The linear stability of flow in a Couette-Taylor system with counterrotating cylinders is posed as an initial-value problem. The time-asymptotic solution is found by the method of steepest descent. We identify the saddle points of the complex dispersion relation and, from the growth rates evaluated at the saddle points, determine a Reynolds number range ${\mathit{R}}_{\mathit{c}}$≤R≤${\mathit{R}}_{\mathit{a}}$ within which the instability is convective and beyond which (R>${\mathit{R}}_{\mathit{a}}$) it is absolute. The amount by which ${\mathit{R}}_{\mathit{a}}$ exceeds ${\mathit{R}}_{\mathit{c}}$ can be of order 1%, but loci in parameter space of zero group velocity are found where the instability is absolute at onset (${\mathit{R}}_{\mathit{a}}$=${\mathit{R}}_{\mathit{c}}$). Bicritical curves separating regions with different azimuthal wave numbers are compared for convective and absolute instabilities. The analysis reveals a new type of bicriticality where two different axial wave numbers simultaneously become unstable.

Nonlinear plasma oscillations against a background supporting an ion pulse or cavity are considered. We treat two physical cases. The first is that of a cold plasma, the second of a cold-ion–warm-electron plasma. The ion background includes a hyperbolic-secant-squared pulse or cavity but is otherwise uniform. An exact solution is obtained for the cold-plasma case. Infinite electric-field gradients result after some time, followed by a three-valued electric field, a physical impossibility. Thus some modification is called for. When the electrons are assumed to be thermal these infinite gradients can be limited. This will be the case if the ratio of pulse strength to background density is less than ${\gamma }^{1/3}$(${\lambda }_{\mathit{D}}$/l${)}^{2/3}$, where ${\lambda }_{\mathit{D}}$ is the Debye length and l a characteristic width of the pulse. Applications are briefly discussed.

We investigate the phase diagram of sols and gels formed by copolymerization of acrylamide and bisacrylamide. In the vicinity of the sol-gel transition, we observe segregated samples with a viscous zone lying above an elastic part. A detailed rheological study has been done in the different domains of concentrations. The interpretation of the data in terms of critical behavior demonstrates that the samples where segregation occurs are gel phases. We also report calculations of the deformation and of the sedimentation kinetics of a tenuous polymer network under its own weight and experimental measurements in the segregated samples of the variations with height of the total monomer concentration and of the mobility of Brownian probes. This set of results shows that the gravitational field is at the origin of this segregation phenomenon.

We report a molecular-dynamics calculation of the entropy of a simple, classical fluid. The two- and three-body contributions to the total entropy were calculated from an expansion recently derived by the present authors [Phys. Rev. A 40, 3817 (1989)]. Both the two- and three-particle contributions to the entropy are monotonically decreasing functions of density at a fixed temperature. The two-body term remains less negative than the excess entropy over the entire fluid range with the largest discrepancy, of ∼15%, occurring at intermediate densities. The sum of the two- and three-body terms gives an accurate estimate of the excess entropy at low and intermediate densities. At intermediate densities the sum crosses the value of the total excess entropy and at still higher densities, close to the freezing line, becomes somewhat more negative (∼30%) than the total excess entropy. These results show that the expansion of the entropy converges less rapidly than might have been assumed from an analysis of the two-body terms alone.

In this paper the relevant dynamical parameters necessary for describing molecular reorientation of a single molecule in the mesophases of 4-n-alkyloxybenzylidene-4’-n-alkylaniline (nO.m) liquid crystals are examined. The spectral densities of motion ${\mathit{J}}_1$(${\mathrm{\omega }}_0$) and ${\mathit{J}}_2$(2${\mathrm{\omega }}_0$) were determined at 15.3 MHz by the Jeener-Broekaert method in partially deuterated 1O.4 and 5O.7 molecules. These results are discussed in the framework of rotational diffusion processes in anisotropic potentials. In particular, the ‘‘anisotropic viscosity’’ model of Freed as modified by Vold and Vold [J. Chem. Phys. 88, 1443 (1988)] is used to determine the spinning (${\mathit{D}}_{\gamma }$) and tumbling (${\mathit{D}}_{\mathrm{\beta }}$) diffusion constants of the molecule. In this model, molecules also rotationally diffuse around the nematic director to give another rotational diffusion constant ${\mathit{D}}_{\mathrm{\alpha }}$. It was reported by Raman and infrared band-shape analysis that in several liquid crystals including 2O.4, the spinning motion of the molecules slows down in the nematic phase as the orientational order decreases. Observation of slowing down in the spinning motion of 5O.7 molecules based on the above model is reported. Molecular reorientation of 1O.4 molecules is found to be slow on the deuterium NMR time scale, thus causing frequency dependences in the spectral densities of motion.

Measurements of the electric conductivity parallel and normal to the nematic director, of the reorientation time in magnetic fields, of the birefringence, and of the density are presented as functions of temperature and concentration, for the system tetradecyltrimethylammonium bromide–${\mathrm{D}}_2$O. The density in the nematic and the isotropic phases decreases with temperature, almost linearly. The variation is described in terms of the expansion of the aqueous phase and the alkyl chains forming the micellar interior. The data also indicate denser packing at the transition to the isotropic phase. The conductivity anisotropy and the birefringence are rather low and show little variation with temperature; the reorientation times are very long, corresponding to rotational viscosities between 1000 and 3000 P. The high viscosity indicates that the micelles have total length much higher than the persistence length, and may show flow properties similar to polymer solutions.

The study of the viscosity of waterless microemulsions glycerol-AOT-isooctane [where AOT represents sodium bis(2-ethylhexyl) sulfosuccinate] shows that there is a quantitative agreement between experimental values and percolation theory. The values of the scaling exponents μ’=2.00±0.25 and s’=1.20±0.20 for viscosity are very close of those of conductivity obtained for dynamical percolation with water-AOT-oil systems. The water-AOT-oil and glycerol-AOT-oil microemulsions behave in a broadly similar way as regards dynamic percolation provided that the conditions of application of the percolation laws are satisfied.

Using the generalized Landau model [Phys. Rev. A 36, 1484 (1987)], the temperature and frequency dependence of the complex dielectric constant of the ferroelectric smectic-${\mathit{C}}^{\mathrm{*}}$ (Sm-${\mathit{C}}^{\mathrm{*}}$) phase and the corresponding smectic-A (Sm-A) phase is calculated. It is demonstrated how the dielectric response of the Sm-${\mathit{C}}^{\mathrm{*}}$ phase generally consists of four modes—two high-frequency polarization modes and two modes of lower frequency that are connected to the reorientation of the director, commonly denoted the soft mode and the Goldstone mode. In the Sm-A phase only two modes are present—one doubly degenerate soft mode and one doubly degenerate polarization mode. The temperature dependences of the dielectric strengths and relaxation frequencies of the modes in question are calculated, and simplified expressions of these quantities are given. The most important feature of the generalized Landau model is the presence of a biquadratic coupling between tilt and polarization in the free-energy density of the system and we show how the general thermodynamic and dielectric properties of the system depend on the strength of this coupling. Comparing the results of the calculations with existing data, we finally conclude that the model provides a description of the Sm-${\mathit{C}}^{\mathrm{*}}$–Sm-A transition that takes all experimentally known features of the dielectric properties of the system into account in a qualitatively correct way.

We find a time dependence different from that reported previously in the literature for the species concentration in the A+B→0 diffusion-limited reaction for dimensions d<2 when the A-B pairs are initially correlated. Whereas an uncorrelated initial distribution leads to the well-known decay law ρ∼${\mathit{t}}^{\mathrm{-}\mathit{d}/4\mathrm{}}$ for d<4 and ρ∼${\mathit{t}}^{\mathrm{-}1}$ for d≥4, a correlated initial distribution leads to the decay law ρ∼${\mathit{t}}^{\mathrm{-}(\mathit{d}+2)/4\mathrm{}}$ for d<2 and ρ∼${\mathit{t}}^{\mathrm{-}1}$ for d≥2. The decay is therefore more rapid in the correlated case and the critical dimension for ‘‘anomalous’’ behavior shifts from 4 to 2.

A cell dynamical system model, which realistically incorporates diffusion, is developed to study various aspects of late-stage crystal growth. The algorithm is computationally efficient, allowing the development of complex spatial structures to be studied, and is motivated by renormalization group considerations. We establish the existence of an asymptotic dense branching morphology and relate it to diffusion-limited aggregation. Our findings indicate that the radius of a dense-branching structure grows linearly with time, despite being diffusion controlled, in agreement with experimental observations of the growth of spherulites. A clear morphological transition from kinetic-effect-dominated growth to surface-tension-dominated growth is observed, marked by a difference in the way growth velocity scales with undercooling. We also study the evolution of interfacial instability and find scaling behavior for the interface power spectra, indicating the nonlinear selection of a unique length scale, insensitive to short length-scale fluctuations.

The consideration of first-class constraints together with gauge conditions as a set of second-class constraints in a given system is shown to be incorrect when carrying out its canonical quantization.

We present experimental results on the growth of a needle-shaped crystal from an undercooled liquid in a rectangular capillary. We have studied the crossover from the Saffman-Taylor solution at small Péclet number to the Ivantsov solution at large Péclet number. Surface tension anisotropy is studied by comparing succinonitrile and pivalic acid for different orientations of the crystalline axis. Finally, we show evidence that, at least above a certain value of the Péclet number, the growth at constant velocity is not steady state.

The annihilation process of pointlike topological defects moving irreversibly is studied as a model for the growth of order in quenched systems with O(N) symmetry in D=N dimensions. On the basis of the time-dependent Ginzburg-Landau model (TDGL), the defect picture is shown to be valid in any dimensions. We consider defects with pairwise power-type interaction. By a mean-field assumption we find that the total number N(t) of defects decreases as N(t)∝${\mathit{t}}^{\mathrm{-}\mathit{D}/(\mathrm{\beta }+1)}$, where β is the exponent indicating the separation dependence of the force. We show analytically that this power law is valid for β<D≤2β and confirm the analysis by the simulation of molecular dynamics of defects for various β’s in two dimensions. The distribution of defect density is well represented by the binomial distribution function in this parameter region. To keep the distribution uniform is a key of exhibiting mean-field behavior. The TDGL model realizes the mean-field power law only in two dimensions.

We present a quasistationary model for soft-x-ray-driven ablation of low- to medium-Z plasmas. In this model, the sonic point density is determined self-consistently with the hydrodynamic conservation laws. When this model is applied to an aluminum plasma created by soft-x-ray irradiation, the calculation results for ablation parameters are in good agreement with the published experimental results obtained in the incident x-ray flux region of ${10}^{12}$–${10}^{13}$ W/${\mathrm{cm}}^2$. Including the higher x-ray flux region, power-law relations for the ablation parameters, such as the sonic point density, the mass ablation rate, and the ablation pressure, are presented. As an application of this model, the rocket foil acceleration due to soft-x-ray-driven ablation is discussed.

We formulate the problem of the interaction of an ultrashort highly intense laser pulse with matter within the framework of the anomalous relativistic skin effect. Analytical solutions for the electron distribution function, the depth of penetration of the electromagnetic field, and the corresponding coefficient of absorption have all been found under the assumption that the radiation interacts with a uniform plasma occupying a half-space in which the ions were immobile. We propose that the interaction of ultrashort (<1 psec) laser pulses with intensities >${10}^{20}$ W/${\mathrm{cm}}^2$ with solid targets results in the generation of relativistic laboratory plasmas. These plasmas are characterized by highly directed hard-x-ray (and possibly γ-ray) emission and the generation of very fast relativistic electrons and highly energetic ions.

The Bohm-Pines Fock-Tani representation for a single fixed proton immersed in a finite-temperature electron gas is derived by a sequence of canonical transformations. The long-range correlations between the charged particles of the system give rise to free-bound, bound-free, free-free, and bound-bound hydrogenic transitions with emission or absorption of plasmons by electrons in the field of the fixed proton. These are all exhibited explicitly in the transformed Hamiltonian. Within this ‘‘proton in jellium model’’ differential cross sections for plasmonic recombination into the highly excited and screened levels of hydrogen (8s,8p,9s,9p) for ${\mathit{n}}_{\mathit{e}}$=${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and ${\mathit{k}}_{\mathit{B}}$T=0.5 eV are evaluated using a screened Coulomb (plane-wave) Born approximation. The resulting cross sections appear to be much larger than those expected for the radiative mode.

A different approach to time-of-flight (TOF) analysis is described in this paper. The view is adopted that average energy must obey a conventional continuity equation like that obeyed by electron density, leading to a pair of coupled equations consisting of an isotropic diffusion equation with two nonuniform transport coefficients and an isotropic-heat-flow equation with three nonuniform transport coefficients. By a finite-difference technique, these equations are solved simultaneously for density and average energy, both of which vary in time and space. This approach is based on energy moments of the scalar equation for the isotropic part of the velocity distribution function ${\mathit{f}}_0$ that results from the well-known two-term Legendre expansion. The nonuniform transport coefficients are expressed as functionals of the average energy of the electrons. These functionals are obtained by evaluating certain integrals involving ${\mathit{f}}_0$, which must be assumed, and the energy-dependent momentum transfer collision frequency. The method is applicable primarily to those gases for which the collision frequency can be expressed as a power of electron energy. In the special case of constant cross section, the predicted transit time of a TOF pulse agrees with the accepted value obtained by the density-gradient-expansion technique of solving the Boltzmann equation, while the predicted pulse width is 11% larger than the accepted value obtained by the same technique. Possible reasons for this difference are discussed.

We describe the motion of an SU(1,1) pseudospin vector in the frame of the mean-field approximation induced by the variational principle on linear-plus-quadratic Hamiltonians. The dynamics of the SU(1,1) states of the Perelomov type obeys a nonlinear Bloch or torquelike equation, and each orbit can be interpreted as the intersection of two quadrics, one representing the energy surface and the other the group manifold, both in the space of the averaged algebra generators or semiclassical pseudospin. The fixed points of the flow can be also determined by resorting to strictly geometric considerations. The evolution of the phase diagram in parameter space is investigated as well for selected Hamiltonians. The bifurcation sets are constructed and the nonthermodynamic phase transitions can be clearly identified for the systems under consideration.

The nonlinear propagation of intense electromagnetic radiation in a pulsar magnetosphere is investigated. The radiation is considered to be a circularly polarized electromagnetic wave, in whose field electrons and positrons acquire ultrarelativistic velocities. The nonlinear frequency shift due to the wave-plasma interaction is found to cause the wave localization, and it produces a new kind of envelope soliton, which in coupling with the ambient magnetic field generates intense ambipolar field along the magnetic lines.

In a recent paper, using the Volkov solution of the minimally coupled Dirac equation, we developed the concept of the quasifree states of the electron from a kinematical point of view [Rashid, Phys. Rev. A 38, 2525 (1988)]. Using these concepts, we present a coupling (decoupling) scheme that separates the kinematical factors from the dynamical ones. When the electrons in a gas are assumed to be in quantum states having quasi-four-momentum, then the Boltzmann equation reduces to a form that lends itself easily to the methods of separation of the variables. The solution is obtained as the product of a time-dependent part and a time-independent part. The latter is assumed to be just the initial distribution function, in which case the time-dependent part is found to be linked to the scattering cross section of the electrons. We assume a high-Z plasma where electron-ion collisions dominate over electron-electron collisions. The complete solution is finally obtained by normalizing the product solution. The first case we consider is a cold plasma, so that the energy of the photon is much greater than the mean kinetic energy of the electron and the electrons are assumed to form a Maxwellian gas. The cross section calculated under the Born approximation from our previous paper is used and the laser intensity is assumed to be such that the Kibble parameter is much smaller than unity. The time-dependent solution is surprisingly found to be Maxwellian still but with the temperature increasing with time. The second case concerns a hot plasma with a mean electron energy much greater than the photon energy but still less than its rest mass energy. The final normalization gives us a non-Maxwellian distribution but is reduced to an analytically closed form so that it is easily tractable. The temperature is still found to be increasing, but now we get a difference in the time dependence between the amplitude part and the exponential part.