Lp theory for the multidimensional aggregation equation

"Vegeu el resum a l'inici del document del fitxer adjunt."

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

A functional equation related to the product in a quadratic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Geodynamic reconstructions of the South America-Antarctica plate system

The South America-Antarctica plate system shows many oceanic accretionary systems and subduction zones that initiated and then stopped. To better apprehend the evolution of the system, geodynamic reconstructions (global) have been created from Jurassic (165 Ma) to present, following the techniques used at the University of Lausanne. However, additional synthetic magnetic anomalies were used to refine the geodynamics between 33 Ma and present. The reconstructions show the break up of Gondwana with oceanisation between South America (SAM) and Antarctica (ANT), together with the break off of `Andean' geodynamical units (GDUs). We propose that oceanisation occurs also east and south of the Scotian GDUs. Andean GDUs collide with other GDUs crossing the Pacific. The west coast of SAM and ANT undergo a subsequent collision with all those GDUs between 103 Ma and 84 Ma, and the Antarctic Peninsula also collides with Tierra del Fuego. The SAM-ANT plate boundary experienced a series of extension and shortening with large strike-slip component, culminating with intra-oceanic subduction leading to the presence of the `V-' and anomalies in the Weddell Sea. From 84 Ma, a transpressive collision takes place in the Scotia region, with active margin to the east. As subduction propagates northwards into an old and dense oceanic crust, slab roll-back initiates, giving rise to the western Scotia Sea and the Powell Basin opening. The Drake Passage opens. As the Scotian GDUs migrate eastwards, there is enough space for them to spread and allow a north-south divergence with a spreading axis acting simultaneously with the western Scotia ridge. Discovery Bank stops the migration of South Orkney and `collides with' the SAM-ANT spreading axis, while the northern Scotian GDUs are blocked against the Falkland Plateau and the North-East Georgia Rise. The western and central Scotia and the Powell Basin spreading axes must cease, and the ridge jumps to create the South Sandwich Islands Sea. The Tierra del Fuego-Patagonia region has always experienced mid-oceanic ridge subduction since 84 Ma. Slab window location is also presented (57-0 Ma), because of its important implication for heat flux and magmatism. (C) 2011 Elsevier Ltd. All rights reserved.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

Plate tectonics, seaways and climate in the historical biogeography of mammals

The marsupial and placental mammals originated at a time when the pattern of geographical barriers (oceans, shallow seas and mountains) was very different from that of today, and climates were warmer. The sequence of changes in these barriers, and their effects on the dispersal of the mammal families and on the faunas of mammals in the different continents, are reviewed. The mammal fauna of South America changed greatly in the Pliocene/Pleistocene, when the newly-complete Panama Isthmus allowed the North American fauna to enter the continent and replace most of the former South American mammal families. Marsupial, but not placental, mammals reached Australia via Antarctica before Australia became isolated, while rats and bats are the only placentals that dispersed naturally from Asia to Australia in the late Cenozoic. Little is known of the early history of the mammal fauna of India. A few mammal families reached Madagascar from Africa in the early Cenozoic over a chain of islands. Africa was isolated for much of the early Cenozoic, though some groups did succeed in entering from Europe. Before the climate cooled in the mid-Cenozoic, the mammal faunas of the Northern Hemisphere were much richer than those of today.

Proximale Humerusmehrfragmentfrakturen--Misserfolge nach T-Platten-Osteosynthesen [Proximal humeral multiple fragment fractures--failures after T-plate osteosynthesis].

Dislocated compound fractures of the proximal humerus are often difficult to treat. The choice of treatment influences the final functional result. From 1984-1991 108 patients with dislocated compound fractures of the proximal humerus were operated with a T-plate osteosynthesis, retrospectively examined and classified according to the Neer-Classification. At an average follow up time of 5 years 72 patients had a clinical and radiological examination. 68% of these patients with 3-fragment fractures and 80% with 4-fragment fractures showed a modest to unsatisfactory result caused by fracture biology, imprecise fracture reduction or poor surgical procedure. Incorrect position of T-plates and inadequate material were distinguishable. The T-plate which was widely used in the late eighties for internal fixation has to be considered a failure for these particular types of fractures and should be limited for Collum chirurgicum fractures.

An alternative plate tectonic model for the Palaeozoic-Early Mesozoic Palaeotethyan evolution of Southeast Asia (northern Thailand-Myanmar)

An alternative model for the geodynamic evolution of Southeast Asia is proposed and inserted in a modern plate tectonic model. The reconstruction methodology is based on dynamic plate boundaries, constrained by data such as spreading rates and subduction velocities; in this way it differs from classical continental drift models proposed so far. The different interpretations about the location of the Palaeotethys suture in Thailand are revised, the Tertiary Mae Yuam fault is seen as the emplacement of the suture. East of the suture we identify an Indochina derived terrane for which we keep the name Shan-Thai, formerly used to identify the Cimmerian block present in Southeast Asia, now called Sibumasu. This nomenclatural choice was made on the basis of the geographic location of the terrane (Eastern Shan States in Burma and Central Thailand) and in order not to introduce new confusing terminology. The closure of the Eastern Palaeotethys is related to a southward subduction of the ocean, that triggered the Eastern Neotethys to open as a back-arc, due to the presence of Late Carboniferous-Early Permian arc magmatism in Mergui (Burma) and in the Lhasa block (South Tibet), and to the absence of arc magmatism of the same age East of the suture. In order to explain the presence of Carboniferous-Early Permian and Permo-Triassic volcanic arcs in Cambodia, Upper Triassic magmatism in Eastern Vietnam and Lower Permian-Middle Permian arc volcanites in Western Sumatra, we introduce the Orang Laut terranes concept. These terranes were detached from Indochina and South China during back-arc opening of the Poko-Song Ma system, due to the westward subduction of the Palaeopacific. This also explains the location of the Cathaysian West Sumatra block to the West of the Cimmerian Sibumasu block.

On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher-Kolmogorov-Petrovskii-Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Garden to Plate

North Tipperary Food Partnership aims to improve access to healthy food and build community and skills through food growing initiatives. `The Garden to Plate` project was set up as part of Nenagh Community Allotments, a voluntary group who lease a site privately containing up to 20 allotments and a communal green house. The North Tipperary VEC Community Education and Back to Education Initiative Projects rent two allotments from NCA offering a certified learning opportunity and generating a space for the wider benefits of learning. The adults engaged are mainly men both recently and long term unemployed with a range of skills and experiences. A small study has been conducted with participants to identify feedback on skills and knowledge gained including those related to health and nutrition. A report is available. North Tipperary Leader Services, VEC Initiative Type Community Food Growing Projects Location Tipperary Funding North Tipperary Leader Services, VEC Partner Agencies NTLS/VEC/HSE/NCA/Council

Limerick Seed to Plate

The aim of the project is to address an identified need in the community, promoting healthy eating and organic home-gardening practices. Building on the success of a pilot intergenerational project entitled "Through the Years", it became apparent that gardening related activities could be implemented and promoted on a larger scale, reaching the wider community, groups and classes. The project serves as a setting for community education and will be inclusive in helping reduce isolation by providing meeting places for all members of their local communities. Key people being targeted are older people, local families and residents, Limerick Youth Service, After School Clubs, the Garda Youth Diversion Project and the Family Resource Centre. The Limerick Seed to Plate works with gardeners whose primary focus is to develop the gardening projects further. There is a strong educational emphasis to the project and the learning is transferred to participants own homes and lifestyles. Southill has a community café and, where possible, food grown in their garden is showcased and cooked in the centre and café. The Community Food Initiative strengthens the existing healthy eating habits in the community and aims to result in increased long-term health benefits arising from a healthier lifestyle. Communities will benefit from the project which will create employment, build bridges between communities, promote social inclusion and provide a focus for the local areas. Part of theDemonstration Programme 2010-2012 Location Limerick Target Groups At risk youth Children ( 4-12 years) Children (0-4 years) Children (13-18 years) Families Lone parents Low income families Men Migrant, minority ethnic groups Older people Travellers Unemployed Women