Loss Allocation in Distribution Networks Based on Aumann-Shapley

This paper outlines a procedure for loss allocation in both radial and meshed distribution networks with distributed generation that could be regulated in various ways. The method is analytically developed based on the theory of electrical circuits combined with game theory based on Aumann&-Shapley, which guarantees both the electrical principles and the fair axioms of game theory. The proposed method obtains unitary participation coefficients for each network user based on the currents demanded/injected by each user and the network topology. The proposed allocation method based on Aumann&-Shapley has been compared with other traditional allocation methods, is adaptable to distribution networks, and shows great potential and ease of implementation. Moreover, it can be applied to any kind of distribution network (radial or meshed) with distributed energy resources

Fracture in distortion gradient plasticity

In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye's tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic stress singularity. This finding is verified by detailed finite element analyses using a new numerical framework, which builds upon a viscoplastic constitutive law that enables capturing both rate-dependent and rate-independent behaviour in a computationally efficient manner. Numerical analysis is used to gain further insight into the stress elevation predicted by distortion gradient plasticity, relative to conventional J2 plasticity, and the influence of the plastic spin under both mode I and mixed-mode fracture conditions. It is found that Nye's tensor contributions have a weaker effect in elevating the stresses in the plastic region, while predicting the same asymptotic behaviour as constitutive choices based on the plastic strain gradient tensor. A minor sensitivity to X, the parameter governing the dissipation due to the plastic spin, is observed. Finally, distortion gradient plasticity and suitable higher order boundary conditions are used to appropriately model the phenomenon of brittle failure along elastic-plastic material interfaces. We reproduce paradigmatic experiments on niobium-sapphire interfaces and show that the combination of strain gradient hardening and dislocation blockage leads to interface crack tip stresses that are larger than the theoretical lattice strength, rationalising cleavage in the presence of plasticity at bi-material interfaces

The multicomponent 2D Toda hierarchy: Discrete flows and string equations

The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix types are proposed and studied. Orlov--Schulman operators, string equations and additional symmetries (discrete and continuous) are considered. The continuous-discrete Lax equations are shown to be equivalent to a factorization problem as well as to a set of string equations. A congruence method to derive site independent equations is presented and used to derive equations in the discrete multicomponent KP sector (and also for its modification) of the theory as well as dispersive Whitham equations.Comment: 27 pages. In the revised paper we improved the presentatio

Gradient-enhanced statistical analysis of cleavage fracture

We present a probabilistic framework for brittle fracture that builds upon Weibull statistics and strain gradient plasticity. The constitutive response is given by the mechanism-based strain gradient plasticity theory, aiming to accurately characterize crack tip stresses by accounting for the role of plastic strain gradients in elevating local strengthening ahead of cracks. It is shown that gradients of plastic strain elevate the Weibull stress and the probability of failure for a given choice of the threshold stress and the Weibull parameters. The statistical framework presented is used to estimate failure probabilities across temperatures in ferritic steels. The framework has the capability to estimate the three statistical parameters present in the Weibull-type model without any prior assumptions. The calibration against experimental data shows important differences in the values obtained for strain gradient plasticity and conventional J2 plasticity. Moreover, local probability maps show that potential damage initiation sites are much closer to the crack tip in the case of gradient-enhanced plasticity. Finally, the fracture response across the ductile-to-brittle regime is investigated by computing the cleavage resistance curves with increasing temperature. Gradient plasticity predictions appear to show a better agreement with the experiments

The time traveler's guide to the quantization of zero modes

We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero mode in the Einstein cylinder. We show how this choice arises from the computation of the vacuum Wightman function and the vacuum renormalized stress-energy tensor in the time-machine geometry. Finally, we relate the previously proposed regularization of the zero mode state as a squeezed state with the time-machine warp parameter, thus demonstrating that the quantization in the latter regularizes the quantization in an Einstein cylinder

Vademécum de cardiología

En este trabajo revisamos los fármacos que pueden emplearse en Cardiología, destacando en negrita aquellos cuyo uso es más frecuente. Los nombres comerciales que citamos no responden a ningún fin publicitario, existiendo otros muchos que pueden ser igualmente utilizados. Las dosis indicadas son aquellas que están internacionalmente reconocidas o, en su defecto, aquellas que los autores consideran adecuadas basándose en su experiencia personal en la Cardiología clínica práctica de los pequeños animales. Cuando no existen dosis reconocidas de algún medicamento, se ha dejado un espacio para poder completar gradualmente este vademécum.This paper reviews the drugs we can use in small animals Cardiology highlighting in bold face those used most often. The brand names named in this report are not used with intention of publicity, existing many other drugs that can be used in their place in Spain. The dosages we indicate are internationaly accepted or they are those the authors employ according to their personal experience in the Cardiology of small animals. When we don 't have recognized dosages of a drug, we have put a space to complete gradually this vademecum

The model equation of soliton theory

We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most interesting result is the simple equation for the generating function of the hierarchy which defines the dynamics for the negative times and also has applications to the second order spectral problems. A rather general theory of integrable 1+1-dimensional equations can be developed by study of polynomial solutions of this equation under condition of regularity of the corresponding potentials.Comment: 17