943 research outputs found
Superposition in nonlinear wave and evolution equations
Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme
superposition procedure are presented and used to generate superposition
solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE)
and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages,
2 figures, style change
Excision for simplicial sheaves on the Stein site and Gromov's Oka principle
A complex manifold satisfies the Oka-Grauert property if the inclusion
\Cal O(S,X) \hookrightarrow \Cal C(S,X) is a weak equivalence for every Stein
manifold , where the spaces of holomorphic and continuous maps from to
are given the compact-open topology. Gromov's Oka principle states that if
has a spray, then it has the Oka-Grauert property. The purpose of this
paper is to investigate the Oka-Grauert property using homotopical algebra. We
embed the category of complex manifolds into the model category of simplicial
sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert
property is equivalent to representing a finite homotopy sheaf on the Stein
site. This expresses the Oka-Grauert property in purely holomorphic terms,
without reference to continuous maps.Comment: Version 3 contains a few very minor improvement
Random perfect lattices and the sphere packing problem
Motivated by the search for best lattice sphere packings in Euclidean spaces
of large dimensions we study randomly generated perfect lattices in moderately
large dimensions (up to d=19 included). Perfect lattices are relevant in the
solution of the problem of lattice sphere packing, because the best lattice
packing is a perfect lattice and because they can be generated easily by an
algorithm. Their number however grows super-exponentially with the dimension so
to get an idea of their properties we propose to study a randomized version of
the algorithm and to define a random ensemble with an effective temperature in
a way reminiscent of a Monte-Carlo simulation. We therefore study the
distribution of packing fractions and kissing numbers of these ensembles and
show how as the temperature is decreased the best know packers are easily
recovered. We find that, even at infinite temperature, the typical perfect
lattices are considerably denser than known families (like A_d and D_d) and we
propose two hypotheses between which we cannot distinguish in this paper: one
in which they improve Minkowsky's bound phi\sim 2^{-(0.84+-0.06) d}, and a
competitor, in which their packing fraction decreases super-exponentially,
namely phi\sim d^{-a d} but with a very small coefficient a=0.06+-0.04. We also
find properties of the random walk which are suggestive of a glassy system
already for moderately small dimensions. We also analyze local structure of
network of perfect lattices conjecturing that this is a scale-free network in
all dimensions with constant scaling exponent 2.6+-0.1.Comment: 19 pages, 22 figure
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Tunable Nanometer Electrode Gaps by MeV Ion Irradiation
We report the use of MeV ion-irradiation-induced plastic deformation of amorphous materials to fabricate electrodes with nanometer-sized gaps. Plastic deformation of the amorphous metal is induced by ion irradiation, allowing the complete closing of a sub-micrometer gap. We measure the evolving gap size in situ by monitoring the field emission current-voltage (I-V) characteristics between electrodes. The I-V behavior is consistent with Fowler-Nordheim tunneling. We show that using feedback control on this signal permits gap size fabrication with atomic-scale precision. We expect this approach to nanogap fabrication will enable the practical realization of single molecule controlled devices and sensors.Engineering and Applied SciencesPhysic
Study of the 12C+12C fusion reactions near the Gamow energy
The fusion reactions 12C(12C,a)20Ne and 12C(12C,p)23Na have been studied from
E = 2.10 to 4.75 MeV by gamma-ray spectroscopy using a C target with ultra-low
hydrogen contamination. The deduced astrophysical S(E)* factor exhibits new
resonances at E <= 3.0 MeV, in particular a strong resonance at E = 2.14 MeV,
which lies at the high-energy tail of the Gamow peak. The resonance increases
the present non-resonant reaction rate of the alpha channel by a factor of 5
near T = 8x10^8 K. Due to the resonance structure, extrapolation to the Gamow
energy E_G = 1.5 MeV is quite uncertain. An experimental approach based on an
underground accelerator placed in a salt mine in combination with a high
efficiency detection setup could provide data over the full E_G energy range.Comment: 4 Pages, 4 figures, accepted for publication in Phys. Rev. Let
An interpolation theorem for proper holomorphic embeddings
Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and
a discrete sequence b_j in C^m where m > [3n/2], there exists a proper
holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,....
This is the interpolation version of the embedding theorem due to Eliashberg,
Gromov and Schurmann. The dimension m cannot be lowered in general due to an
example of Forster
Grothendieck groups and a categorification of additive invariants
A topologically-invariant and additive homology class is mostly not a natural
transformation as it is. In this paper we discuss turning such a homology class
into a natural transformation; i.e., a "categorification" of it. In a general
categorical set-up we introduce a generalized relative Grothendieck group from
a cospan of functors of categories and also consider a categorification of
additive invariants on objects. As an example, we obtain a general theory of
characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic
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