21,922 research outputs found
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
We review the latest progress and properties of the families of bright and
dark one-dimensional periodic waves propagating in saturable Kerr-type and
quadratic nonlinear media. We show how saturation of the nonlinear response
results in appearance of stability (instability) bands in focusing (defocusing)
medium, which is in sharp contrast with the properties of periodic waves in
Kerr media. One of the key results discovered is the stabilization of
multicolor periodic waves in quadratic media. In particular, dark-type waves
are shown to be metastable, while bright-type waves are completely stable in a
broad range of energy flows and material parameters. This yields the first
known example of completely stable periodic wave patterns propagating in
conservative uniform media supporting bright solitons. Such results open the
way to the experimental observation of the corresponding self-sustained
periodic wave patterns.Comment: 29 pages, 10 figure
Master stability functions reveal diffusion-driven pattern formation in networks
We study diffusion-driven pattern-formation in networks of networks, a class
of multilayer systems, where different layers have the same topology, but
different internal dynamics. Agents are assumed to disperse within a layer by
undergoing random walks, while they can be created or destroyed by reactions
between or within a layer. We show that the stability of homogeneous steady
states can be analyzed with a master stability function approach that reveals a
deep analogy between pattern formation in networks and pattern formation in
continuous space.For illustration we consider a generalized model of ecological
meta-foodwebs. This fairly complex model describes the dispersal of many
different species across a region consisting of a network of individual
habitats while subject to realistic, nonlinear predator-prey interactions. In
this example the method reveals the intricate dependence of the dynamics on the
spatial structure. The ability of the proposed approach to deal with this
fairly complex system highlights it as a promising tool for ecology and other
applications.Comment: 20 pages, 5 figures, to appear in Phys. Rev. E (2018
D-Sphalerons and the Topology of String Configuration Space
We show that unstable D-branes play the role of ``D-sphalerons'' in string
theory. Their existence implies that the configuration space of Type II string
theory has a complicated homotopy structure, similar to that of an infinite
Grassmannian. In particular, the configuration space of Type IIA (IIB) string
theory on has non-trivial homotopy groups for all even
(odd).Comment: 29pp, harvmac (b),trivial typo fixe
Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF
A hybrid scheme obtained by combining 3DVar with the Assimilation in the
Unstable Subspace (3DVar-AUS) is tested in a QG model, under perfect model
conditions, with a fixed observational network, with and without observational
noise. The AUS scheme, originally formulated to assimilate adaptive
observations, is used here to assimilate the fixed observations that are found
in the region of local maxima of BDAS vectors (Bred vectors subject to
assimilation), while the remaining observations are assimilated by 3DVar.
The performance of the hybrid scheme is compared with that of 3DVar and of an
EnKF. The improvement gained by 3DVar-AUS and the EnKF with respect to 3DVar
alone is similar in the present model and observational configuration, while
3DVar-AUS outperforms the EnKF during the forecast stage. The 3DVar-AUS
algorithm is easy to implement and the results obtained in the idealized
conditions of this study encourage further investigation toward an
implementation in more realistic contexts
Statistical mechanics and stability of a model eco-system
We study a model ecosystem by means of dynamical techniques from disordered
systems theory. The model describes a set of species subject to competitive
interactions through a background of resources, which they feed upon.
Additionally direct competitive or co-operative interaction between species may
occur through a random coupling matrix. We compute the order parameters of the
system in a fixed point regime, and identify the onset of instability and
compute the phase diagram. We focus on the effects of variability of resources,
direct interaction between species, co-operation pressure and dilution on the
stability and the diversity of the ecosystem. It is shown that resources can be
exploited optimally only in absence of co-operation pressure or direct
interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended,
references adde
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