Existence of Quasi-stationary states at the Long Range threshold

In this paper the lifetime of quasi-stationary states (QSS) in the $\alpha-$HMF model are investigated at the long range threshold ($\alpha=1$). It is found that QSS exist and have a diverging lifetime $\tau(N)$ with system size which scales as \mbox{\ensuremath{\tau}(N)\ensuremath{\sim}}\log N, which contrast to the exhibited power law for $\alpha<1$ and the observed finite lifetime for $\alpha>1$. Another feature of the long range nature of the system beyond the threshold ($\alpha>1$) namely a phase transition is displayed for $\alpha=1.5$. The definition of a long range system is as well discussed

Emergence of a collective crystal in a classical system with long-range interactions

A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove the statistical equivalence with the Hamiltonian Mean Field model (HMF) and $\alpha$-HMF: a second order phase transition is indeed observed at the critical energy threshold $\varepsilon_c=0.75$. Conversely, when the thermodynamic limit is performed at infinite density (while keeping the length of the hosting interval $L$ constant), the critical energy $\varepsilon_c$ is modulated as a function of $L$. At low energy, a self-organized collective crystal phase is reported to emerge, which converges to a perfect crystal in the limit $\epsilon \rightarrow 0$. To analyze the phenomenon, the equilibrium one particle density function is analytically computed by maximizing the entropy. The transition and the associated critical energy between the gaseous and the crystal phase is computed. Molecular dynamics show that the crystal phase is apparently split into two distinct regimes, depending on the the energy per particle $\varepsilon$. For small $\varepsilon$, particles are exactly located on the lattice sites; above an energy threshold $\varepsilon{*}$, particles can travel from one site to another. However, $\varepsilon{*}$ does not signal a phase transition but reflects the finite time of observation: the perfect crystal observed for $\varepsilon >0$ corresponds to a long lasting dynamical transient, whose life time increases when the $\varepsilon >0$ approaches zero.Comment: 6 pages, 4 figure

Mixing properties in the advection of passive tracers via recurrences and extreme value theory

In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincar\'e recurrences analysis, our method provides reliable estimations of the characteristic mixing times and distinguishes between barriers and unstable fixed points. The method is based on a check of convergence for extreme value laws on finite datasets. We define the mixing times in terms of the shortest time intervals such that extremes converge to the asymptotic (known) parameters of the Generalized Extreme Value distribution. Our technique is suitable for applications in the analysis of other systems where mixing time scales need to be determined and limited datasets are available.Comment: arXiv admin note: text overlap with arXiv:1107.597

Chaotic Jets

The problem of characterizing the origin of the non-Gaussian properties of transport resulting from Hamiltonian dynamics is addressed. For this purpose the notion of chaotic jet is revisited and leads to the definition of a diagnostic able to capture some singular properties of the dynamics. This diagnostic is applied successfully to the problem of advection of passive tracers in a flow generated by point vortices. We present and discuss this diagnostic as a result of which clues on the origin of anomalous transport in these systems emerge.Comment: Proceedings of the workshop Chaotic transport and complexity in classical and quantum dynamics, Carry le rouet France (2002

From techno-scientific grammar to organizational syntax. New production insights on the nature of the firm

The paper aims at providing the conceptual building blocks of a theory of the firm which addresses its "ontological questions" (existence,boundaries and organization) by placing production at its core. We draw on engineering for a more accurate description of the production process itself, highlighting its inner complexity and potentially chaotic nature, and on computational linguistics for a production-based account of the nature of economic agents and of the mechanisms through which they build ordered production sets. In so doing, we give a "more appropriate" production basis to the crucial issues of how firm's boundaries are set, how its organisational structure is defined, and how it changes over time. In particular, we show how economic agents select some tasks to be performed internally, while leaving some other to external suppliers, on the basis of criteria based on both the different degrees of internal congruence of the tasks to be performed (i.e. the internal environment), and on the outer relationships carried out with other agents (i.e. the external environment)

You Won the Battle. What about the War? A Model of Competition between Proprietary and Open Source Software

Although open source software has recently attracted a relevant body of economic literature, a formal treatment of the process of com- petition with its proprietary counterpart is still missing. Starting from an epidemic model of innovation di?usion, we try to ?ll this gap. We propose a model where the two competing technologies depend on dif- ferent factors, each one speci?c to its own mode of production (prof- its and developers’ motivations respectively), together with network e?ects and switching costs. As the speed of di?usion of these tech- nologies is crucial for the ?nal outcome, we endogenize the parame- ter in?uencing it across the population of adopters. We ?nd that an asymptotically stable equilibrium where both technologies coexist can always be present and, when the propagation coe?cient is endogenous, it coexists with winner–take–all solutions. Furthermore, an increase in the level of the switching costs for one technology increases the num- ber of its adopters, while reducing the number of the other one. If the negative network e?ects increase for one of the two technologies, then the equilibrium level of users of that technology decrease.Increasing returns; Open-source software; Technological competition; Technology di?usion

Reliable Parallel Solution of Bidiagonal Systems

This paper presents a new efficient algorithm for solving bidiagonal systems of linear equations on massively parallel machines. We use a divide and conquer approach to compute a representative subset of the solution components after which we solve the complete system in parallel with no communication overhead. We address the numerical properties of the algorithm in two ways: we show how to verify the ? posteriori backward stability at virtually no additional cost, and prove that the algorithm is ? priori forward stable. We then show how we can use the algorithm in order to bound the possible perturbations in the solution components