Dynamics of bubbles in a two-component Bose-Einstein condensate

The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross--Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The B\'enard--von K\'arm\'an vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.Comment: 6 pages, 7 figure

Computing stationary free-surface shapes in microfluidics

A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven pressure and flow fields compete with the surface tension for the shape of a stationary free surface. The free surface shape is represented by the boundaries of finite elements that move according to the stress applied by the adjacent fluid. Additionally, the surface tends to minimize its free energy and by that adapts its curvature to balance the normal stress at the surface. The numerical approach consists of the iteration of two alternating steps: The solution of a fluidic problem in a prescribed domain with slip boundary conditions at the free surface and a consecutive update of the domain driven by the previously determined pressure and velocity fields. ...Comment: Revised versio

Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: B\'{e}nard Convection and Zonal flow

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Phys. Plasmas {\bf 15}, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven

Rhythmic inhibition allows neural networks to search for maximally consistent states

Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to search for network configurations that best reconcile external inputs with an internal consistency model encoded in the network connectivity. We show that Hebbian plasticity allows the networks to learn the consistency model by example. The search dynamics driven by rhythmic inhibition enable the described networks to solve difficult constraint satisfaction problems without making assumptions about the form of stochastic fluctuations in the network. We show that the search dynamics are well approximated by a stochastic sampling process. We use the described networks to reproduce perceptual multi-stability phenomena with switching times that are a good match to experimental data and show that they provide a general neural framework which can be used to model other 'perceptual inference' phenomena

Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate

The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean-field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.Comment: 5 pages, 4 figure

Lie conformal algebra cohomology and the variational complex

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a g-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.Comment: 56 page

The Unique Determination of Neuronal Currents in the Brain via Magnetoencephalography

The problem of determining the neuronal current inside the brain from measurements of the induced magnetic field outside the head is discussed under the assumption that the space occupied by the brain is approximately spherical. By inverting the Geselowitz equation, the part of the current which can be reconstructed from the measurements is precisely determined. This actually consists of only certain moments of one of the two functions specifying the tangential part of the current. The other function specifying the tangential part of the current as well as the radial part of the current are completely arbitrary. However, it is also shown that with the assumption of energy minimization, the current can be reconstructed uniquely. A numerical implementation of this unique reconstruction is also presented

Electrophoresis of a polyelectrolyte through a nanopore

A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a weak dependence of the translocation speed on polymer length that is not accounted for by the present model. It is hypothesized that this is due to secondary effects that are neglected here.Comment: 5 pages, 2 column, 2 figure

Stratified shear flow instabilities at large Richardson numbers

Numerical simulations of stratified shear flow instabilities are performed in two dimensions in the Boussinesq limit. The density variation length scale is chosen to be four times smaller than the velocity variation length scale so that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the choice of the global Richardson number Ri. Three different values of Ri were examined Ri =0.2, 2, 20. The flows for the three examined values are all unstable due to different modes namely: the Kelvin-Helmholtz mode for Ri=0.2, the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has been discovered recently and it is the first time that it is examined in the non-linear stage. It is found that the amplitude of the velocity perturbation of the second Holmboe mode at the non-linear stage is smaller but comparable to first Holmboe mode. The increase of the potential energy however due to the second Holmboe modes is greater than that of the first mode. The Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy than the Holmboe modes and about ten times larger in potential energy than the Holmboe modes. The results in this paper suggest that although mixing is suppressed at large Richardson numbers it is not negligible, and turbulent mixing processes in strongly stratified environments can not be excluded.Comment: Submitted to Physics of Fluid

Crossover between Kelvin-Helmholtz and counter-superflow instabilities in two-component Bose-Einstein condensates

Dynamical instabilities at the interface between two Bose--Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin--Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.Comment: 10 pages, 9 figure