关于β稳定线公式的一个评注

指出β稳定线公式应在理论框架下通过自洽的计算决定.这与传统的β稳定线公式略有区别.本文还对在Hartree-Fock近似下的β稳定线公式给出了一个评注.     

Magnesium-Based Clusters as Building Blocks of Electrolytes in Lithium-Ion Batteries

Superhalogens, owing to their large electron affinity (EA, exceeding those of any halogen atom), play an essential role in physical chemistry as well as new material design. They have applications in hydrogen storage and lithium-ion batteries. Owing to the unique geometries and electronic features of magnesium-based clusters, their potential to form a new class of lithium salts has been investigated here theoretically. The idea is assessed by conducting ab initio computations on Li⁺/Mg_nF_2n+1-2mO_m⁻ compounds (n=2, 3; m=0-3) and analyzing their performance as potential Li-ion battery electrolytes. The Mg₃F₇⁻ cluster, with large electron binding energy (EA of 7.93 eV), has been proven to serve as a building block for lithium salts. It is shown that, apart from high electronic stability, the new superhalogen-based electrolytes exhibit a set of desirable properties, including a large band gap, high electrolyte stability window, easy mobility of the Li⁺, and favorable insensitivity to water.     

Strategies to cure numerical shock instability in the HLLEM Riemann solver

The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver that is known to be plagued by various forms of numerical shock instability. In this paper, we clarify that the shock instability exhibited by this scheme is primarily triggered by the spurious activation of the antidiffusive terms present in the first and third Riemann flux components on the transverse interfaces adjoining the shock front due to numerical perturbations. These erroneously activated terms are shown to counteract the favorable damping mechanism provided by its inherent HLL-type diffusive terms, causing an unphysical variation of the conserved quantity ρu both along and across the numerical shock. To prevent this, two distinct strategies are proposed termed as S elective W ave M odification and A nti D iffusion C ontrol. The former focuses on enhancing the quantity of the favorable HLL-type dissipation available on these critical flux components by carefully increasing the magnitudes of certain nonlinear wave speed estimates, while the latter focuses on directly controlling the magnitude of these critical antidiffusive terms. A linear perturbation analysis is performed to gauge the effectiveness of these cures and to estimate a von Neumann–type stability bounds on the CFL number associated with their use. Results from a variety of classic shock instability test cases show that the proposed strategies are able to provide excellent shock stable solutions even on grids that are highly elongated across the shock front without compromising the accuracy on inviscid contact or shear dominated viscous flows.     

Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid-structure interaction

Fluid-structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one-dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two-dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.     

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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

Nonlocal stochastic differential equations with time-varying delay driven by G-Brownian motion

This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function.     

Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.