793 research outputs found
Collective behavior of heterogeneous neural networks
We investigate a network of integrate-and-fire neurons characterized by a
distribution of spiking frequencies. Upon increasing the coupling strength, the
model exhibits a transition from an asynchronous regime to a nontrivial
collective behavior. At variance with the Kuramoto model, (i) the macroscopic
dynamics is irregular even in the thermodynamic limit, and (ii) the microscopic
(single-neuron) evolution is linearly stable.Comment: 4 pages, 5 figure
Collective chaos in pulse-coupled neural networks
We study the dynamics of two symmetrically coupled populations of identical
leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon
varying the coupling strength, we find symmetry-breaking transitions that lead
to the onset of various chimera states as well as to a new regime, where the
two populations are characterized by a different degree of synchronization.
Symmetric collective states of increasing dynamical complexity are also
observed. The computation of the the finite-amplitude Lyapunov exponent allows
us to establish the chaoticity of the (collective) dynamics in a finite region
of the phase plane. The further numerical study of the standard Lyapunov
spectrum reveals the presence of several positive exponents, indicating that
the microscopic dynamics is high-dimensional.Comment: 6 pages, 5 eps figures, to appear on Europhysics Letters in 201
Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics
We study the effect of a higher-order nonlinearity in the standard
Kuramoto-Sivashinsky equation: \partial_x \tilde G(H_x). We find that the
stability of steady states depends on dv/dq, the derivative of the interface
velocity on the wavevector q of the steady state. If the standard nonlinearity
vanishes, coarsening is possible, in principle, only if \tilde G is an odd
function of H_x. In this case, the equation falls in the category of the
generalized Cahn-Hilliard equation, whose dynamical behavior was recently
studied by the same authors. Instead, if \tilde G is an even function of H_x,
we show that steady-state solutions are not permissible.Comment: 4 page
Collective Atomic Recoil Laser as a synchronization transition
We consider here a model previously introduced to describe the collective
behavior of an ensemble of cold atoms interacting with a coherent
electromagnetic field. The atomic motion along the self-generated
spatially-periodic force field can be interpreted as the rotation of a phase
oscillator. This suggests a relationship with synchronization transitions
occurring in globally coupled rotators. In fact, we show that whenever the
field dynamics can be adiabatically eliminated, the model reduces to a
self-consistent equation for the probability distribution of the atomic
"phases". In this limit, there exists a formal equivalence with the Kuramoto
model, though with important differences in the self-consistency conditions.
Depending on the field-cavity detuning, we show that the onset of synchronized
behavior may occur through either a first- or second-order phase transition.
Furthermore, we find a secondary threshold, above which a periodic self-pulsing
regime sets in, that is immediately followed by the unlocking of the
forward-field frequency. At yet higher, but still experimentally meaningful,
input intensities, irregular, chaotic oscillations may eventually appear.
Finally, we derive a simpler model, involving only five scalar variables, which
is able to reproduce the entire phenomenology exhibited by the original model
A new approach to partial synchronization in globally coupled rotators
We develop a formalism to analyze the behaviour of pulse--coupled identical
phase oscillators with a specific attention devoted to the onset of partial
synchronization. The method, which allows describing the dynamics both at the
microscopic and macroscopic level, is introduced in a general context, but then
the application to the dynamics of leaky integrate-and-fire (LIF) neurons is
analysed. As a result, we derive a set of delayed equations describing exactly
the LIF behaviour in the thermodynamic limit. We also investigate the weak
coupling regime by means of a perturbative analysis, which reveals that the
evolution rule reduces to a set of ordinary differential equations. Robustness
and generality of the partial synchronization regime is finally tested both by
adding noise and considering different force fields.Comment: 5 pages, 3 eps figure
Absence of stable collinear configurations in Ni(001)ultrathin films: canted domain structure as ground state
Brillouin light scattering (BLS) measurements were performed for (17-120)
Angstrom thick Cu/Ni/Cu/Si(001) films. A monotonic dependence of the frequency
of the uniform mode on an in-plane magnetic field H was observed both on
increasing and on decreasing H in the range (2-14) kOe, suggesting the absence
of a metastable collinear perpendicular ground state. Further investigation by
magneto-optical vector magnetometry (MOKE-VM) in an unconventional canted-field
geometry provided evidence for a domain structure where the magnetization is
canted with respect to the perpendicular to the film. Spin wave calculations
confirm the absence of stable collinear configurations.Comment: 6 pages, 3 figures (text, appendix and 1 figure added
Fracture precursors in disordered systems
A two-dimensional lattice model with bond disorder is used to investigate the
fracture behaviour under stress-controlled conditions. Although the cumulative
energy of precursors does not diverge at the critical point, its derivative
with respect to the control parameter (reduced stress) exhibits a singular
behaviour. Our results are nevertheless compatible with previous experimental
findings, if one restricts the comparison to the (limited) range accessible in
the experiment. A power-law avalanche distribution is also found with an
exponent close to the experimental values.Comment: 4 pages, 5 figures. Submitted to Europhysics Letter
Self-Consistent Mode-Coupling Approach to 1D Heat Transport
In the present Letter we present an analytical and numerical solution of the
self-consistent mode-coupling equations for the problem of heat conductivity in
one-dimensional systems. Such a solution leads us to propose a different
scenario to accomodate the known results obtained so far for this problem. More
precisely, we conjecture that the universality class is determined by the
leading order of the nonlinear interaction potential. Moreover, our analysis
allows us determining the memory kernel, whose expression puts on a more firm
basis the previously conjectured connection between anomalous heat conductivity
and anomalous diffusion.Comment: Submitted to Physical Review
The spider cuticle : a remarkable material toolbox for functional diversity
Engineered systems are typically based on a large variety of materials differing in composition and processing to provide the desired functionality. Nature, however, has evolved materials that are used for a wide range of functional challenges with minimal compositional changes. The exoskeletal cuticle of spiders, as well as of other arthropods such as insects and crustaceans, is based on a combination of chitin, protein, water and small amounts of organic cross-linkers or minerals. Spiders use it to obtain mechanical support structures and lever systems for locomotion, protection from adverse environmental influences, tools for piercing, cutting and interlocking, auxiliary structures for the transmission and filtering of sensory information, structural colours, transparent lenses for light manipulation and more. This paper illustrates the ‘design space’ of a single type of composite with varying internal architecture and its remarkable capability to serve a diversity of functions. This article is part of the theme issue ‘Bio-derived and bioinspired sustainable advanced materials for emerging technologies (part 1)’
Dynamic model of fiber bundles
A realistic continuous-time dynamics for fiber bundles is introduced and
studied both analytically and numerically. The equation of motion reproduces
known stationary-state results in the deterministic limit while the system
under non-vanishing stress always breaks down in the presence of noise.
Revealed in particular is the characteristic time evolution that the system
tends to resist the stress for considerable time, followed by sudden complete
rupture. The critical stress beyond which the complete rupture emerges is also
obtained
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