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

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

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.

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.

Recombinant " Physcomitrella patens " as a sensitive tool to study heat sensing and heat-shock signal transduction in plants

SUMMARY When exposed to heat stress, plants display a particular set of cellular and molecular responses, such as chaperones expression, which are highly conserved in all organisms. In chapter 1, I studied the ability of heat shock genes to become transiently and abundantly induced under various temperature regimes. To this aim, I designed a highly sensitive heat-shock dependent conditional gene expression system in the moss Physcomitrella patens, using the soybean heatinducible promoter (hsp17.3B). Heat-induced expression of various reporter genes was over three orders of magnitude, in tight correlation with the intensity and duration of the heat treatments. By performing repeated heating/cooling cycles, a massive accumulation of recombinant proteins was obtained. Interestingly, the hsp17.3B promoter was also activated by specific organic chemicals. Thus, in chapter 2, I took advantage of the extreme sensitivity of this promoter to small temperature variations to further address the role of various natural and organic chemicals and develop a plant based-bioassay that can serve as an early warning indicator of toxicity by pollutants and heavy metals. A screen of several organic pollutants from textile and paper industry showed that chlorophenols as well as sulfonated anthraquinones elicited a heat shock like response at noninducing temperatures. Their effects were synergistically amplified by mild elevated temperatures. In contrast to standard methods of pollutant detection, this plant-based biosensor allowed to monitor early stress-responses, in correlation with long-term toxic effect, and to attribute effective toxicity thresholds for pollutants, in a context of varying environmental cues. In chapter 3, I deepened the study of the primary mechanism by which plants sense mild temperature variations and trigger a cellular signal leading to the heat shock response. In addition to the above described heat-inducible reporter line, I generated a P. patens transgenic line to measure, in vivo, variations of cytosolic calcium during heat treatment, and another line to monitor the role of protein unfolding in heat-shock sensing and signalling. The heat shock signalling pathway was found to be triggered by the plasma membrane, where temperature up shift specifically induced the transient opening of a putative high afimity calcium channel. The calcium influx triggered a signalling cascade leading to the activation of the heat shock genes, independently on the presence of misfolded proteins in the cytoplasm. These results strongly suggest that changes in the fluidity of the plasma membrane are the primary trigger of the heatshocksignalling pathway in plants. The present thesis contributes to the understanding of the basic mechanism by which plants perceive and respond to heat and chemical stresses. This may contribute to developing appropriate better strategies to enhance plant productivity under the increasingly stressful environment of global warming. RÉSUME Les plantes exposées à des températures élevées déclenchent rapidement des réponses cellulaires qui conduisent à l'induction de gènes codant pour les heat shock proteins (HSPs). En fonction de la durée d'exposition et de la vitesse à laquelle la température augmente, les HSPs sont fortement et transitoirement induites. Dans le premier chapitre, cette caractéristique aété utilisée pour développer un système inductible d'expression de gènes dans la mousse Physcomitrella patens. En utilisant plusieurs gènes rapporteurs, j'ai montré que le promoteur du gène hsp17.3B du Soja est activé d'une manière. homogène dans tous les tissus de la mousse proportionnellement à l'intensité du heat shock physiologique appliqué. Un très fort taux de protéines recombinantes peut ainsi être produit en réalisant plusieurs cycles induction/recovery. De plus, ce promoteur peut également être activé par des composés organiques, tels que les composés anti-inflammatoires, ce qui constitue une bonne alternative à l'induction par la chaleur. Les HSPs sont induites pour remédier aux dommages cellulaires qui surviennent. Étant donné que le promoteur hsp17.3B est très sensible à des petites augmentations de température ainsi qu'à des composés chimiques, j'ai utilisé les lignées développées dans le chapitre 1 pour identifier des polluants qui déclenchent une réaction de défense impliquant les HSPs. Après un criblage de plusieurs composés, les chlorophénols et les antraquinones sulfonés ont été identifiés comme étant activateurs du promoteur de stress. La détection de leurs effets a été réalisée seulement après quelques heures d'exposition et corrèle parfaitement avec les effets toxiques détectés après de longues périodes d'exposition. Les produits identifiés montrent aussi un effet synergique avec la température, ce qui fait du biosensor développé dans ce chapitre un bon outil pour révéler les effets réels des polluants dans un environnement où les stress chimiques sont combinés aux stress abiotiques. Le troisième chapitre est consacré à l'étude des mécanismes précoces qui permettent aux plantes de percevoir la chaleur et ainsi de déclencher une cascade de signalisation spécifique qui aboutit à l'induction des gènes HSPs. J'ai généré deux nouvelles lignées afin de mesurer en temps réel les changements de concentrations du calcium cytosolique ainsi que l'état de dénaturation des protéines au cours du heat shock. Quand la fluidité de la membrane augmente après élévation de la température, elle semble induire l'ouverture d'un canal qui permet de faire entrer le calcium dans les cellules. Ce dernier initie une cascade de signalisation qui finit par activer la transcription des gènes HSPs indépendamment de la dénaturation de protéines cytoplasmiques. Les résultats présentés dans ce chapitre montrent que la perception de la chaleur se fait essentiellement au niveau de la membrane plasmique qui joue un rôle majeur dans la régulation des gènes HSPs. L'élucidation des mécanismes par lesquels les plantes perçoivent les signaux environnementaux est d'une grande utilité pour le développement de nouvelles stratégies afin d'améliorer la productivité des plantes soumises à des conditions extrêmes. La présente thèse contribue à décortiquer la voie de signalisation impliquée dans la réponse à la chaleur.

Nuclear phenotype changes after heat shock in Panstrongylus megistus (Burmeister)

The nuclear phenotypes of Malpighian tubule epithelial cells of male nymphs of the blood-sucking insect, Panstrongylus megistus, subjected to short- and long-duration heat shocks at 40ºC were analyzed immediately after the shock and 10 and 30 days later. Normal nuclei with a usual heterochromatic body as well as phenotypes indicative of survival (unravelled heterochromatin, giants) and death (apoptosis, necrosis) responses were observed in control and treated specimens. However, all nuclear phenotypes, except the normal ones, were more frequent in shocked specimens. Similarly altered phenotypes have also been reported in Triatoma infestans following heat shock, although at different frequencies. The frequency of the various nuclear phenotypes observed in this study suggests that the forms of cell survival observed were not sufficient or efficient enough to protect all of the Malpighian tubule cells from the deleterious effects of stress. In agreement with studies on P. megistus survival following heat shock, only long-duration shock produced strongly deleterious effects.

Survival of tubercle bacilli in heat-fixed and stained sputum smears

We used a slide culture technique to detect tubercle bacilli surviving in sputum smears (n=46) after conventional heat fixation and Ziehl-Neelsen staining. In all heat-fixed sputum smears, tubercle bacilli survived after time 0 (n=22), 24 h (n=7), 48 h (n=7), 72 h (n=4), and seven days (n=6). None of the stained sputum smears showed growth on slide cultures. Viable tubercle bacilli remaining in heat-fixed sputum smears for at least seven days may present an infection risk to laboratory staff. Thus, sputum smears should be stained immediately by the Ziehl-Neelsen method or stored in a safe container to avoid transmission of tuberculosis.

Mieloma múltiple: rendimiento del estudio del cariotipo por técnicas convencionales y de hibridación in situ fluorescente. Significado pronóstico de las ganacias de 1 q.

En éste estudio analizamos el rendimiento de las técnicas citogenéticas utilizadas en los protocolos diagnósticos del MM (CC y técnicas de FISH). En primer lugar caracterizamos la serie de pacientes y los estratificamos en grupos de riesgo según los sistemas de estadificación actuales. Después estudiamos el porcentaje de cariotipos patológicos con cada una de las técnicas y en conjunto, encontrando un 40% de cariotipos patológicos por CC y de estos un 11,5% pertenecían a estudios con recuentos de CP ≤20% por citomorfología. La técnica de FISH aumentó hasta un 68% los cariotipos patológicos. También hemos realizado la caracterización de los pacientes con ganancias de 1q y su impacto en la evolución de la enfermedad.