The Kohn Sham Equation For Deformed Crystals
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The Kohn Sham Equation For Deformed Crystals
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Author : Weinan E
language : en
Publisher:
Release Date : 2012
The Kohn Sham Equation For Deformed Crystals written by Weinan E and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Deformations (Mechanics) categories.
The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, we also establish a number of fundamental properties of the Kohn-Sham map.
The Kohn Sham Equation For Deformed Crystals
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Author : Weinan E
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-01-25
The Kohn Sham Equation For Deformed Crystals written by Weinan E and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-25 with Mathematics categories.
The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.
The Sine Gordon Equation In The Semiclassical Limit Dynamics Of Fluxon Condensates
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Author : Robert J. Buckingham
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-23
The Sine Gordon Equation In The Semiclassical Limit Dynamics Of Fluxon Condensates written by Robert J. Buckingham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Mathematics categories.
The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
A Complete Classification Of The Isolated Singularities For Nonlinear Elliptic Equations With Inverse Square Potentials
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Author : Florica C. Cîrstea
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-08
A Complete Classification Of The Isolated Singularities For Nonlinear Elliptic Equations With Inverse Square Potentials written by Florica C. Cîrstea and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.
Global Regularity For The Yang Mills Equations On High Dimensional Minkowski Space
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Author : Joachim Krieger
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-22
Global Regularity For The Yang Mills Equations On High Dimensional Minkowski Space written by Joachim Krieger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on $(6+1)$ and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space $\dot{H}_A^{(n-4)/{2}}$. Regularity is obtained through a certain ``microlocal geometric renormalization'' of the equations which is implemented via a family of approximate null Cronstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.
Strange Attractors For Periodically Forced Parabolic Equations
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Author : Kening Lu
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-28
Strange Attractors For Periodically Forced Parabolic Equations written by Kening Lu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-28 with Mathematics categories.
The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.
Elliptic Partial Differential Equations With Almost Real Coefficients
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Author : Ariel Barton
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-22
Elliptic Partial Differential Equations With Almost Real Coefficients written by Ariel Barton and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. He shows that for such operators, the Dirichlet problem with boundary data in $L^q$ can be solved for $q1$ small enough, and provide an endpoint result at $p=1$.
Kuznetsov S Trace Formula And The Hecke Eigenvalues Of Maass Forms
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Author : Andrew Knightly
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-28
Kuznetsov S Trace Formula And The Hecke Eigenvalues Of Maass Forms written by Andrew Knightly and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-28 with Mathematics categories.
The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.
Weighted Bergman Spaces Induced By Rapidly Increasing Weights
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Author : Jose Angel Pelaez
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-01-08
Weighted Bergman Spaces Induced By Rapidly Increasing Weights written by Jose Angel Pelaez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-08 with Mathematics categories.
Relative Equilibria In The 3 Dimensional Curved N Body Problem
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Author : Florin Diacu
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-03-05
Relative Equilibria In The 3 Dimensional Curved N Body Problem written by Florin Diacu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-05 with Mathematics categories.