441 research outputs found
Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis
Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure
Non-Hermitian Localization in Biological Networks
We explore the spectra and localization properties of the N-site banded
one-dimensional non-Hermitian random matrices that arise naturally in sparse
neural networks. Approximately equal numbers of random excitatory and
inhibitory connections lead to spatially localized eigenfunctions, and an
intricate eigenvalue spectrum in the complex plane that controls the
spontaneous activity and induced response. A finite fraction of the eigenvalues
condense onto the real or imaginary axes. For large N, the spectrum has
remarkable symmetries not only with respect to reflections across the real and
imaginary axes, but also with respect to 90 degree rotations, with an unusual
anisotropic divergence in the localization length near the origin. When chains
with periodic boundary conditions become directed, with a systematic
directional bias superimposed on the randomness, a hole centered on the origin
opens up in the density-of-states in the complex plane. All states are extended
on the rim of this hole, while the localized eigenvalues outside the hole are
unchanged. The bias dependent shape of this hole tracks the bias independent
contours of constant localization length. We treat the large-N limit by a
combination of direct numerical diagonalization and using transfer matrices, an
approach that allows us to exploit an electrostatic analogy connecting the
"charges" embodied in the eigenvalue distribution with the contours of constant
localization length. We show that similar results are obtained for more
realistic neural networks that obey "Dale's Law" (each site is purely
excitatory or inhibitory), and conclude with perturbation theory results that
describe the limit of large bias g, when all states are extended. Related
problems arise in random ecological networks and in chains of artificial cells
with randomly coupled gene expression patterns
Quantum Speed Limit for Perfect State Transfer in One Dimension
The basic idea of spin chain engineering for perfect quantum state transfer
(QST) is to find a set of coupling constants in the Hamiltonian, such that a
particular state initially encoded on one site will evolve freely to the
opposite site without any dynamical controls. The minimal possible evolution
time represents a speed limit for QST. We prove that the optimal solution is
the one simulating the precession of a spin in a static magnetic field. We also
argue that, at least for solid-state systems where interactions are local, it
is more realistic to characterize the computation power by the couplings than
the initial energy.Comment: 5 pages, no figure; improved versio
The NASTRAN theoretical manual
Designed to accommodate additions and modifications, this commentary on NASTRAN describes the problem solving capabilities of the program in a narrative fashion and presents developments of the analytical and numerical procedures that underlie the program. Seventeen major sections and numerous subsections cover; the organizational aspects of the program, utility matrix routines, static structural analysis, heat transfer, dynamic structural analysis, computer graphics, special structural modeling techniques, error analysis, interaction between structures and fluids, and aeroelastic analysis
Small amplitude lateral sloshing in a cylindrical tank with a hemispherical bottom under low gravitational conditions Summary report
Small amplitude lateral sloshing in cylindrical tank with hemispherical bottom under low gravitational condition
Single particle calculations for a Woods-Saxon potential with triaxial deformations, and large Cartesian oscillator basis
We present a computer program which solves the Schrodinger equation of the
stationary states for an average nuclear potential of Woods-Saxon type. In this
work, we take specifically into account triaxial (i.e. ellipsoidal) nuclear
surfaces. The deformation is specified by the usual Bohr parameters. The
calculations are carried out in two stages. In the first, one calculates the
representative matrix of the Hamiltonian in the cartesian oscillator basis. In
the second stage one diagonalizes this matrix with the help of subroutines of
the EISPACK library. If it is wished, one can calculate all eigenvalues, or
only the part of the eigenvalues that are contained in a fixed interval defined
in advance. In this latter case the eigenvectors are given conjointly. The
program is very rapid, and the run-time is mainly used for the diagonalization.
Thus, it is possible to use a significant number of the basis states in order
to insure a best convergence of the results.Comment: no figures, but tbles in separate pdf file
Matrix geometric approach for random walks: stability condition and equilibrium distribution
In this paper, we analyse a sub-class of two-dimensional homogeneous nearest
neighbour (simple) random walk restricted on the lattice using the matrix
geometric approach. In particular, we first present an alternative approach for
the calculation of the stability condition, extending the result of Neuts drift
conditions [30] and connecting it with the result of Fayolle et al. which is
based on Lyapunov functions [13]. Furthermore, we consider the sub-class of
random walks with equilibrium distributions given as series of product-forms
and, for this class of random walks, we calculate the eigenvalues and the
corresponding eigenvectors of the infinite matrix appearing in the
matrix geometric approach. This result is obtained by connecting and extending
three existing approaches available for such an analysis: the matrix geometric
approach, the compensation approach and the boundary value problem method. In
this paper, we also present the spectral properties of the infinite matrix
- …