Related papers: Boussinesq-like problems in discrete media
We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore…
We present a simple stochastic quadrant model for calculating the transport and de- position of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a…
We study the statistical properties of the yielding transition in model amorphous solids in the limit of slow, athermal deformation. Plastic flow occurs via alternating phases of elastic loading punctuated by rapid dissipative events in the…
We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface fluid. In such a fluid the rheological behaviour at the interface includes surface viscosity effects, in addition to the classical surface tension effects. We…
We consider the 2D Boussinesq equations with a velocity damping term in a strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical scenario, where the \textit{Boussinesq approximation} is accurate when density/temperature…
The present paper studies finite element discretizations of second-order elliptic boundary value problems with homogeneous right-hand side and inhomogeneous boundary conditions. We establish discrete spatial decay estimates on element…
This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we…
The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their…
Stress transmission inside three dimensional granular packings is investigated using computer simulations. Localized force perturbation techniques are implemented for frictionless and frictional shallow, ordered, granular arrays confined by…
The transmission of forces through a disordered granular system is studied by means of a geometrical-topological approach that reduces the granular packing into a set of layers. This layered structure constitutes the skeleton through which…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on…
We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a…
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We…
We present a comprehensive review of the discrete Boussinesq equations based on their three-component forms on an elementary quadrilateral. These equations were originally found by Nijhoff et al using the direct linearization method and…
In a recent letter (Denkov et al., Phys. Rev. Lett., vol. 100 (2008) p. 138301) we calculated theoretically the macroscopic viscous stress of steadily sheared foam/emulsion from the energy dissipated inside the transient planar films,…
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…
The article deals with the description of the statistical behavior of Gaussian packets on a metric graph. Semiclassical asymptotics of solutions of the Cauchy problem for the Schr\"{o}dinger equation with initial data concentrated in the…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…