3.

Small-angle neutron scattering spectra of a polydispersed population of dipalmitoylphosphatidylcholine (DPPC) unilamellar vesicles in heavy water in the presence of dimethyl sulfoxide (DMSO) are analyzed by means of the separated form-factor method. An increase in the mole fraction of DMSO in water from 0 to 15% was shown to lead to an increase in the thickness of the bilayer to the characteristics repeat distances of DPPC multilamellar membranes. This fact is indicative of dehydration of the intermembrane space and a steric contact between adjacent DPPC bilayers at 15% mole fraction of DMSO.

The computation of the real part of the nucleus-nucleus optical potential based on the microscopic double-folding model was implemented within both the MPI and OpenMP parallelising techniques. Test calculations of the total cross section of the 6He + 28Si scattering at the energy 50 A MeV show that both techniques provide significant comparable speedup of the calculations.

A microscopic analysis of the optical potentials (OPs) and cross sections of quasielastic scattering of $^{12,14}\mathrm{Be}$ on $^{12}\mathrm{C}$ at 56 MeV/nucleon and on protons at an energy near 700 MeV is carried out. For lower energy scattering the real part of the OP is calculated by using the double-folding procedure accounting for the antisymmetrization effects, while the imaginary part is obtained on the basis of the high-energy approximation (HEA). The HEA is also applied to the calculations of both real and imaginary OPs when solving the relativistic equation for the high-energy proton-nucleus elastic scattering. The neutron and proton density distributions computed in different microscopic models for $^{12}\mathrm{Be}$ and $^{14}\mathrm{Be}$ are used. In the present hybrid model of the optical potential the only free parameters are the depths of the real and imaginary parts of the OP obtained by fitting the experimental data. The role of the inelastic scattering channel to the first excited ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in $^{12}\mathrm{C}$ when calculating the quasielastic cross sections, as well as the modified density of the $^{12}\mathrm{C}$ target accounting for the surface effects, are studied. In addition, the cluster model, in which $^{14}\mathrm{Be}$ consists of a $2n$ halo and the $^{12}\mathrm{Be}$ core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in $^{14}\mathrm{Be}+^{12}\mathrm{C}$ scattering and longitudinal momentum distributions of $^{12}\mathrm{Be}$ fragments at an energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both quasielstic scattering and breakup processes is obtained.

We have studied the current–voltage characteristic of a system of long Josephson junctions taking into account the inductive and capacitive coupling. The dependence of the average time derivative of the phase difference on the bias current and spatiotemporal dependences of the phase difference and magnetic field in each junction are considered. The possibility of branching of the current–voltage characteristic in the region of zero field step, which is associated with different numbers of fluxons in individual Josephson junctions, is demonstrated. The current–voltage characteristic of the system of Josephson junctions is compared with the case of a single junction, and it is shown that the observed branching is due to coupling between the junctions. The intensity of electromagnetic radiation associated with motion of fluxons is calculated, and the effect of coupling between junctions on the radiation power is analyzed.

The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π ±-mesons on 28Si, 40Ca, 58Ni, and 208Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2+ and 3− collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β 2) and octupole (β 3) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.

Analysis of the differential cross sections of scattering of neutron-rich nuclei 12,14Be on 12C at 56 MeV/nucleon and on protons at energy near 700 MeV/nucleon is carried out within the microscopic model of optical potential (OP). The real part of the 12,14Be+12C OP is calculated by using the double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part of OP is obtained in the framework of the high-energy approximation (HEA). As to the 12,14Be+p scattering at relativistic energies, calculations of the both real and imaginary OPs were made within the HEA approach. In this framework, the only free parameters of OP are the depths of its real and imaginary parts obtained by fittingto experimental data. The role of the 12,14Be density models is considered when reproducing the experimental data. A contribution of the inelastic channels with excitations of 2+ and 3− states in 12C when calculating the quasielastic cross sections is analysed. Also, the 14Be cluster model, in which this nucleus consists of a 2n-halo and the 12Be core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in the 14Be+12C collisions at the energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both scattering and breakup processes is obtained.

We consider a stiff system of ordinary differential equations within a spintronic model of the superconductor-ferromagnetic/superconductor Josephson junction (SFS JJ). For some values of parameters, the explicit algorithms failed for numerical solution of this system and special numerical approaches like the implicit two-stage Gauss-Legendre method are required. In our study, we use both explicit and implicit numerical schemes which have been implemented in the respective interactive software on the basis of Wolfram Mathematica technique. In this software, we employ the 4-step explicit Runge-Kutta algorithm and the two-stage Gauss–Legendre method of the 4th accuracy order (also known as the implicit Runge-Kutta scheme), combined with the fixed point method. We analyze the effectiveness of two numerical approaches and demonstrate an advantage of implicit method over the explicit scheme. Results of numerical simulation of superconducting processes in the SFS JJ depending on parameters are presented.

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.

Parameters of the phospholipid vesicular systems are determined by means of minimization of the discrepancy between experimental data on the small angle scattering intensity and the numerical results within the frame of the separated form factors method. Effectiveness of parallel implementation is tested at the cluster HybriLIT. Results of numerical analysis of small angle neutron scattering data on polydispersed population of unilamellar vesicles of phospholipid transport nanosystem are presented.

The parallel Asynchronous Differential Evolution (ADE) method with adaptive correlation matrix (ACM) is utilized for numerical solution of the global minimization problem within the Separated Form Factors model (SFF) for analysis of structure of the drug-delivering phospholipid transport nanosystem (PTNS). In this framework, parameters of the SFF model are fitted to experimental data of the small angle scattering of X-rays (SAXS) and of neutrons (SANS). The ADE-SFF approach is described, the results of numerical study of polydispersed PTNS-based systems in water solutions depending on the disaccharide concentration, are presented.

A user software for numerical study of a Josephson junction model with magnetic momenta is presented. Computer implementation has been done by means of Wolfram Mathematica using the extensive capabilities of this system to create interactive dynamic objects. Two methods for numerical solution of the respective system of ordinary differential equations are implemented: the four-step Runge-Kutta algorithm and the Runge-Kutta-Fehlberg method with predetermined accuracy. Results of numerical simulation are presented to confirm the correctness of the calculations done with the developed software.

The phase dynamics of a stack of long Josephson junctions has been studied. Both inductive and capacitive couplings between Josephson junctions have been taken into account in the calculations. The IV-curve, the dependence on the bias current of the radiation power and dynamics of each JJs of the stack have been investigated. The coexistence of the charge traveling wave and fluxon states has been observed. This state can be considered as a new collective excitation in the system of coupled Josephson junctions. We demonstrate that the observed collective excitation leads to the decrease of radiation power from the system.

A microscopic analysis of the optical potentials (OPs) and cross sections of elastic scattering of 8B on 12C, 58Ni, and 208Pb targets at energies 20 < E < 170 MeV and 12,14Be on 12C at 56 MeV/nucleon is carried out. The real part of the OP is calculated by a folding procedure and the imaginary part is obtained on the base of the high-energy approximation (HEA). The density distributions of 8B evaluated within the variational Monte Carlo (VMC) model and the three-cluster model (3CM) are used to construct the potentials. The 14Be densities obtained in the framework of the the generator coordinate method (GCM) are used to calculate the optical potentials, while for the same purpose both the VMC model and GCM densities of 12Be are used. In the hybrid model developed and explored in our previous works, the only free parameters are the depths of the real and imaginary parts of OP obtained by fitting the experimental data. The use of HEA to estimate the imaginary OP at energies just above the Coulomb barrier is discussed. In addition, cluster model, in which 8B consists of a p-halo and the 7Be core, is applied to calculate the breakup cross sections of 8B nucleus on 9Be, 12C, and 197Au targets, as well as momentum distributions of 7Be fragments. A good agreement of the theoretical results with the available experimental data is obtained. It is concluded that the reaction studies performed in this work may provide supplemental information on the internal spatial structure of the proton- and neutron-halo nuclei.

The structure of a polydispersed population of unilamellar dimyristoylphosphatidylcholine (DMPC) vesicles in sucrose solutions has been investigated by small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS). Calculations within the model of separated form factors (SFF) show that the structure of the vesicle system depends strongly on the sucrose concentration.

The 11Li scattering and breakup on protons is considered under the assumption that the 11Li nucleus consists of two interacting clusters, which are a c = 9Li core and a h = 2n dineutron halo. The single-particle density of the 11Li nucleus, amicroscopic optical potential, and the cross section for 11Li+p scattering for various choices of cluster shape are obtained and analyzed by folding the density distribution for either cluster with the probability density for the relative motion of two clusters. A comparison with experimental data of the scattering cross section at low, 60–75 MeV, and intermediate, 700 MeV, energies is performed. The momentum distribution of c fragments upon 11Li breakup is calculated and studied with a help of the obtained p + c and p + h microscopic optical potentials.

The φ0-Josephson Dushanbe, Tajikistanjunction model with a coupling between the magnetic moment and the Josephson current in the “superconductor–ferromagnet–superconductor” system has been investigated. Numerical solution of the respective system of nonlinear differential equations is based on the two-stage Gauss–Legendre algorithm. For numerical simulation in a wide range of parameters which requires a significant computer time, a parallel MPI=C++ computer code has been developed. Results of numerical study of the magnetization effect depending on physical parameters, as well as results of methodological calculations demonstrating the efficiency of the parallel implementation, are presented. Calculations have been carried out at the Heterogeneous Platform “HybriLIT” and on the supercomputer “Govorun” of the Multifunctional Information and Computing Complex of the Laboratory of Information Technologies, JINR (Dubna).

The density distributions of 10,11Be nuclei obtained via the generator coordinate method (GCM) and quantum Monte Carlo (QMC) model are used to calculate the microscopic optical potentials (OP) and elastic scattering cross sections of these nuclei on protons and the 12C nucleus. The real part of the OP is obtained by means of folding while the imaginary part is estimated within a high-energy approximation. The depths of the real and imaginary parts of OP are varied by fitting these calculations to experimental data on cross sections. The known energy dependence of the respective volume integrals of potentials is used to resolve ambiguities in magnitudes of these depths. These OPs can be applied to the further calculations of the cross sections of different reactions in which they take part.

Amicroscopic optical potential is used to calculate cross sections for elastic 11Li +p scattering at the energies of 62, 68.4, and 75 MeV per nucleon, and the results are compared with available experimental data. The potential used does not involve free parameters, but the depths of its real and imaginary parts are renormalized. The known trend in the energy dependence of the volume integrals of the optical potential is taken into account in analyzing experimental data. The role of spin-orbit interaction is studied, and the total reaction cross sections that are proposed to be measured in future experiments are calculated.

The breakup cross-sections in the reaction 6 He + 12 C are calculated at about 40 MeV/nucleon using the high-energy approximation (HEA) and with the help of microscopic optical potentials (OP) of interaction with the target nucleus 12 C of the projectile nucleus fragments 4 He and 2n. Considering the di-neutron h = 2n as a single particle the relative motion hα wave function is estimated so that to explain both the separation energy of h in 6 He and the rms radius of the latter. The stripping and absorbtion total cross-sections are calculated and their sum is compared with the total reaction cross-section obtained within a double-folding microscopic OP for the 6 He + 12 C scattering. It is concluded that the breakup cross-sections contribute to about 50% of the total reaction cross-section.

We construct time-periodic solitons of the parametrically driven damped nonlinear Schrodinger equation as solutions of a boundary value problem for the space-dependent Fourier coefficients.

The aim of this work is the mathematical modeling of static distributions of the magnetic flux in long Josephson junctions (JJ), taking into account the second harmonic in the decomposition of the Josephson current and the sequential comparison of the results with the conventional model. For the analysis of stability, each concrete distribution of magnetic current in the junction is put into relationship with the Sturm-Liouville spectral problem; the nullification of its minimal eigenvalue indicates the bifurcation distribution by one of the problem parameters. The corresponding nonlinear boundary problem is numerically solved by a continuous analog of the Newton’s method with the spline-collocation scheme for linearized problems at each Newtonian iteration. The main distributions of the magnetic flux have been found and their stability against changes of model parameters investigated. The obtained results were compared with the results of the JJ conventional model of the superconductor-insulator-superconductor type.

The 6He + 12C elastic scattering at E = 3.0, 38.3, and 41.6 MeV/nucleon is analyzed using the microscopic model of optical potential. According to this approach, two or three parameters are fitted that renormalize the depth of real, imaginary, and surface parts of the calculated optical potential. In this case, the ambiguity of the obtained sets of fitting parameters remains, but can be reduced by introducing an additional criterion of selection: the dependence of the volume integrals of the optical potential on the energy. The structure of the obtained optical potential, the role of the nuclear medium, the formation of the imaginary part of the optical potential, and the interconnection between the surface potential and the 6He breakup channels are discussed.

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 data on the 12,14Be + p elastic scattering cross sections at 700 Mev are compared with those obtained by solving the relativistic wave equation with the microscopic optical potentials calculated as folding of the NN amplitude of scattering with densities of these nuclei in the form of the symmetrized Fermi function with the fitted radius and diffuseness parameters, and also with the densities obtained in two microscopic models, based on the Generator Coordinate Method (GCM) and the other one – on the Variational Method of Calculations (VMC). For 12Be, above models turn out to be in a small disagreement with the data at "large" angles of scattering θ ≥ 9°, while for the 14Be one sees some inconsistence at smaller angles, too.

The intrinsic reaction mechanism of proton-induced composite particle pre-equilibrium emission is well known to be a statistical multistep process. However, until recently it was still not clear how important the competition between pickup and knockout is to produce a composite ejectile in the multistep sequence. An evaluation of recent ([Formula: see text]) results at incident energies from 65 to 160[Formula: see text]MeV and on representative target nuclei is presented. The virtue of analyzing power angular distributions to unravel the details of the reaction mechanism is discussed and future possible avenues of investigation are explored.

We obtain time-periodic solitons of the parametrically driven, damped nonlinear Schrodinger equation as solutions of the boundary value problem on a two-dimensional domain. We classify the stability and bifurcations of singly and doubly periodic solutions.

The optical potential of 8He+p scattering is calculated using the folding model for its real part and the high-energy approximation for the imaginary part. On this basis, the experimental differential elastic scattering cross sections are analyzed at energies below 100 MeV/nucleon. Conclusions are drawn on the applicability of the optical potential model and on the selection of an adequate model of the 8He nucleus structure.

Data on cross sections for the 6He + p elastic scattering at energies of tens of MeV/nucleon are analyzed by calculating the microscopic optical potential (OP) (its real and imaginary parts). The effect produced on the cross section by the dependence of the nucleon-nucleon potential on the nuclear matter density, the role of the spin-orbit interaction, and the role of nonlinearity and renormalization of the microscopic OP are studied. A comparison with the experimental data allows sensitivity of cross sections to these effects to be tested.

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of 17O from a series of nuclei with excitation of the 2+ level.

We consider a model of system of long Josephson junctions (LJJ) with inductive and capacitive coupling. Corresponding system of nonlinear partial differential equations is solved by means of the standard three-point finite-difference approximation in the spatial coordinate and utilizing the Runge-Kutta method for solution of the resulting Cauchy problem. A parallel algorithm is developed and implemented on a basis of the MPI (Message Passing Interface) technology. Effect of the coupling between the JJs on the properties of LJJ system is demonstrated. Numerical results are discussed from the viewpoint of effectiveness of parallel implementation.

Recent results for the inclusive reaction 93 Nb(p ,α ) between incident energies of 65 and 160 MeV are shown to be consistent with a competition between knockout and pickup. The pre-equilibrium statistical multistep process terminates in either mechanism. The incident-energy dependence of the reaction reflects the dynamics of the participating reaction components. It is consequently not surprising to observe knockout to dominate at the lower and highest incident energies, with pickup very prominent in between.