Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

Nonlinear Enhancement of the Multiphonon Coulomb Excitation in Relativistic Heavy Ion Collisions

We propose a soluble model to incorporate the nonlinear effects in the transition probabilities of the multiphonon Giant Dipole Resonances based on the SU(1,1) algebra. Analytical expressions for the multi-phonon transition probabilities are derived. Enhancement of the Double Giant Resonance excitation probabilities in relativistic ion collisions scales as $(2 k +1)(2k)^{-1}$ for the degree of nonlinearity $(2k)^{-1}$ and is able to reach values $1.5-2$ compatible with experimental data. The enhancement factor is found to decrease with increasing bombarding energy. [KEYWORDS: Relativistic Heavy Ion Collisions,Double Giant Resonance]Comment: 12 pages, 2 figure

Local Detailed Balance : A Microscopic Derivation

Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints when the latter are enforced by reservoirs exchanging conserved microscopic quantities. At a mesoscopic scale only the energies of the macroscopic bodies are accessible together with the configurations of the contact system. We consider a class of models where the contact system, as well as macroscopic bodies, have a finite number of possible configurations. The global system with only discrete degrees of freedom has no microscopic Hamiltonian dynamics, but it is shown that, if the microscopic dynamics is assumed to be deterministic and ergodic and to conserve energy according to some specific pattern, and if the mesoscopic evolution of the global system is approximated by a Markov process as closely as possible, then the mesoscopic transition rates obey three constraints. In the limit where macroscopic bodies can be considered as reservoirs at thermodynamic equilibrium (but with different intensive parameters) the mesoscopic transition rates turn into transition rates for the contact system and the third constraint becomes local detailed balance ; the latter is generically expressed in terms of the microscopic exchange entropy variation, namely the opposite of the variation of the thermodynamic entropy of the reservoir involved in a given microscopic jump of the contact system configuration. For a finite-time evolution after contact has been switched on we derive a fluctuation relation for the joint probability of the heat amounts received from the various reservoirs. The generalization to systems exchanging energy, volume and matter with several reservoirs, with a possible conservative external force acting on the contact system, is given explicitly.Comment: 26 pages. arXiv admin note: substantial text overlap with arXiv:1302.453

Approximation of symmetrizations by Markov processes

Under continuity and recurrence assumptions, we prove that the iteration of successive partial symmetrizations that form a time-homogeneous Markov process, converges to a symmetrization. We cover several settings, including the approximation of the spherical nonincreasing rearrangement by Steiner symmetrizations, polarizations and cap symmetrizations. A key tool in our analysis is a quantitative measure of the asymmetry

Foldy-Wouthuysen transformation for relativistic particles in external fields

A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed. It permits determination of the Hamilton operator in the Foldy-Wouthuysen representation with any accuracy. Interactions between a particle having an anomalous magnetic moment and nonstationary electromagnetic and electroweak fields are investigated.Comment: 22 page