Related papers: Stokes flow analogous to viscous electron current …
We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…
Electron transport through a nanostructure can be characterized in part using concepts from classical fluid dynamics. It is thus natural to ask how far the analogy can be taken, and whether the electron liquid can exhibit nonlinear…
We investigate the effects of a two-dimensional, incompressible, turbulent flow on mono-disperse soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag (measured through the Stokes…
Motivated by recent experimental progress in preparing encapsulated graphene sheets with ultra-high mobilities up to room temperature, we present a theoretical study of dc transport in doped graphene in the hydrodynamic regime. By using the…
This paper seeks to carry out the rigorous homogenization of a particulate flow consisting of a non-dilute suspension of a viscous Newtonian fluid with magnetizable particles. The fluid is assumed to be described by the Stokes flow, while…
The electro-osmotic flow through a channel between two undulated surfaces induced by an external electric field is investigated. The gap of the channel is very small and comparable to the thickness of the electrical double layers. A lattice…
We study the Stokes-transport system in a two-dimensional channel with horizontally moving boundaries, which serves as a reduced model for oceanography and sedimentation. The density is transported by the velocity field, satisfying the…
Conventionally, a microscopic particle that performs a reciprocal stroke cannot move through its environment. This is because at small scales, the response of simple Newtonian fluids is purely viscous and flows are time-reversible. We show…
The similarity between electromagnetics and hydrodynamics has been noticed for a long time. Maxwell developed an analogy, where the magnetic field and the vector potential in electromagnetics are compared to the vorticity and velocity in…
Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the…
The stability of a flow of an electrically conducting, incompressible fluid in a channel with an imposed uniform wall-normal magnetic field and electrically insulating walls is studied using linear stability analysis and direct numerical…
The appearance of sharp vorticity gradients in two-dimensional hydrodynamic turbulence and their influence on the turbulent spectra is considered. We have developed the analog of the vortex line representation as a transformation to the…
We measure transport through a Ga[Al]As heterostructure at temperatures between 0.1 K and 30 K. Increasing the temperature enhances the electron-electron scattering rate and viscous effects in the two-dimensional electron gas arise. To…
We present numerical studies for finitely extensible nonlinear elastic (FENE) dumbbells which are dispersed in a turbulent plane shear flow at moderate Reynolds number. The polymer ensemble is described on the mesoscopic level by a set of…
`More is Different' (Anderson, 1972) in graphene. A bilayer and a twist spring surprises. Recently discovered superconductivity (T$_c\approx$ 1.7 K) at an ultra low doping density $\sim 10^{11}$cm${}^{-2}$ has alerted the community to look…
Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behaviour. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence - a unique, chaotic…
In very clean solid-state systems, where carrier-carrier interactions dominate over any other scattering mechanisms, the flow of electrons can be described within a hydrodynamic framework. In these cases, analogues of viscous fluid…
Stokes drift has been as central to the history of wave theory as it has been distressingly absent from experiment. Neither wave tanks nor experiments in open bodies detect this without nearly canceling "eulerian flows." Acoustic waves have…
Vortices in the simplest superconducting state of graphene contain very low energy excitations, whose existence is connected to an index theorem that applies strictly to an approximate form of the relevant Bogoliubov-deGennes equations.…
The equations of viscous evolution of 3D arbitrarily shaped vortices in an isotropic type II superconductor and necessary boundary conditions are formulated in the frame of London approximation. The theory is applied to analyse…