We study the stability of the replica-symmetric solution for a perceptron learning from examples. By examining the replicon mode, we find the Almeida-Thouless (AT) line signaling a spin-glass phase transition. We find an interesting phase diagram where the AT line crosses the line of zero entropy. Entropy is still negative in a low-temperature region above the AT line. The possibility of a discontinuous phase transition to the replica-symmetry-breaking phase is also discussed.

We present two-cell correlation functions ${\mathit{m}}_{\mathit{l}}$(n), which give the average number of l-sided cells adjacent to n-sided ones, obtained experimentally from vegetable tissues and through a numerical simulation that includes mitosis of biological-tissue growth. The correlation functions are not always linear in n, but the Aboav-Weaire law is obeyed, indicating that it is valid for biological tissues and that recent arguments applied to purely topological models are not valid for all natural systems.

The intermediate time dependence of the survival probability in two-dimensional diffusive dynamics is investigated on a model myoglobin-CO potential-energy surface. For small diffusion anisotropy, we derive a scaling relation for the characteristic time and exponent of the observed power-law dependence, which is verified by exact two-dimensional calculations. At higher anisotropy values, we report a critical-like jump in the anisotropy dependence of the power-law exponent. Possible experimental implications are discussed.

We propose a model for phase transitions involving hydrogen bonding in lipid bilayers. The model is an interacting model with five states on each site of a two-dimensional square lattice. This model describes both the hydrogen bonding network proposed for phosphatidylethanolamine lipids by x-ray spectroscopy and its disruption by lipid-water interactions. The phase transitions predicted by the model are identified by use of numerical simulation in conjunction with recent extrapolation and finite-size-scaling methods. The percolation properties were also investigated, and it is found that the percolation exponents cannot be described by random percolation theory. The relationship of the results to experiment and extensions of the model is discussed.

We analyze the fluctuations in the correlation exponents obtained for noncoding DNA sequences. We find prominent sample-to-sample variations as well as variations within a single sample in the scaling exponent. To determine if these fluctuations may result from finite system size, we generate correlated random sequences of comparable length and study the fluctuations in this control system. We find that the DNA exponent fluctuations are consistent with those obtained from the control sequences having long-range power-law correlations. Finally, we compare our exponents for the DNA sequences with the exponents obtained from power-spectrum analysis and correlation-function techniques, and demonstrate that the original ‘‘DNA-walk’’ method is intrinsically more accurate due to reduced noise.

We consider a network of N globally coupled nonlinear overdamped oscillators subject to Langevin noise and a weak periodic modulation. Assuming that one of the oscillators relaxes to its steady state on a time scale far slower than the remaining oscillators in the network, we obtain its dynamics from the coupled stochastic differential equations describing the system, via adiabatic elimination. The bifurcation properties of this ‘‘reduced oscillator’’ model are discussed, together with cooperative stochastic effects (e.g., stochastic resonance) that result from the presence of the modulation.

The approach of scaling behavior of open dissipative systems, which was proposed by Hentschel and Family [Phys. Rev. Lett. 66, 1982 (1991)], is developed to analyze several models. The results show there are two scaling regions, a strong-coupling region and a weak-coupling region, in each model. The dynamic renormalization-group results are exactly the same as the results in the weak-coupling region. The scaling exponents in the strong-coupling region and the crossover behavior are also discussed.

In this paper we report the dynamical behavior occurring in a nematic liquid-crystal film during the optically induced molecular reorientation. The system at first undergoes an incomplete period-doubling cascade, then a biperiodic regime appears, and finally a transition to a chaotic regime occurs. This sequence is experimental evidence of a physical system that mixes two different routes for the transition to a chaotic regime.

The path-integral formalism for classical Brownian motion in a general environment is derived from the first principles of microdynamics by using the path-integral formulation of classical mechanics. The classical influence functional, which contains a nonlocal dissipation term and a colored noise term, is introduced. We show that there exists a classical fluctuation-dissipation relation. We also compare this classical influence functional theory with the well-known quantum influence-functional theory.

In this paper we consider a system of noninteracting paramagnetic particles with a spin S in a dc magnetic field. The exact expression for the probability distribution function of a transverse spin component is obtained for the gas in thermodynamic equilibrium. Dependences of the probability on the thermofield parameter βμH (β is the inverse temperature, μ is the Bohr magneton, H is a field strength) and S are investigated. It is shown that this distribution reflects the quantum nature of the spin and both the spin-wave and the classical approximation formulas are obtained.

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short-time scales to finite values of deterministic chaos at longer-time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos.

Monte Carlo simulations are performed for the elementary batch reaction A+B→0 on a one-dimensional lattice. The initial densities of the A and B species are always identical but the relative mobility is varied. We investigate the rates, rate laws, and particle distribution functions. The rate power law is conserved, i.e., the density always decays in time algebraically with exponent 1/4. The rate coefficient is proportional to the relative mobility, as expected. The interparticle distribution functions (‘‘gaps’’ and nearest-neighbor distances) show that the aggregation does depend on the relative mobility but the segregation does not. However, this subtle difference has no effect on the asymptotic reaction order, which is close to 5.

Propagating wave fronts resulting from autocatalytic chemical reactions have been the focus of much recent research. For the most part, the hydrodynamics resulting from such reactions has been neglected. In this work, a relation is derived for the normal speed of a propagating wave front as a function of the local curvature when fluid motion is allowed. This ‘‘eikonal’’ equation is a generalization of one which was derived in the absence of fluid flow. It is also shown that small variations in the fluid density due to the chemical reaction do not change the form of the relation.

A numerical solution is obtained for the generalized Onsager problem for the isotropic-nematic interface of rigid rods, which accounts for the biaxial effect that was ignored in previous calculations. It is found that the biaxial effect on interfacial tension is indeed weak, as previously expected. The biaxiality becomes significant only near the isotropic side of the interface.

We have investigated the growth kinetics and aggregate structure for temperature-induced aggregation of silica colloids in a binary mixture of 2,6-lutidine and water. Using static light scattering, we find that the structure factor obeys Porod’s law, the average cluster mass M¯(t)∼t, and the average cluster radius R¯(t)∼${\mathit{t}}^{1/3}$. This indicates that the clusters are compact, M¯∼R${\mathrm{¯}}^3$, and that the rate of aggregation is diffusion limited. Such a dense structure suggests that the bonds between the colloids are not rigid, in contrast to what is currently found for colloidal aggregation of solid particles.

We determine in a mean field approximation the spin-1/2 Ising model line tension τ along the boundary between surface states at the prewetting transition in the neighborhood of the wetting transition at bulk phase coexistence. We find very close agreement with the predictions of the interface displacement model for short-range interactions, i.e., τ increases (with a square-root dependence on the bulk external field h) towards a finite limit with diverging slope at wetting. Our findings help both in settling the discussion on the limiting value of τ and in understanding the origin of its singular behavior.

An alternative theoretical model that incorporates the experimentally measurable dispersion relation is used to study the curvature effect and the dynamics of spiral waves in two-dimensional excitable media. The model is constructed to abstract the most significant factors leading to phenomena observed universally in excitable media. The analytically derived curvature relation and critical radius show an excellent agreement with numerical simulations of the model. Both stationary rotating spirals and a meandering motion are observed numerically, in accord with other experimental and theoretical studies.

We investigate the propagation of high-intensity short laser pulses in a plasma. A two-parameter perturbation expansion is used to consistently treat the nonlinear mass variation and ponderomotive contribution to self-focusing, including plasma inhomogeneity. An analytical expression for the critical power is given and it is found that it greatly depends on the plasma inhomogeneity. A tailoring of the preformed plasma is suggested in order to obtain a strong reduction of the critical power. The temporal evolution of the pulse and plasma dynamics are also considered.

Some phenomena induced by placing an electrode at the center of a cylindrical apparatus confining ions or electrons, such as magnetic and electrodynamic traps, are analyzed on the basis of an electrostatic model. It is shown that a purely two-dimensional system of charges can be formed on a cylindrical surface under appropriate conditions.

In this work, we make use of a Hamiltonian formalism to analyze the wave-particle dynamical interaction that takes place in cyclotronic systems. It is shown that the usual model of test particles moving in externally given wave fields is good only when the amplitude of the radiation is large enough; otherwise, wave dynamics must be considered and the dynamics mentioned undergoes some considerable changes. In this regard, the appearance of new fixed points and the saturation of the autoresonance process are both analyzed as functions of the dispersion relation of the laser field.