1,960 research outputs found
Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion
We consider the space-time evolution of initial discontinuities of depth and
flow velocity for an integrable version of the shallow water Boussinesq system
introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq
model" for which a flat water surface is modulationally stable, we speak below
of "positive dispersion" model. This model also appears as an approximation to
the equations governing the dynamics of polarisation waves in two-component
Bose-Einstein condensates. We describe its periodic solutions and the
corresponding Whitham modulation equations. The self-similar, one-phase wave
structures are composed of different building blocks which are studied in
detail. This makes it possible to establish a classification of all the
possible wave configurations evolving from initial discontinuities. The
analytic results are confirmed by numerical simulations
Quantifier elimination in ordered abelian groups
We give a new proof of quantifier elimination in the theory of all ordered
abelian groups in a suitable language. More precisely, this is only "quantifier
elimination relative to ordered sets" in the following sense. Each definable
set in the group is a union of a family of quantifier free definable sets,
where the parameter of the family runs over a set definable (with quantifiers)
in a sort which carries the structure of an ordered set with some additional
unary predicates.
As a corollary, we find that all definable functions in ordered abelian
groups are piecewise affine linear on finitely many definable pieces.Comment: 30 page
Comparative study of in situ and ex situ MgB2 films deposited by pulsed laser deposition
Two types of MgB2 films were prepared by pulsed laser deposition (PLD) with
in situ and ex situ annealing processes respectively. Significant differences
in properties between the two types of films were found. The ex situ MgB2 film
has a Tc of 38.1K, while the in situ film has a depressed Tc of 34.5K. The
resistivity at 40K for the in situ film is larger than that of the ex situ film
by a factor of 6. The residual resistivity ratios (RRR) are 1.1 and 2.1 for the
in situ and ex situ films respectively. The Jc-H curves of the in situ film
show a much weaker field dependence than those of the ex situ film,
attributable to stronger flux pinning in the in situ film. The small-grain
feature and high oxygen level may be critical for the significant improvement
of Jc in the in situ annealed MgB2 film.Comment: 6 pages, 6 figure
Magnetic cloaking by a paramagnet/superconductor cylindrical tube in the critical state
Cloaking of static magnetic fields by a finite thickness type-II
superconductor tube being in the full critical state and surrounded by a
coaxial paramagnet shell is studied. On the basis of exact solutions to the
Maxwell equations, it is shown that, additionally to previous studies assuming
the Meissner state of the superconductor constituent, perfect cloaking is still
realizable at fields higher than the field of full flux penetration into the
superconductor and for arbitrary geometrical parameters of both constituents.
It is also proven that simultaneously the structure is fully undetectable under
the cloaking conditions. Differently from the case of the Meissner state the
cloaking properties in the application relevant critical state are realized,
however, only at a certain field magnitude.Comment: 5 pages, 4 figures; to be published in Applied Physics Letters. arXiv
admin note: substantial text overlap with arXiv:1401.356
Towards an ASM thesis for reflective sequential algorithms
Starting from Gurevich's thesis for sequential algorithms (the so-called
"sequential ASM thesis"), we propose a characterization of the behaviour of
sequential algorithms enriched with reflection. That is, we present a set of
postulates which we conjecture capture the fundamental properties of reflective
sequential algorithms (RSAs). Then we look at the plausibility of an ASM thesis
for the class of RSAs, defining a model of abstract state machine (which we
call reflective ASM) that we conjecture captures the class of RSAs as defined
by our postulates
Descriptive Complexity of Deterministic Polylogarithmic Time and Space
We propose logical characterizations of problems solvable in deterministic
polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We
introduce a novel two-sorted logic that separates the elements of the input
domain from the bit positions needed to address these elements. We prove that
the inflationary and partial fixed point vartiants of this logic capture
PolylogTime and PolylogSpace, respectively. In the course of proving that our
logic indeed captures PolylogTime on finite ordered structures, we introduce a
variant of random-access Turing machines that can access the relations and
functions of a structure directly. We investigate whether an explicit predicate
for the ordering of the domain is needed in our PolylogTime logic. Finally, we
present the open problem of finding an exact characterization of
order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science
Giant molecular clouds as regions of particle acceleration
One of the most interesting results of investigations carried out on the satellites SAS-II and COS-B is the discovery of unidentified discrete gamma sources. Possibly a considerable part of them may well be giant molecular clouds. Gamma emission from clouds is caused by the processes with participation of cosmic rays. The estimation of the cosmic ray density in clouds has shown that for the energy E approx. = I GeV their density can 10 to 1000 times exceed the one in intercloud space. We have made an attempt to determine the mechanism which could lead to the increase in the cosmic ray density in clouds
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