Event-Triggered Observers and Observer-Based Controllers for a Class of Nonlinear Systems

In this paper, we investigate the stabilization of a nonlinear plant subject to network constraints, under the assumption of partial knowledge of the plant state. The event triggered paradigm is used for the observation and the control of the system. Necessary conditions, making use of the ISS property, are given to guarantee the existence of a triggering mechanism, leading to asymptotic convergence of the observer and system states. The proposed triggering mechanism is illustrated in the stabilization of a robot with a flexible link robot.Comment: Proceedings of the 2015 American Control Conference - ACC 201

Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182

Collisions of particles in locally AdS spacetimes I. Local description and global examples

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph $\Gamma$. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than $2\pi$ on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of $\Gamma$). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.Comment: This is a rewritten version of the first part of arxiv:0905.1823. That preprint was too long and contained two types of results, so we sliced it in two. This is the first part. Some sections have been completely rewritten so as to be more readable, at the cost of slightly less general statements. Others parts have been notably improved to increase readabilit

Electroweak Evolution Equations

Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings.Comment: 15 pages, 3 figure

Slow-slip events in semi-brittle serpentinite fault zones

Slow-slip events are earthquake-like events only with much lower slip rates. While peak coseismic velocities can reach tens of meters per second, slow-slip is on the order of 10^(−7±2) m/s and may last for days to weeks. Under the rate-and-state model of fault friction, slow-slip is produced only when the asperity size is commensurate with the critical nucleation size, a function of frictional properties. However, it is unlikely that all subduction zones embody the same frictional properties. In addition to friction, plastic flow of antigorite-rich serpentinite may significantly influence the dynamics of fault slip near the mantle wedge corner. Here, we show that the range of frictional parameters that generate slow slip is widened in the presence of a serpentinized layer along the subduction plate interface. We observe increased stability and damping of fast ruptures in a semi-brittle fault zone governed by both brittle and viscoelastic constitutive response. The rate of viscous serpentinite flow, governed by dislocation creep, is enhanced by high ambient temperatures. When effective viscosity is taken to be dynamic, long-term slow slip events spontaneously emerge. Integration of rheology, thermal effects, and other microphysical processes with rate-and-state friction may yield further insight into the phenomenology of slow slip

Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

The management of student´s virtual money – sensibilisation and learning for life

The advanced technological age, marketing and society of the abundance in which we live, have a strong influence on the consumption and eating habits of the children. Every day in schools, these little human beings make autonomous choices and their parents, despite seeking to control and know their actions, cannot do it entirely for many reasons. The study was carried out in a group of the fifth grade and their results were subjected to a descriptive and inferential analysis, in which the purpose was to study the relation of some of the variables in question. The conclusions point for example to the parents' lack of knowledge in what concerns the type of consumption and on how their students spend their money. So it can be said that the role of the school in raising responsible citizens in managing their money is a necessary and continuous learning throughout the school life.info:eu-repo/semantics/publishedVersio

Fuchsian convex bodies: basics of Brunn--Minkowski theory

The hyperbolic space \H^d can be defined as a pseudo-sphere in the $(d+1)$ Minkowski space-time. In this paper, a Fuchsian group $\Gamma$ is a group of linear isometries of the Minkowski space such that \H^d/\Gamma is a compact manifold. We introduce Fuchsian convex bodies, which are closed convex sets in Minkowski space, globally invariant for the action of a Fuchsian group. A volume can be associated to each Fuchsian convex body, and, if the group is fixed, Minkowski addition behaves well. Then Fuchsian convex bodies can be studied in the same manner as convex bodies of Euclidean space in the classical Brunn--Minkowski theory. For example, support functions can be defined, as functions on a compact hyperbolic manifold instead of the sphere. The main result is the convexity of the associated volume (it is log concave in the classical setting). This implies analogs of Alexandrov--Fenchel and Brunn--Minkowski inequalities. Here the inequalities are reversed

Integrating hydraulic modelling and GIS for wastewater systems management: a case study

The increasing costs related to operation and maintenance of urban wastewater systems has led to a special attention of utilities in promoting studies to address the key problem of water infiltration, inflow and improper connections entering the separate drainage networks. This is a common and hard to predict operational situation that needs to be identified and minimized as it negatively affects the managerial conditions of the network and the downstream wastewater treatment plant (WWTP) efficiency. Management difficulties in separate drainage networks seldom occur when unexpected groundwater inflow, stormwater infiltration, and flows from improper connections enter into the dedicated sanitary sewer systems. Although the consequences that improper flows may have on wastewater systems are known, the problem is difficult to locate and quantify. The use of modelling tools is of special relevance to the planning, management and rehabilitation of these types of systems, which can be very useful for: (i) evaluating the capacity of existing systems in real time; (ii) testing alternative solutions to solve problems detected; or testing different procedures to operate the systems in extreme events scenarios. The implementation of mathematical models for determining the hydrodynamics behaviour of dry-weather and wet-weather flows in sewers was applied in a small urban wastewater network of the city of Braga in Portugal (Figure 1). The free user program US EPA SWMM was applied with the integration of GIS InterAqua information related to the wastewater collection system

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page