103 research outputs found
Out-of-equilibrium versus dynamical and thermodynamical transitions for a model protein
Equilibrium and out-of-equilibrium transitions of an off-lattice protein
model have been identified and studied. In particular, the out-of-equilibrium
dynamics of the protein undergoing mechanical unfolding is investigated, and by
using a work fluctuation relation, the system free energy landscape is
evaluated. Three different structural transitions are identified along the
unfolding pathways. Furthermore, the reconstruction of the the free and
potential energy profiles in terms of inherent structure formalism allows us to
put in direct correspondence these transitions with the equilibrium thermal
transitions relevant for protein folding/unfolding. Through the study of the
fluctuations of the protein structure at different temperatures, we identify
the dynamical transitions, related to configurational rearrangements of the
protein, which are precursors of the thermal transitions.Comment: Proceedings of the "YKIS 2009 : Frontiers in Nonequilibrium Physics"
conference in Kyoto, August 2009. To appear in Progress of Theoretical
Physics Supplemen
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
Ensemble inequivalence: A formal approach
Ensemble inequivalence has been observed in several systems. In particular it
has been recently shown that negative specific heat can arise in the
microcanonical ensemble in the thermodynamic limit for systems with long-range
interactions. We display a connection between such behaviour and a mean-field
like structure of the partition function. Since short-range models cannot
display this kind of behaviour, this strongly suggests that such systems are
necessarily non-mean field in the sense indicated here. We further show that a
broad class of systems with non-integrable interactions are indeed of
mean-field type in the sense specified, so that they are expected to display
ensemble inequivalence as well as the peculiar behaviour described above in the
microcanonical ensemble.Comment: 4 pages, no figures, given at the NEXT2001 conference on
non-extensive thermodynamic
Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations
Pattern formation often occurs in spatially extended physical, biological and
chemical systems due to an instability of the homogeneous steady state. The
type of the instability usually prescribes the resulting spatio-temporal
patterns and their characteristic length scales. However, patterns resulting
from the simultaneous occurrence of instabilities cannot be expected to be
simple superposition of the patterns associated with the considered
instabilities. To address this issue we design two simple models composed by
two asymmetrically coupled equations of non-conserved (Swift-Hohenberg
equations) or conserved (Cahn-Hilliard equations) order parameters with
different characteristic wave lengths. The patterns arising in these systems
range from coexisting static patterns of different wavelengths to traveling
waves. A linear stability analysis allows to derive a two parameter phase
diagram for the studied models, in particular revealing for the Swift-Hohenberg
equations a co-dimension two bifurcation point of Turing and wave instability
and a region of coexistence of stationary and traveling patterns. The nonlinear
dynamics of the coupled evolution equations is investigated by performing
accurate numerical simulations. These reveal more complex patterns, ranging
from traveling waves with embedded Turing patterns domains to spatio-temporal
chaos, and a wide hysteretic region, where waves or Turing patterns coexist.
For the coupled Cahn-Hilliard equations the presence of an weak coupling is
sufficient to arrest the coarsening process and to lead to the emergence of
purely periodic patterns. The final states are characterized by domains with a
characteristic length, which diverges logarithmically with the coupling
amplitude.Comment: 9 pages, 10 figures, submitted to Chao
Desynchronization in diluted neural networks
The dynamical behaviour of a weakly diluted fully-inhibitory network of
pulse-coupled spiking neurons is investigated. Upon increasing the coupling
strength, a transition from regular to stochastic-like regime is observed. In
the weak-coupling phase, a periodic dynamics is rapidly approached, with all
neurons firing with the same rate and mutually phase-locked. The
strong-coupling phase is characterized by an irregular pattern, even though the
maximum Lyapunov exponent is negative. The paradox is solved by drawing an
analogy with the phenomenon of ``stable chaos'', i.e. by observing that the
stochastic-like behaviour is "limited" to a an exponentially long (with the
system size) transient. Remarkably, the transient dynamics turns out to be
stationary.Comment: 11 pages, 13 figures, submitted to Phys. Rev.
Low frequency fluctuations in a Vertical Cavity Lasers: experiments versus Lang-Kobayashi dynamics
The limits of applicability of the Lang-Kobayashi (LK) model for a semiconductor laser with optical feedback are analyzed. The model equations, equipped with realistic values of the parameters, are investigated below solitary laser threshold where Low Frequency Fluctuations (LFF) are usually observed. The numerical findings are compared with experimental data obtained for the selected polarization mode from a Vertical Cavity Surface Laser (VCSEL) subject to polarization selective external feedback. The comparison reveals the bounds within which the dynamics of the LK can be considered as realistic. In particular, it clearly demonstrates that the deterministic LK, for realistic values of the linewidth enhancement factor , reproduces the LFF only as a transient dynamics towards one of the stationary modes with maximal gain. A reasonable reproduction of real data from VCSEL can be obtained only by considering noisy LK or alternatively deterministic LK for extremely high -values
Discrete synaptic events induce global oscillations in balanced neural networks
Neural dynamics is triggered by discrete synaptic inputs of finite amplitude.
However, the neural response is usually obtained within the diffusion
approximation (DA) representing the synaptic inputs as Gaussian noise. We
derive a mean-field formalism encompassing synaptic shot-noise for sparse
balanced networks of spiking neurons. For low (high) external drives (synaptic
strengths) irregular global oscillations emerge via continuous and hysteretic
transitions, correctly predicted by our approach, but not from the DA. These
oscillations display frequencies in biologically relevant bands.Comment: 6 pages, 3 figure
A reduction methodology for fluctuation driven population dynamics
Lorentzian distributions have been largely employed in statistical mechanics
to obtain exact results for heterogeneous systems. Analytic continuation of
these results is impossible even for slightly deformed Lorentzian
distributions, due to the divergence of all the moments (cumulants). We have
solved this problem by introducing a `pseudo-cumulants' expansion. This allows
us to develop a reduction methodology for heterogeneous spiking neural networks
subject to extrinsinc and endogenous noise sources, thus generalizing the
mean-field formulation introduced in [E. Montbri\'o et al., Phys. Rev. X 5,
021028 (2015)].Comment: 10 pages (with supplementary materials), 3 figure
Entropy potential and Lyapunov exponents
According to a previous conjecture, spatial and temporal Lyapunov exponents
of chaotic extended systems can be obtained from derivatives of a suitable
function: the entropy potential. The validity and the consequences of this
hypothesis are explored in detail. The numerical investigation of a
continuous-time model provides a further confirmation to the existence of the
entropy potential. Furthermore, it is shown that the knowledge of the entropy
potential allows determining also Lyapunov spectra in general reference frames
where the time-like and space-like axes point along generic directions in the
space-time plane. Finally, the existence of an entropy potential implies that
the integrated density of positive exponents (Kolmogorov-Sinai entropy) is
independent of the chosen reference frame.Comment: 20 pages, latex, 8 figures, submitted to CHAO
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