اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOnset of Singularities in the Pattern of Fluctuational Paths of a Nonequilibrium System
92
0
0.0
(
0
)
تأليف
Oleg Kogan
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Fluctuations in systems away from thermal equilibrium have features that have no analog in equilibrium systems. One of such features concerns large rare excursions far from the stable state in the space of dynamical variables. For equilibrium systems, the most probable fluctuational trajectory to a given state is related to the fluctuation-free trajectory back to the stable state by time reversal. This is no longer true for nonequilibrium systems, where the pattern of the most probable trajectories generally displays singularities. Here we study how the singularities emerge as the system is driven away from equilibrium, and whether a driving strength threshold is required for their onset. Using a resonantly modulated oscillator as a model, we identify two distinct scenarios, depending on the speed of the optimal path in thermal equilibrium. If the position away from the stable state along the optimal path grows exponentially in time, the singularities emerge without a threshold. We find the scaling of the location of the singularities as a function of the control parameter. If the growth away from the stable state is faster than exponential, characterized by the ability to reach infinity in finite time, there is a threshold for the onset of singularities, which we study for the model.
قيم البحث
اقرأ أيضاً
Dynamics of a system that performs a large fluctuation to a given state is essentially deterministic: the distribution of fluctuational paths peaks sharply at a certain optimal path along which the system is most likely to move. For the general case
of a system driven by colored Gaussian noise, we provide a formulation of the variational problem for optimal paths. We also consider the prehistory problem, which makes it possible to analyze the shape of the distribution of fluctuational paths that arrive at a given state. We obtain, and solve in the limiting case, a set of linear equations for the characteristic width of this distribution.
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated with the att
ractors at period-doubling accumulation points and at tangent bifurcations to describe features of glassy dynamics, critical fluctuations and localization transitions. We recall that trajectories pertaining to the routes to chaos form families of time series that are readily transformed into networks via the Horizontal Visibility algorithm, and this in turn facilitates establish connections between entropy and Renormalization Group properties. We discretize the replicator equation of game theory to observe the onset of chaos in familiar social dilemmas, and also to mimic the evolution of high-dimensional ecological models. We describe an analytical framework of nonlinear mappings that reproduce rank distributions of large classes of data (including Zipfs law). We extend the discussion to point out a common circumstance of drastic contraction of configuration space driven by the attractors of these mappings. We mention the relation of generalized entropy expressions with the dynamics along and at the period doubling, intermittency and quasi-periodic routes to chaos. Finally, we refer to additional natural phenomena in complex systems where these conditions may manifest.
We show that there exist a class of nonequilibrium systems for which a non-equilibrium analog of the Ginzburg-Landau (GL) functional can be constructed and propose the procedure for its derivation. As an example, we consider a small superconductor is
land of the size less than the coherence length in a stationary nonequlibrium state. We find the GL expansion of the free energy functional of such a system and analyze the dependence of the coefficients of the expansion upon the external drive and the non-equilibrium distribution functions.
We study transport properties in a slowly driven diffusive system where the transport is externally controlled by a parameter $p$. Three types of behavior are found: For $p<p$ the system is not conducting at all. For intermediate $p$ a finite fractio
n of the external excitations propagate through the system. Third, in the regime $p>p_c$ the system becomes completely conducting. For all $p>p$ the system exhibits self-organized critical behavior. In the middle of this regime, at $p_c$, the system undergoes a continuous phase transition described by critical exponents.
We extend the phase field crystal method for nonequilibrium patterning to stochastic systems with external source where transient dynamics is essential. It was shown that at short time scales the system manifests pattern selection processes. These pr
ocesses are studied by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed by means of numerical simulations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
