Related papers: Mixing at the Batchelor Scale for White-In-Time Fl…
We solve the set of hydrodynamic (HD) equations for optically thin Advection Dominated Accretion Flows (ADAFs) by assuming radially self-similar in spherical coordinate system $ (r, \theta, \phi) $. The disk is considered to be steady state…
We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle…
Two-dimensional Boussinesq convection is studied numerically with very fine spatial resolutions up to 4096^2. Our numerical study starts with a smooth asymmetric initial condition, which is chosen to make the flow field well confined in the…
We extend the well-known Serrin's blowup criterion for the three-dimensional (3D) incompressible Navier-Stokes equations to the 3D viscous compressible cases. It is shown that for the Cauchy problem of the 3D compressible Navier-Stokes…
A general analytic solution to the fractional advection diffusion equation is obtained in plane parallel geometry. The result is an infinite series of spatial Fourier modes which decay according to the Mittag-Leffler function, which is cast…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
We solve the two-dimensional hydrodynamic equations of hot accretion flow in the presence of the thermal conduction. The flow is assumed to be in steady-state and axisymmetric, and self-similar approximation is adopted in the radial…
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the $L^q$-energy inequality and speed estimate in Wasserstein spaces under some integrability conditions on the drift term.…
We prove that an implicit time Euler scheme for the 2D-Boussinesq model on the torus $D$ converges. Various moment of the $W^{1,2}$-norms of the velocity and temperature, as well as their discretizations, are computed. We obtain the optimal…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…
Mixing fronts form when fluids with different chemical compositions are brought into contact. They influence a large range of biogeochemical processes in hydrological systems. An important mechanism governing mixing rates in such fronts is…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. That corresponds to the…
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary…
We study the low Mach number limit for a viscous compressible two-fluid model with algebraic pressure closure in the three-dimensional torus $\mathbb{T}^3$. The pressure is determined implicitly through the densities of the two phases,…
We use Diffusing Wave Spectroscopy (DWS) to perform the first direct space- and time-resolved measurement of the dissipation rate~$\epsilon$ at the boundary of a turbulent flow. We have shown in a previous publication that this technique…
A grid of numerical simulations of double-diffusive convection is presented for astrophysical conditions. As in laboratory and geophysical cases convection takes place in a layered form. A translation between the astrophysical fluid…