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Diffusion of particles in complex fluids and gels is difficult to describe and often lies beyond the scope of the classical Stokes-Einstein relation. One of the main lines of research over the past few decades has sought to relate…
This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform…
We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…
Neglecting the second order corrections in weak lensing measurements can lead to a few percent uncertainties on cosmic shears, and becomes more important for cluster lensing mass reconstructions. Existing methods which claim to measure the…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
We investigate how the presence of a vertically sheared current affects wave statistics, including the probability of rogue waves, and apply it to a real-world case using measured spectral and shear current data from the Mouth of the…
In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…
In this paper, we first present a Gearhardt-Pr\"uss type theorem with a sharp bound for m-accretive operators. Then we give two applications: (1) give a simple proof of the result proved by Constantin et al. on relaxation enhancement…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
The dispersion and dissipation properties of a scheme are important to realize high-fidelity simulations of the compressible flow, especially the cases with broadband length scales. It has been recognized that the minimization of dispersion…
We prove dispersive estimates for two models~: the adjacency matrix on a discrete regular tree, and the Schr\"odinger equation on a metric regular tree with the same potential on each edge/vertex. The latter model can be thought of as an…
The large-distance approximation of a sandwich gravitational wave by a continuous but not necessarily smooth profile provides us with an approximate analytic description of particle motion in a gravitational wave as spelled out for the…
We solve the stationary Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosty in domains with unbounded outlets, in the case of shear thickening viscosity, i.e. the viscosity is given by the shear…
For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the $N$-th order Born approximation gives the exact solution of…
Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order…
This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena,…
The influence of a small relative density difference on the displacement of two miscible liquids is studied experimentally in transparent 2D networks of micro channels. Both stable displacements in which the denser fluid enters at the…
In finite-volume-based flow simulations, absorbing layers are widely used to reduce pressure wave reflections at boundaries of the computational domain. A disadvantage of absorbing layers is that they contain case-dependent parameters; thus…
A general dispersion-dissipation condition for finite difference schemes is derived by analyzing the numerical dispersion and dissipation of explicit finite-difference schemes. The proper dissipation required to damp spurious…
A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous…