5,491 research outputs found
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
An Equation-Free Approach for Second Order Multiscale Hyperbolic Problems in Non-Divergence Form
The present study concerns the numerical homogenization of second order
hyperbolic equations in non-divergence form, where the model problem includes a
rapidly oscillating coefficient function. These small scales influence the
large scale behavior, hence their effects should be accurately modelled in a
numerical simulation. A direct numerical simulation is prohibitively expensive
since a minimum of two points per wavelength are needed to resolve the small
scales. A multiscale method, under the equation free methodology, is proposed
to approximate the coarse scale behaviour of the exact solution at a cost
independent of the small scales in the problem. We prove convergence rates for
the upscaled quantities in one as well as in multi-dimensional periodic
settings. Moreover, numerical results in one and two dimensions are provided to
support the theory
Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory
Linear-response time-dependent (TD) density-functional theory (DFT) has been
implemented in the pseudopotential wavelet-based electronic structure program
BigDFT and results are compared against those obtained with the all-electron
Gaussian-type orbital program deMon2k for the calculation of electronic
absorption spectra of N2 using the TD local density approximation (LDA). The
two programs give comparable excitation energies and absorption spectra once
suitably extensive basis sets are used. Convergence of LDA density orbitals and
orbital energies to the basis-set limit is significantly faster for BigDFT than
for deMon2k. However the number of virtual orbitals used in TD-DFT calculations
is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT
calculations in deMon2k. As a reality check, we report the x-ray crystal
structure and the measured and calculated absorption spectrum (excitation
energies and oscillator strengths) of the small organic molecule
N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1,2-a]pyridin-3-amine
Institute for Computational Mechanics in Propulsion (ICOMP)
The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described
Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a
base for the construction of conformally invariant quantum (field) theory,
either as phase or configuration spaces. We follow a gauge-invariant Lagrangian
approach (of nonlinear sigma-model type) and use a generalized Dirac method for
the quantization of constrained systems, which resembles in some aspects the
standard approach to quantizing coadjoint orbits of a group G. Physical wave
functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels
are explicitly calculated in and holomorphic picture in these Cartan domains
for both scalar and spinning quantum particles. Similarities and differences
with other results in the literature are also discussed and an extension of
Schwinger's Master Theorem is commented in connection with closure relations.
An adaptation of the Born's Reciprocity Principle (BRP) to the conformal
relativity, the replacement of space-time by the 8-dimensional conformal domain
at short distances and the existence of a maximal acceleration are also put
forward.Comment: 33 pages, no figures, LaTe
Human boday damage analysis by SPH method
In order to evaluate the biological properties of a human head response at impacts accidents, authors
have been developing the SPH (Smooth Particle Hydrodynamics) particle model of the whole human head and analyzing dynamically in simulating high velocity impact accident. In this report, authors have shown how to make a particle model of a head from real CT scan images directly and how to render the model in computer graphics using GPU and the algorithm for elastic-plastic analysis of a head model. The results from the simulations could explain one of injury mechanisms of a human head in actual car accidents
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