Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations /

"Presented at the Differential Equation Workshop, Center for Interdisciplinary Research (Zif), University of Bielefeld, West Germany, April 21, 1980."

Stability of variable-step methods for ordinary differential equations /

Bibliography: leaf 11.

Die partiellen Differential-Gleichungen der mathematischen Physid nach Riemann's Vorlesungen

Mode of access: Internet.

I miei integrafi per equazioni differenziali.

Available on demand as hard copy or computer file from Cornell University Library.

Parameters affecting the performance of wetting and drying in a two-dimensional finite element long wave hydrodynamic model

The marsh porosity method, a type of thin slot wetting and drying algorithm in a two-dimensional finite element long wave hydrodynamic model, is discussed and analyzed to assess model performance. Tests, including comparisons to simple examples and theoretical calculations, examine the effects of varying the marsh porosity parameters. The findings demonstrate that the wetting and drying concept of marsh porosity, often used in finite element hydrodynamic modeling, can behave in a more complex manner than initially expected.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Mine waste beach profile and flow resistance equations

Four mine waste beach longitudinal profile equations are compared theoretically and in statistical analyses of profile data from 64 field and laboratory beaches formed by mine tailings, co-disposed coal mine wastes, and sand. All four equations fit the profile data well. The best performing equation both accounts for particle sorting and satisfies hydraulic constraints, and the combination of assumptions underlying it is considered to best represent the processes occurring on mine waste beaches. Combining these assumptions with the Lacey normal equation leads to a variant of the Manning resistance equation. Features that it is desirable to incorporate in theoretical and numerical models of mine waste beaches are listed.

Recent development in the mechanics of superplasticity and its applications

This paper reviews the recent developments in the mechanics of superplasticity and its applications in industrial practice. After introducing the phenomena of superplasticity, the basic experiments for determining material deformation behavior and related parameters, and constructing superplastic constitutive equations, are reviewed. Finite element related formulations and techniques for simulating superplastic forming are discussed, together with some practical applications. (C) 2004 Elsevier B.V. All rights reserved.

A preform design method for sheet superplastic bulging with finite element modeling

Superplastic bulging is the most successful application of superplastic forming (SPF) in industry, but the non-uniform wall thickness distribution of parts formed by it is a common technical problem yet to be overcome. Based on a rigid-viscoplastic finite element program developed by the authors, for simulation of the sheet superplastic forming process combined with the prediction of microstructure variations (such as grain growth and cavity growth), a simple and efficient preform design method is proposed and applied to the design of preform mould for manufacturing parts with uniform wall thickness. Examples of formed parts are presented here to demonstrate that the technology can be used to improve the uniformity of wall thickness to meet practical requirements. (C) 2004 Elsevier B.V. All rights reserved.

Analytical solutions of linear finite- and small-strain one-dimensional consolidation

Analytical solutions are presented for linear finite-strain one-dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one- and two-way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small-strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small-strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non-linear finite-strain consolidation. They also clarify a formerly perplexing aspect of finite-strain solution charts first noted in numerical solutions. Copyright (C) 2004 John Wiley Sons, Ltd.

Existence of solutions for p(x)-Laplacian problems on a bounded domain

In this paper we study the following p(x)-Laplacian problem: -div(a(x)&VERBAR;&DEL; u&VERBAR;(p(x)-2)&DEL; u)+b(x)&VERBAR; u&VERBAR;(p(x)-2)u = f(x, u), x ε &UOmega;, u = 0, on &PARTIAL; &UOmega;, where 1< p(1) &LE; p(x) &LE; p(2) < n, &UOmega; &SUB; R-n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in W-0(1,p(x)) for the p(x)-Laplacian problems in the superlinear and sublinear cases. © 2004 Elsevier Inc. All rights reserved.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Advances in distributed parameter approach to the dynamics and control of activated sludge processes for wastewater treatment

This paper presents a review of modelling and control of biological nutrient removal (BNR)-activated sludge processes for wastewater treatment using distributed parameter models described by partial differential equations (PDE). Numerical methods for solution to the BNR-activated sludge process dynamics are reviewed and these include method of lines, global orthogonal collocation and orthogonal collocation on finite elements. Fundamental techniques and conceptual advances of the distributed parameter approach to the dynamics and control of activated sludge processes are briefly described. A critical analysis on the advantages of the distributed parameter approach over the conventional modelling strategy in this paper shows that the activated sludge process is more adequately described by the former and the method is recommended for application to the wastewater industry (c) 2006 Elsevier Ltd. All rights reserved.