Novel variational formulations for nonlocal plasticity

A nonlocal structural model of softening plasticity is considered in the framework of the internal variable theories of inelastic behaviours of associative type. The finite-step nonlocal structural problem in a geometrically linear range is formulated according to a backward difference scheme for time integration of the flow rule. The related finite-step variational formulation in the complete set of local and nonlocal state variables is recovered. A family of mixed nonlocal variational formulations, with different combinations of state variables, is provided starting from the general variational formulation. The specialization of a mixed variational formulation to existing nonlocal models of softening plasticity, assuming both linear and nonlinear constitutive behaviour, is provided to show the effectiveness of the theory.     

量子Monte Carlo处理激发态

提出了用于电子激发态的剩余函数变分量子ＭｏｎｔｅＣａｒｌｏ（ＳＦＶＭＣ）方法,已经证明：若激发态的初始波函数与基态的初始波函数属于对称性不同的不可约表示时,该激发态的ＳＦＶＭＣ方法与基态的ＳＦＶＭＣ方法完全相同;若激发态的初始波函数与基态的初始波函数有相同的对称性时,只要对激发态的初始波函数作正交性修正,则其态的ＳＦＶＭＣ方法亦可推到该激发态的情况。文章导出了这第二类激发态的ＳＦＶＭＣ方法的详细计     

Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem

Abstract In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R ³ or R ² are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in R ³ or R ² are also planar equilateral triangle circular solutions. *Partially supported by the NNSF and MCME of China, the Qiu Shi Sci. and Tech. Foundation, and Edu. Comm. of Tianjin City. Associate Member of the ICTP. **Partially supported by the NNSF of China     

Origin and System Effects of Polarization Mode Dispersion in Chirped Bragg Gratings

Polarization mode dispersion of chirped Bragg gratings is analyzed in terms of key birefringence phenomena and impact on telecommunication systems performance. The influence on polarization mode dispersion (PMD) of fiber birefringence, grating chromatic dispersion, and ripples of the group delay curve is pointed out. Polarization mode dispersion influence on systems performance is investigated by numerical simulations and transmission experiments at 10 Gbit/s. The deterministic nature of Bragg gratings PMD determines a moderate, upper-limited system penalty for a transmission line employing a single compensating device. However, in the case of broadband components, a non-negligible PMD penalty may be observed due to the difficulty of controlling accurately the group delay linearity.     

基于KCCA的特征匹配方法

特征匹配问题是计算机视觉和模式识别中一个关键步骤,在很多领域都有着重要的应用。借助核典型相关分析思想,提出了一种基于空间相关性的特征匹配方法,该方法通过核典型相关分析,将特征点集投影到核空间中,并将投影向量作为匹配特征,根据投影向量之间的相似性进行匹配。仿真实验结果表明,该算法优于基于谱分解的特征匹配算法,在图像含有噪声和存在结构误差的情况下,算法具有较高的匹配率。     

A Strongly Convergent Combined Relaxation Method in Hilbert Spaces

We consider a combined relaxation method for variational inequalities in a Hilbert space setting. Methods of this class are known to solve finite-dimensional variational inequalities under mild monotonicity type assumptions, whereas in Hilbert space strong monotonicity is the standard assumption for strong convergence. Here, we relax this condition and show strong convergence of such a method, when strong monotonicity holds only on a subspace of finite co-dimension. Thus, the method applies to semi-coercive unilateral boundary value problems in mathematical physics.     

Convex regularization of multi-channel images based on variants of the TV-model

Abstract

We discuss existence and regularity results for multi-channel images in the setting of isotropic and anisotropic variants of the TV-model.     

On elliptic problems with two critical Hardy–Sobolev exponents at the same pole

In this paper we study an elliptic problem involving two different critical Hardy–Sobolev exponents at the same pole. By variational methods and concentration compactness principle, we obtain the existence of positive solution to the considered problem.     

A generalization of ekellandz’s variational principle

This paper presents a vector valued variational principle by using a general concept of ?-efficiency and a nonconvex separation theorem     

Spectral characteristics of background error covariance and multiscale data assimilation

The spatial resolutions of numerical atmospheric and oceanic circulation models have steadily increased over the past decades. Horizontal grid spacing down to the order of 1 km is now often used to resolve cloud systems in the atmosphere and sub‐mesoscale circulation systems in the ocean. These fine resolution models encompass a wide range of temporal and spatial scales, across which dynamical and statistical properties vary. In particular, dynamic flow systems at small scales can be spatially localized and temporarily intermittent. Difficulties of current data assimilation algorithms for such fine resolution models are numerically and theoretically examined. An analysis shows that the background error correlation length scale is larger than 75 km for streamfunctions and is larger than 25 km for water vapor mixing ratios, even for a 2‐km resolution model. A theoretical analysis suggests that such correlation length scales prevent the currently used data assimilation schemes from constraining spatial scales smaller than 150 km for streamfunctions and 50 km for water vapor mixing ratios. These results highlight the need to fundamentally modify currently used data assimilation algorithms for assimilating high‐resolution observations into the aforementioned fine resolution models. Within the framework of four‐dimensional variational data assimilation, a multiscale methodology based on scale decomposition is suggested and challenges are discussed. Copyright © 2016 John Wiley & Sons, Ltd.