The paper treats the stability of a periodic unidirectional three-dimensional flow. It is shown that at sufficiently high Reynolds numbers a flow of this type is unstable to long-wavelength disturbances. This instability can be interpreted in terms of negative effective viscosity of the corresponding large-scale flow. The problem is solved using the mode-elimination methods of field theory. It is shown that the results are exact in the limit k→0 for any finite Reynolds number. Also discussed is long-wavelength instability of the flow generated by an unidirectional force field which varies randomly with respect to both the space coordinates and time.

To examine the effects of nonlinear transport processes on the flow properties of a real fluid, we study the plane Couette flow under a temperature gradient in a Lennard-Jones fluid over a range of gas pressure. The analysis is based on the nonlinear transport coefficients derived in the modified moment method. The linear transport coefficients appearing in the theory are those constructed by Ashurst and Hoover from the nonequilibrium molecular-dynamics simulations, while for the equation of state for the Lennard-Jones fluid we use the empirical form proposed by Ree. Examples for the flow characteristics at two extreme conditions when either the gas is very dilute, or when it is very dense, are presented. It is shown that the temperature and velocity profiles for nonlinear transport processes are significantly different from the ones obtained with the linear transport coefficients. In the dilute-gas limit, slip boundary conditions are used which are derived by applying the Langmuir theory of gas-surface interaction. Flow profiles show pronounced boundary-layer structures near the wall when the product of the Knudsen number and the Mach number is sufficiently large.

We investigate the kinetics of aggregation of polystyrene particles of 481 nm in a solution of a univalent-univalent salt in the concentration range from 0.05 to 2.6 mol/l. Using quasielastic light scattering to measure the linewidth and hence the hydrodynamic radius of the clusters, we find the value 1.75±0.03 for the fractal dimension of the aggregates in the fast coagulation regime, when the salt content is high, while we get a slow exponential kinetics with low salt content. Using scaling arguments and the mean-field Smoluchowski equation we describe our results in terms of collisions of clusters during purely Brownian diffusion.

We have studied the effect of chiral strain on phase transitions in a chiral material by examining the cholesteric (Ch) blue-phase (BP) liquid-crystal system in the Cano-wedge configuration. We observe both Ch and BP Cano rings whose positions are explained by Ch elastic theory. In the phase-transition region, chiral strain causes the positions of the Ch-BP coexistence rings to be temperature dependent and to exhibit reentrancy with respect to chiral strain. A free-energy model is presented which explains the gross features of the positions of the coexistence rings.

We show analytically that for a class of simple periodic motions in a general Hamiltonian system of n dimensions, if C is a parameter of the system and $C_{\rho }$ one of its generally many critical values at which the motion undergoes a stability-instability transition, the behavior of the largest Lyapunov exponent μ as C approaches $C_{\rho }$ from the unstable region is given by μ=const×‖C-$C_{\rho }$${\Vert }^{\beta }$, where β=(1/2), independent of the transition point, type of transitions, or the dimensionality of the system. We present numerical results for a three-dimensional Hamiltonian system which exhibits three types of stability-instability transitions, and for a two-dimensional Hamiltonian system which exhibits two types of transitions.

We consider here the hopping of an electron among a band of localized electronic states on a d-dimensional lattice. The hopping rates are assumed to be stochastic variables determined by some probability distribution. We restrict our attention to nearest-neighbor transport in the limit in which the fluctuations in the hopping rates are large. In this limit we construct an exact expansion for the frequency-dependent diffusion coefficient D(ɛ) that is applicable to a wide range of transport phenomena (d=1 conductors, trapping phenomena, molecularly based electronic devices, etc.) in any spatial dimension. For the case of hopping transport with d=1, our method confirms earlier results that strong fluctuations in the hopping rates give rise to a non-Markovian ${\varepsilon }^{1/2}$ correction to normal diffusion. In two dimensions, we establish explicitly the existence of a non-Markovian logarithmic correction ɛ lnɛ to D(ɛ). The formalism is then extended to d dimensions and the frequency corrections are discussed. For d=3, two frequency corrections must be retained. One is linear in ɛ and the other proportional to ${\varepsilon }^{3/2}$. It is shown that only the ${\varepsilon }^{3/2}$ correction contributes to the long-time tail $t^{\mathrm{-}3/2}$ in the time-dependent diffusion coefficient D(t). From these results we show that the long-time tail in the velocity autocorrelation function which is a consequence of the strong fluctuations in the hopping rates is of the form $t^{\mathrm{-}(1+d/2)}$. Comparison is made with earlier results.

In a recent paper [P.D. Poll and N. W. Ashcroft, Phys. Rev. A 32, 1722 (1985)], numerical solutions of the modified hypernetted-chain (MHNC) equation were presented for a system near its critical point. The particles in this system were assumed to interact through a double-Yukawa pair potential. For a proposed crossover form of bridge function, universal power-law behavior was found in the isothermal compressibility. On the critical isochore and for a fixed set of parameters defining the form of crossover in the bridge function, we present here results for nonuniversal quantities, specifically the excess internal energy and specific heat per particle. These quantities, together with the isothermal compressibility, critical temperature, and critical density are compared with experimental results for argon. Good agreement is found, particularly when experimental results are scaled with parameters taken from an effective state-dependent pair potential partially incorporating many-body effects in the vicinity of the critical region. The parameters defining the form of cross-over in the bridge function are also varied in order to investigate the effect of thermodynamic inconsistency in the MHNC equation on nonuniversal quantities. It is found essential to include pure hard-sphere behavior in the short-range structure of the bridge function in order to reasonably determine these quantities in the critical region.

Theory for the generation and decay of high-lying Rydberg states in beam-foil experiments is presented. Our theory is designed to check the assumption that electron capture in the foil proceeds via a direct transition from a free state. The success of the theory in explaining the observed (primary and secondary) oscillatory structure and underlying smooth background of the ionization signal, as a function of additional variable electric fields, justifies this assumption. In addition, existence of asymmetry with respect to sign change of the variable fields is predicted to be detectable at high field values. Generation of Rydberg atoms in beam-foil experiments is shown to be a sensitive probe of the state distribution prepared during the beam’s passage through the foil. Our theory substantiates the claim that Rydberg atoms produced in the beam-foil encounter exit the foil in a pure superposition state.

The radiative-transfer equation describes the collection of paths taken by an element of radiation as it travels from one location to another. When backscatter can be ignored, the exact solution is constructed as a formal sum (path integral) over all such paths. In the appropriate limit the usual (diffusive) small-angle solution and the multiple-scattering solution can be obtained. Another small-angle solution has also been found which includes some of the nonlinear and large-angle behavior not present in the diffusive solution. After several attenuation lengths, length scales are characterized by a parameter constructed out of the absorption and scattering coefficients, and the rms scattering angle per scattering event. The two solutions are compared in the case of a point beam.

The effect of small-amplitude additive Gaussian white noise on maps with periodic attractors is studied. An expansion in powers of the mean-square noise strength is derived for the moments of the conditional probability distribution of position. The results are compared to numerical simulations of the logistic and Hénon maps, and agree to within the numerical uncertainty.

Dynamical theory of soliton excitations in deoxyribonucleic acid (DNA) double helices has been studied by a revised Hamiltonian in which the dipole-dipole interaction and the dipole–induced-dipole interaction between two bases in a complementary base pair are taken into account in addition to the hydrogen-bond energy. The motion equations of bases are a set of coupled sine-Gordon equations. The soliton solutions of these equations are studied in detail and the results are compared with the experimental data in the H-D exchange measurements of DNA chains.

By constraining the perturbed velocity and temperature fields to vanish exponentially radially, the coupled system of equations can be seen to give a unique form of the temperature lapse rate of the atmosphere which corresponds to the unstable regime. We then show that finite disturbances in the condensation rate, or equivalently smooth horizontal variation of the large scale fields, do not allow such localization of steady-state perturbations, though in the time-dependent case the possibility remains.

A suitably modified version of the polaron theory of Chandler et al. [J. Chem. Phys. 81, 1975 (1984)] is applied to the study of the solvation of electrons in molten salts. The results obtained compare favorably with recent numerical simulations and confirm the picture of the formation in the melt of an F-center analog. A novel expression for the explicit evaluation of the electron kinetic energy is given.

We present a new method of determining quantum defects which is based on the generalized quantum-defect theory of Greene, Fano, and Strinati. This method calculates a reaction matrix below threshold using a ‘‘smooth’’ Green’s function which is free of poles and unbounded asymptotically. This approach is compared to our earlier method which determines quantum defects by using a bounded Green’s function to search the negative real-energy axis for the poles of the Schwinger T matrix. Applications are made to ions in the lithium isoelectronic sequence.

The triple-differential cross sections for the ionization of helium by fast electrons in the large-angle coplanar symmetric energy-sharing case are studied by using the modified Glauber approximation. Comparison with experimental data indicates that the higher-order terms of the scattering amplitude contribute quite significantly to the cross section. They, however, make the results worse than those of the second-Born approximation.

The shifted 1/N expansion method is applied to the Hulthén potential. Numerical results for the energy values for n=1–5 states are presented. For l=0 states, the agreement between our results and the exact analytical solution is excellent.

We have measured the far-wing collisional redistribution profiles for the reactive ${\mathrm{MgH}}_2$ and the inert MgHe collision systems. The results are consistent with the suggestion that the far-red-wing profile in the ${\mathrm{MgH}}_2$ case is dominated by absorption leading to the nonradiative reactive exit channels. Theoretical spectral profiles based on available potential-curve data indicate quite reasonable agreement with the experimental results.

Dielectronic recombination cross sections for K-shell excitation are evaluated theoretically for Ca(xiii, xii, xi). The relationship between dielectronic recombination and resonant-transfer-excitation cross sections is discussed. The peak ratios of cross sections for ions with different degrees of ionization are compared with the experimental results for the Ca(xiii, xii, xi)+${\mathrm{H}}_2$ systems. Cascade processes are found to have a large effect on cross sections for the intermediate states with two electrons in the M and higher shells.

By including the effect of atomic recoil, the fluorescence spectrum for a two-level atom can become asymmetric whether the atom is in a uniform field or in a field gradient. This predicted asymmetry in a field gradient accounts for some of the previously observed but hitherto unexplained asymmetry in the fluorescence spectrum.

Using the theory of generalized imprimitivities for the description of weakly localized single-photon states, the spatial dependence of the photodetection of such states is calculated and an $x^{\mathrm{-}7}$ falloff is found. A general technique for determining the falloff of densities associated with weakly localized states is given and in particular the same spatial dependence is found for the falloff of energy density in agreement with the previous work of Amrein.