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Whole Space (whole + space)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Simultaneous untangling and smoothing of moving grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2008
Ezequiel J. López
Abstract In this work, a technique for simultaneous untangling and smoothing of meshes is presented. It is based on an extension of an earlier mesh smoothing strategy developed to solve the computational mesh dynamics stage in fluid,structure interaction problems. In moving grid problems, mesh untangling is necessary when element inversion happens as a result of a moving domain boundary. The smoothing strategy, formerly published by the authors, is defined in terms of the minimization of a functional associated with the mesh distortion by using a geometric indicator of the element quality. This functional becomes discontinuous when an element has null volume, making it impossible to obtain a valid mesh from an invalid one. To circumvent this drawback, the functional proposed is transformed in order to guarantee its continuity for the whole space of nodal coordinates, thus achieving the untangling technique. This regularization depends on one parameter, making the recovery of the original functional possible as this parameter tends to 0. This feature is very important: consequently, it is necessary to regularize the functional in order to make the mesh valid; then, it is advisable to use the original functional to make the smoothing optimal. Finally, the simultaneous untangling and smoothing technique is applied to several test cases, including 2D and 3D meshes with simplicial elements. As an additional example, the application of this technique to a mesh generation case is presented. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Fitting complex potential energy surfaces to simple model potentials: Application of the simplex-annealing method

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 6 2005
Raúl A. Bustos Marún
Abstract A stochastic method of optimization, which combines simulated annealing with simplex, is implemented to fit the parameters of a simple model potential. The main characteristic of the method is that it explores the whole space of the parameters of the model potential, and therefore it is very efficient in locating the global minimum of the cost function, in addition to being independent of the initial guess of the parameters. The method is employed to fit the complex intermolecular potential energy surface of the dimer of water, using as a reference the spectroscopic quality anisotropic site,site potential of Feller et al. The simple model potential chosen for its reparameterization is the MCY model potential of Clementi et al. The quality of the fit is assessed by comparing the geometry of the minimum, the harmonic frequencies, and the second virial coefficients of the parameterized potential with the reference one. Finally, to prove more rigorously the robustness of this method, it is compared with standard nonstochastic methods of optimization. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 523,531, 2005 [source]

RISK MEASURES ON ORLICZ HEARTS

MATHEMATICAL FINANCE, Issue 2 2009
Patrick Cheridito
Coherent, convex, and monetary risk measures were introduced in a setup where uncertain outcomes are modeled by bounded random variables. In this paper, we study such risk measures on Orlicz hearts. This includes coherent, convex, and monetary risk measures on Lp -spaces for 1 ,p < , and covers a wide range of interesting examples. Moreover, it allows for an elegant duality theory. We prove that every coherent or convex monetary risk measure on an Orlicz heart which is real-valued on a set with non-empty algebraic interior is real-valued on the whole space and admits a robust representation as maximal penalized expectation with respect to different probability measures. We also show that penalty functions of such risk measures have to satisfy a certain growth condition and that our risk measures are Luxemburg-norm Lipschitz-continuous in the coherent case and locally Luxemburg-norm Lipschitz-continuous in the convex monetary case. In the second part of the paper we investigate cash-additive hulls of transformed Luxemburg-norms and expected transformed losses. They provide two general classes of coherent and convex monetary risk measures that include many of the currently known examples as special cases. Explicit formulas for their robust representations and the maximizing probability measures are given. [source]

Stationary solutions to the drift,diffusion model in the whole spaces

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2009
Ryo Kobayashi
Abstract We study the stationary problem in the whole space ,n for the drift,diffusion model arising in semiconductor device simulation and plasma physics. We prove the existence and uniqueness of stationary solutions in the weighted Lp spaces. The proof is based on a fixed point theorem of the Leray,Schauder type. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On the convergence of Fourier series of computable Lebesgue integrable functions

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 5 2010
Philippe Moser
Abstract This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp -computable functions (computable Lebesgue integrable functions) with a size notion, by introducing Lp -computable Baire categories. We show that Lp -computable Baire categories satisfy the following three basic properties. Singleton sets {f } (where f is Lp -computable) are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp -computable functions is not meager. We give an alternative characterization of meager sets via Banach-Mazur games. We study the convergence of Fourier series for Lp -computable functions and show that whereas for every p > 1, the Fourier series of every Lp -computable function f converges to f in the Lp norm, the set of L1 -computable functions whose Fourier series does not diverge almost everywhere is meager (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Cloaking via change of variables for the Helmholtz equation in the whole space

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2010
Hoai-Minh Nguyen
This paper is devoted to the study of a cloaking device that is composed of a standard near cloak based on a regularization of the transformation optics, i.e., a change of variables that blows up a small ball to the cloaked region, and a fixed lossy layer for the Helmholtz equation in the whole space of dimension 2 or 3 with the outgoing condition at infinity. We establish a degree of near invisibility, which is independent of the content inside the cloaked region, for this device. We also show that the lossy layer is necessary to ensure the validity of the degree of near invisibility when no constraint on physical properties inside the cloaked region is imposed. © 2010 Wiley Periodicals, Inc. [source]