Critical properties at the orientational first order transition in solid o-H2 in MFA

The mean field approximation (MFA) is used to study critical phenomena in the orientational transition of solid o-H₂. The time independent correlations as well as the time dependent ones, calculated within the Glauber model, show critical behaviour at the stability limits of the ordered and disordered phase with critical indices 1/2 and 1 resp. At the equilibrium transition point the correlation lengths and relaxation times of both phases are found to be equal.     

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

The effect of various initial magnetizations m₀ and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m₀ These subclasses correspond to the system evolution from the high-temperature (m₀ = 0) and low-temperature (m₀ = 1) initial states with limit FDRs characteristic of these states.     

Correlations for parameter— dependent random matrices

Correlations for parameter-dependent Gaussian random matrices, intermediate between symmetric and Hermitian and antisymmetric Hermitian and Hermitian, are calculated. The (dynamical) density-density correlation between eigenvalues at different values of the parameter is calculated for the symmetric to Hermitian transition and the scaledN→∞ limit is computed. For the antisymmetric Hermitian to Hermitian transition the equal-parametern-point distribution function is calculated and the scaled limit computed. A circular version of the antisymmetric Hermitian to Hermitian transition is formulated. In the thermodynamic limit the equal-parameter distribution function is shown to coincide with the scaled-limit expression of this distribution for the Gaussian antisymmetric Hermitian to Hermitian transition. Furthermore, the thermodynamic limit of the corresponding density-density correlation is computed. The results for the correlations are illustrated by comparison with empirical correlations calculated from numerical data obtained from computer-generated Gaussian random matrices.     

Angular correlation measurements in the B10(d,p,γ)B11 reaction

Proton gamma angular correlations through the 6.76 and 8.92 MeV excited states of B¹¹ are measured at deuteron bombarding energies from 1.6 to 2.4 MeV. The correlations are measured at laboratory proton scattering angles 35? in both reaction and azimuthal planes. The correlation coefficientA ₂ ⁰ and the distortion parameterλ are calculated. A systematic shift of the symmetry axis from the recoil direction is observed. This shift tends to zero asE _d→Q. For the 8.92 MeV excited state of B¹¹(Q=0.32 MeV) the distortion parameterλ is close to the plane wave limit. The possible values of incoming channel spins as well as gamma-ray multipole mixing ratio for the 6.76 and 8.92 MeV states are obtained.     

Perturbation of the angular correlation of γ-rays by molecular motion

The time dependent angular correlation of successive gamma rays emitted by a nucleus coupled by a quadrupolar field to a randomly reorienting molecule is calculated for a complete range of rates of molecular motion using a strong collision model. The results in the fast and slow motion limits are similar to those previously obtained using a diffusional model. Calculated curves of G ₂₂(t) are given in the intermediate range of rates of motion and the results compared with published experimental observations.     

The stability of gadolinium-based contrast agents in human serum: A reanalysis of literature data and association with clinical outcomes

PurposeTo reanalyze literature data of gadolinium (Gd)-based contrast agents (GBCAs) in plasma with a kinetic model of dissociation to provide a comprehensive assessment of equilibrium conditions for linear GBCAs.MethodsData for the release of Gd from GBCAs in human serum was extracted from a previous report in the literature and fit to a kinetic dissociation/association model. The conditional stabilities (logK_cond) and percent intact over time were calculated using the model rate constants. The correlations between clinical outcomes and logK_cond or other stability indices were determined.ResultsThe release curves for Omniscan®, gadodiamide, OptiMARK®, gadoversetamide Magnevist® and Multihance® were extracted and all fit well to the kinetic model. The logK_conds calculated from the rate constants were on the order of ~ 4–6, and were not significantly altered by excess ligand or phosphate. The stability constant based on the amount intact by the initial elimination half-life of GBCAs in plasma provided good correlation with outcomes observed in patients.ConclusionsEstimation of the kinetic constants for GBCA dissociation/association revealed that their stability in physiological fluid is much lower than previous approaches would suggest, which correlates well with deposition and pharmacokinetic observations of GBCAs in human patients.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

Dimension and entropy analysis of MEG time series from human α-rhythm

Magnetoencephalograms (MEG) from human brain were measured by means of a 37 channel SQUID magnetometer (KRENIKON). Correlation integrals were calculated from time series exhibiting strong -rhythm in order to give estimates of correlation dimension andK ₂ entropy. The results are discussed regarding the length and the stationarity of the data. It is shown that low spurious correlation dimensions andK ₂-entropies may easily be obtained as artefacts due to time correlations in phase space and data length. When time correlations are avoided and the length of time series is taken into account, estimates of correlation dimension andK ₂ entropy indicate no evidence of the existence of low dimensionality.     

Ising models on the pentagon lattice

We solve inhomogeneous Ising models on the pentagon lattice using the transfer matrix formalism. As two special cases we study the ferromagnetic and the fully frustrated antiferromagnetic model on this lattice. The ferromagnet shows a phase transition at someT _c>0 with the usual Ising behaviour. In the frustrated case no transition occurs at any temperature due to frustration. Frustration also causes a nonvanishing rest entropy. We also calculate the spin-spin-correlation for large distance in both cases. In the ferromagnetic model we thus get the magnetization and the expected algebraic (exponential) decay of the correlations at (above)T _c. The correlations of the frustrated model decay exponentially for all temperatures, includingT=0, indicating that evenT=0 belongs to the disordered high temperature phase. Superimposed to the exponential decay the correlation shows an interesting oscillatory behaviour with temperature dependent wave number, i.e. an incommensurate structure.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Weak-coupling treatment of electronic (anti-)ferroelectricity in the extended Falicov-Kimball model

We study the (spinless) Falicov-Kimball model extended by a finite band width (hopping t _f ) of the localized (f-) electrons in infinite dimensions in the weak-coupling limit of a small local interband Coulomb correlation U for half filling. In the case of overlapping conduction- and f-bands different kinds of ordered solutions are possible, namely charge-density wave (CDW) order, electronic ferroelectricity (EFE) and electronic antiferroelectricity (EAFE). The order parameters are calculated as a function of the model parameters and of the temperature. There is a first-order phase transition from the CDW-phase to the EFE- or EAFE-phase. The total energy is calculated to determine the thermodynamically stable solution. The quantum phase diagrams are calculated.     

Numerical investigation of scaling regimes in a model of an anisotropically advected vector field

Influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Turbulent fluctuations of the velocity field are taken to have the Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy, but the corresponding stability of the two-dimensional system can be corrupted by the presence of anisotropy. A borderline dimension d _c below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters. The text was submitted by the authors in English.     

Microscopic correlation functions for the QCD Dirac operator with chemical potential

A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with nonvanishing chemical potential. The new correlation functions derived from it are conjectured to predict the local fluctuations of complex Dirac operator eigenvalues at zero virtuality. The parameter measuring the non-Hermiticity of the random matrix is related to the chemical potential. In the phase with broken chiral symmetry all spectral correlations are calculated for finite matrix size N and in the large-N limit at weak and strong non-Hermiticity. The derivation uses the orthogonality of the Laguerre polynomials in the complex plane.     

Inclusive two-particle rapidity correlations at ISR energies and fireball production

ISR data on two-particle rapidity correlations in the region y₁ ≈ y₂ can be understood in terms of the multiperipheral fireball model and indicate an energy independent upper limit of the average fireball mass. The diffractive contribution to the fireball production leads to characteristic shapes of long range correlations. Data on long range rapidity correlations may be used to determine the fractions of non-diffractive and diffractive one- and two-fireball production.     

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

Exact results for the dynamics of the classical one dimensional easy plane ferromagnet at low temperatures

The in-plane and out-of-plane dynamical correlation functions for the classical one dimensional easy plane ferromagnet are calculated asymptotically exactly at low temperatures. The results are restricted to temperatures much below the crossover temperature at which spins begin aligning in the plane. The long wavelength behavior of the in-plane fluctuations is consistent with dynamical scaling, in contrast to the isotropic case, and agrees with the results of Villain and of Nelson and Fisher. The linewidths for the in-plane fluctuations at short wavelengths are calculated exactly, and approach those of the isotropic model for small anisotropy. The theory of Villain, the theory of Cieplak and Sjolander, and the simulations of Loveluck, Jauslin, Schneider and Stoll all give incorrect results for these linewidths. The out of plane linewidths show an anomalous temperature dependence due to a singularity in the three spin wave density of states that is characteristic of one dimensional systems. The linewidth is proportional toT ² lnT except at the wavevector for which the second derivative of the spin wave frequency with respect to wavevector vanishes (/2 for CsNiF₃) where the linewidth is proportional toT ^5/3. The linewidth has a strong discontinuity as the wavevector increases as a result of a catastrophe occurring in the calculation of the three spin wave density of states. The position and strength of the discontinuity are temperature dependent. The diffusion coefficient is logarithmically dependent on the anisotropy, and diverges as (T ² lnD)^–1, which is consistent with the (lnT)^–1 behavior predicted for the isotropic ferromagnet in earlier work. The results are derived for the case of single ion anisotropy, using a spin wave theory for static correlations and the spin current damping function, and can be readily extended to the case of anisotropic exchange.     

Dynamical correlations for vicious random walk with a wall

A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. N Brownian particles start from the origin at time t=0 and undergo mutually avoiding motion until a finite time t=T. Dynamical correlation functions among the walkers are exactly evaluated in the case with a wall at the origin. Taking an asymptotic limit N→∞, we observe discontinuous transitions in the dynamical correlations. It is further shown that the vicious walk model with a wall is equivalent to a parametric random matrix model describing the crossover between the Bogoliubov–deGennes universality classes.     

Electron correlation energy in confined two-electron systems

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05-10a₀. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z?1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy.     

Dynamical perturbation for classical fluids: A solvable model

We investigate on a one-dimensional model the perturbation to the timedependent correlations in a classical fluid when a small interaction is added to a hard core. Various formulas have already been proposed for this correction. We verify on this model, for which everything can be calculated explicitly, that the expressions proposed by Frisch and Berne yield strongly divergent time integrals for the diffusion coefficient. On the contrary, when all corrections are accounted for, the correction to the velocity time correlation is shown to decay like (Int)/t ₂ at large times, yielding a finite first-order correction to the diffusion coefficient. The extension of this calculation to a gas of hard rods in the case of a perturbation with an infinite range is discussed.     

Intensity,correlations, and linewidths of two mode lasers with intensity coupling near threshold

Two mode lasers with intensity coupling are treated by simple fluctuation theory. The intensities of the two modes as functions of pump power are calculated together with the correlation matrix. Equations of motion for the intensities are derived from which the decay times of correlations are found by a method of quasilinearization as well as by decoupling the hierarchy of correlation functions. Details of photon fluctuation linewidths are reported together with the time dependent correlations between different modes.