Convexity of Reduced Energy and Mass Angular Momentum Inequalities

In this paper, we extend the work in Chru?ciel and Costa (Class. Quant. Grav. 26:235013, 2009), Chru?ciel et al. (Ann. Phy. 323:2591–2613, 2008), Costa (J. Math. Theor. 43:285202, 2010), Dain (J. Diff. Geom. 79:33–67, 2008). We weaken the asymptotic conditions on the second fundamental form, and we also give an L ⁶?norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr–Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr–Newman solution.     

On the Formulation of Mass,Momentum and Energy Conservation in the KdV Equation

The Korteweg-de Vries (KdV) equation is widely recognized as a simple model for unidirectional weakly nonlinear dispersive waves on the surface of a shallow body of fluid. While solutions of the KdV equation describe the shape of the free surface, information about the underlying fluid flow is encoded into the derivation of the equation, and the present article focuses on the formulation of mass, momentum and energy balance laws in the context of the KdV approximation. The densities and the associated fluxes appearing in these balance laws are given in terms of the principal unknown variable η representing the deflection of the free surface from rest position. The formulae are validated by comparison with previous work on the steady KdV equation. In particular, the mass flux, total head and momentum flux in the current context are compared to the quantities Q, R and S used in the work of Benjamin and Lighthill (Proc. R. Soc. Lond. A 224:448–460, 1954) on cnoidal waves and undular bores.     

Modelling and Simulation of the Transport of Protein Foams

The behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions ϕ ≤ 0.6 and small bubble deformations (i.e. N_Ca ≪ 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Limits on the Transport of Heat and Momentum by Turbulent Convection with Large-Scale Flow

Under certain conditions, high-Rayleigh-number convection in a horizontal layer exhibits an organized pattern of large-scale flow superposed on an irregular structure of turbulent plumes. Bounds on the heat and momentum fluxes in such a flow, which provide upper estimates of the possible level of the large-scale flow, are presented.     

Significance of Truckenbrodt's Energy and Momentum Coefficients for Loss Calculation in Ramified Pipe Systems

For one-dimensional simulation of flow in ramified pipe systems loss prediction in junctions is essential. In the standard literature (e.g. [1]) total pressure loss coefficients serve this purpose. Elementary formulas follow from the principle of momentum and some simple assumptions [2]. They yield rather crude estimates, often twice as large as experimental values. Modifications described by Idelchik [3] look nice, but after all turn out to be not more accurate. We explain deviations and propose improved loss formula based on Truckenbrodt's energy and momentum coefficients [4], thus paying regard to velocity distributions over pipe cross-sections. We further discuss extraction of the coefficient's values from experiments. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mass Transport and Variants of the Logarithmic Sobolev Inequality

We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev case. The idea behind many of these conditions is that measures with a non-convex potential may enjoy such functional inequalities provided they have a strong integrability property that balances the lack of convexity. In addition, several known criteria are recovered in a simple unified way by transportation methods and generalized to the Riemannian setting. The research of A.V. Kolesnikov was supported by RFBR 07-01-00536, DFG Grant 436 RUS 113/343/0 and GFEN 06-01-39003.     

L~1空间中具有周期边界条件的迁移方程的性质

在L~1空间研究板几何中具有周期边界条件的迁移方程.证明了迁移算子是预解正算子,得到了微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

Momentum and Energy Transfer During Phase Change of Water Under High Hydrostatic Pressure

In this study, the first visualization of distributed phase change effects and thermodynamical properties under high pressure have been carried out by means of HP-DPIV and HP-DPIT (High Pressure Digital Particle Image Velocimetry and Thermography) methods [1]. The main objective of this study was to investigate the thermofluiddynamical behaviour in the high pressure cell during Pressure Induced Thawing of Ice I, Pressure Shift Freezing of Ice I and Pressure Assisted Thawing of Ice III. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transport Properties of Doubly Periodic Arrays of Circular Cylinders and Optimal Design Problems

We solve an R -linear problem for a multiple-connected circular domain in a class of doubly periodic functions in analytic form by a method of functional equations. This problem models transport properties of two-dimensional composite materials made from a collection of disks embedded in an otherwise uniform host. Accepted 25 January 2001. Online publication 26 May 2001.     

板几何中一类具周期边界条件的奇异迁移算子的谱

在Lp(1相似文献   

冠状动脉狭窄情况下的非牛顿血液流动和大分子传质

针对冠状动脉狭窄的情况,采用数值模拟方法求解了牛顿流体与非牛顿流体(幂次律流体和Casson流体)的定常与脉动的流场。在此基础上,求解了LDL(低密度脂肪蛋白)和Albumin(血清白蛋白)的浓度场。根据计算结果,详细讨论了壁面剪应力、非牛顿流效应、分子大小等因素对大分子传质的影响;并对牛顿流体与非牛顿流体、定常流动与脉动流动的大分子浓度场进行了比较,这些结果对于了解动脉硬化成因与流动特性和大分子传质的联系提供了较为丰富的信息。     

The Effect of Mean Flows on Enhanced Diffusivity in Transport by Incompressible Periodic Velocity Fields

Avellaneda and one of the authors ([1], [3]) have recently established that an upper bound for the enhanced diffusivity in the large scale, long time advection-diffusion with periodic steady incompressible velocity fields has the form where Pe is the Peclet number and is the reciprocal of the Prandtl number. In this paper, flow fields with maximal and minimal enhanced diffusion are studied. Maximal enhanced diffusion requires that in some directions the enhanced diffusion tensor also has the lower bound . For minimal enhanced diffusion, the effect of the velocity field is to boost the enhanced diffusivity by a negligible amount that is bounded by a fixed constant times the bare diffusivity regardless of Peclet number. Stieltjes measure formulas are used to develop a simple, necessary, and sufficient condition for maximal enhanced diffusion and also to characterize minimal enhanced diffusion. It is established here that constant mean flows can have a dramatic effect on maximal and minimal enhanced diffusion. In particular, for flows in two space dimensions, an explicit criterion is developed that guarantees the surprising fact that mean flows with rational ratios typically generate maximal enhanced diffusion through interaction with an arbitrary steady periodic incompressible flow with zero mean. In contrast, a simple criterion for flows without stagnation points is developed here that guarantees that the effect of mean flows with irrational ratios on advection-diffusion in two dimensions creates minimal enhanced diffusion. The theory for the phenomena mentioned above is elementary yet mathematically rigorous. Examples are emphasized throughout this work including a discussion of enhanced diffusivity for a class of flows recently introduced by Childress and Soward [8]. The theory developed here is also supplemented by a series of numerical experiments that both verify the theoretical predictions and display interesting crossover phenomena at rather large but finite Peclet numbers.     

Spectral Analysis of a Transport Operator Arising in Growing Cell Populations

The present paper is concerned with the spectral analysis of a transport-like operator derived from a model introduced by Rotenberg describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ and its maturation velocity v. The biological boundaries of μ = 0 and μ = a (a > 0) are fixed and tightly coupled through mitosis. At mitosis daughter cells and mother cells are related by a general reproduction rule which covers all known biological ones. We first discuss in detail the spectrum of the streaming operator for smooth and partly smooth boundary conditions. Next, we discuss the existence and nonexistence of eigenvalues of the transport operator in the half plane {λ ∈ ℂ : Reλ > where denotes the spectral bound of the streaming operator. In particular, the strict monotonicity of the leading eigenvalue (when it exists) of the transport operator with respect to different parameters of the equation is also considered. We close the paper by describing in detail the various essential spectra of the transport operator for wide classes of collision and boundary operators.     

多货种多供需地海陆联运格局及对世界能源运输的预判

为优化国际货运规划方案,对可兼容配载的多种货物、多供需地、双港节点直达海运的海陆联运问题进行研究,由其运输关系结构研究其运输系统整体经济性组织的航线分布与货流路径模型.设定相关各量后,以营运期内所有供需地间陆运和海运总成本为目标,以供需能力、港口通过能力、船队收益及船舶停时等约束建立模型,并改进传统盈利航速的计算,模型可实现船舶航速和运输总成本的双重优化.以世界原油和致密油供需为例,划分各国主要产销地区和油港,应用模型结果显示出未来各贸易国间的基本经济航线及一定能力约束产生的航线分布、运力配置及物流路径,表明远距离航线的最优航速偏高,且海运段成本具有支配性影响.     

Groundwater Mass Transport and Heterogenous Equilibrium Chemical Reaction-----A Kind of Free Boundary Problem

This paper considers another kind of chemical reaction different from [1]. The difference is that the chemical reactions under consideration are assumed to be heterogeneous,, fast, reversible.and classical. As a typical example, the author reduces this problem to an one phase Stefan problem with nohcommon data, and investigates the classical solution as well as the weak solution.     

Numerical Simulation of Thermal Effects in Electric Circuits via Energy Transport equations

In this work we present the coupling of stationary energy-transport (ET) equations with Modified Nodal Analysis (MNA)-equations to model electric circuits containing semiconductor devices. The one-dimensional ET-equations are discretised in space by an exponential fitting mixed hybrid finite element approach to ensure current continuity and positivity of charge carriers. The discretised ET-equations are coupled to MNA-equations and the resulting system is solved with backwarddifference formulas. Numerical examples are shown for a test circuit containing a pn-diode, and the results are compared to those achieved using the drift-diffusion model to describe the semiconductor devices in the circuit. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Numerical Methods for an Anisotropic,Nonisothermal, Two-Phase Transport Model of Proton Exchange Membrane Fuel Cell

We carry out model and numerical studies for a three-dimensional, anisotropic, nonisothermal, two-phase steady state transport model of proton exchange membrane fuel cell (PEMFC) in this paper. Besides fully addressing the conservation equations of mass, momentum, species, charge and energy equations arising in the PEMFC, we present some efficient numerical methods for this model to achieve a fast and convergent nonlinear iteration, comparing to the oscillatory and nonconvergent iteration conducted by commercial flow solvers or in-house codes with standard finite element/volume method. In a framework of a combined finite element-upwind finite volume method, Kirchhoff transformation plays an important role in dealing with the discontinuous and degenerate water diffusivity in its transport equation. Preconditioned GMRES solver together with Newton’s linearization scheme make the entire numerical simulation more efficient. Three-dimensional numerical simulations demonstrate that the convergent physical solutions can be attained within 30 steps. Numerical convergence tests are also performed to verify the efficiency and accuracy of the presented numerical algorithms and techniques.     

Evolution Theory,Periodic Particles,and Solitons in Cellular Automata

A theory for soliton automata is developed and applied to the analysis and prediction of patterns in their behavior. A complete characterization and method of construction of 1-periodic particles is given. A general evolution theorem (GET) is obtained which provides significant information for a state in terms of preceding states. Application of this theorem yields several interesting results predicting periodicity and solitonic collisions. The GET explains and is based on a fundamental property of soliton automata, observed and analyzed in this paper, namely that pieces of information are lost on the left and reappear on the right.