1,030 research outputs found
A macroscopic model that connects the molar excess entropy of a deeply supercooled liquid near its glass transition temperature to its viscosity
For a deeply supercooled liquid near its glass transition temperature, we
suggest a possible way to connect the temperature dependence of its molar
excess entropy to that of its viscosity by constructing a macroscopic model,
where the deeply supercooled liquid is assumed to be a mixture of solid-like
and liquid-like micro regions. In this model, we assume that the mole fraction
x of the liquid-like micro regions tends to zero as the temperature T of the
liquid is decreased and extrapolated to a temperature Tg*, which we assume to
be below but close to the lowest glass transition temperature Tg attainable
with the slowest possible cooling rate for the liquid. Without referring to any
specific microscopic nature of the solid-like and liquid-like micro regions, we
also assume that near Tg, the molar enthalpy of the solid-like micro regions is
lower than that of the liquid-like micro regions. We then show that the
temperature dependence of x is directly related to that of the molar excess
entropy. Close to Tg, we assume that an activated motion of the solid-like
micro regions controls the viscosity and that this activated motion is a
collective motion involving practically all of the solid-like micro-regions so
that the molar activation free energy for the activated motion is proportional
to the mole fraction, 1-x, of the solid-like micro regions. The temperature
dependence of the viscosity is thus connected to that of the molar excess
entropy through the temperature dependence of the mole fraction x. As an
example, we apply our model to a class of glass formers for which the molar
excess entropy at temperatures near Tg is proportional to 1-T/TK with TK < Tg
\sim Tg* and find their viscosities to be well approximated by the
Vogel-Fulcher-Tamman equation for temperatures very close to Tg. We estimate
the values of three parameters in our model for three glass formers in this
class.Comment: 29 pages. Extensively revised in sections I, II, III.G, III.H, IV,
VI, and VI
Ensaios em análise assintótica de regressão não-paramétrica
This work is composed of three essays in the eld of nonparametric inference, all closely inter-related. The rst essay aims to stablish uniform convergence rates under mixing conditions for the local linear estimator under a xed-design setting of the form t/T, t ∈ {1, . . . , T}, T ∈ N. It was found that the order of the weak and the strong uniform convergence is the same as that of stablished by Hansen (2008) and Kristensen (2009) for the random design setting. The second essay studies the asymptotic properties of the estimators derived from reversing the three-step procedure of Vogt and Linton (2014). Weak uniform convergence rates was given to the trend and the periodic sequence estimators. Furthermore, the consistency of the fundamental period estimator and the asymptotic normality of the trend estimator was also stablished. The last study investigates the nite sample behavior of the estimators considered in the second essay. A plug-in type bandwith was proposed for the trend estimator. From our simulation results, the plug-in bandwidth performed well and the period estimator showed to be quite robust with respect to di erent bandwidth choices. The study was complemented with two applications, one in climatology and the other in economics.Este trabalho é composto por três ensaios na área de inferência não-paramétrica, bastante inter-relacionados. O primeiro ensaio visa estabelecer ordens de convergência uniforme sob condições mixing para o estimador linear local quando a estrutura de pontos é xa e da forma t/T, t ∈ {1, . . . , T}, T ∈ N. A ordem encontrada para as convergências uniforme, em probabilidade e quase certa, é a mesma daquela estabelecida por Hansen (2008) e Kristensen (2009) para o caso de estrutura de pontos aleatórios. O segundo ensaio estuda as propriedades assintóticas de estimadores obtidos ao se inverter o esquema de estimação em três etapas de Vogt e Linton (2014). Foram fornecidas as ordens de convergência uniforme em probabilidade para os estimadores da função de tendência e da sequência periódica. Além disso, a consistência do estimador do período fundamental e a normalidade assintótica do estimador de tendência também foram estabelecidas. O último estudo investiga o comportamento em amostras nitas dos estimadores considerados no segundo ensaio. Foram propostas janelas para o estimador de tendência do tipo plug-in. Para as simulações realizadas, a janela plug-in mostrou bom desempenho e o estimador do período revelou-se bastante robusto em resposta à diferentes escolhas de janelas. O estudo foi complementado com duas aplicações, uma em climatologia e outra em economia
Chromo-field flux sheets as confining gauge field configurations in the SU(N) Euclidean Yang-Mills theory in the Landau gauge
For the four-dimensional SU(N) Euclidean Yang-Mills theory in the Landau
gauge, we present two sets of gauge field configurations that satisfy the
Euclidean equations of motion. These configurations generate four-dimensional
chromo-field flux sheets whose spatial cross sections are three-dimensional
chromo-field flux tubes. In lattice simulations, they may be detected as center
vortices. The first set of gauge field configurations generates chromo-electric
flux tubes that should contribute to a chromo-electric flux tube between two
static color charges. The string tension for two static color charges in
representation r then naturally satisfies the Casimir scaling. Applying a gauge
transformation to this set of gauge field configurations, we can transform them
into those in the maximal Abelian gauge. These transformed configurations
generate chromo-electric flux tubes that should contribute to those observed
between two static quarks in lattice simulations performed in the maximal
Abelian gauge. The second set of gauge field configurations generates
chromo-magnetic flux tubes. When rotated in a plane that includes the
temporal-axis and is perpendicular to the flux tube axis, the rotated gauge
field configuration generates a chromo-electric flux tube and should contribute
to the chromo-electric flux tubes observed in lattice simulations in the Landau
gauge. We also argue that when regulated on a lattice, any of the flux sheet
gauge field configuration with a finite flux sheet thickness is located on the
Gribov horizon in the infinite lattice volume limit. We thus suggest that these
sets of gauge field configurations contribute significantly to the low energy
properties of QCD, particularly the quark confinement.Comment: 31 pages. The version to appear in Physical Review
Filmy Cloud Removal on Satellite Imagery with Multispectral Conditional Generative Adversarial Nets
In this paper, we propose a method for cloud removal from visible light RGB
satellite images by extending the conditional Generative Adversarial Networks
(cGANs) from RGB images to multispectral images. Satellite images have been
widely utilized for various purposes, such as natural environment monitoring
(pollution, forest or rivers), transportation improvement and prompt emergency
response to disasters. However, the obscurity caused by clouds makes it
unstable to monitor the situation on the ground with the visible light camera.
Images captured by a longer wavelength are introduced to reduce the effects of
clouds. Synthetic Aperture Radar (SAR) is such an example that improves
visibility even the clouds exist. On the other hand, the spatial resolution
decreases as the wavelength increases. Furthermore, the images captured by long
wavelengths differs considerably from those captured by visible light in terms
of their appearance. Therefore, we propose a network that can remove clouds and
generate visible light images from the multispectral images taken as inputs.
This is achieved by extending the input channels of cGANs to be compatible with
multispectral images. The networks are trained to output images that are close
to the ground truth using the images synthesized with clouds over the ground
truth as inputs. In the available dataset, the proportion of images of the
forest or the sea is very high, which will introduce bias in the training
dataset if uniformly sampled from the original dataset. Thus, we utilize the
t-Distributed Stochastic Neighbor Embedding (t-SNE) to improve the problem of
bias in the training dataset. Finally, we confirm the feasibility of the
proposed network on the dataset of four bands images, which include three
visible light bands and one near-infrared (NIR) band
The Lax pairs and conserved quantities of the delay Lotka-Volterra equation
The delay Lotka-Volterra equation is a delay-differential extension of the
well known Lotka-Volterra equation, and is known to have N-soliton solutions.
In this paper, Backlund transformations, Lax pairs and infinite conserved
quantities of the delay Lotka-Volterra equation and its discrete analogue are
constructed. The conserved quantities of the delay Lotka-Volterra equation turn
out to be complicated and described by using the time-ordered product of linear
operators.Comment: 11 page
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