Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation

Decay of the energy for the Cauchy problem of the wave equation of variable coeffcients with a dissipation is considered.It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coeffcients.In particular,some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.     

The Convergence Analysis of the Decomposition Method for the (1+1)-Parabolic Problem in Nonuniform Media

A modified Adomian decomposition method is used to find approximate solutions for the reaction diffusion convection equation in nonuniform medium, i.e., with space-dependent coefficients. In this approach, the solutions are found in the form of a convergent power series with easily computed components. Convergence analysis of modified Adomian series solution for a class of these type of PDEs is discussed.     

Three-Dimensional Variational Analysis of Composite Structures Using Bernstein Polynomial Approximations. Report 1

The paper overviews the previous 3D variational analysis approaches and the numerical results obtained with the use of piecewise polynomial splines. A recently developed 3D displacement-assumed variational analysis approach is also described, where the Bernstein approximation polynomials of arbitrary degree are used as the shape functions for a 3D hexahedral discrete element of a composite body.     

COBRA: A New Formulation of the Classic p-Median Location Problem

The p-median problem was first formulated as an integer-linear programming problem by ReVelle and Swain (1970) and further revised by Rosing, ReVelle and Rosing-Vogelaar (1979). These two forms have withstood the test of time, as they have been used by virtually everyone since then. We prove that a property associated with geographical proximity makes it possible to eliminate many of the model variables through a substitution process. This new substitution technique has resulted in the elimination of up to 60% of the variables needed in either of these classic model formulations.     

Dynamic Programming Formulation of the Redundancy Allocation Problem

Dynamic programming formulation for obtaining the optimum number of redundancies at each stage in a system is explained in detail. It is also emphasized and illustrated by examples, that the ‘summation’ form of functional equations, as suggested in the paper, provide a faster solution to an otherwise computationally voluminous method.     

Probabilistic Formulation of the Emergency Service Location Problem

The problem of locating emergency service facilities is studied under the assumption that the locations of incidents (accidents, fires, or customers) are random variables. The probability distribution for rectilinear travel time between a new facility location and the random location of the incident P _i is developed for the case of P _i being uniformly distributed over a rectangular region. The location problem is considered in a discrete space. A deterministic formulation is obtained and recognized to be a set cover problem. Probabilistic variation of the central facility location problem is also presented.An example and some computational experience are provided to emphasize the impact of the probabilistic formulation on the location decision.     

A Mixed-Integer Goal-Programming Formulation of the Standard Flow-Shop Scheduling Problem

Until recently, the majority of models used to find an optimal sequence for the standard flow-shop problem were based on a single objective, typically makespan. In many applications, the practitioner may also want to consider other criteria simultaneously, such as mean flow-time or throughput time. As makespan and flow-time are equivalent criteria for optimizing machine idle-time and job idle-time, respectively, these additional criteria could be inherently considered as well. The effect of job idle-time, measuring in-process inventory, could be of particular importance.This paper presents an extension of an earlier model developed by the authors, formulating the generalized N job, M machine standard flow-shop problem as a mixed-integer goal-programming model. The formulation was empirically tested through a comparison of the generated optimal solutions to their mathematically derived counterparts. For this, a special flow-shop problem with certain permutation properties was selected. In addition, a randomly chosen problem was solved to show the general applicability of the derived formulation.The model allows the incorporation of the makespan as well as the mean flow-time criteria, instead of optimization being based on a single objective.     

Inverse Problems of the Mechanics of Thin-Walled Composite Structures

New formulations and methods for the solution of the inverse problems of thin-walled layered and reinforced shells and plates are discussed. Rational projects with regard for the requirements of nonflexural deformations in layered structural members, the given deformability of particular surfaces, the realization of a strictly momentless state, an equally stressed reinforcement, and the breaking strength of the binder at the interfaces are investigated. A brief review of the known solutions to these problems is given, and solutions to some new problems are described.     

Three-Dimensional Variational Analysis of Composite Structures Using Bernstein Polynomial Approximations. Report 2

The application of the previously developed 3D varionational analysis approach to the investigation of crack propagation in composite bonded joints is presented. In this application, the propagation of three different types of a 2D planar crack (adhesive, cohesive, and interfacial) is modeled by relaxing the respective continuity conditions for displacements between adjacent bricks in the mosaic structure. The crack propagation process is then characterized by the release rate of the total potential energy between two consecutive states of the mosaic body with different crack lengths. Numerical examples illustrate the 3D analysis of double-lap adhesively bonded joints with unidirectional and cross-ply laminated composite adherends. The numerical results provide an illustration of various characteristics of the crack propagation process. The values of the ultimate failure load predicted by analyzing the initial stage of crack propagation are found to be in a good agreement with experimental data.     

Manufacturing and Testing of Composite Materials and Structures. European Cooperative Research Examples

This article describes several European cooperative research examples in the field of polymer composite materials. The projects, which were carried out in collaboration between industrial and academic partners, were all supported by the European Union. They deal, e.g., with (a) the manufacturing and crash testing of thermoplastic composite structures, (b) the production of thermoplastic composite preforms, and (c) the energy absorption behavior of aluminum foams, and other interesting subjects.     

An Improved IP Formulation for the Uncapacitated Facility Location Problem: Capitalizing on Objective Function Structure

In this paper we examine the Uncapacitated Facility Location Problem (UFLP) with a special structure of the objective function coefficients. For each customer the set of potential locations can be partitioned into subsets such that the objective function coefficients in each are identical. This structure exists in many applications, including the Maximum Cover Location Problem. For the problems possessing this structure, we develop a new integer programming formulation that has all the desirable properties of the standard formulation, but with substantially smaller dimensionality, leading to significant improvement in computational times. While our formulation applies to any instance of the UFLP, the reduction in dimensionality depends on the degree to which this special structure is present. This work was supported by grants from NSERC.     

A Case Study of Stochastic Optimization in Health Policy: Problem Formulation and Preliminary Results

We use Bayesian decision theory to address a variable selection problem arising in attempts to indirectly measure the quality of hospital care, by comparing observed mortality rates to expected values based on patient sickness at admission. Our method weighs data collection costs against predictive accuracy to find an optimal subset of the available admission sickness variables. The approach involves maximizing expected utility across possible subsets, using Monte Carlo methods based on random division of the available data into N modeling and validation splits to approximate the expectation. After exploring the geometry of the solution space, we compare a variety of stochastic optimization methods –- including genetic algorithms (GA), simulated annealing (SA), tabu search (TS), threshold acceptance (TA), and messy simulated annealing (MSA) –- on their performance in finding good subsets of variables, and we clarify the role of N in the optimization. Preliminary results indicate that TS is somewhat better than TA and SA in this problem, with MSA and GA well behind the other three methods. Sensitivity analysis reveals broad stability of our conclusions.     

Cauchy Problem for the Equation of Longitudinal Vibrations of a Thick Rod with Allowance for Transverse Inertia

Differential Equations - For a nonlinear differential equation of Sobolev type describing the longitudinal vibrations of a thick rod with allowance for its transverse inertia, we study the...     

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.