Difference scheme for dynamic simulation describing stochastic kinetics of molecules in ceramics

A conservative and monotonous finite difference scheme is proposed for solving PDE describing the kinetics of molecules in ceramics. Numerical results of computational experiments are presented. First Published Online: 14 Oct 201

Monte Carlo test of the Goldstone mode singularity in 3D XY model

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L=384 (significantly exceeding the largest size L=160 considered in work published previously), and fields h ≥ 0.0003125 at two different coupling constants β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ∥ has a Goldstone mode singularity such that χ∥ ∝h-1/2 holds when h↦0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form χ∥ ∝hρ-1, where 1/2<ρ<1 is a universal exponent related to the ∼hρ variation of the magnetization

Modeling of Surface Structure Formation after Laser Irradiation

The Stefan problem in a semi-infinite media under laser irradiation is consideres. It is related to the melting and solodification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calsulate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutte method are presented, asuming that the solid-liquid interface has a parabolic shape. The calculated crossection of the surface structure shows a characteristic cone in the cernet, in agreement with experimental observations

Modeling of Surface Structure Formation after Laser Irradiation

The Stefan problem in a semi-infinite media under laser irradiation is consideres. It is related to the melting and solodification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calsulate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutte method are presented, asuming that the solid-liquid interface has a parabolic shape. The calculated crossection of the surface structure shows a characteristic cone in the cernet, in agreement with experimental observations

Mathematical model for determination of exhaust concentration dynamics in urban atmosphere under unknown turbulent air flow velocity

The paper proposes the 3-D nonlinear mathematical model for analytic determination of exhaust concentration dynamics in the city regions under the important stipulation that an airflow velocity is not a priory known. To determine an unknown airflow velocity the nonlinear mathematical model is proposed and this nonlinear model is solved by analytical method. In this model it is provided that the turbulent and molecular diffusion coefficient changes depending on the vertical remoteness above the ground surface. The proposed model can be used for solutions of operative problems on urban traffic organization, of long-term planning of urban agglomeration development and new highway building

Mechanism of Nanocones Formation by Laser Radiation on a Surface of Si,Ge and SiGe

The nanocones formed on the irradiated surface of semiconductors by Nd:YAG laser possessing the properties of 1D graded band gap has been found for Si, Ge and SiGe. The observed properties are explained in the frame of Quantum confinement effect. On the basis of analysis of experimental results a two-stage mechanism of nanocones formation on the irradiated surface of semiconductors by Nd:YAG laser is proposed for elementary semiconductors, such as: Si, Ge and their solid solution SiGe. The first stage - Laser Redistribution of Atoms (LRA) is characterized by formation of hetero-structures such as: Ge/Si due to drift of Ge atoms toward the irradiated surface of the sample in the gradient of temperature, the so-called Thermogradient effect [1]. This process is characterized by positive feedback: after every laser pulse, the gradient of temperature increases due to increase of Ge atoms’ concentration at the irradiated surface. New Ge phase is formed at the end of the process. Ge atoms are localized at the surface of Si like a thin film. As a result, LRA stage gradually transits to Selective Laser Annealing (SLA) stage. The second stage, SLA, is characterized by formation of nanocones on the irradiated surface of a semiconductor by selective laser heating of the top layer with following mechanical plastic deformation of the layer as a result of relaxation of the mechanical compressive stress arising between these layers due to mismatch of their crystal lattices and selective laser heating. SLA occurs due to higher absorption of the laser radiation by the top layer than the buried layer. The proposed model is confirmed by “blue shift” bands in photoluminescence spectrum, “red shift” of LO line in Raman back scattering spectrum of Ge crystal and non-monotonous dependence of Si crystal micro-hardness as function of the laser intensity

Time-dependent problem for determination of exhaust concentration in urban transport system

The paper proposes the 3-D mathematical model for analytic determination of exhaust concentration dynamics in the city regions under a priori information on airflow velocity. In this model it is provided that the turbulent and molecular diffusion coefficient changes depending on the vertical remoteness above the ground surface. The numerical example of problem solving is presented. The created model can be used for solutions of operative problems on urban traffic organization, of long-term planning of urban agglomeration development and new highway building

Monte Carlo test of the Goldstone mode singularity in 3D XY model

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L=384 (significantly exceeding the largest size L=160 considered in work published previously), and fields h ≥ 0.0003125 at two different coupling constants β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ ∥ has a Goldstone mode singularity such that χ ∥ ∝h -1/2 holds when h↦0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form χ ∥ ∝h ρ-1 , where 1/2>ρ>1 is a universal exponent related to the ∼h ρ variation of the magnetization. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200705.10.Ln Monte Carlo methods, 75.10.Hk Classical spin models, 05.50.+q Lattice theory and statistics (Ising, Potts, etc.),