Related papers: Nonequilibrium liquid theory for sheared granular …
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general…
Mode-coupling theory (MCT) of sheared dense granular liquids %in the vicinity of jamming transition is formulated. Starting from the Liouville equation of granular particles, the generalized Langevin equation is derived with the aid of the…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…
In this paper, we consider the advective unstable Cahn-Hilliard equation in 2D with shear flow: \begin{equation*} \begin{cases} u_t+Av_1(y) \partial_x u+\varepsilon \Delta^2 u= \Delta(a u^3+ b u^2) \quad & \quad \textrm{on} \quad \mathbb…
Shear viscosity of nuclear matter is extracted via the Green-Kubo formula and the Gaussian thermostated SLLOD algorithm (the shear rate method) in a periodic box by using an improved quantum molecular dynamic (ImQMD) model without mean…
The energy method, also known as the Reynolds-Orr equation, is widely utilized in predicting the unconditional stability threshold of shear flows owing to the zero contribution of nonlinear terms to the time derivative of perturbation…
A formal derivation of linear hydrodynamics for a granular fluid is given. The linear response to small spatial perturbations of the homogeneous reference state is studied in detail using methods of non-equilibrium statistical mechanics. A…
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
The aim of this paper is to present a modeling for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory (Ref. 6) is first generalized to take into account…
We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based on the corresponding elliptic Liouville type theorems and…
We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…
An equation of state of the hard sphere fluid which is not analytical at the freezing density is proposed and tested. The nonanalytical term is based on the the classical nucleation theory and is able to capture the observed ``anomalous…
We introduce a theory of "odd viscodiffusive fluids," which exhibit three-dimensional odd transport phenomena through the coupling of viscous and diffusive transport. In these fluids, diffusive fluxes may arise from orthogonal velocity…
The continuum theory of partially fluidized shear granular flows is tested and calibrated using two dimensional soft particle molecular dynamics simulations. The theory is based on the relaxational dynamics of the order parameter that…
This article is focused on a multidimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle arising form the theory of nematic liquid crystals. By using the method of characteristics, we…
Second-order phase transitions are characterized by a divergence of the spatial correlation length of the order parameter fluctuations. For confined systems, this is known to lead to remarkable equilibrium physical phenomena, including…
We revisit the paradigm of unified dark energy discussing in detail the averaging problem in this type of scenarios, highlighting the need for a full non-linear treatment. We also address the question of if and how models with one or…
The equations for a self-similar solution of an inviscid incompressible fluid are mapped into an integral equation which hopefully can be solved by iteration. It is argued that the exponent of the similarity are ruled by Kelvin's theorem of…