An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem

In this paper, we propose an iterative two-grid method for the edge finite element discretizations (a saddle-point system) of Perfectly Matched Layer (PML) equations to the Maxwell scattering problem in two dimensions. Firstly, we use a fine space to solve a discrete saddle-point system of $H(grad)$ variational problems, denoted by auxiliary system 1. Secondly, we use a coarse space to solve the original saddle-point system. Then, we use a fine space again to solve a discrete$\boldsymbol{H}(curl)$-elliptic variational problems, denoted by auxiliary system 2. Furthermore, we develop a regularization diagonal block preconditioner for auxiliary system 1 and use $H$-$X$ preconditioner for auxiliary system 2. Hence we essentially transform the original problem in a fine space to a corresponding (but much smaller) problem on a coarse space, due to the fact that the above two preconditioners are efficient and stable. Compared with some existing iterative methods for solving saddle-point systems, such as PMinres, numerical experiments show the competitive performance of our iterative two-grid method.     

Quantum dots with disorder and interactions: a solvable large-g limit

We analyze the problem of interacting electrons on a ballistic quantum dot with chaotic boundary conditions, where the effective interactions at low energies are characterized by Landau parameters. When the dimensionless conductance g of the dot is large, the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as g --> infinity (as in a large-N theory), leading to a phase transition in each Landau interaction channel. In the weak-coupling phase constant charging and exchange interactions dominate the low-energy physics, while the strong-coupling phase displays a spontaneous distortion of the Fermi surface, smeared out by disorder.     

Functional integral methods for quantum spin systems

The partition function of quantum spin systems is represented by a functional integral over “time”-dependent magnetic fields. It is evaluated in the saddle-point approximation. In this way, the excitations of the system are derived from first principles, and their interactions are obtained.     

Assessment of saddle-point-mass predictions for astrophysical applications

Using available experimental data on fission barriers and ground-state masses, a detailed study of the predictions of different models concerning the isospin dependence of saddle-point masses is performed. Evidence is found that several macroscopic models yield unrealistic saddle-point masses for very neutron-rich nuclei, which are relevant for the r-process nucleosynthesis.     

Some considerations on the nonlinear stability of stationary planar Euler flows

We give sufficient conditions for the nonlinear stability of possibly nonsmooth stationary solutions of the two-dimensional Euler equation in symmetric bounded domains. We use, as Lyapunov functions, first integrals due to the symmetry of the problem. Moreover, we investigate the stability of smooth solutions under perturbations of the boundary. The last result is based on a generalization of the well known Arnold approach.Research partially supported by Italian CNR and Ministero della Pubblica Istruzione     

The Arctic Curve of the Domain-Wall Six-Vertex Model

The problem of the form of the ‘arctic’ curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of q-enumerated (with 0<q ≤4) large alternating sign matrices. In particular, as q→0 the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.     

Dynamical aspects of nucleus-nucleus collisions

This is an extension of the macroscopic theory of nucleus-nucleus reactions described by Swiatecki. The fusion or reseparation of two colliding nuclei is treated according to a schematic model based on the “chaotic regime dynamics” (liquid-drop potential energy plus one-body dissipation). Attention is focused on three hurdles or “milestone configurations” that a colliding system may be faced with: the touching configuration, the conditional saddle-point configuration at frozen mass asymmetry, and the unconditional saddle-point configuration. Semi-empirical formulae are derived for the “extra push” (the extra energy needed in some situations to carry the system from the first to the second hurdle) and for the “extra-extra push” (the energy needed to carry the system from the first to the third hurdle). The theoretical formulae are confronted with measurements of fusion and evaporation-residue cross sections. A discussion of the implications for super-heavy-element reactions is given, using the production of element 107 in the bombardment of ²⁰⁹Bi with ⁵⁴Cr as a calibrating reaction.     

On a trajectory method for evaluating the transition probability in a quantum system

A version of calculation of the transition probability in a quantum system based on the representation of the transition probabilities in the form of a path integral and its evaluation by the saddle-point method for part of the variables. Some problems associated with the analytic continuation of the integrand are discussed. The proposed approach is compared to related methods widely used in chemical physics.     

Automatic spectral collocation for integral,integro-differential,and integrally reformulated differential equations

Automatic Chebyshev spectral collocation methods for Fredholm and Volterra integral and integro-differential equations have been implemented as part of the chebfun software system. This system enables a symbolic syntax to be applied to numerical objects in order to pose and solve problems without explicit references to discretization. The same objects can be used in matrix-free iterative methods in linear algebra, in order to avoid very large dense matrices or allow application to problems with nonsmooth coefficients. As a further application of the ability to implement operator equations, a method of Greengard [1] for the recasting of differential equations as integral equations is generalized to mth order boundary value and generalized eigenvalue problems. In the integral form, large condition numbers associated with differentiation matrices in high-order problems are avoided. The ability to implement the recasting process generally follows from implementation of the operator expressions in chebfun. The integral method also can be extended to first-order systems, although chebfun syntax does not currently allow easy implementation in this case.     

类锂离子内壳激发态的能量、俄歇宽度和俄歇分支率（英文）

采用鞍点变分方法和鞍点复数转动方法并考虑相对论修正和质量极化效应,计算了类锂离子内壳激发态的能量、俄歇宽度、俄歇分支率和俄歇电子能量.进一步采用截断变分方法饱和空间波函数.计算结果与其他理论结果以及实验数据符合得很好.     

Electron self-trapping at quantum and classical critical points

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only singular perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.     

广义BVP电路系统的振荡行为及其非光滑分岔机理

探讨了具有分段线性特性的广义BVP电路系统随参数变化的复杂动力学演化过程. 其非光滑分界面将相空间划分成不同的区域, 分析了各区域中平衡点的稳定性, 得到其相应的简单分岔和Hopf分岔的临界条件. 给出了不同分界面处广义Jacobian矩阵特征值随辅助参数变化的分布情况, 讨论了分界面处系统可能存在的分岔行为, 指出当广义特征值穿越虚轴时可能引起Hopf分岔, 导致系统由周期振荡转变为概周期振荡, 而当出现零特征值时则导致系统的振荡在不同平衡点之间转换. 针对系统的两种典型振荡行为, 结合数值模拟验证了理论分析的结果.     

时域相位光码分多址系统性能分析

给出了时域相位光码分多址系统(OCDMA)的噪声模型,提出了由码间串扰(ISI)所引起的自差拍噪声(SB)概念.利用鞍点近似法分析了多址干扰(MAD、码间串扰、自差拍等噪声对系统性能的影响,给出了系统误码率公式.对最佳门限接收系统以及采用光硬件限幅器的系统性能进行了仿真研究.表明"1"码的误判概率是影响系统的决定性因素.也是开关键控(OOK)系统难以克服的主要问题.最后给出一种采用双编/解码器平衡检测系统的原理框图,分析其性能,并与传统OOK系统比较,结果表明其性能有较大的提高.     

类锂离子2s2p2p^2S三激发态的能量和宽度

采用马鞍点变分方法和复数转动技术，计算了类锂离子２ｓ２ｐ２ｐ２Ｓ三激发共振态的能量，并运用截断变分方法得到能量改进量，以及计算了相对论效应、质量极化效应，从而获得了高精度的能量计算值。还计算了该系统的Ａｕｇｅｒ宽度，位移和辐射跃迁率。     

Critical conditions for dislocation nucleation at surface steps

Dislocation nucleation at a surface step is analyzed based on a general variational boundary integral formulation of the Peierls–Nabarro dislocation model. By modelling the surface step as part of the surface of a three-dimensional crack, the free surface effect is taken into account by transferring the half space problem into an equivalent one in the infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along the slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress-dependent activation energies required to activate the embryonic dislocations from their stable to unstable saddle-point configurations. In particular, the effect of the step geometry, such as the height of the step, the dip angle of the slip plane and the inclined angle of the step surface on dislocation nucleation, is quantitatively ascertained. The results show that the atomic-scale surface step can rapidly reduce the critical stress required for dislocation nucleation from the surface by nearly an order of magnitude. The decrease in critical stress as a function of the height of the step is more significant for slip planes with smaller dip angles and surface steps with smaller inclined angles.     

Statistical description of nonequilibrium self-gravitating systems

Self-gravitating systems are non-equilibrium a priori. A new approach is proposed, which employs a non-equilibrium statistical operator that takes account inhomogeneous distribution of particles and temperature. The method involves a saddle-point procedure to find the dominant contributions to the partition function, thus obtaining all thermodynamic parameters of the system. Probable peculiar features in the behavior of the self-gravitating systems are considered for various conditions. The equation of state for self-gravitating systems has been determined. A new length of the statistical instability is obtained for a real gravitational system, as are parameters of the spatially inhomogeneous distribution of particles and temperature.     

On the Eckhaus instability for spatially periodic patterns

The range of stable wavevectors is near the threshold for appearance of periodic patterns in quasi-one-dimensional systems limited by the long-wavelength Eckhaus instability. At this instability saddle-point solutions characterizing the wavelength-changing processes inside the stable range merge with the periodic solutions. We first analyse this bifurcation near threshold using the amplitude expansion in lowest order. Then a nonlinear equation for the evolution of slow modulations of the periodic pattern far from threshold but near the Eckhaus instability is derived and used to analyse the universal properties of the Eckhaus bifurcation. More detailed information concerning the spatial symmetry of saddle-point solutions is obtained by numerical integration of simple model systems.     

Saddle-point energies and Monte Carlo simulation of the long-range order relaxation in CoPt

We present atomic-scale computer simulations in equiatomic L1₀-CoPt where Molecular Dynamics and Monte Carlo techniques have both been applied to study the vacancy-atom exchange and kinetics relaxation. The atomic potential is determined using a Tight-Binding formalism within the Second-Moment Approximation. It is used to evaluate the different saddle-point energies involved in a vacancy-atom exchange between nearest-neighbour sites. The potential and the saddle-point energies have been used to simulate the relaxation of the long-range order in CoPt using a Monte Carlo technique. A vacancy migration energy of 0.73±0.15 eV and an order-disorder transition temperature of 935 K have been found.