94,402 research outputs found
Multi-breathers and high order rogue waves for the nonlinear Schr\"odinger equation on the elliptic function background
We construct the multi-breather solutions of the focusing nonlinear
Schr\"odinger equation (NLSE) on the background of elliptic functions by the
Darboux transformation, and express them in terms of the determinant of theta
functions. The dynamics of the breathers in the presence of various kinds of
backgrounds such as dn, cn, and non-trivial phase-modulating elliptic solutions
are presented, and their behaviors dependent on the effect of backgrounds are
elucidated. We also determine the asymptotic behaviors for the multi-breather
solutions with different velocities in the limit , where the
solution in the neighborhood of each breather tends to the simple one-breather
solution. Furthermore, we exactly solve the linearized NLSE using the squared
eigenfunction and determine the unstable spectra for elliptic function
background. By using them, the Akhmediev breathers arising from these
modulational instabilities are plotted and their dynamics are revealed.
Finally, we provide the rogue-wave and higher-order rogue-wave solutions by
taking the special limit of the breather solutions at branch points and the
generalized Darboux transformation. The resulting dynamics of the rogue waves
involves rich phenomena: depending on the choice of the background and
possessing different velocities relative to the background. We also provide an
example of the multi- and higher-order rogue wave solution.Comment: 45 pages, 16 figure
Asymptotic behavior of the Poisson--Dirichlet distribution for large mutation rate
The large deviation principle is established for the Poisson--Dirichlet
distribution when the parameter approaches infinity. The result is
then used to study the asymptotic behavior of the homozygosity and the
Poisson--Dirichlet distribution with selection. A phase transition occurs
depending on the growth rate of the selection intensity. If the selection
intensity grows sublinearly in , then the large deviation rate function
is the same as the neutral model; if the selection intensity grows at a linear
or greater rate in , then the large deviation rate function includes an
additional term coming from selection. The application of these results to the
heterozygote advantage model provides an alternate proof of one of Gillespie's
conjectures in [Theoret. Popul. Biol. 55 145--156].Comment: Published at http://dx.doi.org/10.1214/105051605000000818 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Heuristic algorithms for the min-max edge 2-coloring problem
In multi-channel Wireless Mesh Networks (WMN), each node is able to use
multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004,
INFOCOM 2005) propose and study several such architectures in which a computer
can have multiple network interface cards. These architectures are modeled as a
graph problem named \emph{maximum edge -coloring} and studied in several
papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016).
Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an
alternative variant, named the \emph{min-max edge -coloring}.
The above mentioned graph problems, namely the maximum edge -coloring and
the min-max edge -coloring are studied mainly from the theoretical
perspective. In this paper, we study the min-max edge 2-coloring problem from a
practical perspective. More precisely, we introduce, implement and test four
heuristic approximation algorithms for the min-max edge -coloring problem.
These algorithms are based on a \emph{Breadth First Search} (BFS)-based
heuristic and on \emph{local search} methods like basic \emph{hill climbing},
\emph{simulated annealing} and \emph{tabu search} techniques, respectively.
Although several algorithms for particular graph classes were proposed by
Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques,
hypergraphs), we design the first algorithms for general graphs.
We study and compare the running data for all algorithms on Unit Disk Graphs,
as well as some graphs from the DIMACS vertex coloring benchmark dataset.Comment: This is a post-peer-review, pre-copyedit version of an article
published in International Computing and Combinatorics Conference
(COCOON'18). The final authenticated version is available online at:
http://www.doi.org/10.1007/978-3-319-94776-1_5
Z-D Brane Box Models and Non-Chiral Dihedral Quivers
Generalising ideas of an earlier work \cite{Bo-Han}, we address the problem of constructing Brane Box Models of what we call the Z-D Type from a new point of view, so as to establish the complete correspondence between these brane setups and orbifold singularities of the non-Abelian G generated by Z_k and D_d under certain group-theoretic constraints to which we refer as the BBM conditions. Moreover, we present a new class of quiver theories of the ordinary dihedral group d_k as well as the ordinary exceptionals E_{6,7,8} which have non-chiral matter content and discuss issues related to brane setups thereof
On the tau-functions of the Degasperis-Procesi equation
The DP equation is investigated from the point of view of
determinant-pfaffian identities. The reciprocal link between the
Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the
two-dimensional Toda system is used to construct the N-soliton solution of the
DP equation. The N-soliton solution of the DP equation is presented in the form
of pfaffian through a hodograph (reciprocal) transformation. The bilinear
equations, the identities between determinants and pfaffians, and the
-functions of the DP equation are obtained from the pseudo 3-reduction of
the two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and
Theoretical, to be publishe
- …