24,054 research outputs found
Matrices coupled in a chain. I. Eigenvalue correlations
The general correlation function for the eigenvalues of complex hermitian
matrices coupled in a chain is given as a single determinant. For this we use a
slight generalization of a theorem of Dyson.Comment: ftex eynmeh.tex, 2 files, 8 pages Submitted to: J. Phys.
Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature
This investigation extends earlier studies of a shear-transformation-zone
(STZ) theory of plastic deformation in amorphous solids. My main purpose here
is to explore the possibility that the configurational degrees of freedom of
such systems fall out of thermodynamic equilibrium with the heat bath during
persistent mechanical deformation, and that the resulting state of
configurational disorder may be characterized by an effective temperature. The
further assumption that the population of STZ's equilibrates with the effective
temperature allows the theory to be compared directly with experimentally
measured properties of metallic glasses, including their calorimetric behavior.
The coupling between the effective temperature and mechanical deformation
suggests an explanation of shear-banding instabilities.Comment: 29 pages, 11 figure
Cover-Encodings of Fitness Landscapes
The traditional way of tackling discrete optimization problems is by using
local search on suitably defined cost or fitness landscapes. Such approaches
are however limited by the slowing down that occurs when the local minima that
are a feature of the typically rugged landscapes encountered arrest the
progress of the search process. Another way of tackling optimization problems
is by the use of heuristic approximations to estimate a global cost minimum.
Here we present a combination of these two approaches by using cover-encoding
maps which map processes from a larger search space to subsets of the original
search space. The key idea is to construct cover-encoding maps with the help of
suitable heuristics that single out near-optimal solutions and result in
landscapes on the larger search space that no longer exhibit trapping local
minima. We present cover-encoding maps for the problems of the traveling
salesman, number partitioning, maximum matching and maximum clique; the
practical feasibility of our method is demonstrated by simulations of adaptive
walks on the corresponding encoded landscapes which find the global minima for
these problems.Comment: 15 pages, 4 figure
Glassy dynamics in granular compaction
Two models are presented to study the influence of slow dynamics on granular
compaction. It is found in both cases that high values of packing fraction are
achieved only by the slow relaxation of cooperative structures. Ongoing work to
study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter,
proceedings of the Trieste workshop on 'Unifying concepts in glass physics
Decision blocks: A tool for automating decision making in CLIPS
The human capability of making complex decision is one of the most fascinating facets of human intelligence, especially if vague, judgemental, default or uncertain knowledge is involved. Unfortunately, most existing rule based forward chaining languages are not very suitable to simulate this aspect of human intelligence, because of their lack of support for approximate reasoning techniques needed for this task, and due to the lack of specific constructs to facilitate the coding of frequently reoccurring decision block to provide better support for the design and implementation of rule based decision support systems. A language called BIRBAL, which is defined on the top of CLIPS, for the specification of decision blocks, is introduced. Empirical experiments involving the comparison of the length of CLIPS program with the corresponding BIRBAL program for three different applications are surveyed. The results of these experiments suggest that for decision making intensive applications, a CLIPS program tends to be about three times longer than the corresponding BIRBAL program
Glassy states in a shaken sandbox
Our model of shaken sand, presented in earlier work, has been extended to
include a more realistic `glassy' state, i.e., when the sandbox is shaken at
very low intensities of vibration. We revisit some of our earlier results, and
compare them with our new results on the revised model. Our analysis of the
glassy dynamics in our model shows that a variety of ground states is obtained;
these fall in two categories, which we argue are representative of regular and
irregular packings.Comment: 10 pages. 3 figures. To appear in Proceedings of Research Workshop on
"Challenges in Granular Physics" (ICTP, Trieste, August 7-11, 2001). Special
issue of Advances in Complex System
Universal features of spin transport and breaking of unitary symmetries
When time-reversal symmetry is broken, quantum coherent systems with and without spin rotational symmetry exhibit the same universal behavior in their electric transport properties. We show that spin transport discriminates between these two cases. In systems with large charge conductance, spin transport is essentially insensitive to the breaking of time-reversal symmetry, while in the opposite limit of a single exit transport channel, spin currents vanish identically in the presence of time-reversal symmetry but can be turned on by breaking it with an orbital magnetic field
Random Matrices with Correlated Elements: A Model for Disorder with Interactions
The complicated interactions in presence of disorder lead to a correlated
randomization of states. The Hamiltonian as a result behaves like a
multi-parametric random matrix with correlated elements. We show that the
eigenvalue correlations of these matrices can be described by the single
parametric Brownian ensembles. The analogy helps us to reveal many important
features of the level-statistics in interacting systems e.g. a critical point
behavior different from that of non-interacting systems, the possibility of
extended states even in one dimension and a universal formulation of level
correlations.Comment: 19 Pages, No Figures, Major Changes to Explain the Mathematical
Detail
Finite-difference distributions for the Ginibre ensemble
The Ginibre ensemble of complex random matrices is studied. The complex
valued random variable of second difference of complex energy levels is
defined. For the N=3 dimensional ensemble are calculated distributions of
second difference, of real and imaginary parts of second difference, as well as
of its radius and of its argument (angle). For the generic N-dimensional
Ginibre ensemble an exact analytical formula for second difference's
distribution is derived. The comparison with real valued random variable of
second difference of adjacent real valued energy levels for Gaussian
orthogonal, unitary, and symplectic, ensemble of random matrices as well as for
Poisson ensemble is provided.Comment: 8 pages, a number of small changes in the tex
Competition and cooperation:aspects of dynamics in sandpiles
In this article, we review some of our approaches to granular dynamics, now
well known to consist of both fast and slow relaxational processes. In the
first case, grains typically compete with each other, while in the second, they
cooperate. A typical result of {\it cooperation} is the formation of stable
bridges, signatures of spatiotemporal inhomogeneities; we review their
geometrical characteristics and compare theoretical results with those of
independent simulations. {\it Cooperative} excitations due to local density
fluctuations are also responsible for relaxation at the angle of repose; the
{\it competition} between these fluctuations and external driving forces, can,
on the other hand, result in a (rare) collapse of the sandpile to the
horizontal. Both these features are present in a theory reviewed here. An arena
where the effects of cooperation versus competition are felt most keenly is
granular compaction; we review here a random graph model, where three-spin
interactions are used to model compaction under tapping. The compaction curve
shows distinct regions where 'fast' and 'slow' dynamics apply, separated by
what we have called the {\it single-particle relaxation threshold}. In the
final section of this paper, we explore the effect of shape -- jagged vs.
regular -- on the compaction of packings near their jamming limit. One of our
major results is an entropic landscape that, while microscopically rough,
manifests {\it Edwards' flatness} at a macroscopic level. Another major result
is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction
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