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Equilibrium Problem (equilibrium + problem)

Distribution by Scientific Domains

Engineering	50%
Mathematics and Statistics	33%

Selected Abstracts

Equilibrium problem for thermoelectroconductive body with the Signorini condition on the boundary

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2001
D. Hömberg
Abstract We investigate a boundary value problem for a thermoelectroconductive body with the Signorini condition on the boundary, related to resistance welding. The mathematical model consists of an energy-balance equation coupled with an elliptic equation for the electric potential and a quasistatic momentum balance with a viscoelastic material law. We prove the existence of a weak solution to the model by using the Schauder fixed point theorem and classical results on pseudomonotone operators. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A comparison between new adaptive remeshing strategies based on point wise stress error estimation and energy norm error estimation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2002
G. Bugeda
Abstract Traditionally, the most commonly used mesh adaptive strategies for linear elastic problems are based on the use of an energy norm for the measurement of the error, and a mesh refinement strategy based on the equal distribution of the error between all the elements. However, little attention has been paid to the study of alternative error norms and alternative refinement strategies. This paper studies the feasibility of using alternative mesh refinement strategies based on , the use of the classical error energy norm and an optimality criterion based on the equal distribution of the density of error, , the use of alternative error norms based on measurements of the point wise error contained in the main magnitudes that control the equilibrium problem and/or the material constitutive equations such as the stresses (e.g. the Von Mises stress). The feasibility of using all the described strategies is demonstrated through the solution of a benchmark example. This example is also used for comparison between the described refinement criteria. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A reliability-based network design problem

JOURNAL OF ADVANCED TRANSPORTATION, Issue 3 2005
Piya Chootinan
Abstract This paper presents a reliability-based network design problem. A network reliability concept is embedded into the continuous network design problem in which travelers' route choice behavior follows the stochastic user equilibrium assumption. A new capacity-reliability index is introduced to measure the probability that all of the network links are operated below their capacities when serving different traffic patterns deviating from the average condition. The reliability-based network design problem is formulated as a bi-level program in which the lower level sub-program is the probit-based stochastic user equilibrium problem and the upper level sub-program is the maximization of the new capacity reliability index. The lower level sub-program is solved by a variant of the method of successive averages using the exponential average to represent the learning process of network users on a daily basis that results in the daily variation of traffic-flow pattern, and Monte Carlo stochastic loading. The upper level sub-program is tackled by means of genetic algorithms. A numerical example is used to demonstrate the concept of the proposed framework. [source]

Universality in the two-matrix model: a Riemann-Hilbert steepest-descent analysis

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2009
Maurice Duits
The eigenvalue statistics of a pair (M1, M2) of n × n Hermitian matrices taken randomly with respect to the measure can be described in terms of two families of biorthogonal polynomials. In this paper we give a steepest-descent analysis of a 4 × 4 matrix-valued Riemann-Hilbert problem characterizing one of the families of biorthogonal polynomials in the special case W(y) = y4/4 and V an even polynomial. As a result, we obtain the limiting behavior of the correlation kernel associated to the eigenvalues of M1 (when averaged over M2) in the global and local regime as n , , in the one-cut regular case. A special feature in the analysis is the introduction of a vector equilibrium problem involving both an external field and an upper constraint. © 2008 Wiley Periodicals, Inc. [source]

BILU implicit multiblock Euler/Navier,Stokes simulation for rotor tip vortex and wake convection

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2007
Bowen Zhong
Abstract In this paper, a block incomplete lower,upper (BILU) decomposition method is incorporated with a multiblock three-dimensional Euler/Navier,Stokes solver for simulation of hovering rotor tip vortices and rotor wake convection. Results of both Euler and Navier,Stokes simulations are obtained and compared with experimental observations. The comparisons include surface pressure distributions and tip vortex trajectories. The comparisons suggest that resolution of the boundary layer is important for the accurate evaluation of the blade surface loading, but is less so for the correct prediction of the vortex trajectory. Numerical tests show that, using Courant,Friedrichs,Lewy (CFL) number of 10 or 30 with the developed BILU implicit scheme can be 6,7 times faster than an explicit scheme. The importance of solution acceleration schemes that increase the permitted time-step is illustrated by comparing the evolving wake structures at different stages of the calculation. In contrast to fixed wing simulations, the extent of the wake structures is shown to require resolution of large physical time. This observation explains the poor performance that is obtained when employing convergence acceleration strategies originally intended for solution of equilibrium problems, such as the multigrid methods. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Nonlinear piezoelectric properties of GaN quantum dots nucleated at the edge of threading dislocations

PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 7 2007
ewski
Abstract It was observed experimentally by Rouviere et al. that GaN/AlN Quantum Dots (QDs) nucleate at the edge of threading dislocations (Appl. Phys. Lett. 75, 2632 (1999) [1]). The preferred nucleation of QDs in this way is generally assumed to be due to the influence of the stress/strain field around the dislocation core, which in turn, gives the chemical and geometric conditions for nucleation of the QDs. We solve the finite element problem for QDs situated at the edge of threading dislocations where different lattice parameters, piezoelectric and spontaneous polarisation coefficients are assumed for the QD and its matrix. By solving the elastic and electric equilibrium problems we obtain both the residual stress and electric fields. The computational scheme employed here was obtained by linking two previous finite element algorithms described inreferences (P. D,u,ewski et al., Comput. Mater. Sci. 29, 379 (2004) [2]) and (G. Jurczak et al., phys. stat. sol. (c) 2, 972 (2005) and S.P. ,epkowski et al., Phys. Rev. B 73, 245201 (2005) [3, 4], respectively). This approach allows us to get a deeper physical insight into the mechanics and electrical properties of QDs and ultimately determine the efficiency of light emission from these objects. [source]