The mean spherical approximation has been applied to study both the thermodynamical and structural properties of fluid hard-sphere mixtures interacting through an attractive Yukawa tail. The solution scheme is the same as the one previously adopted by the authors for the case of hard-sphere mixtures. The problem of phase stability is more specifically treated in the paper. In the absence of computer simulation results to compare the theory with, reference is made to Monte Carlo calculations for Lennard-Jones (LJ) potentials, performed by other authors, and to experimental results for an Ar-Kr mixture in the fluid phase. A procedure is described which allows us to mimic these two different systems in terms of a proper adjustment of the parameters specifying the Yukawa potential, and of the diameter ratio of the hard spheres. The theory is able to locate the boundary of the phase stability for the LJ mixture rather accurately, and in good agreement with the computer simulation results. It also predicts pressure-concentration phase diagrams which reproduce all the qualitative features of the experimental data for the noble-gas mixture. Due to the simplicity of the solution scheme, one can explore the behavior of the system in a wide range of concentrations, potential strengths, and diameter ratios. It is thus possible to determine how the phase instability temperature depends on these parameters and to discuss the general conditions under which phase separation can take place.

The semiclassical Bloch-Maxwell system is studied for chaos. Diagnostic criteria for chaos such as continuous power spectra and rapidly decaying correlations are shown not to be definitive. They may occur simultaneously with a vanishing maximum Liapunov exponent. The presence of a feedback effect on the radiation field is shown to lead to the possibility of bona fide chaos with a continuous spectrum and a positive Liapunov exponent. Whether or not chaos is exhibited in this system depends upon initial conditions as well, and cannot be deduced from the Hamiltonian alone.

A nonlinear oscillator driven by both a coherent external field and a (weak) fluctuation-dissipation process of standard type is studied. It is shown that in the extremely-low-friction regime an additional random process comes into play which makes the linear-response theory work in spite of the scarce amount of standard fluctuation. This additional random process depends on the interplay of the nonlinear character of the oscillator under study and the weak fluctuation-dissipation process of standard type, but it is of transverse type, i.e., it does not involve any energy-dissipation process. On the theoretical side, this result rests on the joint use of a procedure of elimination of ‘‘irrelevant’’ variables and a rotating-wave-approximation technique which makes the role played by the transverse relaxation-process transparent. These predictions are checked by means of an analog experiment. Furthermore, light is shed onto an incorrect conclusion on the range of validity of the linear-response theory arrived at in an earlier report. This incorrect conclusion is now traced back to an ambiguous feature of the experimental results. The frequency position of the absorption peak does not change significantly upon increase of the excitation field up to a certain value of the excitation field. After this initial plateau the frequency of the absorption peak exhibits a rapid increase with increasing the intensity of the radiation field. Then the increase of the linewidth of the absorption peak becomes slower again with a parallel slow increase of the linewidth of the absorption spectrum, the shape of which, furthermore, does not show any sign of saturation, thereby generating the false impression, when the experimental investigation is carried out in this region, of a complete breakdown of the linear-response theory.

It is shown that, depending upon the lattice, there are two different trapping mechanisms for a genuine self-avoiding walk (GSAW), also called kinetic growth walk. Normal trapping, which may occur anywhere on the lattice, occurs with probability one and with a finite value for the average walk length. Abnormal trapping, exemplified by GSAW on a two-dimensional oriented square lattice, requires return to the neighborhood of the starting point, and occurs (we conjecture) with probability one but with infinite average walk length. The walk length distribution and the distribution of trapped walkers are provided for GSAW on the square lattice, and for 2-tolerant GSAW in one dimension. In the latter case the average walk length is 25 steps, and the average displacement of a trapped walker from his starting point is ten lattice spacings.

We provide perturbative, nonperturbative, and renormalization-group treatments of the symmetric electrolyte problem which permits us to obtain the corrections to the known Debye-Hückel results in a systematic way. In addition, nonperturbative methods enabled us to obtain some results for the case of dense electrolyte systems. The renormalization-group method is used to investigate the possibility of phase transitions. Our results indicate the absence of phase transitions in three dimensions for a sufficiently diluted symmetric electrolyte in complete agreement with the results of Kosterlitz.

A recent finding of Meakin et al. and Halsey et al. is that the surface of diffusion-limited aggregates (DLA) requires an infinite hierarchy of fractal dimensions for its characterization. In this work, we seek to understand this discovery and to place it into perspective. To this end, we study the distribution of hit probabilities near the surface of a variety of suitably chosen fractal and nonfractal objects—ranging from DLA and screened-growth aggregates on the one hand to simple A-arm stars and S-sided polygons on the other. We show physically how the infinite hierarchy of fractal dimensions arises, even for nonfractal objects. An important difference however, is that the infinite hierarchy is characterized by a constant gap exponent for the nonfractal objects, while for DLA a constant gap exponent is not sufficient.

Measurements of the resonance frequencies of the acoustic modes and of the microwave modes of a single cavity can determine u/c, the ratio of the speed of sound of a gas to the speed of light. Such measurements with a monatomic gas would determine the thermodynamic temperature T with unprecedented accuracy. By judicious choices of cavity geometry and resonance modes, u/c can be measured to part-per-million accuracy using cavities whose geometry is known only to parts per thousand. These techniques can also be applied to measurements of the universal gas constant R. A measurement of R would also require an accurate determination of the average atomic mass of the monatomic gas.

A novel concept for quantum chaos in spin systems is proposed which differs distinctively from concepts currently in use. It is argued (a) that the definition of quantum chaos cannot be based on the correspondence principle and (b) that quantum chaos is not equivalent to statistical behavior. Quantum chaos in spin systems implies the existence of a new type of spectrum consisting of excitations which do not form regular patterns with a multiparameter continuum structure in the thermodynamic limit, thus removing the constraint imposed by van Hove singularities that time-dependent correlation functions for pure quantum states cannot decay more rapidly than as powers of t. The irregular spectrum is caused by strong level repulsion resulting from the lack of a sufficient number of conservation laws in nonintegrable quantum many-body systems. The similarities and differences between quantum and classical chaos and, more generally, between quantum (non)integrability and classical (non)integrability are discussed in detail.

We have been studying the two-dimensional continuum percolation problem, using patterns on square cellular structures (square meshes) generated by computer simulation. The metallic critical volume fractions for the metal-insulator transition and the effective conductivities of their patterns agreed well with those of actual materials formed by deposition of metal films on insulator substrates. In this paper we obtain the fractal dimensions of percolation clusters of the two-dimensional continuum percolation models formed by computer simulation, and compare the factal dimensions with the results from the actual experiments of Voss, Laibowitz, and Alessandrini and of Kapitulnik and Deutscher, using transmission electron micrographs of thin metal films deposited on insulator substrates. We clearly show that the fractal properties of percolation clusters on square cellular structures agree well with those of actual experiments. The fractal dimensions are 1.9 for the large percolation clusters occurring when the metallic volume fraction is close to the critical volume fraction for the metal-insulator transition.

A Gaussian polymer chain in the presence of hydrodynamic interactions and subjected to steady linear flows is investigated renormalization-group theoretically. To order ε (=4-d, d being the spatial dimensionality) and to the lowest nontrivial order in the flow strength, we consider the hydrodynamic effect on the mean-square end-to-end distance. From our general formula, we extract results for the physically interesting cases of shear and elongational flow. In the light of recent experimental results there is a possibility that the Gaussian model is of limited validity, even below the stretching transition.

The scattering matrix, differential cross section, and the total cross section for a small nematic droplet are derived in the Rayleigh-Gans approximation. Different nematic director configurations are considered for the droplet. Those studied are the configurations which result in a spherical droplet from different molecular anchoring angles at the droplet wall. Configurations both in the absence and presence of an applied field are derived and their scattering properties are examined. Some simple cases are treated in detail and the results presented in closed form. In other more practical cases numerical results are presented for the differential and total cross section. Strong dependencies on the impact and scattering angles are found. The possibilities of determining droplet size and nematic director structure from experimental light scattering data are discussed, as well as features relevant to electro-optic light shutters.

Lorenz has introduced a fourth-order nonlinear system of ordinary differential equations with fourfold symmetry and numerically investigated in detail its chaotic behavior for the single parameter c=100. Here the pitchfork bifurcations of equilibria, a Hopf bifurcation to periodic solutions, and a subsequent cascade of period doublings, which illustrate the virtual Hopf phenomenon in a fourth-order system, are studied as c increases from 0 to 17.4290.

The unit-sphere description of nematic liquid-crystal configurations first introduced by Thurston [J. Appl. Phys. 52, 3040 (1981)] and dealing with elastic properties of nematic liquid crystals only is extended to include also the study of nematic flows. It is shown how the general features of the flow properties of nematic liquid crystals can be studied by the mapping of the hydrodynamic torque on the unit sphere. The effects of the application of electric or magnetic fields to a nematic liquid crystal under shear are discussed by adding the corresponding torque to the maps. Introducing a dimensionless quantity ɛ, which is the ratio of the hydrodynamic and the electric (magnetic) torques, one can deduce whether the hydrodynamic effects are dominating over the field effects or vice versa. By drawing the sequence of torque maps which appears as ɛ goes from minus to plus infinity [ɛ having the same sign as the dielectric (magnetic) anisotropy] it is shown how one can get a good qualitative understanding of the flow behavior just by the inspection of these maps. By calculating the eigenvalues of the singular points of the torque maps, their stability is determined. The stable ones correspond to flow alignment of the director, while the unstable ones can lend themselves to the study of hydrodynamic instabilities. It is also shown how one in a simple manner can derive expressions of relaxation times, boundary layers, and thresholds of hydrodynamic instabilities by knowing the eigenvalues of the singular points. Finally, it is proven that the equations governing the director profile are formally equivalent to those of a particle moving on a smooth sphere upon which the hydrodynamic torque pattern is imposed, the elastic constant (in the one-constant approximation) playing the same role as the mass of the particle. Using this equivalence it is discussed how one can approach the shear-flow problem of nematic liquid crystals by using the powerful tools of analytical mechanics.

Laser-noise analysis is presented for colored, multiplicative noise, as well as additive, spontaneous emission noise. A novel technique employing first-passage-time analysis recently used by Roy et al. provides the measured data and a two-dimensional dynamical model of the phenomena. A one-dimensional, contracted model is proposed which enables one to derive formulas characterizing the mean first-passage time and its variance. The agreement with the measured data strongly supports the validity of the effective Fokker-Planck equation recently introduced for colored, multiplicative noise.

The structure of the photosynthetic reaction center recently resolved by Deisenhofer et al. is discussed in relation to design principles for energy-storing systems. The rates of the primary electron transfer reactions are deduced by taking the electronic structure of the chromophores and their geometrical arrangement explicitly into account, while the protein portion is considered as a dielectric continuum which is rigid to an extent that the free-energy loss by solvent reorganization can be neglected. The values of the different rate constants thus obtained are in good agreement with experimental data. Each chromophore component in the reaction center appears to be positioned optimally for the purpose of energy storage in electron transfer. This can be shown by repeating the calculations for various arrangements that differ somewhat from the arrangement obtained by Deisenhofer et al. The device can only operate as an energy-storing system if each functional component molecule is exactly adjusted to each other sterically and energetically. It is shown by proposing a reasonable evolutionary pathway that the emergence of the specific arrangement of chromophores and proteins in the reaction center can be made plausible.

We discuss rational approximations to a single irrational number and pairs of mutually irrational irrational numbers and show that the binary ‘‘Farey’’ tree organization of the rationals extends naturally to a binary organization of pairs of rationals with a common denominator. There are obvious applications to theory and experiments in dynamical systems.

A general theory of spin-glass-like neural networks with a Monte Carlo dynamics and finitely many attractors (stored patterns) is presented. The long-time behavior of these models is determined by the equilibrium statistical mechanics of certain infinite-range Ising spin glasses, whose thermodynamic stability is analyzed in detail. As special cases we consider the Hopfield and the Little model and show that the free energy of the latter is twice that of the former because of a duplication of spin variables which occurs in the Little model. It is also indicated how metastable states can be partly suppressed or even completely avoided.

The time-dependent electrolyte friction on a single-charged spherical polyion is calculated analytically within the Debye-Hückel approximation for the bulk interionic correlations of the supporting electrolyte. Its time integral is the generalization of Schurr’s previous result for the electrolyte friction for arbitrary charges and mobilities of the ions of the supporting ionic solution (with an arbitrary number of species). The relationship between these results and analogous results available in the theory of ionic conductance and in the theory of self-diffusion of interacting polyions is established, and the finite-size effects of the electrolyte ions are calculated.

The electron correlations of the double-excited states in the helium isoelectronic sequence are investigated.

The recent experiment by Springer, Bennett, and Baisden on M-x-ray energy shifts is reanalyzed, taking advantage of existing extensive work on K x-rays. The shifts, calculated by use of relativistic Dirac-Fock wave functions, are about a factor of 3 smaller than the experimental values. It is pointed out that x-ray energy shifts can provide information on the healing process in metals.