On Optimization of the Full Radiative Heat Transfer System

Solving the full radiative heat transfer equation, moderately discretized in space, time, frequency and direction, results in a tremendously huge system of equations. A common approach to avoid this problem is to use moment methods neglecting the directional dependence on radiation. Our approach, however, is to solve the full radiative heat transfer system with all dependencies and to optimize the heat distribution and the radiative flux, respectively, for a desired temperature function or desired radiative flux function. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of Temperature Dependent Parameters in Radiative Heat Transfer

Laser-induced thermotherapy (LITT) is an established minimally invasive percutaneous technique of tumor ablation. Nevertheless, there is a need to predict the effect of laser applications and optimizing irradiation planning in LITT. Optical attributes (absorption, scattering) change due to thermal denaturation. The work presents the possibility to identify these temperature dependent parameters from given temperature measurements via an optimal control problem. The solvability of the optimal control problem is analyzed and results of successful implementations are shown. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

梯度折射率介质内瞬态辐射传递的扩散近似法

基于瞬态时域与频域扩散近似方程求解了一维梯度折射率介质内辐射传递问题.通过计算在不同梯度折射率分布下的穿透率与反射率,对扩散近似的适用性展开研究.结果表明:求解时域穿透率时,扩散近似法始终能够准确计算出平行光的时间延迟,而对漫射部分时间延迟的计算不准确;对时域反射率而言,扩散近似法在反射率出现峰值之前与间断有限元法结果相吻合,随着折射率梯度的增大,扩散近似结果在出现峰值后的时间内偏大,且有明显的时移.对于频域穿透率和反射率计算,扩散近似法精度几乎不受折射率梯度变化的影响,能够较为准确地预测频域穿透率,但是对于频域反射率计算误差较大.     

Stationary Problem of Radiative Heat Transfer with Cauchy Boundary Conditions

Computational Mathematics and Mathematical Physics - A stationary problem of radiative-conductive heat transfer in a three-dimensional domain is studied in the $${{P}_{1}}$$ -approximation of the...     

混合偏熵与关联熵

定义联系模糊性和随机性的混合集、混合偏熵与关联熵以及混合关联系数，研究了其性质，并举例说明混合关联系数在现实生活中的应用。     

A Numerical Treatment of One-dimensional Models of Radiative Heat Transfer in Co-current Tube Furnaces

A model of a top-fired furnace, such as is used in chemicalindustrial plants, is described. The model gives rise to a systemof first-order differential equations, with boundary conditionsat both the top and bottom of the furnace. This also involvesa non-linear coupling of the radiation field to the energy ofthe gases flowing. Published accounts of this problem make useof shooting methods which converge extremely slowly. An alternativemethod will be described in which the radiative field equationsare solved by an algorithm of Grant and, to deal with the non-linearitiesof the system, a generalized Newton-Raphson method is employed.     

Shape Optimal Design Problem with Convective and Radiative Heat Transfer: Analysis and Implementation

We present a study of an optimal design problem for a coupled system, governed by a steady-state potential flow equation and a thermal equation taking into account radiative phenomena with multiple reflections. The state equation is a nonlinear integro-differential system. We seek to minimize a cost function, depending on the temperature, with respect to the domain of the equations. First, we consider an optimal design problem in an abstract framework and, with the help of the classical adjoint state method, give an expression of the cost function differential. Then, we apply this result in the two-dimensional case to the nonlinear integro-differential system considered. We prove the differentiability of the cost function, introduce the adjoint state equation, and give an expression of its exact differential. Then, we discretize the equations by a finite-element method and use a gradient-type algorithm to decrease the cost function. We present numerical results as applied to the automotive industry.     

On Analytical Results for the Optimal Control of the quasi-stationary Radiative Heat Transfer System

We state an optimal control problem of the coupled quasi-stationary radiative heat equations consisting of the radiative transfer equation and the instationary heat transfer equation that model radiative-conductive heat transfer. We give an existence and uniqueness result for the state equations and the adjoint equations of the quasi-stationary radiative heat transfer system. For the optimal control problem the existence of a minimizer is proven. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fuzzy集的偏熵与关联熵

在文献[1]的基础上,推广模糊熵的概念。首次定义Fuzzy集的偏熵、关联熵和关联熵系数等新概念。对其主要性质进行讨论,并与模糊散度建立联系．得到一些重要结果。     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.     

Approximation by Partial Isometries and Symmetric Approximation of Finite Frames

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.     

Gaussian Approximation to the Partial Sum Processes of Moving Averages

The authors study approximation to the partial sum processes which is based on the stationary sequences of random variables having the structure of the so-called moving averages of independent identically distributed observations. In particular, the rates of convergence both in Donsker's and Strassen's invariance principles are obtained in the case when the limit Gaussian process is a fractional Brownian motion with an arbitrary Hurst parameter.     

Solution for a Non-Stationary Radiative Transfer Equation

The operators radiative transfer equation constructed by Chandrasekhar has been extended to the non-stationary case by Bellman and Wang. The local existence of solution of such non-stationary equation is established based on the construction of scattering matrices from a co-propagation group with unbounded generator. In case the system is dissipative, the local existence will extend to the global existence.     

多目标minimax问题的极大熵逼近收敛性

本文利用极大熵逼近函数，展开了多目标ｍｉｎｉｍａｘ问题的逼近方法的研究，并讨论了该逼近方法的收敛性，所得结果是目前已有的结果进一步拓广．     

The Numerical Approximation of Stochastic Partial Differential Equations

The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of development roughly similar to that of stochastic ordinary differential equations (SODEs) in the 1970s, when stochastic Taylor schemes based on an iterated application of the Itô formula were introduced and used to derive higher order numerical schemes. An Itô formula in the generality needed for Taylor expansions of the solution of a SPDE is however not available. Nevertheless, it was shown recently how stochastic Taylor expansions for the solution of a SPDE can be derived from the mild form representation of the SPDE, which avoid the need of an Itô formula. A brief review of the literature is given here and the new stochastic Taylor expansions are discussed along with numerical schemes that are based on them. Both strong and pathwise convergence are considered.     

Approximation of Metric Spaces by Partial Metric Spaces

Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.     

Data-Driven Model Reduction and Transfer Operator Approximation

In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods.     

Modeling of Radiative Heat Conduction on High-Performance Computing Systems

Doklady Mathematics - For problems related to radiative heat conduction, an algorithm is proposed that is well adapted to the architecture of systems with extramassive parallelism. According to the...     

Entropy,Universal Coding,Approximation, and Bases Properties

We shall present here results concerning the metric entropy of spaces of linear and nonlinear approximation under very general conditions. Our first result computes the metric entropy of the linear and m-terms approximation classes according to a quasi-greedy basis verifying the Temlyakov property. This theorem shows that the second index r is not visible throughout the behavior of the metric entropy. However, metric entropy does discriminate between linear and nonlinear approximation. Our second result extends and refines a result obtained in a Hilbertian framework by Donoho, proving that under orthosymmetry conditions, m-terms approximation classes are characterized by the metric entropy. Since these theorems are given under the general context of quasi-greedy bases verifying the Temlyakov property, they have a large spectrum of applications. For instance, it is proved in the last section that they can be applied in the case of L _p norms for R ^d for 1 < p < \infty. We show that the lower bounds needed for this paper in fact follow from quite simple large deviation inequalities concerning hypergeometric or binomial distributions. To prove the upper bounds, we provide a very simple universal coding based on a thresholding-quantizing constructive procedure.