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The simulation of fibre orientation in dilute suspension with a front moving is carried out using the projection and level set methods. The motion of fibres is described using the Jeffery equation and the contribution of fibres to the flow…
For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first…
We revisit the variational characterization of conservative diffusion as entropic gradient flow and provide for it a probabilistic interpretation based on stochastic calculus. It was shown by Jordan, Kinderlehrer, and Otto that, for…
Lagrangian stochastic methods are widely used to model turbulent flows. Scarce consideration has, however, been devoted to the treatment of the near-wall region and to the formulation of a proper wall-boundary condition. With respect to…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
Suspensions of anisotropic particles are commonly encountered in a wide spectrum of applications, including industrial and architectural coatings, targeted drug delivery and manufacturing of fiber-reinforced composites. A grand challenge in…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion,…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
We investigate the orientational properties of a homogeneous and inhomogeneous tetrahedral 4-patch fluid (Kern--Frenkel model). Using integral equations, either (i) HNC or (ii) a modified HNC scheme with simulation input, the full…
We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By…
Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual…
We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The…
We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct…
This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…
We study properties of dilute polymer solutions which are known to depend strongly on polymer elongation. The probability density function (PDF) of polymer end-to-end extensions $R$ in turbulent flows is examined. We demonstrate that if the…
The purpose of the present paper is to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of the velocity field of a turbulent flow. The PDF PDE is a highly non-linear…
Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved…
Biological and synthetic microswimmers display a wide range of swimming trajectories depending on driving forces and torques. In this paper we consider a simple overdamped model of self-propelled particles with a constant self-propulsion…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…