Related papers: The Kupershmidt hydrodynamic chains and lattices
Hydrodynamics can be formulated in terms of a perturbative series in derivatives of the temperature, chemical potential, and flow velocity around an equilibrium state. Different formulations for this series have been proposed over the…
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish…
An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second…
We study bi-Hamiltonian systems of hydrodynamic type with non-singular (semisimple) non-local bi-Hamiltonian structures and prove that such systems of hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. Ferrari in arXiv:0811.0682, is a classical example of (2+1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In…
We discuss the Lagrangian-Eulerian framework for hydrodynamic models and provide a proof of Lipschitz dependence of solutions on initial data in path space. The paper presents a corrected version of the result in \cite{c1}.
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 work out some properties of a recently proposed globally N = 1 supersymmetric extension of relativistic fluid mechanics in four-dimensional Minkowski space. We construct the lagrangean, discuss its symmetries and the corresponding…
Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain…
Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…
We present the hydrodynamics of fluids in three spatial dimensions with helical symmetry, wherein only a linear combination of a rotation and translation is conserved in one of the three directions. The hydrodynamic degrees of freedom…
The hydrodynamic description of transversally thermalized matter, possibly formed at the early stages of ultra-relativistic heavy-ion collisions, is developed. The formalism is based on the thermodynamically consistent approach with all…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…
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…
In this paper we consider a new class of Hamiltonian hydrodynamic type systems, whose conservation laws are polynomial with respect to one of field variables.
We derive and investigate several hydrodynamic formalisms that emerge from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. The specific form of the total cross-section enables the…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…