Exponential convergence to equilibrium for the homogeneous Boltzmann equation for hard potentials without cut-off

This paper deals with the long time behavior of solutions to the spatially homogeneous Boltzmann equation. The interactions considered are the so-called (non cut-off and non mollified) hard potentials. We prove an exponential in time convergence towards the equilibrium, improving results of Villani from \cite{Vill1} where a polynomial decay to equilibrium is proven. The basis of the proof is the study of the linearized equation for which we prove a new spectral gap estimate in a $L^1$ space with a polynomial weight by taking advantage of the theory of enlargement of the functional space for the semigroup decay developed by Gualdani and al in \cite{GMM}. We then get our final result by combining this new spectral gap estimate with bilinear estimates on the collisional operator that we establish.Comment: 22 page

Exploring grassroots leprosy organisations : is social inclusion and empowerment possible for members? : case studies in Ethiopia and China : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Development Studies at Massey University

This thesis explores reasons for the recent emergence of grassroots leprosy organisations and through case studies of two such organisations, ENAELP in Ethiopia and HANDA in China, shows that varying measures of social inclusion and empowerment are achievable by members working collectively and in solidarity. Two major factors contributing to the emergence of these organisations are the common experience of leprosy plus the failure of welfare programmes, both of which provide significant impetus to members for collective action. The key to success for a grassroots leprosy organisation is recognising the importance of operating with a participatory development approach which attributes equal importance to processes and results, cultivating a strong sense of ownership by members and opening the way to the empowering journey of self-determination. While some international anti-leprosy organisations cling to assumptions that decision-making and self-determination by leprosy affected people for themselves is not possible, others strongly support these grassroots endeavours. Although leprosy has been a scourge and a source of fear for thousands of years with social exclusion and disempowerment resulting for millions of people, this thesis concludes that grassroots leprosy organisations have the potential to transform historical perceptions of the disease. In addition, these organisations provide opportunities for leprosy-affected people to demonstrate how they wish society to regard and consider them. This thesis did not take a static view of social inclusion and empowerment, but rather analysed changes in terms of how they are moving towards these two inter-related goals. There is no doubt that movement towards both social inclusion and empowerment is occurring, showing that the finest struggles with the best results are those fought by oppressed people themselves (Freire, 1989)

Liquid meniscus friction on a wet plate: Bubbles, lamellae and foams

Many microfluidics devices, coating processes or diphasic flows involve the motion of a liquid meniscus on a wet wall. This motion induces a specific viscous force, that exhibits a non-linear dependency in the meniscus velocity. We propose a review of the theoretical and experimental work made on this viscous force, for simple interfacial properties. The interface is indeed assumed either perfectly compressible (mobile interface) or perfectly incompressible (rigid interface). We show that, in the second case, the viscous force exerted by the wall on the meniscus is a combination of two power laws, scaling like $Ca^{1/3}$ and $Ca^{2/3}$, with $Ca$ the capillary number. We provide a prediction for the stress exerted on a foam sliding on a wet solid and compare it with experimental data, for the incompressible case

Rodlike Complexes of a Polyelectrolyte (Hyaluronan) and a Protein (Lysozyme) observed by SANS

We study by Small Angle Neutron Scattering (SANS) the structure of Hyaluronan -Lysozyme complexes. Hyaluronan (HA) is a polysaccharide of 9 nm intrinsic persistence length that bears one negative charge per disaccharide monomer (Mmol = 401.3 g/mol); two molecular weights, Mw = 6000 and 500 000 Da were used. The pH was adjusted at 4.7 and 7.4 so that lysozyme has a global charge of +10 and + 8 respectively. The lysozyme concentration was varied from 3 to 40 g/L, at constant HA concentration (10 g/L). At low protein concentration, samples are monophasic and SANS experiments reveal only fluctuations of concentration although, at high protein concentration, clusters are observed by SANS in the dense phase of the diphasic samples. In between, close to the onset of the phase separation, a distinct original scattering is observed. It is characteristic of a rod-like shape, which could characterize "single" complexes involving one or a few polymer chains. For the large molecular weight (500 000) the rodlike rigid domains extend to much larger length scale than the persistence length of the HA chain alone in solution and the range of the SANS investigation. They can be described as a necklace of proteins attached along a backbone of diameter one or a few HA chains. For the short chains (Mw ~ 6000), the rod length of the complexes is close to the chain contour length (~ 15 nm)

A spatial analysis of residential land prices in Belgium : accessibility, linguistic border and environmental amenities

This paper explores the spatial variation of land prices in Belgium. The originality of the methodology is threefold : (1) to work at the spatial extent of an entire country, (2) to compute several accessibility measures to all jobs and several representations of the environmental amenities and, more importantly, (3) to test the hypothesis that jobs influence land prices only in the same linguistic region. Spatial autocorrelation is accounted for by estimating spatial models. The results show that the linguistic border acts as a strong barrier in the spatial pattern of land prices and that environmental variables have no significant effect at this scale of spatial analysis.land price ; accessibility ; border effect ; environment ; Belgium

Search for new physics in top events with the D0 detector

This review is focused on the search for new processes, performed with top quark events in D{\O}. It presents four updated or new D{\O} results. The two first analyses deal with top production properties: they search for a new heavy resonance decaying to top-antitop. The two last results concern top decay properties: the measurement of the $W$ helicity as a probe of the $tWb$ coupling structure, and the top quark branching ratio to $Wb$. Neither of these measurements reveal any deviation with respect to the standard model predictions.Comment: Submitted for the SUSY07 conference proceeding. 4 pages, LateX, 6 eps figures, 2 LateX style file