A neural-network model is constructed in which the activation state V(t) of a neuron is of the general form V(t)=${\mathit{tsum}}_{\mathit{j}}$F${\mathrm{\chi }}_{\mathit{j}}$(t,s)${\mathit{w}}_{\mathit{j}}$${\mathit{a}}_{\mathit{j}}$(s)ds, where ${\mathit{w}}_{\mathit{j}}$ is the weight of the jth input line, ${\mathit{a}}_{\mathit{j}}$(s) is the input at time s, and ${\mathrm{\chi }}_{\mathit{j}}$ is a response function that incorporates details concerning the passive membrane properties of dendrites. The response function is determined using a compartmental model of the dendrites. A simple analytical expression for ${\mathrm{\chi }}_{\mathit{j}}$ is derived in the special case of an infinite uniform chain of compartments along similar lines to the analysis of diffusion on a one-dimensional lattice. This is then used to study the response of the model neuron to input patterns of specific spatial frequency across the chain. It is also shown how the inclusion of shunting effects results in the neuron’s activation state being a nonlinear function of inputs, and that this provides a possible solution to the problem of high firing rates in neural-network models. Finally, perceptronlike learning in the model neuron is discussed, and the ability of the neuron to extract temporal features of an input signal is investigated.

We study the efficiency of a neural-net filter and deconvolution method for estimating jet energies and spectra in high-background reactions such as nuclear collisions at the relativistic heavy-ion collider and the large hadron collider. The optimal network is shown to be surprisingly close but not identical to a linear high-pass filter. A suitably constrained deconvolution method is shown to uncover accurately the underlying jet distribution in spite of the broad network response. Finally, we show that possible changes of the jet spectrum in nuclear collisions can be analyzed quantitatively, in terms of an effective energy loss, with the proposed method.

A computer model of reaction-limited colloid aggregation with diverse step lengths, allowing us to reach steps as short as one-twentieth of the diameter, together with very low sticking probabilities (0.001), is studied. In this paper a description is made of the algorithm, its importance, and the results obtained from it.

An alternative method is presented for computing wave propagation in two-dimensional nonhomogeneous media. The method is based on computing the exact Green’s function for a domain using a recursive Green’s-function approach. In comparison with the finite-difference time-domain method, our approach requires substantially less memory and computational time, enabling the modeling of larger and more complex domains. The method is validated by comparing with exact analytical solutions and is found to be highly accurate.

As a second-order phase transition is traversed critical scattering appears; these fluctuations serve notice of the impending loss of stability of the equilibrium phase. For a model first-order phase transition we rigorously prove, using exact thermodynamic quantities obtained from strip-transfer-matrix calculations, as well as finite-size-scaling analysis, that as a temperature-driven, symmetry-breaking, first-order phase transition is approached, no enhancement of fluctuations into the future product phase occurs. To be specific, we study the probability of occupation of the product phase (stable below the transition temperature), and demonstrate that this is a monotonically decreasing function as the transition temperature is approached from above. The relation of this pedagogical result to x-ray scattering experiments is discussed.

Our recent heat-capacity measurements on four-layer free-standing liquid-crystal films near the smectic-A–hexatic-B transition of n-heptyl-4’-n-pentyloxybiphenyl-4-carboxylate (75OBC) exhibit separate heat-capacity anomalies associated with the distinct ordering of the interior and surface layers. Employing the Metropolis Monte Carlo technique, we have simulated these transitions in a layered system with finite thickness (for example, 30×30×4). Comparison between our experimental and simulation results indicates that the anisotropy between inter- and intralayer interactions plays an important role in our experimental findings. Furthermore, the ratio of intra- to interlayer interactions strength should be more than 100.

Experimental observations of stick-slip friction are reported in an electrorheological fluid. The results are consistent with shear-induced phase transitions between solid and liquid phases. During the slip, there is a liquid flowing between two columnar solid phases. When the liquid turns solid (reconnecting the columns), the structure supports a shear, and thus sticks.

Here we demonstrate the evolution of an unusual phase-separated pattern caused by a double quench: a first quench from a one-phase to a two-phase region and a subsequent second quench within the two-phase region. The resulting pattern evolution strongly depends upon the type of a double-quench sequence. A deeper second quench causes a level structure, while a shallower one causes a long-range interface instability coming from a mismatch in the local volume-surface ratio. The response of a domain structure to a second quench is qualitatively discussed on the basis of the phase diagram and existing theories for the coarsening dynamics of usual phase separation.

A statistical correlation function of basic importance in the study of two-phase random media (such as suspensions, porous media, and composites) is the chord-length distribution function p(z). We show that p(z) is related to another fundamentally important morphological descriptor studied by us previously, namely, the lineal-path function L(z), which gives the probability of finding a line segment of length z wholly in one of the phases when randomly thrown into the sample. We derive exact series representations of the chord-length distribution function for media comprised of spheres with a polydispersivity in size for arbitrary space dimension D. For the special case of spatially uncorrelated spheres (i.e., fully penetrable spheres), we determine exactly p(z) and the mean chord length ${\mathit{l}}_{\mathit{C}}$, the first moment of p(z). We also obtain corresponding formulas for the case of impenetrable (i.e., spatially correlated) polydispersed spheres.

Molecular-dynamics simulations are used to investigate the dynamical properties of a ferroelectric nematic liquid crystal. The results are also relevant to electrorheological fluids and to ferrofluids. Translational and rotational diffusion constants parallel and perpendicular to the director are reported and discussed. Dipole-dipole reorientational correlation functions are calculated and compared with theoretical methods.

Recent theoretical analyses of the two-time joint-probability density for electric-field dynamics in a strongly coupled plasma have included formal short-time expansions. Here we compare the short-time-expansion results for the associated generating function with molecular-dynamics-simulation results for the special case of fields at a neutral point in a one-component plasma with plasma parameter Γ=10. The agreement is quite good for times ${\mathrm{\omega }}_{\mathit{p}}$t≤2, although more general application of the short-time expansion requires some important qualifications.

We examine the ability of a feedforward Boolean network to learn to implement the parity function of n input bits. It is shown, on the basis of exact enumerations, as well as theoretical analysis, that, in the absence of teaching, the probability of implementing correctly increasing lengths of the truth table has a staircase structure. This allows us to predict that, in the process of teaching the network, a sharp learning transition would take place at a fraction of teaching which goes to zero as n$2^{\mathrm{-}\mathit{n}}$ in the limit n→∞.

In a recent Brief Report and subsequently [Phys. Rev. A 43, 2050 (1991); 44, 8439 (1991)], Berdichevsky, Kunin, and Hussain claim that the ‘‘Boltzmann temperature’’ of a bounded point vortex system is always positive, and that the spatial inhomogeneities that evolve at high energies in such a system are incompatible with ergodicity of the dynamics. The argument given to support these claims neglected the presence of the fluid boundary. We prove that the Boltzmann temperature is in fact always negative, and present evidence that the vortex clumping that has been observed in simulations is consistent with ergodic dynamics.

We respond to the questions raised in the preceding Comment [K. O’Neil and L. J. Campbell, Phys. Rev. A 47, 2966 (1993)]. We explain why our statement ‘‘vortex temperature is always positive’’ is equivalent to the ‘‘opposite’’ statement in the Comment: ‘‘vortex temperature is always negative,’’ and why we viewed the negative temperature states as paradoxical. We discuss also the notion of temperature for the limit case of infinite number of vortices.

For quantum problems on the pseudosphere generated by arithmetic groups there exist special trace formulas, called trace formulas for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject we present the Hecke operators’ trace formulas for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical-type relations are in good agreement with the directly computed eigenfunctions.

We have studied the homogeneous Burridge-Knopoff spring-block model with nonlinear friction introduced by Carlson and Langer [Phys. Rev. Lett. 62, 2632 (1989); Phys. Rev. A 40, 6470 (1989)]. There are several different velocity scales that define the model and divide the behavior of the system into distinct regimes. Over much of the parameter space defined by these velocities the system appears to be self-organized to what is reminiscent of a first-order transition. As the friction nonlinearity is varied, there appears to be a continuous (critical) transition to a regime where a global event is continually occurring.

The effect of two-frequency driving of a symmetric double well is investigated classically and quantum mechanically. By computing Husimi distributions it is shown that control and suppression of tunneling may be achieved by driving the system with two fields whose frequencies are in a 1:2 ratio. In particular, a second field of finite duration can be used to selectively trap the wave packet in either well.

A theory is proposed to describe two-dimensional avalanches in granular materials. The theoretical framework is based on a set of experiments in which avalanches are generated intermittently by means of a rotating drum. From measurements of the instantaneous average angle of the free surface, α(t), the relevant quantities that characterize avalanches, such as critical angles and times, are found to be given by distributions. It is then shown that α(t) is a stochastic Markov process. Consequently, a master equation is constructed for P(α,t), the conditional probability that the slope is α, at time t, given an initial state. Finally, a consistency test is carried out, finding full agreement with the experimental data.

We show that the generating function for d-dimensional staircase polygons (by perimeter) can be expressed in terms of the generating function for the square of d-dimensional multinomial coefficients. This latter generating function is found to satisfy a linear, homogeneous differential equation of order d-1. This equation is solved for d≤4. For d=3 and d=4 the solution is obtained in terms of Heun functions, which are then shown to be expressible in terms of the complete elliptic integral of the first kind. The solutions are also shown to be related to lattice Green functions on three-dimensional lattices. The critical behavior of this model is determined exactly in all dimensions.

We have observed a localized structure and the spontaneous nucleation of topological defects in an experiment on electrohydrodynamic convection. They are created by a phase instability via the coupling between the oscillatory mode and the underlying cellular pattern. By measuring the coefficients of the phase equations derived from coupled complex Ginzburg-Landau equations, we have confirmed that the equations quantitatively describe the instability.