Related papers: Recurrence and transience for suspension flows
We establish that $C^\infty$ three-dimensional flows with positive topological entropy admit only finitely many ergodic measures of maximal entropy, even when singularities (zero-velocity points) are present. Furthermore, every ergodic…
We establish a variational inequality formulation that captures the transonic shock for a steady compressible potential flow. Its critical point satisfies the transonic equation; moreover the associated jump conditions across its free…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…
We consider a direct product of a suspension flow over a substitution dynamical system and an arbitrary ergodic flow and give quantitative estimates for the speed of convergence for ergodic integrals of such systems. Our argument relies on…
We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit…
We introduce a new measure for the stability of structures, such as the cross-section of the deck of a suspension bridge, subject to a 2D fluid force, such as the lift exerted by a laminar wind. We consider a wide class of possible flows,…
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal…
Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity…
Given a compact topological dynamical system (X, f) with positive entropy and upper semi-continuous entropy map, and any closed invariant subset $Y \subset X$ with positive entropy, we show that there exists a continuous roof function such…
We review the key steps of the relativistic fluid dynamics formalism with spin degrees of freedom initiated recently. We obtain equations of motion of the expansion of the system from the underlying definitions of quantum kinetic theory for…
Thermodynamics is usually formulated on the presumption that the observer has complete information about the system he/she deals with: no parasitic current, exact evaluation of the forces that drive the system. For example, the acclaimed…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite…
The usable limits of the customary and relaxational filtrational theories are considered. The questions of applicable the locality and local thermodynamical equilibrium principles to depict the nonstationary flows are discussed. The…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
The so-called Fundamental Theorem of Dynamical Systems -- which(1) relates attractors and repellers to the chain recurrent set and (2) gives the existence of a complete Lyapunov function -- can be seen as a means of separating out…