An explicit finite‐difference method for the approximate solutions of a generic class of anharmonic dissipative nonlinear media

We develop an explicit finite‐difference method to approximate solutions of modified, Fermi–Pasta–Ulam media, which consider the presence of parameters, such as external damping, relativistic mass, a coefficient for the nonlinear term, and a coefficient of coupling in the case of discrete systems. We propose discrete expressions to approximate consistently the total energy of the system and the average energy flux, and prove that the discrete rate of change of energy is a consistent estimate of its continuous counterpart. The method is thoroughly tested in the energy domain, and our results show that the method gives an approximately constant energy in the case of conservative systems, which fluctuates within a narrow margin of error that may be attributed to truncation errors. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Finite element methods for problems with solid-liquid-solid phase transitions and free melt surface

Modeling and computation of a process with solid-liquid-solid phase transitions and a free capillary surface is discussed. The main components of the model are heat conduction, a free melt surface, a moving phase boundary, and its coupling with the Navier-Stokes equations. We present two different approaches for handling the phase transitions by applying in a FE method, namely an energy conservation based approach, and a sharp interface approach with moving mesh. By combining both methods, we benefit from the advantages of the respective approach. The methods are applied to a problem where material is accumulated by melting the tip of thin steel wires using laser heating. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Ground State Energy of the Massless Spin-Boson Model

We provide an explicit combinatorial expansion for the ground state energy of the massless spin-Boson model as a power series in the coupling parameter. Our method uses the technique of cluster expansion in constructive quantum field theory and takes as a starting point the functional integral representation and its reduction to an Ising model on the real line with long range interactions. We prove the analyticity of our expansion and provide an explicit lower bound on the radius of convergence. We do not need multiscale nor renormalization group analysis. A connection to the loop-erased random walk is indicated.     

BEM‐FEM coupling for the 1D Klein–Gordon equation

A transmission (bidomain) problem for the one‐dimensional Klein–Gordon equation on an unbounded interval is numerically solved by a boundary element method‐finite element method (BEM‐FEM) coupling procedure. We prove stability and convergence of the proposed method by means of energy arguments. Several numerical results are presented, confirming theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 2042–2082, 2014     

Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential

We solve the Dirac equation approximately for the attractive scalar S(r) and repulsive vector V(r) Hulthén potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number κ. In the framework of the spin and pseudospin symmetric concept, we obtain the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov-Uvarov method in closed form. The limit of zero tensor coupling and the non-relativistic solution are obtained. The energy spectrum for various levels is presented for several κ values under the condition of exact spin symmetry in the presence or absence of tensor coupling.     

The Bipolaron in the Strong Coupling Limit

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr?hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar–Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum P, provided P is not too large. Tadahiro Miyao: This work was supported by Japan Society for the Promotion of Science (JSPS). Permanent address: The graduate school of natural science and technology, Okayama university, Okayama 700-8530, Japan. Submitted: December 14, 2006. Accepted: March 20, 2007.     

Stabilization of a transmission wave/plate equation

We consider a stabilization problem, for a model arising in the control of noise, coupling the damped wave equation with a damped Kirchhoff plate equation. We prove an exponential stability result under some geometric condition. Our method is based on an identity with multipliers that allows to show an appropriate energy estimate.     

Thevenin decomposition and large-scale optimization

The Thevenin theorem, one of the most celebrated results of electric circuit theory, provides a two-parameter characterization of the behavior of an arbitrarily large circuit, as seen from two of its terminals. We interpret the theorem as a sensitivity result in an associated minimum energy/network flow problem, and we abstract its main idea to develop a decomposition method for convex quadratic programming problems with linear equality constraints, of the type arising in a variety of contexts such as the Newton method, interior point methods, and least squares estimation. Like the Thevenin theorem, our method is particularly useful in problems involving a system consisting of several subssystems, connected to each other with a small number of coupling variables.This research was supported by NSF under Grant CCR-91-03804.     

Spinor soliton with electromagnetic field

In this paper, the spinor soliton coupling with its own electromagnetic field is computed by the first order approximation of the energy functional. The numerical calculation disclosed that (1) the soliton do exists, and only a few of meaningful solutions exist, (2) this nonlinear model for an electron implies the abnormal magneton, (3) the structural parameters of the soliton such as the rest massm, the mean radius, the weakly coupling constantw, are determined by empirical data. Besides, the method used in the paper is verified to be an efficient tool for solving the nonlinear spinor equation. The results are compared with those of the dark soliton.     

Analysis of partitioned methods for the Biot System

In this work, we present a comprehensive study of several partitioned methods for the coupling of flow and mechanics. We derive energy estimates for each method for the fully‐discrete problem. We write the obtained stability conditions in terms of a key control parameter defined as a ratio of the coupling strength and the speed of propagation. Depending on the parameters in the problem, give the choice of the partitioned method which allows the largest time step. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1769–1813, 2015     

Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case

Summary. The integrated autocovariance and autocorrelation time are essential tools to understand the dynamical behavior of a Markov chain. We study here these two objects for Markov chains with rare transitions with no reversibility assumption. We give upper bounds for the autocovariance and the integrated autocorrelation time, as well as exponential equivalents at low temperature. We also link their slowest modes with the underline energy landscape under mild assumptions. Our proofs will be based on large deviation estimates coming from the theory of Wentzell and Freidlin and others [4, 3, 12], and on coupling arguments (see [6] for a review on the coupling method). Received 5 August 1996 / In revised form: 6 August 1997     

Effect of aggregation of a dispersed rigid filler on the elastic characteristics of a polymer composite

Conclusions We proposed a method for describing the effective elastic characteristics of a polymer composite with a rigid aggregating filler. An important feature of such a medium is the variable coupling of the inclusion phase in relation to its volume content. A change in the degree of coupling of the filler is accounted for by introducing an additional parameter. We examined a method of determining the coupling parameter from the results of statistical modeling of the geometry of the medium. Using the example of a calcite-HDPE composite, we showed that aggregation has a significant effect on the dependence of the elastic modulus on the volume content of filler; satisfactory agreement was obtained between the theoretical and experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 14–22, January–February, 1986.     

Numerical modeling of atomistic-to-continuum coupling based on bridging domain method

Nano-submodeling is an approach that enables insertion of nano-refined submodel (atomistic) in the global model (continuum). In this work analysis of the spurious effects that may arise in the concurrent atomistic-to-continuum coupling is performed. The coupling is based on the overlapping domain decomposition (ODD) method called bridging domain [1, 2] (similar is Arlequin [3] method) where different models are overlapped and the displacements compatibility is enforced via Lagrange multipliers (LM). Some coupling options such as energy weighting, coupling zone geometry and LM field interpolation are tested. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radiative transport limit for the random Schrödinger equation with long-range correlations

In this paper we study the asymptotic phase space energy distribution of solution of the Schrödinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. We show that the Wigner transform of a solution of the random Schrödinger equation converges in probability to the solution of a radiative transfer equation. Moreover, we show that this radiative transfer equation with long-range coupling has a regularizing effect on its solutions. Finally, we give an approximation of this equation in term of a fractional Laplacian. The derivations of these results are based on an asymptotic analysis using perturbed-test-functions, martingale techniques, and probabilistic representations.     

The rigorous derivation of the T2 focusing cubic NLS from 3D

We derive rigorously the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics describing a dilute Bose gas with periodic boundary condition in the x-direction and a well of infinite-depth in the z-direction. Physical experiments for these systems are scarce. We find that, to fulfill the empirical requirement for observing NLS dynamics in experiments, namely, that the kinetic energy dominates the potential energy, it is necessary to impose an extra restriction on the system parameters. This restriction gives rise to an unusual coupling constant.     

Low-Temperature Localisation for Continuous Spin-Systems

We study the free energy of continuous spin-systems on Z ^d , in the framework of Laplace integrals and transfer operators. Under a weak coupling condition, we show that the free energy in the low-temperature limit is determined, up to an exponentially small error, by the restriction to a neighbourhood of global minima of the energy. We have results for some single- and double-well problems.     

Synchronization analysis through coupling mechanism in realistic neural models

Synchronization which relates to the system’s stability is important to many engineering and neural applications. In this paper, an attempt has been made to implement response synchronization using coupling mechanism for a class of nonlinear neural systems. We propose an OPCL (open-plus-closed-loop) coupling method to investigate the synchronization state of driver-response neural systems, and to understand how the behavior of these coupled systems depend on their inner dynamics. We have investigated a general method of coupling for generalized synchronization (GS) in 3D modified spiking and bursting Morris–Lecar (M-L) neural models. We have also presented the synchronized behavior of a network of four bursting Hindmarsh–Rose (H-R) neural oscillators using a bidirectional coupling mechanism. We can extend the coupling scheme to a network of N neural oscillators to reach the desired synchronous state. To make the investigations more promising, we consider another coupling method to a network of H-R oscillators using bidirectional ring type connections and present the effectiveness of the coupling scheme.     

A stochastic multiscale model for electricity generation capacity expansion

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models.     

电热耦合综合能源系统双阶段多目标规划研究

多能耦合系统是未来分布式能源供给方式的重要发展方向。为了实现电热耦合能源供给系统的合理规划、促进能源供给与消费的经济与环保的协调发展,提出一种面向电热耦合能源系统的综合能源系统双阶段规划优化方法。模型的第一阶段是在投资和环境最优的目标下实现电热耦合综合能源系统的合理规划,第二阶段是在考虑设备运行特性的基础上对规划的结果进行运行优化,以获得能源系统的最优运行方案,并从多个指标验证规划方案的合理性。利用NSGA-II算法求得模型进的帕累托解集,使用多准则妥协优化法从帕累托解集中决策出最优配置方案。仿真结果表明,提出的双阶段多目标综合能源规划方法能够实现能源供给系统的经济与环保双优。