396 research outputs found
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.Comment: 11 pages including 6 figure
Correlating densities of centrality and activities in cities : the cases of Bologna (IT) and Barcelona (ES)
This paper examines the relationship between street centrality and densities of commercial and service activities in cities. The aim is to verify whether a correlation exists and whether some 'secondary' activities, i.e. those scarcely specialized oriented to the general public and ordinary daily life, are more linked to street centrality than others. The metropolitan area of Barcelona (Spain) is investigated, and results are compared with those found in a previous work on the city of Bologna (Italy). Street centrality is calibrated in a multiple centrality assessment (MCA) model composed of multiple measures such as closeness, betweenness and straightness. Kernel density estimation (KDE) is used to transform data sets of centrality and activities to one scale unit for correlation analysis between them. Results indicate that retail and service activities in both Bologna and Barcelona tend to concentrate in areas with better centralities, and that secondary activities exhibit a higher correlation
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 greater than d whereas it decays as an inverse
power law of N for alpha smaller than d. A recent theoretical calculation based
on Pettini's geometrization of the dynamics is consistent with these numerical
results (M.-C. Firpo and S. Ruffo, cond-mat/0108158). 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.Comment: 5 pages, no figure
Vulnerability and Protection of Critical Infrastructures
Critical infrastructure networks are a key ingredient of modern society. We
discuss a general method to spot the critical components of a critical
infrastructure network, i.e. the nodes and the links fundamental to the perfect
functioning of the network. Such nodes, and not the most connected ones, are
the targets to protect from terrorist attacks. The method, used as an
improvement analysis, can also help to better shape a planned expansion of the
network.Comment: 4 pages, 1 figure, 3 table
Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions
A N-sized inertial classical Heisenberg ferromagnet, which consists in a
modification of the well-known standard model, where the spins are replaced by
classical rotators, is studied in the limit of infinite-range interactions. The
usual canonical-ensemble mean-field solution of the inertial classical
-vector ferromagnet (for which recovers the particular Heisenberg
model considered herein) is briefly reviewed, showing the well-known
second-order phase transition. This Heisenberg model is studied numerically
within the microcanonical ensemble, through molecular dynamics.Comment: 18 pages text, and 7 EPS figure
Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps
We introduce, and numerically study, a system of symplectically and
globally coupled standard maps localized in a lattice array. The global
coupling is modulated through a factor , being the distance
between maps. Thus, interactions are {\it long-range} (nonintegrable) when
, and {\it short-range} (integrable) when . We
verify that the largest Lyapunov exponent scales as , where is positive when
interactions are long-range, yielding {\it weak chaos} in the thermodynamic
limit (hence ). In the short-range case,
appears to vanish, and the behaviour corresponds to {\it
strong chaos}. We show that, for certain values of the control parameters of
the system, long-lasting metastable states can be present. Their duration
scales as , where appears to be
numerically consistent with the following behavior: for , and zero for . All these results exhibit major
conjectures formulated within nonextensive statistical mechanics (NSM).
Moreover, they exhibit strong similarity between the present discrete-time
system, and the -XY Hamiltonian ferromagnetic model, also studied in
the frame of NSM.Comment: 8 pages, 5 figure
Network structure of multivariate time series.
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail
Enhancement of cooperation in highly clustered scale-free networks
We study the effect of clustering on the organization of cooperation, by
analyzing the evolutionary dynamics of the Prisoner's Dilemma on scale-free
networks with a tunable value of clustering. We find that a high value of the
clustering coefficient produces an overall enhancement of cooperation in the
network, even for a very high temptation to defect. On the other hand, high
clustering homogeneizes the process of invasion of degree classes by defectors,
decreasing the chances of survival of low densities of cooperator strategists
in the network.Comment: 4 pages, 3 figure
Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: A computational discussion
We implement a general numerical calculation that allows for a direct
comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs
canonical distribution in Gibbs -space. Using paradigmatic
first-neighbor models, namely, the inertial XY ferromagnet and the
Fermi-Pasta-Ulam -model, we show that at intermediate energies the
Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law
(). At higher energies we discuss partial agreement
between time and ensemble averages.Comment: New title, revision of the text. EPJ latex, 4 figure
Universal Behavior of Lyapunov Exponents in Unstable Systems
We calculate the Lyapunov exponents in a classical molecular dynamics
framework. The system is composed of few hundreds particles interacting either
through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are
chosen to give an Equation of State that resembles the nuclear and the atomic
Equation Of State respectively near the critical point for liquid-gas
phase transition. We find the largest fluctuations for an initial "critical
temperature". The largest Lyapunov exponents are always positive and
can be very well fitted near this "critical temperature" with a functional form
, where the exponent is
independent of the system and mass number. At smaller temperatures we find that
, a universal behavior characteristic of an order
to chaos transition.Comment: 11 pages, RevTeX, 3 figures not included available upon reques
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