Reduced‐order modeling for nonlocal diffusion problems

In several settings, diffusive behavior is observed to not follow the rate of spread predicted by parabolic partial differential equations (PDEs) such as the heat equation. Such behaviors, often referred to as anomalous diffusion, can be modeled using nonlocal equations for which points at a finite distance apart can interact. An example of such models is provided by fractional derivative equations. Because of the nonlocal interactions, discretized nonlocal systems have less sparsity, often significantly less, compared with corresponding discretized PDE systems. As such, the need for reduced‐order surrogates that can be used to cheaply determine approximate solutions is much more acute for nonlocal models compared with that for PDEs. In this paper, we consider the construction, application, and testing of proper orthogonal decomposition (POD) reduced models for an integral equation model for nonlocal diffusion. For certain modeling parameters, the model we consider allows for discontinuous solutions and includes fractional Laplacian kernels as a special case. Preliminary computational results illustrate the potential of using POD to obtain accurate approximations of solutions of nonlocal diffusion equations at much lower costs compared with, for example, standard finite element methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Spin-Dependent Thermoelectric Transport in Cobalt-Based Heusler Alloys

Sitting at the intersection of spintronics and thermoelectricity, research investigating the coupling of thermoelectric, magnetic, and electrical transport properties in materials has recently found that the ferromagnetic Heusler alloys are the ideal testbeds. These materials have attracted a lot of attention due to their useful magnetotransport properties and the possibility of tailoring these properties by modifying their composition or producing heterostructures. With the diverse range of interesting phenomena in the Heusler alloys, ferromagnetic Heusler alloys are also ideal candidates for engineering spin caloritronic devices that can take advantage of the interplay of the physics of heat flow, magnetism, and electric potential. The fundamental physical concepts important to spin-dependent thermoelectrics research are introduced and recent studies of several ferromagnetic Heusler compounds are reviewed, highlighting some exceptional latest experiments on half-metallic Co₂TiSn and the ferromagnetic Weyl semimetal Co₂MnGa. Furthermore, the potential to generate useful magnetothermoelectric voltages in electronic devices based on the anomalous Nernst effect is discussed.     

Dissipativity and stability for semilinear anomalous diffusion equations involving delays

We analyze the dissipativity and stability of solutions to a class of semilinear anomalous diffusion equations involving delays. The existence of absorbing set, the stability, and weak stability will be shown under suitable assumptions on the nonlinearity. Our analysis is based on new Halanay-type inequality, local estimates, and fixed-point arguments.     

‘True’ self-avoiding walks with generalized bond repulsion on ℤ

We consider a nearest-neighbor random walk on , for which the probability of jumping along a bond of the lattice is proportional to exp[–g. (number of previous jumps along that bond) ^k ], withg>0,k(0,1]. After a review of earlier results obtained for the casek=1 we outline the generalizations fork(0,1), obtaining a whole range of anomalous diffusion limits.Dedicated to Oliver Penrose on the occasion of his 65th birthday     

莱维噪声诱发的速度双模分布

研究了非线性阻尼驱动的惯性莱维飞行在自由势场中的反常输运。通过引入依赖于速度的非线性阻尼,长程跳跃的莱维粒子被束缚,粒子的动力学行为由发散收敛为与时间呈正比的正常扩散。观察到在自由势场中莱维飞行的速度的定态概率分布呈双模分布形式,更为重要的是,观察到双模形式与莱维系数及非线性阻尼系数相关。     

Dielectric loss measurements on silver halide sheet crystals

Abstract

A series of studies on the partial X-ray diffuse scattering intensities from ternary alloys analysed through synchrotron radiation experiments has been reviewed. An intensity expression for the short-range order diffuse scattering has been developed, which is necessary in understanding the separation method of an observed X-ray diffuse intensity into partial intensities contributed from different origins. Techniques have been described in detail mainly concerning the Cu₂NiZn alloy, which have shown the benefits of the anomalous scattering effect of synchrotron radiation. The negative partial intensity maximum for the Cu-Ni pair found in the Cu-Ni-Zn alloy has been discussed from the viewpoints of crystallography and thermodynamics. In addition, at the end of the paper, local atomic arrangements causing the diffuse scatterings have been discussed.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

The Interacting Boson Model for Anomalous Rotational Bands

The interacting boson model for anomalous rotational bands is proposed. In the rotational SU(3) limit,an asymptotic limit is discussed. Within the framework of the model several analytic relations for energies and electro-magnetic transition rates are derived.     

Modelling of linearly chirped fiber bragg gratings by the method of single expression

To model chirped fiber Bragg gratings (FBGs) for dispersion compensation in optical fibers a novel method of single expression (MSE) is used. The reformulation of Helmholtz’s equation in the MSE to the full set of first-order differential equations leads to dealing with the electric field amplitude, its derivative, power flow density and phase distributions in any aperiodic media. The phase derivative obtained numerically permits to compute the dispersion slope in the time delay of investigated chirped gratings. Reflective and time delay spectra of linearly chirped gratings of different lengths and chirp coefficients are computed. A self-similarity law for the gratings of the same strength but different lengths and chirp coefficients is revealed. The apodization of gratings is applied to reduce sidelobes in gratings’ reflection spectra and eliminate oscillations in the time delay characteristics.     

高能电子-正电子碰撞中产生喷注的标度

对高能电子-正电子对撞产生实验上可以直接观察的可视喷注的标度进行了仔细研究.根据在s=17—30Gev的电子-正电子对撞实验中最先观察到三喷注这一历史事实,论证了可视喷注的相对横动量kt.在5—10GeV/c的范围.并通过一个具体例子说明,只有k_t在这一范围时才能正确地判定事件中的喷注数.仔细比较了由不同k_t得到的喷注内部的动力学起伏,发现只有k_t在5—10GeV/c范围时,喷注内部系统才有最好的反常标度性.从而得到,可视喷注的标度是k_t～5—10GeV/c.讨论了这一标度和微扰QCD的标度1—2GeV之间的关系.