اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRandom fluctuation leads to forbidden escape of particles
35
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.
قيم البحث
اقرأ أيضاً
The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domains boundary. Here we develop a formalism that allows us to evaluate the emph{non-escape p
robability} of a gas of diffusing particles that may interact with each other. In some cases the non-escape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gau
ssian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractors basin is equivalent to that of a closed system with an appropriately chosen hole. Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of a two-dimensional map with noise.
The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In previous work the coefficients of such an expansion for a one-dimensional map were fitted to a general form containing a few parameters.
These parameters were found to be related to the fractal structure of the repeller of the system. The parameter alpha, the noise dimension, remains to be interpreted. This report presents new data for alpha showing that the relation to the dimensions is more complicated than predicted in earlier work and oscillates as a function of the map parameter, in contrast to other dimension-like quantities.
The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the oscillator d
ensity at the synchronizing frequency. This is the source for the unusual values assumed by the correlation size exponent $ u$. Locally coupled oscillators on a $d$-dimensional lattice exhibit two types of frequency entrainment: symmetry-breaking at $d > 4$, and aggregation of compact synchronized domains in three and four dimensions. Various critical properties of the transition are well captured by finite-size scaling relations with simple yet unconventional exponent values.
At finite concentrations of reacting molecules, kinetics of diffusion-controlled reactions is affected by intra-reactant interactions. As a result, multi-particle reaction statistics cannot be deduced from single-particle results. Here we briefly rev
iew a recent progress in overcoming this fundamental difficulty. We show that the fluctuating hydrodynamics and macroscopic fluctuation theory provide a simple, general and versatile framework for studying a whole class of problems of survival, absorption and escape of interacting diffusing particles.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
