Red blood cells show a remarkable flicker phenomenon under physiological conditions. Using a closed biconcave-discoid model, we have studied this effect theoretically by calculating the fluctuations of the thickness of the cell. This model avoids the divergency difficulty encountered in previous theory and leads to a more reasonable value of the curvature elastic modulus, ${\mathit{k}}_{\mathit{c}}$∼1.5×${10}^{\mathrm{-}12}$ erg. The well-known local flicker effect, i.e., the flicker occurring predominantly in the central region of the cell, is explained theoretically.

This is the third in a series of papers devoted to a lattice model for thermotropic nematic and smectic liquid crystals. The model system consists of N molecules, each with a rigid central core and two identical semiflexible tails, on a face-centered-cubic lattice. Molecular cores are restricted to three mutually orthogonal orientations, while each tail bond can have five possible orientations with respect to the preceding bond (representing five of the nine possible rotational-isomeric states of a pair of successive C-C bonds). This Brief Report presents the detailed derivation of several quantities related to the configurational statistics of the semiflexible molecular tails.

Recently interest in nonlinear diffusion processes, such as the conductivity as a simple function of concentration, has increased. However, a symmetry of an important class of relevant nonlinear diffusion equations seems to have been missed in the published literature. This symmetry can be useful in constructing new solutions, the most important example corresponding to the diffusion of a δ-shaped pulse located at the origin at time t=0. .AE

We have considered the problem of random multiplication of particles or fields in a diffusive medium. Both the short-time and asymptotic behavior is evaluated. We have used already known results on the density of states in disordered systems and on transverse spin depolarization in a medium with random magnetic fields. We have treated both bounded and unbounded random potentials. We reaffirm certain recent results and also point out some differences.

A simple damping term is proposed, to be added to the Hamiltonian in Schrödinger’s equation. It is shown that this term removes energy without altering the wave-function normalization. It is also demonstrated that the dynamics of the damped wave function are in reasonable agreement with (in one dimension): classical motion in a harmonic potential; tunneling in a cubic potential in a Caldeira-Leggett oscillator bath; and spreading in a flat potential, also in the oscillator-bath model. The use of this new damping term should allow direct simulation in the time domain of several problems, including the dynamic behavior of nanometer scale Josephson junctions.

We present the results of extensive large-scale numerical integrations of the Kardar-Parisi-Zhang equation for stochastic interface growth in 1+1 and 2+1 dimensions as a function of the nonlinearity parameter ε. We find results for the growth exponents α and β close to those obtained for discrete models. In particular, we find that for large values of ε, the values of the exponents are close to the conjecture of Kim and Kosterlitz, indicating that the smaller values obtained previously are due to crossover effects. In contrast to recent studies of discrete models, our results do not show evidence of a phase transition in 2+1 dimensions for ε≥1.

We find that the dynamics of growth phenomena exhibits the feature that growing sites are naturally partitioned into two ‘‘dynamical phases,’’ an extinct phase (the sites at which no further growth occurs, in a statistical sense) and a surviving phase (where growth occurs at some later time). As examples, we treat two common growth phenomena, invasion percolation and diffusion-limited aggregation. For both examples, we find ‘‘subclusters’’ which exhibit spatio-temporal fluctuations that are scale invariant. We find a 1/${\mathit{f}}^{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ power spectrum for both models. Also, we identify an order parameter and find an associated exponent β.

We develop the method of supersymmetric partners for random walks in one dimension. The key ingredient is a factorization of the master equation. This opens the possibility of many applications. As an example we show how to construct multistable models with a given spectrum that can be solved explicitly.

A simple two-component irreversible surface reaction model introduced by Ziff, Gulari, and Barshad has been studied using computer simulations. The model has a second-order kinetic phase transition. We have determined some of the critical exponents and find that the model belongs to the universality class of Reggeon field theory and directed percolation.

We present numerical results for the first and second moments of the distribution of collision times of the d=2 Lorentz lattice gas with density q in the range 0.2–0.8. They are used to calculate the mean-square displacement 〈${\mathit{X}}^2$(${\mathit{T}}_{\mathit{k}}$)〉 as a function of the number of collisions k. Using an asymptotic relation the mean-square displacement 〈${\mathit{X}}^2$(t)〉 as function of time is obtained from the latter quantity. As a result we are able to predict in an accurate numerical way the long-time tail of the velocity-autocorrelation function.

We present light-scattering experiments on various He + Xe gas mixtures. Our results give evidence that the sound mode for large wave vectors propagates with a velocity which is of the order of the adiabatic sound velocity of pure xenon.

We give a rigorous proof for the following result that combines those discussed earlier by Krüger and Poffyn [Physica 85A, 84 (1976)] and by Springborg [J. Phys. A 16, 535 (1983)]: The Wigner correspondence of a quantum operator can be obtained by simple substitutions under an arbitrary linear phase-space transformation. This property cannot be generalized to any other transformations or rules of phase-space correspondence. As an application of this result, the Wigner distribution functions of an anisotropic harmonic-oscillator system in crossed magnetic and electric fields are obtained.

A method for quantizing a classical system, based upon the notion of localization on phase space, is developed. This method, to which is given the name prime quantization, is based upon the mathematical theory of positive-operator-valued measures and their relationship to reproducing kernel Hilbert spaces, and to a notion of generalized kinematical variables related to phase space. For a system with ${\mathrm{openR}}^n$ as its configuration space, it has the advantage of being able to connect the well-known problem of ordering in quantum mechanics to the choice of a measuring apparatus in a joint measurement of position and momentum (within the limits of the uncertainty principle). Moreover, for such a system, a choice of ordering in the present context also turns out to be a choice of polarization in the method of geometric quantization.

The motion of a particle subject to an external force and coupled to a large number of harmonic oscillators is reducible to a nonlinear integro-differential equation for the position operator. This is achieved by eliminating the degrees of freedom corresponding to the motion of the oscillators. Upon this elimination the commutator of the position and the mechanical momentum of the particle becomes time dependent and a c number for a quadratic potential, but in general a q number for other fields of force. For a harmonically bound particle interacting with the heat bath the time evolution of the position and momentum operators are given in terms of the solutions of an integro-differential equation. Certain forms of the coupling of the motion of the particle to the heat bath allow for further reduction of these equations to quartic differential equations with constant coefficients. For these cases the time dependence of the position-momentum commutator, the energy of the particle as well as the heat bath are studied.

Asymptotic formulas of the energy eigenvalues for the states that ‘‘originate’’ from the side wells of the one-dimensional Schrödinger equation with the potential U(x)=$x^2$($R^2$-$x^2$${)}^2$/8$R^4$ are studied. We also analyze the results obtained by numerical solution of the Schrödinger equation and calculated from perturbation series by the Borel summation. Notwithstanding the similarity between the problem we study here and the double-well problems, there are fundamental differences between them.

An asymptotic expansion of the wave functions for the fragmentation channels of three-body systems is developed in hyperspherical coordinates. It is shown that, to any finite power in 1/R, where ${\mathrm{mR}}^2$= is the trace of the inertia tensor, the expanded wave function is an analytic finite sum of Sturmian functions. The expansion is carried out explicitly through order 1/$R^4$. These asymptotic states converge (as R→∞) to polarized orbitals for two-electron systems, and also provide improved dissociation channels for molecular ions, such as ${\mathrm{HD}}^{+}$. Asymptotic potential curves for He and ${\mu }^{\mathrm{-}}$-H systems are presented as illustrations.

The negative ions of the alkaline-earth-metal atoms (Be to Ba) have been studied by means of a pseudopotential model together with configuration-interaction and multiconfiguration self-consistent-field techniques. Only the heavier ions ${\mathrm{Sr}}^{\mathrm{-}}$ and ${\mathrm{Ba}}^{\mathrm{-}}$ have been predicted to be stable. For Ca atoms the situation is very complicated, and our calculations do not permit us to decide whether the negative ion is stable with respect to the neutral atom or not. The calculated electron affinities are very small and depend strongly on the correlation energy. It has been found that the core-valence correlation contribution to the electron affinities is important and reduces their values significantly.

Bethe logarithms accurate to 14 or 15 places to the right of the decimal are tabulated for all states of hydrogen up to n=20. Approximation methods for Rydberg states of two-electron atoms are discussed.