Light-scattering correlation spectroscopy measurements were made on a water-in-oil microemulsion at a constant volume fraction of water φ as a function of the temperature. The density correlation function shows nonexponential decay, which is analyzed in terms of cooperative or structural motion and of single-particle diffusional motion. The system shows a critical behavior at T=41 °C. The fast relaxation rate (cooperative diffusion) gives information about the details of the critical transition via the hypothesis of droplet clustering. The slow relaxation rate is connected to the self-tracer motion.

The hysteresis effects of fluids confined in porous media are studied by means of a new microscopic model. We consider a slitlike pore of infinite area and finite height. In contrast to the unbounded parallel-plate case, the new model allows the formation and the disappearance of curved menisci at the open ends of the pore. This effect has a profound influence on the extent of the hysteresis loops. On the other hand, we find that the presence of the menisci does not play a significant role in locating the equilibrium first-order transition in long pores. The present treatment reconciles the traditional picture of capillary condensation with the modern microscopic treatment based on the density-functional formalism.

A model is presented for the radial distribution of ion and electron densities and electric field strength in the positive column of a dc discharge for a plasma consisting of a singly charged positive-ion species, electrons, and neutral species. The set of equations involved consists of the particle- and momentum-conservation equations for the ions and electrons and Poisson’s equation. Utilizing this single set of equations and appropriate assumptions, the model has been solved, through suitable numerical techniques, for various gas pressures $p_0$ and tube radii R. These calculations show the development of both the electric field in the ‘‘bulk’’ of the positive column and the sheath field ‘‘near’’ the discharge wall. The results also demonstrate the existence of a nonzero difference between the ion and electron densities at the discharge axis, with an increase in this difference for decreasing $p_0$R. The importance of including the various terms in the momentum-conservation equations of both the ions and electrons when solving the model has been investigated. The model can be used to calculate the radial properties of positive-column discharges for conditions ranging from the ambipolar diffusion limit to the free-diffusion limit.

The microstructure in a [n-dodecyltetraoxyethylene glycol monoether (${\mathrm{C}}_{12}$${\mathrm{E}}_4$)]-water-hexadecane system was investigated by the small-angle x-ray scattering (SAXS) technique for various surfactant concentrations and solution temperatures at a constant ratio of water and hexadecane (1:1 by weight). At 25 °C, a sharp distinct peak was observed in the SAXS curves. On the basis of the analysis of the surfactant concentration dependence of the peak position, it was concluded that a lamella structure had been formed. At 45 °C, the scattering curves showed a single, broad peak. With increasing ${\mathrm{C}}_{12}$${\mathrm{E}}_4$ concentration, the peak position shifted toward higher angles. An analysis of the peak position suggested that oil-in-water (O-W) -type microemulsion droplets had been formed. At lower surfactant concentrations, the possibilities, that W-O droplets had been formed and that a bicontinuous structure had been constructed at the intermediate concentrations, were pointed out. The scattering profiles were not in contradiction with the theoretical ones for spheres if the polydispersity was considered. From a consideration of the peak position, which is related to the interparticle distance through the Bragg equation, it was suggested that the (spherical) droplets were distributed in a more or less ordered manner, probably in fcc or bcc symmetry, and not in simple-cubic symmetry. The radius and the aggregation number of the droplet were estimated to be about 13–17 Å and 35–1400, respectively, depending on the surfactant concentration.

The 13-mode Lorenz model previously introduced to describe hexagons and rolls in a Rayleigh-Bénard cell with periodic modulation of the lower plate is generalized to arbitrary time dependence of both upper and lower plates. Earlier results of Krishnamurti [J. Fluid Mech. 33, 445 (1968); 33, 457 (1968)] for the case of a linear ramp with constant temperature difference are recovered. The conditions for observing hexagons are derived analytically for periodic modulation with different frequencies, amplitudes, and phases at the two plates.

An attempt has been made to detect the presence of 1/f fluctuations in ${\beta }^{\mathrm{-}}$ decay using the Allan variance theorem. For counting periods less than about 800 min, the counting statistics were found to be Poissonian and for periods greater than about 800 min, the statistics were found to be non-Poissonian. 1/f fluctuations in the ${\beta }^{\mathrm{-}}$ emissions were observed leading to a flicker floor. It was also found that the flicker floor varies with energy of the emitted ${\beta }^{\mathrm{-}}$ particles from ${}_{}{}^{204}{}_{}{}^{}\mathrm{Tl}$ used in the experiment.

A more general model of endoreversible cycles is constructed on the basis of the models of endoreversible three-heat-source cycles and generalized Carnot cycles. Its optimal configuration and fundamental optimum formula are studied. It is pointed out that the optimum formula may be used to discuss the effect of finite heat source and thermal resistance on the performances of various thermodynamic cycles. Some more significant results than those of classical thermodynamics can be obtained. They may provide some new theoretical bases for the exploitation and application of the new technology of three-heat-source cycles applying low-level heat sources such as solar energy, geothermal energy, waste heat, and so on. Simultaneously, it is also expounded that many important conclusions in the current literature concerned with endoreversible cycles may all be included in the optimum formula. It is thus clear that the formula can make a unified description of various endoreversible cycles discussed in finite-time thermodynamics. Obviously, the major significance of such a description lies in that it can promote the development of finite-time thermodynamics and the establishment of a systematic theory.

A theoretical explanation for the phenomenon of stochastic resonance in a double well is presented. Starting with the standard Langevin description for this process, a systematic, time-dependent, perturbation-theory analysis of the associated Fokker-Planck equation yields stochastic resonance. In order to get stochastic resonance, the governing parameters must satisfy special inequalities. The analysis also produces these inequalities.

A detailed scaling argument is used to derive an expression for the thermal diffusivity in terms of the heat capacity, correlation length, and susceptibility. This simple model gives good fits to our experimental data near the smectic-A–hexatic-B transition of one liquid-crystal compound and the smectic-A–smectic-C transition of another. The critical dynamics of both transitions is assumed to be described by the conventional theory.

Detailed thermal-conductivity measurements have been performed in the vicinity of the smectic-C–smectic-I transition of racemic 4-(2’-methylbutyl)-phenyl-4’-n-octyloxybiphenyl-4-carboxylate (2M4P8OBC or 8OSI). We observe a large rounded anomaly in the thermal conductivity that can be crudely described by a simple power law. A dip in the thermal diffusivity at the transition-temperature signals the critical slowing down of thermal fluctuations.

Coherent sidebranching of deep cells has been observed experimentally in the vicinity of the cell to dendrite transition. We propose that this phenomenon results from an oscillatory instability of deep cells, where cell widths and tip positions oscillate coherently in phase. We perform a linear-stability analysis of a periodic array of deep cells in the small-Péclet-number limit and derive the stability limits of the oscillatory mode.

We have fitted computer simulation data for the A+B→0 reaction (where [A]<[B]) to a kinetic scheme based on the decay equation [A]=[A${]}_0$exp ($k_1$${\mathrm{Qt}}^{2g}$-$k_2$${\mathrm{Qt}}^g$) previously utilized in luminescence quenching in microemulsion droplets [P. Lianos, J. Chem. Phys. 89, 5237 (1988)]. We used a percolation model of clusters below the critical threshold with a specified range in cluster size. The [A]/[B] density ratio was either constant or varying as a function of p (p is the probability for an allowed site). Our conclusions show that the resulting spectral dimension of the reaction process is always smaller numerically than the customary value $d_s$=(4/3, and that it is strongly dependent on the size and shape of the reaction space. Relevant experiments where these situations arise are also discussed.

A trail is a random walk on a lattice for which two bonds are not allowed to overlap. However, the chain may cross itself and one may associate with each such intersection an attractive energy ɛ. We study trails at infinite temperature T=∞ (i.e., trails without attractions) on a square lattice using the scanning simulation method. Our results for the radius of gyration and the end-to-end distance strongly suggest (as do previous studies) that the shape exponent is ν=0.75, similar to that for self-avoiding walks (SAW’s). We obtain significantly more accurate estimates than have been obtained before for the entropy exponent γ=1.350±0.012 and for the effective growth parameter μ=2.720 58±0.000 20 (95% confidence limit). The persistence length is found to increase with increasing chain length N and the data fit slightly better an exponential function $N^w$ where w=0.047±0.009 than a logarithmic one. Guttmann [J. Phys. A 18, 567 (1985)] has shown exactly that trails and SAW’s on the hexagonal lattice at T=∞ have the same exponents. Our results suggest that this is true also for the square lattice.

We study by the scanning simulation method trails on a square lattice at finite temperatures. This method constitutes a very efficient tool since it enables one to obtain results at many temperatures from a single sample generated at any given temperature. The tricritical temperature at which the collapse transition occurs is -ɛ/$k_B$$T_t$=1.086±0.002. The tricritical exponents of the trail shape and its free energy are, respectively, ${\nu }_t$=0.569±0.008 and ${\gamma }_t$=1.133±0.024 (95% confidence limits). They are equal within the error bars to the exact values of self-attracting self-avoiding walks (SAW’s). However, the crossover exponent ${\phi }_t$=0.807±0.005 is significantly larger than the exact value 0.423 of SAW’s. We also carry out a detailed scaling analysis near $T_t$ and demonstrate that the various properties scale as predicted by theory. At sufficiently low temperatures (T≤$T_t$) the persistence length appears to be ∼1.

We present experimental results showing that such macromolecules as bovine serum albumin (BSA) and deoxyribonucleic acid (DNA) in water solutions build aggregates of fractal structure. We use light scattering techniques, including dynamic (light-beating spectroscopy) and static (intensity) measurements. The BSA results show a behavior similar to that of polystyrene solutions, while for DNA we have observed a restructuring process analogous to those occurring in colloidal silica and gold aggregates.

Mixtures of polar liquid crystals are studied microscopically via the development of the frustrated spin-gas theory, previously applied to single-component systems. Phase diagrams are calculated in the composition and temperature variables, with nematic, smectic-$A_d$, and smectic-$A_1$ phases joined in a variety of topologies, including multiple reentrances and bubbles. Thus experimentally observed topologies are reproduced and new topologies are presented. It is found that the doubly and quadruply reentrant phase diagrams, seen experimentally in mixtures of successive homologs such as the phenyl nitrobenzoyloxy benzoates, ${\mathrm{DB}}_{\mathrm{n}}$${\mathrm{ONO}}_2$, are obtained for molecules with steric hindrance increasing with tail length. These model mixtures also yield reentrant phase diagrams in the pressure-temperature plane that are similar to those seen experimentally.

The ground state of an N-boson assembly interacting through two-body attractive Yukawa forces is analyzed in the Hartree approximation. The solution, which is not universal, can be adequately characterized by a unique parameter μ̃ proportional to μ$N^{\mathrm{-}1}$, where ${\mu }^{\mathrm{-}1}$ is the range of the force. It is found that for μ̃ larger than a critical value, there is no bound solution for the system. Our solutions are shown to rigorously fulfill the virial theorem.

Multifractal dimension spectra for the stable and unstable manifolds of invariant chaotic sets are studied for the case of invertible two-dimensional maps. A dynamical partition-function formalism giving these dimensions in terms of local Lyapunov numbers is obtained. The relationship of the Lyapunov partition functions for stable and unstable manifolds to previous work is discussed. Numerical experiments demonstrate that dimension algorithms based on the Lyapunov partition functions are often very efficient. Examples supporting the validity of the approach for hyperbolic chaotic sets and for nonhyperbolic sets below the phase transition (q<$q_T$) are presented.

An information-theoretic approach is used to give a straightforward procedure that allows one to determine whether dissipative behavior can be attained for a given Hamiltonian. This technique stresses the importance of an adequate set of initial conditions in order to obtain dissipative evolution. It is shown that, although dissipative solutions may be compatible with the set of dynamical equations, they may not be realized just because it is impossible to construct the adequate set of initial conditions that would result in dissipative behavior. This is illustrated by reference to the well-known Bateman generalized problem of two interacting harmonic oscillators. We demonstrate the impossibility of obtaining dissipative evolution in linear, time-independent Hamiltonian systems generated with any combination of bilinear products of creation and annihilation operators.

We present an x-ray scattering study of the intralayer molecular, and the lamellar ordering, in thin substrate-deposited multilayers of the phospholipid dipalmitoylphosphatidylcholine, maintained in a dry or water-saturated helium atmosphere. Unexpectedly, we find that, in the regime of low hydration, water adsorption and desorption do not conform to the widely held notion of a continuous swelling process, but instead occur in discrete steps. As a result, a series of distinct states of hydration appears. These are homogeneously hydrated states of the multilayer in which an integral number of water monolayers is associated with each bilayer. Disordered intermediate states arise in the multilayer in the course of water intercalation as a consequence of the coexistence of two such hydration states. In the present and the accompanying article we show how a quantitative theory of x-ray scattering, developed on the basis of this simple and physically appealing picture, provides a unifying account of a wide variety of observations when applied to the analysis of the lamellar, or (00l) scattering line shapes. This analysis permits conclusions pertaining to the type of layer sequences adopted in the disordered intermediate states. Inspection of the intralayer ordering reveals that throughout the regime of low hydration (≲15% water by weight) examined here the multilayers are in a state consistent with that of tilted hexatic phases.