Effect of enrichment functions on GFEM solutions of time-dependent conduction heat transfer problems

This article investigates the effect of the selection of enrichment functions on the formulation of the Generalized Finite Element Method (GFEM) for the solutions of transient heat conduction problems. We present the study of an a-posteriori error estimate with the aim to show it as a reliable tool for the selection of enrichment functions to efficiently capture the sharp thermal gradients of the solutions. Problems in two- and three-dimensional domains are considered to demonstrate the robustness of the proposed error estimate. Numerical experiments consider two different types of enrichment functions that mimic the solution behaviour and capture the time-varying thermal gradients. The presented study shows that the error estimate is independent of the heuristically selected enrichment functions and can be used for any type of enrichment functions. It is concluded that the proposed error estimate efficiently reflects the errors in the GFEM solutions for both types of enrichment functions and can be used as an effective tool for the selection of more suitable enrichment functions that produce lower errors under the considered thermal conditions.     

Optimal consumption and investment problem with random horizon in a BMAP model

In this paper, we consider the consumption and investment problem with random horizon in a Batch Markov Arrival Process (BMAP) model. The investor invests her wealth in a financial market consisting of a risk-free asset and a risky asset. The price processes of the riskless asset and the risky asset are modulated by a continuous-time Markov chain, which is the phase process of a BMAP. The possible consumption or investment are restricted to a sequence of random discrete time points which are determined by the same BMAP. The investor has only consumption opportunities at some of these random time points, has both consumption and investment opportunities at some other random time points, and can do nothing at the remaining random time points. The object of the investor is to select the consumption–investment strategy that maximizes the expected total discounted utility. The purpose of this paper is to analyze the impact of the consumption–investment opportunity and the economic state on the value functions and consumption–investment strategies. The general solution and the exact solution under the assumption that the consumption and the terminal wealth are evaluated by the power utility are obtained. Finally, a numerical example is presented.     

New construction of special Lagrangian submanifolds in <Emphasis Type="Italic">T</Emphasis>*R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.     

拟似然非线性模型的某些渐近推断:几何方法

Abstract. A modified Bates and Watts geometric framework is proposed for quasi-likelihoodnonlinear models in Euclidean inner product space. Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi-likelihood nonlinear models is stud-ied. Several previous results for nonlinear regression models and exponential family nonlinearmodels etc. are extended to quasi-likelihood nonlinear models.     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.     

Strength reliability of statically indeterminate heterogeneous beams

The strength reliability of linearly elastic (up to failure) beams, made from random heterogeneous microstructures is studied, based on the weakest link approach. Heterogeneity is confined to the longitudinal direction. The problem is statically indeterminate, and the local stress at each point in any cross section is a function of the stiffness morphology of the whole beam. External loading is not random, but reaction forces are, due to their statistical correlation with the beam morphology. The case of one degree of indeterminacy is studied here, for simplicity. The strength and reliability of the beam, being a stochastic function of local stresses, is therefore morphology dependent, in addition to (coupled with) the classical inherent probabilistic nature, associated with surface defects and irregularities. This dependence is found analytically as a function of external loading shape. A simple design formula for the bound of these effects on the beam strength has been found, covering any possible external loading. For example, for a beam of 10 grains (compliance correlation length of 0.1L) and a 10% compliance variance, the bound of the heterogeneity effect on strength is about 8%.     

On a new FeOF polymorph: Synthesis and stability

A new polymorph of FeOF (up to now only known in its rutile type structure) was prepared by using a new synthesis approach formally based on anionic exchange using the well-known layered FeOCl as precursor. The synthesis was achieved using [CH₃C(CH₂O–)₂(COO–)B] to vehicle fluorine through the formation of soluble (CH₃)₄N⁺ [CH₃C(CH₂O–)₂(COO–)BF]⁻ and using N,N-dimethylformamide (DMF) as the reacting medium. The XRD pattern of layered FeOF can be indexed with an orthorhombic cell which doubles along the b axis (which is the direction perpendicular to the layers) with respect to that of pristine FeOCl (a = 3.792(1) Å, b = 12.699(1) Å, c = 3.321(1) Å). Both thermal analysis and diffraction indicate similar stability for the layered and rutile polymorphs. Such findings are rationalized through Density Functional Theory calculations. It is found that the energy difference between the more stable rutile and layered polymorphs is practically nul. The origin of the similar stability lies in the fact that although the number of Fe–F and Fe–O bonds is different in the two structures, the strength of both the total number of Fe–O as well as Fe–F bonds are found to be almost identical. Even if the crystal and electronic structures are considerably different, the total bonding and thus, the stability of the two polymorphs, is comparable. The stability of different FeOF rutile type structures is also analyzed.     

基频谐振过电压的稳定性(Ⅰ)

运用Galerkin方法和Runge-Kuta法模拟了电力系统中发生的基频谐振过电压的稳定性,给出了这种稳定性与系统参数变化之间的关系,为认识电力系统中更深层次的分叉现象打下基础。