Global pointwise estimates for Green's matrix of second order elliptic systems

We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate. Moreover, we prove that such a local boundedness estimate for weak solutions of the system is equivalent to the usual global pointwise bound for the Green's matrix. In the scalar case, such an estimate is a consequence of De Giorgi-Moser-Nash theory and holds for equations with bounded measurable coefficients in arbitrary domains. In the vectorial case, one need to impose certain assumptions on the coefficients of the system as well as on domains to obtain such an estimate. We present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result.Comment: 17 pages, accepted in J. Differential Equations, references adde

Equilibrium Initialization and Stability of Three-Dimensional Gas Disks

We present a new systematic way of setting up galactic gas disks based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disk. We first show that the required circular velocity has no dependence on the height above or below the midplane so long as the gas pressure is a function of density only. The assumption of disks being very thin enables us to decouple the vertical structure from the radial direction. Based on that, the equation of hydrostatic equilibrium together with the reduced Poisson equation leads to two sets of second-order non-linear differential equation, which are easily integrated to set-up a stable disk. We call one approach `density method' and the other one `potential method'. Gas disks in detailed balance are especially suitable for investigating the onset of the gravitational instability. We revisit the question of global, axisymmetric instability using fully three-dimensional disk simulations. The impact of disk thickness on the disk instability and the formation of spontaneously induced spirals is studied systematically with or without the presence of the stellar potential. In our models, the numerical results show that the threshold value for disk instability is shifted from unity to 0.69 for self-gravitating thick disks and to 0.75 for combined stellar and gas thick disks. The simulations also show that self-induced spirals occur in the correct regions and with the right numbers as predicted by the analytic theory.Comment: 17 pages, 10 figures, accepted by MNRA

Origin of superconductivity transition broadening in MgB2

We report resistivity and magnetization of single crystal MgB2, focusing on the broadening of superconducting (SC) transition in magnetic fields. In-plane and out-of-plane resistivity indicate that the broadening of superconducting transition is independent of Lorentz force and that it is merely dependent on the magnetic field direction. In magnetization, diamagnetic signal begins to appear at almost the same temperature as the onset temperature of resistivity transition. These results suggest that the broadening is attributed not to the surface superconductivity but to the superconducting fluctuation or the vortex-liquid picture, owing to the short coherence length and the high transition temperature of MgB2.Comment: 8pages, 6 figures, to be published in Physica

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

The pseudo scalar form factor of the nucleon, the sigma-like term, and the L0+L_0^+ amplitude for charged pion electro-production near threshold

The pseudo scalar form factor, which represents the pseudo scalar quark density distribution due to finite quark masses on the nucleon, is shown to manifest itself with the induced pseudo scalar form factor in the $L_0^+$ amplitude for the charged pion electro-production. Both form factors show their own peculiar momentum dependence. Under the approximation on which the Goldberg-Treimann relation holds, a sum of both form factors' contributions accounts for the t-channel contribution in the charged pion electro-production near threshold.Comment: 10 page

Neural Image-based Avatars: Generalizable Radiance Fields for Human Avatar Modeling

We present a method that enables synthesizing novel views and novel poses of arbitrary human performers from sparse multi-view images. A key ingredient of our method is a hybrid appearance blending module that combines the advantages of the implicit body NeRF representation and image-based rendering. Existing generalizable human NeRF methods that are conditioned on the body model have shown robustness against the geometric variation of arbitrary human performers. Yet they often exhibit blurry results when generalized onto unseen identities. Meanwhile, image-based rendering shows high-quality results when sufficient observations are available, whereas it suffers artifacts in sparse-view settings. We propose Neural Image-based Avatars (NIA) that exploits the best of those two methods: to maintain robustness under new articulations and self-occlusions while directly leveraging the available (sparse) source view colors to preserve appearance details of new subject identities. Our hybrid design outperforms recent methods on both in-domain identity generalization as well as challenging cross-dataset generalization settings. Also, in terms of the pose generalization, our method outperforms even the per-subject optimized animatable NeRF methods. The video results are available at https://youngjoongunc.github.io/ni

Metastability, Mode Coupling and the Glass Transition

Mode coupling theory (MCT) has been successful in explaining the observed sequence of time relaxations in dense fluids. Previous expositions of this theory showing this sequence have required the existence of an ideal glass transition temperature $T_0$. Recent experiments show no evidence of $T_0$. We show here how the theory can be reformulated, in a fundamental way, such that one retains this sequence of relaxation behaviors but with a smooth temperature dependence and without any indication of $T_0$. The key ingredient in the reformulation is the inclusion of the metastable nature of the glass transition problem through a coupling of the mass density to the defect density. A main result of our theory is that the exponents governing the sequence of time relaxations are weak functions of the temperature in contrast to the results from conventional MCT.Comment: 14 pages (2 figures upon request), REVTEX

A New Satellite-Based Retrieval of Low-Cloud Liquid-Water Path Using Machine Learning and Meteosat SEVIRI Data

Clouds are one of the major uncertainties of the climate system. The study of cloud processes requires information on cloud physical properties, in particular liquid water path (LWP). This parameter is commonly retrieved from satellite data using look-up table approaches. However, existing LWP retrievals come with uncertainties related to assumptions inherent in physical retrievals. Here, we present a new retrieval technique for cloud LWP based on a statistical machine learning model. The approach utilizes spectral information from geostationary satellite channels of Meteosat Spinning-Enhanced Visible and Infrared Imager (SEVIRI), as well as satellite viewing geometry. As ground truth, data from CloudNet stations were used to train the model. We found that LWP predicted by the machine-learning model agrees substantially better with CloudNet observations than a current physics-based product, the Climate Monitoring Satellite Application Facility (CM SAF) CLoud property dAtAset using SEVIRI, edition 2 (CLAAS-2), highlighting the potential of such approaches for future retrieval developments

Le tourbillon des sentiments amoureux dans la poésie de Marceline Desbordes-Valmore ou la poétisation d’une histoire amoureuse

Oubliées à tort pendant plusieurs siècles, les femmes de lettres, dont Christine de Pisan, Louise Labé, Madelaine et Catherine des Roches, Marceline Desbordes-Valmore et beaucoup d’autres, prêtaient à maintes reprises leur plume prolixe au service des épanchements du cœur. La voix féminine de la poésie courtoise, Christine de Pisan, s’est inscrite dans l’histoire comme la première Française à avoir jamais vécu de ses écrits. D’origine vénitienne, elle s’est permis, à la fin du XIVe, début du XVe siècle, de célébrer le mariage et chanter, en son propre nom, l’amour pour son mari et le délice de la nuit de noces afin de montrer du doigt le concept erroné de l’amour courtois, vanté par les troubadours. Néanmoins, ce n’est qu’à la Renaissance que la scène littéraire assiste à « l’avènement » de la figure de la femme écrivaine/poétesse, incarnée par-dessus tout dans le personnage de Louise Labé, femme dotée de la liberté d’esprit, qui assumait pleinement sa féminité dans ses vers. À l’aube du XIXe siècle, le cercle s’agrandit avec Marceline Desbordes-Valmore, connue de nos jours comme prédécesseure de la poésie romantique