Universal conductance fluctuations in non-integer dimensions

We propose an Ansatz for Universal conductance fluctuations in continuous dimensions from 0 up to 4. The Ansatz agrees with known formulas for integer dimensions 1, 2 and 3, both for hard wall and periodic boundary conditions. The method is based solely on the knowledge of energy spectrum and standard assumptions. We also study numerically the conductance fluctuations in 4D Anderson model, depending on system size L and disorder W. We find a small plateau with a value diverging logarithmically with increasing L. Universality gets lost just in 4D.Comment: 4 pages, 4 figures submitted to Phys. Rev.

Langevin description of speckle dynamics in nonlinear disordered media

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies $\Omega$ below some $\Omega_{\mathrm{max}}$, provided that the nonlinearity exceeds some $\Omega$-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of $1/\Omega_\mathrm {max}$.Comment: 6 pages, 3 figure

Nonuniversal correlations in multiple scattering

We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a non-universal space-time correlation which depends explicitly on the short-distance properties of disorder, source size, and dynamics of disorder in the immediate neighborhood of the source. This correlation has an infinite spatial range and is long-ranged in time. We suggest that a technique of "diffuse microscopy" might be developed employing spatially-selective sensitivity of the considered correlation to the disorder properties.Comment: 15 pages, 3 postscript figures, accepted to Phys. Rev.

Stability of Negative Image Equilibria in Spike-Timing Dependent Plasticity

We investigate the stability of negative image equilibria in mean synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of external electric fields. We derive a necessary and sufficient condition for stability, for arbitrary postsynaptic potential functions and arbitrary learning rules. We then apply the general result to several examples of biological interest.Comment: 13 pages, revtex4; uses packages: graphicx, subfigure; 9 figures, 16 subfigure

Information transfer through disordered media by diffuse waves

We consider the information content h of a scalar multiple-scattered, diffuse wave field $\psi(\vec{r})$ and the information capacity C of a communication channel that employs diffuse waves to transfer the information through a disordered medium. Both h and C are shown to be directly related to the mesoscopic correlations between the values of $\psi(\vec{r})$ at different positions $\vec{r}$ in space, arising due to the coherent nature of the wave. For the particular case of a communication channel between two identical linear arrays of $n \gg 1$ equally-spaced transmitters/receivers (receiver spacing a), we show that the average capacity $\propto n$ and obtain explicit analytic expressions for $/n$ in the limit of $n \to \infty$ and $k \ell \to \infty$, where $k= 2\pi/ \lambda$, $\lambda$ is the wavelength, and $\ell$ is the mean free path. Modification of the above results in the case of finite but large n and $k \ell$ is discussed as well.Comment: REVTeX 4, 12 pages, 7 figure

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with travelling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases that the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems (Asatryan, et al., Phys. Rev. E {\bf 67}, 036605 (2003).)Comment: 8 pages 9 figure

How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in Phys. Rev.

Anisotropy in granular media: classical elasticity and directed force chain network

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.Comment: 34 pages, 17 figures (eps), submitted to PRE, figures amended, partially to compare better to recent exp. wor