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Turbulent wall flows offer the most direct means for understanding the effects of boundaries and viscosity on turbulent fluctuations. Available data on mean-square fluctuations in these flows show apparent contradiction with classical…
In this paper, the solutions of Navier-Stokes equations with Dirichlet boundary conditions governing 2-D incompressible fluid flows are considered. A condition for boundary layer separation, which is determined by initial values and…
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow time scale. By generalizing the multiple-scale weakly nonlinear expansion…
We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and…
We provide a new convergence proof of the celebrated Merriman-Bence-Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface tensions and mobilities, including typical…
Two-dimensional (axially symmetric) numerical hydrodynamical calculations of accretion flows which cannot cool through emission of radiation are presented. The calculations begin from an equilibrium configuration consisting of a thick torus…
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
The linear response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceeding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are…
We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting $N$-particle system, and the $N$ times tensorized product of solution to the corresponding limit nonlinear conservation law. It…
Statistical surrogate modeling of fluid flows is hard because dynamics are multiscale and highly sensitive to initial conditions. Conditional diffusion surrogates can be accurate, but usually need hundreds of stochastic sampling steps. We…
In this paper, we consider an aggregation equation with fractional diffusion and large shear flow, which arise from modelling chemotaxis in bacteria. Without the advection, the solution of aggregation equation may blow up in finite time.…
We establish a set of equations for moments of the distribution function. In the relaxation time approximations, these moments obey a coupled set of equations that can be truncated order-by-order. Solving the equations of moments, we are…
We prove a complete family of `cylindrical estimates' for solutions of a class of fully non-linear curvature flows, generalising the cylindrical estimate of Huisken-Sinestrari for the mean curvature flow. More precisely, we show that, for…
Taylor dispersion in periodic but highly corrugated channels is studied. Exact analytical expressions for the long-time diffusion constant and drift along the channel are derived to next-to-leading order in the limit of small channel…
Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…
We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…