Inexactness of the Hydro-Thermal Coordination Semidefinite Relaxation

Hydro-thermal coordination is the problem of determining the optimal economic dispatch of hydro and thermal power plants over time. The physics of hydroelectricity generation is commonly simplified in the literature to account for its fundamentally nonlinear nature. Advances in convex relaxation theory have allowed the advent of Shor's semidefinite programming (SDP) relaxations of quadratic models of the problem. This paper shows how a recently published SDP relaxation is only exact if a very strict condition regarding turbine efficiency is observed, failing otherwise. It further proposes the use of a set of convex envelopes as a strategy to successfully obtain a stricter lower bound of the optimal solution. This strategy is combined with a standard iterative convex-concave procedure to recover a stationary point of the original non-convex problem.Comment: Submitted to IEEE PES General Meeting 201

Probing the gluon density of the proton in the exclusive photoproduction of vector mesons at the LHC: A phenomenological analysis

The current uncertainty on the gluon density extracted from the global parton analysis is large in the kinematical range of small values of the Bjorken - $x$ variable and low values of the hard scale $Q^2$. An alternative to reduces this uncertainty is the analysis of the exclusive vector meson photoproduction in photon - hadron and hadron - hadron collisions. This process offers a unique opportunity to constrain the gluon density of the proton, since its cross section is proportional to the gluon density squared. In this paper we consider current parametrizations for the gluon distribution and estimate the exclusive vector meson photoproduction cross section at HERA and LHC using the leading logarithmic formalism. We perform a fit of the normalization of the $\gamma h$ cross section and the value of the hard scale for the process and demonstrate that the current LHCb experimental data are better described by models that assume a slow increasing of the gluon distribution at small - $x$ and low $Q^2$.Comment: 8 pages, 6 figures, 1 table. Version published in European Physical Journal

The influence of the Al stabilizer layer thickness on the normal zone propagation velocity in high current superconductors

The stability of high-current superconductors is challenging in the design of superconducting magnets. When the stability requirements are fulfilled, the protection against a quench must still be considered. A main factor in the design of quench protection systems is the resistance growth rate in the magnet following a quench. The usual method for determining the resistance growth in impregnated coils is to calculate the longitudinal velocity with which the normal zone propagates in the conductor along the coil windings. Here, we present a 2D numerical model for predicting the normal zone propagation velocity in Al stabilized Rutherford NbTi cables with large cross section. By solving two coupled differential equations under adiabatic conditions, the model takes into account the thermal diffusion and the current redistribution process following a quench. Both the temperature and magnetic field dependencies of the superconductor and the metal cladding materials properties are included. Unlike common normal zone propagation analyses, we study the influence of the thickness of the cladding on the propagation velocity for varying operating current and magnetic field. To assist in the comprehension of the numerical results, we also introduce an analytical formula for the longitudinal normal zone propagation. The analysis distinguishes between low-current and high-current regimes of normal zone propagation, depending on the ratio between the characteristic times of thermal and magnetic diffusion. We show that above a certain thickness, the cladding acts as a heat sink with a limited contribution to the acceleration of the propagation velocity with respect to the cladding geometry. Both numerical and analytical results show good agreement with experimental data.Comment: To be published in Physics Procedia (ICEC 25 conference special issue

Radiation in 1.5 GeV and 12 GeV laser wakefield acceleration stages from PIC simulations

WOS:000287176200029 (Nº de Acesso Web of Science)A massivelly parallel post-processing radiation diagnostic for PIC codes is presented, which is then used to study the main features of the radiation from single LWFA stages (1.5 GeV and 12 GeV). This diagnostic also allows to examine radiation signatures associated with the physics of self-injection

Models as arrows: the role of dialgebras

A large number of computational processes can suitably be described as a combination of construction, i.e. algebraic, and observation, i.e. coalgebraic, structures. This paper suggests dialgebras as a generic model in which such structures can be combined and proposes a small calculus of dialgebras including a wrapping combinator and se- quential composition. To take good care of invariants in software design, the paper also discusses how dialgebras can be typed by predicates and proves that invariants are preserved through composition. This lays the foundations for a full calculus of invariant proof-obligation discharge for dialgebraic models.Fundação para a Ciência e a Tecnologia (FCT

Refinement via interpretation

Traditional notions of refinement of algebraic specifications, based on signature morphisms, are often too rigid to capture a number of relevant transformations in the context of software design, reuse and adaptation. This paper proposes an alternative notion of specification refinement, building on recent work on logic interpretation. The concept is discussed, its theory partially developed, its use illustrated through a number of examples.This research was supported by FCT (the Portuguese Foundation for Science and Technology) under contracts PTDC/EIA/73252/2006, at Minho University, as well as PTDC/MAT/68723/2006 and the Unidade de Investigacao Matematica e Aplicaoes of University of Aveiro

Reasoning about complex requirements in a uniform setting

The paper formulates HEQ, an institution for hybrid equational logic to provide a uniform setting to express and reasoning about different sorts of properties of complex software. It is also shown how, through the definition of a suitable comorphism to FOL, this can be integrated in Hets, providing suitable tool support for teaching and re- search. The whole exercise was motivated by the need to unify, in a single undergraduate course in a Computer Science curriculum, the specification of data and behavioural constraints of reconfigurable systems.Fundação para a Ciência e a Tecnologia (FCT