An experiment to probe the (quasi)localization of the photon is proposed, in which optical layers are constructed following the Fibonacci sequence. The transmission coefficient has a rich structure as a function of the wavelength of light and, in fact, is multifractal. For particular wavelengths for which the resonance condition is satisfied, the light propagation has scaling with respect to the number of layers, as well as an interesting fluctuation.

A high-energy linear collider consisting of two beams, a driver beam of electrons and a high-energy beam, in which the intense low-energy driver beam is bunched, is analyzed theoretically. The low-energy beam is made to travel through resonant transfer cavities, in which it radiates microwave energy that is used to accelerate the second beam to very high energies. The low-energy beam is maintained at a constant energy by periodic induction acceleration cavities.

We develop a quantum theory of propagation in dispersive nonlinear media. Quantum fluctuations are handled via the coherent-state positive-P representation. A stochastic nonlinear Schrödinger equation in the field variables is obtained which predicts wide band squeezing in the region of anomalous dispersion. For soliton inputs, fluctuations are reduced over the soliton bandwidth. This leads to quantum solitons which have quadrature fluctuations less than the level of vacuum fluctuations.

High-accuracy numerical results are shown which go against current conjecture that dimensionless finger width λ in the Saffman-Taylor problem is a monotonically increasing function of dimensionless surface tension τ, asymptotically approaching 1/2 as τ→0. Specifically, quasi steady-state fingers are shown for finite τ with λ significantly below 0.5. These solutions are consistent with published experimental results obtained in a Hele-Shaw cell, indicating that the Saffman-Taylor equations are sufficient to explain this phenomenon.

With a Biot-Savart model of vortex filaments to provide initial conditions, a finite difference scheme for the incompressible Navier-Stokes equation is used in the region of closest approach of two vortex rings. In the Navier-Stokes solution, we see that the low pressure which develops between the interacting vorticity regions causes the distortion of the initially circular vortex cross section and forces the rearrangement of vorticity on a convective time scale which is much faster than that estimated from viscous transport.

The structure of the cores of interacting vortex tubes in three-dimensional incompressible hydrodynamics has been simulated by a pseudospectral method. A fast reconnection is observed for Reynolds numbers of order 1 000. At higher Reynolds numbers, the core tends to flatten, suggesting the formation of vortex ribbons.

Deterministic chaos in the intensity of the beam produced by a barium titanate self-pumped phase-conjugate mirror has been observed. The correlation exponent of the strange attractor is found to depend on the crystal orientation and to lie within the range 1.2 to 2.4, and the order-two Renyi entropy is found to increase with increasing laser intensity and to be as large as 22 bits/sec. A standard model of self-pumped phase conjugation due to four-wave mixing has been generalized to include time dependence. This model predicts frequency shifts and chaotic behavior for the reflectivity.

Results of a theoretical study of the permeability k and proton relaxation rate ${\mathrm{T}}_1^{\mathrm{-}1}$ in fully and partially saturated porous media are presented. Numerical calculations on two distinct geometrical models of granular materials predict a strong correlation between k and ${\mathrm{\phi }}^4$${\mathrm{T}}_1^2$ for fully saturated systems (with porosity φ) in agreement with a recent experimental study.

Self-induced stochastic behavior for the evolution of light along a periodically perturbed two-mode nonlinear optical waveguide is predicted. Implications for recently demonstrated all-optical switching using birefringent fibers are discussed.

A Lagrangian has been developed that leads to equations of motion which are isomorphic to the full Navier-Stokes equation, including dissipation. This Lagrangian has been developed to give a many-body description turbulence along the standard lines of most field theories.

We present experimental measurements of the velocity of a convective vortex front propagating into an unstable conductive state in a Rayleigh-Bénard system for the wide range of ε (ε≡ΔT/Δ${\mathrm{T}}_{\mathrm{c}}$-1) between 4×${10}^{\mathrm{-}4}$ and 2.5×${10}^{\mathrm{-}1}$. The results are found to be in excellent quantitatitve agreement with the theoretical predictions following from an amplitude equation, exhibiting a sharp selection mechanism in the propagation velocity. Wave-number selection by this dynamical mechanism is also studied.

We introduce a stochastic process called a Lévy walk which is a random walk with a nonlocal memory coupled in space and in time in a scaling fashion. Lévy walks result in enhanced diffusion, i.e., diffusion that grows as ${\mathrm{t}}^{\mathrm{\alpha }}$,α>1. When applied to the description of a passive scalar diffusing in a fluctuating fluid flow the model generalizes Taylor’s correlated-walk approach. It yields Richardson’s ${\mathrm{t}}^3$ law for the turbulent diffusion of a passive scalar in a Kolmogorov -(5/3) homogeneous turbulent flow and also gives the deviations from the (5/3) exponent resulting from Mandelbrot’s intermittency. The model can be extended to studies of chemical reactions in turbulent flow.

We consider the interaction of counterpropagating pulses via a ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearity, in an isotropic electrostriction medium. The polarization is taken into account and can vary through each pulse; group-velocity dispersion is neglected. We find a family of analytic solutions, termed polarization solitons, which play a central role in the dynamics. Upon interaction, the net effect on their polarization profiles is a rigid rotation in Stokes vector space. As special cases, they include the first nontrivial examples of polarization-transparent and orthogonally switched pulses.

Highly nonlinear phenomena are observed in Taconis oscillations which are spontaneous oscillations of gas columns thermally induced in a tube with steep temperature gradients. Near the overlapped region and the intersection of the stability curves for two different modes with incommensurate frequencies, we find that both modes can be excited simultaneously and competition between them leads to complex quasiperiodic and chaotic states. Experimental data are anlayzed by use of recent methods from the theory of nonlinear dynamical systems.

Electromagnetic fields with photon-number fluctuation reduced below the standard quantum limit have been generated in a constant-current–driven semiconductor laser. The generation is based on a new principle of high impedance suppression for pump-amplitude fluctuation in a highly saturated laser oscillator. The observed noise level is 7.3% (31% after correction for detection quantum efficiency) in power below the standard quantum limit in the entire frequency range between 350 and 450 MHz.

When a resonance mode is excited in a two-dimensional array of dielectric spheres, the local-field intensity is enhanced inside the spheres. This resonance frequency decreases with the increase of the dielectric constant. By use of these two properties, a new mechanism is proposed to realize optical bistability at a low laser power.

Hydrodynamic fluctuations in a dilute gas subjected to a constant heat flux are studied by both a computer simulation and the Landau-Lifshitz formalism. The latter explicitly incorporates the boundary conditions of the finite system, thus permitting quantitative comparison with the former. Good agreement is demonstrated.

The frequency offset of the sideband instability in a free-electron laser (FEL) should depend on (1-$v_{?}$/$v_g$${)}^{\mathrm{-}1}$, where $v_{?}$ is the average longitudinal velocity of the electrons and $v_g$ is the group velocity of the electromagnetic waves. We have tested the $v_{?}$/$v_g$ dependence of the sideband shift in a 2-mm, Raman-regime FEL oscillator. A change of $v_{?}$/$v_g$ from 0.93 to 0.98, accomplished by an increase in the undulator period, resulted in the measured sideband shift increasing from 6% to 40%, in approximate agreement with theory.

A method is given for analytic determination of new stationary configurations of objects with logarithmic pair potentials in two dimensions such as vortices, charges, and screw dislocations. The method is applicable to configurations with arbitrary mixed strengths in the presence of background fields. New stationary and uniformly translating vortex configurations are presented, some of which can be generated from N-soliton solutions of the Korteweg–de Vries equation.

Without resort to any modeling, subgrid-scale eddy viscosity is computed from the results of high-resolution (${64}^3$ and ${128}^3$ grid points) direct numerical simulations of three-dimensional homogeneous, isotropic, decaying turbulence. In these simulations the eddy viscosity peaks sharply at the cutoff wave number, in rough agreement with the results of Kraichnan. In addition, in the low–wave-number range the eddy viscosity may be negative, contrary to the generally accepted concept of a subgrid-scale eddy viscosity. Some possible explanations of this behavior are discussed.