32,091 research outputs found
On the water-bag model of dispersionless KP hierarchy
We investigate the bi-Hamiltonian structure of the waterbag model of dKP for
two component case. One can establish the third-order and first-order
Hamiltonian operator associated with the waterbag model. Also, the dispersive
corrections are discussed.Comment: 19 page
On the Metric Dimension of Cartesian Products of Graphs
A set S of vertices in a graph G resolves G if every vertex is uniquely
determined by its vector of distances to the vertices in S. The metric
dimension of G is the minimum cardinality of a resolving set of G. This paper
studies the metric dimension of cartesian products G*H. We prove that the
metric dimension of G*G is tied in a strong sense to the minimum order of a
so-called doubly resolving set in G. Using bounds on the order of doubly
resolving sets, we establish bounds on G*H for many examples of G and H. One of
our main results is a family of graphs G with bounded metric dimension for
which the metric dimension of G*G is unbounded
Transverse electric plasmons in bilayer graphene
We predict the existence of transverse electric (TE) plasmons in bilayer
graphene. We find that their plasmonic properties are much more pronounced in
bilayer than in monolayer graphene, in a sense that they can get more localized
at frequencies just below ~eV for adequate doping values. This
is a consequence of the perfectly nested bands in bilayer graphene which are
separated by ~eV
An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
We propose an adaptive finite element method for the solution of a
coefficient inverse problem of simultaneous reconstruction of the dielectric
permittivity and magnetic permeability functions in the Maxwell's system using
limited boundary observations of the electric field in 3D. We derive a
posteriori error estimates in the Tikhonov functional to be minimized and in
the regularized solution of this functional, as well as formulate corresponding
adaptive algorithm. Our numerical experiments justify the efficiency of our a
posteriori estimates and show significant improvement of the reconstructions
obtained on locally adaptively refined meshes.Comment: Corrected typo
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Covariant Charges in Chern-Simons AdS_3 Gravity
We try to give hereafter an answer to some open questions about the
definition of conserved quantities in Chern-Simons theory, with particular
reference to Chern-Simons AdS_3 Gravity. Our attention is focused on the
problem of global covariance and gauge invariance of the variation of Noether
charges. A theory which satisfies the principle of covariance on each step of
its construction is developed, starting from a gauge invariant Chern-Simons
Lagrangian and using a recipe developed in gr-qc/0110104 and gr-qc/0107074 to
calculate the variation of conserved quantities. The problem to give a
mathematical well-defined expression for the infinitesimal generators of
symmetries is pointed out and it is shown that the generalized Kosmann lift of
spacetime vector fields leads to the expected numerical values for the
conserved quantities when the solution corresponds to the BTZ black hole. The
fist law of black holes mechanics for the BTZ solution is then proved and the
transition between the variation of conserved quantities in Chern-Simons AdS_3
Gravity theory and the variation of conserved quantities in General Relativity
is analysed in detail.Comment: 30 pages, no figures. References adde
Separable reduction theorems by the method of elementary submodels
We introduce an interesting method of proving separable reduction theorems -
the method of elementary submodels. We are studying whether it is true that a
set (function) has given property if and only if it has this property with
respect to a special separable subspace, dependent only on the given set
(function). We are interested in properties of sets "to be dense, nowhere
dense, meager, residual or porous" and in properties of functions "to be
continuous, semicontinuous or Fr\'echet differentiable". Our method of creating
separable subspaces enables us to combine our results, so we easily get
separable reductions of function properties such as "be continuous on a dense
subset", "be Fr\'echet differentiable on a residual subset", etc. Finally, we
show some applications of presented separable reduction theorems and
demonstrate that some results of Zajicek, Lindenstrauss and Preiss hold in
nonseparable setting as well.Comment: 27 page
Conditions implying regularity of the three dimensional Navier-Stokes equation
We obtain logarithmic improvements for conditions for regularity of the
Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda.
Some of the proofs make use of a stochastic approach involving Feynman-Kac like
inequalities. As part of the our methods, we give a different approach to a
priori estimates of Foias, Guillope and Temam.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints/
(Changes: this is a substantial rewrite of the previous version.
A note on maximal estimates for stochastic convolutions
In stochastic partial differential equations it is important to have pathwise
regularity properties of stochastic convolutions. In this note we present a new
sufficient condition for the pathwise continuity of stochastic convolutions in
Banach spaces.Comment: Minor correction
Estimates in the Hardy-Sobolev space of the annulus and stability result
The main purpose of this work is to establish some logarithmic estimates of
optimal type in the Hardy-Sobolev space
of an annular domain. These results are considered as a continuation of a
previous study in the setting of the unit disk by L. Baratchart and M. Zerner:
On the recovery of functions from pointwise boundary values in a Hardy-sobolev
class of the disk. J.Comput.Apll.Math 46(1993), 255-69 and by S. Chaabane and
I. Feki: Logarithmic stability estimates in Hardy-Sobolev spaces
. C.R. Acad. Sci. Paris, Ser. I 347(2009), 1001-1006.
As an application, we prove a logarithmic stability result for the inverse
problem of identifying a Robin parameter on a part of the boundary of an
annular domain starting from its behavior on the complementary boundary part.Comment: 14 pages. To be published in Czechoslovak Mathematical Journa
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