Distribution of Magnetization in the Vicinity of Point Defects in Ferromagnetics

The localized distributions of magnetization, which slowly decrease with distance in the vicinity of magnetic imperfections in homogeneously magnetized ferromagnetics, were calculated in this work. It is shown that, in the case of the slowest decrease with distance, such distributions of magnetization interact with the domain wall, according to a formula that differs from that for the energy of the interaction between the homogeneous magnetic defect and the domain wall. The potential of the interaction between such imperfections was obtained.     

The Design of axisymmetric ducts for incompressible flow with vorticity.

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function and the function as independent variables where for irrotational flow can be recognized as the velocity potential function, for rotational flow ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on finite differences on a uniform mesh is employed. The technique described is capable of tackling the so–called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct wall shapes. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polynomial Time Samplable Distributions

This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small factor by sampling algorithms in time polynomial in the length of their outputs. The paper shows that common assumptions in complexity theory yield the separation of polynomial-time samplable distributions from the polynomial-time computable distributions with respect to polynomial domination, average-polynomial domination, polynomial equivalence, and average-polynomial equivalence.     

主动脉弓及分支血管内非稳态血流分析

运用流体力学中的三维非定常Navier-Stokes方程作为血液流动的控制方程,并采用计算流体力学方法对人体主动脉弓及分支血管内非Newton(牛顿)血液黏度模型下血流进行瞬态数值模拟.分析了一个心动周期内不同时刻血流动力学特征参数的分布对动脉粥样硬化斑块形成的影响,并与Newton血液黏度模型下的血管壁面压力和壁面切应力特征参数进行对比.结果表明:与Newton血液模型相比,非Newton血液模型下血流分布更符合真实血流特性;在心动收缩期,分支血管外侧壁附近存在面积较大的低速涡流区,该区域内血管壁面压力与壁面切应力具有较大的变化量,血液中的血小板、脂质和纤维蛋白等易沉积,血管内壁易疲劳损伤并发生血管重构,促使动脉粥样硬化斑块形成;而在心动舒张期,分支血管内血流速度分布均匀,血管壁面压力与壁面切应力变化量较小,血管壁受到较小的应力作用,对动脉粥样硬化斑块形成的作用较小.     

A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow

In this paper the effects catheterization and non-Newtonian nature of blood in small arteries of diameter less than 100 μm, on velocity, flow resistance and wall shear stress are analyzed mathematically by modeling blood as a Herschel–Bulkley fluid with parameters n and θ and the artery and catheter by coaxial rigid circular cylinders. The influence of the catheter radius and the yield stress of the fluid on the yield plane locations, velocity distributions, flow rate, wall shear stress and frictional resistance are investigated assuming the flow to be steady. It is shown that the velocity decreases as the yield stress increases for given values of other parameters. The frictional resistance as well as the wall shear stress increases with increasing yield stress, whereas the frictional resistance increases and the wall shear stress decreases with increasing catheter radius ratio k (catheter radius to vessel radius). For the range of catheter radius ratio 0.3–0.6, in smaller arteries where blood is modeled by Herschel–Bulkley fluid with yield stress θ = 0.1, the resistance increases by a factor 3.98–21.12 for n = 0.95 and by a factor 4.35–25.09 for n = 1.05. When θ = 0.3, these factors are 7.47–124.6 when n = 0.95 and 8.97–247.76 when n = 1.05.     

基于线性涡模型的风洞孔壁干扰特性分析

发展了一种适用于二元翼型试验洞壁干扰特性的评估和修正方法.基于Prandtl-Glauert速度势方程和布置在模型及洞壁表面的线性涡,采用迭代方法计算了风洞孔壁对翼型表面压力分布特性的影响,分析了不同孔壁透气特性参数的影响规律和量值,利用与国外参考结果及风洞试验结果的对比确定了该方法的准确性.结果表明,孔壁对翼型绕流的影响主要反映在上翼面吸力峰和最大厚度位置之间,使压力系数减小,积分后的升力系数降低,且随着孔壁透气特性参数的增大,洞壁干扰由实壁特性向开口特性发展,洞壁干扰、影响量急剧增大.与传统方法相比,该方法计算快速,结果可靠,同时具备试验前评估的能力,可用于亚临界范围内翼型表面压力的快速估算,以及翼型试验的洞壁干扰修正.     

Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality

Asymptotic cumulants of the distributions of the sample singular vectors and values of cross covariance and correlation matrices are obtained under nonnormality. The asymptotic cumulants are used to have the approximations of the distributions of the estimators by the Edgeworth expansions up to order O(1/n) and Hall’s method with variable transformation. The cases of Studentized estimators are also considered. As an application of the method, the distributions of the parameter estimators in the model of inter-battery factor analysis are expanded. Interpreting the singular vectors and values in the context of the factor model with distributional conditions, the asymptotic robustness of some lower-order normal-theory cumulants of the distributions of the sample singular vectors and values under nonnormality is shown.     

Viscous flow over a shrinking sheet with an arbitrary surface velocity

In this paper, an analytical solution in a closed form for the boundary layer flow over a shrinking sheet is presented when arbitrary velocity distributions are applied on the shrinking sheet. The solutions with seven typical velocity profiles are derived based on a general closed form expression. Such flow is usually not self-similar and the solution can only be implemented when the mass transfer at the wall is prescribed and determined by the moving velocity of the wall. The characteristics of the flows with the typical velocity distributions are discussed and compared with previous similarity solutions. The flow is observed to have quite different behavior from that of the self-similar flow reported in the literature and the results demonstrate distinctive momentum and energy transport characteristics. Some plots of the stream functions are also illustrated to show the difference in flow field between the shrinking sheet and the stretching sheet. An integral approach to solve boundary layer flow over a shrinking or stretching sheet with uncoupled arbitrary surface velocity and wall mass transfer velocity is outlined and the effectiveness of this approach is discussed.     

静脉壁的力学特性及负压失稳问题

应用一类超弹性应变能函数,通过非线性弹性理论,研究了静脉壁在跨壁压及轴向拉伸联合作用下的变形和应力分布等力学特性,并分析了静脉壁的负压失稳问题．首先利用超弹性材料薄壁圆筒模型,得到了静脉壁在跨壁压及轴向拉伸联合作用下的变形方程,给出了正常静脉压下静脉壁的变形曲线和应力分布曲线,讨论了静脉壁的变形和应力分布规律．然后给出了负跨壁压下静脉壁的变形曲线,并由能量比较讨论了静脉壁的负压失稳问题．     

Monte Carlo Microflow Simulation for the Gas Film Lubrication in Modern Magnetic Disk Storage

A two‐dimensional unsteady problem of gas flow in an extremely narrow channel with an inclined upper wall and moving lower one is studied by the DSMC method. This is a model of gas film lubrication which occurs in modern magnetic disk storage, that is now under development. Far from the magnetic head the flow produced by the disk motion could be described by solution of the Rayleigh problem. Space and time distributions of the pressure on the upper wall as well as density and average velocity inside and outside of the channel were obtained. They show that as a result of the flow slowing‐down by the front wall of the magnetic head the region with an increased density is formed there. At the same time marked non‐homogeneity of gas velocity before the inlet of the channel is observed.     

On solutions to min (X,{\text{ Y}})\mathop = \limits^d aX and min (X,{\text{ Y}})\mathop = \limits^d aX\mathop = \limits^d bY

Suppose that the minimum of a pair of independent non-negative random variables X and y has the same distribution, up to a scale factor, as the first of the two random variables. The restricted class of possible distributions for X and Y is identified. If in addition it is required that X and Y have distributions only differing by a scale factor, it is shown under mild regularity conditions that X and Y have Weibull distributions.     

A new family of unsteady boundary layers over a stretching surface

In this paper, a new family of unsteady boundary layers over a stretching flat surface was proposed and studied. This new class of unsteady boundary layers involves the flows over a constant speed stretching surface from a slot, and the slot is moving at a certain speed. Depending on the slot moving parameter, the flow can be treated as a stretching sheet problem or a shrinking sheet problem. Both the momentum and thermal boundary layers were studied. Under special conditions, the solutions reduce to the unsteady Rayleigh problem and the steady Sakiadis stretching sheet problem. Solutions only exist for a certain range of the slot moving parameter, α. Two solutions are found for −53.55° < α < −45°. There are also two solution branches for the thermal boundary layers at any given Prandtl number in this range. Compared with the upper solution branch, the lower solution branch leads to simultaneous reduction in wall drag and heat transfer rate. The results also show that the motion of the slot greatly affects the wall drag and heat transfer characteristics near the wall and the temperature and velocity distributions in the fluids.     

Mixed convection of heat generating nanofluid in a lid-driven cavity with uniform and non-uniform heating of bottom wall

Steady state two-dimensional mixed convection in a lid-driven square cavity filled with Cu  –water nanofluid is investigated numerically in the presence of internal heat generation. In the present investigation, bottom wall is uniformly and non-uniformly heated while two vertical walls are fixed and they are thermally insulated. The top wall is moving from left to right at a constant speed. The governing equations are normalized and solved numerically with boundary conditions by finite volume approach using third order accurate upwinding scheme (deferred QUICK). Effects of the pertinent physical parameters are investigated in terms of the flow and temperature fields, as well as Nusselt number distributions. The presented results show that the solid volume fraction plays a significant role on the flow and thermal fields and the Nusselt number distributions for different flow configurations. It is found that Richardson number strongly affect the fluid flow and heat transfer in the cavity. For Ri<1$\mathit{Ri}<1$, the forced convection becomes dominant in the entire cavity, the natural convection relatively weak.     

On Infinitely Divisible Distributions on Locally Compact Abelian Groups

Our aim in this paper is to characterize some classes of infinitely divisible distributions on locally compact abelian groups. Firstly infinitely divisible distributions with no idempotent factor on locally compact abelian groups are characterized by means of limit distributions of sums of independent random variables. We introduce semi-selfdecomposable distributions on topological fields, and in case of totally disconnected fields we give a limit theorem for them. We also give a characterization of semistable laws on p-adic field and show that semistable processes are constructed as scaling limits of sums of i.i.d.     

A class of infinitely divisible distributions connected to branching processes and random walks

A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Lévy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions.     

Turbulent boundary layer on a plate with transpiration: Dynamical and thermal problems

Scaling laws are established for the profiles of mean velocity and temperature, Reynolds-stress components, turbulent heat flux and mean-square temperature fluctuation, skin friction and wall heat transfer in the turbulent boundary layer on a flat plate with transpiration. In the case of blowing, the velocity and temperature distributions represented in scaling variables outside the viscous sublayer have universal forms known from experimental data for flow over an impermeable flat plate. The turbulent shearing stress and heat flux also can be represented in terms of these two functions. In the case of suction, the mean quantities are described by one-parameter families of curves. Universal skin-friction and heat-transfer laws provide a basis for representation of the skin-friction and heat-flux distributions corresponding to different Reynolds numbers and transpiration velocities in terms of universal functions of one variable. The results are obtained without invoking any special closure hypotheses. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the optical density of human coronary arterial walls

Conclusions 1. The greatest thickness is found for the segment of a coronary artery adjacent to the myocardium; this effect is observed even in a neonate.2. At a young age, the greatest thickness is found for the middle and outer wall layers of both coronary arteries.3. In individuals reaching age 40 and having atherosclerosis of the major branches of the cardiac arteries, the walls of both coronary arteries become thicker due to the inner and middle layers, but the thickening of the individual layers is most pronounced in the wall of the left coronary artery.4. The method of optical densitometry relative to stained histological sections of the vascular wall may be used for the relative determination of the densities of tissues and their distributions over the individual wall layers.5. The optical density of elastic tissue of the walls of the coronary arteries reaches a maximum in the third decade of life in the human and decreases after age 40 (especially in the distal segment of the left coronary artery).6. The optical density of the total connective tissue in the walls of the left coronary artery increases with increasing age, especially in the distal segment of this artery. In youth, the optical density of connective tissue is greater in the wall of the right coronary artery, but with increasing age this density decreases markedly.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–318, March–April, 1978.     

Residual stress distribution in different types of adhesion joints

The results of a photoelastic investigation of the distributions of shrinkage and temperature residual stresses in glued joints and coatings are compared. The degree of nonuniformity of the residual stress distribution over the length and thickness is determined as a function of the scale factor. It is shown that the bulk of the residual stresses in metal joints glued with K-115 epoxy adhesive are temperature stresses, which may reach 130 kgf/cm². The shrinkage and temperature residual stress distributions are similar in character.Kucherenko Central Scientific-Research Institute of Building Structures. Translated from Mekhanika Polimerov, No. 4, pp. 738–742, July–August, 1971.     

Optimal quantization for dyadic homogeneous Cantor distributions

For a large class of dyadic homogeneous Cantor distributions in ?, which are not necessarily self‐similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non‐existence of the quantization coefficient. The class contains all self‐similar dyadic Cantor distributions, with contraction factor less than or equal to 1/3. For these distributions we calculate the quantization errors explicitly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

浅水横流中异重冲击射流的大尺度涡结构

采用RNG湍流模型对浅水横流中异重冲击射流的大尺度涡结构进行了详细的数值研究．分析了冲击区滞止点上游壁面涡结构和近区Scarf涡结构的尺度、形成机理和演化特征．计算得到了上游壁面涡的特征尺度,结果表明上游壁面涡具有高度的三维性,其特征尺度依赖于流速比和环境水深．近区Sarf涡结构对横流冲击射流的横向浓度分布具有重要的影响．当流速比相对较小时,在底层壁射流与环境横流的横向边界附近出现明显的高浓度聚集现象,计算结果表明Scarf涡结构对这一高浓度聚集区的形成起主导作用．