We present the results of experiments where we have measured the absorption of laser light by plasmas generated by 20–120-psec duration pulses of Nd laser radiation incident upon solid targets at intensities exceeding ${10}^{14}$ W/${\mathrm{cm}}^2$. The results were obtained using box calorimetry, supported by ion calorimetry, ion probe data, and 2ω calorimetry. We have found a marked asymmetry in the absorption for 120-psec pulses with irradiation geometry with the absorption dropping by 60% when the beam diverged at the target surface. The results were analyzed using a simple rigid plasma model and show that resonance absorption is not the dominant mechanism, but the absorption is caused by the presence of a narrow region near the critical surface having a strongly enhanced collision frequency most probably due to the presence of long-wavelength ion acoustic waves in the plasma.

The fcc (100) and (111) Lennard-Jones fluid-solid interfaces are examined via a molecular dynamics simulation at a temperature of 1.15ɛ/k for a system of 35 000 particles. The (100) layers are found to expand as the fluid is approached, whereas the (111) layers keep nearly the same spacing, indicating that the density difference between the two phases is established through different mechanisms for the two interfaces. The (100) interface is stress free, but the (111) interface is under compression. These interfaces are found to be inhomogeneous, with ordered and disordered regions, as well as rough, with significant deviations from planarity. It appears that the characterization of the interface as consisting of islands of solid and fluid is reasonable.

A perturbation analysis is presented of an exchange of stability between two mechanical equilibrium conformations of a torsionally deformed, linearly elastic, cylindrical polymer whose ends are held together to form a topologically circular structure. The imposed constraint is the twist angle ζ through which one end of the polymer is rotated relative to the other. The value ζ=0 corresponds to the relaxed state, in which no torsional deformation is imposed. Close to the relaxed state, the stable equilibrium conformation is a torsionally deformed circle in which the imposed constraint is expressed entirely as twist. A threshold value of ζ is shown to exist, whose location depends on the ratio of the polymer bending stiffness A to its torsional stiffness C. Beyond this threshold the stable equilibrium conformation involves nonplanar bending, also called writhing. As this threshold is surpassed, a smooth onset of writhing occurs as a form of torsional buckling. These results are applied to the analysis of torsional fluctuations in nicked circular DNA. A critical molecular length is found, at which the root-mean-square twist induced by thermal fluctuations just suffices to initiate writhing. Comparison with the analogous critical length for linear polymers shows that the constraint imposed by circularity greatly increases the stability of the unwrithed conformation. Although twisting and bending are not coupled either energetically or topologically in nicked circular molecules, the exchange of stability between unwrithed and writhed conformations provides a mechanical coupling between them. Because sufficiently large torsional deformations drive writhing, fluctuations in the parameters scrT and scrW are not statistically independent in nicked molecules, but instead are positively correlated.

A generalization of the diffusion-limited aggregation (DLA) model, originally proposed by Witten and Sander [Phys. Rev. B 27, 5686 (1983)], has been studied on a very large square lattice. This model has a sticking probability p for a random walker which is assumed to depend on the number of occupied nearest-neighbor sites in the cluster B, as p=${\alpha }^{3\mathrm{-}B}$. A dynamical phase transition between growth along the axes and growth along the diagonals is observed at a critical ${\alpha }_c$≊0.175. Our simulations also show that ${\alpha }_c$ changes with the amount of noise reduction. Thus we show for the first time that noise reduction may change the asymptotic behavior of DLA models.

As a model displaying typical features of two-frequency quasiperiodically forced systems, we discuss the circle map with quasiperiodic coupling. We present numerical and analytical evidence for the existence of strange nonchaotic attractors, and we use examples to illustrate various types of dynamical behavior that can arise in typical quasiperiodically forced systems. We investigate the behavior of the system in the two-dimensional parameter plane of nonlinearity strength versus one of the driving frequencies. We find that the set in this parameter plane for which the system exhibits strange nonchaotic attractors has Cantor-like structure and is enclosed between two critical curves. One of these curves marks the transition from three-frequency quasiperiodic attractors to strange nonchaotic attractors; the other marks the transition from strange nonchaotic attractors to chaotic attractors. This suggests a possible route to chaos in two-frequency quasiperiodically forced systems: (three-frequency quasiperiodicity)→(strange nonchaotic behavior)→(chaos).

Binary mixtures of octyloxyphenyl-nitrobenzoyloxy benzoate (${\mathrm{DB}}_8$${\mathrm{ONO}}_2$) and decycloxyphenyl-nitrobenzoyloxy benzoate (${\mathrm{DB}}_{10}$${\mathrm{ONO}}_2$) exhibit a rich variety of smectic polymorphism. An ac calorimetric study has been carried out on six mixtures with mole percent X of the decyl homolog between 51 and 57, a range that includes the Sm-$A_d$–$N_r$–Sm-$A_1$ point at X≃56. The sample with X=57 exhibits a first-order direct Sm-$A_d$–Sm-$A_1$ transition, while the sample with X=51.3 exhibits two transitions—a second-order Sm-$A_d$–$N_r$ transition with a very small excess heat-capacity peak and a tricritical $N_r$–Sm-$A_1$ transition with a large heat-capacity peak. For samples with intermediate compositions, only weakly first-order $N_r$–Sm-$A_1$ heat-capacity peaks are observed in the vicinity of the Sm-$A_d$–$N_r$–Sm-$A_1$ point. All six investigated samples exhibit the Sm-$A_1$–Sm-C̃–Sm-$C_2$ phase sequence at lower temperatures. The Sm-$A_1$–Sm-C̃ transition is a weakly first-order phase transition with pretransitional excess heat capacity below the transition temperature. In contrast, the Sm-C̃–Sm-$C_2$ transition is a weakly first-order inverted Landau transition with no pretransitional behavior in the Sm-$C_2$ phase below the transition but a large mean-field excess heat capacity observed in the Sm-C̃ phase above the transition.

The organization of multiple coexisting basins of attraction in two-dimensional driven dynamical systems is studied. This study is carried out, in particular, for the laser with modulated parameter and the Hénon map. Basin organization is governed primarily by the ordering of heteroclinic and homoclinic connections of regular saddles. This organization is complex yet systematic, with accumulation structures governed by the order of saddle connections. We study the evolution of a basin in the presence of multiple coexisting basins, from (before) birth to (beyond) death. Many of the processes that occur are canonical. These include the reorganization of existing basins in preparation for the creation of a new basin by saddle-node bifurcation, the increased intertwining, in Poincaré section, of the components of a basin, and the increased wrinkling of each component as the basin evolves from birth to death. These also include the processes that mark disintegration and the ultimate demise of the basin, beginning at homoclinic tangency and terminating in its disappearance or enlargement in a crisis.

We present the results of applying an analytical method, using a new concept involving a periodic stability around a line of initial values, to two Hamiltonian systems with two degrees of freedom each with several parameters. By requiring the systems to have this type of stability, we have been led to known integrable cases for the systems. For one of the systems, our analysis gives six other cases, two of which turn out to be nonintegrable. The status of the remaining four cases has not been established.

A new simulated-annealing method based on stochastic-dynamic programming is proposed to obtain a rapid convergence to a global minimum of multivariable optimization problems. A central concern is to provide appropriate temperature values that determine the convergence of the cooling schedule. By use of the stochastic-dynamic programming method, the present cooling schedule is derived by minimizing the time that the system requires to reach the global minimum from an initial state. Monte Carlo simulation shows that the present schedule gives a convergence 10 to 100 times faster than traditional schedules.

Deformation of vesicles at fixed volume and surface area is considered, and the spherical limit is derived in a new way, making essential use of Galilean invariance of the deformation energy. The spherical limit of the deformation energy is singular, and depends upon the bifurcation branch along which the spherical shape is approached.

A new experimental technique, fluorescence cross correlation, is proposed to directly measure correlations in motion of pairs of interacting particles. The theoretical basis of the technique is worked out, taking into account, in addition, nonideal features of the experiment. Preliminary experimental results are obtained on latex suspensions. They demonstrate the possibility of measuring not only a distinct correlation function but also the corresponding self-contribution as well as a collective correlation function of the suspension simultaneously in one experiment.

The alignment of a nematic liquid crystal, 4’-n-pentyl-4-cyanobiphenyl (5CB), on several smooth metal (Cr, Cu, Ag, and Au) surfaces was observed experimentally. Perpendicular (homeotropic) induced alignment was observed for Cu and Ag boundary layers, whereas parallel alignment was observed for Cr and Au. These differences are discussed in relation to the differences in chemical bonding interactions at the surfaces as described by theoretical calculations performed for the cases of Cu, Cr, and Au. Several differences in orbital interactions, as well as a sensitivity to bonding configurations, are illustrated with the aid of extended Hückel calculations on hypothetical organometallic complexes and extended-Hückel–tight-binding calculations of the interface for parallel versus perpendicular adsorbate orientations.

The Fermi-liquid transport theory of electrical conductivity formulated by Eliashberg [Zh. Eksp. Teor. Fiz. 41, 1241 (1961)] is further developed, using the analytic continuation of the finite-temperature Ward-Takahashi relations obtained by the present author [Ann. Phys. (N.Y.) 173, 226 (1987)] to maintain the theoretical consistency of approximation schemes for solving the Bethe-Salpeter equation. In particular, the finite-temperature Ward-Takahashi relations corresponding to the local conservation of the electron number density and to the conservation of the electron momentum are considered. A general expression for the electrical conductivity in terms of the proper vertex part is also obtained. In the formula, cancellation of the quasiparticle renormalization factors at the Fermi surface is explicitly shown in a general way without assuming a particular model. In the case that the electrons are scattered by phonons, the formula gives the Grüneisen-Bloch formula for the on-shell phonons. For the impurity resistivity, the theory of Edwards [Philos. Mag. 3, 1020 (1958)] is developed to finite temperature by introducing a hypothetical boson field that replaces the impurity averaging.

A recently presented model of long-range interatomic interactions in a DNA polymer is compared to an earlier approach. Comparison of the results of both approaches is made to existing experiments. The newer method consistently produces good experimental agreement within the context of a single, physically reasonable parametrization. It is therefore sensible to consider some observable but not yet observed features of the calculation as valid predictions. We offer a dozen or so resonances in the frequency range from ${10}^{10}$ to ${10}^{12}$ Hz as potentially new observable absorption lines.

Static and dynamic light scattering are used to study the aggregation kinetics and structure of colloidal gold. Fast aggregation is achieved by either addition of pyridine, lowering of the pH, or addition of salt. The kinetics of rapid growth is followed by measurement of the polarized relaxation time ${\tau }_{\mathrm{vv}}$ (proportional to the mean cluster radius). We observe a power law, ${\tau }_{\mathrm{vv}}$∝(Ct${)}^x$, with x=0.38±0.04, where t is the time and C is the initial sol concentration. Measurements of the depolarized relaxation time ${\tau }_{\mathrm{vh}}$ as Q→0 (Q is the wave vector) are found to be proportional to the third power of the cluster radius, typical of rotational diffusion. Such measurements allow independent confirmation of the kinetics as ${\tau }_{\mathrm{vh}}$=(Ct${)}^{3x}$, with x=0.38±0.04. The static light scattering intensity I from these rapidly grown clusters obeys a power law, I∝$Q^{\mathrm{-}y}$ with y=1.74±0.1, at a wavelength of λ=633 nm (optical resonance is 680 nm), with the value of y increasing away from resonance to a value of 2.0±0.1 at λ=457 nm. Under diluted conditions the scattering behavior is identical on and off resonance with y=2.0±0.1. These results are inconsistent with the diffusion-limited cluster aggregation model which predicts y≊1.75 and x≊0.56. Finally, it is shown that slow pyridine-induced aggregation of diluted gold sols results in linear growth of the cluster radius with time, but the resulting aggregates still obey I∝$Q^{\mathrm{-}y}$, with y=1.8±0.1. Simple models of reaction-limited aggregation cannot account for the latter observations.

An extension of Hopfield’s model with adaptive threshold and inhibitory interactions yields a network capable of nearly optimal storage of patterns of low activity. A replica symmetric solution of the mean-field equations is presented for the noise-free case. The following properties are demonstrated: For a low level of activity a the storage capacity increases as -(a lna${)}^{\mathrm{-}1}$; up to 0.38 bits per synapse can be stored; spurious states can be suppressed; the network is not opinionated, i.e., it can categorize inputs as not similar enough to patterns stored.

The results of a study of the dielectric properties of a room-temperature ferroelectric liquid crystal in the frequency range from 5 Hz to 13 MHz are presented here. Measurements of complex electric permittivity versus temperature have been taken on aligned samples of different thicknesses with the electric measuring field being parallel or perpendicular to the layer planes. In homogeneously aligned samples two dielectric relaxation regions have been observed in the smectic-$C^{\mathrm{*}}$ phase, one known as the Goldstone mode and the other showing up in the vicinity of the smectic-$C^{\mathrm{*}}$–smectic-$A^{\mathrm{*}}$ transition called the soft mode. In homeotropically aligned samples the low-frequency molecular relaxation was observed in both smectic phases. Temperature dependences of both dielectric increments and relaxation times suggest that the system studied exhibits a ferroelectric phase transition of the first-order type.

Synchrotron x-ray diffraction has been used to study the surface and the interior hexatic-to-liquid (smectic-I to smectic-C) melting transitions of freely suspended liquid-crystal films of N-[4’-(n-heptyl)benzylidene]-4-(n-heptyl)aniline (7O.7) five molecular layers thick. Both the surface hexatic monolayers and the interior hexatic layers melt via hysteretic first-order transitions. After the two surface layers undergo a first-order transition to the smectic-I phase, the surface hexatic correlation length ξ evolves smoothly from ∼100 to ∼300 Å with a roughly square-root form, ξ∼‖T-$T_c$${\Vert }^{1/2}$.

The method of complex-coordinate rotation is applied to investigate autoionization states of positronium molecules. Using elaborate Hylleraas-type wave functions in which all six interparticle coordinates are used, resonance parameters for six S-wave resonant states are determined. It is believed that three of them belong to a Rydberg series in which the two positrons form a singlet spin state, and the other three resonances belong to the triplet spin state for the two positrons. All these two Rydberg series are converging on the ground state of the ${\mathrm{Ps}}^{\mathrm{-}}$ threshold.

The recently developed bivariational coupled-cluster approach was earlier used for the derivation of equations for first-order properties in a two-body approximation. In this paper we introduce a linearized form of this approach in which the bra vector is linearized. In such a form the bivariational coupled-cluster approach reduces to the nonvariational-response-type approach, and thus it can also be more easily generalized to any higher-order property in a more extended approximation. This also gives us an alternative variational derivation of the original nonvariational-response equations of Monkhorst.