Related papers: Mixing and Small-Scale Formation in a Passive Dive…
This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…
In this paper, we prove a new identity for divergence free vector fields, showing that \begin{equation*} \left<-\Delta S,\omega\otimes\omega\right>=0, \end{equation*} where $S_{ij}=\frac{1}{2}\left(\partial_iu_j+\partial_ju_i\right)$ is the…
We study numerically joint mixing of salt and colloids by a chaotic velocity field $\mathbf{V}$, and how salt inhomogeneities accelerate or delay colloid mixing by inducing a velocity drift $\mathbf{V}_{\rm dp}$ between colloids and fluid…
Mixing of binary fluids by moving stirrers is a commonplace process in many industrial applications, where even modest improvements in mixing efficiency could translate into considerable power savings or enhanced product quality. We propose…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
An elegant model for passive scalar mixing was given by Kraichnan assuming the velocity to be delta-correlated in time. We generalize this model to include the effects of a finite correlation time, $\tau$, using renewing flows. The…
Numerous mixing strategies in microfluidic devices rely on chaotic advection by time-dependent body forces. The question of determining the required forcing function to achieve optimal mixing at a given kinetic energy or power input remains…
In this paper, we investigate the use of compactly supported divergence-free wavelets for the representation of the Navier-Stokes solution. After reminding the theoretical construction of divergence-free wavelet vectors, we present in…
The vector $U$-bosons, or so called 'dark photons', are one of the possible candidates for the dark matter mediators. We present a procedure to derive theoretical constraints on the upper limit of kinetic mixing parameter $\epsilon^2(M_U)$…
We study the Cauchy problem for the advection-diffusion equation $\partial_t u + \mathrm{div} (u b ) = \Delta u$ associated with a merely integrable divergence-free vector field $b$ defined on the torus. We discuss existence, regularity and…
We quantitatively study the interaction between diffusion and mixing in both the continuous, and discrete time setting. In discrete time, we consider a mixing dynamical system interposed with diffusion. In continuous time, we consider the…
This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise…
We study the mixing and dissipation properties of the advection-diffusion equation with diffusivity $0 < \kappa \ll 1$ and advection by a class of random velocity fields on $\mathbb T^d$, $d=\{2,3\}$, including solutions of the 2D…
The compelling experimental evidences for oscillations of solar and atmospheric neutrinos imply the existence of 3-neutrino mixing in vacuum. We briefly review the phenomenology of 3-neutrino mixing, and the current data on the 3-neutrino…
We introduce a class of divergence-free vector fields on $\mathbb{R}^3$ obtained after a suitable localization of Beltrami fields. First, we use them as initial data to construct unique global smooth solutions of the three dimensional…
We systematically construct flipped SU(5) X U(1)_X models without and with bulk vector-like particles from F-theory. To realize the decoupling scenario, we introduce sets of vector-like particles in complete SU(5) X U(1) multiplets at the…
A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear…
We introduce and analyze a partially augmented fully-mixed formulation and a mixed finite element method for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and…
In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…
Many neutrino mixing scenarios that have \mu-\tau symmetry with \theta_{13}=0 are in disagreement with recent experimental results that indicate a nonzero value for \theta_{13}. We investigate the effect of small perturbations on Majorana…