A regularization procedure of the Chapman-Enskog expansion is introduced. It extends the hydrodynamical description into higher gradients domains. This was intended but never accomplished satisfactorily by the Burnett equations. The resulting macroscopic system formally has the same form (and complexity) as the Navier-Stokes equations, with the new transport coefficients being wavelength dependent. It reduces in the long-wavelength limit to the Burnett equations. In agreement with experimental evidence, strong shock layers are narrower in comparison with the predictions of the Navier-Stokes theory.

The critical Reynolds number for the linear instability of primary flow is calculated for a Taylor-Couette system in which the rotation rate of either cylinder is modulated sinusoidally in time. The method used is based on that of Hall [J. Fluid Mech. 67, 29 (1975)] and is restricted to small amplitudes of modulation but allows for a finite gap. For the case of outer-cylinder modulation, we find that the critical Reynolds number is larger than that for the unmodulated system, while, if the inner cylinder is modulated, it is smaller.

The analysis of optical data for critical adsorption from a fluid (or fluid mixture) onto a wall or interface is discussed theoretically with emphasis on elucidating the universal, scaled adsorption profile P(z/ξ), where ξ(T) is the correlation length and z is the distance from the interface. A novel strategy, which embodies theoretically well-established features, is applied to recent reflectivity and ellipsometry experiments on binary mixtures against glass and vapor substrates. Overall, the data indicate relatively strong surface fields and clearly reveal crossover from a power-law regime, P(x)≊$P_0$/$x^{\beta /\nu }$, as x->0, to P(x)≊$P_{\infty }$$e^{\mathrm{-}x}$, as x->∞, occurring around x≃1.4 with $P_{\infty }$/$P_0$≃0.85. The relative merits of reflectivity and ellipsometry techniques are assessed (the latter currently proving more definitive) and various experimental issues are identified which must be resolved before more details of the adsorption profile could be extracted from further observations.

A two-dimensional system of hard cyclic hexamers is shown to display an anomalous (negative) Poisson ratio in a high-density crystalline phase. The anomaly can be reproduced qualitatively by a simple free-volume (FV) approximation. The FV approximation and a lattice model indicate the crucial role of broken mirror symmetry for this phenomenon.

A theoretical and molecular dynamics analysis of hydrogen and oxygen density correlation functions in liquid water is presented with the aim of clarifying the present experimental situation. In the theoretical study, besides the ordinary sound mode, a high-frequency ‘‘optical-like’’ collective mode is found to propagate through the hydrogen atoms. The dispersion relation of the two modes is discussed. Computer-simulation results for the partial intermediate scattering functions are reported and confirm the theoretical predictions. The direct comparison of the theoretical predictions and the computer-simulation results with the experimental findings suggests an interpretation of the nature of the two modes. Finally the collective character of the propagating modes is pointed out by comparing the self-part of the scattering function with the total one.

Relaxation oscillations are very commonly found in nature. When modulation by an external force is present, a global hysteresis connected with chaos is often encountered. In addition to this kind of hysteresis a qualitatively different ‘‘local’’ form is found in some systems. We describe the circumstances under which one observes local hysteresis. A specific system treated in detail is the Fohlmeister model, originally derived to describe a neuronal encoder. In the limit of small damping an analytical solution is obtained. Furthermore, we derive an upper limit to the hysteresis. The results are compared to numerical calculations on the full system and agree quite well. In contrast to the driven damped-pendulum equation, the hysteresis is limited in size as compared to the phase-locked region.

Intermittent auto-oscillations of the dynamic magnetization prior to chaotic behavior have been observed in microwave transverse pumping of the subsidiary resonance in a yttrium iron garnet sphere at room temperature. These intermittencies appear simultaneously with a period-doubling bifurcation. Diversely from the type-III Pomeau-Manneville intermittency, the observed chaotic bursts do not seem to be associated with an increase in the amplitude of the subharmonic mode, which remains essentially constant during the laminar phases. From time-series data the distribution of the laminar period lengths has been measured, and a return map has been constructed. These results are in reasonable agreement with a theory based on a symmetrical mapping that describes the dynamics of Lorenz-type flows. Experimental evidences of new scenarios for the onset of chaos are also presented.

The problem of fluctuations on the charged track length by electromagnetic cascades in an absorber of finite thickness is investigated by means of a model. General expressions for the deterioration of the energy resolution are derived and compared with the predictions of the (electron-gamma shower) code for radiation transport.

We analyze the interactions of the first and second mode arising in the one-sided and the symmetric model of directional solidification of a dilute binary alloy if a planar interface loses stability and stationary cellular structures are formed. Algebraic bifurcation equations for the coupled amplitudes of the two unstable modes are derived from the nonlinear equations of motion with the interface velocity as a control parameter. The transitions from planar to cellular interfaces are described in terms of normal forms and bifurcation diagrams. Thereby we predict that each of the two bifurcating solution branches can show hysteretic behavior and that for suitable values of the parameters involved there exist tertiary Hopf bifurcations to time-periodic interface shapes. The results are compared to recent numerical work and the nature of the one-sided limit is discussed.

Ideas from the theory of dynamical systems are applied to a collection of N identical point masses interacting via one-dimensional ‘‘gravity,’’ with a two-body force F=-G sgn($x_a$-$x_b$). This Hamiltonian system is viewed as a geodesic flow on a curved, but conformally flat, N-dimensional space, the curvature of which exhibits certain interesting features. In the large-N limit, the Ricci tensor can be written approximately in the form $R_a^b$=-Λ${\delta }_a^b$+$B_a^b$, where Λ is a smooth, negative-definite quantity which, oftentimes, can be viewed as nearly constant, and $B_a^b$ is a positive sum of δ functions of codimension 1. The curvature K(u,δx)==$R_{\mathrm{abcd}}$$u^b$$u^d$δ$x^a$δ$x^c$ associated with a small change δ$x^a$ in the N-velocity $u^a$ of the system is not negative definite. However, in the large-N limit, the smooth piece of K associated with a ‘‘generic’’ change δ$x^a$ of a generic $u^a$ is in fact negative, the fraction of $u^a$’s and δ$x^a$’s leading to a positive K decreasing at least as fast as $N^{\mathrm{-}1}$. If the δ-function contributions to K could be ignored, as they can for D-dimensional ‘‘gravity’’ with D≥2, this would imply an average ‘‘mixing’’ very much akin to the astrophysicists’ ‘‘violent relaxation’’ on a time scale τ given essentially as the free-fall time for the system. This conclusion fails, however, because of the singular contributions to K reflecting physical collisions which, for one-dimensional gravity, cannot be ignored. The similarities and differences between one- and three-dimensional ‘‘gravitational’’ systems are discussed, and it is argued that numerical simulations of one-dimensional systems need say little about real three-dimensional systems.

A time-dependent variational principle (TDVP) is used to describe the evolution of a molecular exciton on a Davydov lattice at T=0. The variational trial state is taken as a linear combination of generalized coherent states with variational parameters given by a set of time-dependent exciton probability amplitudes ${\phi }_n$, lattice-displacement amplitudes $d_{\mathrm{kn}}$, and phonon-pair amplitudes $g_{\mathrm{kk}\mathcal{’}n}$ (n labels the exciton sites and k the phonon modes). Previous applications of the TDVP to the Davydov lattice have ignored pair contributions ($g_{\mathrm{kk}\mathcal{’}n}$=0) and have either (1) set $d_{\mathrm{kn}}$=$d_k$ (the mean-displacement approximation of standard Davydov theory) or (2) left $d_{\mathrm{kn}}$ unrestricted. In the present work we introduce the mean-pair approximation $g_{\mathrm{kk}\mathcal{’}n}$=$g_{\mathrm{kk}\mathcal{’}}$ while leaving $d_{\mathrm{kn}}$ unrestricted. We obtain new evolution equations that provide a basis for testing the adequacy of case (2) above. We have integrated these equations numerically and find that the mean-pair corrections to case (2) are quite small over the range of exciton-phonon coupling constant considered.

A Laplacian growth model with the third boundary condition, (1-P)∂Φ/∂n-PΦ=0, is considered in order to study the effect of the sticking probability of the diffusion-limited aggregation (DLA), where Φ is the harmonic function satisfying the Laplace equation and ∂Φ/∂n the derivative normal to the interface. The crossover from the dense structure to the DLA fractal is investigated by using a two-parameter position-space renormalization-group method. A global flow diagram in two-parameter space is obtained. It is found that there are two nontrivial fixed points, the Eden point and the DLA point. The DLA point corresponding to the DLA fractal is stable in all directions, while the Eden point is a saddle point. When the sticking probability P is not 1, the aggregate must eventually cross over to the DLA fractal. The crossover exponent φ and crossover radius $r_{\times }$ are calculated.

The velocity and alignment of T4 and λ DNA have been measured during field-inversion gel electrophoresis (FIGE) at field strengths E between 6 and 14 V/cm. Immediately after E changed sign, the velocity exhibited an oscillatory behavior before reaching a steady value. The times at which these oscillations occurred were shorter for λ DNA (48.5 kilo-base-pairs) and longer for smaller E. However, the distance each DNA had traveled, when scaled by its contour length L, was about 0.1 for the first velocity peak and 0.15–0.3 for the undershoot for both molecular weights and all values of E studied, provided that E was on for at least 12 s prior to the field inversion. If the field was on for only a short time before inversion, the first sharp peak in velocity was progressively reduced in magnitude and duration. The alignment function f=(3〈${\cos }^2$θ〉-1)/2, where θ is the angle between the helix axis and E, was measured for the same DNA’s, field strengths, and pulse times. The alignment was at all times parallel to E but decreased sharply immediately after field inversion to a minimum, followed by an overshoot and then a plateau. The time after field inversion at which the minimum in f occurred was approximately the same as that of the velocity maximum. The anticorrelation between the velocity and f, as well as the invariance of x/L for the velocity overshoot, support the idea, first suggested by computer simulations, that DNA undergoing gel electrophoresis spends much time hooked over gel fibers in ssU-shaped chain configurations. The measured velocity curves of T4 DNA were integrated to compute the net displacement after a series of positive and negative field inversions. The average velocity computed from this displacement showed a pronounced ‘‘antiresonance’’ or minimum at the same pulse period as observed in practical FIGE separations.

Results of light-scattering experiments on helium and xenon gas mixtures are presented for a large range of wave vectors, densities, and compositions. In the experiments these variables are varied independently from each other. In this manner we are able to show that the hydrodynamic eigenfrequencies, reduced with respect to the product of the wave vector k and the adiabatic sound velocity $c_s$, are a function of the product of the wave vector and the mean free path $l_{\mathrm{He}}$ only. By comparing the experimentally obtained dispersion curves and the predictions of the hydrodynamic theory, we find that the value of ${\mathrm{kl}}_{\mathrm{He}}$ at which the theory ceases to be valid is independent of the composition. We show that the longitudinal current-current correlation function ${\omega }^2$I(k,ω) is a useful function in the study of light-scattering spectra that are featureless. For large reduced wave vectors we find a sound mode that is solely supported by the fluctuations in the xenon density. This is the slow sound mode.

A detailed discussion of the path-integral formalism for stochastic processes described by a stochastic differential equation driven by a nonwhite noise is given. The path-integral representation in the configuration space of the transition probability for a process driven by Ornstein-Uhlenbeck noise is derived. We show how to treat in this approach any kind of initial conditions, including the question of the coupling with the noise at initial time. Known approximations are reobtained in this context. Markovian approximations based on the Lagrangian are also discussed. The stationary distribution of the process in the weak-noise limit is obtained from the Lagrangian without relying on the use of Fokker-Planck or Markovian approximations.

In this paper we continue our study of the (discretized) evolution of regular and fractal patterns initiated by a site-specific reactive event. By formulating and solving (numerically) the stochastic master equation descriptive of the model introduced (for two classes of initial conditions and for two locations of the target site), we are able to demonstrate that symmetry-breaking instabilities which generate fractal patterns (here the Sierpinski gasket) propagate slower than those which generate Euclidean ones (here the triangular lattice). A connection is made between (two) characteristics of the system’s evolution (the zero-mode relaxation time and an effective relaxation time descriptive of the overall decay of the initial state) and results calculated using the theory of finite Markov processes (the mean walk length of a coreactant diffusing on the underlying lattice). Using this relationship, the trends observed in our study are interpreted in light of recent theoretical work on the problem of diffusion on fractal lattices and in terms of the notion of a ‘‘fractal’’ valency, a concept that places stress on insights drawn from earlier analytic and numerical studies of random processes on finite planar lattice of integral dimension d=2. Finally, the possible relevance of our results to a specific problem in pattern formation and development, the generation of neural networks of the Purkinje type, is discussed.

The first-passage time density for nearest-neighbor random walks on various deterministic fractal lattices is calculated. The procedure consists of the derivation of a renormalization equation, similar to that derived by Machta for a random walk in one dimension [Phys. Rev. B 24, 5260 (1981)], and in its solution in terms of an auxiliary function, defined by a functional equation. Both the cases of waiting times with finite first moment or with fractal time properties are discussed. By rescaling time and length in the appropriate way, the first-passage time density approaches a ‘‘universal’’ asymptotic form ψ(τ). The scaling properties are consistent with subdiffusive behavior 〈δ$r^2$(t)〉∼$t^{2/\mathrm{dw}}$, with $d_w$>2, as discussed previously in the literature. The overall shape of ψ(τ) is found to be very similar to that for a random walk in one dimension, except that the small-τ behavior is qualitatively different in both cases. The existence of these two time regimes was already suggested by Guyer [Phys. Rev. A 29, 2751 (1984)] and explains why different scaling forms for the Green’s function have been proposed in the literature.

The structure factors for two thermodynamic states of the mixture He-Xe have been measured by neutron diffraction. These two thermodynamic states are the coexisting ones at the phase transition of the gas-gas demixing process. The Xe-Xe correlations, in the mixture, appear to be similar to those in pure Xe near the coexistence curve and having the same Xe number densities. These results suggest that this phase transition is of the liquid-gas type.

The multichannel quantum defect theory (MQDT) of fine structure has been extended to hyperfine structure by dividing the configuration space into three parts: The α region, the i region, and the $i_F$ region, according to the competition among short-range interaction, spin-orbit interaction, and hyperfine interaction. Then an unperturbative theory of hyperfine structure in high Rydberg states is derived. The MQDT parameters of hyperfine structure have been categorized into two parts: one is contributed by short-range and spin-orbit interactions and has been given by an analogy with the MQDT parameters of fine structure; the other is contributed by spin-orbit and hyperfine interactions and has been given analytically. The hyperfine structure in high Rydberg states can then be calculated directly from the MQDT parameters of fine structure.

We prove that for any nonrelativistic rotationally invariant two-particle quantum system whose interaction is velocity independent the total angular momentum of the ground state is bounded by the sum of the spins; i.e., $j_{\max =s_1+s_2}$. .AE