Biomedical subjects

R Folk

Publications and source records attributed to R Folk.

At least 19 recordsLinked to original sources

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.

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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.

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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).

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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.

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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.

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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.

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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.

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PubMed2001

Algorithm for molecular dynamics simulations of spin liquids.

A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the algorithm exactly conserves spin lengths and can be used with much larger time steps than those inherent in standard predictor-corrector schemes. The results obtained for time correlation functions demonstrate the evident dynamic interplay between the liquid and magnetic subsystems.

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PubMed2000

Critical light scattering in liquids

We compare theoretical results for the characteristic frequency of the Rayleigh peak calculated in one-loop order within the field theoretical method of the renormalization group theory with experiments and other theoretical results. Our expressions describe the nonasymptotic crossover in temperature, density, and wave vector. In addition we discuss the frequency dependent shear viscosity evaluated within the same model and compare our theoretical results with recent experiments in microgravity.

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PubMed1999

Frequency-dependent shear viscosity, sound velocity, and sound attenuation near the critical point in liquids. III. The shear viscosity.

We compare theoretical results for the shear viscosity calculated in one-loop order within the field-theoretical method of the renormalization-group theory with experiments. Our expressions describe the nonasymptotic crossover in both temperature and density, and allow us to consider effects of finite gravitation and finite frequency at which the experiments are performed. In doing so we treat the critical exponent x(eta) of the shear viscosity as an independent parameter, keeping the one-loop value of the Kawasaki amplitude fixed. Within our model we also consider the temperature and density dependence of the thermal diffusion including gravitational effects.

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PubMed1996