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Articles 151 - 170 of 170
Full-Text Articles in Physical Sciences and Mathematics
Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston
Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work the curvature of Weinhold (thermodynamical) metric is studied in the case of systems with two thermodynamical degrees of freedom. Conditions for the Gauss curvature R to be zero, positive or negative are worked out. Signature change of the Weinhold metric and the corresponding singular behavior of the curvature at the phase boundaries are studied. Cases of systems with the constant Cv, including Ideal and Van der Waals gases, and that of Berthelot gas are discussed in detail.
Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz
Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.
Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz
Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz
Mathematics and Statistics Faculty Publications and Presentations
This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a nonelliptic indefinite operator. With the help of a few new estimates, the …
A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan
A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we give a new characterization of the approximate solution given by hybridized mixed methods for second order self-adjoint elliptic problems. We apply this characterization to obtain an explicit formula for the entries of the matrix equation for the Lagrange multiplier unknowns resulting from hybridization. We also obtain necessary and sufficient conditions under which the multipliers of the Raviart–Thomas and the Brezzi–Douglas–Marini methods of similar order are identical.
A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat
A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat
Mathematics and Statistics Faculty Publications and Presentations
A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.
A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan
A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the ux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners for the lowest order case of the Raviart-Thomas method have been constructed previously by exploiting its connection with a nonconforming method, our approach is different, in that we use a new variational characterization of the Lagrange multiplier equation. This allows us to …
Conformal Laplacian And Conical Singularities, Boris Botvinnik, Serge Preston
Conformal Laplacian And Conical Singularities, Boris Botvinnik, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
We study a behavior of the conformal Laplacian operator $\L_g$ on a manifold with \emph{tame conical singularities}: when each singularity is given as a cone over a product of the standard spheres. We study the spectral properties of the operator $\L_g$ on such manifolds. We describe the asymptotic of a general solution of the equation $\L_g u = Q u^{\alpha}$ with 1≤α≤n+2 near each singular point. In particular, we derive the asymptotic of the Yamabe metric near such singularity.
On The Evolution Of Simple Material Structures, Marek Elźanowski, Ernst Binz
On The Evolution Of Simple Material Structures, Marek Elźanowski, Ernst Binz
Mathematics and Statistics Faculty Publications and Presentations
The evolution of a distribution of material inhomogeneities is investigated by analyzing the evolution of the corresponding material connections. Some general geometric relations governing such evolutions are derived. These relations are then analyzed by looking at the restrictions imposed by the material symmetry group.
Stochastic Properties Of Spacings In A Single-Outlier Exponential Model, Baha-Eldin Khaledi, Subhash C. Kochar
Stochastic Properties Of Spacings In A Single-Outlier Exponential Model, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
Let X1,..., Xn be independent exponential random variables with possibly different scale parameters. Kochar and Korwar [J. Multivar. Anal. 57 (1996)] conjectured that, in this case, the successive normalized spacings are increasing according to hazard rate ordering. In this article, we prove this conjecture in the case of a single-outlier exponential model when all except one of the parameters are identical. We also prove that the spacings are more dispersed and larger in the sense of hazard rate ordering when the vector of scale parameters is more dispersed in the sense of majorization.
The Multiplicities Of A Dual-Thin Q-Polynomial Association Scheme, Bruce E. Sagen, John S. Caughman Iv
The Multiplicities Of A Dual-Thin Q-Polynomial Association Scheme, Bruce E. Sagen, John S. Caughman Iv
Mathematics and Statistics Faculty Publications and Presentations
Let Y=(X,{Ri}1≤i≤D) denote a symmetric association scheme, and assume that Y is Q-polynomial with respect to an ordering E0,...,ED of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities mi (0≤i≤D) of Yis unimodal. Talking to Terwilliger, Stanton made the related conjecture that mi≤mi+1 and mi≤mD−i for i<D/2. We prove that if Y is dual-thin in the sense of Terwilliger, then the …
Dependence Among Spacings, Baha-Eldin Khaledi, Subhash C. Kochar
Dependence Among Spacings, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we study the dependence properties of spacings. It is proved that if X1,..., Xn are exchangeable random variables which are TP2 in pairs and their joint density is log-convex in each argument, then the spacings are MTP2 dependent. Next, we consider the case of independent but nonhomogeneous exponential random variables. It is shown that in this case, in general, the spacings are not MTP2 dependent. However, in the case of a single outlier when all except one parameters are equal, the spacings are shown to be MTP2 dependent and, hence, …
An Efficient Method For Band Structure Calculations In 3d Photonic Crystals, David C. Dobson, Jay Gopalakrishnan, Joseph E. Pasciak
An Efficient Method For Band Structure Calculations In 3d Photonic Crystals, David C. Dobson, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
A method for computing band structures for three-dimensional photonic crystals is described. The method combines a mixed finite element discretization on a uniform grid with a fast Fourier transform preconditioner and a preconditioned subspace iteration algorithm. Numerical examples illustrating the behavior of the method are presented.
About Non-Spherically Symmetric Deformations Of An Incompressible Neo-Hookean Sphere, Marek Elźanowski
About Non-Spherically Symmetric Deformations Of An Incompressible Neo-Hookean Sphere, Marek Elźanowski
Mathematics and Statistics Faculty Publications and Presentations
A class of non-spherically symmetric deformations of a neo-Hookean incompressible elastic ball is considered. It is shown that the only possible solution, the cavitated radially symmetric solution and the deformation of radial inflation and polar stretching. These are the same solutions as found by Polignone-Warne and Warne [6] for a smaller class of deformations. This fact shows once again that the radial deformations are the only deformations, at least within the class considered, which may support a formation of a cavity in the center of an incompressible, isotropic, elastic sphere.
Estimation Of A Monotone Mean Residual Life, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego
Estimation Of A Monotone Mean Residual Life, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego
Mathematics and Statistics Faculty Publications and Presentations
In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x,M(x), defined by M(x)=E[X?x|X>x], where X is a lifetime. M is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of M and their properties. Although tests for a monotone M are discussed in the literature, we are not aware of any estimators of M under these order restrictions. In …
Multigrid For The Mortar Finite Element Method, Jay Gopalakrishnan, Joseph E. Pasciak
Multigrid For The Mortar Finite Element Method, Jay Gopalakrishnan, Joseph E. Pasciak
Mathematics and Statistics Faculty Publications and Presentations
A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed. These problems are posed on domains partitioned into subdomains, each of which is independently triangulated in a multilevel fashion. The multilevel mortar finite element spaces based on such triangulations (which need not align across subdomain interfaces) are in general not nested. Suitable grid transfer operators and smoothers are developed which lead to a variable Vcycle preconditioner resulting in a uniformly preconditioned algebraic system. Computational results illustrating the theory are also presented.
Mortar Estimates Independent Of Number Of Subdomains, Jay Gopalakrishnan
Mortar Estimates Independent Of Number Of Subdomains, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
The stability and error estimates for the mortar finite element method are well established. This work examines the dependence of constants in these estimates on shape and number of subdomains. By means of a Poincar´e inequality and some scaling arguments, these estimates are found not to deteriorate with increase in number of subdomains.
Geometrical Models For Grain Dynamics, Giovani L. Vasconcelos, J. J. P. Veerman
Geometrical Models For Grain Dynamics, Giovani L. Vasconcelos, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We study models for the gravity-driven, dissipative motion of a single grain on an inclined rough surface. Imposing some conditions on the momentum loss due to the collisions between the particle and the surface, we arrive at a class of models in which the grain dynamics is described by one-dimensional maps. The dynamics of these maps is studied in detail. We prove the existence of various dynamical phases and show that the presence of these phases is independent of the restitution law (within the class considered).
Geometrical Modeling Of Material Aging, Alexander Chudnovsky, Serge Preston
Geometrical Modeling Of Material Aging, Alexander Chudnovsky, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
Material aging is understood as changes of material properties with time. The aging is usually observed as an improvement of some properties and a deterioration of others. For example an increase of rigidity and strength and reduction in toughness with time are commonly observed in engineering materials. In an attempt to model aging phenomena on a continuum (macroscopical) level one faces three major tasks. The first is to identify an adequate age parameter that represents, on a macroscopic scale, the micro and sub microscopical features, underlying the aging phenomena such as nucleation, growth and coalescence of microdefects, physico-chemical transformations etc. …
On Non-Holonomic Second-Order Connections With Applications To Continua With Microstructure, Marek Elźanowski, Serge Preston
On Non-Holonomic Second-Order Connections With Applications To Continua With Microstructure, Marek Elźanowski, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
Motivated by the theory of uniform elastic structures we try to determine the conditions for the local flatness of locally integrable connections on non-holonomic frame bundles of order 2. Utilizing the results of Yuen as well as our results for the holonomic case, we show that the locally integrable non-holonomic 2-connection is locally flat if, and only if, its projection to the bundle of linear frames is symmetric and the so-called inhomogeneity tensor vanishes. In the last section of this short paper we show how these results can be interpreted in the framework of the theory of uniformity of simple …
The Decay And Formation Of One-Dimensional Nonconservative Shocks, Marek Elźanowski, Marcelo Epstein
The Decay And Formation Of One-Dimensional Nonconservative Shocks, Marek Elźanowski, Marcelo Epstein
Mathematics and Statistics Faculty Publications and Presentations
The method of singular surfaces is used to obtain explicit conditions under which a one-dimensional acceleration wave develops into a shock when some dissipation mechanism is present. The conditions which secure the initial growth of the strong shock wave propagating into an undeformed nonlinear and dissipative medium are also derived. The analysis is pre- sented for a single balance law, one-dimensional elasticity, and the non- linear Maxwellian continuum.