Viscous flow past a porous sphere with an impermeable core : effect of stress jump condition

An arbitrary flow of a viscous, incompressible fluid past a porous sphere of radius `a' with an impermeable core of radius `b', using Brinkman's equation in the porous region is discussed. At the interface of the clear fluid and porous region, stress jump boundary condition for the tangential stresses along with the continuity of normal stresses and the velocity components are used. On the surface of the impermeable core no slip condition is used. The corresponding Faxen's laws are derived to compute the drag and torque acting on the surface r=a. It is found that the drag and torque not only change with the change of the permeability, but also a significant effect of the stress jump co-efficient is observed. The variation of drag and torque with permeability for different thickness (a-b) of the porous region as well as for different values of stress jump coefficient is discussed when the basic flow is due to uniform flow, two dimensional irrotational flow, doublet in a uniform flow, stokeslet, rotlet. In case of uniform flow the flow field has been plotted. In all the cases, a significant effect of the stress jump coefficient has been realized.     

Parameter Estimation for Periodically Stationary Time Series

Abstract. The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper, we compute the asymptotic distribution for these estimates in the case, where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule–Walker estimates.     

Controller synthesis with guaranteed closed-loop phase constraints

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval [−α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where 07S-1-26/0?wchp=dGLbVlW-zSkzk" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=16 width="39"/>, we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function.     

On mesh restrictions to satisfy comparison principles,maximum principles,and the non-negative constraint: Recent developments and new results

This article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.     

Some fixed point theorems in 1-M-complete fuzzy metric-like spaces

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.     

Input-output properties of the Page-Hinkley detector

We consider the stochastic input-output properties of a simple non-linear dynamical system, the so-called Page-Hinkley detector, playing a key role in change detection, and also in queuing theory. We show that for L-mixing inputs with negative expectation the output process of this system is L-mixing. The result is applied to get an upper bound for the false alarm rate. The proof is then adapted to get a similar result for the case of random i.i.d. inputs. Possible extensions and open problems are given in the discussion.     

Efficient Collision Detection for Moving Ellipsoids Using Separating Planes

We present a simple, accurate and efficient algorithm for collision detection among moving ellipsoids. Its efficiency is attributed to two results: (i) a simple algebraic test for the separation of two ellipsoids, and (ii) an efficient method for constructing a separating plane between two disjoint ellipsoids. Inter-frame coherence is exploited by using the separating plane to reduce collision detection to simpler subproblems of testing for collision between the plane and each of the ellipsoids. Compared with previous algorithms (such as the GJK method) which employ polygonal approximation of ellipsoids, our algorithm demonstrates comparable computing speed and much higher accuracy.     

基于07MnNiMoDR钢热处理工艺窗口的热处理工艺

研究了07MnNiMoDR钢淬火和回火制度与晶粒尺寸和多边形铁素体含量的关系,建立了淬火保温时奥氏体尺寸窗口和回火保温时多边形铁素体含量窗口,确定了更为精准的热处理工艺。结果表明:奥氏体晶粒尺寸随淬火温度的升高、保温时间的延长而变大,均匀性存在最佳区间,合理的淬火制度为加热温度(940±10) ℃保温(80±10) min;随回火温度升高,约650 ℃出现多边形铁素体,其含量随回火温度的升高、保温时间的延长而增加,合理的回火制度为:加热温度(665±5) ℃、保温时间(165±15) min。优选后最佳热处理工艺为940 ℃×80 min淬火和660 ℃×180 min回火,最终性能测试结果表明:伸长率、冲击吸收能量和屈服强度相比国标分别提升了40.88%、206.25%和12.1%。     

Implicitization of Parametric Curves via Lagrange Interpolation

A simple algorithm for finding the implicit equation of a parametric plane curve given by its parametric equations is presented. The algorithm is based on an efficient computation of the Bézout resultant and Lagrange interpolation. One of main features of our approach is the fact that it considerably reduces the problem of computing intermediate expressions.