Moving walls accelerate mixing

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario,the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.Comment: 17 pages, 13 figures. PDFLaTeX with RevTeX 4-1 styl

Moving Walls and Geometric Phases

We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.Comment: 16 pages, 5 figure

Static continuous electrophoresis device

An apparatus is disclosed for carrying out a moving wall type electrophoresis process for separation of cellular particles. The apparatus includes a water-tight housing containing an electrolytic buffer solution. A separation chamber in the housing is defined by spaced opposed moving walls and spaced opposed side walls. Substrate assemblies, which support the moving wall include vacuum ports for positively sealing the moving walls against the substrate walls. Several suction conduits communicate with the suction ports and are arranged in the form of valleys in a grid plate. The raised land portion of the grid plat supports the substrate walls against deformation inwardly under suction. A cooling chamber is carried on the back side of plate. The apparatus also has tensioner means including roller and adjustment screws for maintaining the belts in position and a drive arrangement including an electric motor with a gear affixed to its output shaft. Electrode assemblies are disposed to provide the required electric field

Granular packings with moving side walls

The effects of movement of the side walls of a confined granular packing are studied by discrete element, molecular dynamics simulations. The dynamical evolution of the stress is studied as a function of wall movement both in the direction of gravity as well as opposite to it. For all wall velocities explored, the stress in the final state of the system after wall movement is fundamentally different from the original state obtained by pouring particles into the container and letting them settle under the influence of gravity. The original packing possesses a hydrostatic-like region at the top of the container which crosses over to a depth-independent stress. As the walls are moved in the direction opposite to gravity, the saturation stress first reaches a minimum value independent of the wall velocity, then increases to a steady-state value dependent on the wall-velocity. After wall movement ceases and the packing reaches equilibrium, the stress profile fits the classic Janssen form for high wall velocities, while it has some deviations for low wall velocities. The wall movement greatly increases the number of particle-wall and particle-particle forces at the Coulomb criterion. Varying the wall velocity has only small effects on the particle structure of the final packing so long as the walls travel a similar distance.Comment: 11 pages, 10 figures, some figures in colo

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.Comment: 13 pages, 2 figure

On Reduction of Critical Velocity in a Model of Superfluid Bose-gas with Boundary Interactions

The existence of superfluidity in a 3D Bose-gas can depend on boundary interactions with channel walls. We study a simple model where the dilute moving Bose-gas interacts with the walls via hard-core repulsion. Special boundary excitations are introduced, and their excitation spectrum is calculated within a semiclassical approximation. It turns out that the state of the moving Bose-gas is unstable with respect to the creation of these boundary excitations in the system gas + walls, i.e. the critical velocity vanishes in the semiclassical (Bogoliubov) approximation. We discuss how a condensate wave function, the boundary excitation spectrum and, hence, the value of the critical velocity can change in more realistic models, in which ``smooth'' attractive interaction between the gas and walls is taken into account. Such a surface mode could exist in ``soft matter'' containers with flexible walls.Comment: 9 pages (RevTeX), two figures (.ps) incorporated by epsf. submitted to Phys. Lett.

Simulations of Field Driven Domain Wall Interactions in Ferromagnetic Nanowires

The interaction of domain walls in a single ferromagnetic nanowire has been observed with micromagnetic simulation. Domain walls separating domains of opposite magnetization move towards each other when an external field is applied along the long axis of the wire resulting in a collision. The final magnetic state of the wire after the collision will contain either zero (domain wall annihilation) or two (domain wall conservation) domain walls. Here we explore the behavior that determines the final state, showing that it depends on the initial domain wall configuration, the speed the domain walls are moving with before the collision, and the dimensions of the nanowire. A model is also presented which helps to determine the repulsive force the conserved domain walls exert on each other