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 CHREST’s 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 $x$ and $y$ directions ($J_x \neq J_y$) 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 $20 \times 20$ 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 YBa2_2Cu3_3O7−δ_{7-\delta}

Motivated by recent angle-resolved photoemission spectroscopy (ARPES) measurement that superconducting YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) exhibits a $d_{x^2-y^2} + s$-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 $\rho^{(L)}$ of exact lower bounds on its ground state energy density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds $\rho^{(L)}$ can be computed numerically on a finite lattice with $L$ 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