A different form of stochastic resonance, in which the weak periodic force is applied multiplicatively (rather than additively) in the noise, has been investigated for a Brownian particle moving in a double-well potential. A regular periodic signal whose amplitude increases sharply with increasing noise intensity is shown to arise when the potential is asymmetric.$-— The experimental measurements are in good agreement with a theoretical analysis.

We study the mean number of distinct sites, ${\mathit{S}}_{\mathit{N}}$(t), visited up to time t by N≫1 noninteracting random walkers all starting from the same origin on a fractal substrate of dimension ${\mathit{d}}_{\mathit{f}}$. Using analytic arguments and numerical simulations, we find ${\mathit{S}}_{\mathit{N}}$(t)∼(lnN${)}_{\mathit{f}}^{\mathit{d}}$/δ${\mathit{t}}_{\mathit{s}}^{\mathit{d}}$/2 for fractals with spectral dimension ${\mathit{d}}_{\mathit{s}}$==2${\mathit{d}}_{\mathit{f}}$/${\mathit{d}}_{\mathit{w}}$<2, where δ==${\mathit{d}}_{\mathit{w}}$/(${\mathit{d}}_{\mathit{w}}$-1) and ${\mathit{d}}_{\mathit{w}}$ is the fractal dimension of a random walk.

We characterize the complex temporal structure of the earthquake activity in a nonconservative spring-block model of earthquakes. The temporal sequence of the occurrence of earthquakes is observed to be multifractal. The clustering (temporal correlations) between earthquakes is characterized by a universal exponent. Those correlations disappear when the model becomes conservative.

We develop an algorithm for generating long-range correlations in the percolation problem and investigate their effect on both structural and dynamical properties of the incipient infinite cluster in two dimensions. We find that the fractal dimensions of the backbone and the red bonds (singly connected bonds) are quite different from uncorrelated percolation and vary with λ, the strength of the correlation. Also, we find that the conductivity exponent varies with λ.

We study chaotic quantum billiards using both microwave cavities and numerical simulations. For the same geometry, viz., a Sinai billiard, agreement to remarkable precision is found for both the eigenvalue magnitudes and the spatial detail of the eigenfunctions. The association of the eigenfunctions with classical periodic orbits is demonstrated, and scarred states are identified. Desymmetrizing the Sinai billiard by slightly moving the central disk is shown to lead to strong localization of the eigenfunction. The calculated eigenstates of the symmetric billiard show an even- and odd-parity pair whose linear combination gives the localized state.

We give a general method for finding the exact solution for the problem of a particle undergoing diffusive motion in a potential in the presence of a δ-function sink of arbitrary position and strength. The solution requires knowledge of the Laplace transform of the Green’s function for the motion in the absence of the sink. We find the exact solution for the case of the parabolic potential. This has long been an unsolved problem and is of considerable importance as a model for nonradiative electronic relaxation of a molecule in solution.

The mechanism by which a one-dimensional pattern of traveling waves changes wavelength (i.e., the Eckhaus instability) is studied in a binary fluid mixture. Long-lived transient phase modulations connect states of uniform wave number. The dynamics of wave-number increases and wave-number decreases are found to be qualitatively different due to a strong dependence of the group velocity on wave number. Relevant theoretical models are discussed.

I describe experiments on nonlinear traveling-wave (TW) convection in a binary fluid with separation ratio ψ=-0.127. When the Rayleigh number of a spatially uniform TW state is reduced below a wave-number-dependent threshold, growing phase modulations that propagate at the TW group velocity are seen. This Eckhaus instability can trigger the creation or annihilation of pairs of convective rolls, leading to complex transients which may or may not bring the system back into the stable wave-number band. It appears that the basic stability properties of the TW states in this experiment cannot be explained using a Ginzburg-Landau-type equation.

We report on the experimental observation of a different type of focal conic domain with positive Gaussian curvature. A particular type of these domains is usually given the name ‘‘spherulites.’’ Their appearance is due to a low (probably negative) value of the saddle-splay elastic constant. These domains are observed in the lamellar ${\mathit{L}}_{\mathrm{\alpha }}$ phase with a low cosurfactant to surfactant (c/s) ratio. The increase of this ratio results in usual focal domains with negative Gaussian curvature. It allows us to conclude that the saddle-splay constant is governed by the c/s ratio, and changes sign from positive to negative when c/s decreases.

A class of spectroscopic line ratios has been adapted as a diagnostic of electron temperature from <100 eV to >1 keV. The diagnostic makes use of the ratio of line intensities from isoelectronic states of different elments in specially prepared targets. The diagnostic is simple to interpret, shows weak dependence on plasma density, requires only low to moderate spectral resolution, uses a single charge state, and can be adapted to minimize line reabsorption and wavelength coincidences with other spectral lines. We present theoretical and experimental results.

We report measurements of the neutron-scattering differential cross section for the He-Xe mixture in the two coexisting states at T=294 K on the 30-MPa isobaric section of the demixing surface corresponding to Xe molar concentration of 0.78 and 0.48, respectively, and for pure orthobaric liquid Xe having the same number density as in the 0.78 mixture. From these data, the total structure factors have been extracted. For the same thermodynamic states we also performed molecular-dynamics simulations using different interatomic potentials. Analyzing the partial pair-correlation functions, we find that, as already found at lower pressure, in this case, where the He concentration is noticeably higher, the partial structure factor of Xe is also essentially unaffected by the presence of He. This supports a simple picture of the He-Xe gas-gas demixing transition in terms of the liquid-gas transition of pure Xe. Analyzing the He-Xe correlations in the mixture, we also discuss the role played by He in the gas-gas immiscibility transition.

Driving electroconvection in a nematic liquid crystal with an electric ac field leads to dielectric convection rolls if the driving frequency is higher than the cutoff frequency. According to the theory, these rolls have a time-dependent velocity and director field that can be described as standing waves which are phase locked to the driving field. The paper reports on measurements of the phase difference between the driving electric field and the director field by means of a stroboscopic technique. Experimental evidence of a symmetry breaking of the oscillations of the director field with respect to the polarity of the electric field is presented, and the possibility to measure flexoelectric coefficients by examining this asymmetry is discussed.

The integral equation of the fluid theory has been solved for the supercooled binary mixtures of fourth-, sixth-, ninth-, and twelfth-inverse-power potentials with a modified hypernetted-chain approximation recently proposed by us. In order to calculate zero-pressure thermodynamic and structural properties, we have incorporated an attractive potential of the Kac form. Using pair distribution functions obtained, we have calculated the concentration-concentration structure factor ${\mathit{S}}_{\mathit{C}\mathit{C}}$(k) and partial coordination numbers, which are useful to investigate mixing properties depending on the softness of the potentials to which some groups of material are attributed. For the mixture of fourth-inverse-power potential with a core-size ratio of 1.2, ${\mathit{S}}_{\mathit{C}\mathit{C}}$(0) and the partial coordination numbers show a remarkable tendency towards phase separation near the freezing temperature, which is in good agreement with experiments on inter-alkali-metallic alloys. For the potentials with n≥6, the mixtures are stable near freezing (even in a highly supercooled regime), which is typical of alloys of the rare-gas families. The interchange energy obtained is also in good agreement with experimental values.

The frequency response of porous electrodes has been investigated using a two-dimensional random-walk algorithm. For simple geometries the values obtained for the characteristic constant-phase-angle exponent is in good agreement with theoretical expectations. The random-walk approach has also been used to study the response of more complex disorderly geometries. In general, the simulation results can be understood in terms of the growth of the ‘‘active length’’ (that part of the electrode-electrolyte interface that participates in the transport process) as the sticking probability or frequency is decreased. The constant-phase-angle exponent η is given by η=1-${\nu }_{\mathit{y}}$ where the exponent ${\nu }_{\mathit{y}}$ describes how the penetration of random walkers into the uniformly porous structure grows with time (number of steps in the walk).

Based on Meakin’s simulation results [Phys. Rev. A 34, 710 (1986); 35, 2234 (1987)], we use the binomial distribution to discuss the growth probability for the screened-growth model and develop a formula of the generalized dimensions. The results from this model are in good agreement with those from the simulations.

New determinations of the surface-tension-anisotropy parameter ${\mathrm{\varepsilon }}_4$ of succinonitrile (SCN), pivalic acid (PVA), and a PVA–1%-ethanol mixture are reported. Effects of temperature gradients and crystal orientation are analyzed in detail. The experiments utilized numerical interpolation techniques previously employed by Dougherty and Gollub to enhance the digital image resolution. The values found for ${\mathrm{\varepsilon }}_4$ in SCN, PVA, and PVA–1%-ethanol are 0.0055±0.0015, 0.025±0.002, and 0.026±0.002, respectively. From these values, the selection parameter ${\mathrm{\sigma }}_{\mathrm{theor}}^{\mathrm{*}}$ predicted by microscopic solvability theory for the three-dimensional axisymmetric case was computed and compared to the ${\mathrm{\sigma }}_{\mathrm{expt}}^{\mathrm{*}}$ values determined directly from previous dendritic-growth experiments. We find that ${\mathrm{\sigma }}_{\mathrm{theor}}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathrm{expt}}^{\mathrm{*}}$ is 0.56±0.20 for SCN, and 2.14±0.50 for PVA. Possible sources for these discrepancies are discussed.

Two functions built from the spherically averaged atomic density, i.e., f(r)=ρ(r)+ρ’(r)/(2Z) and g(r)=${\mathrm{\rho }}_{\mathit{s}}$(r)+ρ’(r)/(2Z), are studied in the Hartree-Fock framework for atoms in the range Z=2–54 and in their ground state. These studies and previous ones show that f(r) is a positive function for all these atoms, and g(r) is also a positive function for all atoms whose least-bounded electron is s type. For these atoms the upper bound ρ(0)≤Z〈${\mathit{r}}^{\mathrm{-}2}$${\mathrm{〉}}_{\mathit{s}}$/2π, which improves the accuracy of the bound of Hoffmann-Ostenhof, Hoffmann-Ostenhof, and Thirring [J. Phys. B 11, L571 (1978)], is found. In addition we obtain sharp lower bounds to ρ(0) and inequalities between total and s-state radial expectation values, 〈${\mathit{r}}^{\mathrm{\alpha }}$〉 and 〈${\mathit{r}}^{\mathrm{\alpha }}$${\mathrm{〉}}_{\mathit{s}}$, respectively.

Bridge functions, the neglected terms in the hypernetted-chain (HNC) theory of classical fluids, are extracted with high precision from Monte Carlo (MC) simulation data for classical one-component plasmas. The MC bridge functions are extended by the use of the exact short-range Widom expansion and of long-range boundary conditions arising from the compressibility sum rule. An explicit analytic expression for the bridge functions is then obtained, leading to improvement on the HNC scheme. Accuracy of the improved HNC scheme is confirmed through comparison with the MC results and by examination of the thermodynamic consistency. The extracted bridge functions are compared with those of other theoretical schemes.

Very recently, using an extrapolation of very accurate ‘‘extra-long-time’’ computer-simulation data for strongly coupled classical plasmas, results for the short-range screening potential were obtained [S. Ogata, H. Iyetomi, and S. Ichimaru, Astrophys. J. 372, 259 (1991)]. These extrapolated results are reported to be of 0.1% accuracy, even for screening potentials at zero separation, and to differ significantly from previous calculations. Using another method, the present extrapolation of the same data finds, however, that these highly accurate simulations are in excellent agreement with the previous calculations, providing an independent test for their validity. Moreover, these high-accuracy simulations provide important support to the ‘‘Onsager-molecule’’ asymptotic limit of the short-range screening potentials in strongly coupled plasmas [Y. Rosenfeld, Phys. Rev. A 35, 938 (1987)].

We present results from a self-consistent Monte Carlo simulation of the cathode fall (CF) of a dc glow. The simulation consists of following electron and ion trajectories under the influence of the electric field which is calculated from Poisson’s equation using the ion and electron densities. The collision cross sections are greatly simplified in order to facilitate understanding of the physical mechanisms which dominate the CF. With this aim, we explicitly sample the electron distribution function and discuss its properties. We also show that it is feasible to simulate the CF in isolation from the negative glow (NG) as long as backscattering from the NG is accounted for. Finally, we take into account the plasma (trapped) electrons in the NG, and formulate a model of the CF-NG boundary region through use of the plasma-sheath equation. We find that the length of the boundary region grows with the NG density, and that there is a corresponding increase in the fraction of the ion flux which enters the CF as opposed to being created in it. For reasonable values of the NG density, we find this fraction to be as high as 25%.