A dynamic depolarized light-scattering experiment in the presence of a symmetry-breaking magnetic field was conducted on homeotropically aligned dihexylazoxybenezene (DHAOB). This experiment gives direct evidence for the presence of a lowest-order fluctuation mode and its dynamical behavior in a destabilizing magnetic field.

It is shown that the Knudsen problem (‘‘paradox’’) can be resolved by the flow-rate formula for a non-Newtonian fluid flowing under a pressure gradient in a circular tube, as reported elsewhere. The flow-rate formula exhibits a minimum in the low-pressure regime but gives the Hagen-Poiseuille linear dependence on pressure in the high-pressure regime. Since the generalized hydrodynamic equations used for the derivation of the flow-rate formula are derived from the Boltzmann equation, the present solution of the Knudsen problem is well founded on the kinetic theory of gases. The nonlinear transport processes, which increasingly manifest themselves as the gas density decreases, are the cause for the emergence of a minimum in the flow rate for rarefied gases in circular tube flow. The entropy production and also the drag coefficient are calculated as a function of pressure difference, Reynolds number, and other parameters characteristic of the system.

Entanglements of polymer chains and deformation of polymer morphology due to shear stress in the interfacial region of segregated polymer metals are discussed. In the case of strong segregation polymer melts slide along the interface for a length scale much larger than the gyration radius of the polymer molecule.

Electric field reversals play an important role in maintaining glow discharges by determining the partitioning of ion flux between cathode and anode. For years, the existence of field reversals in the negative glow has been the subject of controversy. For a range of pressures, gas compositions, and electrode spacings, we observe field reversals using laser optogalvanic (LOG) spectroscopy: The discharge current is increased by excitation of molecular ions to a state with larger mobility. The sign of the LOG signal is a direct measure of the sign of the electric field. A single-beam electron model, where it is assumed that the glow is sustained by a monoenergetic, unidirectional beam of electrons emanating from the cathode, is in good agreement with most experimental observations. The model accurately predicts the existence of field reversals and the spatial dependence of both LOG and laser-induced fluorescence signals. By including momentum and energy dispersion in the beam, the model could be further improved.

We present an experimental study of free convection in binary mixtures when convection is theoretically predicted to appear in the form of rolls of large extent. Quantitative measurements of the very slow velocities associated with this convective pattern are presented.

Results on a Rayleigh-Bénard experiment in helium gas at 5 K in a cylindrical cell of aspect ratio 1 are presented. The Rayleigh number spans a range from ${10}^5$ to ${10}^{12}$. A large-scale coherent flow is observed via the correlation of two adjacent temperature probes. This flow-velocity measurement shows clear transitions between different turbulent states. In hard turbulence, the dimensionless velocity [V/(κ/L)] scales with the Rayleigh number, with an exponent close to 1/2. The horizontal temperature difference across the cell is another measure of the different turbulent states. The temperature signals in the side-wall region (the large mean vertical velocity region) give clear pictures of various turbulent states. The measured velocity has been compared with the calculated free-fall velocity and also the heat transfer rate with the one calculated from the flow advection. The coherent frequency ${\omega }_p$ is found to be associated with the large-scale flow. In the side-wall region the power spectrum of the local temperature signal has a power-law dependence for Rayleigh numbers between ${10}^8$ and ${10}^{11}$. Both the exponent and the range of the power law change with the Rayleigh number. For Rayleigh numbers above ${10}^{11}$, a power law independent of Rayleigh number (exponent 1.4) develops at low frequency.

An expression for the indirect interaction of surfaces through a liquid is derived that accounts for inhomogeneity of the boundary conditions, which mimics the regular, irregular, or stochastic nature of liquid structure perturbation along the surfaces. This leads to a new picture of hydration forces, which gives an explanation of their main observable features: the dependence of the decay length on the nature of the surfaces and its variation range, and the effect of surface ordering on the magnitude of the force.

The exact equations of motion for a stacked system are derived and their properties are discussed. Results of numerical simulations of soliton dynamics are presented and compared with the previously published ones using an approximate treatment. Qualitative and quantitative differences are found. The intermolecular dispersion energy is included via London’s formula into our model of solitary waves in stacked systems. It is shown that first-neighbor terms are of sufficient accuracy. The explicit London formula is fitted by a sixth-order Taylor series. The qualitative properties of solitary waves are not changed too much upon inclusion of dispersion energy. Quantitative changes in velocity, kinetic energy, and effective mass of the waves are found.

The effects of explicit electron-electron interactions described by the semiempirical Pariser-Parr-Pople Hamiltonian on soliton dynamics in formamide stacks as a model system are investigated. It is shown that explicit treatment of electron-electron interactions does not influence the properties of solitary waves in the model system. Possibilities that solitary waves might serve as charge carriers in stacked systems after doping are discussed.

In this paper we present global coordinates for the kink-antikink breather sine-Gordon phase space with a separatrix and singular points. Using these coordinates we derive reduced equations governing perturbed dynamics, and we use them in a Melnikov calculation to establish the presence of chaos in the reduced sine-Gordon system.

We examine the dynamic behavior of a simple mechanical model of an earthquake fault. This model, introduced originally by Burridge and Knopoff [Bull. Seismol. Soc. Am. 57, 341 (1967)], consists of an elastically coupled chain of masses in contact with a moving rough surface. Our version of the model retains the full Newtonian dynamics with inertial effects and contains no externally imposed stochasticity or spatial inhomogeneity. The only nonlinear feature is a velocity-weakening stick-slip friction force between the masses and the moving surface. This system is being driven persistently toward a slipping instability and, therefore, exhibits noisy sequences of earthquakelike events. We observe these events in numerical simulations and are able to predict many of their features analytically. Their size distributions are found numerically to be consistent with the Gutenberg-Richter law. Some aspects of the size distributions can be understood by scaling arguments.

We show that the quantum corrections to the classical correlations of a Coulomb fluid do not decay exponentially fast for all values of the thermodynamical parameters. Specifically, the ${ħ}^4$ term in the Wigner-Kirkwood expansion of the equilibrium charge-charge correlations of the quantum one-component plasma is found to decay like ‖r${\Vert }^{\mathrm{-}10}$. More generally, using functional integration, we present a diagrammatic representation of the ħ expansion of the correlations in a multicomponent fluid with a locally regularized Coulomb potential and Maxwell-Boltzmann statistics. The ${ħ}^{2n}$ terms are found to decay algebraically for all n≥2. Furthermore, an analysis of the hierarchy equations for the correlations provides upper bounds that are compatible with the findings of the perturbative expansion. Except for the monopole, all higher-order multipole sum rules do not hold, in general, in the quantum system. This violation of the multipole sum rules as well as the related algebraic tails are due to the intrinsic quantum fluctuations that prevent a perfect organization of the screening clouds. This phenomenon is illustrated in a simpler model where the large-distance correlations between two quantum particles embedded in a classical plasma can be exactly computed.

The effect of a particular type of thermal fluctuation in a DNA molecule is to reduce the hydrogen-bond force constants locally. In this paper we study the effect of such thermal fluctuations on the vibrational spectra of B-form poly(dG)⋅poly(dC) and B-form poly(dA)⋅poly(dT). We find the fluctuations create a defect (decrease in H-bond force constants) that is localized to a single base pair. In both polymers the presence of such a defect induces prominent defect modes in the frequency region between 60 and 72 ${\mathrm{cm}}^{\mathrm{-}1}$. The mode found in poly(dG)⋅poly(dC) is quasilocal (inband), whereas the mode found in poly(dA)⋅poly(dT) is local (lies in the band gap). Our calculations indicate that it is easier to create the defect mode in poly(dA)⋅poly(dT) than in poly(dG)⋅poly(dC). The local mode in poly(dA)⋅poly(dT) is at a frequency where infrared absorption occurs.

This paper begins a study of impurity pinning in general incommensurate charge-density-wave systems using the replica trick. In particular, models based on the impurity-phase interactions cos(θ+2$k_f$x) or cos(θ+φ) (with φ a random field evenly distributed on [0,2π]) are investigated. With the replica method, adequate information about the low-frequency linear conductivity is contained in the diagonal component (with respect to the replica indices) of the phase propagator. Two types of fluctuations are contained in the replica-averaged action. First, for a given impurity configuration one has ordinary thermodynamic fluctuations. Second, the replica-averaged model contains the additional effects of impurity fluctuations. An exact symmetry of the averaged Lagrangian is found for certain impurity distributions. Using various approximations, the massless mode associated with this symmetry is found to be unbroken and is a manifestation of impurity fluctuations. Unfortunately, while these fluctuations dominate approximate solutions to the model, it is the thermodynamic fluctuations that are physically relevant, and it is necessary to separate the two. This is partially accomplished using a shift of variable, and the resulting model is found to resemble the random-field Ising model (which contains no zero mode). A variational method is then used to study the behaviors of the two models. For the standard model, it is found that the phason self-energy must vanish in the ${\omega }_p$→0 limit under the most general quadratic trial interaction (i.e., the averaged excitation spectrum is predicted to be gapless), supporting the earlier analysis. Moreover, the extremal mass matrix is unstable in the n→0 limit, limiting the usefulness of the result. In contrast, a nonvanishing, stable mass is found for the shifted model. The pole in the resulting propagator (in an approximation valid for ω→0) is in qualitative agreement with expectation, predicting a gap that initially grows linearly with the standard deviation of the impurity distribution.

Pattern-formation processes and the associated defect motions are experimentally studied for various rectangular cells with aspect ratios Γ ranging from 8 to 15 in the electrohydrodynamic instability (EHD). Wave-number selection arises from the competition between the most rapidly growing mode $k_c$, which dominates initially, and the final stable mode $k_m$ in the Williams domain (WD) state, which is influenced by the cell boundaries as well as nonlinear effects. Defect motion is associated with such competitive growth into the final stage. The fluctuating Williams domains (FWD’s) are strongly related to the oscillatory gliding motion of defects. A temporally nonperiodic change of the number of defects is observed in the FWD state with a power spectrum of 1/f type (defect chaos). For a step change in the external voltage, a clear threshold for the onset of FWD is determined. On the other hand, when the voltage is increased continuously no defect is formed at the threshold for WD, and nondecaying defect motion starts at a certain threshold value. A large hysteresis is observed near the onset of FWD.

The step change of the external field leads to defect formation more easily than the continuous change. A detailed phase diagram of stable convective patterns in the plane spanned by the threshold voltage and the applied frequency is presented. The characteristic behavior of defect motions, for example, its oscillatory activity of gliding and climbing motions, is strongly related to the pattern following the second pattern instability. In the case of the strong gliding oscillation, a pattern with temporal order appears above the second threshold. Contrary to this, in the case of the weakly oscillatory motion of defects, a stationary pattern is usually observed above its threshold. The magnetic field suppresses the defect chaos and stabilizes the system, that is, the threshold of the applied electric field for the onset of EHD is raised when the magnetic field is increased. The magnetic field can also change the direction of the roll axis so that it is perpendicular to the external field, which leads more easily to the zigzag and oblique patterns. A detailed phase diagram for the magnetic field effect is also given.

We study the mean first-passage time (MFPT) for random walks on the backbone of loopless aggregates. We derive an exact expression for the MFPT on a general aggregate model. The exact MFPT for several deterministic and random disordered structures is calculated. We find that, in general, the exponent τ(1) describing the asymptotic dependence of the MFPT on the linear size of the system for diffusion is τ(1)=1+$d_f$, where $d_f$ is the fractal dimension of the aggregate.

We have measured the temperature-dependent transmittance of a polymer-dispersed liquid-crystal (PDLC) film in its isotropic phase. We show that the measured transmittance can be quantitatively described within experimental error over a wide temperature range using Rayleigh-Gans light-scattering theory with film parameters previously determined from refractive-index studies and scanning electron microscopy; no freely adjustable parameters or normalization constants are necessary to describe the measured transmittance data. We obtained equally good agreement between theory and experiment regardless of whether or not we included droplet correlation effects in our transmittance calculations. The precision with which the refractive index of the matrix material in a cured PDLC film can be determined is the main factor preventing us from quantitatively assessing the role of droplet correlation effects in PDLC films at this time. We have also compared the transmittance characteristics of our PDLC film with the published transmittance of a film composed of liquid crystal in the pores of a solid matrix. We find that the published results are consistent with the form of the equations of scattering theory; however, quantitative agreement between measured and calculated transmittance would require film parameters different from those published.

Using a chemical oscillation model, a transition sequence in a chaotic region was studied in detail, and its fine structure in the vicinity of a critical point where a simple oscillation with a small amplitude becomes unstable and diverges to a new oscillatory state was reported. Neither a combined complex oscillation nor a chaotic oscillation appears between the two complex oscillations in this region, contrary to other cases reported already. Moreover, coexistence of a complex oscillation and a simple oscillation with a small amplitude was found to appear.

Extending some previous work of Bollé [Phys. Rev. A 36, 3259 (1987)], we construct expressions for the n-particle cluster coefficients that remedy difficulties associated with the presence of both an infinite number of bound states and strongly repulsive potentials. Applying the existence theorems for cluster coefficients implicit in the work of Ginibre [J. Math. Phys. 6, 238 (1965); 6, 252 (1965); 6, 1432 (1965)], we demonstrate the validity of these expressions. We apply the formalism to obtain a well-behaved expression for $b_3$ at the Efimov point. As a by-product we are able to directly observe the divergence in $b_3$ due to the continuum part of the three-body resolvent together with the counterterms that render it convergent.

Displacement sensors that work by taking advantage of the nonlinear displacement-current relationship of an electron vacuum-tunneling probe (VTP) are theoretically analyzed in this paper. We show, using the language of electromechanical two-port transducers, that the VTP is nonreciprocal and that its noise is intrinsically quantum limited. We present a semiquantitative analysis of a VTP used to monitor the displacement of a simple mechanical harmonic oscillator and show that the Heisenberg uncertainty relation for the position and momentum of the mechanical oscillator is enforced by the noise in the VTP. The results of an optimal filter calculation of the sensitivity of the VTP-mechanical oscillator system for impulsive force detection are presented. These results are contrasted with results for a conventional capacitive transducer, and we show that the VTP may offer vastly increased sensitivity as a consequence of its nonreciprocity. The maximum sensitivity of the VTP system is calculated as a function of the temperature, the dc tunneling current, and the mass, frequency, and quality factor of the mechanical oscillator. For typical operating conditions the maximum sensitivity is obtained for small-mass systems, which makes the VTP ideal for miniature accelerometers and related devices.