The thermodynamic implications of the first deviations with respect to the classical hydrodynamic behavior in high-frequency, short-wavelength phenomena are examined. The constitutive equations arising from an extended irreversible-thermodynamic formalism taking into account spatial inhomogeneities in the space of state variables are compared with those used in generalized hydrodynamics. The so-called exponential model for the memory function of the transverse-velocity correlation function is derived under the assumptions of extended irreversible thermodynamics only. Furthermore, it is also shown how more complicated memory functions can be derived. The results are carefully analyzed and compared with some microscopic derivations.

Analog simulations of the hopping noise of a current-biased Josephson tunnel junction shunted with an inductor in series with a resistor reveal a 1/ω spectral density over two decades of frequency ω for a narrow range of bias currents. The amplitude of the low-frequency part of the spectrum decreases when white noise, representing Nyquist noise in the resistor at a few degrees Kelvin, is added to the simulation. We explain the shape of the power spectrum and its dependence on bias current and added white noise in terms of a deterministic process, involving a one-dimensional mapping, that is analogous to that found in Pomeau-Manneville intermittency. Moreover, we are able to establish a detailed relationship between the origin of the mapping and the differential equation describing the dynamics of the system.

The manifold of equilibrium states for a fixed number of moles of ideal gas, when provided with a Riemannian metric based on the second derivatives of internal energy (studied by F. Weinhold), is found to have zero intrinsic curvature, in fact to be isometric to the Riemann surface of the natural logarithmic function. This and three other closely related flat spaces associated with an ideal gas are studied by means of explicit isometries.

A theory of quantum corrections for thermal-neutron scattering in almost-classical liquids is developed that goes beyond the usual quasiclassical approximations, which take only detailed balance and translational recoil into account, by also including quantum effects in the structure and dynamics of the liquid itself. The method that we use is similar to one which we have recently developed for calculating corrections for final-state interactions in deep-inelastic neutron scattering. In the present application the method requires an expansion of the moments of the dynamic structure factor in powers of ${ħ}^2$. We show that the required expansions can conveniently be obtained by an extension of a method due originally to Nelkin.

Measured relative intensities of a number of allowed 2$s^2$2$p^k$-2s2$p^{k+1\mathrm{}}$ transitions (60–200 Å) in the F i– to B i–like ions of titanium, chromium, iron, nickel, and germanium are compared with values from level-population calculations. The measurements are from Princeton Large Torus (PLT) tokamak plasmas with electron densities of ∼2.5×${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}3}$. For titanium and chromium, data from plasmas with densities of ∼5×${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}3}$ are also presented; a number of density-dependent line-intensity ratios are found. The spectra were obtained with use of a grazing-incidence time-resolving spectrograph which was radiometrically calibrated with use of synchrotron radiation from the National Bureau of Standards Synchrotron Ultraviolet Radiation Facility (SURF II). The measured relative intensities are therefore reliable. For the majority of the observed lines, agreement between the measured and calculated relative intensities is within 30%, the estimated accuracy of the measurements; significant discrepancies are found in the titanium ions at the low density. The discrepancies, some of which are due to blends, are discussed. Thus, the level-population calculations may be used with some confidence for spectroscopic plasma diagnostics. In the C i–like ions, there is some evidence that calculations which include proton-collisional excitation and deexcitation between the levels of the ground configuration are in better agreement with the measurements than those that do not, indicating that proton collisions should be included in the calculations for these ions.

In a thin dielectric liquid layer, electroconvection can be generated by means of charge injection to the liquid under a vertical electric field. When a parameter which gives the critical condition of the onset of convection is rapidly increased up to some value across the critical point, a propagating transition of the system from the quiescent state to the convecting state is expected to appear. We have tried to show such propagating transitions in two different models. One for a bipolar-injection type with free-free boundaries was analyzed with use of the amplitude-equation approach of Newell and Whitehead, and the other for a unipolar-injection type with rigid-rigid boundaries was numerically analyzed. Both cases have shown propagating transitions of convecting state with definite velocities.

The equilibrium properties of a relativistic non-neutral electron layer confined in a magnetically insulated cylindrical diode are investigated within the framework of the steady-state (∂/∂t=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long cylindrical electron layer with axis of symmetry parallel to an applied magnetic field $B_0$e→${^}_z$, which provides radial confinement of the electrons. The theoretical analysis is specialized to the class of self-consistent Vlasov equilibria $f_b^0$(x→,p→) in which all electrons have the same canonical angular momentum ($P_{\theta }$=$P_0$=const) and the same energy (H=${\mathrm{mc}}^2$), i.e., $f_b^0$=(n${^}_b$$R_c$/2πm)δ(H-${\mathrm{mc}}^2$ )δ($P_{\theta }$-$P_0$). One of the most important features of the analysis is that the closed analytic expressions for the self-consistent electrostatic potential ${\phi }_0$(r) and the θ component of vector potential $A_0$(r) are obtained. Moreover, all essential equilibrium quantities, such as electron density profile $n_b^0$(r), total magnetic field $B_{0z}$(r), perpendicular temperature profile $T_{\perp b}^0$(r), etc., can be calculated self-consistently from these potentials. As a special case, the equilibrium properties of a planar diode are investigated in the limit of large aspect ratio, further simplifying the functional form of the electrostatic and vector potentials. Detailed equilibrium properties are investigated numerically for a cylindrical diode over a broad range of system parameters, including diode voltage $V_0$, cathode electric field, electron density n${^}_b$ at the cathode, diode polarity, and applied magnetic field $B_0$.

A mode-mode coupling theory of the critical diffusion of a binary mixture confined between two parallel plates of infinite extent separated by a distance 2L is presented. The effect of boundaries, which we assume constrain the fluid in contact with them to be stationary, modifies the transport properties of the hydrodynamic shear modes and, consequently, the resulting critical relaxation rate. This rate, as measured by light-scattering experiments, is obtained for wave vector q→ parallel to the boundaries by expanding it in powers of (qL${)}^{\mathrm{-}1}$. Under the assumption that none of the components in the fluid has preferential wetting to the boundaries, the term of order (qL${)}^{\mathrm{-}1}$ is explicitly calculated, yielding a suppression to the bulk relaxation rate of the form Γ=${\Gamma }_B$[1-(1/ qL)(lnqL+1.20)], where ${\Gamma }_B$ is the bulk expression in which the weak critical divergent behavior of the viscosity has been taken into account. This result, which is valid in the asymptotic qL≫1 and qξ≫1 region but for ξ/L arbitrary and where ξ is the correlation length, is shown to produce important deviations from the bulk case. In particular, for values of qL∼3, which are within the present experimentally accessible range, it yields approximately a 40% suppression to the bulk value. It is also concluded that the effect of the boundaries completely precludes any crossover to a two-dimensional divergent behavior which would be obtained if physically unrealistic nonsticking boundary conditions are assumed, as has been done in the literature.

The mode-mode coupling formalism is applied to calculate the nonlocal critical diffusion coefficient for a binary-mixture film close to the consolute point. The system is confined between two parallel walls, of infinite extent, separated by a distance 2L. Assuming that the mixture exhibits no preferential wetting to the walls, the boundary effects are calculated. These boundaries are assumed to constrain the fluid on contact with them to remain stationary and, therefore, modify the transport properties of the hydrodynamic shear modes and, consequently, the diffusion coefficient. The Fourier transform of this coefficient is expanded in inverse powers of L($q^2$+${\kappa }^2$${)}^{1/2}$, where q is the Fourier wave vector and κ is the inverse of the concentration correlation length. The term of order [L($q^2$+${\kappa }^2$${)}^{1/2}$${]}^{\mathrm{-}1}$, yielding the first correction to the bulk value, is calculated explicitly giving an expression which is valid for L($q^2$+${\kappa }^2$${)}^{1/2}$≫1 but for arbitrary κ/q. It is found that the walls always suppress the diffusion coefficient and have their maximal effect at the critical point, κ=0. For κ>0 and fixed q, the suppression effect decreases monotonically with increasing κ.

Line shapes of $P_{\alpha }$ (λ=4686 Å) and $P_{\beta }$ (λ=3203 Å) of He ii and of some C iv lines are analyzed for plasmas in the parameter range ${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$≤${\mathrm{N}}_{\mathrm{e}}$≤5×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$ and ${\mathrm{kT}}_e$≤11 eV for the electron density and temperature. The light source is a gas-liner pinch, a quite new device, which is optimized to produce a homogeneous test plasma. The light emission of helium and carbon takes place only from a very limited region of the central plasma. The spectral lines are analyzed with respect to the line broadening and the He ii lines additionally to the asymmetry. For the investigation of the C iv lines, transitions were selected which came from different upper energy levels and which were broad and intense enough for a reliable measurement. They cover the wavelength region 948 to 5805 Å. By comparing the results with different theories, it is found that the experimental values are about a factor of 2 higher than the theoretical ones.

Spark-breakdown delay times were measured for ${\mathrm{N}}_2$, ${\mathrm{H}}_2$, Ar, ${\mathrm{SF}}_6$, and ${\mathrm{CCl}}_2$${\mathrm{F}}_2$ in a uniform field gap provided with a small current (∼${10}^{\mathrm{-}15}$ A) of free electrons by uv illumination of the cathode. Laue plots of the delay times yielded straight lines with slope iP, where i is the photocurrent and P is the breakdown probability. The dependence of the breakdown probability on voltage for ${\mathrm{N}}_2$, ${\mathrm{H}}_2$, and Ar was in good agreement with predictions of the Townsend breakdown mechanism. In ${\mathrm{SF}}_6$ and ${\mathrm{CCl}}_2$${\mathrm{F}}_2$, a transition was observed with increasing pressure from a dependence that agreed with the Townsend theory to a more gradual rise with voltage, characteristic of a streamer mechanism. This transition was ascribed to a decrease in the secondary-ionization coefficient with increasing pressure in ${\mathrm{SF}}_6$ and ${\mathrm{CCl}}_2$${\mathrm{F}}_2$, which resulted in an average electron-avalanche size at the static breakdown voltage that approached the critical value for streamer formation. A unified breakdown-probability theory, for which the Townsend and streamer mechanisms are limiting cases, was developed to account for the data over the full pressure range. The implications of these results for measurement of the static breakdown voltage and the secondary-ionization coefficient are discussed.

First we demonstrate that the extended mean-field model suggested by Huang and Viner is necessary and sufficient to describe the nature of the smectic-A–smectic-C (or –chiral-smectic-C) transition. The rest of the expansion terms in the mean-field free energy can be treated as higher-order correction terms. Then a general scheme is proposed to normalize the smectic-C (or chiral smectic-C) order parameter. As a result, the mean-field coefficients near the smectic-A–smectic-C (or –chiral-smectic-C) transition are found to vary systematically with the size of the smectic-A temperature range for all single-component liquid-crystal compounds with smectic-A–smectic-C (or –chiral-smectic-C) transition.

An aggregate is formed by a kinetic process in which particles move in parallel straight lines and stick to a structure at the point of first contact. The corresponding structure looks like a fan. Two different scaling regions are investigated: one in the body of the fan and the other in the fuzzy region near its edges.

The diffusion problem between the two stable limit cycles of a generalized van der Pol oscillator is studied for the case where these can be approximated by circles in the phase plane. The Fokker-Planck operator is transformed into a self-adjoint one and the stationary and metastable properties of the oscillator are analyzed in terms of the approximate eigenvalues and eigenfunctions of the related self-adjoint problem.

We consider N particles, each of mass m and diameter d, moving on a line and interacting via elastic collisions. The particles are enclosed by a freely movable, massless box of length L. The center of mass is assumed to be at rest. We state results on ergodic properties (equivalence of time and ensemble averages, approach to equilibrium) and outline their proof. We also list exact expressions for some expectation values (pair distribution function, pressure, collision frequency, no-collision probability, velocity autocorrelation function) obtained for fixed parameters N,m,d,L and three kinds of ensembles (smallest stationary, microcanonical, canonical) and discuss their thermodynamic limits. The derivation of these results, based on a generalization of a method already used for small systems (N≤3), is illustrated here with specific examples.

A general formulation for the spectral noise $S_R$ of random linear resistor networks of arbitrary topology is given. General calculational methods based on Tellegen’s theorem are illustrated for one- and two-probe configurations. For self-similar networks, we show the existence of a new exponent b, member of a whole new hierarchy of exponents characterizing the size dependence of the normalized noise spectrum ${\mathrm{scrS}}_R$=$S_R$/$R^2$. is shown to lie between the fractal dimension d¯ and the resistance exponent -βsubL. b has been calculated for a large class of fractal structures: Sierpiński gaskets, X lattices, von Koch structures, etc. For percolating systems, scrSsubR is investigated for p<psubc as well as for p>psubc. In particular, an anomalous increase of the noise at p→psubcsup+ is obtained. A finite-size-scaling function is proposed, and the corresponding exponent b is calculated in mean-field theory.

A free-energy density functional for a system of hard spheres is derived on a semiempirical basis. It is constructed to reproduce the thermodynamics and direct correlation function of a homogeneous fluid and then is tested in two highly inhomogeneous situations: the hard-wall–hard-sphere interface and the hard-sphere solid. The results are very good in both cases, showing that this density-functional model may be used with advantage in the study of the hard-sphere model by itself, or used as a reference system in a perturbative analysis.

We point out that in experiments on muon-catalyzed $d-d$ and $d-t$ fusion very sensitive tests of the theory of resonant molecular formation are provided by varying the ratio of ortho- to paradeuterium in the target. Results of calculations for the temperature dependence of the molecular formation rates for three different target conditions are presented.

It is proved that the mapping, time-dependent potential → time-dependent density, is not invertible, in general, over the class of all potentials expandable in a Taylor series with respect to time coordinates. However, an invertible mapping does exist between the time-dependent potential and time-dependent current density. To explore this in detail, a one-body time-dependent problem is examined in an attempt to seek a time-dependent current-density-functional formalism.

A simple relationship between the two spherical bases $|n\lambda m〉$ and $|nlm〉$ is presented and is used to deduce the relative parity and the large-$n$ behavior of the former. Approximate energy levels obtained in these bases from perturbation theory are compared with the eigenvalues obtained by diagonalizing the first-order perturbation matrix.