Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

Finite time blow-up and breaking of solitary wind waves

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

Valuation bubbles and sequential bubbles

Price bubbles in an Arrow-Debreu valuation equilibrium in infinite-timeeconomy are a manifestation of lack of countable additivity of valuationof assets. In contrast, known examples of price bubbles in sequentialequilibrium in infinite time cannot be attributed to the lack of countableadditivity of valuation. In this paper we develop a theory of valuation ofassets in sequential markets (with no uncertainty) and study the nature ofprice bubbles in light of this theory. We consider an operator, calledpayoff pricing functional, that maps a sequence of payoffs to the minimumcost of an asset holding strategy that generates it. We show that thepayoff pricing functional is linear and countably additive on the set ofpositive payoffs if and only if there is no Ponzi scheme, and providedthat there is no restriction on long positions in the assets. In the knownexamples of equilibrium price bubbles in sequential markets valuation islinear and countably additive. The presence of a price bubble indicatesthat the asset's dividends can be purchased in sequential markers at acost lower than the asset's price. We also present examples of equilibriumprice bubbles in which valuation is nonlinear but not countably additive.

Properties of a risk measure derived from ruin theory

This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Cellulase effect on anaerobic digestion of maize silage under discontinuous operation

ABSTRACT This paper studied the effect of adding an enzyme (ellulose) on anaerobic digestion of maize silage. We compared materials at chopping lengths of 8 mm (MSL), 4mm (MSS) and natural size (Ms) under a mesophilic and discontinuous operation (batch process). Hence, we found the process to be significantly influenced by particle size. Moreover, the ellulose addition did not significantly impact biogas production after a 35-day digestion period. Ms and MSS displayed an improved response to all variables when compared with MSL and MSL+C, with significant differences. Studies on the refractory fraction at infinite time (R0) have demonstrated that the lowest values correspond to Ms and MSS (0.122 and 0.155, respectively). The Kinetic approach and the Ultimate Biodegradability test are useful tools to evaluate the effect of the addition of an enzyme to the anaerobic process.

Destierro y redención: el «síndrome de Adán y Eva» en La belleza del mundo de Héctor Tizón (Crítica)

En este ensayo, el autor plantea un diálogo entre la novela La belleza del mundo, de Héctor Tizón, y los arquetipos bíblicos de Adán y Eva, la pérdida del paraíso y el destierro, y el retorno al Edén. A partir de la traición primigenia de la esposa del protagonista, se inicia la integración a un tiempo cíclico e infinito –el del exilio. En el destierro, el protagonista está marcado por su afán de anular la temporalidad real y, a la vez, su propia identidad, intenta forzosamente olvidar la propia historia, lo cual lo conduce a una crisis de identidad. Al cabo de un largo recorrido, se plantea la necesidad de incorporar los acontecimientos de la vida a un tiempo mítico que regenere y perpetúe todas las acciones, y en el cual se busque el sufrimiento para alcanzar la salvación. El autor evidencia paralelismos diversos del texto con la doctrina cristiana: el protagonista comprende que para regresar a su propio centro debe perdonar. Y eso solo es posible regresando, enfrentando su pasado: el tiempo de redención es un regreso, pero el mismo-nuevo sitio no vuelve a ser jamás el paraíso.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Estabilidade estocástica de sistemas lineares com Saltos Markovianos e Sistemas Lineares com Saltos Semimarkovianos

Pós-graduação em Matematica Aplicada e Computacional - FCT

Carbon sequestration in Himalaya's alpine meadows: Mitigating cropping encroachment on pastures in Northern Pakistan

Rangelands store about 30% of the world’s carbon and support over 120 million pastoralists globally. Adjusting the management of remote alpine pastures bears a substantial climate change mitigation potential that can provide livelihood support for marginalized pastoralists through carbon payment. Landless pastoralists in Northern Pakistan seek higher income by cropping potatoes and peas over alpine pastures. However, tilling steep slopes without terracing exposes soil to erosion. Moreover, yields decline rapidly requiring increasing fertilizer inputs. Under these conditions, carbon payment could be a feasible option to compensate pastoralists for renouncing hazardous cropping while favoring pastoral activities. The study quantifies and compares C on cropped and grazed land. The hypothesis was that cropping on alpine pastures reduces former carbon storage. The study area located in the Naran valley of the Pakistani Himalayas receives an annual average of 819 mm of rain and 764 mm of snow. Average temperatures remain below 0°C from November to March while frost may occur all year round. A total of 72 soil core samples were collected discriminating land use (cropping, pasture), aspect (North, South), elevation (low 3000, middle 3100, and high 3200 m a.s.l.), and soil depth (shallow 0-10, deep 10-30 cm). Thirty six biomass samples were collected over the same independent variables (except for soil depth) using a 10x10x20 cm steal box inserted in the ground for each sample. Aboveground biomass and coarse roots were separated from the soil aggregate and oven-dried. Soil organic carbon (SOC) and biomass carbon (BC) were estimated through a potassium dichromate oxidation treatment. The samples were collected during the second week of October 2010 at the end of the grazing and cropping season and before the first snowfall. The data was statistically analyzed by means of a one-way analysis of variance. Results show that all variables taken separately have a significant effect on mean SOC [%]: crop/pasture 1.33/1.6, North/South 1.61/1.32, low/middle/high 1.09/1.62/1.68, shallow/deep 1.4/1.53. However, for BC, only land use has a significant effect with more than twice the amount of carbon in pastures [g m-2]: crop/pasture 127/318. These preliminary findings suggest that preventing the conversion of pastures into cropping fields in the Naran valley avoids an average loss of 12.2 t C ha-1 or 44.8 t CO2eq ha-1 representing a foreseeable compensation of 672 € ha-1 for the Naran landless pastoralists who would renounce cropping. The ongoing study shall provide a complete picture for carbon payment integrating key aspects such as the rate of cropping encroachment over pastures per year, the methane leakage from the system due to livestock enteric fermentation, the expected cropping income vs. livestock income and the transaction costs of implementing the mitigation project, certifying it, and verifying carbon credits. A net present value over an infinite time horizon for the mitigation scenario shall be estimated on an iterative simulation to consider weather and price uncertainties. The study will also provide an estimate of the minimum price of carbon at which pastoralists would consider engaging in the mitigation activity.

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Formación tardía de etringita en fibrocemento.

La temperatura de curado, utilizada por la industria de fibrocemento como catalizador en la hidratación del cemento para lograr alta resistencia inicial en sus productos, genera la hipótesis de expansión causada por formación tardía de etringita. Para el planteamiento de dicha hipótesis, el siguiente estudio contempló dos grupos de muestras con el objetivo de estudiar aisladamente su comportamiento químico y físico: uno de los grupos conformado por pasta cementicia con 35% de sustitución de calcario, y el otro conformado por fibrocemento con incorporación de PVA y celulosa. Por calorimetría isotérmica se observó la cinética de reacción de dos pastas, una de ellas curada a 23 ºC y la otra a 85 ºC donde esta última experimentó un efecto catalizador en sus reacciones. Ensayos de DRX y DTG/TG mostraron la presencia de etringita a 23 °C durante todas las edades de hidratación exhibiendo una tendencia de aumento en la intensidad de los picos y en la cantidad, respectivamente, en función del tiempo; sin embargo, a 85 ºC la presencia de esta fase fue inconstante durante las primeras edades de hidratación, a partir de mes de hidratación mostró aumento en cada una de las siguientes medidas realizadas mensualmente; a 85 °C hubo una menor formación de portlandita en comparación con los resultados obtenidos a 23 °C. Utilizando el método Rietveld y análisis químico fueron determinadas las cantidades y las composiciones químicas, respectivamente, de las fases del cemento anhidro y del calcario para alimentar el programa GEMS y simular la hidratación de la pasta estudiada en laboratorio para un tiempo infinito bajo la influencia de la temperatura. Simulaciones de la hidratación de la pasta se aproximaron a los resultados reportados por la revisión bibliográfica permitiendo predecir la presencia de fases en función de la estabilidad termodinámica. Resultados de porosimetría por inyección de mercurio mostraron una mayor concentración de poros, asociados a defectos, en muestras curadas a 85°C con respecto a las de 23 °C. Finalmente, medidas de variación longitudinal para muestras de fibrocemento elaboradas en laboratorio y en fábrica presentaron dispersión en los resultados de expansión para cada uno de los escenarios sin poder correlacionar todos los datos con el aumento de masa exhibido por cada una de las muestras; no obstante, se resalta el riesgo de deterioro del fibrocemento por el aumento de defectos causado por la temperatura así como la creación de todas las condiciones necesarias que favorecen la formación tardía de etringita a partir del proceso de fabricación empleado para este producto.

Carboplatin pharmacokinetics following a single-dose infusion in sulphur-crested cockatoos (Cacatua galerita)

Objective To determine the pharmacokinetics of carboplatin in sulphur-crested cockatoos, so that its use in clinical studies in birds can be considered. Design A pharmacokinetic study of carboplatin, following a single intravenous (IV) or intraosseus (10) infusion over 3 min, was performed in six healthy sulphur-crested cockatoos (Cacatua galerita). Procedure Birds were anaesthetised and a jugular vein cannulated for blood collection. Carboplatin (5 mg/kg) was infused over 3 min by the IV route in four birds via the contralateral jugular vein, and by the 10 route in two birds via the ulna. Serial blood samples were collected for 96 h after initiation of the infusion. Tissue samples from 11 organs were obtained at necropsy, 96 h after carboplatin administration. Total Pt and filterable Pt in plasma and tissue Pt concentrations were assayed by inductively coupled plasma-mass spectrometry. A noncompartmental pharmacokinetic analysis was performed on the plasma data. Results The mean +/- SD for the C-max of filterable Pt was 27.3 +/- 4.06 mg/L and in all six birds occurred at the end of the 3 min infusion, thenceforth declining exponentially over the next 6 h to an average concentration of 0.128 +/- 0.065 mg/L. The terminal half-life (T-1/2) was 1.0 +/- 0.17 h, the systemic clearance (CI) was 5.50 +/- 1.06 mL/min/kg and the volume of distribution (Vss) was 0.378 +/- 0.073 L/kg. The extrapolated area under the curve (AUC(0-x)) was 0.903 +/- 0.127 mg/mL.min; the area extrapolated past the last (6 h) data point to infinite time averaged only 1.25% of the total AUC(0-x). The kidneys had the greatest accumulation of Pt (7.04 +/- 3.006 mug/g), followed by the liver (3.08 +/- 1.785 mug/g DM). Conclusions and clinical relevance Carboplatin infusion in sulphur-crested cockatoos produced mild, transient alimentary tract signs and the Pt plasma concentration was similar whether carboplatin was given intravenously or intraosseously. Filterable plasma Pt concentrations for carboplatin persisted longer than for cisplatin, due mostly to the difference in systemic clearance between these drugs in sulphur-crested cockatoos. The distribution of tissue Pt after carboplatin administration was similar to that reported for cisplatin in sulphur-crested cockatoos. Despite anatomical, physiological and biochemical differences among animal species, the pharmacokinetic disposition of filterable Pt in the sulphur-crested cockatoo shares some features with the kinetics reported previously in other animals and human beings.

Towards input/output-free modelling of linear infinite-dimensional systems in continuous time

This dissertation describes a networking approach to infinite-dimensional systems theory, where there is a minimal distinction between inputs and outputs. We introduce and study two closely related classes of systems, namely the state/signal systems and the port-Hamiltonian systems, and describe how they relate to each other. Some basic theory for these two classes of systems and the interconnections of such systems is provided. The main emphasis lies on passive and conservative systems, and the theoretical concepts are illustrated using the example of a lossless transfer line. Much remains to be done in this field and we point to some directions for future studies as well.