Using the standard many-body perturbation theory at finite temperature, we exhibit diagrams, not included in the usual random-phase-approximation ring summation, that lead to a 1/‖x${\mathrm{\Vert }}^{10}$ decay of the charge-charge correlation. The quantum origin of this absence of exponential screening is clearly displayed in a semiclassical representation of the electron gas by functional integration, where the effective potential obtained by chain summation is of the dipolar type.

We analyze the cosine-modulated heat kernel g(L)= ${\mathcal{J}}_{\mathit{n}}$ cos(√${\mathit{E}}_{\mathit{n}}$ L)exp(-β${\mathit{E}}_{\mathit{n}}$) of the quantum spectra {${\mathit{E}}_{\mathit{n}}$} within the framework of the periodic-orbit theory and show that it is possible to distinguish between periodic orbits that are isolated and those that occur in families. The graph of g(L) can, therefore, be used to extract the nature of the corresponding classical dynamics.

The dynamical similarities between the three-dimensional (3D) electron fluid ‘‘jellium’’ model and the exactly soluble 1D fermion fluid with attractive δ-function pairwise potentials motivates solving the Cooper-pair problem in this model for all couplings and/or densities. This is accomplished exactly in graphical form. For weak coupling, the essential singularity characteristic of standard 3D low-temperature superconductivity reemerges, and for infinite coupling, BCS theory reproduces the exact ground-state system energy.

We present the results of a numerical investigation of, and supporting analytic arguments for, the behavior of coupled sine maps with a locally conserved variable on a square lattice, with and without noise. By varying parameters we find two distinct conservation-induced routes to chaos: One is a first-order transition from a periodic 2-cycle phase with broken time-translational invariance and long-range, striped, spatial order, to a chaotic, spatially disordered phase in which time-translation invariance is restored; this transition is accompanied by a discontinuous jump in the maximum Lyapunov exponent, ${\lambda }_{\max }$. The other is a continuous onset of temporal chaos occurring without any change in the spatial symmetry of the phase, which has striped (‘‘antiferromagnetic’’) long-range order on both sides of the chaotic onset. In this latter case, ${\lambda }_{\max }$ increases continuously from zero as the control parameter R is increased above the value R=${\mathit{R}}^{\mathrm{*}}$ where chaos sets in; in the presence of noise, the numerics show ${\lambda }_{\max }$ growing linearly with R-${\mathit{R}}^{\mathrm{*}}$, in agreement with simple arguments. Numerical and analytic evidence (strong for the nonchaotic and weaker for the chaotic phases) is presented for the algebraic decay in time of autocorrelations. The asymptotic behavior of spatial correlations is also discussed. We also verify numerically the absence of ‘‘collective chaos,’’ i.e., of chaotic fluctuations of appropriately normalized Fourier amplitudes in the system, consistent with earlier arguments. We briefly discuss the relationship of these results to those of recent experiments on surface waves.

Following a recent work [Sevryuk and Lahiri, Phys. Lett. A 154, 104 (1991)], we study the bifurcation of four-dimensional reversible maps in which the eigenvalues of the Jacobian of the map at a symmetric fixed point move off the unit circle along a pair of conjugate rays as some parameter ε crosses a threshold value. We construct a perturbation scheme to show that, depending on a control parameter γ, the bifurcation can be either ‘‘normal’’ or ‘‘inverted’’ in nature. In the former case, two one-parameter families of elliptic invariant curves passing arbitrarily close to the fixed point (which coexist with Kolmogorov-Arnold-Moser tori) merge together and move away from the fixed point. In the latter case, the families of elliptic invariant curves meet a family of hyperbolic invariant curves. As ε is varied, all these invariant curves shrink to the fixed point and are annihilated. The problem of determining whether an invariant curve is elliptic or hyperbolic is related to a tight-binding model on a linear quasiperiodic chain familiar in solid-state theory. Numerical evidence confirming these results is presented. A few areas for further study are indicated.

The evolution of a gas in an N-dimensional rectangular box is solved for complete generality in the free-molecular regime. By exploiting the linearity of the related equations, the solution is obtained from that of the one-dimensional problem in the case in which the gas is initially concentrated into one point in the box. For this problem, the evolution of the velocity distribution, as well as the hydrodynamical fields, are studied for two particular examples. The long-time behavior of the system is shown to depend strongly on the initial velocity distribution, showing a power-law decay only when the support of that distribution is bounded.

We study the dependence of D, a quantity that has previously been associated with the fractal dimension of an atomic trajectory, on the time scale on which it is measured. Single-particle and relative trajectories are generated by molecular-dynamics simulations of Lennard-Jones atoms permanently trapped in a spherical pore. Transient trapping is studied with a generalized Langevin model of dynamics. Confinement of trajectories allows D to exceed 2; in the case of permanent trapping, D diverges.

The hydrodynamic behavior of fluids in the finite-(k,ω) region is usually described by means of generalized hydrodynamics through (k,ω)-dependent transport coefficients. Here we have developed Grad’s-solution method for solving the Boltzmann equation up to 26 moments; the fluxes associated with the heat flow and the viscosity tensor are considered physically relevant for the description of the system. We obtain the characteristic equations of the generalized hydrodynamics scheme and the following additional results: (i) some particular stationary solutions leading to the usual transport coefficients; (ii) constitutive equations for the viscous tensor and the heat flux, which in the wave-vector space lead to k-dependent transport coefficients; (iii) Maxwell-Cattaneo-like equations in nonstationary states with relaxation times expressed in terms of collision integrals; and (iv) the (k,ω)-dependent transport coefficients associated with the generalized hydrodynamic regime and their relationship with the relaxation times associated with the fluxes.

We discuss the dispersion of particles suspended in time-periodic flows. It is found that this dispersion becomes maximal if the stochastic process describing the intrinsic random motion of the suspended particles is in ‘‘resonance’’ with the time-periodic flow. Furthermore, the dispersion coefficient is found to be proportional to the spectrum of the stochastic process, evaluated at the frequency of the flow. The dispersion is calculated for several cases of interest, including a two-layer, non-Markovian model and field flow fractionation.

Binary diffusive-convective gas flows in a two-dimensional channel with atomically rough walls were studied by molecular-dynamics simulations. We found that, similar to the behavior of monocomponent flows investigated in our earlier work [Phys. Rev. A 42, 4688 (1990)], the no-slip condition arises when the mean free path in the gas mixture is of the same order of magnitude as or smaller than the atomic-wall-roughness amplitude. However, if there are concentration gradients along the wall, the component velocities at the wall do not vanish. Thus the no-slip condition is established via the mutual cancellation of the nonvanishing, opposing slip velocities of the components.

Using a systematic perturbation expansion for slightly supercritical driving, the equation for the slow spatiotemporal variation of the amplitude of convective rolls is derived when the temperatures of the horizontal fluid boundaries are modulated harmonically in time. The modulation frequencies are considered to be large compared with the amplitude growth rate, but small enough to avoid the generation of thermal Stokes layers. The marginally stable, time-dependent linear functions determining the fast spatiotemporal periodic variations of the convective fields as well as all coefficients entering into the amplitude equation depend on the modulation and the Prandtl number. Analytic expressions for all these quantities are given for small modulation amplitudes and idealized horizontal boundary conditions. The time-dependent convective heat current is compared with previous results from few-mode Galerkin approximations.

The aim of this work is to show that, in the condensed phases, the flux of thermal energy couples with a flux of momentum. This follows from considerations of rational mechanics and can be also deduced as a corollary of a theorem established by Boltzmann, following a straightforward reasoning already developed by Ehrenfest in a somewhat simpler case than the one considered by us. When heat flux crosses the boundary between two adjoining media, the momentum flux changes, and ‘‘thermal radiation forces’’ should appear. Accordingly, the momentum-balance equation of continuous-field hydrodynamics should include, when applied to nonisothermal media, the momentum flux due to heat flow. When this is done, analytical expressions for thermal radiation forces are obtained with reference to various simple physical systems. The theoretical predictions lend themselves to direct experimental verification. Very good qualitative and quantitative agreement between theory and experiment has been found in various experimental systems, as described here, lending strong support to the proposed approach. Interestingly, experimental results obtained with macroscopic objects and with molecular or ionic particles both lead to analogous conclusions concerning the properties of thermal radiation forces, a circumstance that broadens the possible field of application of these concepts. Finally, it is suggested that the concept of momentum flux coupled to transport of thermal energy in the condensed phases can be fruitfully employed in the investigation of complex phenomena such as acoustic streaming and the Bérnard-Rayleigh instabilities.

Accurate neutron-diffraction measurements on saturated liquid iodine, up to Q=16 Å ${}_{}{}^{\mathrm{-}1}{}_{}{}^{}$, at T=409 K are presented. The intermolecular structure factor has been derived and a study performed on the presence of orientational correlations and their contribution to the intensity distribution. The experimental intermolecular pair correlation function has been compared with the results of a simulation performed using the anisotropic atom-atom pair potential proposed by Rodger, Stone, and Tildesley [Mol. Phys. 63, 173 (1988)], giving excellent agreement. A comparison with previous neutron and x-ray data is also discussed.

The nonlocal-density-functional theory for hard-sphere mixtures proposed in an earlier paper [Phys. Rev. A 42, 3382, (1990)] is used to investigate the structure and the thermodynamics of binary simple liquid mixtures adsorbed on substrates. We study (i) the adsorption of Lennard-Jones fluids in slit-shaped pores with varying pore size, (ii) the selective adsorption of liquid argon-methane mixtures onto a planar graphite surface at constant pressure, (iii) the density profiles of charged hard spheres in the vicinity of a highly charged hard wall (primitive model of the electrical double layer). We compare our calculations to computer-simulation data and to the predictions of other recent theories. In all cases, packing effects are very well described by the theory, and most discrepancies can be ascribed to the mean-field treatment of attractive forces.

Immiscible fluid-fluid displacement was studied experimentally and numerically in porous models consisting of uniform pores on a square lattice where all nearest neighbors were connected by bonds randomly given one of two permeabilities. Patterns formed by a high-viscosity fluid (glycerol) being displaced by a low-viscosity fluid (air) injected at the center of the model network were studied and compared with the results of diffusion-limited-aggregation (DLA) simulations using a network with identical geometry. For a bond permeability ratio κ≃0.004 close to the bond percolation threshold ${\mathit{f}}_{\mathit{c}}$=0.5 of high-permeability bonds, simulated and experimental patterns exhibit a high degree of overlap. The displacement patterns generated in experiments and in simulations can be characterized by the same effective fractal dimension ${\mathit{D}}_{\mathit{c}}$≃1.5. We find that the model geometry strongly influences the structure of the displacement pattern formed, and that Meakin et al.’s [Physica A 115, 1 (1989)] modified-DLA algorithm provides a good model for the displacement.

Binary mixtures of liquid crystals whose constituent molecules are not cylindrically symmetric are considered. For a mixture consisting of biaxial molecules with ${\mathit{D}}_{2\mathit{h}}$ symmetry, two tensor order parameters are required to specify the orientational order of each component. Using mean-field theory, expressions for the free energy of the mixture and the orientational order parameters are obtained as functions of temperature. In the geometric-mean approximation, the parameters of the theory are ratios of anisotropic interaction strengths, which can be determined from measurements on the pure components. The theoretical predictions are compared with recent experimental results of ${}_{}{}^2{}_{}{}^{}\mathrm{NMR}$ measurements on the binary mixture of the liquid-crystal 2-fluorenyl-4’-tetradecyloxy-benzoate-${\mathit{d}}_9$ (${\mathrm{FLOC}}_{14}$) and p-xylene-${\mathit{d}}_{10}$ (p-Xy).

A computational method for the spinodal decomposition is presented on the basis of a nonlinear theory proposed by Langer, Bar-on, and Miller [Phys. Rev. A 11, 1417 (1975)] (LBM) with an application of Suzuki’s [Prog. Theor. Phys. 56, 77 (1976); 56, 477 (1976); 57, 380 (1977); Adv. Chem. Phys. 46, 195 (1981); J. Stat. Phys. 49, 977 (1987)] general scaling theory for transient phenomena. The results were compared with experimental observations for a typical polymer-blend system with respect to the experimentally accessible quantities such as the structure factor and the single-point distribution function. The main features observed in scattering experiments were reproduced by this method. The inequality β>3α was found in the numerical analyses when fitting the power-law relations expressed by ${\mathit{q}}_{\mathit{m}}$∝${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ and ${\mathit{S}}_{\mathit{m}}$∝${\mathit{t}}^{\mathrm{\beta }}$ to the time variations of the dominant Fourier component of concentration fluctuations ${\mathit{q}}_{\mathit{m}}$ and the corresponding structure factor ${\mathit{S}}_{\mathit{m}}$. It is shown that the LBM theory can be used to describe the phase-separation behavior up to intermediate stages.

A calorimetric characterization of a second-order nematic (N)-smectic-${\mathit{A}}_2$ (Sm-${\mathit{A}}_2$) transition and a detailed heat-capacity study of a Sm-${\mathit{A}}_2$–Sm-${\mathit{C}}_2$ (smectic-${\mathit{C}}_2$) transition have been carried out on 4’-n-heptyloxy-carbonylphenyl-4’-(4’’-cyanobenzoyloxy) benzoate (7APCBB). The N–Sm-${\mathit{A}}_2$ heat capacity is well described by the three-dimensional XY model with critical exponent α=-0.007 and amplitude ratio ${\mathit{A}}^{\mathrm{-}}$/${\mathit{A}}^{+}$=0.98. The excess heat capacity Δ${\mathit{C}}_{\mathit{p}}$ associated with the Sm-${\mathit{A}}_2$–Sm-${\mathit{C}}_2$ transition increases in a steplike fashion from zero in the Sm-${\mathit{A}}_2$ phase to a constant value in the Sm-${\mathit{C}}_2$ phase. This behavior agrees with that observed previously in octylphenyl-2-chloro-4-(p-cyanobenzoyloxy) benzoate (${\mathrm{DB}}_8$ClCN). In both cases, the Sm-${\mathit{A}}_2$–Sm-${\mathit{C}}_2$ behavior is markedly different from the ${\mathit{C}}_{\mathit{p}}$ behavior at Sm-A–Sm-C transitions in nonpolar systems, all of which conform to a Landau model with a large sixth-order term.

In the leveled-wave model, random porous morphologies are simulated by discrete maps of continuous stochastic standing waves generated by adding sinusoids over suitable distributions of wave vectors and phase constants. The mathematical structures obtained this way appear to be useful models for certain kinds of random geometries, such as the bicontinuous morphologies that occur in microemulsions and porous glasses. Properties of the leveled-wave method are developed, and the scattering behavior is derived. Scattering from an arbitrary three-phase system can be analyzed by adding different instances of scattering from a generalized film morphology in which the scattering phase is confined to the interior of the interspatial region bounded by two leveled-wave interfaces that are separated everywhere. General results for this interspace scattering are derived. Fractal surfaces, dimension 2≤D≤3, are incorporated into the leveled-wave scheme by using a wave-number distribution having an appropriate long-tailed asymptotic behavior. Scenarios are discussed for the scattering as D→2 from above and for D→3 from below. For D=3 the asymptotic scattering falls faster than algebraically as the scattering wave vector Q→∞.

A numerical analysis of the photothermal probe-beam signal generated at first- and second-order phase transitions in 4-n-octyl-4’-cyanobiphenyl (8CB) is proposed. A criterion for photothermal signal sensitivity in detection of phase transitions is given. The influences of probe-beam transverse offset and modulation frequency, as well as thermal parameters of the probed medium, on this sensitivity are investigated experimentally and theoretically. It is shown that the photothermal signal may be insensitive to the phase transitions for certain values of the modulation frequency and the probe-beam transverse offset, while a maximum of sensitivity is obtained for a range of values of these parameters. It is also shown that this sensitivity is improved if we use a probed medium with an effusivity smaller than the sample effusivity. A comparison of some of the results of the theory with experimental results is given.