Visualizing diffusion tensor fields on streamsurfaces with merging ellipsoids

Streamsurfaces in diffusion tensor fields are used to represent structures with primarily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously characterize the local tensor details- anisotropy- on them and portray the shape of the streamsurfaces.The weight between the streamsurfaces continuity and the discrete local tensors can be interactively adjusted by changing some given parameters. The second one generates a dense LIC(line integral convolution) texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes.To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.     

多传感器分布式检测和估计融合

随着科学和工业的发展,信息科学领域涌现出许多应用数学科学问题,这些问题的研究拓宽和加速了基础数学理论的研究.另一方面,基础数学理论的进展以及在信息科学领域的成功应用也促使了工业领域的蓬勃发展.数学与其他学科的相互渗透已成为当今应用数学的主要特点之一,如在2010年ICM(国际数学家大会)上有2个分别关于控制和图像科学的1小时大会报告、7个关于"Mathematical Aspects of Computer Science"的特邀报告和8个关于"Mathematics in Science and Technology"的特邀报告.多源信息融合是数学和信息科学结合的一个重要研究方向.本文主要考虑其中两类基本问题:多传感器检测融合和估计融合,主要创新点包括:(1)对一般传感器观测相关条件下的多传感器分布式检测融合系统,获得同时搜索最优传感器律和最优融合律的高效算法;(2)对失序观测、错误观测和异步观测多传感器分布式估计融合系统,给出统一的全航迹(不仅仅校正当前状态估计)全局最优估计融合公式和算法;(3)对有偏不确定系统估计融合提出极小化Euclid误差准则,并基于多传感器和多算法估计融合获得极小化Euclid误差的抗偏估计高效算法.     

A Non-linear Stability Analysis of the Solidification of a Pure Substance

An investigation is made of the stability of the shape of amoving planar interface between the solid and liquid phasesduring the solidification of a pure substance. The prototypeproblem of controlled two-dimensional growth of a pure solidinto a thermally undercooled liquid bath is considered. Themodel employed postulates diffusion of heat with equal thermaldiffusivities in both phases under the simplifying assumptionsthat these phases are infinite in extent and there is no convectionin the liquid phase. In addition, modified versions of the conservationof heat boundary condition and the Gibbs—Thomson equation,developed by Wollkind and Maurer in earlier work, are imposedat the solid—liquid interface. The main results of ournon-linear analysis, which can be represented in a plot of undercoolingversus solidification speed are that the interface can be unstableto finite amplitude disturbances in some regions where lineartheory predicts stability to infinitesimal disturbances andthat it can exhibit finite amplitude equilibrium for other rangesof parameter values. These results are interpreted in relationto the growth and structure of dendrites.     

基于社会网络结构的创新扩散动力机制及其仿真研究

随着社会资本的大量涌入,创新扩散逐渐受到社会网络关系的影响。在分析了创新扩散机理的基础上,构建了基于不同拓扑结构的创新扩散演化动力模型。将信息获取、领导者创新能力及机会利益作为创新扩散的动力因子。通过利用复杂网络的演化博弈仿真分析,揭示了小世界、无标度等不同网络拓扑结构下,创新技术的扩散情况。仿真结果表明:在网络结构相同的情况下,信息获取对创新扩散的影响较大;在动力因子设定相同的情况下,网络主体连接越规则,创新扩散越充分。     

Boundary feedback stabilization of the transmission problem of Naghdi's model

We consider the stabilization of the transmission problem of Naghdi's model by boundary feedbacks where the model has a middle surface of any shape. The exponential decay rate for the problem is established under some checkable geometric conditions on the middle surface.     

An Improved Implementation of An Iterative Method in Boundary Identification Problems

In this paper, an inverse problem of determining geometric shape of a part of the boundary of a bounded domain is considered. Based on a conjugate gradient method, employing the adjoint equation to obtain the descent direction, an identification scheme is developed. The implementation of the method based on the boundary element method (BEM) is also discussed. This method solves the inverse boundary problem accurately without a priori information about the unknown shape to be estimated.     

A Class of Solvable Impulse Control Problems

We consider a class of stochastic impulse control problems where the controlled process evolves according to a linear, regular, and time homogeneous diffusion. We state a set of easily verifiable sufficient conditions under which the problem is explicitly solvable. We also state an algebraic equation from which the optimal impulse boundary can be determined and, given this threshold, we present the value of the optimal policy in terms of the minimal increasing r-excessive mapping for the controlled diffusion. We also consider the comparative static properties of the optimal policy and state a set of typically satisfied conditions under which increased volatility unambiguously increases the value of the optimal policy and expands the continuation region where exercising the irreversible policy is suboptimal. We also illustrate our results explicitly in two models based on geometric Brownian motion.     

Optimal liquidation under partial information with price impact

We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis. We use stochastic filtering to reduce the optimal liquidation problem to an equivalent optimization problem under complete information. This leads to a stochastic control problem for piecewise deterministic Markov processes (PDMPs). We carry out a detailed mathematical analysis of this problem. In particular, we derive the optimality equation for the value function, we characterize the value function as continuous viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with numerical results illustrating the impact of partial information and price impact on the value function and on the optimal liquidation rate.     

Follower loads for high order finite elements

Finite element modelling of hydrostatic compaction where the applied pressure acts normal to the deformed surface requires a geometric nonlinear formulation and follower load terms [1, 5, 7]. These concepts are applied to high order [6] (p-FEM) elements with hierarchic shape functions. Applying the blending function method allows to precisely describe curved boundaries on coarse meshes. High order elements exhibit good performance even for high aspect ratios and strong distortion and therefore allow an efficient discretization of thin-walled structures. Since high order finite elements are less prone to locking effects a pure displacement-based formulation can be chosen. After introducing the basic concept of the p-version the application of follower loads to geometrically nonlinear high order elements is presented. For the numerical solution the displacement based formulation is linearized yielding the basis for a Newton-Raphson iteration. The accuracy and performance of the high order finite element scheme is demonstrated by a numerical example. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于对数极坐标及对称循环矩阵的形状特征描述

在形状检索算法中,满足尺度和旋转不变是基本要求.本文将形状的边界用对数极坐标表示,使得形状的放缩和旋转化为简单的平移.由于计算机读取形状边界信息时与起点有关,当形状旋转时会带来边界点列的循环,影响旋转不变性.为消除边界点列循环带来的影响,本文首先证明"奇数阶对称循环矩阵,当生成元循环时,所得循环矩阵的特征值不变",在这个数学理论基础上,把形状边界点数插值到奇数,构造相应的对称循环矩阵,通过这个循环矩阵的特征值来描述形状特征,由此得到一种具有放缩旋转不变的形状检索新算法.实验表明,本文算法对运动目标和非刚性形变的形状检索具有良好的鲁棒性和快捷的运行速度,这在目标跟踪方面将发挥作用.     

On Surfaces with Prescribed Shape Operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. It is shown that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.     

On the Geometric Diversity of Wavefronts for the Scalar Kolmogorov Ecological Equation

We answer three fundamental questions concerning monostable traveling fronts for the scalar Kolmogorov ecological equation with diffusion and spatiotemporal interaction: These are the questions about their existence, uniqueness and geometric shape. In the particular case of the food-limited model, we give a rigorous proof of the existence of a peculiar, yet substantive and nonlinearly determined class of non-monotone and non-oscillating wavefronts.

     

Risk averse elastic shape optimization with parametrized fine scale geometry

Shape optimization of the fine scale geometry of elastic objects is investigated under stochastic loading. Thus, the object geometry is described via parametrized geometric details placed on a regular lattice. Here, in a two dimensional set up we focus on ellipsoidal holes as the fine scale geometric details described by the semiaxes and their orientation. Optimization of a deterministic cost functional as well as stochastic loading with risk neutral and risk averse stochastic cost functionals are discussed. Under the assumption of linear elasticity and quadratic objective functions the computational cost scales linearly in the number of basis loads spanning the possibly large set of all realizations of the stochastic loading. The resulting shape optimization algorithm consists of a finite dimensional, constraint optimization scheme where the cost functional and its gradient are evaluated applying a boundary element method on the fine scale geometry. Various numerical results show the spatial variation of the geometric domain structures and the appearance of strongly anisotropic patterns.     

Cooperative Sensing and Distributed Control of a Diffusion Process Using Centroidal Voronoi Tessellations

<正>This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.     

Optimization of open cross sections of thin-walled beams with plate-shell-flanges

The paper is devoted to a monosymetrical cold-formed thin-walled beam with open cross section. Its flange consists of plates and circular shells. The beam is under pure bending. The cross section is characterized by dimensionless parameters. The authors are searching for an optimal cross section shape of considered beam. This optimal shape is determined by means of parametric optimization. The dimensionless objective function is so defined as to comprise both cross section area and a maximal allowable bending moment. The constraints follow from the local buckling conditions and geometric restrictions. Moreover, there are optimized cross sections of beams, for which the shear center is located either in the web or in the centroid of the cross section. Results are compared and analyzed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation for a reaction–diffusion system with unilateral and Neumann boundary conditions

We consider a reaction–diffusion system of activator–inhibitor or substrate-depletion type which is subject to diffusion-driven instability if supplemented by pure Neumann boundary conditions. We show by a degree-theoretic approach that an obstacle (e.g. a unilateral membrane) modeled in terms of inequalities, introduces new bifurcation of spatial patterns in a parameter domain where the trivial solution of the problem without the obstacle is stable. Moreover, this parameter domain is rather different from the known case when also Dirichlet conditions are assumed. In particular, bifurcation arises for fast diffusion of activator and slow diffusion of inhibitor which is the difference from all situations which we know.     

Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems with uncertain linguistic information. Motivated by the ideal of Bonferroni mean and geometric Bonferroni mean, we develop two aggregation techniques called the uncertain linguistic Bonferroni mean (ULBM) operator and the uncertain linguistic geometric Bonferroni mean (ULGBM) operator for aggregating the uncertain linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the uncertain linguistic weighted Bonferroni mean (ULWBM) operator and the uncertain linguistic weighted geometric Bonferroni mean (ULWGBM) operator, based on which we develop two procedures for multiple attribute decision making under the uncertain linguistic environments. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Splitting a Concave Domain to Convex Subdomains

1.IntroductionTurninglargescaleproblemtosmallscalesubproblemsandregularizingirregularproblemaretwomainsubjectsofdomaindecomposition.Inregularization,regularizingirregularregionisoffirstimportance.Irregularityoftenmeansconcavity,forexample,L-shaped,T--shapedandC-shapeddomainsareirregulardomains.Inthispaperswewillstudydomaindecompositionmethodforellipticproblemsdefinedonirregularregion.SchwarzalternatingInethodisthebasisofalmostalldomaindecompositionmethoddeveloped.Othermethodsarevariationsof…     

C1 monotone cubic Hermite interpolant

Constraining an interpolation to be shape preserving is a well established technique for modelling scientific data. Many techniques express the constraint variables in terms of abstract quantities that are difficult to relate to either physical values or the geometric properties of the interpolant. In this paper, we construct a piecewise monotonic interpolant where the degrees of freedom are expressed in terms of the weights of the rational Bézier cubic interpolant.