Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure

We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and V\'azquez, where the pressure is obtained as a Riesz potential associated to the density. We take advantage of the displacement convexity of the Riesz potential in one dimension to show a functional inequality involving the entropy, entropy dissipation, and the Euclidean transport distance. An argument by approximation shows that this functional inequality is enough to deduce the exponential convergence of solutions in self-similar variables to the unique steady states

Investigation of the Nicole model

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behaviour to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemi model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur

A Study of a Road Landslide in Puerto Rico

Numerous landslides have plagued the construction of a 1.3 mile road sector in the mountainous region of central Puerto Rico. The area is underlain by a sequence of landslide deposits overlying a muddy limestone and hard overconsolidated clayey soils. Landslides have occurred in both cuts and fills that have delayed the road construction for a period of more than two years, bringing as a result, great economic losses for the Puerto Rico Highway Authority. The landslide trigger mechanism has been intimately related to high rainfall, commonly observed in this region. The geotechnical and geological studies performed previous to the construction of this road sector were few and meager. These studies did not recognize the presence of unstable deposits along the road sector alignment. As a result, several large slope failures developed during construction that halted the completion of the road. For investigating the slope failures, detailed geological and geotechnical studies were performed, including monitoring of groundwater levels, rainfall, and slope movements followed by laboratory and slope stability analyses. Remedial measures have been provided in the form of excavation, drainage, and stability berms. Renewal of the road construction with the remedial measures is prompt to start

Modelos de producción de madera sólida en plantaciones de Eucalyptus globulus de Galicia

El objetivo de este trabajo es establecer las interacciones existentes entre crecimiento diametral, crecimiento en altura y la dinámica de poda natural de Eucalyptus globulus con el objetivo de evaluar la eficiencia de distintas opciones de gestión forestal para producir madera de alta calidad. Para ello se ha desarrollado un modelo de crecimiento basados en el árbol individual. La toma de muestras comprende más de 900 Eucalyptus globulus medidos en diferentes localizaciones de Galicia (España). En esos árboles se ha encontrado una elevada correlación significativa entre el diámetro normal y el diámetro de la copa. El modelo basado en el ancho de copa permite calcular el espacio vital requerido por un árbol para alcanzar un diámetro predefinido a una cierta edad. Una vez conocido, es también posible calcular el número de árboles por hectárea así como el momento y la intensidad de las claras. Se ha podido comprobar que los eucaliptos orientados a la producción de madera aserrada en rotaciones cortas tienen que podarse y, dada la tendencia de los árboles a incluir el tocón de las ramas muertas, es recomendable realizar la poda mientras las ramas todavía están verdes. Para optimizar la producción de madera limpia, es esencial conocer el impacto de los tratamientos silvícolas y condiciones de crecimiento en el proceso de formación de la base de la copa. Se ha encontrado que la altura de la base de copa viva muestra una buena correlación con el diámetro normal, la altura del árbol y la edad. Empleando estas tres variables se ha desarrollado un modelo multivariable para predecir la altura de la primera rama viva, que puede ser de utilidad para optimizar el momento y la intensidad de las claras para producir madera de sierra de eucalipto en plantaciones de corta rotación._________________________________The study aims to point out the interactions between diameter and height growth and the self-pruning dynamics of Eucalyptus globulus in order to evaluate different management regimes according to their efficiency for high value timber production. Therefore a growth model for individual trees has been developed. The database contains over 900 trees of Eucalyptus globulus measured at different sites in Galicia / Spain. For these trees a significant relationship between diameter at breast height (d1,3) and crown diameter calculated from this area was found. The crown width model enables us to calculate the growing space needed by a tree to get a pre-defined diameter at a given age. Knowing this, it is also possible to calculate the number of trees/ha as well as time and intensity of thinning interventions. It could be shown that eucalypt grown for sawlogs in short rotations have to be pruned. Since the trees tend to include dead branches partly into the bole, it is recommendable to prune branches when still green. In order to optimize production of knot free timber, it is essential to know the impact of silvicultural treatments and growth conditions on the process of living crown base recession. It was found that height of living crown base shows good correlations with d1,3, tree height and age. Using these 3 variables a multivariate model for predicting height of the first living branch has been developed, which may be helpful to optimize time and intensity of pruning for eucalypt sawlog production in short rotation plantations

Millimeter polarisation of the protoplanetary nebula OH 231.8+4.2: A follow-up study with CARMA

In order to investigate the characteristics and influence of the magnetic field in evolved stars, we performed a follow-up investigation of our previous submillimeter analysis of the proto-planetary nebula (PPN) OH 231.8+4.2 (Sabin et al. 2014), this time at 1.3mm with the CARMA facility in polarisation mode for the purpose of a multi-scale analysis. OH 231.8+4.2 was observed at ~2.5" resolution and we detected polarised emission above the 3-sigma threshold (with a mean polarisation fraction of 3.5 %). The polarisation map indicates an overall organised magnetic field within the nebula. The main finding in this paper is the presence of a structure mostly compatible with an ordered toroidal component that is aligned with the PPN's dark lane. We also present some alternative magnetic field configuration to explain the structure observed. These data complete our previous SMA submillimeter data for a better investigation and understanding of the magnetic field structure in OH 231.8+4.2.Comment: 7 pages, 5 figures, 2 tables. Accepted for publication in MNRA

Plasmonic coupling in closed-packed ordered gallium nanoparticles

Plasmonic gallium (Ga) nanoparticles (NPs) are well known to exhibit good performance in numerous applications such as surface enhanced fluorescence and Raman spectroscopy or biosensing. However, to reach the optimal optical performance, the strength of the localized surface plasmon resonances (LSPRs) must be enhanced particularly by suitable narrowing the NP size distribution among other factors. With this purpose, our last work demonstrated the production of hexagonal ordered arrays of Ga NPs by using templates of aluminium (Al) shallow pit arrays, whose LSPRs were observed in the VIS region. The quantitative analysis of the optical properties by spectroscopic ellipsometry confirmed an outstanding improvement of the LSPR intensity and full width at half maximum (FWHM) due to the imposed ordering. Here, by engineering the template dimensions, and therefore by tuning Ga NPs size, we expand the LSPRs of the Ga NPs to cover a wider range of the electromagnetic spectrum from the UV to the IR regions. More interestingly, the factors that cause this optical performance improvement are studied with the universal plasmon ruler equation, supported with discrete dipole approximation simulations. The results allow us to conclude that the plasmonic coupling between NPs originated in the ordered systems is the main cause for the optimized optical responseThe research is supported by the MINECO (CTQ2014-53334-C2-2-R, CTQ2017-84309-C2-2-R and MAT201676824-C3-1-R) and Comunidad de Madrid (P2018/NMT4349 and S2018/NMT-4321 NANOMAGCOST) projects. ARC acknowledges Ramón y Cajal program (under contract number RYC-2015-18047

Nonlinear Relativistic and Quantum Equations with a Common Type of Solution

Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way that the standard linear equations are recovered in the limit $q \rightarrow 1$. Interestingly, these equations present a common, soliton-like, travelling solution, which is written in terms of the $q$-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of $q$

Three-dimensional numerical simulation of 1GeV/Nucleon U92+ impact against atomic hydrogen

The impact of 1GeV/Nucleon U92+ projectiles against atomic hydrogen is studied by direct numerical resolution of the time-dependent wave equation for the atomic electron on a three-dimensional Cartesian lattice. We employ the fully relativistic expressions to describe the electromagnetic fields created by the incident ion. The wave equation for the atom interacting with the projectile is carefully derived from the time-dependent Dirac equation in order to retain all the relevant terms.Comment: 12 pages and 7 figures included in the tex