Related papers: Arnold Hydrodynamics Revisited
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
It has recently been understood that the hydrodynamic series generated by the M\"uller-Israel-Stewart theory is divergent, and that this large order behaviour is consistent with the theory of resurgence. Furthermore, it was observed, that…
Physical systems made of many interacting quantum particles can often be described by Euler hydrodynamic equations in the limit of long wavelengths and low frequencies. Recently such a classical hydrodynamic framework, now dubbed…
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge…
This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…
We show that the following three systems related to various hydrodynamical approximations: the Korteweg--de Vries equation, the Camassa--Holm equation, and the Hunter--Saxton equation, have the same symmetry group and similar bihamiltonian…
Since its very beginnings, topology has forged strong links with physics and the last Nobel prize in physics, awarded in 2016 to Thouless, Haldane and Kosterlitz " for theoretical discoveries of topological phase transitions and topological…
We develop a general hydrodynamic theory describing a system of interacting actively propelling particles of arbitrary shape suspended in a viscous fluid. We model the active part of the particle motion using a slip velocity prescribed on…
Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the…
In rapidly rotating bose systems we show that there is a region of anomalous hydrodynamics whilst the system is still condensed, which coincides with the mean field quantum Hall regime. An immediate consequence is the absence of a normal…
We have applied the Andreev-Lifshitz hydrodynamic theory of supersolids to an ordinary solid. This theory includes an internal pressure $P$, distinct from the applied pressure $P_a$ and the stress tensor $\lambda_{ik}$. Under uniform static…
The theory of uniformly hyperbolic dynamical systems was initiated in the 1960's (though its roots stretch far back into the 19th century) by S. Smale, his students and collaborators, in the west, and D. Anosov, Ya. Sinai, V. Arnold, in the…
In this paper, we describe a new hydrodynamics code for 1D and 2D astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian…
In his famous undergraduate physics lectures, Richard Feynman remarked about the problem of fluid turbulence: "Nobody in physics has really been able to analyze it mathematically satisfactorily in spite of its importance to the sister…
We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with…
We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the…
The purpose of the current paper is twofold: to provide a conceptual link between the quantization framework based on Lie integration of algebroids proposed by N.P. Landsman in the book "Mathematical Topics between Classical and Quantum…
Building upon the recent findings regarding inverse phase transitions in the early universe, we present the first natural realisation of this phenomenon within a supersymmetry-breaking sector. We demonstrate that inverse hydrodynamics,…