One-dimensional asymmetrically coupled maps with defects

In this letter we study chaotic dynamical properties of an asymmetrically coupled one-dimensional chain of maps. We discuss the existence of coherent regions in terms of the presence of defects along the chain. We find out that temporal chaos is instantaneously localized around one single defect and that the tangent vector jumps from one defect to another in an apparently random way. We quantitatively measure the localization properties by defining an entropy-like function in the space of tangent vectors.Comment: 9 pages + 4 figures TeX dialect: Plain TeX + IOP macros (included

Boltzmann entropy and chaos in a large assembly of weakly interacting systems

We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the growth with time of the Boltzmann entropy, S_B, in this system as a function of the coarse graining resolution. We show that a characteristic scale emerges, and that the behavior of S_B vs t, at variance with the Gibbs entropy, does not depend on the coarse graining resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth depends essentially on the single-particle chaotic dynamics (for t not too small). It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.Comment: 21 pages, 11 figures, submitted to Journal of Statistical Physic

Numerical Observation of a Tubular Phase in Anisotropic Membranes

We provide the first numerical evidence for the existence of a tubular phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes without self-avoidance. Incorporating anisotropy into the bending rigidity of a simple model of a tethered membrane with free boundary conditions, we show that the model indeed has two phase transitions corresponding to the flat-to-tubular and tubular-to-crumpled transitions. For the tubular phase we measure the Flory exponent $\nu_F$ and the roughness exponent $\zeta$. We find $\nu_F=0.305(14)$ and $\zeta=0.895(60)$, which are in reasonable agreement with the theoretical predictions of RT --- $\nu_F=1/4$ and $\zeta=1$.Comment: 8 pages, LaTeX, REVTEX, final published versio

Recurrence quantification analysis of heart rate variability to detect both ventilatory thresholds

Aims of this study were: To verify if Recurrence Quantification Analysis (RQA) of Heart Rate Variability (HRV) time series could determine both ventilatory thresholds in individuals with different fitness levels, and to assess the validity of RQA method compared to gasexchange method (GE). The two thresholds were estimated in thirty young individuals during incremental exercise on cycle-ergometer: Heart rate (HR), Oxygen consumption (VO2) and Workload were measured by the two methods (RQA and GE). Repeated measures ANOVA was used to assess main effects of methods and methods-by-groups interaction effects for HR, VO2 and Workload at aerobic (AerT) and anaerobic (AnT) thresholds. Validity of RQA at both thresholds was assessed for HR, VO2 and Workload by Ordinary Least Products (OLP) regression, Typical Percentage Error (TE), Intraclass Correlation Coefficients (ICC) and the Bland Altman plots. No methods-by-groups interaction effects were detected for HR, VO2 and Workload at AerT and AnT. The OLP analysis showed that at both thresholds RQA and GE methods had very strong correlations (r >0.8) in all variables (HR, VO2 and Workload). Slope and intercept values always included the 1 and the 0, respectively. At AerT the TE ranged from 4.02% (5.48 bpm) to 10.47% (8.53 Watts) (HR and Workload, respectively) and in all variables ICC values were excellent (≥0.85). At AnT the TE ranged from 2.53% (3.98 bpm) to 6.64% (7.81 Watts) (HR and Workload, respectively) and in all variables ICC values were excellent (≥0.90). Therefore, RQA of HRV time series is a new valid approach to determine both ventilatory thresholds in individuals with different physical fitness levels, it can be used when gas analysis is not possible or not convenient

Effect of permethrin plus antioxidants on locomotor activity and striatum in adolescent rats

Pyrethroids are important insecticides used largely because of their high activity as an insecticide and their low mammalian toxicity. Some studies have demonstrated that these products show neurotoxic effects on the mammalian central nervous system. The aim of the present study was to investigate the propensity of permethrin to induce oxidative stress in adolescent rats and its possible attenuation by Vitamin E alone or + Coenzyme Q10. Data indicated that adolescent rats exposed to permethrin exhibited alteration in the locomotor activity and plasma membrane fluidity of striatum. Vitamin E +Q10 and Vitamin E alone supplementation reversed the negative effect on central nervous system. Permethrin alteration of striatum plasma membrane fluidity was restored by Vitamin E +Q10. Data obtained from red blood cells showed that permethrin did not induce any modification of plasma membrane fluidity in adolescent rats, whereas antioxidants supplementation induced pro-oxidant effect. In summary some differences between antioxidant treatments were observed at striatum level: Coenzyme Q10 + Vitamin E maintains plasma membrane fluidity, while Vitamin E is more effective to preserve GSH level

Fluctuation-response relation in turbulent systems

We address the problem of measuring time-properties of Response Functions (Green functions) in Gaussian models (Orszag-McLaughin) and strongly non-Gaussian models (shell models for turbulence). We introduce the concept of {\it halving time statistics} to have a statistically stable tool to quantify the time decay of Response Functions and Generalized Response Functions of high order. We show numerically that in shell models for three dimensional turbulence Response Functions are inertial range quantities. This is a strong indication that the invariant measure describing the shell-velocity fluctuations is characterized by short range interactions between neighboring shells

Linear instability and statistical laws of physics

We show that a meaningful statistical description is possible in conservative and mixing systems with zero Lyapunov exponent in which the dynamical instability is only linear in time. More specifically, (i) the sensitivity to initial conditions is given by $\xi =[1+(1-q)\lambda_q t]^{1/(1-q)}$ with $q=0$; (ii) the statistical entropy $S_q=(1-\sum_i p_i^q)/(q-1) (S_1=-\sum_i p_i \ln p_i)$ in the infinitely fine graining limit (i.e., $W\equiv$ {\it number of cells into which the phase space has been partitioned} $\to\infty$), increases linearly with time only for $q=0$; (iii) a nontrivial, $q$-generalized, Pesin-like identity is satisfied, namely the $\lim_{t \to \infty} \lim_{W \to \infty} S_0(t)/t=\max\{\lambda_0\}$. These facts (which are in analogy to the usual behaviour of strongly chaotic systems with $q=1$), seem to open the door for a statistical description of conservative many-body nonlinear systems whose Lyapunov spectrum vanishes.Comment: 7 pages including 2 figures. The present version is accepted for publication in Europhysics Letter

The prediction of future from the past: an old problem from a modern perspective

The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincar\'e's recurrence. Using such a connection, a very general result of ergodic theory - Kac's lemma - can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability results to be hindered rather by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, regardless the regular or chaotic nature of the system, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models.Comment: 9 pages, 4 figure

Critical properties of the four-state Commutative Random Permutation Glassy Potts model in three and four dimensions

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulation and of a finite size scaling analysis. Thanks to the use of a field programmable gate array we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in d=4 and to study the critical properties of the transition. In d=3, our results are consistent with the presence of a Kosterlitz-Thouless transition, but we cannot exclude transient effects due to a value of the lower critical dimension slightly below 3.Comment: 9 pages, 8 Postscript figure

Library Design in Combinatorial Chemistry by Monte Carlo Methods

Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.Comment: 5 pages, 3 figure