We have determined the microscopic symmetry of the J-band-forming amphiphatic cyanine dye (S120) to be $C_2$ by means of second-harmonic generation. We also demonstrate that the macroscopic distribution of the J aggregates is not isotropic, a result that facilitates our determination of the microscopic symmetry.

Ergodic behavior in liquids, supercooled liquids, and glasses is examined with a focus on the time scale needed to obtain ergodicity. A measure, d(t), which is based on the time-averaged energies of the individual particles and which is referred to as the ‘‘energy metric,’’ is introduced to probe the approach to ergodic behavior. We suggest that d(t) obeys a dynamical scaling law for long but finite times and that it can be used to characterize the degree of stochasticity in measure preserving systems with large numbers of degrees of freedom. Examination of d(t) indicates that the configuration space is explored by a ‘‘diffusive’’ process in the space of the dynamical energy variables used in constructing the energy metric. The characteristic diffusion constant associated with this process is argued to be analogous to the well-known maximal Lyapunov exponent which is often used to characterize stochasticity in systems with few degrees of freedom. Based on the long-time behavior of d(t) it is shown that ergodicity is effectively broken in the glassy state. In addition to broken ergodicity, the possibility that a subtle symmetry is broken as the liquid-to-glass transition takes place is examined. It is suggested that a ‘‘discrete’’ symmetry, to be referred to as the statistical symmetry, is broken in the glassy phase. This is illustrated by analyzing the distribution of the energy of the particles. Based on this, we expect long-time dynamics and structural relaxation in glasses to be dominated by fluctuations in domains of finite length within which the particles are highly correlated. This is in accord with the ideas of Adams and Gibbs. All of the above arguments are illustrated with the aid of molecular-dynamics simulations of soft-sphere mixtures.

The nonlinear response of a barotropic quasigeostrophic fluid to a δ forcing by the rotation of the wind stress is discussed in terms of the symmetry properties related to the multipole structure of the response’s relative vorticity field and the gradient of planetary vorticity. It is shown that by a global and local renormalization of the β plane, introducing an effective absolute vorticity gradient by means of the global derivatives of the relative vorticity distribution, the three basic symmetry properties, as they are known from numerical simulations, can be explained analytically. This is achieved by means of a renormalized perturbation series which gives the factors that govern the symmetry properties as a function of the parameter measuring the strength of the nonlinearity. These properties are (1) the turning of the symmetry axis for increasing nonlinearity in the direction of the rotation of the wind stress, (2) the concurrent weakening of the symmetry breaking for increasing nonlinearity, and (3) the maximum strength of symmetry breaking around the vorticity dipole axis for intermediate nonlinearity. The first two properties are related to the vorticity distribution’s dipole character and the third one to its quadrupole character. The shape of the induced circulation is shown to vary from an oval-shaped pattern with an east-west symmetry axis for weak nonlinearity over a completely asymmetrical swirl for intermediate nonlinearity to a butterfly pattern for the almost-free, strongly nonlinear, inertial mode that is again asymptotically symmetric around the north-south axis.

For any multifractal growth process we calculate how the probability of advance of a fixed site on the boundary of the structure changes as the fractal increases in size. We are then able to find expressions for the dimension of the active zone of the fractal and the distribution of ages of points from which growth occurs in terms of the scaling function f(α). For the case of diffusion-limited aggregation (DLA) and the screened-growth model, we offer a geometrical interpretation of the results. For DLA in arbitrary space dimensions we find a relation between the third moment of the probability distribution and the Hausdorff dimension D, which generalizes a result by Halsey [Phys. Rev. Lett. 59, 2067 (1987)].

The modified-moment method is applied to solve the Fokker-Planck equation in such a way that the solution is consistent with the requirements of the thermodynamic laws. The formal solution has an attendant mathematical structure for the entropy which is similar to that obtained from the Boltzmann equation. A generalized Gibbs relation is obtained for such a thermodynamic branch of solution. The formalism therefore may be used to study thermodynamic aspects of stochastic processes underlying the Fokker-Planck equation. The method is shown to yield the same analytical results as other methods in the case of linear processes, and in the case of nonlinear processes the moment series converges sufficiently fast to justify a lower-order truncation of the moment series for the distribution function, if the diffusion constant (D) is less than a critical value. In this case the solution of the Fokker-Planck equation tends to the steady-state distribution function. It is shown that the second variation of the nonequilibrium part of the entropy may be used as a Lyapunov function, which provides local criteria of evolution only.

We derive two expansions in powers of the density for the autocorrelation function of a spectral-line profile in a plasma. The expansions can be regarded as systematic generalizations of the well-known unified theory and of the scalar theory which appear in a natural way as the respective first-order terms. Under the additional assumption of completeness of collisions, but without assuming nonoverlapping, we obtain a simplified expansion. It is a generalization of the impact theory, and the latter results again from the first-order term. We present quick and direct derivations of the first- and second-order terms for all three density expansions. The Nth-order terms contain time-development operators and S matrices for N or fewer particles.

The availability loss -Δ$A^u$ in a process is equal to the flow of the extensive thermodynamic quantities multiplied by the respective intensity differences only if the degraded work, the ‘‘uncompensated heat’’ of Clausius, is disposed of into the environment. We define work deficiency as the above product in all situations and relate it to the dissipation bound based on thermodynamic length.

We present a Landau theory for smectic liquid crystals in a magnetic field, and apply it to systems exhibiting the smectic-A (Sm-A), smectic-C (Sm-C), and smectic-$C^{\mathrm{*}}$ (Sm-$C^{\mathrm{*}}$) phases; our theory provides a unified explanation of two phenomena, the temperature dependence of the pitch in the Sm-$C^{\mathrm{*}}$ phase and the re-entrance of the Sm-$C^{\mathrm{*}}$ phase. We find that the Sm-$C^{\mathrm{*}}$ phase is always re-entrant. Two types of phase diagrams are found, depending on the relative signs of two of the Landau parameters; in one case, the Sm-$C^{\mathrm{*}}$ phase is re-entrant only for fields greater than some value, while in the other case it is re-entrant for all field values (but the helicity has different sign above and below the Sm-C phase). The results are in qualitative agreement with experiment. The order parameter in the Sm-$C^{\mathrm{*}}$ phase has a well-developed domain structure only near the Sm-C–Sm-$C^{\mathrm{*}}$ boundary; a new feature is that the order parameter is almost sinusoidal at low temperatures, well below the boundary. We provide a complete analytical treatment of the Sm-C–Sm-$C^{\mathrm{*}}$ transition, extending previous results in the theory of commensurate-incommensurate transitions.

We have investigated higher-order packing entropy effects on the fundamental elastic properties of a liquid-density nematic system of hard spherocylinders as a function of molecular geometrical anisotropy by starting with the systematic density-functional formalism. We have constructed the free energy and the direct pair-correlation function for hard nonspherical bodies from a generalization of those for hard spheres, and then derived molecular expressions for the elastic moduli in a simple and physically transparent way. Numerical calculations are performed for a variety of the length-to-diameter ratios of hard spherocylinders, with the aid of an accurate orientational distribution function. At similar densities the qualitative features exhibited by the calculations agree fairly well with the results of recent Monte Carlo simulations on a system of short spherocylinders. It is found that the present approach quantitatively reproduces existing molecular field theories in the low-density limit as the length-to-diameter ratio increases.

An algorithm to estimate the average local intrinsic dimension of an attractor is described. Of particular concern is the ability to estimate local attractor dimensionality at moderate values of signal-to-noise ratio (SNR). The algorithm is based on the estimation of the local intrinsic dimension (LID) of various randomly chosen regions around the attractor. The LID is determined by the number of significant singular values, or rank, of the data matrix for data points within the local region. The rank of this matrix is an integer and, in general, varies with position on the attractor. To obtain an overall estimate of the local attractor dimension a weighted average of all the local regions is calculated. Results are then compared to conventional estimates of fractal dimension. For high SNR results are in good agreement with the fractal dimension as calculated by the Grassberger-Procaccia algorithm. Limited test results indicate that the LID technique may be more robust when trying to estimate, or bound, the fractal dimension in the presence of moderate amounts of noise.

We study the effect of thermal isolation on metastability, describing the metastability in the Ginzburg-Landau formalism. We find that metastability is always strengthened by thermal isolation. For an isolated body it is thus even possible to obtain, in principle, certain new kinds of quasithermodynamic states stabilized by virtue of their isolation, which would not be attainable for the body kept at any constant temperature. These are configurations where, although the free energy is at local maximum, the total (negative) entropy is at a minimum. We interpret this to mean that the body is metastable when in isolation, but becomes unstable in contact with a heat bath, nevertheless at the same temperature. The systems in question are small in the sense that the energy involved with the metastability must not be negligible relative to the heat capacity. The example of a thin type-1 superconducting sheet is examined. By isolating the body in the usual metastable (‘‘superheated’’) state in the neighborhood of the superheating field and then raising the magnetic field, one may attain the ‘‘isolation metastable’’ state.

Two different approaches (quantum and semiclassical) used to calculate time-dependent transition rates for a multilevel molecular system stochastically interacting with a thermal bath are presented. While the former is based on the use of a relationship between the real and the imaginary parts of the time autocorrelation function (TAF) associated with the interaction Hamiltonian, the latter relies on the replacement of a quantum TAF by the corresponding anticommutator. Two well-known examples for a stochastic interaction Hamiltonian, an Ornstein-Uhlenbeck process and a white-noise process, have been considered. In both cases, explicit expressions for the transition rates in terms of a reduced set of parameters characterizing the bath are obtained. In the Gaussian regime both quantum and semiclassical transition rates show a time-damped oscillatory behavior towards the same steady value. In the white-noise (δ-correlated) regime, while the quantum transition rates are time dependent, the semiclassical rates are not. The high- and the low-temperature limits for the quantum and the semiclassical transition rates are also reported. The semiclassical results reduce to the quantum results only in the high-temperature limit.

The passive convection of vector fields and scalar functions by a prescribed incompressible fluid flow v(x,t) is considered for the case where v(x,t) is chaotic. By chaotic v(x,t) it is meant that typical nearby fluid elements diverge from each other exponentially in time. It is shown that in such cases, as time increases, a convected vector field and the gradient of a convected scalar will generally concentrate on a set which is fractal. The present paper relates the stretching properties of the flow to the resulting fractal dimension spectrum. Motivation for these considerations is provided by the kinematic magnetic dynamo problem (in the vector case) and (in the scalar case) by recent experiments which demonstrate the possibility of measuring the fractal dimension of the gradient squared of convected passive scalars.

We present a theory for nucleation at a first-order phase transition where the mediating forces are long range. We find that the long-range force induces cooperative nucleation and growth processes, and that this feedback mechanism produces a well-defined delay time with a sharp onset in the transformation to the stable phase. Closed-form expressions for the characteristic onset time and width of the transition are developed, in good agreement with numerical and existing experimental results.

The QED contributions to the Li-like 2$p_{1/2}$-2$s_{1/2}$ and 2$p_{3/2}$-2$s_{1/2}$ transition energies have been calculated using Grant’s multiconfiguration Dirac-Fock computer package [Grant et al., Comput. Phys. Commun. 21, 207 (1980); McKenzie et al., ibid. 21, 233 (1980)]. The QED contributions were combined with the energies that were recently calculated by Johnson, Blundell, and Sapirstein [Phys. Rev. A 37, 2764 (1988)] using many-body perturbation theory. The resulting transition energies are in excellent agreement with the observed transition energies that are available for the ions with atomic numbers up to Z=36. Transition energies are predicted for the ions up to Z=54.

It has been found that in the x-ray fluorescence spectra for ${\mathrm{CaF}}_2$ the full width at half maximum (FWHM) of the Ca K${\alpha }_1$ structure is significantly narrower than that in other calcium compounds, and also that the CaSi Ca K${\alpha }_1$ is accompanied by a strong satellite Kα’’. This Kα’’ satellite has been assigned to a ${\mathrm{KM}}^2$→${\mathrm{LM}}^2$ transition, in which the spectator holes originate from the shakeoff of M electrons during the photoionization of a 1s electron. Other satellites within the natural width of the K${\alpha }_1$ structure were also found, using numerical deconvolution of the measured spectra. The origin of the chemical effect on the FWHM modification is interpreted using cluster molecular-orbital calculations of (${\mathrm{CaF}}_8$${)}^{6\mathrm{-}}$ for both ground and 1$s^{\mathrm{-}1}$ hole states: The pseudocrossing of atomic orbitals of Ca 3p and F 2s transfers the shakeoff hole from the Ca 3p to F 2s at the creation of a Ca 1$s^{\mathrm{-}1}$ hole; consequently, the satellite of ${\mathrm{CaF}}_2$ is weakened.

A recent prediction about the scaling behavior of the first passage time of bistable systems close to threshold as a function of noise is tested.

Axially propagating phase-matched parametric four-wave and six-wave mixing in pure sodium vapor is an easily documented process that may be confused with other resonant processes such as amplified spontaneous emission or stimulated hyper-Raman emission. We demonstrate and characterize the process in sodium vapor under near-resonant two-photon excitations.

The complex viscosity of dense hard-sphere dispersions has been determined recently over a large frequency range. If conceived as a homogeneous system with continuously distributed elasticity and viscosity, the complex viscosity can be described theoretically with a constant relaxation strength and relaxation times ${\tau }_p$=${\tau }_1$/$p^2$, with p the relaxation number. This is consistent with the empirical analysis of the data. The distributed elasticity can be interpreted microscopically as due to statistical springs acting between the spheres. The springs are modeled as Fraenkel springs to take into account the excluded-volume effect. The relaxation strength has been calculated quantitatively. The resulting deduced relaxation strengths are in fair agreement with the experimentally observed ones. The given interpretation is compared with literature theory.

We present a diffusional model for chemoreception processes under biological conditions. The reactant undergoes both translational and rotational diffusion and is ‘‘adsorbed’’ at the surface of the enzyme (or cell) only within a limited range of its possible angular orientation with respect to the surface. We discuss the effect of the rotational diffusion on the molecular flux at the surface for typical values of the diffusion constants.