Maximum entropy principle in relativistic radiation hydrodynamics II: Compton and double Compton scattering

Recently [1], a procedure has been proposed in order to close the set of the moment equations of relativistic radiative fluid dynamics. In particular explicit expressions for the moments of the bremsstrahlung and Thomson scattering source terms have been given. In this work, as anticipated in [1], we shall treat in a systematic way Comptonization and double Compton scattering too. Numerical results relative to the Compton cooling of hot electrons are shown. Received November 14, 2001 / Published online June 4, 2002 RID="a" ID="a" e-mail: mascali@dmi.unict.it Communicated by Ingo Müller, Berlin     

Second‐order entropy diminishing scheme for the Euler equations

This paper presents a method of controlling the water levels in a conduit system by employing optimal control theory and the finite element method. A shallow‐water equation is employed for the analysis of flow behaviour. Optimal control theory is utilized to obtain a control value for the target state value. The Sakawa–Shindo method is employed as a minimization technique. For the computational storage requirements, the time domain decomposition method is applied. The Crank–Nicolson method is used for temporal discretization. In addition to a method for optimally controlling water level, a method is presented for determining transversality conditions, the terminal condition of the Lagrange multiplier. Copyright © 2006 John Wiley & Sons, Ltd.     

求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义,本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式,此方法将Roe型熵稳定格式与自适应移动网格算法结合,空间方向采用熵稳定格式对磁流体动力学方程进行离散,利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布,在此基础上采用守恒型插值公式实现新旧节点上的量值传递,利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明,该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高,通用性好,具有强鲁棒性。     

Generalized Darboux transformation and localized waves in coupled Hirota equations

In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an N$N$th-order localized wave solution on the plane backgrounds with the same spectral parameter is derived through the direct iterative rule. In particular, some semi-rational, multi-parametric localized wave solutions are obtained: (1) vector generalization of the first- and the second-order rogue wave solutions; (2) interactional solutions between a dark–bright soliton and a rogue wave, two dark–bright solitons and a second-order rogue wave; (3) interactional solutions between a breather and a rogue wave, two breathers and a second-order rogue wave. The results further reveal the striking dynamic structures of localized waves in complex coupled systems.     

On Chien's question to the Hu-Washizu three-field functional and variational principle

There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the comb...     

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.     

随机温度场的渐近-最大熵分析

针对具有随机参数的稳态温度场分析,利用拉普拉斯多维积分的渐近展开及函数的泰勒级数展开等方法,求得了节点温度响应的原点矩近似解析表达式。在最大熵原理基础上,获得了节点温度响应的概率密度函数。算例将该方法与Monte-Carlo模拟法进行比较,表明该方法具有较好的精度,且在参数变异性较大时也能获得较满意的结果。     

Generalized variational principle on nonlinear theory of naturally curved and twisted closed thin-walled composite beams

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Mixed variational principle in elasticity theory and canonical systems of equations

The paper proposes a modification of the mixed variational principle from which stationarity conditions are derived in the form of a mixed system of equations resolved for the first derivatives of the displacement and stress components acting in a plane perpendicular to one of the coordinate axes. The variational principle allows decreasing the dimension of the problem of elasticity thus reducing the system of equations to a canonical form. The modified mixed principle helps immediately obtain a canonical system of equations for various applied theories. This possibility is demonstrated with the example of the Timoshenko theory of plates __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 55–62, May 2007.     

Viscous regularization of the full set of nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation‐Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here, we extend the theoretical grounds for the method and derive an entropy minimum principle for the full set of nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation‐hydrodynamic shock simulations. Radiative shock calculations using constant and temperature‐dependent opacities are compared against semi‐analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations. Copyright © 2017 John Wiley & Sons, Ltd.     

On the numerical computation of Generalized Burmester Points

This note describes a procedure for plane higher-curvature path analysis and synthesis. All coefficients have been written in terms of elementary instantaneous invariants. This facilitates the numerical computation of Generalized Burmester Points for a moving link of a planar mechanism in a non-symmetric position. FORTRAN subroutines have been written and a numerical example is provided.

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Sommario Si descrive una procedura di analisi e sintesi per meccanismi piani generatori di traiettoria con approssimazione del quarto ordine. Nella formulazione adottata, l'impiego degli invarianti istantanei elementari consente di valutare analiticamente i termini delle equazioni per la ricerca dei punti generalizzati di Burmester. Sono state implementate subroutines in linguaggio FORTRAN ed è stato sviluppato un esempio numerico.

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Nomenclature P _o velocity pole - inflection circle diameter - angle of rotation of the moving body - r _f ,r _m radii of curvature of the fixed and moving polodes, respectively - dl infinitesimal arc length measured on the polode - a,b coordinates ofP _o , in the canonical reference system¹ - a _i ,b _i i-th derivatives ofa andb, respectively, computed at the initial position (i.e. =0). These are the elementary instantaneous invariants - h,* polar coordinates of the moving point in the canonical reference system (0 ) - radius of curvature of the point-path trajectory - _E radius of curvature of the evolute of the point-path trajectory - _E ^/(2) radius of curvature of the evolute of the evolute of the point-path trajectory A canonical reference system is a rectangular right-handed cartesian system having they-axis directed toward inflexion pole, origin in the velocity pole.     

D'alembert principle in the velocity space

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Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method

In this paper, we constructed the equations of generalized magneto-thermoelasticity in a perfectly conducting medium. The formulation is applied to generalizations, the Lord–Shulman theory with one relaxation time, and the Green–Lindsay theory with two relaxation times, as well as to the coupled theory. The material of the cylinder is supposed to be nonhomogeneous isotropic both mechanically and thermally. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, displacement, radial stress, and hoop stress are represented graphically. The results indicate that the effects of nonhomogeneity, magnetic field, and thermal relaxation times are very pronounced. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and/or classical dynamical thermoelasticity, respectively. Results carried out in this paper can be used to design various nonhomogeneous magneto-thermoelastic elements under magnetothermal load to meet special engineering requirements. An erratum to this article can be found at     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

On the relation between the entropy balance and the numerical solutions of systems of conservation laws

This work deals with the relation between the numerical solutions of hyperbolic systems of conservation laws and the associated entropy evolution. An analysis of the continuum problem by means of variational calculus clearly emphasizes the consequences of the adopted reconstruction procedure on the induced entropy balance. A methodology is proposed that allows for a posterior local and global spurious entropy production estimates on the basis of an additional equation representing a discrete approximation to the entropy inequality. The problem of defining a consistent approximation of the numerical entropy flux is also addressed in detail. Properly designed numerical experiments support the analysis and contribute to providing a more comprehensive evaluation of the numerical entropy dynamics. © 1997 John Wiley & Sons, Ltd.     

The application of the variational principle in the constrained control system

ＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＴＨＥＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＩＮＴＨＥＣＯＮＳＴＲＡＩＮＥＤＣＯＮＴＲＯＬＳＹＳＴＥＭＤｅｎｇＺｉ－ｃｈｅｎ（邓子辰）（ＮｏｒｔｈｗｅｓｔｅｒｎＰｏｌｙｔｅｃｈｎｉｃａｌＵｎｉｖｅｒｓｉｔｙＸｉ＇ａｎ...     

关于扁担挑运力学原理的注记

扁担是常见的运输工具. 人双脚交替向前, 肩部高低变化可以激励扁担作为悬臂梁牵引荷物上下振动; 而行走速度的脉动可以引起悬挂于扁担两端的荷物前后摆动, 绳索对扁担的水平作用力和竖直作用力均周期变化, 后者可引起扁担振动而得到放大. 合适的扁担可以使挑担者在肩部承载较小时迈步向前.     

飞石系绳的力学分析

旋转绳索使拴在前端的沙包获得速度后甩出; 待其飞过前方高处的铁杆后, 收紧绳索使沙包以铁杆为悬挂点作圆周运动; 当沙包接近最低点时快速抽拉绳索; 基于动量矩守恒定律, 沙包的切向速度因旋转半径缩短而增加, 继而牵引绳索对铁杆缠绕. 摩擦力可以使绳索具有极高的承载能力.