Combinatorial Formulae for Vassiliev Invariants from Chern-Simons Gauge Theory

We analyse the perturbative series expansion of the vacuum expectation value of a Wilson loop in Chern-Simons gauge theory in the temporal gauge. From the analysis emerges the notion of the kernel of a Vassiliev invariant. The kernel of a Vassiliev invariant of order n is not a knot invariant, since it depends on the regular knot projection chosen, but it differs from a Vassiliev invariant by terms that vanish on knots with n singular crossings. We conjecture that Vassiliev invariants can be reconstructed from their kernels. We present the general form of the kernel of a Vassiliev invariant and we describe the reconstruction of the full primitive Vassiliev invariants at orders two, three and four. At orders two and three we recover known combinatorial expressions for these invariants. At order four we present new combinatorial expressions for the two primitive Vassiliev invariants present at this order.Comment: 73 pages, latex, epsf, 18 figures, 2 table

Tsetse and human trypanosomiasis challenge in south eastern Uganda

Pièges pyramidaux (8000) ont été mis en place contre #Glossina fuscipes fuscipes afin de lutter contre la maladie du sommeil à #Trypanosoma rhodésiense dans le Busoga. Dans le but de comprendre les modalités du contact homme/mouche, la récolte des données sur la densité, la distribution spatiale et la mobilité des mouches, ont été mis en relation avec la dynamique de la transmission de la trypanosomiase humaine dans le Bugosa. Comme pour #T. gambiense$, peu de corrélations entre la densité globale de mouche et l'incidence de la maladie ont été trouvées. Cependant, des observations de terrain avec un enregistrement daté des mouvements saisonniers des hommes et des animaux dans des habitats favorables aux mouches demeure la clé de la compréhension de la transmission de la maladie. (Résumé d'auteur

Three-manifold invariant from functional integration

We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1- forms. The result of the functional integration is compared with the abelian U(1) Reshetikhin-Turaev surgery invariant

Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

We investigate here the ability of a Green-Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green-Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration

Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a disturbance moving at constant speed on top of two layers of fluids of different densities. Starting from the full Euler equations, we present several nonlinear asymptotic models, in the long wave regime. These models are rigorously justified by consistency or convergence results. A careful theoretical and numerical analysis is then provided, in order to predict the behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit

Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique solution on [0,{T}/\eps] for some \eps independent of constant $T.$ We shall prove in the subsequent paper \cite{MZZ2} that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D capillary-gravity waves) into two parts, this is the first on

Transforming education for the just transition

Society faces many challenges in promoting a just transition to a low-carbon economy, a transition that does not create or exacerbate injustices. Notably, the just transition can only be attained with new educational approaches which revolve around social, climate and environmental justice. This paper advances that for a just transition, the shift to a greener economy cannot be driven by the traditional neoliberal engine, which has captured educational practices. Rather, the necessary educational transformation needs the principles of critical pedagogy and the dimensions of justice provided by the JUST Framework. We bring these two important schools together and draw on the experience of the global periphery and Latin America in particular, to develop a unique theoretical framework that contributes to the literature on education for sustainable development. Therefore, this conceptual research provides a theoretical framework that should guide education for a just transition. This paper establishes what is referred to as CCR Education Framework which involves: Critical thinking about climate, environmental and social costs of fossil fuels; Coexistence with nature and the other; and Resistance against neoliberalism and other forces that jeopardise the just transition. The CCR Education Framework is a response to the question of what education needs to include to achieve a just transition. The paper also opens the discussion about the implications of the Framework in terms of teacher training and education and appropriate pedagogical approaches. The key theoretical advancements here is that education for the just transition must affirm the importance of teachers and students as agents of transformation, and promote critical educational practices and approaches which support the transition to a low-carbon economy, and which value the characteristics of justice (which include equity, equality, fairness, and inclusiveness) to build a curriculum that advocates sustainable growth and a societal just transition.<br/

Derivation of the Zakharov equations

This paper continues the study of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler-Maxwell equations in terms of WKB approximate solutions which leading terms are solutions of the Zakharov equations. Because of transparency properties of the Euler-Maxwell equations, this study is led in a supercritical (highly nonlinear) regime. In such a regime, resonances between plasma waves, electromagnetric waves and acoustic waves could create instabilities in small time. The key of this work is the control of these resonances. The proof involves the techniques of geometric optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of pseudodifferential operators, and a semiclassical, paradifferential calculus

Global well-posedness of the 3-D full water wave problem

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial interface that is sufficiently small in its steepness and velocity, we show that there exists a unique smooth solution of the full water wave problem for all time, and the solution decays at the rate $1/t$.Comment: 60 page