Stochastic Computer Model of the Kinetics of Multicomponent Intercrystalline Adsorption in Solid Solutions

The basic principles of constructing a stochastic computer model of intergranular adsorption kinetics controlled by interatomic pair interactions and the volume diffusion mobility of the components of a solid solution are developed, allowing for the bulk structure of crystals and the equilibrium atomic configuration of intergranular boundaries. The results are presented from computer simulations of the grain boundary segregation of S and P in α-Fe-based alloys.     

Stochastic optimal control for norovirus transmission dynamics by contaminated food and water

Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rs<1 for disease extinction.Finally,two simulation examples are used to exemplify the analytical results.We employed optimal control theory and examined stochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.     

On the initiation of chemical reactions by electronic excitations in molecular solids

In this article we briefly review the results of theoretical simulations for the initiation of chemistry processes in high-explosive crystals from a solid-state-physics viewpoint. We analyze the possibility of initiation of chemical reactions from excited electronic states. In other words, we look for conditions that facilitate electronic excitations in the crystal. Specifically, we describe modifications to the electronic structure of RDX (cyclotrimethylene trinitramine) induced by lattice defects and by a shock wave traversing the solid. Our approach is based on ab initio Hartree–Fock band-structure calculations with electronic correlation corrections. An excitonic mechanism and a hole model, suggested earlier, are discussed in connection with the most recent experimental and theoretical advances in ultrafast optical techniques. We also consider here possible new avenues in the development of detonation theory. Received: 3 December 2001 / Accepted: 9 July 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +1-301/744-4451, E-mail: KuklaMM@ih.navy.mil     

Stability of thin nematic films

We discuss the peculiarity of thin nematic films on solid substrates with a free surface, underlining the differences with what is usually seen in dewetting. We review the thermodynamic basis of the coupled phase/thickness separation that has previously been shown experimentally. We give new experimental evidences for the origin of the coupling force chosen in our previous theoretical model. This additional information contributes to the discussion raised by the article of Ziherl and Zumer in this issue [19].Received: 3 December 2003PACS: 68.15. + e Liquid thin films - 64.70.Md Transitions in liquid crystals - 61.30 Surface phenomena in liquid crystals including anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions and wetting transitions     

Temperature and pressure dependence of some thermal characteristics of magnesium

The theoretical values of the Debye-Waller factor, specific heat and the phonon dispersion relations as functions of temperature for magnesium are derived from a simple model of lattice dynamics proposed by Czachor for hexagonal crystals.. The pressure dependence of the dispersion curves is also derived. The theoretical results have been found to be in very good agreement with experimental data available.     

The solid–liquid interface energy of organic crystals

A simple thermodynamic model, originally developed for metals based on the Gibbs–Thomson equation and related considerations for homogeneous nucleation, has been extended to predict the solid–liquid interface energy γ_sl of organic crystals. The model predictions correspond to available experimental and other theoretical results for 38 organic crystals. Copyright © 2007 John Wiley & Sons, Ltd.     

Elastic constants of solid solutions of single crystals of the alkali halides

On the basis of the Leibfried-Ludwig theory of anharmonic effects in crystals, a theoretical calculation is given of the elastic constants of solid solutions of alkali halide single crystals. The results of the calculations are compared with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 57–61, July, 1973.     

Theory of melting of molecular crystals within the new modified model: The complete pictures of the transition temperatures

The new modified form of the Pople–Karasz theory of melting of molecular crystals was introduced and applied to investigate the thermodynamics of melting, solid–solid, solid–nematic and nematic–isotropic liquid transitions in the previous papers. In this paper, we give the complete pictures of the transition temperatures and compare with the original Pople–Karasz (PK) theory and its previous modified theories. We also found that the new modified model also gives a much better agreement with available experimental data for the solid–nematic transition than the PK and its previous modified theories by using the different adjustable parameters.     

Effect of phonon decay processes on the formation of a phonon nonequilibrium signal in crystals with two two-level subsystems

The effect of phonon decay on the characteristic propagation time and shape of a phonon nonequilibrium signal in disordered crystals, including crystals containing inelastic phonon scattering centers, is studied theoretically. Attention is focused on slow processes, which are typical of yttrium-aluminum garnet solid solutions and erbium-doped aluminates. It is shown that the temperature dependence of the arrival time of a phonon nonequilibrium signal in these systems can be governed, to a considerable extent, by phonon-phonon interactions. The results of the theoretical studies are compared with experimental data on the propagation of weakly nonequilibrium thermal phonons in solid solutions of rare-earth yttrium-aluminum garnets and aluminates.     

Phonon dispersion and symmetry of solid-J2

The phonon dispersion curves, spectrum and specific heat of solid J₂ and Br₂ are calculated using a general central force parameter model, which is fitted to the available experimental data. The influence of the intramolecular degrees of freedom on the elastic constants and the compressibility is shown. The usefulness of group theoretical methods in the investigation of normal modes of vibrations in crystals is illustrated by applying them to the decomposition of the dynamical matrix.     

Lifetime measurements with the pinhole method in presence of radiation trapping: II—application to Yb<Superscript>3+</Superscript> doped ceramics and crystals

In this paper, we present an experimental verification of a theoretical model for the evaluation of the results of the so-called pinhole method for the measurement of the upper level lifetime in doped optical materials where the resonant reabsorption of the emitted fluorescence determines significant radiation trapping effects. As an experimental verification of the model, we measured the lifetime of the upper laser level of Yb³⁺ in various crystals and ceramic samples usually employed for the realization of solid state laser sources.     

Theoretical studies of adatom diffusion on metal surfaces

We propose in this paper a theoretical model to investigate surface self-diffusion of single adatoms on two different low-index planes, closely packed (001) and densely packed (111), of face-centered-cubic rhodium, nickel and copper metal crystals. Two realistic model potentials are applied to describe the interatomic interaction of the adatom-substrate systems. The first model is a Morse-type potential, which involves several empirical fittings of bulk of solid. The second, newly popular, potential was introduced by Sutton and Che, which incorporates many-body effects. With these potentials, conventional molecular dynamics (MD) is employed to obtain trajectories of the atoms. The average squared didplacements are computed for a range of initial kinetic energies, and the surface diffusion constants can be obtained by means of the Einstein relation. The estimated random walk exponential prefactors and activation energies exhibit an Arrhenius behavior, and are compared with previous results.     

ONE-DIMENSIONAL SANDPILE MODEL WITH STOCHASTIC SLIDE

A new kind of theoretical one-dimensional sandpile model is proposed. In contrast to the models studied previously, the sliding process in this model is assumed to be of stochastic nature. Numerical simulations show that the behavior of this model is apparently closer to the reality of true sandpile than the models considered previously. The universality and sealing of this model is also discussed.     

Studies of adsorption kinetics by means of the stochastic numerical simulation

This paper surveys the methods used in the theoretical studies of kinetics with a special emphasis on the works dealing with the stochastic methods and their application in studies of adsorption kinetics. One of the stochastic methods — Monte Carlo numerical simulation of the stochastic time evolution — is mainly discussed. Numerous studies show that this method, introduced by Gillespie [J. Comput. Phys. 22 (1976) 403], is very useful to investigate the adsorption kinetics. The systematic studies of adsorption kinetics of single gases and gas mixtures on solid surfaces are presented. The kinetic adsorption isotherms, involving the lateral interactions between molecules in the surface phase, energetic heterogeneity of the adsorbent surface and surface diffusion, are numerically simulated by means of the numerical program, which is presented in the appendix. These simulations show influence of the adsorbent heterogeneity, lateral interactions and surface diffusion on the adsorption kinetics.     

Measuring birefringence of curved sheet and single crystals by double-exposure speckle photography

In this work, a new theoretical and experimental approach for measuring birefringence of solid materials was described. Dispersions of birefringence of quartz, calcite crystals and Fortypan sheet were determined in the visible region. The results were compared with other interferometric methods to verify the accuracy of this approach.     

Orientational disordering in crystals—I: A model for the evaluation of thermodynamic properties of melting transitions in atomic and plastic crystals

A generalisation of two-sublattice models of melting transitions in atomic and molecular crystals (Lennard-Jones and Devonshire; Pople and Karasz; Amzel and Becka) has been attempted. The intention was to develop a scheme by which parameters, such as the number of sublattices and distinguishable molecular orientations can be selected. It is found that the choice of these parameters made by Lennard Jones and Devonshire, and by Pople and Karasz, protects the theory to some extent from some of the more difficult physical issues. A single-lattice model also emerges as another possibility in the series of models that may be called upon. Thus a single-lattice model, based on concepts from Eyring's Significant Structure Theory of Liquids for the melt, and standard thermodynamic functions for the solid, has been developed to evaluate thermodynamic properties of melting transitions in atomic and molecular crystals. Despite the remarkable simplicity of the model predicted values of entropy of fusion for both argon and methane are in good agreement with experimental data. Mean positional disordering energies for the same substances have also been computed.     

Formation dynamics of nonvolatile crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals: Theoretical investigation

The formation dynamics of crossed-beam photorefractive gratings formed by the method of two-center holographic recording in doubly doped LiNbO₃ crystals is investigated in this paper based on the theoretical model combining the two-center band transport model with the two-dimensional coupled-wave theory. The numerical simulations are presented for two-center holographic recording crossed-beam photorefractive gratings in LiNbO₃:Fe:Mn crystals. The temporal and spatial evolutions of the refractive index modulation and the diffraction efficiency are shown. The spatial variation of the wave intensity is also presented.     

2μm人眼安全波段太阳光抽运激光器的理论研究

太阳光直接抽运激光器在空间光通信、遥感等领域有着重要的潜在应用,但是一直以来人们对太阳光抽运激光器的研究局限于以掺Nd3+粒子为增益介质的1μm波段.通过对现有固体激光工作物质的吸收谱进行分析,发现掺Tm3+离子在太阳辐射较强的可见光波段具有强的吸收峰,使2μm人眼安全波段实现太阳光直接抽运激光输出成为可能.本文对Tm:YAG和Tm:YAP两种常见晶体的吸收谱与太阳光谱匹配度进行了分析计算,得出两种材料用于太阳光抽运激光器的阈值抽运功率密度分别为1.14和1.434 kW/cm3.选择与抽运阈值功率密度低的Tm:YAG晶体作为增益介质,使用TracePro软件建立太阳光抽运激光器的二级抽运模型,并对模型进行优化,得到了锥形腔窗口与菲涅耳透镜的最佳距离、晶体棒的最佳长度以及锥形腔最佳锥度.本文的工作为实现太阳光直接抽运2μm激光输出做了理论上的准备.