Biomedical subjects

R Folk

Publications and source records attributed to R Folk.

At least 19 recordsLinked to original sources

PubMed2006

Two-loop field theory and nonasymptotic properties of the dynamical model for the lambda transition in 3He-4He mixtures.

Model F' introduced by Siggia and Nelson [Phys. Rev. B 15, 1427 (1977)] describes the critical dynamics of 3He-4He mixtures near the superfluid transition. Using the minimal subtraction scheme this model is renormalized within dynamical field theory. The dynamic zeta functions needed for the nonasymptotic flow properties are presented in two-loop order. The fixed points are discussed and the stable fixed points are identified. The transition to limiting models contained in model F' is shown analytically by performing the corresponding limits and numerically by calculating the nonlinear flow. These results are the basis for further experimental comparison of the transport coefficents in 3He-4He mixtures at higher concentrations including the tricritical point.

Journal Article↗

PubMed2005

Integral equation study of an ideal Ising mixture.

We construct an integral equation scheme for magnetic binary mixtures of an ideal soft-core Ising fluid and a soft-sphere fluid by mapping the system onto an equivalent nonmagnetic ternary mixture. We apply the multicomponent Ornstein-Zernike equation together with a closure relation based on the soft mean spherical approximation and a field constraint for the Ising fluid component. Phase coexistence curves are calculated both by directly evaluating the chemical potentials via the bridge function, and by using a Maxwell-like construction which is derived in the text. Our results are compared to Monte Carlo data obtained earlier, and we find that the second method yields a much better agreement with the simulations.

Journal Article↗

PubMed2005

XY-spin fluids in an external magnetic field: an integral equation approach.

We develop an integral equation approach to study anisotropic fluids with planar spins in the presence of an external field. As a result, the integral equation calculations for these systems appear to be no more difficult than those for ordinary isotropic liquids. The method presented is applied to the investigation of phase coexistence properties of ferromagnetic XY-spin fluids in a magnetic field. The soft mean spherical approximation is used for the closure relation connecting the orientationally dependent two-particle direct and total correlation functions. The Lovett-Mou-Buff-Wertheim and Born-Green-Yvon equations are employed to describe the one-particle orientational distribution. The phase diagrams are obtained in the whole range of varying the external field for a wide class of XY-spin fluid models with various ratios of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of changing the screening radii of the interaction potentials is also considered. Different types of the phase diagram topology are identified. They are characterized by the existence of critical, tricritical, critical end, and triple points related to transitions between gas, liquid, and para- and ferromagnetic states, accompanied by different external field dependencies of critical temperatures and densities corresponding to the gas-liquid and liquid-liquid transitions. As is demonstrated, the integral equation approach leads to accurate predictions of the complicated phase diagram behavior which coincide well with those evaluated by the cumbersome Gibbs ensemble simulation and multiple-histogram reweighting techniques.

Journal Article↗

PubMed2005

Critical dynamics of diluted relaxational models coupled to a conserved density.

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a nonconserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics; however, it is the effective critical behavior that is often observed in experiments and in computer simulations, and this is described by the full set of dynamical equations of diluted model C. Indeed, different scenarios of effective critical behavior are predicted.

Journal Article↗

PubMed2005

Phase behavior of Ising mixtures.

We present phase diagrams that were calculated both in mean-field theory and via Monte Carlo (MC) simulations for binary mixtures of a ferromagnetic Ising fluid and a nonmagnetic fluid (Ising mixtures) in the absence of an external field. We look at both the simple ideal Ising mixture, consisting of an ideal Ising fluid and a hard-sphere fluid, as well as at the general case with one component being a nonideal Ising fluid and the other a van der Waals fluid. It is shown that the mean-field phase diagram of the ideal Ising mixture in the limit of infinite pressure is identical to that of the Blume-Capel model for 3He-4He mixtures. The MC phase diagrams were obtained using the Gibbs ensemble, the cumulant intersection technique, and the multi-histogram re-weighting method, adapted to the semi-grand ensemble. The results are qualitatively compared with mean-field theory, and both types of tri-critical lines occurring there are verified in the computer simulations.

Journal Article↗

PubMed2005

Critical dynamics of stochastic models with two conserved densities (model C' ).

We calculate the field-theoretic functions of the generalized dynamical model C(*') , where two conserved secondary densities are coupled to a nonconserved complex order parameter (OP), in two-loop order. A transformation to "orthogonalized" densities can be performed where only one secondary density with nontrivial static coupling to the OP exists while the second one remains Gaussian. The secondary densities remain dynamically coupled by the nondiagonal diffusion coefficent. General relations for the field-theoretic functions allow us to relate the asymptotic critical properties of model C(*') to the simpler model C(*) with only one conserved density coupled to the OP. The nonasymptotic properties, however, differ as can be seen from the flow of the dynamic parameters, which is presented for the case of a real OP with componets n=1,2,3 .

Journal Article↗

PubMed2005

XY spin fluid in an external magnetic field.

A method of integral equations is developed to study anisotropic fluids with planar spins in an external field. As a result, the calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids. The approach proposed is applied to the ferromagnetic XY spin fluid in a magnetic field using a soft mean spherical closure and the Born-Green-Yvon equation. This provides an accurate reproduction of the complicated phase diagram behavior obtained by cumbersome Gibbs ensemble simulation and multiple histogram reweighting techniques.

Journal Article↗

PubMed2004

Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster.

The scaling properties of self-avoiding walks on a d -dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Phys. Rev. Lett. 63, 2819 (1989)] and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree with the results of other methods our analytic result gives an accurate description of the available MC and exact enumeration data in a wide range of dimensions 2</=d</=6 .

Journal Article↗

PubMed2004

Ising fluids in an external magnetic field: an integral equation approach.

The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field H for a wide class of Ising fluid models with various ratios R of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths z(1) and z(2), corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in R as well as in z(1) and z(2) can lead to different topologies of the phase diagrams. In particular, depending on the value of R, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing H. The para-ferro magnetic transition is also affected by changes in R and the screening lengths. At H=0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For H--> infinity, it reduces to a pure nonmagnetic fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when z(1) and z(2) are large). In the Kac limit z(1), z(2) -->+0, both approaches tend to nearly the same results.

Journal Article↗

PubMed2004

Critical dynamics of stochastic models with energy conservation (model C).

We calculate the field-theoretic functions of the generalized dynamical model C*, in which a conserved secondary density is coupled to a nonconserved complex order parameter, in two-loop order. We show that the fixed points in this extended model are equal to the fixed points obtained in model C with a real order parameter, which has been introduced by Halperin, Hohenberg, and Ma. Our results correct long-standing errors in the field-theoretic functions in model C published by several authors leading also to different fixed point values w* for the ratio of the two time scales involved. The stability regions of the fixed points, which remained partially unclear, considered in a "phase diagram"--whose axes are the spatial dimension d and number of order parameter components n--are now clarified. Especially an anomalous region found by previous authors, in which the scaling properties remained unsolved, does not exist. There are only two regions: one with a finite fixed point w* where the dynamical exponent z of the order parameter is z=2+alpha/nu and another region where w*=0 and z is equal to the model A value.

Journal Article↗

PubMed2003

Phase diagrams of classical spin fluids: the influence of an external magnetic field on the liquid-gas transition.

The influence of an external magnetic field on the liquid-gas phase transition in Ising, XY, and Heisenberg spin fluid models is studied using a modified mean field theory and Gibbs ensemble Monte Carlo simulations. It is demonstrated that the theory is able to reproduce quantitatively all characteristic features of the field dependence of the critical temperature T(c)(H) for all the three models. These features include a monotonic decrease of T(c) with rising H in the case of the Ising fluid as well as a more complicated nonmonotonic behavior for the XY and Heisenberg models. The nonmonotonicity consists in a decrease of T(c) with increasing H at weak external fields, an increase of T(c) with rising H in the strong field regime, and the existence of a minimum in T(c)(H) at intermediate values of H. Analytical expressions for T(c)(H) in the large field limit are presented as well. The paramagnetic-ferromagnetic phase transition is also considered in simulations and described within the mean field theory.

Journal Article↗

PubMed2003

Critical dynamics of model C resolved.

We analyze the field theoretic functions of the dynamical model C in two-loop order. Our results correct long-standing errors in these functions published by several authors. We discuss, in particular, the fixed points for the ratio w* of the two time scales involved, as well as their stability. The regions of the "phase diagram," whose axes are the spatial dimension d and number of order parameter components n, correspond to these fixed points; previous authors have found, in addition, an anomalous region in which the scaling properties were unclear. We show that such an anomalous region does not exist. There are only two regions: one with a finite fixed-point w* where the dynamical exponent z=2+alpha/nu, and another where w*=0 and z is equal to the model A value. We show how the one-loop result is recovered from the two-loop result in the limit epsilon=4-d going to zero.

Journal Article↗

PubMed2003

Binary mixtures of magnetic fluids.

We study a binary mixture of a van der Waals fluid and a ferromagnetic fluid at zero magnetic field on the basis of the mean field Ising fluid model and the van der Waals theory with quadratic mixing rules. Depending on three reduced parameters, the phase diagram shows a surface of magnetic phase transitions and lines of tricritical points, critical end points, and magnetic consolute points. First-order phase transition surfaces and critical lines are calculated numerically. For the line of tricritical points, which can occur in two different topologies, an analytic expression is derived. All higher-order lines and coexistence surfaces are visualized in three-dimensional x, T, p and xi, T, p diagrams, where xi is a mapping of delta, the conjugated field of the mole fraction x, on the unit interval.

Journal Article↗

PubMed2002

Dynamic critical behavior near the superfluid transition in 3He-4He mixtures in two loop order.

We calculated in two loop order the field theoretic renormalization group functions taking into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. The observation of this nonperturbative structure simplifies the theoretical expressions obtained by perturbation theory considerably and makes tractable a complete two loop calculation of the critical dynamics near the superfluid transition of 3He-4He mixtures (model F'). As a result, we obtain various transport coefficients, which govern the nonasymptotic and nonuniversal temperature dependence. We also correct long-standing results for the critical dynamics of the superfluid transition in pure 4He (model F) and for the dynamics of structural or magnetic phase transitions (model C).

Journal Article↗

PubMed2002

Construction of high-order force-gradient algorithms for integration of motion in classical and quantum systems.

A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic algorithms are first derived up to the eighth order by direct decompositions of exponential propagators and further collected using an advanced composition scheme to obtain the algorithms of higher orders. Contrary to the scheme proposed by Chin and Kidwell [Phys. Rev. E 62, 8746 (2000)], where high-order algorithms are introduced by standard iterations of a force-gradient integrator of order four, the present method allows one to reduce the total number of expensive force and its gradient evaluations to a minimum. At the same time, the precision of the integration increases significantly, especially with increasing the order of the generated schemes. The algorithms are tested in molecular dynamics and celestial mechanics simulations. It is shown, in particular, that the efficiency of the advanced fourth-order-based algorithms is better approximately in factors 5 to 1000 for orders 4 to 12, respectively. The results corresponding to sixth- and eighth-order-based composition schemes are also presented up to the sixteenth order. For orders 14 and 16, such highly precise schemes, at considerably smaller computational costs, allow to reduce unphysical deviations in the total energy up in 100 000 times with respect to those of the standard fourth-order-based iteration approach.

Journal Article↗

PubMed2002

Optimized Verlet-like algorithms for molecular dynamics simulations.

Explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the proposed algorithms appear to be more efficient than the original Verlet versions that correspond to a particular case when the introduced parameter is equal to zero. Like the original versions, the extended counterparts are symplectic and time reversible, but lead to an improved accuracy in the generated solutions at the same overall computational costs. The advantages of the optimized algorithms are demonstrated in molecular dynamics simulations of a Lennard-Jones fluid.

Journal Article↗

PubMed2001

Molecular dynamics simulations of spin and pure liquids with preservation of all the conservation laws.

A methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the time step, all the conservation laws inherent in the description without breaking the time reversibility. As a result, an implicit second-order algorithm is derived and applied to pure liquids, as well as spin liquids, for which the dynamics is characterized by the conservation of total energy, linear and angular momenta, as well as magnetization and individual spin lengths. It is demonstrated on the basis of Lennard-Jones and Heisenberg fluid models that when such quantities as energy and magnetization must be conserved perfectly, the algorithm turns out to be more efficient than popular decomposition integrators and standard predictor-corrector schemes.

Journal Article↗

PubMed2001

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling.

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.

Journal Article↗