146 research outputs found
Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations
In this paper we perform the parameter-dependent center manifold reduction
near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf
bifurcations in delay differential equations (DDEs). This allows us to
initialize the continuation of codimension one equilibria and cycle
bifurcations emanating from these codimension two bifurcation points. The
normal form coefficients are derived in the functional analytic perturbation
framework for dual semigroups (sun-star calculus) using a normalization
technique based on the Fredholm alternative. The obtained expressions give
explicit formulas which have been implemented in the freely available numerical
software package DDE-BifTool. While our theoretical results are proven to apply
more generally, the software implementation and examples focus on DDEs with
finitely many discrete delays. Together with the continuation capabilities of
DDE-BifTool, this provides a powerful tool to study the dynamics near
equilibria of such DDEs. The effectiveness is demonstrated on various models
Existence and Stability of Standing Pulses in Neural Networks : I Existence
We consider the existence of standing pulse solutions of a neural network
integro-differential equation. These pulses are bistable with the zero state
and may be an analogue for short term memory in the brain. The network consists
of a single-layer of neurons synaptically connected by lateral inhibition. Our
work extends the classic Amari result by considering a non-saturating gain
function. We consider a specific connectivity function where the existence
conditions for single-pulses can be reduced to the solution of an algebraic
system. In addition to the two localized pulse solutions found by Amari, we
find that three or more pulses can coexist. We also show the existence of
nonconvex ``dimpled'' pulses and double pulses. We map out the pulse shapes and
maximum firing rates for different connection weights and gain functions.Comment: 31 pages, 29 figures, submitted to SIAM Journal on Applied Dynamical
System
An integrable discretization of the rational su(2) Gaudin model and related systems
The first part of the present paper is devoted to a systematic construction
of continuous-time finite-dimensional integrable systems arising from the
rational su(2) Gaudin model through certain contraction procedures. In the
second part, we derive an explicit integrable Poisson map discretizing a
particular Hamiltonian flow of the rational su(2) Gaudin model. Then, the
contraction procedures enable us to construct explicit integrable
discretizations of the continuous systems derived in the first part of the
paper.Comment: 26 pages, 5 figure
Nonradiating anapole modes in dielectric nanoparticles
Nonradiating current configurations attract attention of physicists for many years as possible models of stable atoms. One intriguing example of such a nonradiating source is known as 'anapole'. An anapole mode can be viewed as a composition of electric and toroidal dipole moments, resulting in destructive interference of the radiation fields due to similarity of their far-field scattering patterns. Here we demonstrate experimentally that dielectric nanoparticles can exhibit a radiationless anapole mode in visible. We achieve the spectral overlap of the toroidal and electric dipole modes through a geometry tuning, and observe a highly pronounced dip in the far-field scattering accompanied by the specific near-field distribution associated with the anapole mode. The anapole physics provides a unique playground for the study of electromagnetic properties of nontrivial excitations of complex fields, reciprocity violation and Aharonov-Bohm like phenomena at optical frequencies.The work of A.E.M. was supported by the Australian Research Council via Future
Fellowship program (FT110100037). The authors at DSI were supported by DSI core
funds. Fabrication, Scanning Electron Microscope Imaging and NSOM works were
carried out in facilities provided by SnFPC@DSI (SERC Grant 092 160 0139). Zhen Ying
Pan (DSI) is acknowledged for SEM imaging. Yi Zhou (DSI) is acknowledged for silicon
film growth. Leonard Gonzaga (DSI), Yeow Teck Toh (DSI) and Doris Ng (DSI) are
acknowledged for development of the silicon nanofabrication procedure. B.N.C.
acknowledges support from the Government of Russian Federation, Megagrant No.
14.B25.31.0019
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
We study the effects produced by competition of two physical mechanisms of
energy localization in inhomogeneous nonlinear systems. As an example, we
analyze spatially localized modes supported by a nonlinear impurity in the
generalized nonlinear Schr\"odinger equation and describe three types of
nonlinear impurity modes --- one- and two-hump symmetric localized modes and
asymmetric localized modes --- for both focusing and defocusing nonlinearity
and two different (attractive or repulsive) types of impurity. We obtain an
analytical stability criterion for the nonlinear localized modes and consider
the case of a power-law nonlinearity in detail. We discuss several scenarios of
the instability-induced dynamics of the nonlinear impurity modes, including the
mode decay or switching to a new stable state, and collapse at the impurity
site.Comment: 18 pages, 22 figure
Energy spectra of the ocean's internal wave field: theory and observations
The high-frequency limit of the Garrett and Munk spectrum of internal waves
in the ocean and the observed deviations from it are shown to form a pattern
consistent with the predictions of wave turbulence theory. In particular, the
high frequency limit of the Garrett and Munk spectrum constitutes an {\it
exact} steady state solution of the corresponding kinetic equation.Comment: 4 pages, one color figur
Discreteness-Induced Oscillatory Instabilities of Dark Solitons
We reveal that even weak inherent discreteness of a nonlinear model can lead
to instabilities of the localized modes it supports. We present the first
example of an oscillatory instability of dark solitons, and analyse how it may
occur for dark solitons of the discrete nonlinear Schrodinger and generalized
Ablowitz-Ladik equations.Comment: 11 pages, 4 figures, to be published in Physical Review Letter
Performance studies of the final prototype for the CASTOR forward calorimeter at the CMS experiment
We present performance results of the final prototype for the CASTOR quartz-tungsten sampling calorimeter, to be installed in the very forward region of the CMS experiment at the LHC. The energy linearity and resolution, the uniformity, as well as the spatial resolution of the prototype to electromagnetic and hadronic showers are studied with 10--200 GeV electrons, 20--350 GeV pions, and 50, 150 GeV muons in beam tests carried out at CERN/SPS in 2007
Equation-Free Analysis of Macroscopic Behavior in Traffic and Pedestrian Flow
Equation-free methods make possible an analysis of the evolution of a few
coarse-grained or macroscopic quantities for a detailed and realistic model
with a large number of fine-grained or microscopic variables, even though no
equations are explicitly given on the macroscopic level. This will facilitate a
study of how the model behavior depends on parameter values including an
understanding of transitions between different types of qualitative behavior.
These methods are introduced and explained for traffic jam formation and
emergence of oscillatory pedestrian counter flow in a corridor with a narrow
door
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