We have studied the growth of interfaces in driven diffusive systems well below the critical temperature by means of Monte Carlo simulations. We consider the region beyond the linear regime and of large values of the external field which has not been explored before. The simulations support the existence of interfacial traveling waves when asymmetry is introduced in the model, a result previously predicted by a linear-stability analysis. Furthermore, the generalization of the Gibbs-Thomson relation is discussed. The results provide evidence that the external field is a stabilizing effect which can be considered as effectively increasing the surface tension.

We have studied the global scaling properties of the Julia sets of the Yang-Lee zeros of the s-state Potts model on the diamond hierarchical lattice. The singularity spectrum f(α) and the generalized dimension $D_q$ are calculated for different s values. General observations are made on their variations.

The potential of the original m-spoke model, conceived by Family and Hentschel (FH) [Faraday Discuss. Chem. Soc. 83, 139 (1987)], does not satisfy the correct boundary conditions for diffusion-limited aggregation (DLA) or dielectric breakdown. Moreover, while the suggested scaling forms hold, if the growth probability exponent η of the dielectric breakdown model is larger than 2, they are not generally valid for η<2. The correct potential of an m-spoke structure is given, and the scaling behavior of this new model is calculated. Since the scaling dependence on the cluster size N is determined by the local-field behavior, the exponent ${\nu }_{?}$ found by FH is recovered with the new potential. For a careful evaluation of the m dependence, however, a nonlocal quantity must be considered, leading to novel results. We conclude that only if the fractal dimension is m dependent can the asymptotic shape of DLA clusters be m-spoke-like.

The scaling structure of attractors at the transition from quasiperiodicity to chaos is studied for an electron-hole plasma instability in a Ge crystal. The scaling function f(α) spectrum calculated from the time series of the plasma current oscillation at the onset of chaos is in good agreement with that of a circle-map model. The experimental power spectrum also confirms that the transition to chaos is well described by the circle map. The extrinsic noise effect on the f(α) spectrum is discussed by using the circle map.

We consider the partial differential equation which describes phase separation in a block copolymer melt. We construct numerically the periodic solution which minimizes the free energy. The lamellar thickness of the final equilibrium pattern is found to scale with the molecular weight as a power law ${\lambda }_L$∼$N^{\theta }$. The exponent θ takes the value (1/2 in the weak-segregation regime and (2/3 in the strong-segregation regime. We propose a scaling theory of the dynamics, from which we obtain θ=2φ, where φ is the scaling exponent in spinodal decomposition, in agreement with a conjecture by Oono and Bahiana [Phys. Rev. Lett. 61, 1109 (1988)]. Lastly, we also study the pattern formed by propagating fronts. The selection of the unique velocity of the front and of the wavelength of the pattern behind the front agrees well with the marginal-stability theory.

The spectrum of singularities in the steady-state phase-space distribution function for two-dimensional two-body planar Couette flow is characterized by calculating numerically the generalized dimension $D_q$ and the Legendre transform of (1-q)$D_q$. The discrete probabilities $p_i$(ε), where ε is the discretization length, scale with the dimension of the initial phase space at equilibrium. Away from equilibrium the $p_i$(ε) scale with a range of indices, extending from the full accessible phase-space dimension to a lower limit which is controlled by the value of the shear rate γ. We compare these results with the Kawasaki nonequilibrium-distribution-function approach.

In a simple nonlinear quantum-dynamical system, described by a two-resonance Hamiltonian, we show that the extension of the wave function in Hilbert space, as parameters of the system are varied, is caused by the overlapping of higher-order nonlinear quantum resonances and is therefore associated with the local destruction of quantum numbers which appears to result from this overlap.

Spatially periodic structures in nematic liquid crystals usually appear as the initial response to a suddenly applied reorienting field. To account for the significant discrepancy between the measured periodicity and the periodicity calculated from a linear instability analysis we derived nonlinear equations of motion and solved them numerically. Our results agree well with the observed wavelength. We propose a novel mechanism responsible for the final wavelength selection.

A one-dimensional chain of forced nonlinear oscillators is investigated. This model exhibits typical behavior in periodically forced, spatially extended, nonlinear systems. At low driving amplitudes characteristic domainlike structure appears accompanied by simple asymptotic time dependence. Before reaching its final state, however, the chain behaves chaotically. The chaotic transients appear as intermittent bursts mainly concentrated at the domain walls. At higher driving, the chaotic transient becomes longer and longer until the time dependence apparently corresponds to sustained chaos with the chain state characterized by the absence of domainlike spatial structure.

A correlation expansion for the entropy of a classical monatomic liquid has been found to give an accurate account of the entropy for liquid sodium and for liquid argon. Here, this correlation expansion is given a conceptually simple derivation in the grand-canonical ensemble. The one- and two-particle terms together are shown to accurately represent the entropy of the hard-sphere liquid. The simplicity of the theory suggests a model for an ‘‘ideal liquid,’’ whose free energy takes on an especially simple form. The correlation expansion for the entropy is compared in detail with previous related work.

A modified theory of late-stage phase separation in two dimensions is presented. We show that direct correlation between two droplets, ignored in an earlier theory, significantly changes the droplet size distribution function even at very low area fraction, although it does not affect the asymptotic droplet growth power law $t^{1/3}$. In the low-area-fraction limit this correlation effect leads to a logarithmic correction term which is larger than any other effects. We also show that there is no finite cutoff for the scaled distribution function due to the associated second-order differential equation.

The concept of stochastic resonance has been introduced previously to describe a curious phenomenon in bistable systems subject to both periodic and random forcing: an increase in the input noise can result in an improvement in the output signal-to-noise ratio. In this paper we present a detailed theoretical and numerical study of stochastic resonance, based on a rate equation approach. The main result is an equation for the output signal-to-noise ratio as a function of the rate at which noise induces hopping between the two states. The manner in which the input noise strength determines this hopping rate depends on the precise nature of the bistable system. For this reason, the theory is applied to two classes of bistable systems, the double-well (continuous) system and the two-state (discrete) system. The theory is tested in detail against digital simulations.

By using an approximate analytical trial density and the consideration of an energy density functional which includes a modified gradient correction, the relationship between the zeroth-order and the first gradient correction is tested and the results compared with those obtained through the use of Hartree-Fock-Roothaan-Clementi densities.

We present a new technique for evaluating the gradient expansion of the one-particle Green’s function of a system of noninteracting particles. The method is based on the fundamental differential equation for the Green’s function and is applicable to relativistic systems as well as to nonrelativistic ones. Explicitly we derive the gradient expansion of the relativistic Green’s function of a system of electrons in an arbitrary time-independent external four potential to second order.

The pressure dependence of the ac Stark effect for the two-photon ${\mathit{A}}^2$${\mathrm{\Sigma }}^{+}$, v’=0←X ${}_{}{}^2{}_{}{}^{}\Pi$, v’’=0 transition in NO is studied by using laser-induced fluorescence. Contrary to earlier results obtained by using multiphoton-ionization detection for the same transition [Demaray et al., J. Chem. Phys. 75, 5772 (1980); Li and Johnson, Phys. Rev. A 37, 3801 (1988)], the ac-Stark-broadened linewidth is constant for pressures between 2×${10}^{\mathrm{-}4}$ and 10 Torr. Possible explanations for this difference are discussed.

A recent measurement with improved (1%) accuracy of the ${\mathrm{Ca}}^{+}$ 4$p_{1/2}$ and 4$p_{3/2}$ lifetimes reported a discrepancy of about 9% with the available theoretical estimates. I report an improved calculation based on a recently developed and employed method which yields excellent agreement with these high-accuracy measurements.

In the presence of an intense laser field we treat the electron as quasifree and develop a modified Boltzmann equation using quasi-four-momentum for the electrons. With this picture one can easily solve the Boltzmann equation by the separation-of-variables method. The solution is a product of the initial distribution function and a time-evolving part. The latter depends on the scattering cross section of the quasifree electron colliding with stationary ions. We apply the result to the case of a Maxwellian electron gas in a quasineutral plasma and calculate under the approximation that the mean electron kinetic energy is very small compared to the energy of the photons absorbed. For the Coulomb potential the final solution is obtained as a Maxwellian distribution but with the temperature increasing with time. The discovery that the Maxwellian distribution remains the same is surprising since no relaxation processes have been assumed in our treatment.

To elucidate the part of hard-core repulsions in the spontaneous helical distortion of the cholesteric phase, the q dependence of the excess free energy due to repulsive interactions is reconsidered in connection with an improved description of the first moment of the excluded volume.

We consider two-dimensional layered systems with an infinite number of ground states, exemplified by the axial next-nearest-neighbor Ising model. We show that under some mild assumptions on interactions, such systems do not have the classical low-temperature expansion of the pressure.