Non-Newtonian thin films with normal stresses: dynamics and spreading

The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line

Renormalization study of two-dimensional convergent solutions of the porous medium equation

In the focusing problem we study a solution of the porous medium equation $u_t=\Delta (u^m)$ whose initial distribution is positive in the exterior of a closed non-circular two dimensional region, and zero inside. We implement a numerical scheme that renormalizes the solution each time that the average size of the empty region reduces by a half. The initial condition is a function with circular level sets distorted with a small sinusoidal perturbation of wave number $k\geq 3$. We find that for nonlinearity exponents m smaller than a critical value which depends on k, the solution tends to a self-similar regime, characterized by rounded polygonal interfaces and similarity exponents that depend on m and on the discrete rotational symmetry number k. For m greater than the critical value, the final form of the interface is circular.Comment: 26 pages, Latex, 13 ps figure

Aboriginal settlements of arid Patagonia: Preserving bio- or sociodiversity? The case of the Mapuche pastoral Cushamen Reserve

Preservation of biodiversity can be at odds with preservation of sociodiversity, i.e., human groups with different cultures, social organization and economic activities coexisting within a region. We analyzed this problem in the Cushamen Reserve, a pastoralist Mapuche aboriginal settlement in Patagonia, Argentina. We found that the current stocking rate of domestic herbivores is twice the rangeland carrying capacity, and this overstocking has resulted in a 20-30% reduction in plant cover, productivity, floristic richness and pastoral value compared to similar sites located on neighboring capitalist farms. The potential economic income of a generic Cushamen farm (625 ha) under the current stocking rate (0.27 sheep units{bullet operator}ha-1) and productive parameters (wool and number of lambs produced per sheep each year and the number of sheep that died or were discarded per year) is above the family poverty line, but this potential may be only rarely achieved due to interannual variability of productive parameters. However, under the carrying capacity, only an improbable combination of 0.84 lambs{bullet operator}sheep-1 yr-1, 5.5 kg wool{bullet operator}sheep-1 yr-1 and a 16% rate of annual sheep discarding would equal the present potential income. Active policies aimed at increasing carrying capacity of the Cushamen Reserve are needed to preserve both bio- and sociodiversity.Fil: Golluscio, Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Román, Marcela Eloísa. Universidad de Buenos Aires. Facultad de Agronomía. Departamento de Economía, Desarrollo y Planeamiento Agrícola. Cátedra de Economía Agraria; ArgentinaFil: Cesa, Ariela. Instituto Nacional de Tecnología Agropecuaria; ArgentinaFil: Rodano, D.. Administración de Parques Nacionales; ArgentinaFil: Bottaro, H.. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Patagonia Sur. Estación Experimental Agropecuaria Esquel; ArgentinaFil: Nieto, M.I.. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Patagonia Sur; ArgentinaFil: Betelú, A.. Programa Social Agropecuario; ArgentinaFil: Golluscio, Lucia Angela. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Lingüística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

BOUNDARY CONTROL OF PDES VIA CURVATURE FLOWS: THE VIEW FROM THE BOUNDARY II

We describe some results on the exact boundary controllability of the wave equation on an orientable two-dimensional Riemannian manifold with nonempty boundary. If the boundary has positive geodesic curvature, we show that the problem is controllable in finite time if (and only if) there are no closed geodesics in the interior of the manifold. This is done by solving a parabolic problem to construct a convex function. We exhibit an example for which control from a subset of the boundary is possible, but cannot be proved by means of convex functions. We shall also describe a numerical implementation of this method