Motivated by recent experiments on the directional solidification of nematic liquid crystals, the standard solidification model is investigated in detail, numerically (by the boundary-integral method) as well as analytically (using amplitude equations). For the parameter values suitable for the experiments, both approaches yield a parity-breaking instability to traveling waves as well as a period-doubling bifurcation. Moreover, they agree with each other quantitatively not only in the immediate vicinity of the expansion point of the amplitude equations but over quite some range of parameters. The resulting phase diagram is in general accord with that obtained in the experiments. Since the amplitude equations describe the interaction of two modes with resonating wave numbers q and 2q, this demonstrates that both experimentally observed transitions have the same origin: the 1:2-mode interaction. In addition, a third oscillatory instability observed experimentally can also be traced back to this interaction. Some questions concerning the direction of some bifurcations are, however, as yet unresolved. Possible causes for these discrepancies are indicated. For other parameter values the amplitude equations predict that no traveling waves will arise from this mode interaction.

We present a method to determine a theoretical expression for the high-frequency effective viscosity of a suspension of hard spheres. In the explicit calculations we have used two-particle hydrodynamic interactions only. The expression of the effective viscosity has a Saito-like form with a pole near cphi≊0.70, which is comparable to the maximum packing fraction of a hard-sphere system. The final result is in good agreement with experimental and numerical results up to higher volume fractions, as will be shown in comparisons with recent experiments and computer-simulation results. Three- and more-particle hydrodynamic interactions are expected to be important for dense suspensions, but with the presented method it appears that these higher-order interactions give more subtle contributions to the presented expression of the effective viscosity in comparison with the commonly used methods to derive a virial expansion of the effective viscosity itself. This advantageous point will be discussed briefly in the discussion.

We study analytically the selection, due to surface tension, of Saffman-Taylor fingers in the sector geometry recently introduced experimentally by Thomé et al. [Phys. Fluids A 1, 224 (1989)]. The finger shape for zero surface tension is written as the solution of an integral equation. This leads to an explicit solution in the case where the sector angle is small. The selection due to surface tension is controlled, as in similar problems, by the singular points of a differential equation. For divergent fingers, we find for these singularities a geometric situation which is qualitatively new. Indeed we obtain one ‘‘axis’’ singularity and two ‘‘side’’ singularities. When the axis singularity is ‘‘dominant,’’ the finger disappears, which explains the branch-merging phenomenon found numerically by Ben Amar [Phys. Rev. A 44, 3673 (1991)]. Our analysis is carried out completely explicitly in the case of small-angle sector, and we indeed find branch merging, either by a WKB analysis or by a numerical solution of our differential equation. For convergent fingers, we find either an ‘‘axis’’ singularity or two ‘‘side’’ singularities, and the results are similar to those for the standard Saffman-Taylor fingers in the linear geometry.

Pseudopotentials have become an important tool for the calculation of electronic and structural properties of molecules and solids. The extensive experience with pseudopotentials shows that they accurately describe the properties of matter. It remains to be understood, however, why the same pseudopotential can describe atoms in different chemical environments. We show that this transferability is related to the existence of a region around the nuclei where the charge density is practically independent of the chemical environment.

We present the method and results of two phase-separation experiments performed on the binary-polymer blend polyisoprene-poly(ethylene-propylene). Elastic light scattering and optical microscopy were used to follow the phase separation after quenches into the coexistence region of the phase diagram. For off-critical quenches, we observed the formation of spherical droplets which obtained nearly monodisperse radius distributions over some fraction of the free-growth period. These results are interpreted within the framework of a heterogeneous nucleation process and diffusion-driven dynamics. For critical quenches, we observed the well-known bicontinuous infinite-cluster morphology normally associated with spinodal decomposition, but with two distinct growth modes. In the bulk, we observed L(t)∼${\mathit{t}}^{1/3}$, which is consistent with diffusion-driven dynamics, whereas near the sample walls we obtained a fast growth with L(t)∼${\mathit{t}}^{3/2}$, inconsistent with either diffusion- or interface-driven dynamics. We attribute this large exponent to wetting effects, but still lack any theoretical understanding of the phonomenon.

The α-relaxation dynamics in a hard-sphere system is studied solving microscopic-mode-coupling equations. The solutions for coherent and incoherent dynamical structure factors, the transversal correlation functions, and the moduli are presented for all wave vectors. The wave-vector dependence of fitted Kohlrausch exponents β and of the relaxation times τ is discussed. Recent experiments on the α relaxation of colloidal systems are quantitatively analyzed.

One of the fundamental approaches to microscopic many-body theory is through the use of perturbation theory. This paper presents a clear derivation of the equations that sum the two-body and three-body reducible diagrams that are generated from some input set of irreducible diagrams (typically the bare interaction) in a crossing-symmetric form. The diagrammatic structure is useful for both bosons and fermions at zero and finite temperature. The essential features of the procedure for the two-body case are the following. (i) All constructions involve only direct diagrams. (ii) Diagrams can be joined together by five different ladder, chain, and vertex correction operations. (iii) The sequences in which these operations are applied satisfy certain associativity relations. (iv) These associativity relations are used to insure that each permitted diagram is generated exactly once. (v) The ladder-and-chain operations are used to construct reducible vertex sums ${\mathrm{\Gamma }}_0$ which have no external vertex corrections. (vi) The full direct vertex Γ consists of the vertex ${\mathrm{\Gamma }}_0$ plus ${\mathrm{\Gamma }}_0$ dressed on either or both sides by the full direct vertex Γ. (vii) Finally, the full vertex is obtained by adding the exchange of the direct vertex. The extension to the three-body formalism proceeds in much the same way.

A fundamental morphological measure of two-phase heterogenous materials is what we refer to as the lineal-path function L(z). This quantity gives the probability that a line segment of length z is wholly in one of the phases, say phase 1, when randomly thrown into the sample. For three-dimensional systems, we observe that L(z) is also equivalent to the area fraction of phase 1 measured from the projected image onto a plane: a problem of long-standing interest in stereology. We develop a theoretical means of representing and computing the lineal-path function L(z) for distributions of D-dimensional spheres with arbitrary degree of penetrability using statistical-mechanical concepts. In order to test our theoretical results, we determined L(z) from Monte Carlo simulations for the case of three-dimensional systems of spheres and found very good agreement between theory and the Monte Carlo calculations.

We develop a microscopic molecular-statistical theory for thermotropic nematic polymers, composed of semiflexible chains of bonded nematogenic monomers. In the framework of a mean-field approximation we account for pair-interaction forces between monomers, including long-range attraction, steric repulsion, and effective rigidity of the bonds between subsequent monomers on the same chain. The functional correction to the probability distribution in a nonuniform orienting field is obtained for the case of very-long-wavelength deformations. We then derive a curvature-elastic free energy for this system, in which the Frank elastic constants are expressed in terms of definite molecular and thermodynamic parameters. It is shown that for a very long semiflexible chain the splay elastic constant is exponentially large and is proportional to the average distance between sharp bends on the chain.

A fluid physisorbed in a narrow pore forms a nearly one- or two-dimensional monolayer, depending on the pore geometry, when the characteristic dimension of the pore is only slightly larger than the molecular size. In such cases, previous work shows that the average density of an adsorbed phase in equilibrium with a bulk phase can be predicted by treating the adsorbate as a low-dimensional (low-D) fluid, when the adsorbate density is low. For example, a fluid of hard spheres adsorbed inside a narrow planar pore resembles a fluid of hard disks. We improve the low-D model by regarding the adsorbate as a polydisperse fluid constrained to a lower dimension; thus, molecular size in the lower-dimensional space replaces the adsorbate position in the dimension normal to the adsorbate surface in the true geometry. The size distribution in the pseudo-low-D mixture is not chosen arbitrarily, but specified by the equilibrium condition between the low-D mixture and the bulk fluid. This equilibrium condition follows naturally from the formalism of the semigrand canonical ensemble, which provides a convenient thermodynamic description of polydisperse mixtures. The mapping of the adsorbed phase onto a polydisperse low-D fluid is examined for examples of hard-particle fluids. We report the average adsorbate density relative to the density of a bulk fluid in equilibrium with the adsorbed phase. The polydisperse low-D model provides a better representation of dense adsorbed layers than the simpler low-D model throughout the entire range of applicability of the models, as demonstrated by comparison to Monte Carlo simulations. The theory also fares better than a well-regarded smoothed density-functional theory in predicting density profiles for hard spheres in very-narrow-slit pores.

The energy shift due to the presence of the extended (dtμ${)}_{11}$ pseudonucleus (in its first excited state with one unit of angular momentum) in the quasihydrogenlike molecule [(dtμ${)}_{11}$-d]ee is estimated using first-order perturbation theory. The quadrupole parts of the electron-(dtμ${)}_{11}$ and deuteron-(dtμ${)}_{11}$ interactions are found to give energy shifts of several meV. The result suggests that the normal practice of calculating the shift in [(dtμ${)}_{11}$-d]ee by scaling the shift calculated for (dtμ${)}_{11}$e may be in error. Calculations of the formation rate of [(dtμ${)}_{11}$-d]ee, which plays an important role in muon-catalyzed fusion, require an accuracy of about 1 meV in the binding energy, and the present result indicates that a shift in this binding energy of several meV, due to the finite (dtμ${)}_{11}$ size, cannot yet be excluded.

The mean-field phase diagram of the cholesteric–smectic-A–smectic-${\mathrm{C}}^{\mathrm{*}}$ (${\mathit{N}}^{\mathrm{*}–}$Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$) point is derived within the framework of the chiral Chen-Lubensky model. We show that on the Sm-${\mathit{C}}^{\mathrm{*}}$ side of the phase diagram, one or two additional twist-grain-boundary (TGB) (or chiral-smectic) phases will occur. These additional chiral-smectic phases, the ${\mathrm{TGB}}_{\mathit{C}}$ and ${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ phases, are highly dislocated versions of smectic-C and smectic-${\mathit{C}}^{\mathrm{*}}$ phases, respectively. According to the de Gennes superconductor analogy, the grain-boundary phase which occurred on the smectic-A side of the phase diagram (known as the ${\mathrm{TGB}}_{\mathit{A}}$ or chiral Sm-${\mathit{A}}^{\mathrm{*}}$ phase) is the analog of the Abrikosov vortex lattice in type-II superconductors. However, the ${\mathrm{TGB}}_{\mathit{C}}$ and ${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ phases would correspond to Abrikosov vortex lattices in a hypothetical superconductor where the Ginzburg parameter κ is negative and the photon has Bose condensed. These additional phases are predicted to occur near the recently observed ${\mathit{N}}^{\mathrm{*}–}$Sm-${\mathit{A}}^{\mathrm{*}–}$Sm-${\mathit{C}}^{\mathrm{*}}$ multicritical point. We discuss the ${\mathit{N}}^{\mathrm{*}\mathrm{-}}$${\mathrm{TGB}}_{\mathit{C}}$, ${\mathrm{TGB}}_{\mathit{A}\mathrm{-}}$${\mathrm{TGB}}_{\mathit{C}}$, and ${\mathrm{TGB}}_{\mathit{A}\mathrm{-}}$${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ phase transitions. Because of the twist, the XY-like Sm-A–Sm-C is (usually) replaced by the Ising-like ${\mathrm{TGB}}_{\mathit{A}\mathrm{-}}$${\mathrm{TGB}}_{\mathit{C}}$. However, if the Sm-${\mathit{C}}^{\mathrm{*}}$ helicoidal pitch length is somewhat smaller than the cholesteric pitch length, then the ${\mathrm{TGB}}_{\mathit{A}\mathrm{-}}$${\mathrm{TGB}}_{\mathit{C}}$ transition would be replaced by the ${\mathrm{TGB}}_{\mathit{A}\mathrm{-}}$${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ transition.

We use density-functional theory to derive an expression for the distortion free energy of molecular ordered phases and expand it in terms of the order parameters characterizing the structure of the phase and the molecular correlation function of an effective isotropic liquid. We derive expressions for the elastic constants of the uniaxial nematic and smectic-A phases of the liquid crystals and express the results in terms of the spherical-harmonic coefficients of the direct pair-correlation function of the effective isotropic liquid. These harmonic coefficients are obtained by solving the Ornstein-Zernike equation using the Percus-Yevick closure relation for a hard-core system and using a perturbation method for a model system interacting via a pair potential that has angle-dependent attractive parts in addition to hard-core repulsion. It is shown that the repulsive part of the pair interaction makes a dominant contribution to the elastic constants of the liquid crystals.

We study the effects of hydrodynamic interactions on the diffusion of hard spheres in concentrated suspensions. Using a multiple-light-scattering technique, we measure [H(q)], a weighted average of H(q), a function that characterizes the hydrodynamic interaction. By changing the size of the spheres we probe the particle size dependence of [H(q)] and find reasonable agreement with recent calculations for volume fractions φ<0.45. For large spheres (diameter 2R>2μm), [H(q)]→H(∞) and thus, we measure the short-time self-diffusion coefficient ${\mathit{D}}_{\mathit{s}}$==${\mathit{D}}_0$H(∞) where ${\mathit{D}}_0$ is the free-particle diffusion coefficient. We find that H(∞)=1-1.77(±0.07)φ for φ≤0.45. This agrees with the linear (low-concentration) term calculated for short-time self-diffusion. The short-time diffusion coefficient is also found to be continuous across the freezing transition.

We investigate the effects of shear flow on the smectic phase of thermotropic and lyotropic liquid crystals. We show that shear flow transforms a smectic-A thermotropic liquid crystal into an orthorhombic solid by the suppression of undulation fluctuations. In contrast, the lyotropic ${\mathit{L}}_{\mathrm{\alpha }}$ phase exhibits, in addition, a very striking enhancement of short-wavelength concentration fluctuations—a phenomenon that is analogous to a well-known effect in polymer solutions. We demonstrate this result, using both hydrodynamic theory and a microscopic model based on the Helfrich theory of membranes. The dispersion relation of the concentration fluctuations is in qualitative agreement with recent experiments on the ${\mathit{L}}_{\mathrm{\alpha }}$ phase in shear flow.

We have measured the absolute wave numbers of a series of transitions from the metastable 2${\mathrm{}}^1$S level of helium to the n ${}_{}{}^1{}_{}{}^{}$P (n=7–74) excited states. From these data we determine the binding energy of the 2 ${}_{}{}^1{}_{}{}^{}$S level to 2.2 parts in ${10}^{10}$ by using a Ritz series formula. This high-precision determination of the 2 ${}_{}{}^1{}_{}{}^{}$S binding energy does not depend on theoretical calculation of the binding energy of any helium level. The result, 32 033.228 855(7) ${\mathrm{cm}}^{\mathrm{-}1}$, confirms our earlier finding of a relatively large discrepancy with the predicted two-electron Lamb shift for the 2 ${}_{}{}^1{}_{}{}^{}$S level.

The photoemission from HI is studied separately for different vibrational levels of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ final ionic states using spin-resolved photoelectron spectroscopy with circularly polarized light. Constant-ionic-state measurements of the cross sections σ and the polarization parameters A indicate that all channels are strongly influenced by autoionization resonances. By combining these data, sums of partial contributions to σ are analyzed in detail to obtain specific information on the coupling of the resonances to the outgoing partial waves ελ. Apart from generally similar trends, the results show pronounced variations for different vibrational levels.

Excitation spectra of undispersed vuv and uv visible emissions from photoionized Xe 5s,5p satellites has been observed in the region between the 5${\mathit{s}}^{\mathrm{-}1}$ threshold and the 5${\mathit{s}}^{\mathrm{-}1}$ Cooper-minimum region. A vuv spectrum shows a number of resonance-enhanced satellites due to an interchannel coupling with doubly excited Rydberg states. Peculiar threshold enhancement in a uv spectrum around the ${\mathrm{Xe}}^{2+}$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ limit is explained by an initial-ionic-state correlation and a post-threshold enhancement (shakedown) after the ${\mathrm{Xe}}^{2+}$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ and ${}_{}{}^1{}_{}{}^{}$D limits by inelastic scattering.

The deflection of an atomic beam passing a standing-wave laser field in front of an oscillating mirror occurs by chaotic diffusive momentum transfer in a classical description and, as we show, is limited by dynamical localization quantum mechanically. An experiment to observe this quantum effect in an atomic beam is proposed.

Self-induced transparency (SIT) has been observed in an erbium-doped resonant fiber waveguide. The waveguide had an erbium ion concentration of 8900 ppm, and was cooled to 4.2 K. The pulse source was a 1.53-μm mode-locked Er-doped glass laser with a pulse width of 500 ps. Stable 2π, 4π, and multiple soliton pulses that broke up were clearly observed.