1,208 research outputs found
Lyapunov spectral analysis of a nonequilibrium Ising-like transition
By simulating a nonequilibrium coupled map lattice that undergoes an
Ising-like phase transition, we show that the Lyapunov spectrum and related
dynamical quantities such as the dimension correlation length~ are
insensitive to the onset of long-range ferromagnetic order. As a function of
lattice coupling constant~ and for certain lattice maps, the Lyapunov
dimension density and other dynamical order parameters go through a minimum.
The occurrence of this minimum as a function of~ depends on the number of
nearest neighbors of a lattice point but not on the lattice symmetry, on the
lattice dimensionality or on the position of the Ising-like transition. In
one-space dimension, the spatial correlation length associated with magnitude
fluctuations and the length~ are approximately equal, with both
varying linearly with the radius of the lattice coupling.Comment: 29 pages of text plus 15 figures, uses REVTeX macros. Submitted to
Phys. Rev. E
Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics
Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue
Information Content of Spontaneous Symmetry Breaking
We propose a measure of order in the context of nonequilibrium field theory
and argue that this measure, which we call relative configurational entropy
(RCE), may be used to quantify the emergence of coherent low-entropy
configurations, such as time-dependent or time-independent topological and
nontopological spatially-extended structures. As an illustration, we
investigate the nonequilibrium dynamics of spontaneous symmetry-breaking in
three spatial dimensions. In particular, we focus on a model where a real
scalar field, prepared initially in a symmetric thermal state, is quenched to a
broken-symmetric state. For a certain range of initial temperatures,
spatially-localized, long-lived structures known as oscillons emerge in
synchrony and remain until the field reaches equilibrium again. We show that
the RCE correlates with the number-density of oscillons, thus offering a
quantitative measure of the emergence of nonperturbative spatiotemporal
patterns that can be generalized to a variety of physical systems.Comment: LaTeX, 9 pages, 5 figures, 1 tabl
Filament tension and phase-locked drift of meandering scroll waves
Rotating scroll waves are self-organising patterns which are found in many
oscillating or excitable systems. Here we show that quasi-periodic (meandering)
scroll waves, which include the rotors that organise cardiac arrhythmias,
exhibit filament tension when averaged over the meander cycle. With strong
filament curvature or medium thickness gradients, however, scroll wave dynamics
are governed by phase-locked drift instead of filament tension. Our results are
validated in computational models of cycloidal meander and a cardiac tissue
model with linear core.Comment: accepted for publication in Physical Review Letters (December 2017
Cavity Light Bullets: 3D Localized Structures in a Nonlinear Optical Resonator
We consider the paraxial model for a nonlinear resonator with a saturable
absorber beyond the mean-field limit and develop a method to study the
modulational instabilities leading to pattern formation in all three spatial
dimensions. For achievable parametric domains we observe total radiation
confinement and the formation of 3D localised bright structures. At difference
from freely propagating light bullets, here the self-organization proceeds from
the resonator feedback, combined with diffraction and nonlinearity. Such
"cavity" light bullets can be independently excited and erased by appropriate
pulses, and once created, they endlessly travel the cavity roundtrip. Also, the
pulses can shift in the transverse direction, following external field
gradients.Comment: 4 pages, 3 figures, simulations files available at
http://www.ba.infn.it/~maggipin/PRLmovies.htm, submitted to Physical Review
Letters on 24 March 200
Decoupling of brain function from structure reveals regional behavioral specialization in humans
The brain is an assembly of neuronal populations interconnected by structural
pathways. Brain activity is expressed on and constrained by this substrate.
Therefore, statistical dependencies between functional signals in directly
connected areas can be expected higher. However, the degree to which brain
function is bound by the underlying wiring diagram remains a complex question
that has been only partially answered. Here, we introduce the
structural-decoupling index to quantify the coupling strength between structure
and function, and we reveal a macroscale gradient from brain regions more
strongly coupled, to regions more strongly decoupled, than expected by
realistic surrogate data. This gradient spans behavioral domains from
lower-level sensory function to high-level cognitive ones and shows for the
first time that the strength of structure-function coupling is spatially
varying in line with evidence derived from other modalities, such as functional
connectivity, gene expression, microstructural properties and temporal
hierarchy
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