558 research outputs found
Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization
In this article, we study an analog of the Bj\"orling problem for isothermic
surfaces (that are more general than minimal surfaces): given a real analytic
curve in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and as principal directions of
curvature. We prove that solutions to that problem can be obtained by
constructing a family of discrete isothermic surfaces (in the sense of Bobenko
and Pinkall) from data that is sampled along , and passing to the limit
of vanishing mesh size. The proof relies on a rephrasing of the
Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its
discretization which is induced from the geometry of discrete isothermic
surfaces. The discrete-to-continuous limit is carried out for the Christoffel
and the Darboux transformations as well.Comment: 29 pages, some figure
Noise Induced Coherence in Neural Networks
We investigate numerically the dynamics of large networks of globally
pulse-coupled integrate and fire neurons in a noise-induced synchronized state.
The powerspectrum of an individual element within the network is shown to
exhibit in the thermodynamic limit () a broadband peak and an
additional delta-function peak that is absent from the powerspectrum of an
isolated element. The powerspectrum of the mean output signal only exhibits the
delta-function peak. These results are explained analytically in an exactly
soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript figure
Invariance Conditions for Nonlinear Dynamical Systems
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to
invariance condition of dynamical system, submitted to Applied Mathematics and
Computation}] proposed a novel unified approach to study, i.e., invariance
conditions, sufficient and necessary conditions, under which some convex sets
are invariant sets for linear dynamical systems.
In this paper, by utilizing analogous methodology, we generalize the results
for nonlinear dynamical systems. First, the Theorems of Alternatives, i.e., the
nonlinear Farkas lemma and the \emph{S}-lemma, together with Nagumo's Theorem
are utilized to derive invariance conditions for discrete and continuous
systems. Only standard assumptions are needed to establish invariance of
broadly used convex sets, including polyhedral and ellipsoidal sets. Second, we
establish an optimization framework to computationally verify the derived
invariance conditions. Finally, we derive analogous invariance conditions
without any conditions
Synchronisation in Coupled Sine Circle Maps
We study the spatially synchronized and temporally periodic solutions of a
1-d lattice of coupled sine circle maps. We carry out an analytic stability
analysis of this spatially synchronized and temporally periodic case and obtain
the stability matrix in a neat block diagonal form. We find spatially
synchronized behaviour over a substantial range of parameter space. We have
also extended the analysis to higher spatial periods with similar results.
Numerical simulations for various temporal periods of the synchronized
solution, reveal that the entire structure of the Arnold tongues and the
devil's staircase seen in the case of the single circle map can also be
observed for the synchronized coupled sine circle map lattice. Our formalism
should be useful in the study of spatially periodic behaviour in other coupled
map lattices.Comment: uuencoded, 1 rextex file 14 pages, 3 postscript figure
Nanoparticle synthesis using high-powered pulse-modulated induction thermal plasma
金沢大学理工研究域電子情報学系Nanoparticle synthesis was performed using the high-powered pulse-modulated induction thermal plasma (PMITP) technique to study the effect of coil current modulation on synthesized nanoparticles. This is the first paper to present a summary of results of TiO2 nanoparticle synthesis using high-power Ar-O2 PMITP at 20 kW. The synthesized particles were analysed using field emission scanning electron microscopy and X-ray diffractometry. In addition, optical emission spectroscopy was used during nanoparticle synthesis experiments to measure TiO spectra and to determine the time-averaged vibrational and rotational temperatures of TiO in the reaction chamber. The results showed that the PMITP produced smaller nanoparticles and a narrower size distribution of particles. Moreover, PMITP provided a lower temperature region in the reaction chamber downstream of the plasma torch than such regions in non-modulated thermal plasmas. © 2010 IOP Publishing Ltd
Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
Small lattices of nearest neighbor coupled excitable FitzHugh-Nagumo
systems, with time-delayed coupling are studied, and compared with systems of
FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of
equilibria in N=2 case are studied analytically, and it is then numerically
confirmed that the same bifurcations are relevant for the dynamics in the case
. Bifurcations found include inverse and direct Hopf and fold limit cycle
bifurcations. Typical dynamics for different small time-lags and coupling
intensities could be excitable with a single globally stable equilibrium,
asymptotic oscillatory with symmetric limit cycle, bi-stable with stable
equilibrium and a symmetric limit cycle, and again coherent oscillatory but
non-symmetric and phase-shifted. For an intermediate range of time-lags inverse
sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of
oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo
oscillators with the same type of coupling.Comment: accepted by Phys.Rev.
Emergent global oscillations in heterogeneous excitable media: The example of pancreatic beta cells
Using the standard van der Pol-FitzHugh-Nagumo excitable medium model I
demonstrate a novel generic mechanism, diversity, that provokes the emergence
of global oscillations from individually quiescent elements in heterogeneous
excitable media. This mechanism may be operating in the mammalian pancreas,
where excitable beta cells, quiescent when isolated, are found to oscillate
when coupled despite the absence of a pacemaker region.Comment: See home page http://lec.ugr.es/~julya
General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
An asymptotic method for finding instabilities of arbitrary -dimensional
large-amplitude patterns in a wide class of reaction-diffusion systems is
presented. The complete stability analysis of 2- and 3-dimensional localized
patterns is carried out. It is shown that in the considered class of systems
the criteria for different types of instabilities are universal. The specific
nonlinearities enter the criteria only via three numerical constants of order
one. The performed analysis explains the self-organization scenarios observed
in the recent experiments and numerical simulations of some concrete
reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E
(April 1st, 1996
The Shapes of Flux Domains in the Intermediate State of Type-I Superconductors
In the intermediate state of a thin type-I superconductor magnetic flux
penetrates in a disordered set of highly branched and fingered macroscopic
domains. To understand these shapes, we study in detail a recently proposed
"current-loop" (CL) model that models the intermediate state as a collection of
tense current ribbons flowing along the superconducting-normal interfaces and
subject to the constraint of global flux conservation. The validity of this
model is tested through a detailed reanalysis of Landau's original conformal
mapping treatment of the laminar state, in which the superconductor-normal
interfaces are flared within the slab, and of a closely-related straight-lamina
model. A simplified dynamical model is described that elucidates the nature of
possible shape instabilities of flux stripes and stripe arrays, and numerical
studies of the highly nonlinear regime of those instabilities demonstrate
patterns like those seen experimentally. Of particular interest is the buckling
instability commonly seen in the intermediate state. The free-boundary approach
further allows for a calculation of the elastic properties of the laminar
state, which closely resembles that of smectic liquid crystals. We suggest
several new experiments to explore of flux domain shape instabilities,
including an Eckhaus instability induced by changing the out-of-plane magnetic
field, and an analog of the Helfrich-Hurault instability of smectics induced by
an in-plane field.Comment: 23 pages, 22 bitmapped postscript figures, RevTex 3.0, submitted to
Phys. Rev. B. Higher resolution figures may be obtained by contacting the
author
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