2,191 research outputs found
Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
Symmetric hyperbolic systems of equations are explicitly constructed for a
general class of tensor fields by considering their structure as r-fold forms.
The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance
of the so-called "superenergy" tensors, which provide the necessary symmetric
positive matrices, is emphasized and made explicit. Thereby, a unified
treatment of many physical systems is achieved, as well as of the sometimes
called "higher order" systems. The characteristics of these symmetric
hyperbolic systems are always physical, and directly related to the null
directions of the superenergy tensor, which are in particular principal null
directions of the tensor field solutions. Generic energy estimates and
inequalities are presented too.Comment: 24 pages, no figure
Attention mechanisms in the CHREST cognitive architecture
In this paper, we describe the attention mechanisms in CHREST, a computational architecture of human visual expertise. CHREST organises information acquired by direct experience from the world in the form of chunks. These chunks are searched for, and verified, by a unique set of heuristics, comprising the attention mechanism. We explain how the attention mechanism combines bottom-up and top-down heuristics from internal and external sources of information. We describe some experimental evidence demonstrating the correspondence of CHRESTâs perceptual mechanisms with those of human subjects. Finally, we discuss how visual attention can play an important role in actions carried out by human experts in domains such as chess
Long-time behavior of an angiogenesis model with flux at the tumor boundary
This paper deals with a nonlinear system of partial differential equations
modeling a simplified tumor-induced angiogenesis taking into account only the
interplay between tumor angiogenic factors and endothelial cells. Considered
model assumes a nonlinear flux at the tumor boundary and a nonlinear
chemotactic response. It is proved that the choice of some key parameters
influences the long-time behaviour of the system. More precisely, we show the
convergence of solutions to different semi-trivial stationary states for
different range of parameters.Comment: 17 page
Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
The localization lengths of long-range correlated disordered chains are
studied for electronic wavefunctions in the Anderson model and for vibrational
states. A scaling theory close to the band edge is developed in the Anderson
model and supported by numerical simulations. This scaling theory is mapped
onto the vibrational case at small frequencies. It is shown that for small
frequencies, unexpectateley the localization length is smaller for correlated
than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure
Anisotropic two-dimensional Heisenberg model by Schwinger-boson Gutzwiller projected method
Two-dimensional Heisenberg model with anisotropic couplings in the and
directions () is considered. The model is first solved in the
Schwinger-boson mean-field approximation. Then the solution is Gutzwiller
projected to satisfy the local constraint that there is only one boson at each
site. The energy and spin-spin correlation of the obtained wavefunction are
calculated for systems with up to sites by means of the
variational Monte Carlo simulation. It is shown that the antiferromagnetic
long-range order remains down to the one-dimensional limit.Comment: 15 pages RevTex3.0, 4 figures, available upon request, GWRVB8-9
Generic theory of colloidal transport
We discuss the motion of colloidal particles relative to a two component
fluid consisting of solvent and solute. Particle motion can result from (i) net
body forces on the particle due to external fields such as gravity; (ii) slip
velocities on the particle surface due to surface dissipative phenomena. The
perturbations of the hydrodynamic flow field exhibits characteristic
differences in cases (i) and (ii) which reflect different patterns of momentum
flux corresponding to the existence of net forces, force dipoles or force
quadrupoles. In the absence of external fields, gradients of concentration or
pressure do not generate net forces on a colloidal particle. Such gradients can
nevertheless induce relative motion between particle and fluid. We present a
generic description of surface dissipative phenomena based on the linear
response of surface fluxes driven by conjugate surface forces. In this
framework we discuss different transport scenarios including self-propulsion
via surface slip that is induced by active processes on the particle surface.
We clarify the nature of force balances in such situations.Comment: 22 pages, 1 figur
Defect and anisotropic gap induced quasi-one-dimensional modulation of local density of states in YBaCuO
Motivated by recent angle-resolved photoemission spectroscopy (ARPES)
measurement that superconducting YBaCuO (YBCO) exhibits a
-symmetry gap, we show possible quasi-one-dimensional
modulations of local density of states in YBCO. These aniostropic gap and
defect induced stripe structures are most conspicuous at higher biases and
arise due to the nesting effect associated with a Fermi liquid. Observation of
these spectra by scanning tunneling microscopy (STM) would unify the picture
among STM, ARPES, and inelastic neutron scattering for YBCO.Comment: 4 pages, 4 figure
Transverse optical Josephson plasmons, equations of motion
A detailed calculation is presented of the dielectric function in
superconducttors consisting of two Josephson coupled superconducting layers per
unit cell, taking into account the effect of finite compressibility of the
electron fluid. From the model it follows, that two longitudinal, and one
transverse optical Josephson plasma resonance exist in these materials, for
electric field polarization perpendicular to the planes. The latter mode
appears as a resonance in the transverse dielectric function, and it couples
directly to the electrical field vector of infrared radiation. A shift of all
plasma frequencies, and a reduction of the intensity of the transverse optical
Josephson plasmon is shown to result from the finite compressibility of the
electron fluid.Comment: 17 pages, ReVTeX, 7 figures in eps forma
Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy
We study the lattice N=1 Wess-Zumino model in two dimensions and we construct
a sequence of exact lower bounds on its ground state energy
density , converging to in the limit . The bounds
can be computed numerically on a finite lattice with sites and
can be exploited to discuss dynamical symmetry breaking. The transition point
is determined and compared with recent results based on large-scale Green
Function Monte Carlo simulations with good agreement.Comment: 32 pages, 12 figure
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