Damage processes coupled with phase separation in elastically stressed alloys

In micro-electronic materials such as solder alloys, phase-separation and coarsening as well as damage phenomena occur at the same time and influences each other. In this note, a unifying model which couples multi-component Cahn-Hilliard systems with elasticity and uni-directional damage processes is presented. We outline the equations and their initial-boundary conditions in a classical setting and cite some existence results for weak solutions recently proved in [8, 9]. The damage is assumed to be incomplete, i.e. the maximal damaged material parts still feature elastic properties. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unified description of bifurcation processes associated with laminar boundary-layer separation

The presentation will concentrate on flows where no steady state exists if an appropriately defined controlling parameter exceeds a critical value while non-uniqueness is observed for sub-critical values of this parameter. Special attention is placed on flow phenomena which are associated with the passage through criticality. Based on a triple deck analysis it found that they can be described as solutions of differential equations of Fisher type which are better known from evolution studies of gene populations. Special examples which will be discussed include 2D marginally separated flows, weakly 3D transonic flows in slender channels and fully 3D subsonic flow past expansion ramps. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preventive maintenance scheduling of power generating units

The problem of preventive maintenance planning of electric power generating units can be formulated as a mixed-integer linear optimization problem. An extension of the model is presented to deal with more realistic assumptions about utilization of power resource. We propose a heuristic iterative exchange procedure to solve these problems. We introduce two methods to prevent jamming situations outside the feasible domain or at a local optimum. The first method is a recursive exchange procedure called multiple exchanges method and the second relies on Lagrangian relaxation. Furthermore, we compare these procedures with a tabu search.This research was supported by NSERC (Grant A8312) and FCAR (Grant ER-0289).Michèle Charest had an NSERC Scholarship to work on this project.     

Asymptotic separation for independent trajectories of Markov processes

We say that n independent trajectories ξ₁(t),…,ξ _n (t) of a stochastic process ξ(t)on a metric space are asymptotically separated if, for some ɛ > 0, the distance between ξ _i (t _i ) and ξ _j (t _j ) is at least ɛ, for some indices i, j and for all large enough t ₁,…,t _n , with probability 1. We prove sufficient conitions for asymptotic separationin terms of the Green function and the transition function, for a wide class of Markov processes. In particular,if ξ is the diffusion on a Riemannian manifold generated by the Laplace operator Δ, and the heat kernel p(t, x, y) satisfies the inequality p(t, x, x) ≤ Ct ^−ν/2 then n trajectories of ξ are asymptotically separated provided . Moreover, if for some α∈(0, 2)then n trajectories of ξ^(α) are asymptotically separated, where ξ^(α) is the α-process generated by −(−Δ)^α/2. Received: 10 June 1999 / Revised version: 20 April 2000 / Published online: 14 December 2000 RID="*" ID="*" Supported by the EPSRC Research Fellowship B/94/AF/1782 RID="**" ID="**" Partially supported by the EPSRC Visiting Fellowship GR/M61573     

Optimization of power production through coordinated use of hydroelectric and conventional power units

In the present work a methodology to tackle the problem of simultaneous utilization of hydroelectric and conventional power units with the goal of optimizing power production operations over the short term is presented. Most problem formulations found in the literature result in the development of nonlinear optimization programs, which are solved with stochastic methods. The methodology presented in this paper leads to the development of a convex mixed integer quadratic programming (MIQP) model, which is a special type of nonlinear model that enables reaching the global optimum solution in short computational time. The efficiency of the proposed approach is demonstrated by its application to a realistic power production system.     

Central limit theorems for power variation of Gaussian integral processes with jumps

This paper presents limit theorems for realized power variation of processes of the form Xt=t0φsdGs+ξt as the sampling frequency within a fixed interval increases to infinity.Here G is a Gaussian process with stationary increments,ξis a purely non-Gaussian L′evy process independent from G,andφis a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral.We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers.     

An analysis of setup cost reduction in a two stage system with power investment function

Recently, a framework for analyzing investment decisions as they relate to setup cost reduction in two stage production processes has appeared in the literature. Closed form results were developed for the case of logarithmic investment function. This paper extends the results to the case of power investment function. We present an algorithm for calculating the optimal values of the decision variables. A numerical example is utilized to reveal some interesting aspects of this system.     

Minimum density power divergence estimator for diffusion processes

In this paper, we consider the robust estimation for a certain class of diffusion processes including the Ornstein–Uhlenbeck process based on discrete observations. As a robust estimator, we consider the minimum density power divergence estimator (MDPDE) proposed by Basu et al. (Biometrika 85:549–559, 1998). It is shown that the MDPDE is consistent and asymptotically normal. A simulation study demonstrates the strong robustness of the MDPDE.     

Unsteady Porous Flow with a Free Surface

Three different numerical methods for solving unsteady two-dimensionalporous flow problems with a free surface are presented. Thevelocity potential is expressed as the solution to a variationalproblem which is solved by a Rayleigh-Ritz expansion, a Kantorovichexpansion and a co-ordinate transformation method. The freesurface equation is solved by a Crank-Nicolson procedure. Thethree methods were tested on the same set of problems and theobtained results are virtually identical.     

Improving the discriminating power of DEA: focus on globally efficient units

We introduce in this paper the global efficiency approach as a means to improve the discriminating power of Data Envelopment Analysis (DEA). To discriminate further among the DEA efficient units, we deal only with the units that can maintain their efficiency score under common weighting structures. Then we proceed further to ranking the whole set of DEA efficient units. We compare the global efficiency approach with the multi-criteria DEA and the cross-efficiency approaches on the basis of characteristic numerical examples drawn from the literature.     

Unsteady flow past a flat plate with suction

A solution is given for the transient response for laminar boundary layer flow past a flat plate to a step-function change in suction velocity. An arbitrary but constant suction velocity normal to the plate is allowed prior to step-change. Using the Laplace transform technique the solutions for the unsteady velocity profile and shear stress are obtained and are graphically sketched when the suction velocity doubles in the stepchange. The results show clear evidence of boundary-layer contraction when suction velocity is increased.     

On the separation power and the completion of partial latin squares

Let n and m be natural numbers, n ? m. The separation power of order n and degree m is the largest integer k = k(n, m) such that for every (0, 1)-matrix A of order n with constant linesums equal to m and any set of k 1's in A there exist (disjoint) permutation matrices P₁,…, P_m such that A = P₁ + … + P_m and each of the k 1's lies in a different P_i. Almost immediately we have 1 ? k(n, m) ? m ? 1, yet in all cases where the value of k(n, m) is actually known it equals m ? 1 (except under the somewhat trivial circumstances of k(n, m) = 1). This leads to a conjecture about the separation power, namely that k(n, m) = m ? 1 if $\text{m ? [}\text{n}\text{2}\text{] + 1}$. We obtain the bound $\text{k(n, m) ? m ? [}\text{n}\text{2}\text{] + 2}$, so that this conjecture holds for n ? 7. We then move on to latin squares, describing several equivalent formulations of the concept. After establishing a sufficient condition for the completion of a partial latin square in terms of the separation power, we can show that the Evans conjecture follows from this conjecture about the separation power. Finally the lower bound on k(n, m) allows us to show, after some calculations, that the Evans conjecture is true for orders n ? 11.     

Natural synchronization in power-grids with anti-correlated units

Synchronization between spatially distributed nodes of a power-grid is a crucial requirement for its proper operation. Using a Kuramoto-like network as a realistic physical model for the distribution of electrical power in a power-grid, we obtain coupling strengths and topological characteristics that favor the synchronous state of those technological networks. Power-grids are highly heterogeneous. They are composed of different classes of nodes and each node behaves differently. We show in this work that if a power-grid is extensive and nodes are highly connected, the coupling strength that leads to synchronization depends mainly on the eigenvalues of the Laplacian matrix, as it happens in homogeneous networks composed of equal nodes. On the other hand, if a power-grid is sparsely connected, the coupling strength that leads to synchronization is also strongly related to the correlation coefficient of the network, which means that a high number of connections between similar nodes (two power plants or two consumer centers) disfavor the synchronizability of the power-grid. We apply our results to the Brazilian power-grid system.     

A computer‐aided methodology for the optimization of electrostatic separation processes in recycling

The rapid growth of technological products has led to an increasing volume of waste electrical and electronic equipments (WEEE), which could represent a valuable source of critical raw materials. However, current mechanical separation processes for recycling are typically poorly operated, making it impossible to modify the process parameters as a function of the materials under treatment, thus resulting in untapped separation potentials. Corona electrostatic separation (CES) is one of the most popular processes for separating fine metal and nonmetal particles derived from WEEE. In order to optimize the process operating conditions (i.e., variables) for a given multi‐material mixture under treatment, several technological and economical criteria should be jointly considered. This translates into a complex optimization problem that can be hardly solved by a purely experimental approach. As a result, practitioners tend to assign process parameters by few experiments based on a small material sample and to keep these parameters fixed during the process life‐cycle. The use of computer experiments for parameter optimization is a mostly unexplored area in this field. In this work, a computer‐aided approach is proposed to the problem of optimizing the operational parameters in CES processes. Three metamodels, developed starting from a multi‐body simulation model of the process physics, are presented and compared by means of a numerical and simulation study. Our approach proves to be an effective framework to optimize the CES process performance. Furthermore, by comparing the predicted response surfaces of the metamodels, additional insight into the process behavior over the operating region is obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

Unsteady flows of fluids with pressure dependent viscosity in unbounded domains

In order to describe the behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the Cauchy stress and the velocity gradient these models are consistent with standard procedures of continuum mechanics. Understanding the mathematical properties of the governing equations is connected with various types of idealizations, some of them lead to studies in unbounded domains. In this paper, we first bring up several characteristic features concerning fluids with pressure dependent viscosity. Then we study the three-dimensional flows of a class of fluids with the viscosity depending on the pressure and the shear rate. By means of higher differentiability methods we establish the large data existence of a weak solution for the Cauchy problem. This seems to be a first result that analyzes flows of considered fluids in unbounded domains. Even in the context of purely shear rate dependent fluids of a power-law type the result presented here improves some of the earlier works.     

Optimal filtering of piecewise deterministic processes for source detection and separation in electric load monitoring

We wish to compute in discrete real time the best estimate for the composition of the total active power recorded at a customer's house, without any intrusion. A new solution for online characterization of the electric load is proposed. The solution is based on issues from the applied stochastic analysis of Markov processes. We specifically suggest that optimal filtering of a hybrid stochastic differential system covers entirely the detection and separation subproblems underlying the main problem.