arXiv subjects

Ph. Blanchard

Publications and source records attributed to Ph. Blanchard.

At least 37 records · Page 2Linked to original sources

arXiv2006

Expectation-driven interaction: a model based on Luhmann's contingency approach

We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the history of the interaction and developed within the confines of the problem of double contingency. We examine interaction strategies in the light of the message-exchange description using analytical and computational methods.

physics.soc-ph↗

arXiv2006

Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as $N\to\infty.$ For the even dimensions of space, $d=2,4,6,...$, the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.

cond-mat.dis-nn↗

arXiv2006

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.

physics.soc-ph↗

arXiv2006

Human activity modeling and Barabasi's queueing systems

It has been shown by A.-L. Barabasi that the priority based scheduling rules in single stage queuing systems (QS) generates fat tail behavior for the tasks waiting time distributions (WTD). Such fat tails are due to the waiting times of very low priority tasks which stay unserved almost forever as the task priority indices (PI) are "frozen in time" (i.e. a task priority is assigned once for all to each incoming task). Relaxing the "frozen in time" assumption, this paper studies the new dynamic behavior expected when the priority of each incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two class of models, namely 1) a population type model with an age structure and 2) a QS with deadlines assigned to the incoming tasks which is operated under the "earliest-deadline-first" policy, we are able to analytically extract some relevant characteristics of the the tasks waiting time distribution. As the aging mechanism ultimately assign high priority to any long waiting tasks, fat tails in the WTD cannot find their origin in the scheduling rule alone thus showing a fundamental difference between the present and the A.-L. Barabasi's class of models.

cond-mat.stat-mech↗

arXiv2005

The Epidemics of Corruption

We study corruption as a generalized epidemic process on the graph of social relationships. The main difference to classical epidemic processes is the strong nonlinear dependence of the transmission probability on the local density of corruption and the mean field influence of the overall corruption in the society. Network clustering and the degree-degree correlation play an essential role in corruption dynamics. We discuss phase transitions, the influence of the graph structure and the implications for epidemic control. Structural and dynamical arguments are given why strongly hierarchically organized societies like systems with dictatorial tendency are more vulnerable to corruption than democracies. A similar type of modelling can be applied to other social contagion spreading processes like opinion formation, doping usage, social disorders or innovation dynamics.

physics.soc-ph↗

arXiv2003

The "Cameo Principle" and the Origin of Scale-Free Graphs in Social Networks

We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on the structure generating distribution we obtain a scale free distribution for the degree. We furthermore introduce and study a "my friends are your friends" local search principle which makes the clustering coefficient large.

cond-mat.dis-nn↗

arXiv2003

Epidemic thresholds on scale-free graphs: the interplay between exponent and preferential choice

We show for a model of scale-free graphs with biased partner choice that knowing the exponent for the degree distribution is in general not sufficient to decide epidemic threshold properties for exponents less than three.We show that the connectivity between the high degree vertices and therefore the diameter is the relevant geometric quantity for epidemic threshold estimations.Absence of epidemic threshold happens precisely when a positive fraction of the nodes form a cluster of bounded diameter.

cond-mat↗

arXiv2003

Small World Graphs by the iterated "My Friends are Your Friends'' Principle

We study graphs obtained by successive creation and destruction of edges into small neighborhoods of the vertices. Starting with a circle graph of large diameter we obtain small world graphs with logarithmic diameter, high clustering coefficients and a fat tail distribution for the degree. Only local edge formation processes are involved and no preferential attachment was used. Furthermore we found an interesting phase transition with respect to the initial conditions.

cond-mat.dis-nn↗

arXiv2003

From quantum to quantum via decoherence

Various physical effects resulting from decoherence are discussed in the algebraic framework. In particular, it is shown that the environment may induce not only classical properties like superselection rules, pointer states or even classical behavior of the quantum system, but, what is more, it also allows the transition from statistical description of infinite quantum systems to quantum mechanics of systems with a finite number of degrees of freedom. It is shown that such transition holds for the quantum spin system in the thermodynamic limit interacting with the phonon field.

math-ph↗

arXiv2002

Self-Organized Criticality and Thermodynamic formalism

We introduce a dissipative version of the Zhang's model of Self-Organized Criticality, where a parameter allows to tune the local energy dissipation. We analyze the main dynamical features of the model and relate in particular the Lyapunov spectrum with the transport properties in the stationary regime. We develop a thermodynamic formalism where we define formal Gibbs measure, partition function and pressure characterizing the avalanche distributions. We discuss the infinite size limit in this setting. We show in particular that a Lee-Yang phenomenon occurs in this model, for the only conservative case. This suggests new connexions to classical critical phenomena.

nlin.CD↗

arXiv2002

Decoherence induced continuous pointer states

We investigate the reduced dynamics in the Markovian approximation of an infinite quantum spin system linearly coupled to a phonon field at positive temperature. The achieved diagonalization leads to a selection of the continuous family of pointer states corresponding to a configuration space of the one-dimensional Ising model. Such a family provides a mathematical description of an apparatus with continuous readings.

quant-ph↗

arXiv2002

An Algorithm Generating Scale Free Graphs

We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature before. The degree statistics of a random graph in our model is governed by the control parameter $η$ stirring the pure exponential statistics for the degree distribution (at $η=0,$ when a threshold is changed each time a new edge added to the graph) to a power law (at $η=1$, when the threshold is frozen). The exponent $γ$ characterizing the power law can vary in the wide range $γ\in(1,\infty)$ and can be tuned in different values $γ_{\mathrm{in}}$ and $γ_{\mathrm{out}}$ for in-degrees and out-degrees probability distributions independently. For the intermediate values of $η$, the decay rate is mixed. Taking different statistics for the threshold changes, one obtains dissimilar asymptotic profiles for the degree distribution having, in general, nothing to do with power laws at $η=1$, but still uniformly exponential at $η=0.$

cond-mat.dis-nn↗

arXiv2001

Transitions to Intermittency and Collective Behavior in Randomly Coupled Map Networks

We study the transitions to spatio-temporal intermittency in networks of randomly coupled Chate-Manneville maps. The relevant paprameters are the network connectivity, coupling strength, and the local parameter of the map. We show that the spatio-temporal intermittency occurs for some intervals or windows of the values of these parameters. Within the intermittency windows, the system exhibits periodic and other nontrivial collective behaviors. The detailed behavior depends crucially upon the topology of the random graph spanning the network. We present a detailed analysis of the results based on the thermodynamic formalism and random graph theory.

nlin.CD↗

arXiv2001

Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active sites, etc ...

cond-mat.stat-mech↗

arXiv2000

Completely Mixing Quantum Open Systems and Quantum Fractals

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the chaotic behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting spin components is shown to lead to a chaotic jump on quantum spin sphere and to generate specific fractal images - nonlinear ifs (iterated function system). The model is purely theoretical at this stage, and experimental confirmation of the chaotic behavior of measuring instruments during simultaneous continuous measurement of several noncommuting quantum observables would constitute a quantitative verification of Event Enhanced Quantum Theory.

quant-ph↗

arXiv2000

Effectively classical quantum states for open systems

Notions of robust and "classical" states for an open quantum system are introduced and discussed in the framework of the isometric-sweeping decomposition of trace class operators. Using the predictability sieve proposed by Zurek, ``quasi-classical'' states are defined. A number of examples illustrating how the ``quasi-classical'' states correspond to classical points in phase space connected with the measuring apparatus are presented.

quant-ph↗

arXiv1999

What can one learn about Self-Organized Criticality from Dynamical Systems theory ?

We develop a dynamical system approach for the Zhang's model of Self-Organized Criticality, for which the dynamics can be described either in terms of Iterated Function Systems, or as a piecewise hyperbolic dynamical system of skew-product type. In this setting we describe the SOC attractor, and discuss its fractal structure. We show how the Lyapunov exponents, the Hausdorff dimensions, and the system size are related to the probability distribution of the avalanche size, via the Ledrappier-Young formula.

cond-mat.stat-mech↗

arXiv1999

How Events Come Into Being: EEQT, Particle Tracks, Quantum Chaos, and Tunneling Time

In sections 1 and 2 we review Event Enhanced Quantum Theory (EEQT). In section 3 we discuss applications of EEQT to tunneling time, and compare its quantitative predictions with other approaches, in particular with Büttiker-Larmor and Bohm trajectory approach. In section 4 we discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, non-linear, iterated function system-type, patterns arising from quantum jumps and from the associated Markov operator. Concluding remarks pointing to possible future development of EEQT are given in section 5.

quant-ph↗