We study shock waves propagating in a rigid heat conductor at low temperature using a generalized Maxwell-Cattaneo equation. The existence of a critical temperature θ̃, characteristic of the material, for which the structure of the shock changes is proved. When the unperturbed temperature ${\mathrm{\theta }}_0$ is less than θ̃ the temperature ${\mathrm{\theta }}_1$ behind the shock wave front is such that ${\mathrm{\theta }}_1$>${\mathrm{\theta }}_0$ (hot shock), and, vice versa, if ${\mathrm{\theta }}_0$>θ̃ then ${\mathrm{\theta }}_1$<${\mathrm{\theta }}_0$ (cold shock. We find θ̃=15.36 K for NaF and θ̃=3.38 K for Bi. These temperatures are very close to the values at which the second sound was identified experimentally in pure NaF and Bi crystals.

For anisotropic porous media of arbitrary topology, it is shown that there exists a rigorous relation between the fluid permeability tensor k and the diffusion-controlled trapping constant γ, namely, k≤${\gamma }^{\mathrm{-}1}$I. It is demonstrated that the equality is achieved for a certain class of microstructures and that the bound can be relatively sharp for other media. The important fundamental as well as practical implications of this relation are discussed.

The transport of photons through a slab of random medium is shown to deviate from the diffusion approximation when z/${\mathit{l}}_{\mathit{t}}$ is small, where z is the thickness of the slab and ${\mathit{l}}_{\mathit{t}}$ is the transport mean free path. When z/${\mathit{l}}_{\mathit{t}}$=10 and z=10 mm, the average time of arrival is about 0.9 times that predicted by diffusion theory. Photons are found to arrive earlier than that predicted by the diffusion theory as z/${\mathit{l}}_{\mathit{t}}$ becomes smaller or the anisotropic scattering increases.

We discuss the superdiffusive motion of a random walk in a medium containing random velocity fields. For a two-dimensional layered medium with y-dependent random velocities in the x direction u(y), 〈${\mathit{x}}^2$(t)〉∼${\mathit{t}}^{2\nu }$, with 2ν=3/2, and with strong sample-to-sample fluctuations. The probability distribution of displacements, averaged over environments, takes a non-Gaussian scaling form at large time, 〈P(x,t)〉∼${\mathit{t}}^{\mathrm{-}3/4}$f(x/${\mathit{t}}^{3/4}$), where v(u)∼exp(-${\mathit{u}}^{\mathrm{\delta }}$) for u≫1, with δ=4/3. For an isotropic two-dimensional medium with ${\mathit{u}}_{\mathit{x}}$(y)=f(y) and ${\mathit{u}}_{\mathit{y}}$(x)=f(x), we find ν=2/3 and δ=1-ν${)}^{\mathrm{-}1}$=3.

We investigate a high-Q cavity partially filled by a medium with ${\mathrm{\chi }}^3$ nonlinear susceptibility with a coherent signal having the form of a series of short pulses injected into it. We show that the electromagnetic field which builds up in the cavity has strong nonclassical features. For appropriate parameters Anderson localization occurs leading to the generation of states with a narrow photon-number probability distribution. We demonstrate that by adiabatic changing of the size of the cavity one may generate from the vacuum a nearly perfect Fock state of a chosen mode.

A relativistic electron beam propagating through a plasma in the ion-focused regime exhibits an electromagnetic instability with peak growth rate near a resonant frequency ω∼2${\gamma }^2$${\mathrm{\omega }}_{\mathrm{\beta }}$. Growth is enhanced by optical guiding in the ion channel, which acts as a dielectric waveguide, with fiber parameter V∼1(I/${\mathit{I}}_{\mathit{A}}$${)}^{1/2}$. A 1D theory for a laser making use of this instability is formulated, scaling laws are derived, and numerical examples are given. Possible experimental evidence is noted.

A spontaneous acoustic oscillation of a gas column induced by temparature gradients is periodically perturbed by an external force. Nonlinear coupling between two oscillating modes can generate abundant nonlinear phenomena, quasiperiodicity, frequency locking, onset of chaos, and quenching phenomenon. Adjusting the frequency ratio to the golden mean, we study the scaling universality for the quasiperiodic transition to chaos. The first experiment in acoustics demonstrates that thermoacoustic systems follow universal scaling properties of the circle map in spite of the complexity of the system.

We report results on the transition from soft to hard turbulence in simulations of 2D Boussinesq convection. The computed probability densities for temperature fluctuations are exponential in form in both soft and hard turbulence, unlike what is observed in experiments; in contrast, we obtain a change in the Nusselt number scaling on Rayleigh number in good agreement with the 3D experiments.

The lifetime of the circulating electron beam in the Naval Research Laboratory modified betatron has been increased by more than 2 orders of magnitude with the addition of strong focusing windings to the device. The injected beam consistently spirals from the injector to the minor axis and is trapped. The ∼0.5-kA trapped electron ring has been accelerated above 10 MeV from the injection energy of 0.5 to 0.6 MeV. The beam acceleration has been confirmed not only by the x-ray attenuation technique but also with the detection of photoneutrons.

The phase diffusion and mean drift equations which describe the behavior of a convection pattern are derived, a step which is essential for obtaining quantitative comparisons between theory and experiment. The theory recovers the boundaries of the Busse Balloon, agrees closely with the dominant wave numbers observed by Heutmaker and Gollub [Phys. Rev. A 35, 242 (1987)] and Steinberg, Ahlers, and Cannell [Phys. Sci. 30, 534 (1985)] in natural and target patterns, predicts a new instability which is important in facilitating wave-number adjustment in circular target patterns and in initiating time dependence, and predicts the Rayleigh numbers at which loss of spatial correlation due to global defect nucleation will occur.

Thermal boundary layers in turbulent Rayleigh-Bénard convection are studied experimentally using a novel system in which the convecting fluid is sheared from below with a flowing layer of mercury. Oscillatory shear substantially alters the spatial structure and frequency of the eruptions, with minimal effect on the heat flux (<5%). The temperature probability distribution function (PDF) just above the lower boundary layer changes from Gaussian to exponential, without significant changes in the interior PDF. Implications for theories of ‘‘hard’’ turbulence are discussed.

The curvature of the boundary is shown to alter the fluid’s slip length, which may even become negative as a result. Due to the mesoscopic curvature of surface roughness, the microscopically calculated and the macroscopically measured slip lengths can be quite different.

In birefringent nonlinear optical media, it is shown that phase-matched wave-mixing processes occur naturally among the extraordinary and ordinary wave components of a strong pump and a weak probe beam. The necessary and sufficient conditions that these parametric processes may lead to amplification and or polarization switching of the probe beam are quantitatively analyzed.

We report strong narrow-band stimulated far-infrared cyclotron-resonance emission from the light holes in germanium in crossed electric and magnetic fields. The emission spectrum consists of a single line which is linearly tunable with magnetic field. The gain of the cyclotron-resonance laser is determined to be 0.05±0.02 ${\mathrm{cm}}^{\mathrm{-}1}$. For the first time we have identified the lasing transition to be the n=2 to n=1 Landau-level transition of the b-set light holes by a comparison of absorption and emission spectra with calculations of the band structure including nonparabolicity corrections.

Viscous fingers have been generated on square lattices of L×L sites using the diffusion-limited aggregation model plus a simple rule that we propose to take into account surface tension. The wi dths (λ) of the generated viscous fingers, as well as mass (m) of the dislodged fluid, depend properly on the capillary number (Ca): They fulfill the hydrodynamic scaling relations λ=${\mathrm{Ca}}^{\mathrm{-}1/2}$f(${\mathrm{Ca}}^{1/2}$L) and m=${\mathrm{Ca}}^{\mathrm{-}1}$g(${\mathrm{Ca}}^{1/2}$L). In addition, m∼${\mathrm{Ca}}^{\mathrm{-}\left[\right(\mathit{d}\mathrm{-}\mathit{D})/2\mathrm{}]}$${\mathit{L}}^{\mathit{D}}$ in the physically interesting regime a≪λ≪L (a is the lattice constant, d=2, and D∼1.6 in our simulations).

A renormalization-group fixed point is found, corresponding to chaotic mixing in the Rayleigh-Taylor instability problem. The outer envelope of the mixing region, adjacent to the heavy fluid, is dominated by a merger of unstable modes ( bubbles of light fluid) and dynamically changing length scales. A statistical model is introduced as an approximation to the full two-fluid Euler equation to describe the mixing envelope. Molecular-chaos and continuous-time approximations to this model define an approximate renormalization-group equation, which is shown to have a nontrivial fixed point.

The behavior of power spectra in a Rayleigh-Bénard convection experiment in a helium-gas cell is reported. The high-frequency part of the data for all Rayleigh numbers from 7×${10}^6$ to 4×${10}^{14}$ is fit by a single functional form, obtained by a natural generalization of a multifractal analysis. Low-frequency data cannot be fit in this form.

Flow between two horizontal coaxial cylinders with a partially filled gap is investigated for the case when the primary instability forms a pattern of traveling inclined rolls which is simply periodic in space and time. Slightly above the onset, there is a second instability which results in a periodic modulation of the rolls with an axial wavelength of ∼3 rolls and a lower frequency. Both the traveling inclined rolls and the ∼3 roll modulation pattern exhibit long-wavelength low-frequency phase modulations and associated defects.

We consider a simple, nonlinear Hamiltonian model for particle motions in two-dimensional turbulence in which the stream function power spectrum has the form ${\mathit{k}}^{\mathrm{-}\gamma }$ (γ constant). We show that fluid particle trajectories, (1) while differentiable and chaotic at small scale, may be fractal space curves at larger scale, (2) undergo anomalous transport, and (3) have frequency spectra ∼${\mathit{f}}^{\mathrm{-}\mathrm{\alpha }}$ in fully stochastic limit, where we obtain α=α(γ), a scaling law. Anomalous diffusion is shown to arise partly as a result of the fractal nature of the particle trajectories.

We report the first operation of a master oscillator-power amplifier in which both devices are free-electron lasers. Gain optimization in the power amplifier was studied. A 35-A electron beam produced up to 60% gain at 3 μm. The gain spectrum was obtained by gap tuning the power amplifier wiggler and evidence was found for violation of the Madey theorem due to high gain effects.