8,255 research outputs found
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 , are considered in
such a way that the standard linear equations are recovered in the limit . Interestingly, these equations present a common, soliton-like,
travelling solution, which is written in terms of the -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
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
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