Related papers: Strong hydrodynamic limit for attractive particle …
A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…
A generalized hydrodynamic theory that systematically incorporates elasticity and viscoelasticity had been derived about a quarter of a century ago. It is based on a strictly Euler point of view, as is natural for hydrodynamics. We used and…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent…
We describe the hydrodynamic behavior of the $k$-step exclusion process. Since the flux appearing in the hydrodynamic equation for this particle system is neither convex nor concave, the set of possible solutions include in addition to…
Carroll hydrodynamics arises in the $c\to 0$ limit of relativistic hydrodynamics. Instances of its relevance include the Bjorken and Gubser flow models of heavy-ion collisions, where the ultrarelativistic nature of the flow makes the…
We consider an interacting particle system which models the sterile insect technique. It is the superposition of a generalized contact process with exchanges of particles on a finite cylinder with open boundaries (see Kuoch et al., 2017).…
Hydrodynamic attractors have recently gained prominence in the context of early stages of ultra-relativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of…
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena…
We classify all possible allowed constitutive relations of relativistic fluids in a statistical mechanical limit using the Schwinger-Keldysh effective action for hydrodynamics. We find that microscopic unitarity enforces genuinely new…
Understanding how hydrodynamics emerges rapidly in the medium produced by relativistic heavy-ion collisions remains a key theoretical challenge. While the attractor solution -- manifesting as a non-thermal fixed point during the early…
This paper develops a geometric approach to the theory of integrability by hydrodynamic reductions to establish an equivalence, for a large class of quasilinear systems, between hydrodynamic integrability and the existence of nets…
Hydrodynamic attractors are a universal phenomenon of strongly interacting systems that describe the hydrodynamic-like evolution far from local equilibrium. In particular, the rapid hydrodynamization of the Quark-Gluon Plasma is behind the…
We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic…
Hydrodynamics of plasma in the random magnetic field is considered, which is characterized by the second moment of magnetic induction. Equations of ideal magnetic hydrodynamics in such field are received for an adiabatic process. It is…
We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order…
For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We…
Unipotent flows are well-behaved dynamical systems. In particular, Marina Ratner has shown that the closure of every orbit for such a flow is of a nice algebraic (or geometric) form. After presenting some consequences of this important…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…
Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the…