A general scheme for determining and studying hydrodynamic type systems describing integrable deformations of algebraic curves is applied to cubic curves. Lagrange resolvents of the theory of cubic equations are used to derive and characterize these deformations.

In this paper, we investigated the corrected plasmon dispersion relation for graphene in presence of a constant magnetic field which it includes a quantum term arising from the collective electron density wave interference effects. By using quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, the longitudinal plasmons ar...

Granular assemblies –made up of macroscopic solid bodies undergoing dissipative interactions– have been shown [1, 2] to frequently exhibit flows similar to those of normal fluids, and for practical purposes are often described by phenomenological hydrodynamic equations, i.e. equations for the density, flow velocity and energy density. This is so even if energy is not a conserved variable (the c...

The equations of hydrodynamics are nonlinear partial differential equations, so they include the possibility of forming singularities in finite time. This means that hydrodynamic fields become infinite or at least non-smooth at points, lines, or even fractal objects. This mathematical possibility is the price one has to pay for the enormous conceptual simplification a continuum theory brings fo...

We address the problem of controllability MHD system in a rectangular domain with control prescribed on side boundary. identify necessary and sufficient condition data to be null-controllable, i.e., can driven zero state. also show that validity this allows states stirred each other. If is not satisfied, one move from state another help simple shear external magnetic force.

(abridged) We present a detailed derivation of simple hydrodynamic two-fluid model, which aims at the description phase separation non-entangled polymer solutions, where viscoelastic effects play role. It is directly based upon coarse-graining well-defined molecular such that all degrees freedom have clear and unambiguous interpretation. The considerations are free-energy functional, dynamics s...

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. Of particular ...

“Generalized Hydrodynamics” (GHD) stands for a model that describes one-dimensional integrable systems in quantum physics, such as ultra-cold atoms or spin chains. Mathematically, GHD corresponds to nonlinear equations of kinetic type, where the main unknown, statistical distribution function f(t,z,θ), lives phase space which is constituted by position variable z, and “kinetic” θ, actually wave...