A single polymer chain can be described by an equation of state for constant end-to-end separation L or constant torque f. Formal relationships among these equations of state and their equivalence are examined. Numerical calculations of these equations of state find them to be inequivalent. This inequivalence has its source in the van der Waals loop and scaling properties of the constant-L equation of state.

The six-dimensional Fokker-Planck equation, a variational functional, and a coordinate transformation are used to derive an expression for the Kramers rate constant. An explicit equation is obtained for the rate of adsorption of a diatomic molecule on a molecular surface as a function of the potential energy between the diatomic molecule and the molecular surface, the physical properties of the diatomic molecule, the viscosity surrounding the active site, and the temperature.

A discrete-ordinate method of solution of the time-dependent Boltzmann-Fokker-Planck equation for electron swarms in rare-gas moderators is employed in the study of the time dependence of the average electron energy, mobility, and transverse diffusion coefficient versus the strength of an externally applied electric field. The solution of the Fokker-Planck equation is based on the expansion of the solution in the eigenfunctions of the Lorentz-Fokker-Planck operator. With the transformation to an equivalent Schrödinger eigenvalue problem, the eigenvalue spectrum is shown to be entirely discrete, thereby validating the eigenfunction-expansion approach. The effects studied include the effect of an electric field on the thermalization times, a comparison of the effects of moderators with and without Ramsauer minima in the momentum-transfer cross sections, and the effect of an external electric field on the transient negative-mobility phenomena predicted in an earlier paper. A comparison with experimental results for Xe shows good agreement with the calculations.

A generalization of linear-response theory is attempted, within the framework of information theory [Y. Alhassid and R. D. Levine, Phys. Rev. A 18, 89 (1978); D. Otero et al., Phys. Rev. A 26, 1209 (1982)], with the idea of developing a formalism capable of dealing with small deviations from a previously well-described situation. The ensuing approach is applied to diverse physical situations that illustrate its flexibility.

In the present work a solid surface is placed in the propagation path in a laser-produced plasma. A substantial increase in the total emission intensity is observed in the resonance lines of the hydrogenlike and heliumlike ions. The results in the x-ray-wavelength range are given spatially along the propagation path. Dynamics of the plasma-wall interaction process is studied in the visible range with both spatial and temporal resolution.

The scanning method proposed by us [J. Phys. A 15, L735 (1982); Macromolecules 18, 563 (1985)] for simulation of polymer chains is further developed and applied, for the first time, to a model with finite interactions. In addition to ‘‘importance sampling,’’ we remove the bias introduced by the scanning method with a procedure suggested recently by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)]; this procedure has the advantage of enabling one to estimate the statistical error. We find these two procedures to be equally efficient. The model studied is an N-step random walk on a lattice, in which a random walk i has a statistical weight &, where p<1 is an attractive energy parameter and $M_i$ is the number of distinct sites visited by walk i.

This model, which corresponds to a model of random walks moving in a medium with randomly distributed static traps, has been solved analytically for N→∞ for any dimension d by Donsker and Varadhan (DV) and by others. 〈M〉 and lnφ, where φ is the survival probability in the trapping problem, diverge like $N^{\alpha }$ with α=d/(d+2). Most numerical studies, however, have failed to reach the DV regime in which d/(d+2) becomes a good approximation for α. On the other hand, our results for α (obtained for N≤150) are close to the DV values for p≤0.7 and p≤0.6 for d=2 and 3, respectively.

This suggests that the scanning method is more efficient than both the commonly used direct Monte Carlo technique, and the Rosenbluth and Rosenbluth method [J. Chem. Phys. 23, 356 (1954)]. Our results support the conclusion of Havlin et al. [Phys. Rev. Lett. 53, 407 (1984)] that the DV regime exists already for φ≤${10}^{\mathrm{-}13}$ for both d=2 and 3. We also find that at the percolation threshold $p_c$ the exponents for the end-to-end distance are small, but larger than zero, and that the probability of a walk returning to the origin behaves approximately as $N^{\mathrm{-}1/3}$ for both d=2 and 3.

We have recently suggested an approximate computer simulation technique, based on the scanning method, which enables one to extract the entropy (and hence the free energy) of polymer chains from a relatively small sample. So far this technique has been discussed in terms of chains with excluded volume (EV); in the present work we extend its scope to chains, which also have finite interactions. In order to obtain better approximations for the entropy we utilize the concepts of the generalized Monte Carlo procedure suggested by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)] (and discussed in the preceding paper). We analyze our results from the preceding paper for self-attracting random walks (without EV) on square and simple-cubic lattices, and show that our techniques lead to accuracy which is better than 0.3% for both the free energy and the entropy. For chain models which include EV, we use, in addition to Schmidt’s procedure, an alternative one based on ‘‘importance sampling.’’ We test these two procedures as applied to self-avoiding walks (SAW’s) on a square lattice, where the SAW’s are unbounded in space or bounded in relatively small ‘‘boxes.’’ Very accurate results for the entropy are also obtained here. It turns out, however, that importance sampling is slightly more efficient than the Schmidt procedure.

The Hamilton-Jacobi canonical transformation theory is extended to treat nonintegrable Hamiltonian systems with a continuous Fourier spectrum. By a natural analytic continuation of the Fourier variable to the complex plane, a nonunitary operator for the canonical transformation is obtained. We apply this transformation to describe Chirikov’s diffusion process near a separatrix in nonlinear systems with two degrees of freedom. Our formalism shows a clear distinction between the irreversible evolution of an ensemble with a finite measure from the reversible evolution of a trajectory in nonintegrable systems with chaotic motion. The condition for obtaining the irreversible kinetic equation in Hamiltonian systems is connected to the condition for the existence of homoclinic points around the separatrix. We also show that Prigogine’s dissipativity condition in nonequilibrium statistical systems is equivalent to the nonintegrability condition for nonlinear systems with a few degrees of freedom.

We investigate the equilibrium state of a one-dimensional fluid of hard-core particles subject to a given external periodic potential. Starting from Percus’s exact theory we obtain accurate numerical results for the density profiles and the free energy. These are used for a quantitative test of an approximate free-energy functional frequently used in classical density-functional theories. We show that the density-functional approach works well in a rather broad range of physically interesting parameters. Limits of its applicability are also discussed.

We introduce a new approximate block-spin transformation, and applying this method to the massless free field on fractals, we obtain approximate values of the spectral dimension. For fractals of the Sierpiński type, the results are smaller than the values obtained by the Migdal-Kadanoff renormalization.

In a bound system of two equal-mass but oppositely charged particles, the electric even-multipole transitions are totally suppressed. Some observations are made.

By extending the work of Casperson [Phys. Rev. A 30, 2749 (1984); A 31, 2743(E) (1985)], a procedure to construct an analytically-solvable second-order linear differential equation with continuous periodic coefficients is found and presented here. An illuminating example with three-parameter coefficients is given which might be applicable to the problem of an electron in two-atom semiconductor materials.

The L-shell x-ray-production process in lead (Pb) by proton impact over the energy range 240–440 keV has been studied. The x rays emitted from a thin (44.4±3.9 μg/${\mathrm{cm}}^2$) Pb target were detected using a high-purity Ge low-energy photon spectroscopy detector. The total x-ray cross sections and the x-ray cross sections for the Ll, L${\alpha }_1$,2, Lβ’s, L${\gamma }_1$, and L${\gamma }_2$,3 components were determined at 20-keV intervals over the bombarding energy range. The experimental x-ray cross sections were found to be in reasonable agreement with those predicted by perturbed stationary-state (PSS) theory with relativistic (R), energy-loss (E), and Coulomb-deflection (C) corrections (ECPSSR).

Multiphoton ionization (MPI) via two-photon resonance with high-lying Rydberg levels is observed on Na and K atoms in modest (12–120 V/cm) dc electric fields. The field-induced MPI signals are manifested to such an extent that the nominally forbidden MPI via two-photon resonance with the np levels is induced at the same signal levels as or more intensely than the allowed MPI via the ns and nd Rydberg levels. The intensity inversion between the allowed and the forbidden MPI signals is observed on the K atoms in the wavelength region where the two-photon energy is very close to the field-ionization limit.

Recent interest in the properties of the negative ion of positronium has encouraged us to compute its lifetime against photodetachment. To simplify the calculation, we have used the asymptotic form of the bound-state wave function and a plane wave for the final-state wave function, following the work of Ohmura and Ohmura in the case of photodetachment of ${\mathrm{H}}^{\mathrm{-}}$. We have obtained the needed normalizaton constant from a very precise and extensive Hylleraas wave function for the three-particle bound state.

Analytic solutions to the two-state-problem Bloch equations are obtained for a class of smooth chirped pulses. The asymmetric pulses introduced by Bambini and Berman as well as the chirped hyperbolic secant pulse of Hioe belong to the class of pulses discussed.

The extended Maier-Saupe theory of binary nematics developed by Palffy-Muhoray et al. is extended to a wider range of interactions. This theory predicted that the biaxial phase is thermodynamically unstable in the absence of an external field, if the interspecies interaction strength satisfies the geometric mean rule. We show that deviations from this assumption can lead to a stable biaxial phase. Our result holds for both the isotropic and anisotropic part of the pseudopotential. The implications for the phase behavior are discussed.

We derive analytic formulas for the interaction and excess-free energies of dense hydrogenic plasmas, which accurately parametrize the numerical data calculated earlier in the hypernetted chain approximation at an intermediate Fermi degeneracy of the electrons and which exactly satisfy the known boundary conditions at complete degeneracy as well as in the weak- and strong-coupling regimes. The resulting equation of state is valid over a wide range of densities and temperatures, as long as the system is in a liquid-metallic state.

It is shown that the power spectrum of chaotic motion near a crisis of a one-dimensional map is made up of two Lorentzian components with different characteristic times.

A modification of diffusion-limited aggregation (DLA) is proposed for the investigation of pattern formation during immiscible displacement in a Hele-Shaw cell. The method accounts for the effects of viscous and capillary forces by postulating an expression for the sticking probability of the particles in the DLA in terms of the mobility ratio and the capillary number. The previously taken approaches arise as special limiting cases of the present method. Extension of the technique to displacement processes in porous media and the connection with the invasion percolation are also discussed.