When a long channel of shallow liquid is driven parametrically, there can occur a 180° kink in the phase of the fundamental cross mode of the surface. The kink is stable and localized, and is nonpropagating in the limit where the system is uniform. The weakly nonlinear theoretical description is a damped driven nonlinear Schrödinger equation supplemented with second harmonics. The kink is a robust state even at amplitudes where the perturbation expansion leading to this equation is unjustified.

We derive formulas which describe the interaction of laser beams with electron beams. Specializing to the case of 1-TeV electron beams from the future generation of electron linear accelerators, we calculate the production rate of backscattered 1-TeV photons, and using these photons, we show that it is possible to organize the photoproduction of beauty particles so as to measure ${10}^9$ bb¯ pairs per year. This should be adequate to study rare decays and CP violation in B meson decay.

Dynamic light scattering at the crystal-melt interface of solidifying salol was followed for 14 days. The hydrodynamic radius deduced from intensity correlation data increased continuously from ∼1 to ∼100 μm. When the scattering layer was trapped by the advancing crystal front, microscopic observation revealed bubbles as inclusions whose size agreed with the light-scattering value. Scattering was also observed to disappear after prolonged pumping on the sample.

We present a renormalization-group (RG) approach to the nonlinear diffusion process ${\mathrm{\partial }}_{\mathit{t}}$u=D ${\mathrm{\partial }}_{\mathit{x}}^2$u, with D=1/2 for ${\mathrm{\partial }}_{\mathit{x}}^2$u>0 and D=(1+ε)/2 for ${\mathrm{\partial }}_{\mathit{x}}^2$u<0, which describes the pressure during the filtration of an elastic fluid in an elastoplastic porous medium. Our approach recovers Barenblatt’s long-time result that, for a localized initial pressure distribution, u(x,t)∼${\mathit{t}}^{\mathrm{-}(\mathrm{\alpha }+1/2)}$f(x/ √t, ε), where f is a scaling function and α=ε(2πe${)}^{1/2}$+O(${\mathrm{\epsilon }}^2$) is an anomalous dimension, which we compute perturbatively using the RG. This is the first application of the RG to a nonlinear partial differential equation in the absence of noise.

We report on convection in horizontal layers of an ethanol-water mixture in a rectangular and an annular container heated from below. When the tempearature difference ΔT exceeds a critical value, localized regions of traveling-wave convection evolve via a backward bifurcation in both geometries and coexist with the conduction state for a range of ΔT. The size, shape, wave number, and frequency of the localized states are reproducible and geometry independent. The coexistence range stands in contrast to systems with a potential, where droplets of a given phase are not stable for first-order transitions at fixed values of the thermodynamic fields.

Theoretical analysis is made of an intense relativistic electron beam moving through a plasma of increasing density, but density always less than that of the beam (underdense). Analysis is made of the beam radiation energy loss and it is noted that the focuser is insensitive to the beam energy spread due to radiation loss. Furthermore, because of the scaling behavior in the nonclassical regimes, the radiation limit on lenses (the Oide limit) can be exceeded.

We report experimental results for wave-number selection in Taylor-vortex flow with slow spatial ramps of the Reynolds number. The accessible range of wave numbers is always much smaller than the Eckhaus-stable range, but the selected wave number depends on the detailed nature of the ramp. For a particular ramp, wave numbers outside the Eckhaus-stable band were selected, leading to a periodic state of traveling vortices. The selected wave numbers and the frequencies of the periodic state agree well with a phase-dynamical calculation by Riecke and Paap.

Recent experiments have found the existence of ‘‘photon bands’’ in periodic dielectric structures analogous to the electron bands in the solid. Using a plane-waves method, we study in the scalar-wave approximation the nature of the photon bands in structures where spherical ‘‘atoms’’ of dielectric constant ${\mathrm{\epsilon }}_{\mathit{a}}$ are periodically arranged in a background dielectric ${\mathrm{\epsilon }}_{\mathit{b}}$. The scalar-wave calculation predicts gaps in the spectrum for ${\mathrm{\epsilon }}_{\mathit{a}}$/${\mathrm{\epsilon }}_{\mathit{b}}$ or ${\mathrm{\epsilon }}_{\mathit{b}}$/${\mathrm{\epsilon }}_{\mathit{a}}$≳3 or so. The nature and symmetry of the wave functions is also discussed.

By means of an asymptotic analysis, two distinct approaches to incompressibility are found for a low-Mach-number ideal fluid, distinguished according to the relative magnitudes of temperature, density, and pressure fluctuations. For heat-conduction-dominated-fluids, temperature and density fluctuations are predicted to be anticorrelated, and the classical passive scalar equation for temperature is recovered, whereas a generalized ‘‘pseudosound’’ relationship for the fluctuations is found for heat-conduction-modified fluids, together with a modified thermal equation. The full set of nearly incompressible dynamical equations is described.

On the route to turbulence in electrohydrodynamic convection of nematic liquid crystals, the last bifurcation is spatially inhomogeneous via nucleation. Such a transition occurs between two different turbulent states (DSM1 and DSM2). We find good agreement between the nucleation rate of DSM2 nuclei and an expression from conventional nucleation theory. The motion of the DSM1-DSM2 interface behaves similar to propagating fronts in other nonequilibrium systems. Disclinations in the director field are created during the transition, similar to the vortex filaments in the TI-TII transition in superfluid He II.

The stability of Taylor-Couette flow subject to an external Coriolis force is studeid experimentally. The external Coriolis force stabilizes the flow. At larger dimensionless rotation rates stabilization is dramatic, reaching a value greater than 300%. The stability behavior of this system exhibits striking qualitative and quantitative similarity to the behavior of Bénard convection subject to rotation, and qualitative similarity to Bénard convection and Taylor-Couette flow subject to a magnetic field.

Symmetry arguments are used to classify the various modes of instabilities of one-dimensional periodic patterns. An important feature of this theory is to point out the coupling between these modes and the phase of the cellular structure. A number of results presented allow to interpret recent observations in hydrodynamical flows, directional solidification, and fingering experiments.

Two-dimensional numerical simulations of compressible, spatially evolving, unforced planar shear flows are used to investigate the role of feedback in the reinitiation of vortex roll up. The calculated pattern of coherent structures shows global self-sustaining instabilities in which new vortex roll ups are triggered in the initial shear layer by pressure disturbances originating in the fluid accelerations downstream. This reinitiation mechanism, absent in the linear treatments of stability, is demonstrated conclusively here.

Experiments show that the addition of small amounts of polymer to a Newtonian fluid undergoing chaotic advection decreases the amount of chaos; regular or unmixed regions increase in size and squeeze out the regions of chaotic behavior while preserving underlying symmetries. The size of the islands increases with increasing elasticity and rate of stirring. Large effects are present at relatively low Deborah numbers (relaxation time of the fluid to the time scale of the flow).

We derive equations of motion for a diluted gas of spiral defects in the two-dimensional complex Ginzburg-Landau equation. The interaction of two defects is treated and our predictions agree with a recent numerical experiment.

Through first-principles hydrodynamic calculations, the macroscopic behavior of the displacement of immiscible fluids in a capillary tube is linked to the microscopic parameters governing the dynamics of the moving contact line. Comparison with experimental data reveals that the contact line is dragged by a frictional force varying as $U^x$, where U is the mean flow velocity and x≃(1/2. Consideration of capillary-wave excitation at the fluid-fluid interface as the source mechanism of this frictional force yields predictions in excellent agreement with experimental data.

Wavelet transformations (WT’s) of two-dimensional fractal aggregates are carried out using coherent optical spatial frequency filtering. The ability of optical WT’s to reveal the construction rules of fractals and to resolve local scaling properties through the determination of local pointwise dimensions is demonstrated. This fast method paves the way to time-resolved studies of dynamical phenomena.

Uniformly translating solutions of the one-dimensional complex Ginzburg-Landau equation are studied near a subcritical bifurcation. Two classes of solutions are singled out since they are often produced starting from localized initial conditions: moving fronts and stationary pulses. A particular exact analytic front solution is found, which is conjectured to control the relative stability of pulses and fronts. Numerical solutions of the Ginzburg-Landau equation confirm the predictions based on this conjecture.

Numerical simulations demonstrate that laminar breakdown in a boundary layer induced by the secondary instability of two-dimensional Tollmien-Schlichting waves to three-dimensional subharmonic disturbances need not take the conventional lambda vortex–high-shear layer path.

The correlations between a homoclinic orbit (HMO) and coherent patterns in the nonlinear Schrödinger model are discussed. In a Hamiltonian situation, two independent patterns are revealed to exist: One corresponds to a motion within an HMO, and the other outside of an HMO. The study further illustrates, when the Hamiltonian constraint is released, the significance of an HMO on the patterns dynamics by presenting the irregular HMO crossings and the resulting chaotic selections between the patterns.