Search results for "Disordered system"
showing 10 items of 244 documents
Rare events and scaling properties in field-induced anomalous dynamics
2012
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long sp…
Immune networks: multitasking capabilities near saturation
2013
Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with $N_T$ T-lymphocytes can manage a number $N_B!=!\order(N_T^\delta)$ of B-lymphocytes simultaneously, with $\delta!<!1$. Here we study this model in the extensive load regime $N_B!=!\alpha N_T$, with also a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivit…
Immune networks: Multi-tasking capabilities at medium load
2013
Associative network models featuring multi-tasking properties have been introduced recently and studied in the low load regime, where the number $P$ of simultaneously retrievable patterns scales with the number $N$ of nodes as $P\sim \log N$. In addition to their relevance in artificial intelligence, these models are increasingly important in immunology, where stored patterns represent strategies to fight pathogens and nodes represent lymphocyte clones. They allow us to understand the crucial ability of the immune system to respond simultaneously to multiple distinct antigen invasions. Here we develop further the statistical mechanical analysis of such systems, by studying the medium load r…
Random walk approach to the analytic solution of random systems with multiplicative noise—The Anderson localization problem
2006
We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized diffusion with a noise-induced first-order phase transition. The generalized diffusion manifests itself in the divergence of averages of wavefunctions (correlators). This divergence is controlled by the Lyapunov exponent $\gamma$, which is the inverse of the localization length, $\xi=1/\gamma$. The appearance of the generalized diffusion arises due to the instability of a fundamental mode corresponding to…
Anderson localization problem: An exact solution for 2-D anisotropic systems
2007
Our previous results [J.Phys.: Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping matrix elements in transverse directions). We discuss the mathematical nature of the metal-insulator phase transition which occurs in the 2-D case, in contrast to the 1-D case, where such a phase transition does not occur. In anisotropic systems two localization lengths arise instead of one length only.
Kardar–Parisi–Zhang scaling in kinetic roughening of fire fronts
1999
Abstract We show that the roughening of fire fronts in slow combustion of paper [7] follows the scaling predictions of the Kardar–Parisi–Zhang equation with thermal noise. By improved experimental accuracy it is now possible to observe the short-time and short-range correlations of the interfaces. These do not adhere to any standard picture, and in particular, do not seem to be related to any of the existing models of front propagation in the presence of quenched disorder.
Value-at-Risk and Tsallis statistics: risk analysis of the aerospace sector
2004
In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is well described by Tsallis distribution. We explore this result and modify the standard Value-at-Risk (VaR), financial risk assessment methodology in order to reflect an asset which obeys Tsallis non-extensive statistics.
Tunable multifunctional topological insulators in ternary Heusler compounds
2010
Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude o…
Electromagnetic behaviour of superconductive amorphous metals
2005
The penetration depth of the magnetic field into an amorphous superconductor is calculated. The ratio of the London penetration depth δL to the electron free path le under zero temperature is above unity for almost all amorphous metals. That is why pure metals, in a superconducting state, change from type I superconductors to type II superconductors during the crystalline–amorphous transition.
Static and dynamical properties of a supercooled liquid confined in a pore
2000
We present the results of a Molecular Dynamics computer simulation of a binary Lennard-Jones liquid confined in a narrow pore. The surface of the pore has an amorphous structure similar to that of the confined liquid. We find that the static properties of the liquid are not affected by the confinement, while the dynamics changes dramatically. By investigating the time and temperature dependence of the intermediate scattering function we show that the dynamics of the particles close to the center of the tube is similar to the one in the bulk, whereas the characteristic relaxation time tau_q(T,rho) of the intermediate scattering function at wavevector q and distance rho from the axis of the p…