7,256 research outputs found
Vortex line representation for flows of ideal and viscous fluids
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid
coincides with the equations of motion of a charged {\it compressible} fluid
moving due to a self-consistent electromagnetic field. Transition to the
Lagrangian description in a new hydrodynamics is equivalent for the original
Euler equations to the mixed Lagrangian-Eulerian description - the vortex line
representation (VLR). Due to compressibility of a "new" fluid the collapse of
vortex lines can happen as the result of breaking (or overturning) of vortex
lines. It is found that the Navier-Stokes equation in the vortex line
representation can be reduced to the equation of the diffusive type for the
Cauchy invariant with the diffusion tensor given by the metric of the VLR
Evolutionary origin of power-laws in Biochemical Reaction Network; embedding abundance distribution into topology
The evolutionary origin of universal statistics in biochemical reaction
network is studied, to explain the power-law distribution of reaction links and
the power-law distributions of chemical abundances. Using cell models with
catalytic reaction network, we find evidence that the power-law distribution in
abundances of chemicals emerges by the selection of cells with higher growth
speeds. Through the further evolution, this inhomogeneity in chemical
abundances is shown to be embedded in the distribution of links, leading to the
power-law distribution. These findings provide novel insights into the nature
of network evolution in living cells.Comment: 11 pages, 3 figure
Derived categories of cubic fourfolds
We discuss the structure of the derived category of coherent sheaves on cubic
fourfolds of three types: Pfaffian cubics, cubics containing a plane and
singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page
Electric double layer effect on observable characteristics of the tunnel current through a bridged electrochemical contact
Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
We study possibilities to suppress the transverse modulational instability
(MI) of dark-soliton stripes in two-dimensional (2D) Bose-Einstein condensates
(BECs) and self-defocusing bulk optical waveguides by means of quasi-1D
structures. Adding an external repulsive barrier potential (which can be
induced in BEC by a laser sheet, or by an embedded plate in optics), we
demonstrate that it is possible to reduce the MI wavenumber band, and even
render the dark-soliton stripe completely stable. Using this method, we
demonstrate the control of the number of vortex pairs nucleated by each spatial
period of the modulational perturbation. By means of the perturbation theory,
we predict the number of the nucleated vortices per unit length. The analytical
results are corroborated by the numerical computation of eigenmodes of small
perturbations, as well as by direct simulations of the underlying
Gross-Pitaevskii/nonlinear Schr\"{o}dinger equation.Comment: 10 pages, 7 figures. To appear on Phys. Rev. A, 201
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