Biomedical subjects

Celia Anteneodo

Publications and source records attributed to Celia Anteneodo.

9 recordsLinked to original sources

PubMed2006

Diffusive anomalies in a long-range Hamiltonian system.

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states for which superdiffusion of rotor phases has been reported. In the present work, we investigate diffusive motion by monitoring the evolution of full distributions of unfolded phases. After a transient, numerical histograms can be fitted by the q -Gaussian form P(x) proportional to {1+(q-1)[x/beta]2}(1/(1-q)) , with parameter q increasing with time before reaching a steady value q approximately 32 (squared Lorentzian). From the analysis of the second moment of numerical distributions, we also discuss the relaxation to equilibrium and show that diffusive motion in quasistationary trajectories depends strongly on system size.

Journal Article↗

PubMed2005

Quasistationary trajectories of the mean-field XY Hamiltonian model: a topological perspective.

We employ a topological approach to investigate the nature of quasistationary states of the mean-field XY Hamiltonian model. We focus on the quasistationary states reached when the system is initially prepared in a fully magnetized configuration. By means of numerical simulations and analytical considerations, we show that, along the quasistationary trajectories, the system evolves in a manifold of critical points of the potential energy function. Although these critical points are maxima, the large number of directions with marginal stability may be responsible for the slow relaxation dynamics and the trapping of the system in such trajectories.

Journal Article↗

PubMed2004

Statistics of finite-time Lyapunov exponents in the Ulam map.

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the calculation of the variance of exponents computed over time intervals of length n. The variance anomalously decays as 1/n(2). The probability density of finite-time exponents noticeably deviates from the Gaussian shape, decaying with exponential tails and presenting 2(n-1) spikes that narrow and accumulate close to the mean value with increasing n. The asymptotic expression for this probability distribution function is derived. It provides an adequate smooth approximation to describe numerical histograms built for not too small n, where the finiteness of bin size trims the sharp peaks.

Journal Article↗

PubMed2003

Analytical results for coupled-map lattices with long-range interactions.

We obtain exact analytical results for lattices of maps with couplings that decay with distance as r(-alpha). We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the Lyapunov spectrum for a completely synchronized state is analytically obtained. The critical line characterizing the synchronization transition is determined from the expression for the largest transversal Lyapunov exponent. In particular, it is shown that in the thermodynamical limit, such transition is only possible for sufficiently long-range interactions, namely, for alpha<alpha(c)=d, where d is the lattice dimension.

Journal Article↗

PubMed2003

Lyapunov exponent of many-particle systems: testing the stochastic approach.

The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent to a few statistical properties of the Hessian matrix of the interaction, which can be calculated as suitable thermal averages. We have verified that there is a satisfactory quantitative agreement between theory and simulations in the disordered phases of the XY models, either with attractive or repulsive interactions. Part of the success of the theory is due to the possibility of predicting the shape of the required correlation functions, because this permits the calculation of correlation times as thermal averages.

Journal Article↗

PubMed2003

Aging in an infinite-range Hamiltonian system of coupled rotators.

We analyze numerically the out-of-equilibrium relaxation dynamics of a long-range Hamiltonian system of N fully coupled rotators. For a particular family of initial conditions, this system is known to enter a particular regime in which the dynamic behavior does not agree with thermodynamic predictions. Moreover, there is evidence that in the thermodynamic limit, when N--> infinity is taken prior to t--> infinity, the system will never attain true equilibrium. By analyzing the scaling properties of the two-time autocorrelation function we find that, in that regime, a very complex dynamics unfolds, in which aging phenomena appear. The scaling law strongly suggests that the system behaves in a complex way, relaxing towards equilibrium through intricate trajectories. The present results are obtained for conservative dynamics, where there is no thermal bath in contact with the system.

Journal Article↗

PubMed2002

Theoretical estimates for the largest Lyapunov exponent of many-particle systems.

The largest Lyapunov exponent of an ergodic Hamiltonian system is the rate of exponential growth of the norm of a typical vector in the tangent space. For an N-particle Hamiltonian system with a smooth Hamiltonian of the type p(2)+V(q), the evolution of tangent vectors is governed by the Hessian matrix V of the potential. Ergodicity implies that the Lyapunov exponent is independent of initial conditions on the energy shell, which can then be chosen randomly according to the microcanonical distribution. In this way, a stochastic process V(t) is defined, and the evolution equation for tangent vectors can now be seen as a stochastic differential equation. An equation for the evolution of the average squared norm of a tangent vector can be obtained using the standard theory in which the average propagator is written as a cumulant expansion. We show that if cumulants higher than the second one are discarded, the Lyapunov exponent can be obtained by diagonalizing a small-dimension matrix that in some cases can be as small as 3 x 3. In all cases, the matrix elements of the propagator are expressed in terms of correlation functions of the stochastic process. We discuss the connection between our approach and an alternative theory, the so-called geometric method.

Journal Article↗

PubMed2002

Molecular modeling and dynamics of the sodium channel inactivation gate.

The intracellular linker L(III-IV) of voltage-gated sodium channels is known to be involved in their mechanism of inactivation. Its primary sequence is well conserved in sodium channels from different tissues and species. However, the role of charged residues in this region, first thought to play an important role in inactivation, has not been well identified, whereas the IFM triad (I1488-M1490) has been characterized as the crucial element for inactivation. In this work, we constructed theoretical models and performed molecular dynamics simulations, exploring the role of L(III-IV)-charged residues in the presence of a polar/nonpolar planar interface represented by a dielectric discontinuity. From structural predictions, two alpha-helical segments are proposed. Moreover, from dynamics simulations, a time-conserved motif is detected and shown to play a relevant role in guiding the inactivation particle toward its receptor site.

Amino Acid Sequence↗

PubMed2001

Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach.

We investigate the laws that rule the behavior of the largest Lyapunov exponent (LLE) in many particle systems with long-range interactions. We consider as a representative system the so-called Hamiltonian alpha-XY model where the adjustable parameter alpha controls the range of the interactions of N ferromagnetic spins in a lattice of dimension d. In previous work the dependence of the LLE with the system size N, for sufficiently high energies, was established through numerical simulations. In the thermodynamic limit, the LLE becomes constant for alpha>d whereas it decays as an inverse power law of N for alpha<d. A recent theoretical calculation based on a geometrization of the dynamics is consistent with these numerical results. Here we show that the scaling behavior can also be explained by a random matrix approach, in which the tangent mappings that define the Lyapunov exponents are modeled by random simplectic matrices drawn from a suitable ensemble.

Journal Article↗