The Kohn-Sham Equation for Deformed Crystals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Kohn-Sham Equation for Deformed Crystals write by Weinan E. This book was released on 2013-01-25. The Kohn-Sham Equation for Deformed Crystals available in PDF, EPUB and Kindle. 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 Kohn-Sham Equation for Deformed Crystals
The Kohn-Sham Equation for Deformed Crystals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Kohn-Sham Equation for Deformed Crystals write by Weinan E. This book was released on 2012. The Kohn-Sham Equation for Deformed Crystals available in PDF, EPUB and Kindle. 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.
Density Functional Theory
Density Functional Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Density Functional Theory write by Eric Cancès. This book was released on 2023-07-18. Density Functional Theory available in PDF, EPUB and Kindle. Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.
The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates
The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates write by Robert J. Buckingham. This book was released on 2013-08-23. The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates available in PDF, EPUB and Kindle. 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
A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials write by Florica C. Cîrstea. This book was released on 2014-01-08. A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials available in PDF, EPUB and Kindle. In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.
