In simulations on the Little-Hopfield model it is found that the convergence time to a stable state close to one of the embedded patterns scales like c($m_0$)log${}_{10}{}^{}{}_{}{}^{}N$, where N is the size of the network and c($m_0$) depends on the initial macroscopic overlap $m_0$ with the pattern. In a related model known as the pseudoinverse model the convergence time to the pattern is much smaller than ${\log }_{10}$N. The results are compared with other possible pattern recognition methods.

The particular chaotic states of Lorenz-type systems are studied when a marginally unstable fixed point is approached by typical trajectories. By analytically investigating a two-dimensional Poincaré map it is shown that these states have a number of interesting properties. They can be weakly or strongly intermittent. In the weak intermittent cases a phase-transition-like phenomenon occurs in the Rényi entropies, and power-law decay of the truncated Kolmogorov-Sinai entropy is found.

Thermal transport in gases is investigated by nonequilibrium molecular-dynamics computer simulations. A homogeneous driving force generates a heat flux in the absence of a temperature gradient. It is uniquely derived from a moment-method analysis of the Boltzmann equation by requiring an identical linear response as would result from a temperature gradient. The algorithm is shown to be identical to the Evans-Gillan method if in the latter only kinetic terms are retained in the equations of motion. The validity of this peculiar approach in the linear regime is demonstrated by simulation results for the heat conductivity and the distorted velocity distribution function. In the nonlinear regime, however, the external force leads to an unphysical divergence of the heat conductivity. The accompanying kinetic theory analysis and other recent related work confirm the long-standing presumption that the Evans-Gillan algorithm gives an incorrect nonlinear response.

In the high-viscosity limit we describe an elementary analytic solution of the one-dimensional translatory motion of three identical masses connected by identical harmonic springs, but subjected to strong viscous drag forces with step-function dependence on spring extension. Responses to step-function and periodically reversing external forces are found. The model may be relevant to DNA gel electrophoresis in time-dependent electric fields.

Elastic and quasielastic light-scattering measurements were made on di-2-ethylhexylsufosuccinate microemulsions as a function of the droplet concentration. Dynamical-measurement data show at high concentrations a $k^3$ dependence typical of systems with large structural order; moreover, in agreement with previous data, they confirm that the system undergoes a structural transition similar to the glass transition. Intensity data show the presence of large cluster aggregates with a fractal structure in the concentration region where the system presents a structural arrest, which is typical of dense-packing liquid. The fractal dimension D=2.1±0.05 gives an indication that the aggregation process is reaction limited.

We employ phenomenological methods to discuss the way that interfacial polar ordering of liquid crystals may affect the orientation (tilt angle) of a bulk nematic phase near an isotropic-nematic interface. The theory invokes the up-down asymmetry of the molecules to account for the anomalous behavior of substances (e.g., the n-alkyl cyanobiphenyls) that exhibit tilt angles other than 0° or 90°. In the absence of this asymmetry, the molecules in the bulk nematic phase must lie either parallel or perpendicular to a diffuse isotropic-nematic interface. We rule out several other ostensibly reasonable mechanisms by which a nematic phase might tilt at an isotropic-nematic interface.

The properties of a simple one-dimensional model for particle drift and coalescence have been explored. In this model particles with a distribution of sizes or masses (s) are injected at the end of a line and move with a velocity given by V(s)∼$s^{\gamma }$. If two particles of sizes $s_1$ and $s_2$ contact, they coalesce, and the combined particle continues to move with velocity ($s_1$+$s_2$${)}^{\gamma }$. In the asymptotic limit (t→∞, where t is time), the mean droplet size S(t) and the number of droplets N(t) are given by S(t)∼$t^z$(z=1) and N(t)∼ln(t). The density as a function of the distance l from the injection point is given by ρ(l)∼$l^{\mathrm{-}\alpha }$ [α=γ/(1+γ)], and the average droplet size s¯(l) at a distance l from the injection point is given by s¯(l)∼$l^{\omega }$[ω=1/(1+γ)]. A variety of other quantities including the time-dependent droplet size distribution [$N_s$(t)] and the distribution of distances between adjacent particles [$N_{\delta }$(t)] have also been measured. The asymptotic properties associated with this model can be understood in terms of a simple scaling model.

By combining nonequilibrium polymer kinetic theory with the renormalization-group method, one can obtain universal predictions for the material functions that describe the properties of dilute polymer solutions undergoing flow. For steady shear flow, double-sum expressions for the shear-rate-dependent excluded-volume contributions to the viscosity and the first normal-stress coefficient are obtained by employing a perturbation scheme previously developed for treating hydrodynamic-interaction effects. In the limit of long chains, these double sums are carried out to yield more explicit results for the zero-shear-rate viscometric functions. The effects of excluded-volume interactions on the shear-rate dependence of the viscometric functions and on experimentally observable, universal ratios involving zero-shear-rate normal-stress coefficients are discussed.

We show that a ferroelectric smectic-$C^{\mathrm{*}}$ film can open up a stable pore under certain conditions when submitted to an external electric field orthogonal to its rest plane.

A model of an artificial neural network for pattern association is discussed, which is dynamically stable and employs a weight matrix with asymmetric connections of a specific kind. The relationship to earlier stable models making use of symmetric connection matrices is established. A Lyapunov function for the system is explicitly specified. It is argued that its behavior as a function of time during the learning phase indicates the quality of the network’s performance regarding pattern association. This view is supported by a numerical example, which, in addition, serves to demonstrate the virtues of this model in comparison to others. The crucial role of the constants entering artificial neural systems is emphasized.

Measurements of scaling behavior at the onset of chaos, including the ‘‘singularity spectrum,’’ or f(α) spectrum, and the fractal dimension D of the quasiperiodic orbit set along the critical transition line, are reported for driven diode resonator systems. A single diode resonator is used for the transition to chaos through the period-doubling scenario. The system of two coupled diode resonators can be driven to exhibit quasiperiodicity and chaos. The second frequency is determined by the system but can be adjusted to give a winding number approximated by the continued fraction 〈4111. . . 〉 to an accuracy of ${10}^{\mathrm{-}6}$. The fractal dimension D is measured to be 0.87±0.01, in agreement with sine-circle map theory. Measured f(α) spectra are compared with those calculated for the circle map (for the quasiperiodic route) and the logistics map (for the period-doubling route). For the quasiperiodic route, f(α) spectra were also obtained for sub- and supercritical orbits. Good agreement with theory is found in all cases, providing experimental evidence for the universality of scaling properties at criticality within certain classes of nonlinear-dynamical systems.

A single diode resonator system is a nonlinear circuit consisting of a series combination of a resistance, an inductance, and a p-n junction diode. Driven single diode resonator systems experimentally show the period-doubling route to chaos, while driven coupled diode resonator systems show the quasiperiodic route to chaos. We present a direct comparison of numerical simulations with experimental measurements on driven diode resonator systems. The numerical simulations are based on an extension of the Rollins and Hunt model [Phys. Rev. Lett. 49, 1295 (1982)] of the diode (ideal diode modified to include a fixed reverse capacitance and a finite reverse recovery time). The extended model allows the reverse recovery time to depend on the forward current of several previous cycles. The model is applied to both the single diode resonator system and a coupled system consisting of two parallel single diode resonators coupled through a series resistance to a sinusoidal generator. In both cases, the numerical simulations show remarkable global agreement with the experimental measurements. The universal scaling behavior of the simulated coupled diode system at the critical line for the quasiperiodic route to chaos is tested by calculating the spectrum of generalized dimensions characterized by the f(α) spectrum. The results show the same f(α) spectrum as obtained for the sine-circle map at the critical line.

A two-dimensional charged polymer chain on a square lattice is studied by Monte Carlo simulations. Monomers on a chain and counterions are assumed to interact through a short-range cutoff Coulomb interaction, and to move on two separate square lattices. Two cases of the interaction range between ions are studied: the nearest-neighbor approximation and the third-nearest-neighbor approximation. It is shown that the condensation of counterions to the polymer chain occurs dramatically at low temperatures so that a phase transition is predicted. Conformation characteristics of the polymer chain as well as the configuration of counterions at low- or high-temperature phases are presented for both cases of different interaction ranges. Both temperature- and interaction-range-dependent properties of the chain conformation are discussed in detail with the radius of gyration $R_G$ (global conformation) and the averaged length of turns of a chain, which is defined by an average of distances between successive inflection points (local conformation).

The results of a high-resolution, synchrotron x-ray powder diffraction study of lattice constants in the $P_{\beta \mathcal{’}}$ (‘‘rippled’’) phase of lecithin-water multilamellar mixtures are given. The variation with water volume fraction ${\phi }_w$ and hydrocarbon chain length $N_c$ of the modulation wave vector $Q_r$ suggests that membrane curvature and hydration interactions between membranes play a significant role in the modulation. The dependence of the membrane thickness and area per head group on $N_c$ indicates that the conformation of hydrocarbon chains is predominantly solidlike. The appearance of significant intensity in higher harmonics of the modulation wave vector rules out simple (e.g., sinusoidal or triangular) membrane density modulations. The results are consistent with a Lifshitz phenomenological model for lamellar phases of interacting membranes proposed by Goldstein and Liebler [Phys. Rev. Lett. 61, 2213 (1988)]. The phase behavior predicted by the model includes a multicritical point called the Lifshitz point where the wavelength of the modulation diverges. The experimental results indicate that this multicritical point lies in the vicinity of $N_c$=9 and ${\phi }_w$=0.18.

Analytic solution of the relativistic Thomas-Fermi differential equation for the description of electronic distribution in matter system at high density is found in terms of expansions in two independent parameters. One of the parameters is related inversely to the density of the matter system, and the other to the charge of the atomic nucleus. The solution is applicable to and of great practical value to the study of dense matter encountered in astrophysics.

We derive the Scott correction to the atomic electron density in momentum space. The implied corrections to expectation values of powers of the momentum, as well as to the Compton profile, are then obtained.

The asymptotic theory of symmetric charge transfer is adapted to apply to ion-ion collisions through allowance for curved nuclear trajectories. The theory compares well with ab initio quantum calculations on ${\mathrm{He}}^{2+}$-${\mathrm{He}}^{+}$ collisions and is applied to five members from each of the Li-like and Na-like sequences.

We have measured the n dependence of the microwave field required to make the single-photon radiatively assisted collision process Na(ns)+Na(ns)+khν→Na(np)+Na ((n-1)p)+(k+m)hν, m=1, 10% as likely as the resonant collision process in which no photons are absorbed, m=0. Experimentally we find an $n^{\mathrm{*}}$ dependence of [2.06(15)×${10}^3$]$n^{\mathrm{*}\mathrm{-}2.0}$ (V/cm), where $n^{\mathrm{*}}$ is the effective quantum number of the Na ns state. Over the range of n studied, 16≤n≤24, this field is within 20% of the field calculated using a theory based on resonant dipole-dipole collisional energy transfer of microwave dressed atoms.

A distorted-wave calculation for electron-impact 1 ${}_{}{}^1{}_{}{}^{}2_{}^1{}_{}{}^{}$P excitation in helium is performed using Slater’s concept of ‘‘transition state’’ for obtaining the distortion potential of the projectile electron. Results for differential cross sections, angular momentum 〈$L_{\perp }$〉, and alignment angle γ are obtained. Present results show good agreement with the available experimental data in the energy range from 60 to 200 eV.

An electric transmission line periodically 100-section loaded with variable capacitance diodes, i.e., a nonlinear lumped LC network, has been constructed to study nonlinear wave (soliton) propagation in the dispersive medium. Experimental results on the head-on collision of solitons with other solitons have been demonstrated. Besides the observation that solitons preserve their line shape and velocity during the collision, it has been observed for the first time that the solitons show a phase shift after the collision. The observed phase shift agrees with the theoretical expectation, which has been derived from an analysis of the nonlinear equation for a one-dimensional Toda lattice equivalent to the transmission line.