Locally one-dimensional difference schemes for the fractional order diffusion equation

Locally-one-dimensional difference schemes for the fractional diffusion equation in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved.     

Collective modes in a one-dimensional nonuniform fluid model

A one-dimensional fluid with short-range repulsive interaction and one period of cosinusoidal attraction in a periodic container is transformed to a two-mode format. The system has both high-temperature single-phase regions and lowtemperature two-phase regions with a very broad spatial interface that can be stabilized by a weak external field. The case of vanishing external field brings out properties of the mode amplitude dependence which one expects to extend to more complex systems.     

掺杂对一维光子晶体带隙传输特性的影响

 基于传输矩阵法,数值研究了掺杂对一维光子晶体带隙特征的影响。研究表明：掺杂时,禁带中心会出现一导带,导带深度会随着掺杂位置、杂质折射率的变化而发生变化。当晶体结构给定时,总存在一个掺杂位置,使其禁带中心的导带深度达到最深;而对于给定的掺杂位置,当杂质折射率为某特定值时,禁带中心同样也会出现一个深度最深的导带,这种特性可应用于滤波器件和光学谐振腔的设计。     

一维受迫谐振子量子运动的经典特性

对经典一维受迫谐振子量子化,求解量子化后体系的时间演化算符.应用相空间准概率分布函数,研究了体系的量子特性.研究结果表明,初始为真空态,经过时间演化,系统波函数是一个二维高斯波包;波包中心的振幅和相位受到作用力的调制,成为调幅、调相波,波包中心的运动与经典受迫谐振子的运动形式相同.     

一维金属光栅的光学反射吸收

利用RCWA(rigid coupled-wave analysis)方法研究了一维金属光栅的反射特性,考察了 瑞利反常、表面等离激元驻波共振和几何共振三种共振吸收机理,分析了这三种机理的相互作用,如表面等离激元驻波共振和几何共振可以形成混合模式. 在反射式复合金属光栅中,确认了第四种共振形式,即相位共振. 数值计算表明相位共振对光学吸收的影响有两种形式: 当光栅周期大于一个波长时,相位共振导致尖锐的吸收峰,峰位在几何共振吸收峰一侧;当光栅周期小于一个波长时,相位共振导致混合模式的共振吸收峰发生劈裂. 对一维金属光栅反射特性的研究增加了对金属光栅共振吸收模式及其相互作用的认识. 关键词： 一维金属光栅 瑞利反常 表面等离激元 相位共振     

A case study of the MSA approach to quantized polarizable media

The mean spherical approximation (MSA) has proved to be a very general and flexible method to analyze equilibrium statistical mechanical systems. In this note we test its accuracy against a simple one-dimensional model, i.e., a lattice gas of polarizable molecules where the internal degree of freedom is treated as quantized harmonic oscillators which interact via harmonic forces. This model can be solved exactly. We find a very good agreement between the MSA and exact solutions.2 The corresponding classical problem of polarizable particles was first solved in a mean spherical approximation (MSA) by M. Wertheim [J. Chem. Phys. 26:1425 (1973)]. He considered the model with nonfluctuating dipole moments. Later L. Pratt [Mol. Phys. 40:347 (1980)] and J. S. Høye and G. Stell [J. Chem. Phys. 73:461 (1980)] solved the corresponding classical problem in the MSA for particles with fluctuating dipole moments.     

Stationary velocity distribution in an external field: A one-dimensional model

The velocity distribution of a charged hard rod coupled to an external field and moving in a neutral equilibrium hard rod gas is studied on the basis of Boltzmann's equation. The exact stationary solution is found. Above a threshold value the field becomes effective in the high-velocity region slowing down the decay of the velocity distribution. The drift velocity and the mean kinetic energy are discussed as functions of the field.     

One-dimensional inhomogeneous Ising model: A new approach

We present a new method for the study of a one-dimensional inhomogeneous Ising chain with nonconstant nearest neighbor interactions. The external field required to produce a given magnetization profile is derived exactly. Some properties of the pair direct correlation function are derived. Our findings generalize previous results of Percus.     

Molecularly engineered graphene surfaces for sensing applications: A review

Graphene is scientifically and commercially important because of its unique molecular structure which is monoatomic in thickness, rigorously two-dimensional and highly conjugated. Consequently, graphene exhibits exceptional electrical, optical, thermal and mechanical properties. Herein, we critically discuss the surface modification of graphene, the specific advantages that graphene-based materials can provide over other materials in sensor research and their related chemical and electrochemical properties. Furthermore, we describe the latest developments in the use of these materials for sensing technology, including chemical sensors and biosensors and their applications in security, environmental safety and diseases detection and diagnosis.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.