On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice

We present a theoretical study of the recently observed dynamical regimes of paramagnetic colloidal particles externally driven above a regular lattice of magnetic bubbles [P. Tierno, T. H. Johansen, and T. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007)]. An external precessing magnetic field alters the potential generated by the surface of the film in such a way to either drive the particle circularly around one bubble, ballistically through the array, or in triangular orbits on the interstitial regions between the bubbles. In the ballistic regime, we observe different trajectories performed by the particles phase locked with the external driving. Superdiffusive motion, which was experimentally found bridging the localized and delocalized dynamics, emerge only by introducing a certain degree of randomness into the bubbles size distribution.

Dynamics of the third order Lyness' difference equation

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Devolution dynamics of Spanish local government

Over the last few years, ther has been a devolutionary tendency in many developed and developing countries. In this article we propose a methodology to decompose whether the benefits in terms of effciency derived from transfers of powers from higher to municipal levels of government "the "economic dividend" of devolution) might increase over time. This methodology is based on linear programming approaches for effciency measurement. We provide anapplication to Spanish municipalities, which have had to adapt to both the European Stability and Growth Pact as well as to domestic regulation seeking local governments balanced budget. Results indicate that efficiency gains from enhaced decentralization have increased over time. However, the way through which these gains accrue differs across municipalities -in some cases technical change is the main component, whereas in others catching up dominates.

Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

Dynamics of diversity within the Mossos d’Esquadra

This chapter offers a case-study of diversity and diversity policies withinthe Mossos d’Esquadra, the police force of the Catalan autonomous communityin Spain. The case is described in a comprehensive way (includingpolicies in all relevant policy areas: recruitment, retention, and promotion)and at the same time analyzed with a new analytical framework (includingthe definition of diversity, the motivation for diversity within the organisation,and the facilitation of diversity within the organisation with policies).The goal of the chapter is twofold. First, offer a deeper understanding ofthe dynamics of diversity within this police force. Second, demonstrate theacademic potential of this new analytical framework.

The dynamics of US inflation: Can monetary policy explain the changes?

We investigate the relationship between monetary policy and inflation dynamics in theUS using a medium scale structural model. The specification is estimated with Bayesiantechniques and fits the data reasonably well. Policy shocks account for a part of the declinein inflation volatility; they have been less effective in triggering inflation responses overtime and qualitatively account for the rise and fall in the level of inflation. A number ofstructural parameter variations contribute to these patterns.

The dynamics of research networks in Brite-Euram

Network formation within the BRITE--EURAM program is investigated.Wedescribe the role of the hub of the network, which is defined as the setofmain contractors that account for most of the participations. We studytheeffects that the conflict of objectives within European research fundingbetween pre-competitive research vs. European cohesion has on theformationof networks and on the relationship between different partnersof the network. \\A panel data set is constructed including the second and third frameworkof theBrite--Euram program. A model of joint production of research results isusedto test for changes in the behavior of partners within the twoframeworks. \\The main findings are that participations are very concentrated, that isasmall group of institutions account for most of the participations, butgoingfrom the second to the third framework the presence of subcontractorsand singleparticipants increases substantially. This result is reinforced by the factthat main contractors receive smaller spill-ins within networks, butspill-insincrease from the second to the third framework.

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

The structural dynamics of US output and inflation: What explains the changes?

We examine the dynamics of US output and inflation using a structural time varyingcoefficient VAR. We show that there are changes in the volatility of both variables andin the persistence of inflation. Technology shocks explain changes in output volatility,while a combination of technology, demand and monetary shocks explain variations inthe persistence and volatility of inflation. We detect changes over time in the transmission of technology shocks and in the variance of technology and of monetary policyshocks. Hours and labor productivity always increase in response to technology shocks.

The structural dynamics of output growth and inflation: some international evidence

We examine the dynamics of output growth and inflation in the US, Euro area and UK using a structural time varying coefficient VAR. There are important similarities in structural inflation dynamics across countries; output growth dynamics differ. Swings in the magnitude of inflation and output growth volatilities and persistences are accounted for by a combination of three structural shocks. Changes over time in the structure of the economy are limited and permanent variations largely absent. Changes in the volatilities of structural shocks matter.