Related papers: Green function and singularities in Stokes flow co…
We study ($p$-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and…
A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a…
Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of…
The Green's function of the incompressible Stokes equations, the stokeslet, represents the singular flow due to a point force. Its classical value in an unbounded fluid has been extended near surfaces of various shapes, including flat walls…
We study the two-phase Stokes flow driven by surface tension for two fluids of different viscosities, separated by an asymptotically flat interface representable as graph of a differentiable function. The flow is assumed to be…
Fluids composed of chiral active components can exhibit odd viscosity, a property that breaks time-reversal and parity symmetries. We investigate the hydrodynamic response to monopole and dipole singularities in a compressible thin fluid…
The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to nontrivial shape dynamics and droplet motility. To understand this behavior, we derive an asymptotic solution for the fluid flow…
For the Stokes system in the half space, Kang [Math.~Ann.~2005] showed that a solution generated by a compactly supported, H\"older continuous boundary flux may have unbounded normal derivatives near the boundary. In this paper we first…
We develop a hydrodynamic framework for the interactions and collective dynamics of force dipoles embedded in a compressible fluid membrane supported by a shallow viscous subphase. Starting from the generalized two-dimensional Stokes…
A deep understanding of the physical interactions between nanoparticles and target cell membranes is important in designing efficient nanocarrier systems for drug delivery applications. Here, we present a theoretical framework to describe…
An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of…
In this note, we present Stokes' calculation of the force exerted by the fluid on an oscillating cylinder. While the calculation of the similar problem in the case of the sphere is treated in several textbooks, the case of the cylinder is…
In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new…
Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…
The Green's function approach of Giles and Pierce is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution…
This paper establishes the existence and uniqueness of classical solutions to the steady Triple-Deck equations, which describe incompressible boundary layer flow over localized roughness at high Reynolds numbers. The triple-deck theory was…
Ciliary flows are generated by a vast array of eukaryotic organisms, from unicellular algae to mammals, and occur in a range of different geometrical configurations. We employ a point torque -- or `rotlet' -- model to capture the…
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…
We study classical binary fluid mixtures in which densities vary on very short time (ps) and length (nm) scales, such that hydrodynamics does not apply. In a pure fluid with a localized heat pulse the breakdown of hydrodynamics was overcome…
The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic…