The dynamical process through a marginal state (saddle point) driven by colored noise is studied. For small correlation time of the noise, the mean first-passage time and its variance are calculated using standard methods. When the correlation time of the noise is finite or large, an alternative approach, based on simple physical arguments, is proposed. It will allow us to study also the passage times of an unstable state. The theoretical predictions are tested satisfactorily by the use of computer simulations.

Chaos at and beyond onset is studied for nonequilibrium current-carrying dissipative states in quasi-one-dimensional dirty superconductors. For the case of ac-driving currents, phase-slip center solutions of the generalized time-dependent Ginzburg-Landau equations show a universal transition at the onset of chaos. For currents below the onset, the pervasive feature is the nonhyperbolicity: homoclinic tangency between stable and unstable manifolds of unstable periodic orbits. Pointwise dimensions α(x) evaluated on the attractors show abnormally low values, indicating regions made of an overlapping of stable and unstable manifolds of saddle orbits. These regions cause a break of self-similarity and a phaselike transition in the multifractal probability measure of the attractor. Finally, one of these tangencies causes a symmetry-increasing bifurcation.

The theory of zero-range potentials is investigated in an arbitrary number of dimensions. Except for the trivial one-dimensional case the zero-range potentials are described by nonlocal operators called Fermi pseudopotentials. It is shown that in odd dimensions the Fermi pseudopotentials involve a very simple regularization operator. In even dimensions with the help of dimensional regularization, explicit formulas for the Fermi pseudopotentials are derived. The Green’s functions, the propagators, and the exact solutions of the Lippmann-Schwinger equations are derived in explicit forms. In odd dimensions d=1 and 3 the Fermi pseudopotentials can be applied to describe multiphoton processes of atoms and molecules with very short-range interactions. In even dimension d=2 the Fermi pseudopotential can be applied to describe tunneling from laser-driven quantum wells. Physical applications involving higher d are also possible.

The thermodynamic properties of maps derived from strongly dissipative Lorenz-type flows are studied by means of generalized Frobenius-Perron operators. Three different types of phase transitions are found: (I) second-order transitions occurring at zero temperatures caused by short-range interactions in an associated spin chain characterizing hyperbolic maps, (II) first-order transitions caused by long-range interactions at finite temperatures induced by anomalous but exponential scaling in nonhyperbolic cases, and (III) transitions of extreme orders induced by nonexponential scaling in certain nonhyperbolic maps. Type-III transitions might also appear in the spectra of generalized entropies at nonzero temperatures. A novel feature of Lorenz-type maps is the existence of type-II-type-III and type-III-type-III double transitions.

We derive the Debye law for the specific heat of solids within the realm of stochastic electrodynamics (i.e., classical electrodynamics with the assumption of a real zero-point field). Random lattice vibrations are generated by the Planck radiation including zero point, which is absorbed by the ions. The equilibrium is accomplished by a fluctuation-dissipation mechanism due to the emission of radiation by the ions in accelerated motion.

Colored-noise systems are described by the two-dimensional Fokker-Planck equation. The stationary probability distribution of the Fokker-Planck equation is analytically expressed in terms of an expansion formalism that can be simultaneously applied to both large and small correlation times. The convergence condition of the expansion is briefly discussed.

We present an experimental study of stationary convection in a binary mixture at positive values of a separation ratio. The interplay between the Rayleigh-Bénard and the Sorét mechanisms of instability and the corresponding boundary conditions gives us the possibility to observe a transition from large- to small-scale structures as well as a transition between patterns with different symmetries. We also investigate an influence of lateral boundaries and the cell geometry on the pattern selection.

Kinetics and continuum emission of negative ions are studied in stationary atomic hydrogen, nitrogen, and oxygen plasmas. The intensity of the negative-ion emission was found to be negligible when compared to those of bound-bound and free-bound emission at low and medium particle densities. However, the negative-ion continuum emission can contribute significantly in certain parts of the emission spectrum at high particle densities.

We formulate the problem of diffusion-decay processes occurring in two half-spaces separated by a boundary (a one-dimensional problem). The equations are solved by Laplace transforms, by finite differences, and by a Green’s-function technique. The inverse Laplace transform integrals are evaluated numerically and agree with the finite-difference calculations. Thus each may be regarded as accurate. Late-time asymptotic approximations are derived from the Laplace representation, and early-time approximations are derived from the Green’s-function representation. These are compared with the numerical integration and finite-difference results. We also introduce a method for modeling the processes by random walks, which treats the complications introduced by the presence of the boundary. All of the above-noted calculational methods are compared. It is especially important that the asymptotic approximations are accurate in their domain of validity, as they allow us to introduce a physical picture regarding the competition of diffusive and decay processes.

The linear stability of exothermic autocatalytic reaction fronts that convert unreacted fluid into a lighter reacted fluid is considered using the viscous thermohydrodynamic equations. For upward front propagation and a thin front, the discontinuous jump in density at the front is reminiscent of the Rayleigh-Taylor problem of an interface between two immiscible fluids, whereas the vertical thermal gradient near the front is reminiscent of the Rayleigh-Bénard problem of a fluid layer heated from below. The problem is also similar to flame propagation, except that here the front propagation speed is limited by catalyst diffusion rather than by activation kinetics. For a thin ascending front and small density changes in a laterally unbounded system, the curvature dependence of the front speed stabilizes perturbations with short wavelengths λ<${\lambda }_{\mathit{c}}$, whereas long wavelengths are unstable to convection, indicating that the density discontinuity dominates over thermal gradients. Simple analytical results for the critical wavelength ${\lambda }_{\mathit{c}}$ for onset of convection, the growth rate near onset of convection, and the maximum growth rate are found. Agreement with experiments on iodate–arsenous acid solutions in vertical tubes motivates linear and nonlinear calculations in cylindrical geometries.

The microscopic dynamics of nonequilibrium gas flows in the transition regime (Knudsen number ∼1) is studied using novel molecular-dynamic (MD) simulations. The Knudsen number dependence of the shear viscosity, temperature jump, slip length, and the entropy production is investigated. It is shown that the assumption of local equilibrium breaks down in supersonic flows. A good agreement of the MD simulation results with available experiments and other theoretical studies is found.

The linear equations governing the onset of convection in a binary fluid subject to the Soret and Dufour effects are solved exactly for rigid boundary conditions by expanding the velocity and temperature as Fourier sine series. The velocity and temperature distributions are found to be those of the free-boundary problem, plus small admixtures of higher harmonics. Exact expressions for the Rayleigh number and oscillation frequency are obtained in terms of infinite series. For the special case of negligible Dufour effect our results agree with exact numerical calculations. Results for the general case are compared with previous approximate methods of solution.

The rotationally resolved absorption spectrum of the 3d ${}_{}{}^2{}_{}{}^{}\mathit{p}$ ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ transition in molecular LiHe has been measured. For each of three isotropic variants ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^3{}_{}{}^{}$He, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^4{}_{}{}^{}$He, and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^4{}_{}{}^{}$He, six vibrational transitions have been observed from the lower 2p ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$(v’’=0,1) electronic state to the upper 3d ${}_{}{}^2{}_{}{}^{}\mathrm{\Delta }$(v’=0,1,2,3) electronic state. Analysis of the observed spectra has yielded values for the well depth and equilibrium separation of 1020(20) ${\mathrm{cm}}^{\mathrm{-}1}$ at 3.37(3)${\mathit{a}}_0$ for the 2p ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ state and 610(20) at 3.52(2)${\mathit{a}}_0$ for the 3d ${}_{}{}^2{}_{}{}^{}\mathrm{\Delta }$ state. Details of our analysis and our experimental technique are presented.

We consider the problem of transport of a passive tracer in the time-dependent flow corresponding to a Rayleigh number scrR slightly above the ${\mathit{scrR}}_{\mathit{t}}$ at the onset of the even oscillatory instability for Rayleigh-Bénard convection rolls. By modeling the flow with a stream function, we show how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity. This approach and symmetry considerations allow us to write explicit formulas that describe the tracer transport for finite times. In the limit of small amplitude of the oscillation, i.e., when (scrR-${\mathit{scrR}}_{\mathit{t}}$${)}^{1/2}$ is small, we show that the amount of fluid transported across a roll boundary grows linearly with the amplitude, in agreement with the experimental and numerical findings of Solomon and Gollub [Phys. Rev. A 38, 6280 (1988)]. The presence of molecular diffusivity introduces a (long) time scale into the problem. We discuss the applicability of the theory in this situation, by introducing a simple rule for determining when the effects of diffusivity are negligible, and perform numerical simulations of the flow in this case to provide an example.

We discuss a possible mechanism for intermittency of the energy dissipation in a model for three-dimensional fully developed turbulence. We compute the structure functions for the velocity field and show that their behavior can be described in the context of a multifractal approach. We also compute the instantaneous maximum Lyapunov exponent and the corresponding (stability) eigenvector. Violent bursts of energy dissipation are related to a sudden increase of the instantaneous Lyapunov exponent, and simultaneous localization of its eigenvector on the high wave numbers at the end of the inertial range. In particular, we relate the correction to the ${\mathit{k}}^{\mathrm{-}5/3}$ Kolmogorov law for the energy spectrum to the fractal dimension extracted by temporal sequences both of the instantaneous Lyapunov exponent and of the eigenvector.

In order to model turbulent channel flow, and establish a closure approximation in lattice-gas hydrodynamics, I implement a Lévy walk at the microscopic level. The algorithm is described and discussed, and results on velocity profile flattening and its shape are presented.

We have investigated experimentally the spatiotemporal behavior of a narrow water stream flowing between two parallel inclined Plexiglass plates bounded laterally by air. Complex broadband dynamics occurs as a result of the velocity dependence of the contact angle at the water-air-Plexiglass contact line, which introduces critical values into the pressure required for contact line motion over the Plexiglass plates. This mechanism causes a stick-slip type of motion similar to that appearing in other systems such as flows in granular materials, models of earthquake dynamics, and charge-density-wave motion in solids. We find that above a certain flow rate ${\mathit{Q}}_{\mathit{s}}$, a stationary spatial modulation of the width of the stream appears. At higher flow rates, a hysteretic transition occurs in which the contact line begins to move, and the pattern slips down the plates with broadband dynamics. The statistical properties of the motion are presented.

Rayleigh-Bénard convection is considered with the top surface of the bounding volume sinusoidally corrugated. Parametric resonance is shown to occur if the wavelength of the corrugation is half the wavelength of the convection rolls that one would have observed with a flat surface.

We present a comprehensive study of the structure of liquid binary alkali-metal alloys using integral-equation techniques. As in the one-component case we find that the soft-mean-spherical approximation is definitively superior to the hypernetted-chain approximation for such potentials, having a harshly repulsive short-ranged part and an oscillating long-ranged part. We find very good agreement with other liquid-state theories (perturbative methods and computer experiments) and good agreement with experimental scattering data, the differences being due to the simple model potential used (Ashcroft empty-core potential). By truncating the interactions at increasing distances (until recovering the full potential), we reveal the strong influence of the long-ranged parts of the interaction on the structure. We finally present an attempt to include thermodynamic self-consistency, being for the case of liquid metals a delicate problem that —for the moment—may not be solved exactly.

Deuterium nuclear magnetic resonance ${(}^2$H NMR) is used to extend studies of confined nematic structures to submicrometer-size cavities. Spectral patterns reveal the escaped-radial configuration in untreated cylindrical cavities of Nuclepore filters. This configuration is found to survive in pore sizes as small as 0.2 μm in radius. Singular point defects are found to be present along the escape axis with the density of the defects being determined from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ NMR spectra. This density is found to be unaffected by cycling between the nematic and isotropic phases with or without the presence of an applied magnetic field.