Lp theory for the multidimensional aggregation equation

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Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

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

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Sedimentology, geochemistry and mineralogy of the Paleocene-Eocene thermal maximum (PETM) : sediment records from Egypt, India and Spain

A gradual increase in Earth's surface temperatures marking the transition from the late Paleocene to early Eocene (55.8±0.2Ma), represents an extraordinary warming event known as Paleocene-Eocene Thermal Maximum (PETM). Both marine and continental sedimentary records during this period reveal evidences for the massive injection of isotopically light carbon. The carbon dioxide injection from multiple potential sources may have triggered the global warming. The importance of the PETM studies is due to the fact that the PETM bears some striking resemblances to the human-caused climate change unfolding today. Most notably, the culprit behind it was a massive injection of heat-trapping greenhouse gases into the atmosphere and oceans, comparable in volume to what our persistent burning of fossil fuels could deliver in coming centuries. The exact knowledge of what went on during the PETM could help us to foresee the future climate change. The response of the oceanic and continental environments to the PETM is different. Many factors might control the response of the environments to the PETM such as paleogeography, paleotopography, paleoenvironment, and paleodepth. To better understand the mechanisms triggering PETM events, two different environments were studied: 1) shallow marine to inner shelf environment (Wadi Nukhul, Sinai; and the Dababiya GSSP, Luxor, Egypt), and 2) terrestrial environments (northwestern India lignite mines) representing wetland, and fluvial environments (Esplugafreda, Spain) both highlighting the climatic changes observed in continental conditions. In the marine realm, the PETM is characterized by negative ö13Ccar and ô13Corg excursions and shifts in Ô15N to ~0%o values above the P/E boundary and persisting along the interval suggesting a bloom and high production of atmospheric N2-fixers. Decrease in carbonate contents could be due to dissolution and/or dilution by increasing detrital input. High Ti, K and Zr and decreased Si contents at the P/E boundary indicate high weathering index (CIA), which coincides with significant kaolinite input and suggests intense chemical weathering under humid conditions at the beginning of the PETM. Two anoxic intervals are observed along the PETM. The lower one may be linked to methane released from the continental shelf with no change in the redox proxies, where the upper anoxic to euxinic conditions are revealed by increasing U, Mo, V, Fe and the presence of small size pyrite framboids (2-5fim). Productivity sensitive elements (Cu, Ni, and Cd) show their maximum concentrated within the upper anoxic interval suggesting high productivity in surface water. The obtained data highlight that intense weathering and subsequent nutrient inputs are crucial parameters in the chain of the PETM events, triggering productivity during the recovery phase. In the terrestrial environments, the establishment of wetland conditions and consequence continental climatic shift towards more humid conditions led to migration of modern mammals northward following the extension of the tropical belts. Relative ages of this mammal event based on bio-chemo- and paleomagnetic stratigraphy support a migration path originating from Asia into Europe and North America, followed by later migration from Asia into India and suggests a barrier to migration that is likely linked to the timing of the India-Asia collision. In contrast, at Esplugafereda, northeastern Spain, the terrestrial environment reacted differently. Two significant S13C shifts with the lower one linked to the PETM and the upper corresponding to the Early Eocene Thermal Maximum (ETM2); 180/160 paleothermometry performed on two different soil carbonate nodule reveal a temperature increase of around 8°C during the PETM. The prominent increase in kaolinite content within the PETM is linked to increased runoff and/or weathering of adjacent and coeval soils. These results demonstrate that the PETM coincides globally with extreme climatic fluctuations and that terrestrial environments are very likely to record such climatic changes. - La transition Paléocène-Eocène (55,8±0,2 Ma) est marquée par un réchauffement extraordinaire communément appelé « Paleocene-Eocene Thermal Maximum » (PETM). Les données géochimiques caractérisant les sédiments marins et continentaux de cette période indiquent que ce réchauffement a été déclenché par une augmentation massive de CO2 lié à la déstabilisation des hydrates de méthane stockés le long des marges océaniques. L'étude des événements PETM constitue donc un bon analogue avec le réchauffement actuel. Le volume de CO2 émis durant le PETM est comparable avec le CO2 lié à l'activité actuelle humaine. La compréhension des causes du réchauffement du PETM peut être cruciale pour prévoir et évaluer les conséquences du réchauffement anthropogénique, en particulier les répercussions d'un tel réchauffement sur les domaines continentaux et océaniques. De nombreux facteurs entrent en ligne de compte dans le cas du PETM, tels que la paléogéographie, la paléotopographie et les paléoenvironnement. Pour mieux comprendre les réponses environnementales aux événements du PETM, 2 types d'environnements ont été choisis : (1) le domaine marin ouvert mais relativement peu profond (Wadi Nukhul. Sinai, Dababiya, Luxor, Egypte), (2) le milieu continental marécageux humide (mines de lignite, Inde) et fluviatile, semi-aride (Esplugafreda, Pyrénées espagnoles). Dans le domaine marin, le PETM est caractérisé par des excursions négatives du ô13Ccar et ô13Corg et un shift persistant des valeurs de 815N à ~ 0 %o indiquant une forte activité des organismes (bactéries) fixant l'azote. La diminution des carbonates observée durant le PETM peut-être due à des phénomènes de dissolution ou une augmentation des apports terrigènes. Des taux élevés en Ti, K et Zr et une diminution des montants de Si, reflétés par des valeurs des indices d'altération (CIA) qui coïncident avec une augmentation significative des apports de kaolinite impliquent une altération chimique accrue, du fait de conditions plus humides au début du PETM. Deux événements anoxiques globaux ont été mis en évidence durant le PETM. Le premier, situé dans la partie inférieur du PETM, serait lié à la libération des hydrates de méthane stockés le long des talus continentaux et ne correspond pas à des variations significatives des éléments sensibles aux changements de conditions redox. Le second est caractérisé par une augmentation des éléments U, Mo, V et Fe et la présence de petit framboids de pyrite dont la taille varie entre 2 et 5pm. Le second épisode anoxique est caractérisé par une forte augmentation des éléments sensibles aux changements de la productivité (Cu, Ni et Co), indiquant une augmentation de la productivité dans les eaux de surface. Les données obtenues mettent en évidence le rôle crucial joué par l'altération et les apports en nutriments qui en découlent. Ces paramètres sont cruciaux pour la succession des événements qui ont conduit au PETM, et plus particulièrement l'augmentation de la productivité dans la phase de récupération. Durant le PETM, le milieu continental est caractérisé par l'établissement de conditions humides qui ont facilité voir provoqué la migration des mammifères modernes qui ont suivi le déplacement de ces ceintures climatiques. L'âge de cette migration est basé sur des arguments chimiostratigraphiques (isotopes stables), biostratigraphiques et paléomagnétiques. Les données bibliographiques ainsi que celles que nous avons récoltées en Inde, montrent que les mammifères modernes ont d'abord migré depuis l'Asie vers l'Europe, puis dans le continent Nord américain. Ces derniers ne sont arrivés en Inde que plus tardivement, suggérant que le temps de leur migration est lié à la collision Inde-Asie. Dans le Nord-Est de l'Espagne (Esplugafreda), la réponse du milieu continental aux événements PETM est assez différente. Comme en Inde, deux excursions signicatives en ô13C ont été observées. La première correspond au PETM et la seconde est corrélée avec l'optimum thermique de l'Eocène précoce (ETM2). Les isotopes stables de l'oxygène mesurés 2 différents types de nodules calcaires provenant de paléosols suggère une augmentation de 10°C pendant le PETM. Une augmentation simultanée des taux de kaolinite indique une intensification de l'altération chimique et/ou de l'érosion de sols adjacents. Ces résultats démontrent que le PETM coïncide globalement avec des variations climatiques extrêmes qui sont très aisément reconnaissables dans les dépôts continentaux.

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.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Epidemiology and Anthropology: an integrated approach dealing with bio-socio-cultural aspects as strategy for the control of endemic diseases

The control of endemic diseases has not attained the desired level of effectiveness in spite of the use of modern efficient thecnologies. The classic interventionist approach for the control of schistosomiasis is centered on systemic control of the snail hosts combined to large scale medical treatment and is usually carried out without social preocupation due to the assisted communities. It is easy to understand the interest and the ethical compromise of public health research while producing studies in which the biological and social determinants as well as the cultural components should be considered and also encompass the historical dimensions and symbolic representations. In face of the recent political decision in favor of decentralizations of health administration to municipal level, we suggest, in the present paper, an integrated approach for the epidemiological diagnosis of an endemic situation at local level. Theoretical and methodological aspects from both, epidemiology and anthropology are discussed. Epidemiological methods can be used to detect the dependent variables (those related to the human infection) and the independent variables (demographic, economic, sanitary and social). Another methodological approach of anthropological /etnographic nature can be conducted in order to make an articulation of the knowledge on the various dimensions or determinant levels of the disease. Mutual comprehension, between researchers and the people under investigation, on the dynamic transmission process would be relevant for a joint construction, at local level, of programmed actions for the control of endemic diseases. This would extend reflections on the health/disease process as a whole.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Activation of the heat shock response in plants by chlorophenols: transgenic Physcomitrella patens as a sensitive biosensor for organic pollutants.

The ability to detect early molecular responses to various chemicals is central to the understanding of biological impact of pollutants in a context of varying environmental cues. To monitor stress responses in a model plant, we used transgenic moss Physcomitrella patens expressing the beta-glucuronidase reporter (GUS) under the control of the stress-inducible promoter hsp17.3B. Following exposure to pollutants from the dye and paper industry, GUS activity was measured by monitoring a fluorescent product. Chlorophenols, heavy metals and sulphonated anthraquinones were found to specifically activate the hsp17.3B promoter (within hours) in correlation with long-term toxicity effects (within days). At mildly elevated physiological temperatures, the chemical activation of this promoter was strongly amplified, which considerably increased the sensitivity of the bioassay. Together with the activation of hsp17.3B promoter, chlorophenols induced endogenous chaperones that transiently protected a recombinant thermolabile luciferase (LUC) from severe heat denaturation. This sensitive bioassay provides an early warning molecular sensor to industrial pollutants under varying environments, in anticipation to long-term toxic effects in plants. Because of the strong cross-talk between abiotic and chemical stresses that we find, this P. patens line is more likely to serve as a direct toxicity bioassay for pollutants combined with environmental cues, than as an indicator of absolute toxicity thresholds for various pollutants. It is also a powerful tool to study the role of heat shock proteins (HSPs) in plants exposed to combined chemical and environmental stresses.

Survival and Molting Incidence after Heat and Cold Shocks in Panstrongylus megistus Burmeister

Survival and molting incidence were studied after heat (40°C) and cold (0°C) shocks in specimens of Panstrongylus megistus with the aim of establishing its response to temperature stress under laboratory rearing conditions and to understand occasional changes in the biological characteristics of specimens captured in nature. The response to the thermal shocks was found to vary as a function of the temperature and duration of the shock, developmental phase and sex of the specimens, and in certain cases, the insect habit and nourishment conditions. P. megistus specimens were found to be less resistant to the heat shock assay than Triatoma infestans, another reduviid species. The short cold shock affected survival of P. megistus more than did the heat shock, survival of fully-nourished specimens being preferential. The response of adults to the short cold shock was affected by sex, males being generally less resistant. The insect sylvatic habit was found to seldom affect the thermal shock response established for specimens with domestic habit. A decrease in molting frequency and sometimes a slowdown of the molting rate were found after the short heat and cold shocks, possibly promoted by change in hormonal balance, and differing from patterns reported for T. infestans. The results indicate that no generalization should be made for different reduviid species in terms of the effects of temperature shocks.