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We introduce an effective theory which extends hydrodynamics into a regime where the critical slowing down would otherwise make hydrodynamics inapplicable.
The hydrodynamic equations for a crystals with interstitials, taking into account the dissipative processes of the viscosity, heat conduction and the interstitial diffusion are derived. To achieve that we use the phenomenological approach…
We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…
This survey gives a basic demonstration of matrix hydrodynamics; the field pioneered by V. Zeitlin, where 2-D incompressible fluids are spatially discretized via quantization theory.
Liquid spreading in gas-liquid concurrent trickle-bed reactors is simulated using an Eulerian twofluid CFD approach. In order to propose a model that describes exhaustively all interaction forces acting on each fluid phase with an emphasis…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
In this paper we introduce a PDE system which aims at describing the dynamics of a dispersed phase of particles moving into an incompressible perfect fluid, in two space dimensions. The system couples a Vlasov-type equation and an…
It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…
The Smoothed Particle Hydrodynamics (SPH) is a particle-based, Lagrangian method for fluid-flow simulations. In this work, fundamental concepts of this method are first briefly recalled. Then, the ability to accurately model granular…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
By adopting the approximations suggested in the theory of thin shells, the hydrodynamic theory of liquid crystals established by Eriksen [Arch. Rational Mech. Anal. 4 (1960) 231; Trans. Soc. Rheol. 4 (1960) 29] and Leslie [Adv. Liq. Cryst.…
The advantages and disadvantages of two approaches to astrophysical hydrodynamics, Smoothed Particle Hydrodynamics and Adaptive Mesh Refinement, are briefly discussed together with some current problems of computational hydrodynamics.
The operator splitting approach applied to the Navier-Stokes equations, gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called…
We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means…
The theory of solute transfer and deposit growth in evaporating sessile drops on a plane substrate is presented. The main ideas and the principal equations are formulated. The problem is solved analytically for two important geometries:…
An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation the flow potential near a small…
Experimental methods allow the shape and chemical composition of solid surfaces to be controlled at a mesoscopic level. Exposing such structured substrates to a gas close to coexistence with its liquid can produce quite distinct adsorption…
This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel…
Understanding of the complex behavior of particles at surfaces requires detailed knowledge of both macroscopic and microscopic processes that take place; also certain processes depend critically on temperature and gas pressure. To link…
The paper considers the nonlinear electrodynamics type model and its relation with relativistic hydrodynamics with no dissipation (including string and membrane hydrodynamics). We are able to convert arbitrary flux of fluid to the family of…