Neutron yields from 1 GeV/nucleon U ion beams on Fe target

Yields of neutrons produced by a ²³⁸U ion beam of 1 GeV/nucleon kinetic energy impinging on a thick Fe target were measured resulting in distributions differential in neutron angle (0° < _n < 20°) and in kinetic energy (T_n > 50 MeV). The data serve in radiation protection planning for next-generation rare-isotope beam facilities. The experimental data are contrasted with predictions from transport codes as currently used in radiation shield design studies.     

A classification of slow convergence near parametric periodic points of discrete dynamical systems

We study the phenomenon of slow convergence in families of discrete dynamical systems where the iteration function has a Puiseux series representation. Such occurrence consists in the slow convergence of orbits near non-hyperbolic parametric periodic points. We provide a precise new definition of the slowness of convergence which is based on literature results for the critical exponents associated with parametric periodic points. Such exponents establish a general classification for slow systems and provide a measure of rates of convergence. For dynamical systems whose iteration functions have Taylor series expansions, the new definition is natural with wider applicability. However, it can be also used for iteration functions where a more sophisticated approach, such as a Lagrange expansion, is needed. In addition, we show that even for such iteration functions, the critical exponent can be easily computed. The presented theoretical results are illustrated by numerical examples having different rates of convergence.     

Formal analysis of piecewise affine systems through formula-guided refinement

We present a computational framework for identifying a set of initial states from which all trajectories of a piecewise affine (PWA) system with additive uncertainty satisfy a linear temporal logic (LTL) formula over a set of linear predicates in its state variables. Our approach is based on the construction and refinement of finite abstractions of infinite systems. We derive conditions guaranteeing the equivalence of an infinite system and its finite abstraction with respect to a specific LTL formula and propose a method for the construction of such formula-equivalent abstractions. While provably correct, the overall method is conservative and expensive. A tool for PWA systems implementing the proposed procedure using polyhedral operations and analysis of finite graphs is made available. Examples illustrating the analysis of PWA models of gene networks are included.     

Numerical simulation of multi-species biofilms in porous media for different kinetics

There are bacteria that can form strong biofilms in porous media. These biofilms can be used as biobarriers to restrict the flow of pollutants. For certain contaminants, a second species of bacteria that can actually react with the contaminants can be added to the biobarrier to actually degrade the pollutants. We propose some mathematical models for the formation of these reacting biobarriers under different hypotheses, and numerically solve the resulting equations for the flow, transport and reactions. Qualitative comparisons with some experimental results are also given.