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277 results on '"Nigam, Nilima"'

57. Korn's inequality and Jones eigenpairs

Author

Dom��nguez, Sebasti��n and Nigam, Nilima

Subjects
Mathematics - Analysis of PDEs, 47A75, 74B05, 74F10, FOS: Mathematics, Analysis of PDEs (math.AP)
Abstract

In this paper we show that Korn's inequality \cite{ref:korn1906} holds for vector fields with a zero normal or tangential trace on a subset (of positive measure) of the boundary of Lipschitz domains. We further show that the validity of this inequality depends on the geometry of this subset of the boundary. We then consider the {\it Jones eigenvalue problem} which consists of the usual traction eigenvalue problem for the Lam\'e operator for linear elasticity coupled with a zero normal trace of the displacement on a non-empty part of the boundary. Here we extend previous works in the literature to show the Jones eigenpairs exist on a broad variety of domains even when the normal trace of the displacement is constrained only on a subset of the boundary. We further show that one can have eigenpairs of a modified eigenproblem in which the constraint on the normal trace on a subset of the boundary is replaced by one on the tangential trace.

Published
2019

67. Numerical Integration for High Order Pyramidal Elements

Author

Nigam, Nilima and Phillips, Joel

Abstract

We examine the effect of numerical integration on the accuracy of high order conformingpyramidal finite element methods. Non-smooth shape functions are indispensable to the construction ofpyramidal elements, and this means the conventional treatment of numerical integration, which requiresthat the finite element approximation space is piecewise polynomial, cannot be applied. We developan analysis that allows the finite element approximation space to include non-smooth functions andshow that, despite this complication, conventional rules of thumb can still be used to select appropriatequadrature methods on pyramids. Along the way, we present a new family of high order pyramidalfinite elements for each of the spaces of the de Rham complex.

Published
2011

69. An integral representation of the Green’s function for a linear array of acoustic point sources

Author

Nigam, Nilima, Kurkcu, Harun, and Reitich, Fernando

Abstract

We present a new algorithm for the evaluation of the periodized Green’s function fora linear array of acoustic point sources such as those arising in the analysis of linearray loudspeakers. A variety of classical algorithms (based on spatial and spectralrepresentations, Ewald transformation, etc.) have been implemented in the past toevaluate these acoustic fields. However as we show, these methods become unstableand/or impractically expensive as the frequency of use of the sources increases. Herewe introduce a new numerical scheme that overcomes some of these limitations allowingfor simulations at unprecedentally large frequencies. The method is based ona new integral representation derived from the classic spatial form, and on suitablefurther manipulations of the relevant integrands to render the integrals amenable toefficient and accurate approximations through standard quadrature formulas. Weinclude a variety of numerical results that demonstrate that our algorithm comparesfavorably with several classical method both for points close to the line where thepoles are located and at high-frequencies while remaining competitive with them inevery other instance.

Published
2010

74. Preface

Author

Gatica, Gabriel N., primary, Pamela Cook, L., additional, Jordan, Kirk E., additional, Nigam, Nilima, additional, Steinbach, Olaf, additional, and Xu, Liwei, additional

Published
2012
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82. Vortex Kelvin Modes with Nonlinear Critical Layers.

Author

Gladwell, G. M. L., Moreau, R., Borisov, Alexey V., Kozlov, Valery V., Mamaev, Ivan S., Sokolovskiy, Mikhail A., Maslowe, Sherwin A., and Nigam, Nilima

Abstract

When helical neutral modes propagate on a vortex with a continuous velocity profile the inviscid equation governing linear stability theory may have a singular critical point at some value of r, the radial coordinate. Viscosity or temporal evolution can be restored locally to treat the critical layer centered on this singular point. Nonlinearity, however, is a more appropriate choice in applications where the Reynolds number is large. The associated theory is outlined in this paper and new solutions to the eigenvalue problem are presented. [ABSTRACT FROM AUTHOR]

Published
2008
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83. Regionalizing muscle activity causes changes to the magnitude and direction of the force from whole muscles—a modeling study.

Author

Rahemi, Hadi, Nigam, Nilima, and Wakeling, James M.

Subjects
MUSCULOSKELETAL system physiology, NEUROMUSCULAR diseases, NEUROSES, SKELETAL muscle physiology, ABDOMINAL muscles
Abstract

Skeletal muscle can contain neuromuscular compartments that are spatially distinct regions that can receive relatively independent levels of activation. This study tested how the magnitude and direction of the force developed by a whole muscle would change when the muscle activity was regionalized within the muscle. A 3D finite element model of a muscle with its bounding aponeurosis was developed for the lateral gastrocnemius, and isometric contractions were simulated for a series of conditions with either a uniform activation pattern, or regionally distinct activation patterns: in all cases the mean activation from all fibers within the muscle reached 10%. The models showed emergent features of the fiber geometry that matched physiological characteristics: with fibers shortening, rotating to greater pennation, adopting curved trajectories in 3D and changes in the thickness and width of the muscle belly. Simulations were repeated for muscle with compliant, normal and stiff aponeurosis and the aponeurosis stiffness affected the changes to the fiber geometry and the resultant muscle force. Changing the regionalization of the activity resulted to changes in the magnitude, direction and center of the force vector from the whole muscle. Regionalizing the muscle activity resulted in greater muscle force than the simulation with uniform activity across the muscle belly. The study shows how the force from a muscle depends on the complex interactions between the muscle fibers and connective tissues and the region of muscle that is active. [ABSTRACT FROM AUTHOR]

Published
2014
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84. Reader Corner.

Author

NIGAM, NILIMA and MURIAN, RICHARD

Subjects
*FORUMS, *COLLEGE teachers
Published
2023

85. High-order conforming finite elements on pyramids.

Author

Nigam, Nilima and Phillips, Joel

Subjects
TETRAHEDRA, FINITE element method, NUMERICAL analysis, POLYNOMIALS, ALGEBRA, APPROXIMATION theory
Abstract

Pyramids—with one quadrilateral and four triangular faces—appear as `glueing' elements in a hybrid mesh consisting of tetrahedral and hexahedral elements. High-order discrete differential forms on tetrahedral and hexahedral elements are well known, but the analogous elements on a pyramid are not. How does one construct high-order approximation spaces on pyramids that are compatible with neighbouring elements? We address this question in this paper. We present a family of high-order finite element approximation spaces on a pyramid and associated unisolvent degrees of freedom. These spaces consist of rational basis functions. We establish conforming, exactness and polynomial approximation properties of these new finite elements. [ABSTRACT FROM PUBLISHER]

Published
2012
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86. How large can the first eigenvalue be on a surface of genus two?

Author

Jakobson, Dmitry, Levitin, Michael, Nadirashvili, Nikolai, Nigam, Nilima, and Polterovich, Iosif

Subjects
EIGENVALUES, LAPLACIAN matrices, GEOMETRIC surfaces, BOUNDARY value problems, LOGICAL prediction
Abstract

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case, and conjecture that the first eigenvalue is maximized on a singular surface which is realized as a double branched covering over a sphere. The six ramification points are chosen in such a way that this surface has a complex structure of the Bolza surface. We prove that our conjecture follows from a lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann boundary value problem on a half-disk. The latter can be studied numerically, and we present conclusive evidence supporting the conjecture. [ABSTRACT FROM AUTHOR]

Published
2005
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87. Numerical integration for high order pyramidal finite elements

Author

Nigam, Nilima and Phillips, Joel

Abstract

We examine the effect of numerical integration on the accuracy of high order conforming pyramidal finite element methods. Non-smooth shape functions are indispensable to the construction of pyramidal elements, and this means the conventional treatment of numerical integration, which requires that the finite element approximation space is piecewise polynomial, cannot be applied. We develop an analysis that allows the finite element approximation space to include non-smooth functions and show that, despite this complication, conventional rules of thumb can still be used to select appropriate quadrature methods on pyramids. Along the way, we present a new family of high order pyramidal finite elements for each of the spaces of the de Rham complex.

Published
2012
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88. Shallow Water Models and Their Analytical Properties

Author

Cheviakov, Alexei, Zhao, Peng, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Cheviakov, Alexei, and Zhao, Peng

Published
2024
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89. Integrability and Other Analytical Properties of Nonlinear PDE Systems

Author

Cheviakov, Alexei, Zhao, Peng, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Cheviakov, Alexei, and Zhao, Peng

Published
2024
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90. Equations of Fluid Dynamics and the Shallow Water Approximation

Author

Cheviakov, Alexei, Zhao, Peng, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Cheviakov, Alexei, and Zhao, Peng

Published
2024
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91. Arens regularity

Author

Dales, Harold Garth, Ülger, Ali, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Dales, Harold Garth, and Ülger, Ali

Published
2024
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92. Banach algebras

Author

Dales, Harold Garth, Ülger, Ali, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Dales, Harold Garth, and Ülger, Ali

Published
2024
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93. Banach algebras on locally compact groups

Author

Dales, Harold Garth, Ülger, Ali, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Dales, Harold Garth, and Ülger, Ali

Published
2024
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94. BSE norms and BSE algebras

Author

Dales, Harold Garth, Ülger, Ali, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Dales, Harold Garth, and Ülger, Ali

Published
2024
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95. Banach function algebras

Author

Dales, Harold Garth, Ülger, Ali, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Dales, Harold Garth, and Ülger, Ali

Published
2024
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96. Banach spaces and operators

Author

Dales, Harold Garth, Ülger, Ali, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, Dales, Harold Garth, and Ülger, Ali

Published
2024
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97. Annex

Author

Novruzi, Arian, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, and Novruzi, Arian

Published
2023
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98. Second-order parabolic and hyperbolic PDEs

Author

Novruzi, Arian, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, and Novruzi, Arian

Published
2023
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99. Second-order linear elliptic PDEs: maximum principle and classical solutions

Author

Novruzi, Arian, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, and Novruzi, Arian

Published
2023
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100. Distributions

Author

Novruzi, Arian, Dilcher, Karl, Series Editor, Lutscher, Frithjof, Series Editor, Nigam, Nilima, Series Editor, Taylor, Keith, Series Editor, Adcock, Ben, Associate Editor, Barlow, Martin, Associate Editor, Bauschke, Heinz H., Associate Editor, Davison, Matt, Associate Editor, Keshet, Leah, Associate Editor, Kamran, Niky, Associate Editor, Kotchetov, Mikhail, Associate Editor, Spiteri, Raymond J., Associate Editor, and Novruzi, Arian

Published
2023
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