The Intrinsic Features of the Specific Heat at?Half-Filled Landau Levels of Two-Dimensional Electron Systems

The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of the specific heat for each case is obtained at half-filling. When the chemical potential is temperature-independent, the temperature is calculated at which the specific heat is a maximum. Here the effects of the broadening of the Landau levels are distinguished from those of the different filling factors. In general, the results derived herein hold for any thermodynamic system having similar resonant states.     

Scaling of the Resistance and Magnetization for High Temperature Superconductors under Pressure

The scaling relation of single parameter scaling hypothesis is applied to the study of the scaling behavior of high temperature superconductors under pressure. The data of resistance and magnetization under various pressures are scaled onto a universal curve according to this scaling relation. The scaling parameters are pressure dependent while temperature independent. It is found that the controlling parameter B _i equals the relative critical temperature t _cP , which indicates that the superconducting energy gap at the zero temperature 2Δ _s0 is the controlling parameter in this scaling.      

Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines

We review the energy spectrum and transport properties of several types of one-dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on an SL is highly collimated. On the other hand, there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytical expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of δ-function barriers, the transmission T through and conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, Pδ(x) = V(x)/?v(F), with v(F) the Fermi velocity. For a Kronig-Penney SL with alternating sign of the height of the barriers, the Dirac point becomes a Dirac line for P = π/2+nπ with n an integer. In bilayer graphene, with an appropriate bias applied to the barriers and wells, we show that several new types of SLs are produced and two of them are similar to type I and type II semiconductor SLs. Similar to single-layer graphene SLs, extra 'Dirac' points are found in bilayer graphene SLs. Non-ballistic transport is also considered.     

A rigorous derivation for T-stress in line crack problem

In this paper, a rigorous derivation for T-stress in line crack problem is presented. Similar to the edge crack case, this paper provides the T-stress dependence on loading with the Dirac delta function property.     

Shear waves from an external acoustic wave generator acting on a crack in a rectangular strip

An analytical solution for the wave equation in a rectangular elastic strip and in the presence of an external harmonic wave generator acting on a crack is derived. This source is spatially distributed in a generalized mathematical form near the vicinity of the tip of the crack and acts normal to its faces. Two limiting cases (1) a uniform distribution and (2) Dirac's delta function distribution are solved. Examples of the relation between the displacement at the epicenter and the crack length for different body force distributions are shown.

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Résumé On établit une solution analytique de l'équation d'onde dans une bande rectangulaire élastique soumise à l'effet d'un générateur extérieur d'ondes harmoniques agissant sur une fissure dans la bande. On suppose que la source est distribuée dans l'espace sous une forme mathématique générale au voisinage de l'extrémité de la fissure, et qu'elle agit normalement aux surfaces de celle-ci. Deux cas limites sont résolus: la distribution uniforme d'une part, et une distribution suivant une fonction delta de Dirac d'autre part. On donne des exemples de la relation existant entre le déplacement à l'épicentre et al longueur de la fissure, et ce pour diverses distributions de forces sur le corps.

     

Self-Fourier functions and self-Fourier operators

The concept of self-Fourier functions, i.e., functions that equal their Fourier transform, is almost always associated with specific functions, the most well known being the Gaussian and the Dirac delta comb. We show that there exists an infinite number of distinct families of these functions, and we provide an algorithm for both generating and characterizing their distinct classes. This formalism allows us to show the existence of these families of functions without actually evaluating any Fourier or other transform-type integrals, a task often challenging and frequently not even possible.     

Detailed comparison of numerical methods for the perturbed sine-Gordon equation with impulsive forcing

The properties of various numerical methods for the study of the perturbed sine-Gordon (sG) equation with impulsive forcing are investigated. In particular, finite difference and pseudo-spectral methods for discretizing the equation are considered. Different methods of discretizing the Dirac delta are discussed. Various combinations of these methods are then used to model the soliton–defect interaction. A comprehensive study of convergence of all these combinations is presented. Detailed explanations are provided of various numerical issues that should be carefully considered when the sG equation with impulsive forcing is solved numerically. The properties of each method depend heavily on the specific representation chosen for the Dirac delta—and vice versa. Useful comparisons are provided that can be used for the design of the numerical scheme to study the singularly perturbed sG equation. Some interesting results are found. For example, the Gaussian approximation yields the worst results, while the domain decomposition method yields the best results, for both finite difference and spectral methods. These findings are corroborated by extensive numerical simulations.     

On the distribution of impulses in inviscid,incompressible flow — the induced downwash on a rotating wing

Summary We consider the prescribing of singularities in inviscid fluid flows by including Dirac delta functions in the Euler momentum equation. Examples are given of the modelling of the flows due to lifting bodies, in particular that due to a wing simultaneously translating and rotating and find the induced downwash due to the trailing vortex wake.With 2 Figures     

Interaction between coplanar cracks under dynamic shock loading

Summary A study is made on the interaction between coplanar cracks in an unbounded body when dynamic loads act on thier surfaces that are described as Heaviside or Dirac delta functions. Graphs are given relating the stress intensity coefficients when there are two disk cracks in the body whose surfaces are loaded by shock external forces.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 50–55, May–June, 1991.     

Nanophysics in graphene: neutrino physics in quantum rings and superlattices

Electrons in graphene at low energy obey a two-dimensional Dirac equation, closely analogous to that of neutrinos. As a result, quantum mechanical effects when the system is confined or subjected to potentials at the nanoscale may be quite different from what happens in conventional electronic systems. In this article, we review recent progress on two systems where this is indeed the case: quantum rings and graphene electrons in a superlattice potential. In the former case, we demonstrate that the spectrum reveals signatures of 'effective time-reversal symmetry breaking', in which the spectra are most naturally interpreted in terms of effective magnetic flux contained in the ring, even when no real flux is present. A one-dimensional superlattice potential is shown to induce strong band-structure changes, allowing the number of Dirac points at zero energy to be manipulated by the strength and/or period of the potential. The emergence of new Dirac points is shown to be accompanied by strong signatures in the conduction properties of the system.     

The time-dependent Green's function of the transverse vibration of a composite rectangular membrane

A new method for the approximate computation of the time-dependent Green's function for the equations of the transverse vibration of a multi stepped membrane is suggested. This method is based on generalization of the Fourier series expansion method and consists of the following steps. The first step is finding eigenvalues and an orthogonal set of eigenfunctions corresponding to an ordinary differential operator with boundary and matching conditions. The second step is a regularization (approximation) of the Dirac delta function in the form of the Fourier series with a finite number of terms, using the orthogonal set of eigenfunctions. The third step is an approximate computation of the Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of eigenfunctions. The computational experiment confirms the robustness of the method.     

Computing the survival probability density function in jump-diffusion models: A new approach based on radial basis functions

We propose a numerical method to compute the survival (first-passage) probability density function in jump-diffusion models. This function is obtained by numerical approximation of the associated Fokker–Planck partial integro-differential equation, with suitable boundary conditions and delta initial condition. In order to obtain an accurate numerical solution, the singularity of the Dirac delta function is removed using a change of variables based on the fundamental solution of the pure diffusion model. This approach allows to transform the original problem to a regular problem, which is solved using a radial basis functions (RBFs) meshless collocation method. In particular the RBFs approximation is carried out in conjunction with a suitable change of variables, which allows to use radial basis functions with equally spaced centers and at the same time to obtain a sharp resolution of the gradients of the survival probability density function near the barrier. Numerical experiments are presented in which several different kinds of radial basis functions are employed. The results obtained reveal that the numerical method proposed is extremely accurate and fast, and performs significantly better than a conventional finite difference approach.     

振荡流作用下受约束的悬臂输流管的分岔特性

引入三次方非线性的Dirac delta函数研究约束条件下悬臂输流管中的分岔特性。输流管内流体因振荡流作用而产生自激振动,是分岔与混沌运动的原因。通过迦辽金截断方法使系统变为标准的有限低维离散的系统。运用龙格库塔数值仿真的方法求解低维系统,获得关于振荡流作用下受约束的悬臂输流管的分岔特性。给出具体的数值算例,研究流速及振荡流参数的分岔影响。     

Modified joint transform correlator binarized by error diffusion. II. Spatially variant range limit

Nonlinear scaling of the joint power spectrum in one approach and noise-subtraction followed by nonlinear scaling in a second approach are analyzed in conjunction with error-diffusion binarization for joint transform correlator configurations in the presence of input-additive white Gaussian noise. Nonlinear scaling is performed with a spatially variant range limit. For the second approach the subtracted noise value is an estimate of the noise power spectral density. Computer simulations and optical experiments demonstrate the advantages of the proposed error-diffusion-based joint transform correlator approaches. In particular the approach based on noise subtraction before nonlinear scaling is advantageous even for very high noise levels.     

Analytic algorithms for determining radiative transfer optical properties of ocean waters

A synthetic model for the scattering phase function is used to develop simple algebraic equations, valid for any water type, for evaluating the ratio of the backscattering to absorption coefficients of spatially uniform, very deep waters with data from upward and downward planar irradiances and the remotely sensed reflectance. The phase function is a variable combination of a forward-directed Dirac delta function plus isotropic scattering, which is an elementary model for strongly forward scattering such as that encountered in oceanic optics applications. The incident illumination at the surface is taken to be diffuse plus a collimated beam. The algorithms are compared with other analytic correlations that were previously derived from extensive numerical simulations, and they are also numerically tested with forward problem results computed with a modified FN method.     

Study of the indirect interaction in the quantum dots of the graphene bilayer in the framework of the <Emphasis Type="Italic">s-d</Emphasis> model

Specific features of the RKKY interaction in triangular quantum dots of the graphene bilayer have been studied according to the s-d exchange model. Theoretical model calculations showed that, with allowance for an electron spectrum limited by the Dirac approximation, the dependence of the exchange interaction energy on the distance between spins ceases to possess a periodic (oscillatory) character.     

A method of numerical solution of one-dimensional stefan problems of two types

A one-dimensional conjugate problem of heat transfer with phase transitions of two types (with interfaces of two phases and with a two-phase zone) is solved by a finite difference method based on the general initial heat conduction equation written with the Dirac delta function. A calculating scheme is developed using a nonuniform spatial net with floating nodes and the method of oppositely directed pivots.Nizhnii Novgorod Polytechnic Institute. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 3, pp. 332–340, September, 1993.     

砷化镓半导体光吸收特性的研究

简叙述了征ＧａＡｓ晶体中的光吸收过程，分析了半导体材料光吸收特性与温度之间的依赖关系。研究表明，一定厚度的ＧａＡｓ晶片对入射光的吸收直接依赖于光源的功率谱特性与温度，文中揭示了光吸收－温度曲线与不我源光谱功率分布之间的关系式。根据这种原理，获得了新的检测温度的方法，同时，给出了相应的实验结果。     

一种基于修正SSPH近似的无网格局部Petrov-Galerkin 法

首先采用奇异权函数对对称光滑粒子流体动力学(SSPH)近似进行了修正,使其构造的形函数近似满足d函数性质,方便无网格法中本质边界条件施加;然后应用修正的SSPH 近似法构造试函数,结合以Heaviside 函数为权函数的局部弱形式,提出了一种新的求解弹性静力问题的无网格局部Petrov-Galerkin 法;最后应用新的无网格法计算了一系列数值算例,结果表明:该方法具有良好的精度和收敛性。