339,772 research outputs found
Genuine converging solution of self-consistent field equations for extended many-electron systems
Calculations of the ground state of inhomogeneous many-electron systems
involve a solving of the Poisson equation for Coulomb potential and the
Schroedinger equation for single-particle orbitals. Due to nonlinearity and
complexity this set of equations, one believes in the iterative method for the
solution that should consist in consecutive improvement of the potential and
the electron density until the self-consistency is attained. Though this
approach exists for a long time there are two grave problems accompanying its
implementation to infinitely extended systems. The first of them is related
with the Poisson equation and lies in possible incompatibility of the boundary
conditions for the potential with the electron density distribution. The
analysis of this difficulty and suggested resolution are presented for both
infinite conducting systems in jellium approximation and periodic solids. It
provides the existence of self-consistent solution for the potential at every
iteration step due to realization of a screening effect. The second problem
results from the existence of continuous spectrum of Hamiltonian eigenvalues
for unbounded systems. It needs to have a definition of Hilbert space basis
with eigenfunctions of continuous spectrum as elements, which would be
convenient in numerical applications. The definition of scalar product
specifying the Hilbert space is proposed that incorporates a limiting
transition. It provides self-adjointness of Hamiltonian and, respectively, the
orthogonality of eigenfunctions corresponding to the different eigenvalues. In
addition, it allows to normalize them effectively to delta-function and to
prove in the general case the orthogonality of the 'right' and 'left'
eigenfunctions belonging to twofold degenerate eigenvalues.Comment: 12 pages. Reported on Interdisciplinary Workshop "Nonequilibrium
Green's Functions III", August 22 - 26, 2005, University Kiel, Germany. To be
published in Journal of Physics: Conference Series, 2006; Typos in Eqs. (37),
(53) and (54) are corrected. The content of the footnote is changed.
Published version available free online at
http://www.iop.org/EJ/abstract/1742-6596/35/1/01
A holistic open-pit mine slope stability index using Artificial Neural Networks
Abstract: The slopes in open-pit mines are typically excavated to the steepest feasible angle to maximize profits. However, there is a greater risk of slope failure associated with steeper slopes. An open-pit slope represents a complex multivariate rock engineering system. Interactions between the factors affecting slope stability in open pit mines are therefore more complex and often difficult to define, impeding the use of conventional methods. To address the problem, the primary role of rock mass structure, in situ stress, water flow, and construction have been extended into 18 key parameters. The stability status of slopes and parameter importance are investigated by means of computational intelligence tools such as Artificial Neural Networks. An optimized Back Propagation network is trained with an extensive database of 141 worldwide case histories of open-pit mines. The inputs refer to the values of extended parameters which include 18 parameters relating to openpit slope stability. The produced output is an estimated potential for instability. To minimize the subjectivity, the method of partitioning the connection weights is applied in order to rate the significance of the involved parameters. The problem of slope stability is therefore modelled as a function approximation. A new Open-pit Mine Slope Stability Index is thus proposed to assess the potential status regime from a holistic point of view. These values are validated by computing the predicted values against the observed status of stability. The reliability of the predictive capability is computed as the Mean Squared Error, and further validated through a Receiver Operating Characteristic curve. Together with a Mean Squared Error of 0.0001, and Receiver Operating Characteristic curve of 98%, the application illustrates that the prediction of slope stability through Artificial Neural Networks produces fast convergence giving reliable predictions, and thus being a useful tool at the preliminary feasibility stage of study
A nested Krylov subspace method to compute the sign function of large complex matrices
We present an acceleration of the well-established Krylov-Ritz methods to
compute the sign function of large complex matrices, as needed in lattice QCD
simulations involving the overlap Dirac operator at both zero and nonzero
baryon density. Krylov-Ritz methods approximate the sign function using a
projection on a Krylov subspace. To achieve a high accuracy this subspace must
be taken quite large, which makes the method too costly. The new idea is to
make a further projection on an even smaller, nested Krylov subspace. If
additionally an intermediate preconditioning step is applied, this projection
can be performed without affecting the accuracy of the approximation, and a
substantial gain in efficiency is achieved for both Hermitian and non-Hermitian
matrices. The numerical efficiency of the method is demonstrated on lattice
configurations of sizes ranging from 4^4 to 10^4, and the new results are
compared with those obtained with rational approximation methods.Comment: 17 pages, 12 figures, minor corrections, extended analysis of the
preconditioning ste
Convergence analysis of Adaptive Biasing Potential methods for diffusion processes
This article is concerned with the mathematical analysis of a family of
adaptive importance sampling algorithms applied to diffusion processes. These
methods, referred to as Adaptive Biasing Potential methods, are designed to
efficiently sample the invariant distribution of the diffusion process, thanks
to the approximation of the associated free energy function (relative to a
reaction coordinate). The bias which is introduced in the dynamics is computed
adaptively; it depends on the past of the trajectory of the process through
some time-averages.
We give a detailed and general construction of such methods. We prove the
consistency of the approach (almost sure convergence of well-chosen weighted
empirical probability distribution). We justify the efficiency thanks to
several qualitative and quantitative additional arguments. To prove these
results , we revisit and extend tools from stochastic approximation applied to
self-interacting diffusions, in an original context
Extended First-Principles Molecular Dynamics Method From Cold Materials to Hot Dense Plasmas
An extended first-principles molecular dynamics (FPMD) method based on
Kohn-Sham scheme is proposed to elevate the temperature limit of the FPMD
method in the calculation of dense plasmas. The extended method treats the wave
functions of high energy electrons as plane waves analytically, and thus
expands the application of the FPMD method to the region of hot dense plasmas
without suffering from the formidable computational costs. In addition, the
extended method inherits the high accuracy of the Kohn-Sham scheme and keeps
the information of elec- tronic structures. This gives an edge to the extended
method in the calculation of the lowering of ionization potential, X-ray
absorption/emission spectra, opacity, and high-Z dense plasmas, which are of
particular interest to astrophysics, inertial confinement fusion engineering,
and laboratory astrophysics
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