Statistics of inter-particle distances and angles in plasmas

Accurate treatment of the plasma density effects requires a detailed knowledge of the spatial distribution of individual ions around a test ion. In the present work, rigorous expressions are derived for the main 2- and 3-particle spatial distribution functions involving the nearest neighbor (NN) and the next-nearest neighbor (NNN) ions. These expressions, valid for both ideal and nonideal plasmas, present the distributions as functionals of the potentials U _NN and U _NNN at the nearest and next-nearest ion locations. All of the distribution functions except one are derived and discussed in the present work for the first time ever. For utilization of our results in practical calculations, we suggest semi-empirical expressions for U _NN and U _NNN in the ion-ion coupling parameter range 0 ?Γ < 1. In order to test the accuracy of our expressions for U _NN and U _NNN we conduct Molecular Dynamics (MD) simulations. The simulations utilize the pure Coulomb particle-particle interaction potentials, regularized at close range to avoid classical Coulomb collapse, and are free from the assumptions made to find U _NN and U _NNN. Thus, the results of the MD simulations provide an independent test of our theoretical results. Excellent agreement has been found between the results of the theory and of the MD simulations. Finally, we outline the implications of the present findings on the problem of tunneling and charge exchange in dense plasmas. Received 27 October 2000 and Received in final form 30 January 2001     

Stability Concepts in Topological Dynamics by Nonstandard Methods

It is known that it is not possible to introduce C⁰ -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rⁿ. Classically these amount to considering the space of all systems on a given subset of Rⁿ as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

一类扩张了的软弹簧型Duffing方程的紊动性态

本文用Melnikov函数方法讨论了一类扩张了的软弹簧型Duffing方程(k=1,2,3,…)在周期激励下的紊动现象.给出了出现二阶同宿切的条件.文中所采用的方法对于不能给出并宿轨道的显式的系统的研究是非常有用的.     

Coherent control of spin tunneling in a driven spin–orbit coupled bosonic triple well

We investigate the coherent control of spin tunneling for a spin–orbit (SO) coupled boson trapped in a driven triple well. In the high-frequency limit, the quasienergies of the system are obtained analytically and the fine energy band structures are shown. By regulating the driving parameters, we reveal that the directed spin-flipping or spin-conserving tunneling of an SO-coupled boson occurs along different pathways and in different directions. The analytical results are demonstrated by numerical simulations and good agreements are found. Further, an interesting scheme of quantum spin tunneling switch with or without spin-flipping is presented. The results may have potential applications in the design of spintronic devices.     

Organic magnetoresistance and spin diffusion in organic semiconductor thin film devices

We review recent work in the field of organic spintronics, focusing on our own contributions to this field. There are two principle magnetoresistance effects that occur in organic devices. (i) Organic magnetoresistance (OMAR), which occurs in nonmagnetic organic semiconductor devices. For example, in devices made from the prototypical small molecule Alq₃ OMAR reaches values of 10% or more at room temperature. (ii) Organic spin‐valve effects that occur in devices that employ ferromagnetic electrodes for spin‐polarized current injection and detection. We undertake an analysis of these two types of magnetoresistance with the goal of identifying the dominant spin‐scattering mechanism. Analysis of OMAR reveals that hyperfine coupling is the dominant spin‐coupling mechanism. Spin–orbit coupling, on the other hand, is important only in organic semiconductor materials containing heavy atoms. We explore the reasons why spin–orbit coupling is relatively unimportant in hydrocarbon materials. Next, we present a theory for spin diffusion in disordered organic semiconductors based on hyperfine coupling, taking into account a combination of incoherent carrier hopping and coherent spin precession in the random hyperfine magnetic fields. We compare our findings with experimental values for the spin‐diffusion length. Finally, we demonstrate a criterion that allows the determination whether the organic spin‐valves operate in the tunneling or injection regimes. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the determination of the potential function from given orbits

The paper deals with the problem of finding the field of force that generates a given (N ? 1)-parametric family of orbits for a mechanical system with N degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov’s problem. We apply the obtained results to generalize the theorem enunciated by Joukovski in 1890, solve the inverse Stäckel problem and solve the problem of constructing the potential-energy function U that is capable of generating a bi-parametric family of orbits for a particle in space. We determine the equations for the sought-for function U and show that on the basis of these equations we can define a system of two linear partial differential equations with respect to U which contains as a particular case the Szebehely equation. We solve completely a special case of the inverse dynamics problem of constructing U that generates a given family of conics known as Bertrand’s problem. At the end we establish the relation between Bertrand’s problem and the solutions to the Heun differential equation. We illustrate our results by several examples.     

A full‐pivoting algorithm for the Cholesky decomposition of two‐electron repulsion and spin‐orbit coupling integrals

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two‐electron spin‐orbit coupling (2e‐SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e‐SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e‐SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full‐pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that is the upper limit for the errors affecting the reconstructed 2e‐SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e‐SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.     

带电粒子在均匀电磁场中的运动

带电粒子在纯电场、纯磁场中运动时,其运动轨迹分别是抛物线和螺旋线.当电磁场并存时,根据相对论基本原理,带电粒子的运动并不是两种情况的简单叠加,运动轨迹与场的大小、方向有关.