Convergence to equilibrium for many particle systems

The goal of this paper is to give a short review of recent results of the authors concerning classical Hamiltonian many particle systems. We hope that these results support the new possible formulation of Boltzmann's ergodicity hypothesis which sounds as follows. For almost all potentials, the minimal contact with external world, through only one particle of $N$, is sufficient for ergodicity. But only if this contact has no memory. Also new results for quantum case are presented

A Finslerian version of 't Hooft Deterministic Quantum Models

Using the Finsler structure living in the phase space associated to the tangent bundle of the configuration manifold, deterministic models at the Planck scale are obtained. The Hamiltonian function are constructed directly from the geometric data and some assumptions concerning time inversion symmetry. The existence of a maximal acceleration and speed is proved for Finslerian deterministic models. We investigate the spontaneous symmetry breaking of the orthogonal symmetry SO(6N) of the Hamiltonian of a deterministic system. This symmetry break implies the non-validity of the argument used to obtain Bell's inequalities for spin states. It is introduced and motivated in the context of Randers spaces an example of simple 't Hooft model with interactions.Comment: 25 pages; no figures. String discussion deleted. Some minor change

Some Remarks on the Use of Deterministic and Probabilistic Approaches in the Evaluation of Rock Slope Stability

The rock slope stability assessment can be performed by means of deterministic and probabilistic approaches. As the deterministic analysis needs only representative values (generally, the mean value) for each physical and geo-mechanical parameter involved, it does not take into account the variability and uncertainty of geo-structural and geo-mechanical properties of joints. This analysis can be usually carried out using dierent methods, such as the Limit Equilibrium method or numerical modeling techniques sometimes implemented in graphical tests to identify dierent failure mechanisms (kinematic approach). Probabilistic methods (kinetic approach) aimed to calculate the slope failure probability, consider all orientations, physical characters and shear strength of joints and not only those recognized as kinematically possible. Consequently, the failure probability can be overestimated. It is, therefore, considered more realistic to perform both kinematic and kinetic analyses and to calculate a conditional probability given by the product of the kinematic and kinetic probabilities assuming that they are statistically independent variables. These approaches have been tested on two rock slopes in the Campanian region of Southern Italy aected by possible plane and wedge failures, respectively. Kinematic and kinetic probabilities have been evaluated both by means of the Markland’s test and the Monte Carlo simulation. Using the Eurocode 7, also a deterministic limit equilibrium analysis was performed. The obtained results were compared and commented on

Advances and applications of automata on words and trees : abstracts collection

From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise

This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a couple consisting of a Markov trend and a linear decision process for which both the "deterministic" and the noise components rely on trend-dependent matrices. We discuss approximate, approximate null and exact null-controllability. Several examples are given to illustrate the links between these concepts and to compare our results with their continuous-time counterpart (given in [16]). We introduce a class of backward stochastic Riccati difference schemes (BSRDS) and study their solvability for particular frameworks. These BSRDS allow one to introduce Gramian-like controllability metrics. As application of these metrics, we propose a minimal intervention-targeted reduction in the study of gene networks