Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime

In this paper, we consider the linearized Vlasov-Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter \eps in front of the collision operator which will tend to $0$. Moreover, we study two cases of collision operators, linear Boltzmann and Fokker-Planck. We prove a result of Landau damping for those equations in Sobolev spaces uniformly with respect to the collision parameter \eps as it goes to $0$

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

Management of migraine

Migraine is a complex neurovascular disease characterised by episodic attacks of severe headache accompanied by autonomic and neurological symptoms. Two types of migraine have been identified: (1) common migraine, or migraine without aura, occurring in about 70% of migraine patients (migraineurs); (2) classic migraine, or migraine with aura. In the latter case, aura symptoms are usually manifested as visual hallucinations such as flashing lights, zig-zag lines or blind spots, although sensory and motor dysfunction may also occasionally occur.peer-reviewe

The formation of polycyclic aromatic hydrocarbons in evolved circumstellar environments

The formation of Polycyclic Aromatic Hydrocarbons in the circumstellar outflows of evolved stars is reviewed, with an emphasis on carbon stars on the Asymptotic Giant Branch. Evidence for PAHs present in their winds is provided by meteoritic studies and recent observations of the Unidentified Infrared bands. We detail the chemical processes leading to the closure of the first aromatic ring as well as the growth mechanisms leading to amorphous carbon grains. Existing studies on PAH formation in evolved stellar envelopes are reviewed and new results for the modelling of the inner wind of the archetype carbon star IRC+10216 are presented. Benzene, C6H6, forms close to the star, as well as water, H2O, as a result of non-equilibrium chemistry induced by the periodic passage of shocks. The growth process of aromatic rings may thus resemble that active in sooting flames due to the presence of radicals like hydroxyl, OH. Finally, we discuss possible formation processes for PAHs and aromatic compounds in the hydrogen-rich R CrB star, V854 Cen, and their implication for the carriers of the Red Emission and the Diffuse Interstellar Bands.Comment: 13 pages, 4 figures, Invited review at the conference 'PAHs and the Universe', Toulouse, France, June 201

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