Discrete structures in continuum descriptions of defective crystals

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular I provide a quite general list of `plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspond-ingly general constitutive specification

Low Energy Solutions for the Semiclassical Limit of Schrodinger–Maxwell Systems

We show that the number of positive solutions of Schrodinger– Maxwell system on a smooth bounded domain depends on the topological properties of the domain. In particular we consider the Lusternik– Schnirelmann category and the Poincaré polynomial of the domain

On the isometry group of RCD∗(K,N)-spaces

This is a post-peer-review pre-copyedit version of an article published in Manuscripta Mathematica. The final authentical version is avaible online https://doi.org/10.1007/s00229-018-1010-7We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition,RCD∗(K,N),is a Lie group. We obtain an optimal upper bound on the dimension of this group, and classify the spaces where this maximal dimension is attained.L. Guijarro and J. Santos-Rodríguez were supported by research grants MTM2014-57769-3-P, and MTM2017-85934-C3-2-P (MINECO) and ICMAT Severo Ochoa Project SEV-2015-0554 (MINECO). J. Santos-Rodríguez was supported by a PhD scholarship awarded byCONACY

Symplectically degenerate maxima via generating functions

We provide a simple proof of a theorem due to Nancy Hingston, asserting that symplectically degenerate maxima of any Hamiltonian diffeomorphism of the standard symplectic 2d-torus are non-isolated contractible periodic points or their action is a non-isolated point of the average-action spectrum. Our argument is based on generating functions.Comment: 25 pages, thoroughly revised version, new titl

A unified approach to Poisson-Hopf deformations of Lie-Hamilton systems based on sl(2)

Producción CientíficaBased on a recently developed procedure to construct Poisson-Hopf deformations of Lie–Hamilton systems, a novel unified approach to nonequivalent deformations of Lie–Hamilton systems on the real plane with a Vessiot–Guldberg Lie algebra isomorphic to sl(2) is proposed. This, in particular, allows us to define a notion of Poisson–Hopf systems in dependence of a parameterized family of Poisson algebra representations. Such an approach is explicitly illustrated by applying it to the three non-diffeomorphic classes of sl(2) Lie–Hamilton systems. Our results cover deformations of the Ermakov system, Milne–Pinney, Kummer–Schwarz and several Riccati equations as well as of the harmonic oscillator (all of them with t-dependent coefficients). Furthermore t-independent constants of motion are given as well. Our methods can be employed to generate other Lie–Hamilton systems and their deformations for other Vessiot–Guldberg Lie algebras and their deformations

Quantization of Midisuperspace Models

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit

Different Host Exploitation Strategies in Two Zebra Mussel-Trematode Systems: Adjustments of Host Life History Traits

The zebra mussel is the intermediate host for two digenean trematodes, Phyllodistomum folium and Bucephalus polymorphus, infecting gills and the gonad respectively. Many gray areas exist relating to the host physiological disturbances associated with these infections, and the strategies used by these parasites to exploit their host without killing it. The aim of this study was to examine the host exploitation strategies of these trematodes and the associated host physiological disturbances. We hypothesized that these two parasite species, by infecting two different organs (gills or gonads), do not induce the same physiological changes. Four cellular responses (lysosomal and peroxisomal defence systems, lipidic peroxidation and lipidic reserves) in the host digestive gland were studied by histochemistry and stereology, as well as the energetic reserves available in gonads. Moreover, two indices were calculated related to the reproductive status and the physiological condition of the organisms. Both parasites induced adjustments of zebra mussel life history traits. The host-exploitation strategy adopted by P. folium would occur during a short-term period due to gill deformation, and could be defined as “virulent.” Moreover, this parasite had significant host gender-dependent effects: infected males displayed a slowed-down metabolism and energetic reserves more allocated to growth, whereas females displayed better defences and would allocate more energy to reproduction and maintenance. In contrast, B. polymorphus would be a more “prudent” parasite, exploiting its host during a long-term period through the consumption of reserves allocated to reproduction