We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on ${\mathrm{CO}}_2$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls, and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two-dimensional model is consistent with the prediction of marginal stability theory for one-dimensional fronts.

We present a phenomenological theory for surface effects on spinodal decomposition in mixtures and related phenomena such as the dynamics of surface segregation. Numerical solutions of our equations show striking similarity to recent results from experiments on polymer mixtures with one component preferentially attracted to a wall.

With the use of optical second-harmonic generation from liquid-crystal (LC) monolayers adsorbed on rubbed polymer surfaces, a close correlation between the rubbing-induced azimuthal orientation distribution of the LC monolayers and the resulting LC bulk pretilt angle has been observed. A simple model based on epitaxial growth of the bulk LC on top of the first LC monolayer is proposed to explain this correlation.

The surface tension of normal liquid alkanes (chain lengths between 15 and 18 carbon atoms) has been measured as a function of temperature. In all cases the tension exhibits a well-defined change in behavior at a temperature close to, but distinct from, the melting point. The phenomena are consistent with a surface-induced phase transition in which the conformational degrees of freedom of molecules close to the surface are inhibited. Various properties of the transition vary smoothly with alkane chain length.

Using an ansatz for an asymmetric profile of the solidification front in lamellar eutectic growth, the von Neuman problem is solved. Imposing the Gibbs-Thomson condition, we derive a general expression for the tilt angle as a function of the control parameters. We find that the front undergoes a supercritical parity-breaking bifurcation at a critical value of σ=${\mathit{d}}_0$l/${\lambda }^2$ (${\mathit{d}}_0$ is the capillary length, l the diffusion length, and λ the wavelength of the pattern). We further find that parity-breaking causes a reduction of the average front undercooling. All these features agree with previous numerical results.

The growth of fingers which develop at the three-phase contact line at the front of a thin film of silicone oil flowing down an inclined plane is studied, and the results compared with those of a recent theoretical treatment of the problem [Troian et al., Europhys. Lett. 10, 25 (1989)]. When the finger length and time are scaled appropriately, the qualitative features of the theoretical predictions are confirmed.

We present a quantitative study of the two-dimensional dendritic growth of liquid-condensed domains observed by fluoresence microscopy in Langmuir monolayers of D-myristoyl alanine. The geometrical analysis of the dendrite tip region shows that the predicted relationship ${\mathrm{\rho }}^2$V/${\mathit{d}}_0$D=const (V is the tip growth velocity, ρ the top curvature radius, ${\mathit{d}}_0$ the capillary length, and D the diffusion coefficient) is reasonably verified. The determination of this constant yields an estimate of the line tension anisotropy.

The mean shape of free dendritic crystals of ${\mathrm{NH}}_4$Cl growing in three dimensions from solution is determined. The mean width w¯ of the dendrites in the plane of the sidebranches is found to scale with the distance z from the tip according to w¯/ρ∼(z/ρ${)}^{0.74\pm 0.06}$, where ρ is the tip radius. This is significantly different from the exponent of 1/2 that would be expected if the mean shape corresponded to a parabolic steady-state solution, as was found in two-dimensional growth [Y. Couder et al., Phys. Rev. A 42, 3499 (1990)]. Estimates of the axially averaged three-dimensional shape and possible implications for steady-state theories of dendritic growth are also discussed.

Relativistic electron distribution functions giving distributions over instantaneous values of electron momenta and energies in an intense femtosecond laser field are derived. They facilitate the understanding of the recent experimental results that reported the production of hot electrons and hard-x-ray radiation on a femtosecond scale.

Efficiency enhancement in a gyrotron backward-wave oscillator through magnetic field tapering is investigated using computer simulations. The results reveal that the magnetic field tapering with a positive gradient tends to increase the initial frequency mismatch and thus lengthen the confinement of most of the electrons in the energy losing phase therefore resulting in higher net energy transfer to the wave.

An experimental demonstration of a multimode feedback stabilization with a single sensor-suppressor pair is presented. Two modes were simultaneously stabilized with a simple state-feedback-type method where more ‘‘state’’ information was generated from a single-sensor Langmuir probe by appropriate signal processing. A single feedback-modulated ion beam served as the remote suppressor. A simple theory shows good agreement with experiment. This experiment may be considered as a paradigm for controlling certain classes of chaotic systems.

We compute the fraction of RNA sequences of fixed length N=220 that fold expeditiously and reproducibly into a unique structure within realistic RNA replication time spans. The search in conformation space is assumed to be concurrent with the assembling of the molecule which occurs by sequential incorporation of nucleotides. Monte Carlo simulations of the folding events concomitant with polymerization events are used to determine the evolutionary consequences of the principle of expeditious and reproducible folding hereby introduced.

In the usual Bell’s-inequality experiments two particles carrying spin or polarization are prepared in an entangled state generated from the decay of an unstable quantum-mechanical system. These particles are then delivered to spin or polarization analyzers. The statistics of the measurements reported by the analyzers are incompatible with our notions of local realism. Here we show that Bell’s-inequality violations occur even when the initial state is a direct product state. In fact, the two particles can come from two independent widely separated sources.

Weber [Phys. Rev. C 31, 1468 (1985); Phys. Rev. D 38, 32 (1988)] has reported the results of several experiments that suggest a total neutrino scattering rate proportional to the square of the number of atoms in a perfect crystal. A solar neutrino experiment with improved sensitivity has given a null result for scattering of that kind.

An algebraic method for studying quantum anharmonic oscillators is proposed. It consists in the iterative application of generalized (squeezing) Bogoliubov transformations to the usual creation and annihilation operators. The convergence of this procedure is analyzed for quartic, cubic plus quartic, and symmetric-double-well Hamiltonians. For these systems, we show the usefulness of the resulting harmonic-oscillator number states in calculating the energy spectra.

In this paper the possible types of the Bethe-Salpeter (BS) irreducible kernels are determined from a phenomenologically reasonable requirement, and the spinor structures of BS wave functions and equations for all the three categories of natural ${\mathit{J}}^{\mathit{P}\mathit{C}}$ mesons are obtained.

We study spatially separated clocks that are Einstein synchronized in one inertial frame and then rigidly accelerated into another inertial frame. It is assumed that the clocks remain Einstein synchronized in the new frame in which they are now at rest. The consequences of this assumption are analyzed with respect to the experiments discussed in the literature as supportive of the accepted clock hypothesis.

We show that if it is possible to manufacture a beam of spin-1/2 heavy atoms corresponding to a quantum-mechanical pure state, then the dark lines of the Stern-Gerlach effect should display a fine structure. The two lips of the open-mouth pattern will each be a doublet; the lighter area between the two lines of the doublet arises from an interference between silver atoms on opposite sides of the incoming beam. We obtain a simple classical model giving exactly the same angular distribution around the open mouth. However, this classical model does not give the fine structure.

By using the Bogoliubov perturbation theory in combination with variational methods, we derive an expression for the ground-state energy for a one-dimensional neutral system containing a large number (N) of locally interacting ‘‘charged’’ bosons in one dimension. When only ‘‘Coulomb-like’’ interactions are considered, the employment of Dirichlet boundary conditions leads to a physically sensible bound state, while using periodic boundary conditions does not. As far as the large-N dependence is concerned, our results agree with those proposed recently, but our derived expression produces a better value for the ground-state energy.

The dynamic behavior of the nonlinear Schrödinger equation (NSE) with an additional high-order Hamiltonian perturbation that displays a nonlinear interaction between Langmuir waves and electrons in plasmas is studied. It is shown that periodic solutions, solitary waves, and recurrence exist, which are also inherent in the cubic NSE. A more important phenomenon, stochasticity, has been found in such a continuum Hamiltonian dynamic system. This phenomenon illustrates that nonintegrability arises from the high-order Hamiltonian perturbation. In addition, our numerical results also show that recurrence, which sensitively depends on initial conditions, is only a special feature of the dynamic system.