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Interaction of a vortex ring with the free surface of ideal fluid
The interaction of a small vortex ring with the free surface of a perfect
fluid is considered. In the frame of the point ring approximation the
asymptotic expression for the Fourier-components of radiated surface waves is
obtained in the case when the vortex ring comes from infinity and has both
horizontal and vertical components of the velocity. The non-conservative
corrections to the equations of motion of the ring, due to Cherenkov radiation,
are derived.Comment: LaTeX, 15 pages, 1 eps figur
Dark matter-wave solitons in the dimensionality crossover
We consider the statics and dynamics of dark matter-wave solitons in the
dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial
Schr\"{o}dinger mean-field model, we find that the anomalous mode of the
Bogoliubov spectrum has an eigenfrequency which coincides with the soliton
oscillation frequency obtained by the 3D Gross-Pitaevskii model. We show that
substantial deviations (of order of 10% or more) from the characteristic
frequency ( being the longitudinal trap
frequency) are possible even in the purely 1D regime.Comment: Phys. Rev. A, in pres
Strong Equivalence Relations for Iterated Models
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical
representation, has become standard for applying topological reasoning to
distributed computing. Its modular structure makes it easier to analyze than
the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS).
It is known that AS and IIS are equivalent with respect to \emph{wait-free
task} computability: a distributed task is solvable in AS if and only if it
solvable in IIS. We observe, however, that this equivalence is not sufficient
in order to explore solvability of tasks in \emph{sub-models} of AS (i.e.
proper subsets of its runs) or computability of \emph{long-lived} objects, and
a stronger equivalence relation is needed. In this paper, we consider
\emph{adversarial} sub-models of AS and IIS specified by the sets of processes
that can be \emph{correct} in a model run. We show that AS and IIS are
equivalent in a strong way: a (possibly long-lived) object is implementable in
AS under a given adversary if and only if it is implementable in IIS under the
same adversary. %This holds whether the object is one-shot or long-lived.
Therefore, the computability of any object in shared memory under an
adversarial AS scheduler can be equivalently investigated in IIS
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