Diffusion in scale-free networks with annealed disorder

The scale-free (SF) networks that have been studied so far contained quenched disorder generated by random dilution which does not vary with the time. In practice, if a SF network is to represent, for example, the worldwide web, then the links between its various nodes may temporarily be lost, and re-established again later on. This gives rise to SF networks with annealed disorder. Even if the disorder is quenched, it may be more realistic to generate it by a dynamical process that is happening in the network. In this paper, we study diffusion in SF networks with annealed disorder generated by various scenarios, as well as in SF networks with quenched disorder which, however, is generated by the diffusion process itself. Several quantities of the diffusion process are computed, including the mean number of distinct sites visited, the mean number of returns to the origin, and the mean number of connected nodes that are accessible to the random walkers at any given time. The results including, (1) greatly reduced growth with the time of the mean number of distinct sites visited; (2) blocking of the random walkers; (3) the existence of a phase diagram that separates the region in which diffusion is possible from one in which diffusion is impossible, and (4) a transition in the structure of the networks at which the mean number of distinct sites visited vanishes, indicate completely different behavior for the computed quantities than those in SF networks with quenched disorder generated by simple random dilution.Comment: 18 pages including 8 figure

A generalized spin model of financial markets

We reformulate the Cont-Bouchaud model of financial markets in terms of classical "super-spins" where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce a fictitious temperature (to model other random influences), and time-dependent local fields to model slowly changing optimistic or pessimistic bias of traders. We point out close similarities between the price variations in our model with $N$ super-spins and total displacements in an $N$-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well as the occurrence of "fat tails" in the distributions of stock price variations.Comment: 11 pages LATEX, 7 postscript figures; longer text with theoretical analysis, more accurate numerical data, better terminology, additional references. Accepted for publication in European Physical Journal

Numerical investigation of novel microwave applicators based on zero-order mode resonance for hyperthermia treatment of cancer

This paper characterizes three novel microwave applicators based on zero-order mode resonators for use in hyperthermia treatment of cancer. The radiation patterns are studied with numerical simulations in muscle tissue-equivalent model at 434 MHz. The relative performance of the applicators is compared in terms of reflection coefficient, current distribution, power deposition (SAR) pattern, effective field size in 2D and 3D tissue volumes, and penetration depth. One particular configuration generated the most uniform SAR pattern, with 25% SAR covering 84 % of the treatment volume extending to 1 cm depth under the aperture, while remaining above 58% coverage as deep as 3 cm under the aperture. Recommendations are made to further optimize this structure

Gregory Butler. Bach's Clavier-Ubung III: The Making of a Print. With a Companion Study of the Canonic Variations on "Vom Himmel Hoch," BWV 769.

This article discusses Gregory Butler's Bach's Clavier-Ubung III' The Making of a Print and the authors thoughts on Bach. At the conclusion of a round table on post-World War II developments in Bach research, a long session in which the manuscript studies of Alfred Durr, Georg von Dadelsen, and Robert Marshall were discussed in some detail, Mendel quipped, with a wry smile: "And if the original manuscripts have revealed a lot about Bach's working habits, wait until we take a closer look at the original prints!" The remark drew laughter, as Mendel intended, and struck one at the time as facetious, for how could the prints of Bach's works ever show as much about chronology and the compositional process as the manuscripts? The surviving manuscript materials, written by Bach and his copyists, display a wealth of information that can be unraveled through source-critical investigation: revisions, corrections, organizational second thoughts. The prints, by contrast, appear inscrutable. Uniform and definitive in appearance, made by engravers rather than Bach or his assistants, they seem to be closed books, telling little-if any thing about the genesis of the texts they contain

A new model of binary opinion dynamics: coarsening and effect of disorder

We propose a model of binary opinion in which the opinion of the individuals change according to the state of their neighbouring domains. If the neighbouring domains have opposite opinions, then the opinion of the domain with the larger size is followed. Starting from a random configuration, the system evolves to a homogeneous state. The dynamical evolution show novel scaling behaviour with the persistence exponent $\theta \simeq 0.235$ and dynamic exponent $z \simeq1.02 \pm 0.02$. Introducing disorder through a parameter called rigidity coefficient $\rho$ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at $\rho = 0^{+}$ is obtained. Close to $\rho =0$, the equilibrium values of the dynamic variables show power law scaling behaviour with $\rho$. We also discuss the effect of having both quenched and annealed disorder in the system.Comment: 4 pages, 6 figures, Final version of PR

Frequency dependent effective conductivity of two-dimensional metal-dielectric composites

We analyze a random resistor-inductor-capacitor $(RLC)$ lattice model of 2-dimensional metal-insulator composites. The results are compared with Bruggeman's and Landauer's Effective Medium Approximations where a discrepancy was observed for some frequency zones. Such a discrepancy is mainly caused by the strong conductivity fluctuations. Indeed, a two-branches distribution is observed for low frequencies. We show also by increasing the system size that at $p_c$ the so-called Drude peak vanishes; it increases for vanishing losses.Comment: 7 pages including all figures, accepted in Int. J. Mod. Phys.

On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?

In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P(\tau)$ and relaxation times $P(\mu)$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your second-nearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P(\tau)$, $P(\mu)$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $\sigma$, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that $\sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.Comment: 22 pages, 20 figures. For related publications see http://www.ais.fraunhofer.de/~fran