Effective Kinetic Theory for High Temperature Gauge Theories

Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. We show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling $g(T)$ of high-temperature gauge theories [and all orders in $1/\log g(T)^{-1}$]. As previously proposed in the literature, a leading-order treatment requires including both $22$ particle scattering processes as well as effective ``$12$'' collinear splitting processes in the Boltzmann equations. The latter account for nearly collinear bremsstrahlung and pair production/annihilation processes which take place in the presence of fluctuations in the background gauge field. Our effective kinetic theory is applicable not only to near-equilibrium systems (relevant for the calculation of transport coefficients), but also to highly non-equilibrium situations, provided some simple conditions on distribution functions are satisfied.Comment: 40 pages, new subsection on soft gauge field instabilities adde

Real-World Repetition Estimation by Div, Grad and Curl

We consider the problem of estimating repetition in video, such as performing push-ups, cutting a melon or playing violin. Existing work shows good results under the assumption of static and stationary periodicity. As realistic video is rarely perfectly static and stationary, the often preferred Fourier-based measurements is inapt. Instead, we adopt the wavelet transform to better handle non-static and non-stationary video dynamics. From the flow field and its differentials, we derive three fundamental motion types and three motion continuities of intrinsic periodicity in 3D. On top of this, the 2D perception of 3D periodicity considers two extreme viewpoints. What follows are 18 fundamental cases of recurrent perception in 2D. In practice, to deal with the variety of repetitive appearance, our theory implies measuring time-varying flow and its differentials (gradient, divergence and curl) over segmented foreground motion. For experiments, we introduce the new QUVA Repetition dataset, reflecting reality by including non-static and non-stationary videos. On the task of counting repetitions in video, we obtain favorable results compared to a deep learning alternative

Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds

The obstruction to the existence of global action-angle coordinates of Abelian and noncommutative (non-Abelian) completely integrable systems with compact invariant submanifolds has been studied. We extend this analysis to the case of noncompact invariant submanifolds.Comment: 13 pages, to be published in J. Math. Phys. (2007

Looking for a time independent Hamiltonian of a dynamical system

In this paper we introduce a method for finding a time independent Hamiltonian of a given dynamical system by canonoid transformation. We also find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of damped oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.Comment: Some references added, LATEX fixing

Detection of X-ray galaxy clusters based on the Kolmogorov method

The detection of clusters of galaxies in large surveys plays an important part in extragalactic astronomy, and particularly in cosmology, since cluster counts can give strong constraints on cosmological parameters. X-ray imaging is in particular a reliable means to discover new clusters, and large X-ray surveys are now available. Considering XMM-Newton data for a sample of 40 Abell clusters, we show that their analysis with a Kolmogorov distribution can provide a distinctive signature for galaxy clusters. The Kolmogorov method is sensitive to the correlations in the cluster X-ray properties and can therefore be used for their identification, thus allowing to search reliably for clusters in a simple way

The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities

We study the long term evolution of the distance between two Keplerian confocal trajectories in the framework of the averaged restricted 3-body problem. The bodies may represent the Sun, a solar system planet and an asteroid. The secular evolution of the orbital elements of the asteroid is computed by averaging the equations of motion over the mean anomalies of the asteroid and the planet. When an orbit crossing with the planet occurs the averaged equations become singular. However, it is possible to define piecewise differentiable solutions by extending the averaged vector field beyond the singularity from both sides of the orbit crossing set. In this paper we improve the previous results, concerning in particular the singularity extraction technique, and show that the extended vector fields are Lipschitz-continuous. Moreover, we consider the distance between the Keplerian trajectories of the small body and of the planet. Apart from exceptional cases, we can select a sign for this distance so that it becomes an analytic map of the orbital elements near to crossing configurations. We prove that the evolution of the 'signed' distance along the averaged vector field is more regular than that of the elements in a neighborhood of crossing times. A comparison between averaged and non-averaged evolutions and an application of these results are shown using orbits of near-Earth asteroids.Comment: 29 pages, 8 figure

Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations

We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric and magnetic field. Special emphasis is placed on an efficient implementation which is achieved by taking advantage of recurrence properties and the tensor-product structure of the chosen shape functions. These recurrences have been derived symbolically with computer algebra methods reminiscent of the holonomic systems approach.Comment: 16 pages, 1 figure, 1 table; Springer Wien, ISBN 978-3-7091-0793-

Looking for CP Violation in W Production and Decay

We describe CP violating observables in resonant $W^\pm$ and $W^\pm$ plus one jet production at the Tevatron. We present simple examples of CP violating effective operators, consistent with the symmetries of the Standard Model, which would give rise to these observables. We find that CP violating effects coming from new physics at the $TeV$ scale could in principle be observable at the Tevatron with $10^6$ $W^\pm$ decays.Comment: 15 pgs with standard LATEX, 7 ps figures embedded with eps

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops

We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c = 1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.Comment: 4 pages; omega' corrected: final result changes slightly to 1.25+/-0.13; references added; several minor change

Emploi de la pré-ozonation pour augmenter la biodégradabilité d'un effluent secondaire dans un système de traitement par inflitration dans le sol

La réutilisation des eaux usées est reconnue comme une technique importante dans les régions arides et /ou grandes consommatrices d'eau. L'une des méthodes actuellement très employée consiste à recharger la nappe phréatique avec des effluents secondaires via des bassins d'infiltration. L'épuration biologique et / ou chimique à travers la zone non-saturée représente une caractéristique importante de cette technologie. Les procédés de ce type sont connus sous l'appellation de Soil Aquifer Treatment (SAT) ou géofiltration. Dans ce travail, le procédé a été étudié comme méthode de réhabilitation d'un effluent secondaire d'eaux usées jusqu'au stade d'eau potable. Cette recherche a été principalement axée sur le comportement, le transport des matières organiques (MO) de l'effluent et particulièrement sur leur rôle de précurseurs potentiels de sous-produits de désinfection lors de la réutilisation de la nappe. Dans la zone vadose, la matière organique est principalement éliminée par biodégradation, et à un degré moindre, par adsorption. Les simulations du procédé, en laboratoire, ont été réalisées en réacteurs recirculés aérobies, en mode cuvée, avec un biofilm acclimaté sur des particules de sable siliceux, afin de déterminer la fraction biodégradable des MO. L'évaluation de celle-ci est essentielle pour prédire leur potentiel de dégradation par la biomasse de la zone vadose. L'effluent mis en oeuvre est issu d'une station d'épuration de l'Arizona (États-Unis) avec biofiltre (lit filtrant à support plastique); sa concentration en carbone organique dissous (COD) se situe entre 10 et 15 mg/L.L'effluent mis 5 jours durant en contact avec le biofilm acclimaté du réacteur montre un abattement de 50-60 % du COD. Il a ainsi été déterminé qu'environ 80 % de l'élimination des MO de l'effluent survient dans les premières 24 heures d'expérimentation, alors que le reste, près de 20 %, est éliminé durant les 48 heures suivantes. Dans ces conditions, le délai de 5 jours apparait suffisant pour dégrader les MO présentes dans ces effluents. Les rendements observés augurent bien de la dégradation dans la zone vadose si l'on tient compte de la combinaison des taux et de la hauteur d'infiltration avec des temps de résidence de 2 à 14 jours ainsi qu'il est proposé dans le procédé. Afin d'accroître la biodégradabilité des MO, une ozonation a été effectuée, en amont du bio-traitement, avec un générateur d'ozone à l'échelle du banc d'essai fonctionnant en mode semi-continu (admission continue de gaz, volume stable de liquide). La pré-ozonation a permis d'accroître la biodégradation de 60-70 %. Bien qu'un fort pourcentage de MO soit éliminé dans ce schéma, il ressort que l'ozone n'a qu'un effet modeste sur la transformation des MO dissoutes non-biodégradables en matières biodégradables par rapport à des expériences similaires effectuées avec des matières organiques naturelles (MON) des eaux de surface. L'eau usée ainsi traitée présente des niveaux de COD comparables à ceux d'une eau de surface employée à des fins de consommation. Les caractéristiques des MO de l'effluent ont été comparées à celles des MON. Une ultrafiltration de l'effluent pour déterminer le poids moléculaire apparent des MO, donne une distribution bimodale de leur poids moléculaire par rapport à une distribution logarithmique normale observée avec des MON typiques. En utilisant des résines non- ioniques pour séparer les fractions hydrophobes et hydrophiles des MO, il ressort que l'ozonation ne transforme pas de façon significative la fraction hydrophobe des MO de l'effluent en fraction hydrophile, tel que cela a été observé durant l'ozonation des MON. Ces eaux ont été chlorées en pilote, selon des conditions similaires à celles des réseaux de distribution (CI2:COD=1:1mg/mg, période d'incubation=24 heures) afin de simuler la post-désinfection après récupération. Les sous-produits réglementés (Trihalométhanes THM) et ceux proposés (Acides holoacétiques, HAA6) ont été formés à des taux inférieurs ou proches des normes en vigueur (ou de celles proposées pour HAA6) pour l'eau potable aux États-Unis. Cependant, une nitrification significative a été observée dans nos simulations de traitement par le sol avec un effluent non-nitrifié, conduisant à des teneurs en nitrates supérieures à la norme américaine pour l'eau potable (10 mg/L).Soil Aquifer Treatment (SAT) is being studied as a means of water quality renovation of a secondary effluent for potable reuse. During SAT, infiltration of effluent through the vadose zone provides removal of effluent organic matter primarily through biodegradation, and to a lesser extent, through sorption. A major concern is that effluent organic matter can function as disinfection by-product (DBP) precursors upon recovery and post-disinfection. Through laboratory simulations of SAT, we have found that 50 - 60 % of the dissolved organic carbon (DOC) present in secondary effluent can potentially be removed by biodegradation, with preozonation increasing removal to 60 - 70 %. The resultant water contains DOC at levels comparable to a typical surface water used for potable purposes; moreover, upon chlorination, regulated DBPs are formed at levels below or near the United States of America's drinking water standards. However, significant nitrification was observed in our SAT simulations with an un-nitrified effluent, yielding levels of nitrate above the USA drinking water standard