Biomedical subjects

Gerhard Kahl

Publications and source records attributed to Gerhard Kahl.

11 recordsLinked to original sources

PubMed2007

Liquid-vapor transition of systems with mean field universality class.

We have considered a system where the interaction, v(r)=v(IS)(r)+xi(2)v(MF)(r), is given as a linear combination of two potentials, each of which being characterized with a well-defined critical behavior: for v(IS)(r) we have chosen the potential of the restricted primitive model which is known to belong to the three-dimensional Ising universality class, while for v(MF)(r) we have considered a long-range interaction in the Kac [J. Math. Phys. 4, 216 (1963)] limit, displaying mean field (MF) behavior. We study the performance of two theoretical approaches and of computer simulations in the critical region for this particular system and give a detailed comparison between theories and simulation of the critical region and the location of the critical point. Having shown by theoretical arguments that the system belongs to the MF universality class for any positive value of xi and shows nonclassical behavior only for xi=0, we examine to which extent theoretical approximations and simulation can reproduce this behavior. While in this limiting case theoretical approaches are known to fail, we find good agreement for the critical properties between the theoretical approaches and the simulations for xi(2) larger than 0.05.

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PubMed2006

Phase behavior of a symmetrical binary fluid mixture.

We have investigated the phase behavior of a symmetrical binary fluid mixture for the situation where the chemical potentials mu(1) and mu(2) of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when mu(1)=mu(2), the phase diagram exhibits both a liquid-vapor critical point and a tricritical point. The corresponding phase behavior for the case mu(1) not equalmu(2) is investigated via integral-equation theory calculations within the mean spherical approximation and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behavior can occur, these being distinguished by the relationship between the triple lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other is also studied, revealing interesting features.

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PubMed2006

Thermodynamically self-consistent liquid state theories for systems with bounded potentials.

The mean spherical approximation (MSA) can be solved semianalytically for the Gaussian core model (GCM) and yields exactly the same expressions for the energy and the virial equations. Taking advantage of this semianalytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the energy or virial route. Utilizing standard thermodynamic relations this leads to two differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integrodifferential-equation-based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.

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PubMed2006

Formation of polymorphic cluster phases for a class of models of purely repulsive soft spheres.

We present results from density functional theory and computer simulations that unambiguously predict the occurrence of first-order freezing transitions for a large class of ultrasoft model systems into cluster crystals. The clusters consist of fully overlapping particles and arise without the existence of attractive forces. The number of particles participating in a cluster scales linearly with density, therefore the crystals feature density-independent lattice constants. Clustering is accompanied by polymorphic bcc-fcc transitions, with fcc being the stable phase at high densities.

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PubMed2005

Type-IV phase behavior in fluids with an internal degree of freedom.

We have identified a fourth archetype of phase diagram in binary symmetrical mixtures, which is encountered when the ratio of the interaction between the unlike and the like particles is sufficiently small. This type of phase diagram is characterized by the fact that the lambda line (i.e., the line of the second-order demixing transition) intersects the first-order liquid-vapor curve at densities smaller than the liquid-vapor critical density.

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PubMed2005

Phase coexistence in a polydisperse charged hard-sphere fluid: polymer mean spherical approximation.

We have reconsidered the phase behavior of a polydisperse mixture of charged hard spheres (CHSs) introducing the concept of minimal size neutral clusters. We thus take into account ionic association effects observed in charged systems close to the phase boundary where the properties of the system are dominated by the presence of neutral clusters while the amount of free ions or charged clusters is negligible. With this concept we clearly pass beyond the simple level of the mean spherical approximation (MSA) that we have presented in our recent study of a polydisperse mixture of CHS [Yu. V. Kalyuzhnyi, G. Kahl, and P. T. Cummings, J. Chem. Phys. 120, 10133 (2004)]. Restricting ourselves to a 1:1 and possibly size-asymmetric model we treat the resulting polydisperse mixture of neutral, polar dimers within the framework of the polymer MSA, i.e., a concept that--similar as the MSA--readily can be generalized from the case of a mixture with a finite number of components to the polydisperse case: again, the model belongs to the class of truncatable free-energy models so that we can map the formally infinitely many coexistence equations onto a finite set of coupled, nonlinear equations in the generalized moments of the distribution function that characterizes the system. This allows us to determine the full phase diagram (in terms of binodals as well as cloud and shadow curves), we can study fractionation effects on the level of the distribution functions of the coexisting daughter phases, and we propose estimates on how the location of the critical point might vary in a polydisperse mixture with an increasing size asymmetry and polydispersity.

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PubMed2005

Predicting equilibrium structures in freezing processes.

We propose genetic algorithms as a new tool that is able to predict all possible solid candidate structures into which a simple fluid can freeze. In contrast to the conventional approach where the equilibrium structures of the solid phases are chosen from a preselected set of candidates, genetic algorithms perform a parameter-free, unbiased, and unrestricted search in the entire search space, i.e., among all possible candidate structures. We apply the algorithm to recalculate the zero-temperature phase diagrams of neutral star polymers and of charged microgels over a large density range. The power of genetic algorithms and their advantages over conventional approaches is demonstrated by the fact that new and unexpected equilibrium structures for the solid phases are discovered. Improvements of the algorithm that lead to a more rapid convergence are proposed and the role of various parameters of the method is critically assessed.

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PubMed2005

Phase diagram of a binary symmetric hard-core Yukawa mixture.

We assess the accuracy of the self-consistent Ornstein-Zernike approximation for a binary symmetric hard-core Yukawa mixture by comparison with Monte Carlo simulations of the phase diagrams obtained for different choices of the ratio alpha of the unlike-to-like interactions. In particular, from the results obtained at alpha=0.75 we find evidence for a critical endpoint in contrast to recent studies based on integral equation and hierarchical reference theories. The variation of the phase diagrams with range of the Yukawa potential is investigated.

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PubMed2004

Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation.

Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions.

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PubMed2002

Pole topology of the structure functions of continuous systems.

We develop a theory of the pole topology of the Laplace transform of the structure functions of continuous N component systems based on the Wiener-Hopf technique. We classify systems according to the spectrum of the NxN matrix Q(t), with elements Q(ij)(t)=delta(ij)-2pi square root [rho(i)rho(j)]integrale(-tr)q(ij)(r)dr, associated with their factor functions q(ij)(r). For the simplest nontrivial class of systems--namely, that with only two eigenvalues of Q(t) different from one--a full and explicit analysis of the pole topology is possible. We illustrate the theory with exactly solvable examples, such as the Percus-Yevick equation for arbitrary mixtures of hard spheres (HS) and polydisperse HS and the mean spherical model for binary mixtures of adhesive spheres.

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PubMed2002

Implementation of the hierarchical reference theory for simple one-component fluids.

Combining renormalization group theoretical ideas with the integral equation approach to fluid structure and thermodynamics, the hierarchical reference theory is known to be successful even in the vicinity of the critical point and for subcritical temperatures. We present here a software package independent of earlier programs for the application of this theory to simple fluids composed of particles interacting via spherically symmetrical pair potentials, restricting ourselves to hard-sphere reference systems. Using the hard-core Yukawa potential with z=1.8/sigma for illustration, we discuss our implementation and the results it yields, paying special attention to the core condition and emphasizing the decoupling assumption's role.

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