Nonlinear propagation in single-mode and multimode fibers in the presence of the optical Kerr effect is described in terms of a number of parameters (four for each propagating mode) which can be interpreted as conjugate variables of a suitable Hamiltonian system. The formal simplicity of this approach, which admittedly furnishes a limited description of nonlinear propagation because of the finiteness of the number of variables employed, is, however, very useful for gaining a straightforward physical insight into the problem. The solution of the pertinent equations, either analytical or numerical, presents a much less formidable task than the solution of the set of nonlinear equations fully describing propagation.

Using the nonlinear oscillator model as a prototype medium exhibiting intrinsic optical bistability, we investigate the inhomogeneous absorption of the electromagnetic field. The forward- and backward-field amplitudes and diffraction effects are retained in the mathematical description. Analytic results are given in the limit of plane-wave propagation under steady-state conditions. The transmitted and reflected intensity exhibit a structure that is determined by the spatial inhomogeneity of the absorption in the longitudinal direction. The transmitted intensity has a structure that is dependent on the length of the medium. The reflected intensity has an interference structure from light reflected at the front surface and the internal boundary separating a high-polarization from a low-polarization branch. A degenerate-four-wave-mixing experiment is predicted to be a very sensitive probe of the internal boundary and the interference between the forward and backward field. The phase-conjugate signal develops large oscillations as the input field is varied. Numerical results for diffraction effects are also given, and we find that the plane-wave results for the center of the beam remain reliable down to Fresnel numbers of order unity and in media that are smaller than the linear absorption length.

We present a model for light-induced drift (LID) in the Na–noble-gas system which should enable direct comparison with experiment. In contrast to previous theories of LID based on a two-level description of the optical absorbers and on a simplified collision treatment, the present model is based on a realistic description of laser-driven Na atoms immersed in a buffer gas. Starting from the generalized Bloch equations, we introduce a rate-equation model for the velocity distributions in the four important Na levels. The velocity-changing and fine-structure-changing collisions are described using composite Keilson-Storer collision kernels in which all adjustable parameters have been eliminated by using available literature data. We apply the model in numerical calculations of LID as a function of all experimentally accessible parameters. It is found that the ground-state hyperfine splitting can have large effects on LID, whereas the excited-state fine-structure splitting has not. The paper establishes criteria for optimum LID effects; when using a single-frequency laser the maximum attainable drift velocity is predicted to be 13.8 m/s. Using a proper set of boundary conditions, we find a pressure dependence of LID qualitatively different from the predictions based on previous work. Finally, the influence of the collision model is investigated. We find that LID is independent of the shape of the collision kernel, indicating that a strong-collision model is always valid.

We study N two-level atoms coupled to a single mode of the electromagnetic field. This system obeys a conservation law that restricts the set of states which can be reached by time evolution from a given initial state. This fact allows one to calculate time-independent bounds for certain observables, in particular, the uncertainty in photon number, Δn. These bounds can be used to determine how sub- or super-Poissonian the photon statistics can become. This is done for an initial coherent state and an initial thermal state. For the coherent state the number of atoms must be greater than the square root of the initial number of photons for highly sub-Poissonian fields to be possible. On the other hand, for the thermal state N must be greater than the initial photon number for this to occur. In the case of the thermal state, we also find that the field will never become sub-Poissonian if the ratio of the initial photon number to N is greater than a quantity of order 1.

In the following we present a new set of phase-space equations, based on Haken’s laser model, for dealing with atom-cavity situations such as the laser or optical bistability. The most important feature of these equations is that they do not require a scaling in terms of the number of atoms to obtain results, and hence can be used in few-atom situations outside the applicability of other equations. There is a mathematical emphasis in the paper as we develop our equations, but we also use the equations to determine the leading noise terms for the one-atom laser as well as outlining their possible usage in other problems.

It is shown that saturation causes the three-peaked four-wave-mixing (FWM) signal at frequency 2${\omega }_1$-${\omega }_2$, obtained from the interaction of a two-level system with a ‘‘probe’’ laser of varying frequency ${\omega }_2$ and a ‘‘pump’’ laser of fixed frequency ${\omega }_1$, to become asymmetrical on increasing the probe-laser intensity. Whereas saturation peaks occur in the population-inversion spectrum at one-photon and multiphoton resonances, this is not so for the FWM spectrum, where often the peaks correspond to nothing more than minima in the population-inversion spectrum.

We discuss the effect of a spectral line with Doppler broadening on optical bistability in a ring cavity which contains a saturable absorber of two-level atoms. In this paper, we first derive a generalized equation that is satisfied by the output light intensity of this system from the Langevin equations in H. Haken’s Laser Theory (Springer, Heidelberg, 1970). Then, we simplify the generalized equation for a single mode. We study the single-mode equation for both nonexisting and existing spontaneous emission and obtain the result that the square of the bistability loop increases with the increase of Doppler broadening of the spectral line.

The problem of two-phase fluid flow in statistically homogeneous but random porous media is addressed. Particular emphasis is placed on the role of the stochastic nature of the porous medium in the development of unstable interfaces at large mobility ratios. A formalism is developed in which the random nature of a real porous medium can be incorporated quantitatively into a numerical simulation scheme based on a discretization of the continuum fluid-mechanical equations. In particular, it is not necessary to set the discretization length close to the pore scale and to perform a detailed structural analysis of the microgeometry in order to characterize the random nature of the porous matrix. The formalism is based on the concepts of tubes and chambers which give rise, on the discretization length scale, to random hydrodynamic conductivity and fluid capacity, respectively, and on larger scales to the macroscopically determined permeability and porosity, respectively. In the absence of detailed information about the statistical properties of the random medium at the discretization length scale, a maximum entropy criterion is used to deduce the most random distribution of properties of tubes and chambers consistent with macroscopically observable quantities. This criterion reveals the fundamental significance of an exponentially distributed fluid capacity. A number of numerical experiments are reported. The relation of the present simulation algorithm to diffusion-limited aggregation (DLA) and related algorithms for the simulation of two-phase flows is revealed, and exponentially distributed fluid capacity is again found to be of fundamental significance. In particular, it is found that a number of further assumptions which are physically plausible but difficult to justify rigorously are required to relate the DLA and similar ‘‘random-walk’’ models to a fluid-mechanical model based on the equations of continuum mechanics applied to a stochastic medium.

A criterion for determining the coupling and the exponent [K(η,β) and ζ(η,β)] of the one-Yukawa generalized mean spherical approximation (GMSA), which better describes a given real fluid, is suggested. The relative spatial configuration of the surface (≡${\Sigma }_{\chi }$) where the compressibility diverges, with respect to the surface (≡${\Sigma }_{\Delta }$) bounding the region where physical solutions of the GMSA equations exist, is studied in terms of K, ζ, and η (the packing fraction). ${\Sigma }_{\chi }$ is found to lie always in the physically accessible region and to become tangent to ${\Sigma }_{\Delta }$ along the η axis; that consequently will be the locus of the critical points of the real systems. By the aforesaid criterion we show that the Baxter solution of the adhesive hard-sphere model can be obtained from the limit of the GMSA solution as ζ→∞. The study of the limit ζ→0 shows that the GMSA critical indices are generally different from the mean-field ones and that their values depend on the way ζ approaches zero as one moves along the critical isochore and the critical isotherm. Attention is also called to the fact that, as ζ→0, K(η,ζ)/${\zeta }^2$ has a minimum at η=0.128, a value rather close to the critical densities of the real fluids.

A general theory of stopping power for electrons and ions in a target medium (gas, liquid, or thin solid foil) containing neutral as well as positive and negative ions is developed. The approach is quite accurate in the low- and medium-energy range (<1 MeV), where the Bethe stopping-power cross section is inaccurate. The energy transfer during individual collisions is treated by the binary-encounter approximation. The theory is applied to determine the stopping power of seawater, whose major components are ${\mathrm{H}}_2$O molecules and ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{\mathrm{-}}$ ions. The stopping-power cross sections for low- and medium-energy protons in water show excellent agreement with existing measurements. The theory is extended to relativistic energies and to cases where the excitation of the incident and target particles is allowed. The approach is quite general and can be applied to other ionic, atomic, and molecular systems.

In this paper we use the recently developed transient-time-correlation function formalism (TTCF) to study the transient rheology of classical fluids. We compare this approach to the calculation of fluid transport properties using the Green-Kubo method (valid only in the linear-response regime), with direct nonequilibrium molecular dynamics (NEMD) simulations, and with the NEMD subtraction technique. The various approaches are compared for a system undergoing isothermal, planar Couette flow. Although less efficient than direct NEMD at large strain rates, the TTCF results agree with direct NEMD to high accuracy. At low strain rates where direct NEMD is not applicable, the TTCF approach is clearly more efficient than the subtraction method.

A self-consistent approach to the Lamm sedimentation equation is proposed for describing the diffusion induced by a centrifugal (or gravitational) field in a two-component condensed system, particularly for a high solute concentration or a high centrifugal field. In this approach, the driving force inducing the diffusion is expressed by introduction of the effective mass of the surrounding mixture (solvent and solutes) which causes the buoyant force. It is self-consistently represented as a function of concentration in place of the constant value in the Lamm equation. The theory is constructed on the basis of nonequilibrium thermodynamics and the Nernst-Einstein relation considering the effect of concentration change. The resulting diffusion equation is presented in a nonlinear form instead of the linear one of the Lamm equation. The concentration profile in equilibrium state is found by solving the nonlinear diffusion equation. It is shown that the nonlinear effect is significant with increase either in the solute concentration or in the centrifugal field.

The viscosity of water/AOT/oil microemulsions (undecane, isooctane, cyclohexane) has been studied as a function of the molar ratio n=[water]/[AOT] and the volume fraction φ (water + AOT) at T=25 °C. [Here AOT is an abbreviation for sodium bis(2-ethylhexyl)sulfosuccinate.] At constant φ and variable n, the presence of a maximum viscosity can be observed. The results are discussed in connection with a percolation model and a very good qualitative agreement is obtained. The results are compatible with those obtained previously on the conductivity and complex permittivity of these microemulsions. The results show the importance of the idea of ‘‘percolation threshold lines.’’ Emphasis is placed on the importance of interactions and on the necessity of following an experimental procedure involving constant interaction (for either ternary or quaternary systems).

Transport of muonic hydrogen and deuterium atoms in gaseous hydrogen and deuterium is studied in the diffusion approximation and by means of the multiple-collision expansion. The diffusion coefficient is derived. Numerical results of the time-dependent problem in slab geometry are presented for a number of initial energies, temperatures, and pressures.

We compute nonequilibrium correlation functions about the stationary state in which the fluid moves as a consequence of tangential stresses on the liquid surface, related to a varying surface tension (thermocapillary motion). The nature of the stationary state makes it necessary to take into account that the system is finite. We then extend a previous analysis on fluctuations about simple stationary states to include some effects related to the finite size of the sample.

A number of phase-separation mechanisms in fluids are hidden in earth-bound experiments due to the influence of gravitationally induced flow. Solutions to this problem can be found by using strictly matched-density systems, such as the partially deuterated cyclohexane and methanol system (${\mathrm{C}}^{\mathrm{*}}$C-M), or by performing experiments in space so as to benefit from the microgravity environment. Both types of studies have been performed here to determine quantitatively to what extent such matched-density systems could recreate, on earth, microgravity conditions; they were restricted to the neighborhood of the liquid-liquid critical point. A 6-min microgravity environment has been provided in the sounding rockets of the TEXUS program: Two experiments have been performed, one (T11) using the nonmatched-density system of fully deuterated cyclohexane and methanol (${\mathrm{C}}^{\mathrm{*}}$-M), and one (T13) using the matched-density system ${\mathrm{C}}^{\mathrm{*}}$C-M. In experiment T13 the phase separation was seen to be characterized by a high-contrast, periodiclike pattern, so that the observations could be performed by a simple optical method. In order to analyze quantitatively the possible differences with the earth-based experiments, the origin of the detected images had to be carefully analyzed. It appeared that they are connected to the interface pattern of the phase-separating fluid. Therefore, after digitization and statistical treatment, it was possible to check the important scaling properties of the phase separation: structure factor, reduced moments, typical wavelength pattern. Experiment T11 was qualitatively different from the earth-bound experiment and can be understood only by an unexpected extreme sensitivity of the growth mechanism to the volume fraction. The T13 results did not evidence any deviation between the microgravity and the earth-based experiments, thereby validating a complete study of the phase separation in the critical region using matched-density systems on earth. Gravity effects on very-long-term periods remain to be estimated, however.

Percolation transitions are analyzed for correlated distributions of occupied sites created by irreversible cooperative filling on a square lattice. Filling can be either autocatalytic, corresponding to island formation, or autoinhibitory. Here percolation problems for occupied and unoccupied clusters are generally distinct. Our discussion focuses on the influence of island formation (associated with correlation lengths of many lattice vectors), and of island perimeter roughness, on percolation. We also discuss the transition to continuum percolation problems as the ratio of island growth to nucleation rates, and thus the average island size, diverges. Some direct analysis of occupied cluster structure is provided, the connection with correlated animals is made, and correlated spreading and walking algorithms are suggested for direct generation of clusters and their perimeters.

Interactions are included in the standard model of site percolation by specifying two numbers, $p_0$ and $p_1$, which are the probabilities of occupying a site on a lattice if none or at least one of the neighboring sites are occupied, respectively. This is expected to be a better description of systems where interactions between neighbors can either enhance or deter site occupation. Monte Carlo methods are used to simulate the irreversible growth of clusters starting from an empty two-dimensional square lattice, and continuing through the percolation threshold. The value of the percolation threshold $p_c$ and other properties of the system depend on the parameter r=$p_1$/$p_0$. For r=1, the system corresponds to random percolation. As r→∞, compact Eden clusters are produced, which link together to form larger, fractal clusters. As r→0, neighboring sites become less easily occupied, resulting in checked ‘‘domains’’ separated by antiphase boundaries. Several quantities are analyzed to determine the critical exponents ν, γ, and β, including the threshold distribution width, the mean cluster size, and the infinite cluster size. For all finite values of r, the data are found to be consistent with the exponents of random percolation.

Several exact recursion relations connecting different Morse oscillator matrix elements associated with the operators $q^{\alpha }$$e^{\mathrm{-}\beta \mathrm{aq}}$ and $q^{\alpha }$$e^{\mathrm{-}\beta \mathrm{aq}}$(d/dr) are derived. Matrix elements of the other useful operators may then be obtained easily. In particular, analytical expressions for ($y^k$d/dr) and [$y^k$d/dr+(d/dr)$y^k$], matrix elements of interest in the study of the internuclear motion in polyatomic molecules, are obtained.

Mean first-passage times (MFPT) of non-Markovian processes driven by Markovian two-state noise of finite correlation time are considered. Absorbing as well as reflecting boundary conditions are constructed, and new results for the first-passage-time density and the MFPT are derived. We extend our study to dichotomic Fokker-Planck processes, i.e., a stochastic dynamics in which the random walker jumps between two different Fokker-Planck processes with a dichotomic noise dynamics. In this general case, too, we derive the boundary conditions explicitly and obtain novel expressions for the MFPT. A number of special cases and limits are considered which elucidate the physics of the more general results. Finally, we consider the problem of bistability driven by dichotomic noise and express the MFPT in terms of the stationary probability density. For the escape rate at weak noise we establish the connection between the MFPT approach and the current overpopulation method.