Category: Uncategorized

Modeling of Orientational Ordering in Lipid Monolayers

Post author By R Hilfer
Post date February 18, 1991

M.Kreer, M.Scheringer, K.Binder, K.Kremer, R.Hilfer

in: Computer Simulation Studies in Condensed Matter Physics IV
edited by: D.P. Landau and K.K. Mon and H.B. Schüttler
Springer Verlag, Berlin, 159 (1993)
https://doi.org/10.1007/978-3-642-84878-0_13
ISBN 978-3-642-84878-0

submitted on
Monday, February 18, 1991

Lipid monolayers at high densities are modelled as rigid rods grafted to an interface at the sites of a regular lattice. The transition between the state where the rods are uniformly tilted to a disordered state with no (average) tilt is studied by computer simulation methods. For the one-dimensional model, the molecular dynamics approach is found much less suitable to equilibrate the system rather than Monte Carlo methods. Both in d=2 discretized versions of Monte Carlo codes are much more efficient than continuum Monte Carlo methods, in spite of huge storage requirements. While in d=l the transition occurs at temperature T=0 via the spontaneous creation of solitons, at d=2 a finite temperature first order transition occurs.

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Frequency Dependent Response and Dynamic Disorder

Post author By R Hilfer
Post date June 20, 1990

R. Hilfer

Journal of Non-Crystalline Solids 131–133, 213 (1991)
https://doi.org/10.1016/0022-3093(91)90303-N

submitted on
Wednesday, June 20, 1990

This paper discusses selected aspects of the application of dynamic percolation models to ionic transport in mixed-ion superionic conductors. The discussion is based on an AB lattice gas model with hard-core repulsions and a ratio r between the transition rates of particles A and B. The frequency-dependent conductivity for a tracer particle is calculated within an effective-medium theory. The motion of the background B-particles is regarded as providing a fluctuating disordered environment for the tracer particles A. A crossover frequency separating high-frequency and low-frequency response is found which scales with the negative square root of r. The results for the dc-limit are compared with simulations and are found to be in very good agreement.

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Correlated Hopping in a Disordered Medium

Post author By R Hilfer
Post date March 6, 1989

R. Hilfer

Physical Review B 44, 628 (1991)
10.1103/PhysRevB.44.628

submitted on
Monday, March 6, 1989

This paper discusses random walks with memory on a percolating network as a model of correlated hopping transport through a disordered system. Correlations can arise from such sources as hard-core and Coulomb repulsions, correlated hops of groups of particles, or lattice-relaxation effects. In general these correlations will result in a difference between the hopping probability for return to the previously visited site and the probability to jump to another nearest neighbor of the currently occupied site. Thus the hopping process possesses a memory of its previous hop. Such a random walk is investigated in this paper for the case of bond percolation on a regular lattice. The frequency-dependent conductivity σ(ω) is calculated using a generalized effective-medium approximation. Results are presented for the linear chain and the hexagonal lattice. New features appear in both the real and the imaginary part of σ. These depend on the strength of the correlations and on the concentration of bonds. As an example, the possibility of a pronounced maximum in the real part of σ(ω) at finite frequencies is found, which is sometimes accompanied by a change of sign in the imaginary part. The results are found to agree qualitatively with experimental data on ionic transport in Na+ β-alumina, where both disorder and correlations are known to be important.

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