Frictional Collisions Off Sharp Objects

This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date

Controllability of a viscoelastic plate using one boundary control in displacement or bending

In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary displacement or bending). By combining operator and moment methods, we prove that the viscoelastic plate inherits the controllability properties of the purely elastic plate

Modelling and solutions to the linear stability of a detonation wave in the kinetic frame

Artigo publicado num número especial da revista.The analysis of linear stability of a steady detonation wave is formulated for the first time at the kinetic level in the frame of the Boltzmann equation extended to reacting gases. Within this context and for a reversible reaction, the stability problem is carried out, in agreement with most classical papers on gas detonation, through a normal mode approach for the one-dimensional disturbances of the steady wave solution, and an acoustic radiation condition at the final equilibrium as closure condition. The proposed modelling leads to an initial value problem, constituted by the linearized reactive Euler equations in the perturbed shock frame with related Rankine-Hugoniot conditions, which can be solved by means of a proper numerical technique. An application is provided for an elementary bimolecular reaction.Centro de Matemática da Universidade do MinhoFundação para a Ciência e a Tecnologia (FCT)Italian INDAM-GNF

Kinetic approach to transport properties of a reacting gas

A multicomponent reacting gas with reversible reactions is studied at a kinetic level with the main objective of deriving the reactive Navier-Stokes equations in dependence on the macroscopic variables, and characterizing the dissipative terms related to shear viscosity, heat conduction and thermal diffusion. A step-by-step procedure, which can be applied to a quite large variety of reactive flows, is proposed in order to identify the transport coefficients, basically resorting to a first-order density approximation of Chapman-Enskog type.Fundação para a Ciência e Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI).National Research Project PRIN 2003

Evolution of the fine-structure constant in runaway dilaton models

We study the detailed evolution of the fine-structure constant $\alpha$ in the string-inspired runaway dilaton class of models of Damour, Piazza and Veneziano. We provide constraints on this scenario using the most recent $\alpha$ measurements and discuss ways to distinguish it from alternative models for varying $\alpha$. For model parameters which saturate bounds from current observations, the redshift drift signal can differ considerably from that of the canonical $\Lambda$CDM paradigm at high redshifts. Measurements of this signal by the forthcoming European Extremely Large Telescope (E-ELT), together with more sensitive $\alpha$ measurements, will thus dramatically constrain these scenarios.Comment: 11 pages, 4 figure

Deciphering large-scale superposed fold systems at shallow crustal levels in collision zones: insights from the Marguareis Massif (southwestern Alps)

We present and discuss the results of a field-based approach including accurate geological mapping and micro- to map-scale structural analysis to highlight the finite strain pattern recorded in Marguareis Unit, a massif deformed at shallow crustal levels at the boundary between Maritime and Ligurian Alps. We describe superposed tectonic structures developed under low-grade metamorphic conditions during the Alpine collision and nowadays exceptionally well recorded in the area of interest. We demonstrate that the structural frame of the Marguareis Unit results from superposition of fourfold systems, later segmented, but without significant displacements, by brittle faults

Spectral distribution of scattered light from a chemical relaxation system

The aim of this work is to describe the light scattering spectra of a quaternary reacting gas mixture from the macroscopic field equations derived from the kinetic BGK-type model proposed by the authors in a previous paper. The study is developed in a hydrodynamic regime for which the system of the field equations of constituent number densities, momentum and temperature of the mixture is closed by the constitutive equations for rate of reaction, diffusion velocities, pressure tensor and heat flux vector. The spontaneous Rayleigh-Brillouin scattering is calculated from the constituent density perturbations of the linearized field equations, and its line shape is drawn for two different mixtures of the Hydrogen-Chlorine system showing the induced chemical reaction effect.Brazilian Research Council (CNPq)Universidade do Minho. Centro de Matemática(CMat)Fundação para a Ciência e a Tecnologia (FCT) - FCT-PTDC/MAT/68615/2006Italian National Project GNFM 2009/1

The worldwide costs of marine protected areas

Declines in marine harvests, wildlife, and habitats have prompted calls at both the 2002 World Summit on Sustainable Development and the 2003 World Parks Congress for the establishment of a global system of marine protected areas (MPAs). MPAs that restrict fishing and other human activities conserve habitats and populations and, by exporting biomass, may sustain or increase yields of nearby fisheries. Here we provide an estimate of the costs of a global MPA network, based on a survey of the running costs of 83 MPAs worldwide. Annual running costs per unit area spanned six orders of magnitude, and were higher in MPAs that were smaller, closer to coasts, and in high-cost, developed countries. Models extrapolating these findings suggest that a global MPA network meeting the World Parks Congress target of conserving 20–30% of the world’s seas might cost between $5 billion and$19 billion annually to run and would probably create around one million jobs. Although substantial, gross network costs are less than current government expenditures on harmful subsidies to industrial fisheries. They also ignore potential private gains from improved fisheries and tourism and are dwarfed by likely social gains from increasing the sustainability of fisheries and securing vital ecosystem services

Linear Operator Inequality and Null Controllability with Vanishing Energy for unbounded control systems

We consider linear systems on a separable Hilbert space $H$, which are null controllable at some time $T_0>0$ under the action of a point or boundary control. Parabolic and hyperbolic control systems usually studied in applications are special cases. To every initial state $y_0 \in H$ we associate the minimal "energy" needed to transfer $y_0$ to $0$ in a time $T \ge T_0$ ("energy" of a control being the square of its $L^2$ norm). We give both necessary and sufficient conditions under which the minimal energy converges to $0$ for $T\to+\infty$. This extends to boundary control systems the concept of null controllability with vanishing energy introduced by Priola and Zabczyk (Siam J. Control Optim. 42 (2003)) for distributed systems. The proofs in Priola-Zabczyk paper depend on properties of the associated Riccati equation, which are not available in the present, general setting. Here we base our results on new properties of the quadratic regulator problem with stability and the Linear Operator Inequality.Comment: In this version we have also added a section on examples and applications of our main results. This version is similar to the one which will be published on "SIAM Journal on Control and Optimization" (SIAM