Related papers: Nonequilibrium liquid theory for sheared granular …
This article examines the Bouton-Lie group invariants of the Navier-Stokes equation (NSE) for incompressible fluids. Bouton's theory is applied to the general scaling transformation admitted by the NSE and is used to derive all self-similar…
Disordered hyperuniform structures are an exotic state of matter having vanishing long-wavelength density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought…
We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite…
Interacting quantum many-body systems constitute a fascinating playground for researchers since they form quantum liquids with correlated ground states and low-lying excitations, which exhibit universal behaviour. In fermionic systems, such…
Percus showed that approximate theories for the structure of nonuniform hard sphere fluids can be generated by linear truncations of functional expansions of the nonuniform density rho (r) about that of an appropriately chosen uniform…
The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at…
We derive the representation of the nonequilibrium steady-state distribution function which is expressed in terms of the excess free energy production. This representation resembles the one derived recently by Komatsu and Nakagawa [Phys.…
It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution…
A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence…
In this paper, basing on a generalized Newtonian dynamics (GND) approach which has been proposed elsewhere we present a conjecture for turbulent flow. We firstly utilize the GND to reasonably unify the two phenomenological methods recently…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…
Liouville-type theorems for the steady incompressible Navier-Stokes system are investigated for solutions in a three-dimensional slab with either no-slip boundary conditions or periodic boundary conditions. When the no-slip boundary…
In this paper we show that steady states $u$ of the pressureless Euler equation which belong to $L^3_{loc}(\mathbb{R}^2,\mathbb{R}^2)$ are shear flows. This is achieved by combining results of degenerate Monge-Amp\`ere-type equations with…
Ancient solutions arise in the study of parabolic blow-ups. If we can categorize ancient solutions, we can better understand blow-up limits. Based on an argument of Giga and Kohn, we give a Liouville-type theorem restricting ancient,…
General theoretical results via a Hamiltonian formulation are developed for zonal shear flows with the inclusion of the vortex stretching effect of the deformed free surface. These results include a generalization of the…
We study a complex Ginzburg-Landau (GL) type model related to fluid instabilities in the boundary of magnetized toroidal plasmas (called edge-localized modes) with a prescribed shear flow on the Neumann boundary condition. We obtain the…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
The BGK model kinetic equation is applied to spatially inhomogeneous states near steady uniform shear flow. The shear rate of the reference steady state can be large so the states considered include those very far from equilibrium. The…