Fractional power-law spatial dispersion in electrodynamics

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type.     

On dispersion relations for optical media with spatial dispersion

An estimate of the ratio of the contributions of relativistic and nonrelativistic factors to the Kramers-Kronig relations for a medium with spatial dispersion is performed in a form taking into account the relativistic requirement of the finiteness of the velocity of propagation of a signal. Even under conditions of comparatively strong spatial dispersion, in the case of Wannier-Mott excitons in typical semiconductors, this ratio proves to be very small—of the order of 10^?4, which justifies the conventional (nonrelativistic) form of the dispersion relations.     

A cellular automata model with probability infection and spatial dispersion

In this article, we have proposed an epidemic model based on the probability cellular automata theory. The essential mathematical features are analysed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic from the practical point of view. A discrete and spatiotemporal approach is shown by using cellular automata theory. It is interesting to note that both the size of the endemic equilibrium and the density of the individuals increase with the increase of the neighbourhood size and infection rate, but the infections decrease with the increase of the recovery rate. The stability of the system around the positive interior equilibrium has been shown by using a suitable Lyapunov function. Finally, experimental data simulation for SARS disease in China in 2003 and a brief discussion are given.     

Mie theory with spatial dispersion

The classícal Mie theory for the scattering and absorption of electromagnetic radiation by a sphere is extended to the case of a dieelectric sphere which exhibits spatial dispersion. This is achieved by imposing the usual Maxwell boundary conditions as well as Pekar's additional boundary conditions at the surface of the sphere.     

Relationships between power-law long-range interactions and fractional mechanics

We investigate the relationships between models of power-law long-range interactions and mechanics based on fractional derivatives. We present the fractional Lagrangian density which gives the Euler–Lagrange equation that serves as the equation of motion for fractional-power-law long-range interactions. We derive this equation by the fractional variational method. In addition, we derive a Noether-like current from the fractional Lagrangian density.     

Finite difference methods for two-dimensional fractional dispersion equation

Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of application. In this paper we discuss a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. First-order consistency, unconditional stability, and (therefore) first-order convergence of the method are proven using a novel shifted version of the classical Grünwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.     

A fractional calculus approach to nonlocal elasticity

If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen nonlocal elastic model. Aim of the present paper is to provide a mechanical interpretation to this nonlocal fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; the static, kinematic and constitutive equations are presented and the governing fractional differential equation highlighted. Two numerical procedures to solve the fractional equation are finally implemented and applied to study the strain field in a finite bar under given edge displacements.     

Permittivity of complex oxide crystals with allowance for spatial dispersion

The temporal and spatial dispersions of the permittivity of complex oxide crystals, which have numerous branches of dipole active oscillations, is considered. Formulas for calculating the susceptibility spectra of complex oxides in the terahertz region with allowance for both types of dispersion are obtained in the resonance approximation of photon-phonon interaction using quantum Green’s functions. The calculation results are used to discuss the well-known experimental data.     

Boundary conditions in media with spatial dispersion

In this paper we discuss the structure of the kernel in the integral relationship between the electric field and the displacement field in a semi-infinite dielectric medium (for the exciton region of spectrum) in the presence of spatial dispersion. Using the model of coupled oscillators we derive an additional boundary condition as a function of frequency shift and damping of surface oscillators.     

Lattice contractions of a nanoparticle due to the surface tension: A model of elasticity

The lattice parameters of a metallic nanoparticle decrease with its size. To describe this phenomenon, a model based on elasticity is developed in this paper. Using this model, we investigate the lattice contraction of a metallic nanoparticle due to its surface tension. The effect of size-dependent surface tension on the lattice contraction is discussed. Furthermore, the lattice contraction of a nanoparticle of non-spherical shape is also approximately estimated by defining a shape factor. The analysis shows that the lattice parameters of metallic nanoparticle are size dependent. However, if the radius of nanoparticle is more than 5.0 nm, the effect of size on lattice contraction is almost negligible.     

Charge interaction in layered systems with spatial dispersion

The potential electrostatic energy of a charge near the surface of a metal with a metal or a dielectric coating (adsorbate), on the interface between metal (semimetal) and insulator (electrolyte) and in layered thin-film sandwich-type systems (MIS structures) has been calculated. The influence of the metal and the dielectric epitaxial coatings of the metal surface upon the interaction of charges is investigated. Taking into account the spatial dispersion effects, it is shown that in thin films surrounded by a medium with a large dielectric constant, the Coulomb repulsion between electrons decreases.     

Boundary conditions in laser oscillators with spatial dispersion

From the stationary solution of the Fokker-Planck equation for a laser oscillator exhibiting spatial dispersion, presented in a previous paper, the equation for the most probable field configuration is derived. An additional boundary condition is found.     

A power-law model of the pseudopotential

A new simple power-law model of the pseudopotential is suggested. The parameters of the pseudopotential are determined for ions of the second period of the periodic system. Excited energy levels calculated for these ions using this model demonstrate its convergence. The accuracy of the energy levels calculated for the excited states is <10⁻³ a.u.     

考虑次近邻作用的行人交通格子流体力学模型

在二维双向行人交通格子流体力学模型的基础上,提出了考虑次近邻行人相互作用进行行人流优化的行人交通格子流体力学模型.通过线性稳定性分析给出新模型的稳定性条件.通过非线性分析得到描述交通堵塞密度波的改进的Korteweg-de Vries方程,并进行了数值模拟.     

Tracer dispersion in a percolation network with spatial correlations

We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolationlike porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We find that the resulting statistical properties of the tracer show a transition from a subdiffusion regime at low Peclet number to an enhanced diffusion regime at high Peclet number.     

Stationary solution of a laser oscillator with spatial dispersion

We present an exact solution of recently proposed differential equation for the space dependence of the most probable field amplitude in laser oscillator near threshold for laser action.