2,001 research outputs found
Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics
This paper is devoted to estimates of the exponential decay of eigenfunctions
of difference operators on the lattice Z^n which are discrete analogs of the
Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our
investigation of the essential spectra and the exponential decay of
eigenfunctions of the discrete spectra is based on the calculus of so-called
pseudodifference operators (i.e., pseudodifferential operators on the group
Z^n) with analytic symbols and on the limit operators method. We obtain a
description of the location of the essential spectra and estimates of the
eigenfunctions of the discrete spectra of the main lattice operators of quantum
mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on
Z^3, and square root Klein-Gordon operators on Z^n
Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition
Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e(N-1)!, i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output
Coarsening in potential and nonpotential models of oblique stripe patterns
We study the coarsening of two-dimensional oblique stripe patterns by
numerically solving potential and nonpotential anisotropic Swift-Hohenberg
equations. Close to onset, all models exhibit isotropic coarsening with a
single characteristic length scale growing in time as . Further from
onset, the characteristic lengths along the preferred directions and
grow with different exponents, close to 1/3 and 1/2, respectively. In
this regime, one-dimensional dynamical scaling relations hold. We draw an
analogy between this problem and Model A in a stationary, modulated external
field. For deep quenches, nonpotential effects produce a complicated
dislocation dynamics that can lead to either arrested or faster-than-power-law
growth, depending on the model considered. In the arrested case, small isolated
domains shrink down to a finite size and fail to disappear. A comparison with
available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.
The 2004 Sumatra tsunami as recorded on the Atlantic coast of South America
The 2004 Sumatra tsunami propagated throughout the World Ocean and was clearly recorded by tide gauges on the Atlantic coast of South America. A total of 17 tsunami records were found and subsequently examined for this region. Tsunami wave heights and arrival times are generally consistent with numerical modeling results. Maximum wave heights of more than 1.2 m were observed on the coasts of Uruguay and southeastern Brazil. Marked differences in tsunami height from pairs of closely located tide gauge sites on the coast of Argentina illustrate the importance that local topographic resonance effects can have on the observed wave response. Findings reveal that, outside the Indian Ocean, the highest waves were recorded in the South Atlantic and not in the Pacific as has been previously suggested
Interface-Induced Plasmon Nonhomogeneity in Nanostructured Metal-Dielectric Planar Metamaterial
Transformations of the electronic structure in thin silver layers in metal-dielectric (TiAlN/Ag) multilayer nanocomposite were investigated by a set of electron spectroscopy techniques. Localization of the electronic states in the valence band and reduction of electron concentration in the conduction band was observed. This led to decreasing metallic properties of silver in the thin films. A critical layer thickness of 23.5 nm associated with the development of quantum effects was determined by X-ray photoelectron spectroscopy. Scanning Auger electron microscopy of characteristic energy losses provided images of plasmon localization in the Ag layers. The nonuniformity of plasmon intensities distribution near the metal-nitride interfaces was assessed experimentally
Routing with Congestion in Acyclic Digraphs
We study the version of the -disjoint paths problem where demand pairs
, , are specified in the input and the paths in
the solution are allowed to intersect, but such that no vertex is on more than
paths. We show that on directed acyclic graphs the problem is solvable in
time if we allow congestion for paths. Furthermore, we
show that, under a suitable complexity theoretic assumption, the problem cannot
be solved in time for any computable function
Cyclic Statistics In Three Dimensions
While 2-dimensional quantum systems are known to exhibit non-permutation,
braid group statistics, it is widely expected that quantum statistics in
3-dimensions is solely determined by representations of the permutation group.
This expectation is false for certain 3-dimensional systems, as was shown by
the authors of ref. [1,2,3]. In this work we demonstrate the existence of
``cyclic'', or , {\it non-permutation group} statistics for a system of n
> 2 identical, unknotted rings embedded in . We make crucial use of a
theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch
relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin
Essential spectra of difference operators on \sZ^n-periodic graphs
Let (\cX, \rho) be a discrete metric space. We suppose that the group
\sZ^n acts freely on and that the number of orbits of with respect to
this action is finite. Then we call a \sZ^n-periodic discrete metric
space. We examine the Fredholm property and essential spectra of band-dominated
operators on where is a \sZ^n-periodic discrete metric space.
Our approach is based on the theory of band-dominated operators on \sZ^n and
their limit operators.
In case is the set of vertices of a combinatorial graph, the graph
structure defines a Schr\"{o}dinger operator on in a natural way. We
illustrate our approach by determining the essential spectra of Schr\"{o}dinger
operators with slowly oscillating potential both on zig-zag and on hexagonal
graphs, the latter being related to nano-structures
A Simple Theory of Condensation
A simple assumption of an emergence in gas of small atomic clusters
consisting of particles each, leads to a phase separation (first order
transition). It reveals itself by an emergence of ``forbidden'' density range
starting at a certain temperature. Defining this latter value as the critical
temperature predicts existence of an interval with anomalous heat capacity
behaviour . The value suggested in literature
yields the heat capacity exponent .Comment: 9 pages, 1 figur
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
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