Bifurcations in fluctuating systems: The center-manifold approach

Bifurcations in fluctuating dynamical systems are studied using the ideas of center-manifold reduction. The method provides not only a systematic procedure for the reduction of the system to a small number of variables-but also a classification scheme for the different kinds of dynamical behavior possible near bifurcation points. The joint probability density factorizes into a stationary Gaussian densityp(v/u) in the fast variablesv, and a time-dependent densityP(u, f) in the slow variablesu describing the dynamics on the center manifoldv=v₀ (u). P(u, t) obeys a reduced Fokker-Planck equation that can be written in a normal form by means of local nonlinear transformations. Both additive and multiplicative white noise are considered, as is colored noise. The results extend and formalize Haken's concept of adiabatic elimination of fast variables.     

Dissipation and large thermodynamic fluctuations

The results of recent work of Kipnis, Olla, and Varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation, including non-equilibrium steady states, as a fluctuation-dissipation hypothesis. The basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation. It is shown that this hypothesis leads to a nonlinear version of Onsager-Machlup fluctuation theory that had previously been proposed by Graham. A direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints (Onsager's principle of least dissipation). Following Graham, the theory leads also to a generalized potential, analogous to an equilibrium free energy, for the nonequilibrium steady state and an associated static variational principle. Finally, a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large-deviations theory on a formal analogy with the results of Freidlin and Wentzell for finite-dimensional systems.     

Vortex washboard voltage noise in type-II superconductors

In order to characterize flux flow through disordered type-II superconductors, we investigate the effects of columnar and point defects on the vortex velocity/voltage power spectrum in the driven non-equilibrium steady state. We employ three-dimensional Metropolis Monte Carlo simulations to measure relevant physical observables including the force-velocity/current-voltage (I-V) characteristics, vortex spatial arrangement and structure factor, and mean flux line radius of gyration.Our simulation results compare well to earlier findings and physical intuition.We focus specifically on the voltage noise power spectra in conjunction with the vortex structure factor in the presence of weak columnar and point pinning centers. We investigate the vortex washboard noise peak and associated higher harmonics,and show that the intensity ratios of the washboard harmonics are determined bythe strength of the material defects rather than the type of pins present.Through varying columnar defect lengths and pinning strengths as well as magnetic flux density we further explore the effect of the material defects on vortex transport.It is demonstrated that the radius of gyration displays quantitatively uniquefeatures that depend characteristically on the type of material defects presentin the sample.     

Evidence of critical fluctuations from the magnetoconductivity data in Bi2Sr2Ca2Cu3O10+x phase

The fluctuation-induced magnetoconductivity of the Bi₂Sr₂Ca₂Cu₃O_10+x phase is studied above zero-field critical temperature Tc(0) and for moderate magnetic fields. It is found that the Gaussian approximation for superconducting fluctuations underestimates the negative fluctuation magnetoconductance drastically in the Tc(0) < T < Tc(0) + 20 K temperature range. Taking into account the critical fluctuation contribution on the base of self-consistent Hartree approximation makes it possible to explain the data quantitatively in terms of the only Aslamazov-Larkin contribution for different magnetic fields and temperatures, consistently with the zero field data. Received 14 April 2000 and Received in final form 13 July 2000     

Composition and polyamorphism in supercooled yttria-alumina melts

By extending recent work on liquid-liquid transitions in supercooled yttria-alumina AYx liquids we draw attention to the compositional dependence of the structure factor of the high density liquid, arguing that this is sufficiently sensitive to discriminate between liquids at the level of a few %. Comparing structure factor differences between liquids of different compositions and in the same liquid AY20 between high and low temperatures straddling the transition at 1788 K between a high density liquid (HDL) and a low density liquid (LDL) enables compositional phase separation to be ruled out. It points instead to kinetic changes in polyhedral configurational order being the drivers for this polyamorphic transformation. Rotor behaviour observed in levitated liquid drops used in the high temperature experiments enables the reversibility of the LLT transition (LLT) and the associated changes in entropy and density to be identified. Evidence for critical-like behaviour in the structural relaxation time and in the fluctuation correlation length is presented. By re-examining recent work which failed to find the structural and thermal signatures for the LLT in liquid AY20 at 1788 K we present evidence for the LLT occurring instead in liquid AY15 at 1940 K, suggesting that the liquid-liquid transition temperature in AYx liquids decreases with increasing yttria content.     

Models of structure and properties of H-bonded molecular mixtures

Results on the modeling of molecular interactions, supramolecular organization and physicochemical properties of binary mixtures of organic solvents are presented. The mixtures, both with negative deviation from ideality, such as propanone–trichloromethane, dimethylsulfoxide–trichloromethane, and with positive deviation, such as 1,4-dioxane–methanol, 1,4-dioxane–ethanol, trichloromethane–methanol, trichloromethane–ethanol, have been studied. Models for the aggregation in mixtures due to specific intermolecular interactions are proposed. Integral and differential parameters of the supramolecular organization were obtained. Thermodynamic characteristics of aggregation (equilibrium constants, Gibbs energy, enthalpy and entropy) and structural parameters of the aggregates have been determined. Long-range molecular correlations and cooperativity of H-bonds have been established. The manifestations of the supramolecular ordering in the physicochemical properties of the mixtures are discussed.     

X-ray reflectivity of solid-supported, multilamellar membranes

We have investigated the structure of solid-supported, multilamellar membranes by X-ray reflectivity. The density profile is obtained by fitting the full q-range to a model using the bilayer Fourier coefficients as fitting parameters. The effect of hydration and the substrate boundary condition are discussed in view of the well-known Landau-Peierls effect and its implications for structure determination. The resulting bilayer density profile agrees remarkably well with previously published data of a molecular dynamics (MD) simulation for 1,2-oleoyl-palmitoyl-sn-glycero-3-phosphocholine (OPPC). Received 1 October 2001 and Received in final form 21 December 2001