We prove that antiplane crack growth governed by the Griffith’s condition and the diffusion-limited-aggregation (DLA) growth law is equivalent to the dielectric-breakdown model with cutoffs on the gradients, introduced by Arian et al. [Phys. Rev. Lett. 63, 2005 (1989)]. We conclude that the crack will evolve from DLA-type patterns (at small sizes) into spiky structures (at large sizes). The same conclusion holds for general crack growth.

We have measured the temperature dependence of parametric x-ray radiation (PXR) from a Si single crystal bombarded by 900-MeV electrons. The radiation intensity is appreciably enhanced when the crystal is cooled to liquid-nitrogen temperature as compared with the case for room temperature. The enhancement factors are larger for the higher-order reflections and are quantitatively consistent with the assumption that the PXR intensities are proportional to the squared Debye-Waller factor.

We propose a self-consistent treatment of the Kardar-Parisi-Zhang equation in d dimensions, in order to calculate the dynamical exponent z and the roughness exponent χ, and also amplitude ratios and subleading corrections. We assume that the dynamics of each mode is purely exponential, and find agreement with known results in d=1 and 2. For d>${\mathit{d}}^{\mathrm{*}}$≃2.85, however, none of our solutions is compatible with this assumption. Our method is distinct from, but akin to, the one recently proposed by M. Schwartz and S. F. Edwards [Europhys. Lett. 20, 301 (1992)].

We derive a nonlinear diffusion equation for a void density in the diffusing-void model of granular assembly [Phys. Rev. Lett. 67, 828 (1991)] and present numerical solutions when the assembly is in dynamic equilibrium. We find that the solutions exhibit unique features of the real granular flow patterns in a confined geometry with and without obstacles; notable examples are the ssV-shaped kink at the free surface, stagnant solids near the wall, and the shock front below the obstacle accompanied by the empty region.

We study the eigenvalue spectrum of the hopping transition probability matrix W for the random walk in randomly diluted clusters, both in critical and weak dilution. We obtain the relations between the spectrum in the limit where the eigenvalue ‖λ‖→1 and the long-time behavior of the velocity autocorrelation function and mean probability of the random walk to return to the starting point after t steps by scaling and by numerical diagonalization of W.

We report on the analysis of space-resolved x-ray emission from the densest part of plasmas created by laser irradiation of plane targets. The plasmas are strongly correlated and not very emissive due to the high electron densities [(1–3)×${10}^{23}$ ${\mathrm{cm}}^{\mathrm{-}3}$] and the low temperatures (≤300 eV) involved. We present an alternative experimental technique that provides an extensive enhancement of the emission profiles. The Stark broadening of the F Lβ and Al Lβ lines is discussed with respect to asymmetries and the possible formation of transient molecules. Red satellites (molecular and dielectronic) on the low-energy wing of Lβ are exhibited.

We describe the modulational instability development in a collisional plasma where the characteristic frequency Δω of the modulated perturbations is much less than ${\nu }_{\mathrm{eff}}^{\mathrm{}\left(\mathrm{eq}\right)\mathrm{}}$, the inverse equalization time of the electron and ion temperatures.

Exchange of stability between periodic orbits of the same winding number is observed in a one-parameter family of quartic potentials. We use numerical simulations to study the exchanges that occur between two values of the parameter for which the system is integrable. The relevance for the survival of Kolmogorov-Arnold-Moser tori is briefly discussed and parallels are drawn to a similar phenomenon earlier observed for area-preserving maps.

We study a nonequilibrium interface growth model that includes the nonlocal shadowing effect in three spatial dimensions. The model is represented by a stochastic partial differential equation for the local growth rate of an interface. The nonlocal effect is modeled by a term in the growth rate that is proportional to the local exposure angle. This leads to a shadowing instability, and the interface develops into a mountain landscape which coarsens in time. The structure factor of the interface shape shows a dynamic scaling form. The scaling exponents are computed.

The differential condition of self-consistency relating the thermodynamic functions and their derivatives locally at a studied point of the phase diagram has been suggested as a closure for the Ornstein-Zernike (OZ) equation. This produces an infinite set of OZ-like equations together with functionals—these are conditions to determine exact values of correlation functions and bridge function. To solve the problem an efficient method was developed that allows one to obtain not only 14 virial terms for a hard-sphere fluid (low-density limit) but the equation of state at high density with good accuracy.

The two-dimensional monomer-monomer (AB) surface reaction model without diffusion is considered for infinitesimal, finite, and infinite reaction rates k. For equal reactant adsorption rates, in all cases, simulations reveal the same form of slow poisoning, associated with clustering of reactants. This behavior is also the same as that found in simulations of the two-dimensional voter model studied in interacting-particle systems theory. The voter model can also be obtained from the dimer-dimer or monomer-dimer surface reaction models with infinitesimal reaction rate. We provide a detailed elucidation of the slow poisoning kinetics via an analytic treatment for the k=$0^{+}$ AB reaction and the voter models. This analysis is extended to incorporate the effects of place-exchange diffusion which slows, but does not prevent poisoning. We also show that the k=$0^{+}$ AB reaction with no diffusion is equivalent to the voter model with diffusion at rate 1/2. Identical behavior of the monomer-monomer reaction and the voter model is also found in an ‘‘epidemic’’ analysis, where one considers the evolution of a surface poisoned by one species, except for a small patch. Finally, we apply our findings to elucidate the behavior of the monomer-dimer surface reaction model for small reaction rates.

We report results of small-angle Rayleigh-scattering experiments performed in an equimolar liquid mixture of toluene and n-hexane that is brought out of thermal equilibrium by the imposition of a stationary temperature gradient ∇T perpendicular to the scattering wave vector. The experiments demonstrate the presence of long-range nonequilibrium fluctuations in temperature, concentration, and momentum and confirm that the strength of these nonequilibrium fluctuations varies with (∇T${)}^2$/${\mathit{k}}^4$, where k is the wave number of the fluctuations. It is suggested that nonequilibrium Rayleigh scattering may provide an alternative technique for measuring Soret coefficients of liquid mixtures.

The motion of shallow-water wave trains is studied in the laboratory in one space dimension and one time dimension (1+1). Our focus is on the nonlinear evolution of the wave trains as recorded at five spatially separated probes. Both the linear Fourier transform and the inverse scattering transform (IST) for the periodic Korteweg–de Vries (KdV) equation are exploited in the analysis of the data. IST provides a set of nonlinear basis functions, which are here computed for measured wave data and compared to the sinusoidal basis of the linear Fourier transform. We find that the scattering-transform mode amplitudes are nearly constants of the motion, while the Fourier modes vary substantially in space and time. The results suggest that the KdV equation more nearly describes the nonlinear evolution of the waves than does linear evolution.

I present experimental observations of weakly nonlinear traveling-wave convection in ethanol-water mixtures in a narrow, rectangular cell of variable aspect ratio. Over ranges in aspect ratio separated by approximately unity, the first nonlinear state seen above the onset of convection consists of irregular ‘‘repeated transients,’’ in which small-amplitude traveling waves initially grow with no change in spatial profile, then lose stability, and finally collapse back down to small amplitude. These states differ qualitatively from the ‘‘blinking’’ states seen just above onset at other aspect ratios, in which wave amplitude alternates regularly back and forth across the cell. The collapse in the ‘‘repeated-transient’’ state appears to be caused by a dephasing of the pattern which is due to the nonlinear dependence of wave number on amplitude. This dephasing shifts the pattern off resonance, causing its decay.

This paper shows that the Taylor dispersion flux is a dissipative flux of extended thermodynamics. Every term in the evolution equations for the Taylor flux components is connected to a thermodynamic function and the entropy production is proved to be positive definite. Thermodynamic restrictions on phenomenological coefficients are also satisfied.

The Taylor-Couette system is an extraordinary hydrodynamic system, showing almost all low-dimensional scenarios for routes to chaos for proper boundary conditions. For a period-doubling route to chaos, bifurcation diagrams were experimentally recorded and the dynamic variables such as fractal dimensions, Lyapunov exponents, and entropies are estimated as a function of Reynolds number. The evolution of the correlation dimension ${\mathit{D}}_2$ with Reynolds number Re shows that ${\mathit{D}}_2$∝(Re-${\mathrm{Re}}_{\mathit{c}}$${)}^{1/4}$, which is similar to continuous phase transitions. An investigation of the critical phenomena must be performed as high-precision hydrodynamic experiments because the results show that the kind of scenario depends sensitively on the boundary conditions.

The theory of thermal radiation forces is extended to the local interactions occurring among phonons and the material particles of a liquid, also in the absence of an external temperature gradient. In a solution, energy and momentum can be transferred by an impinging phonon to a particle, or the latter may perform work on the first, shifting it to a higher frequency. Upon time reversal, each of these elementary interactions commutes into the other. Isothermal diffusion, thermomechanical and mechanothermal effects in solutions can be interpreted within this unifying frame of reference. The density of the ‘‘gas’’ of thermal excitations, and the average of energy exchanged per interaction can be calculated from experimental data for common liquids. Nonequilibrium statistical mechanics and irreversible thermodynamics might be fruitfully revisited on the basis of the notion of phonon-particle interactions, since these are processes that occur at a more elementary level than the regression of fluctuations. Accordingly, the statistical approach proposed here may lead to a microscopic interpretation of Onsager’s reciprocity relations.

An investigation is made of the coupling between Soret-driven convection, at positive separation ratio, and a solid-liquid interface. This phase boundary forms upon the solidification of an upper portion of a thin layer of a dilute binary mixture that is confined between highly conducting and nearly impermeable horizontal plates. Using a long-wavelength expansion, a nonlinear evolution equation is derived that includes the coupled effects of solidification and thermosolutal convection due to the Soret effect. The validity of the derivation is found to be limited to regions, in the parameter space, that are determined as functions of the separation ratio, the Lewis number, and the thickness of the solid layer. The numerical solutions of the evolution equation show that the formation of the solid layer affects the leading-order concentration profile, and that the deviation of the interface from its planar state is weakly affected by the convective currents in the liquid. The interface morphology, however, has the same form as the convective pattern in the fluid mixture. The consideration of boundaries that are poor conductors of heat leads to a problem that is characterized by a heat-transfer Biot number γ and a mass-transfer Biot number β. The threshold values for the onset of convection are determined, and their dependence on β and γ is discussed.