Biomedical subjects
Publications and source records attributed to A Blumen.
We investigate the trapping of random walkers on small-world networks (SWN's), irregular graphs. We derive bounds for the survival probability Phi(SWN)(n) and display its analysis through cumulant expansions. Computer simulations are performed for large SWNs. We show that in the limit of infinite sizes, trapping on SWNs is equivalent to trapping on a certain class of random trees, which are grown during the random walk.
We introduce a fractional Fokker-Planck equation (FFPE) for Lévy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Lévy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation toward the Boltzmann equilibrium distribution. The properties of the Lévy-flight FFPE derived here are compared with earlier findings for a subdiffusive FFPE. The latter is characterized by a nonexponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached, and modifications of the Boltzmann thermodynamics are not required.
Using a one-dimensional model that takes into account ideal plasticity of the surface layer, we investigate the fragmentation of thin coatings under uniaxial tension. The coating is modeled as a chain of plastically deforming elements that are connected via leaf springs to a uniformly stretched substrate. Each coating element can only withstand a maximum elongation, which is randomly distributed. From simulations of the fragmentation process we find that the average crack spacing scales with applied strain epsilon, i.e., proportional to epsilon(-kappa). Simulations and analytical arguments show that the scaling exponent kappa depends on the disorder parameters of the model.
We study random walks on a one-dimensional lattice that contains weak connections, so-called "bridges." Each time the walker crosses the bridge from the left or attempts to cross it from the right, the bridge may be destroyed with probability p; this restricts the particle's motion and directs it. Our model, which incorporates asymmetric aspects in an otherwise symmetric hopping mechanism, is very akin to "Brownian ratchets" and to front propagation in autocatalytic A+B-->2A reactions. The analysis of the model and Monte Carlo simulations show that for large p the velocity of the directed motion is extremely sensitive to the distribution of bridges, whereas for small p the velocity can be understood based on a mean-field analysis. The single-particle model advanced by us here allows an almost quantitative understanding of the front's position in the A+B-->2A many-particle reaction.
In this work we focus on reactions on small-world networks (SWN's), disordered graphs of much recent interest. We study the target problem, since it allows an exact solution on regular lattices. On SWN's we find that the decay of the targets (for which we extend the formalism to disordered lattices) is again related to S(n), the mean number of distinct sites visited in n steps, although the S(n) vs n dependence changes here drastically in going from regular linear chains to their SWN.
We introduce a model of random layered media, extending the Matheron-de Marsily model: Here we allow for the flows to change in time. For such layered structures, we solve exactly the equations of motion for single particles and also for polymers modelled as Rouse chains. The results show a rich variety of dynamical patterns.
The autocatalytic scheme A+B-->2A in a discrete particle system is studied in one dimension via Monte Carlo simulations. We find considerable differences in the results for the front velocities and front forms compared to the classical, continuous picture, which is only valid in the limit of very small reaction probabilities p. Interestingly, we also obtain front propagation velocities fairly below the classical minimal velocity.
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems that combine simultaneously properties of regular and random lattices. In this work we study diffusion processes defined on such structures by considering explicitly the probability for a random walker to be present at the origin. The results are intermediate between the corresponding ones for fractals and Cayley trees.
Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this paper we explore (based on physical models) a new variant of SWN, in which the probability of realizing an AL depends on the chemical distance between the connected sites. We assume a power-law probability distribution and study random walkers on the network, focusing especially on their probability of being at the origin. We connect the results to Levy flights, which follow from a mean-field variant of our model.
The fragmentation of two-phase composite systems such as coatings on substrates and fibers in matrices under uniaxial tension shows two regimes: the evolution of the mean fragment length with applied strain displays different power laws for small and for large strains. From theoretical arguments, we find that in both cases the scaling exponent depends on the shape parameter of the strength distribution. The exponent for large applied strains depends also, as we show, on the way (linear or nonlinear) in which the stress transfer between the two constituents takes place. We present experimental data on the sequential cracking of SiOx coatings on thermoplastic substrates that indeed show the two regimes; the detailed analysis of the data supports our theory.
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We evaluate numerically the mobility of DNA chains under field-inversion gel electrophoresis (FIGE) conditions in the framework of the lakes-straits model introduced by Zimm (Phys. Rev. Lett. 1988, 61, 2965-2968; J. Phys. Chem. 1991, 94, 2197-2206). We extend the model by allowing both simple and also multiple-branched hernias; this is achieved by arranging the data structure used in the algorithm so that each fragment in a lake can be treated separately. We show that the existence of hernias allows the probe to migrate faster and that with hernias the mobility minimum in FIGE shifts to smaller field periods. These effects occur only if the electric field is strong enough. We also discuss the influence of the model's parameters on the mobility.
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Explore the source record for details and available documents.