No Arabic abstract
Time evolution of the position-velocity correlation functions (PVCF) plays a key role in a new formalism of Brownian motion. A system of differential equations, which governs PVCF, is derived for magnetic Skyrmions on a 2-dimensional magnetic thin film with thermal agitation. In the formalism, a new type of diffusion coeffcient is introduced which does not come out in the usual diffusion equations. The mean-square displacement (MSD) is obtained from the PVCF and found that it oscillates in time when the damping constant is small. It is also shown, even for a structureless particle, that the famous Ornstein-Fuerth formula should be corrected taking a proper initial value of PVCF into account.
We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.
We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new Screening Transition in the DBM at large eta.
Enhanced diffusion and anti-chemotaxis of enzymes have been reported in several experiments in the last decade, opening up entirely new avenues of research in the bio-nanosciences both at the applied and fundamental level. Here, we introduce a novel theoretical framework, rooted in non-equilibrium effects characteristic of catalytic cycles, that explains all observations made so far in this field. In addition, our theory predicts entirely novel effects, such as dissipation-induced switch between anti-chemotactic and chemotactic behavior.
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles interact, we give them stochastic kicks which conserve center of mass. We find that the density fluctuations in the active phase decay in the fastest manner possible for a disordered isotropic system, and we present arguments that the large scale fluctuations are determined by a competition between a noise term which generates fluctuations, and a deterministic term which reduces them. Our results may be relevant to shear experiments and may further the understanding of hyperuniformity which occurs at the critical point.