Armin Bunde

Mixed alkali effects in ionic conductors : a new model and computer simulations

Abstract A new model theory of the mixed alkali effect that is consistent with the most recent EXAFS data of cation environments in mixed alkali silicate glass is presented. The dynamics of ion transport and the memory effects of site occupancy are brought out by computer simulations based on the model in an infinite percolation cluster. The salient features of the mixed alkali effect in the diffusion coefficients of the two cations are reproduced in the results of computer simulations.

On controlled diffusion‐limited drug release from a leaky matrix

How fast can drug molecules randomly escape from a polymer matrix? This important question is of both scientific and practical importance, as increasing emphasis is placed on design considerations that can be addressed only if the physics of drug release is better understood. We study this problem using high accuracy Monte Carlo computer simulations. We find that the nature of drug release depends drastically on the dimension of the matrix and is different depending on whether the matrix is a normal Euclidean space or a fractal material such as a polymer, corresponding to the fact that the basic laws of physics are quite different in a fractal environment. We also find the surprising result that drug release is the same for noninteracting particles as it is for particles with hard‐core excluded volume interactions, suggesting that the nature of the matrix is more important than the nature of the interactions among the drug particles in determining drug release.

INFLUENCE OF THE CUBIC ANISOTROPY CONSTANTS ON THE HYSTERESIS LOOPS OF SINGLE-DOMAIN PARTICLES : A MONTE CARLO STUDY

The influence of the first and second cubic anisotropy constants on the hysteresis loops of noninteracting single-domain magnetic particles is studied by Monte Carlo simulation, which turns out to be a very powerful method for studying simple magnetic models. Both signs in the anisotropy constants are taken into account. Relevant properties such as coercivity and remanence are studied as a function of temperature when the second anisotropy constant is negligible. The influence of the second term of the anisotropy energy is studied in detail for T=0 K. It is concluded that this term has a big influence on the static magnetic behavior when the first anisotropy constant is negative.

Diffusion with memory: a model for mixed alkali effects in vitreous ionic conductors

The authors present a novel theory of the mixed alkali effect which focuses on the fact that each alkali prefers and maintains its own distinct characteristic environment in the mixed glass. This leads to mismatch between cations and sites recently occupied by unlike cations, and the existence of a memory effect which strongly influences the process of ion migration. This view of glass is consistent with both EXAFS and infrared measurements, and computer simulations reproduce the essential features of the mixed alkali effect including the mobility crossover and the conductivity minimum.

Comment on "Scaling of atmosphere and ocean temperature correlations in observations and climate models".

In a recent letter [K. Fraedrich and R. Blender, Phys. Rev. Lett. 90, 108501 (2003)], Fraedrich and Blender studied the scaling of atmosphere and ocean temperature. They analyzed the fluctuation functions F(s) ~ s^alpha of monthly temperature records (mostly from grid data) by using the detrended fluctuation analysis (DFA2) and claim that the scaling exponent alpha over the inner continents is equal to 0.5, being characteristic of uncorrelated random sequences. Here we show that this statement is (i) not supported by their own analysis and (ii) disagrees with the analysis of the daily observational data from which the grid monthly data have been derived. We conclude that also for the inner continents, the exponent is between 0.6 and 0.7, similar as for the coastline-stations.

Probability densities of random walks in random systems

Abstract We review recent results for the probability distribution of random walkers in random systems, where diffusion is anomalous and the mean-square displacement scales with time as R 2 ( t )∼ t 2 w , d w > 2. The random systems are characterized by structural disorder and by random transition rates. In general, the mean distribution function 〈 P ( r , t )〉 of the random walkers is a stretched Gaussian and scales as log [ P(r,t) P(r,0) ]∼−[ r R(t) ] u , where u= d w (d w −1) . On random fractals, the fluctuations of the density distribution P ( r , t ), for fixed distance r and time t , have a broad logarithmic distribution. The average moments 〈 P q 〉 scale in a multifractal way as 〈 P 〉 τ ( q ) , where τ ( q )∼ q τ , γ l -space the fluctuations of P are narrow and 〈 P q 〉∼〈 P 〉 q .

Monte Carlo studies of ionic conductors containing an insulating second phase

Abstract The ionic conductivity in solid ionic conductors containing a dispersed insulating phase (like LiI/Al 2 O 3 ) is studied within percolation theory. We develop a realistic three dimensional model which takes into account both the blocking of the mobile ions by the insulator and the enhanced conductivity along the internal interfaces. We calculate the overall conductivity by Monte Carlo simulations and find that the distinct conduction properties of the composites are explained satisfactorily by our model. In addition, we predict that dispersed ionic conductors should show critical behaviour of both random-superconducting and random-resistor networks near two different concentrations of the insulator, features which might be experimentally observable.

Diffusion in disordered systems : non-Debye relaxation due to long-range interactions

Abstract Transport in disordered systems, where the mobile particles are coupled by nearest-neighbor interactions, is discussed. It is found that due to the mutual interaction, novel crossover phenomena occur in the density distribution and the mean square displacement R2(t) of tagged particles. At intermediate time-scales t1 ⪡ t ⪡ t2, R2(t) is described by a new exponent k′, enhanced. The frequency dependent conductivity scales as σ(ω) ∼ ωn′, with n′ = 1 − k′, at intermediate frequencies. In agreement with the experimental situation, n′ can be considerably larger than the asymptotic exponent n = 1−k which is the same as for non-interacting particles.

Dynamic mechanisms of disorderly growth: Recent approaches to understanding diffusion limited aggregation

We briefly review some recent attempts to achieve some genuine understanding of diffusion-limited aggregation (DLA), the paradigm model for dynamical mechanisms of disorderly growth processes. We shall see that the seminal ideas of Professor Cyril Domb have influenced to a great degree many of the recent theoretical approaches. In particular, the Domb-Hunter constant-gap scaling hypothesis becomes replaced by a continuum of gap exponents. Moreover, while the growth probabilities for the tips of the DLA structure do scale in the conventional fashion, there is evidence that the growth probabilities of the fjords do not scale. Does this competition between one part of DLA that does scale, and another that does not, underlie many of the unusual properties of this model?

On the survival probability of a random walk in a finite lattice with a single trap

We consider the survival of a random walker in a finite lattice with periodic boundary conditions. The initial position of the random walker is uniformly distributed on the lattice with respect to the trap. We show that the survival of a random walker, 〈Un>, can be exactly related to the expected number of distinct sites visted on a trap-free lattice by 〈Un〉=1−〈Sn〉/ND (*) whereND is the number of lattice points inD dimensions. We then analyze the behavior of 〈Sn〉 in any number of dimensions by using Tauberian methods. We find that at sufficiently long times 〈Sn〉 decays exponentially withn in all numbers of dimensions. InD = 1 and 2 dimensions there is an intermediate behavior which can be calculated and is valid forN2≫N ≫ 1 whenD = 1 andN lnN ≫n≫ 1 whenD = 2. No such crossover exists when Z⩾3. The form of (*) suggests that the single trap approximation is indeed a valid low-concentration limit for survival on an infinite lattice with a finite concentration of traps.