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