We suggest an insight into level dynamics of classically nonintegrable quantum systems. When several nonintegrability parameters are varied in a Hamiltonian, the desymmetrized energy spectrum generally exhibits degeneracies. In this case the fundamental equation of level dynamics is altered as follows: (i) Euclidean ‘‘space-time’’ coordinates are needed instead of a single ‘‘time’’ coordinate; (ii) gauge structures around diabolical degenerate points are incorporated into level dynamics. With these changes we obtain an alternative field-theoretical model for interacting energy surfaces.

When a Turing bifurcation occurs close to a Hopf bifurcation in the parameter space of a reaction-diffusion system, the Turing and Hopf modes may interact nonlinearly to form, a priori, a variety of complex spatiotemporal patterns. We have studied this type of interaction for three models of chemically active media: the Lengyel-Epstein model of the ${\mathrm{ClO}}_2^{\mathrm{-}}$–${\mathrm{I}}^{\mathrm{-}}$–malonic acid system, a model that describes the ferroin-catalyzed Belousov-Zhabotinsky reaction, and the Brusselator. One and two spatial dimensions are considered. The Poincaré-Birkhoff method was implemented for the reduction of the models to the Turing-Hopf normal forms. The normal-form analyses show that the stability regions of stationary periodic patterns and of homogeneous oscillations usually overlap over a wide region in parameter space, forming a domain of bistability. Mixed-mode (spatiotemporal) patterns do not occur in the models considered except for a very small region in the parameter space for two-dimensional hexagonal patterns.

The effect of external random noise on the transition to chaos at critical circle maps with golden-mean winding number is studied by three different methods with particular stress on the method of quasipotential scaling. A comparison of the various methods serves to explain why former computations of noise-scaling factors were valid only for Gaussian noise and shows how to deal with a larger class of noise distributions.

A systematic numerical technique for the calculation of unstable periodic orbits in the stadium billiard is presented. All of the periodic orbits up to order p=11 are calculated and then used to calculate the average Lyapunov exponent and the topological entropy. Applications to semiclassical quantization and to experiments in mesoscopic systems and microwave cavities are noted.

The time evolution of a dynamical system is examined in a space where two or more strange repellers coexist under the absence of any other attractors. Depending on the characteristics of every individual transient chaos we can model dynamical processes with different statistical properties.

The integral equation for the dynamic pair correlation function derived previously from the modified moment method is solved for a non-Newtonian soft-sphere fluid undergoing a plane Couette flow. In this approach, the dynamic pair correlation function is a functional of the shear stress, which determines the macroscopic state of the nonequilibrium fluid. The distortions of the structure factor at high shear rates are examined for a non-Newtonian fluid. Normal stress effects are included in the study presented. It is found that as the shear rate increases, the structure factor fractures into domains of high intensity in the xy (shear), xy, and yz planes in the wave-vector space. At packing fractions in the range of η=0.3–0.45, the structure factor exhibits a plateau behavior at reduced shear rates γ¯≥100, and this behavior is seen to be directly related to the thixotropy of the fluid. In all planes considered, the structure factor suggests, essentially, a distorted-fluid-like structure, although there is evidence indicating that the approach to an ordered phase is also a probable interpretation. These effects are in qualitative agreement with the observations made on colloidal suspensions and low-shear-rate molecular-dynamics simulation results. In the presence of normal stresses, the structure factor in the xy plane is rotated in the direction of the shear flow. The angle of rotation is determined by the magnitude of the primary normal stress difference and also by the thermodynamic state of the fluid. The structure factor in the yz plane is similar to the case without normal stresses, and the xz plane is undistorted.

For coupled transfer of the energy and mass in a multicomponent system at mechanical equilibrium a simple thermodynamic theory is developed, and the damped wave equations of change are derived. We show that under nonstationary conditions, where relaxation of diffusive fluxes is essential, the evolution of the distributed coupled transfer of the energy and mass follows the path that minimizes the difference between the total entropy generated within the system and that exchanged by the system. The principle is also valid in the limit in which flux relaxation effects are negligible and the heat and mass transfer, whether steady or not, obeys Onsager’s generalization of the Fourier and Fick laws. For coupled steady-state processes the principle goes into that of Onsager, yielding his phenomenological equations. In contrast to the local steady-state nature of Onsager’s principle the new principle is global, valid for both stationary and transient situations, and requires no frozen fields. For an isolated, distributed system, in which transient relaxation to equilibrium is the only possible process, the principle implies the least possible increase of the system entropy between any two successive configurations.

Concepts of hydrodynamics and hydrodynamic modes are explored for dense fluids under conditions for which mode-coupling effects are important. Dispersion relations associated with the matrix of equilibrium time correlation functions for conserved densities are studied to isolate the hydrodynamic part of its spectrum. An Enskog-like model for hard spheres, including lowest-order bilinear density mode-coupling effects, is used for the analysis over a wide range of dense fluid conditions and for wavelengths extending down to those of the order of the correlation length. The hydrodynamic branch is identified as that which vanishes in the long-wavelength limit. The dispersion relations are investigated to determine the existence of such a hydrodynamic spectrum, and its possible extension to short wavelengths. Mode-coupling effects are shown to complicate the usual simple pole structure by introducing branch points that also vanish in the long-wavelength limit. Emphasis of this study is placed on the mode corresponding to heat diffusion. It is found that mode-coupling effects introduce significant changes in the extended modes, but the soft heat mode at wavelengths of the order of the correlation length remains a simple pole and provides the dominant contribution to the density autocorrelation function.

In this work we describe the spectral properties of the daily medium temperature fluctuations measured from 1951 to 1989 in Hungary. We compare our observations with the experiments of Libchaber and co-workers, in which the local temperature fluctuations were measured in a helium cell. We suggest that the dynamics of the daily temperature fluctuations is determined by the soft turbulent state of the atmospheric boundary layer.

Turbulent flow between concentric cylinders is studied in experiments for Reynolds numbers 800<R<1.23×${10}^6$ for a system with radius ratio η=0.7246. Despite predictions for the torque scaling as a power law of the Reynolds number, high-precision torque measurements reveal no Reynolds-number range with a fixed power law. A well-defined nonhysteretic transition at R=1.3×${10}^4$ is marked by a change in the Reynolds-number dependence of the torque. Flow quantities such as the axial turbulent diffusivity, the time scales asociated with the fluctuations of the wall shear stress, and the root-mean-square fluctuations of the wall shear stress and its time derivative are all shown to be simply related to the global torque measurements. Above the transition, the torque measurements and observed time scales indicate a close correspondence between this closed-flow system and open-wall–bounded-shear flows such as pipe flow, duct flow, and flow over a flat plate.

A simple microscopic model of chemical reactions is explored for diatomic exchange reactions 2AB?${\mathit{A}}_2$+${\mathit{B}}_2$. A pair of atoms bind chemically when they lie within a ‘‘square’’ attractive well. The presence of a bond, however, leaves the bound atoms in a state in which they have only hard-sphere repulsion for other atoms. A calculation combining the canonical-ensemble Monte Carlo technique with molecular dynamics is used to determine the equilibrium composition and thermodynamic properties of equimolar binary mixtures of A and B atoms, subject to this square-well, hard-sphere interaction potential for temperatures and densities accessible to detonation waves in a fluid consisting of metastable AB molecules at an initial temperature ${\mathrm{\varepsilon }}_{\mathit{A}\mathit{B}}$/20${\mathit{k}}_{\mathit{B}}$ (in which ${\mathrm{\varepsilon }}_{\mathit{a}\mathit{b}}$ is the well depth of the ab interaction and ${\mathit{k}}_{\mathit{B}}$ is the Boltzmann constant), with ${\mathrm{\varepsilon }}_{\mathit{A}\mathit{A}=3\mathrm{}}$${\mathrm{\varepsilon }}_{\mathit{A}\mathit{B}}$ and ${\mathrm{\varepsilon }}_{\mathit{B}\mathit{B}}$=${\mathrm{\varepsilon }}_{\mathit{A}\mathit{B}}$. The calculations for systems of both 216 and 1728 atoms include the pressure, the internal energy, and the mean free times for various types of collisions. The Hugoniot curve for states behind detonation waves is determined for six values of the density for the smaller systems and one value for the larger; finite-system effects are found to be small. The Hugoniot curve is shown to have a concave shape in the pressure-volume plane, typical of exothermic materials, and the Chapman-Jouguet state is determined.

A finite-dimensional su(N) Lie algebra equation is discussed that in the infinite N limit tends to the two-dimensional, inviscid vorticity equation on the torus. The equation is numerically integrated, for various values of N, and the time evolution of an (interpolated) stream function is compared with that obtained from a simple mode truncation of the continuum equation. The time-averaged vorticity moments and correlation functions are compared with canonical ensemble averages.

I describe experiments on one-dimensional states of nonlinear traveling-wave convection in a narrow annular cell. Spatially uniform states are found to be stable within a band of wave numbers whose width grows approximately as the square root of the distance above a saddle-node Rayleigh number. Inside the band, I have measured the static properties of the traveling waves, including their response to spatial inhomogeneities in the Rayleigh number. Outside the stability band, traveling-wave states become unstable to temporally growing modulations of the spatial wave-number profile that propagate through the system at the group velocity of the underlying traveling waves. If allowed to grow, this Eckhaus instability leads, via a subcritical bifurcation, to spatiotemporal defects in which pairs of rolls are created or annihilated. In contrast with the action of the Eckhaus instability in stationary pattern-forming systems, the recurrent appearance and propagation of defects leads to long, erratic transients in which the system may or may not be driven back into the stable wave-number band.

This paper continues a description of experiments on one-dimensional, nonlinear, traveling-wave convection in a binary fluid with separation ratio ψ=-0.127 in a narrow annular cell. It is possible to create and manipulate steady-state sources and sinks of traveling waves in this system, as well as to produce stable fronts that separate convecting and quiescent regions. Source defects tend to drift at constant velocity, emitting Doppler-shifted traveling waves whose wave number lies outside the Eckhaus boundary measured for spatially uniform traveling-wave states. I present both qualitative descriptions of such phenomena and quantitative measurements of the amplitude and wave-number profiles of sources, sinks, and fronts.

The phase diagram of a lattice microemulsion model proposed by Ciach, Ho/ye, and Stell [J. Phys. A 21, L777 (1988); J. Chem. Phys. 90, 1214 (1989)] is studied using mean-field theory and Monte Carlo simulations. Surfactant directional degrees of freedom are summed out exactly before mean-field theory is applied, and the resulting phase diagrams are much improved compared with previous mean-field results. The critical line and tricritical point are located using Monte Carlo simulations and finite-size scaling.

Neutron-specular-reflectivity measurements were made on liquid surfaces of disordered one-phase microemulsions consisting of mixtures of nonionic surfactant ${\mathrm{C}}_{10}$${\mathrm{E}}_4$, ${\mathrm{D}}_2$O, and octane, with equal volume fractions of water and oil, in the region of the phase diagram where the bulk microemulsion structure was known to be bicontinuous. From these measured reflectivity data, the one-dimensional scattering-length-density profiles in the vertical direction of the air-microemulsion interfaces were reconstructed directly by using a model-independent inversion scheme developed recently by one of us. From the reconstructed scattering-length-density profiles, we constructed the one-dimensional Debye correlation functions. From these correlation functions, we deduced the surface-induced layering with periods that correlate well with the bulk water-water domain average repeat distance known from a previous small-angle neutron-scattering study. We discuss in particular the effect of a finite-Q range of data on the height of the first ${\mathrm{D}}_2$O layer.

We develop a general field-theoretical approach for computing fluctuation-induced forces between manifolds immersed in a correlated fluid. Both isotropic, e.g., a superfluid or critical binary mixture, and anisotropic, e.g., nematic or smectic liquid crystals, are considered. The effects of different types of boundary conditions are explored, and in particular the role of deformations from perfect geometries is studied. Specific results include the following: The Casimir force between a flat and a self-affinely rough surface acquires a correction term that decays with the average separation of the plates through an exponent related to the roughness of the boundary. Surface fluctuations in films of correlated fluids may be enhanced, or suppressed by such forces, depending on whether the boundaries are alike or different. We also compute the resulting two-body force between a line (directed polymer) and a surface, and the three-body interaction (repulsive) between three lines.

The dynamics of phase separation in a critical micellar solution of pentaethylene glycol mono-n-dodecyl ether and water was examined by time-resolved low-angle light scattering in the spinodal region. It was found that the time evolution of the phase separation is well scaled by use of the characteristic lengths and the exponent in the power-law expression of such lengths as a function of the quenching depth is in good agreement with the value for the three-dimensional Ising model.

A phenomenological equation of motion for an unstable planar crystalline interface is derived and used to describe the early stages of hill and valley formation. We calculate the critical wave number for the growth of instabilities and the scattering structure function. Predictions for the temperature dependence of the width-to-length ratio and the front propagation velocity in Si are presented. The importance of an elastic interaction on the domain formation process is demonstrated and shown to explain existing experiments. Elastic interactions are also found to modify the decay rate of perturbations of stable surfaces at arbitrarily long wavelengths.

A generalized coherent-potential-approximation (GCPA) approach is developed for the identification of quasimodes in dispersed random media and the calculation of their dispersion relations. Application of this approach to colloidal suspensions of solid spheres yields the prediction of two acoustic modes in excellent agreement with the observations of a recent Brillouin-scattering experiment [J. Liu, L. Ye, D. A. Weitz, and P. Sheng, Phys. Rev. Lett. 65, 2602 (1990)]. We show that whereas the high-frequency mode is associated with the solid-sphere antiresonances, the low-frequency mode arises from the coupling of the internal resonances between neighboring spheres. Our theory yields quantitative agreement with the measured dispersion relations with no adjustable parameters, and provides a theoretical explanation for the observed frequency gaps in the excitation spectra. Application of the GCPA to the electromagnetic wave in dispersed random media is also described.