Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Effect of temperature on percentage of germination of canistel seeds (Pouteria campechiana)

The canistel is a fruit originated in Mexico and Central America, being introduced in Brazil in 1986. The plants present medium size, however it can reach up to 15 meters of height; the leaves measure about 10 to 25 cm; the flowers are complete and small and the fruit presents yellow coloration when ripe, with whitish pulp and sweet flavor. The propagation can be realized by seed or grafting. In view of almost total absence of information about the culture and the possibility to have a commercial cultivation, the present work, was live in which the effect of the temperature was evaluated in the percentage of germination of the seeds. It was checked that the best averages were obtained in temperature of 30ºC and the minor in 15ºC, 20ºC and 40ºC could be considerate the worst of them.

Evolution of superficial lake water temperature profile under diurnal radiative forcing

In lentic water bodies, such as lakes, the water temperature near the surface typically increases during the day, and decreases during the night as a consequence of the diurnal radiative forcing (solar and infrared radiation). These temperature variations penetrate vertically into the water, transported mainly by heat conduction enhanced by eddy diffusion, which may vary due to atmospheric conditions, surface wave breaking, and internal dynamics of the water body. These two processes can be described in terms of an effective thermal diffusivity, which can be experimentally estimated. However, the transparency of the water (depending on turbidity) also allows solar radiation to penetrate below the surface into the water body, where it is locally absorbed (either by the water or by the deployed sensors). This process makes the estimation of effective thermal diffusivity from experimental water temperature profiles more difficult. In this study, we analyze water temperature profiles in a lake with the aim of showing that assessment of the role played by radiative forcing is necessary to estimate the effective thermal diffusivity. To this end we investigate diurnal water temperature fluctuations with depth. We try to quantify the effect of locally absorbed radiation and assess the impact of atmospheric conditions (wind speed, net radiation) on the estimation of the thermal diffusivity. The whole analysis is based on the results of fiber optic distributed temperature sensing, which allows unprecedented high spatial resolution measurements (∼4 mm) of the temperature profile in the water and near the water surface.

Effects of packaging and temperature on postharvest of atemoya

Effects of refrigerated storage and different packages on postharvest behaviour of fruits of atemoya (Annona cherimola x A. squamosa) cv. PR3 were investigated. Fruits were individually sealed in copolymer (PD-955) and low-density polyethylene (LDPE) bags and stored for 21 days at 15°C or 25°C. Then they were unwrapped and maintained at 25°C, for ripening. Weight loss and firmness of fruits were both affected by storage time, temperature and packaging. Weight loss in packaged atemoyas was lower than in the control, non-wrapped fruits. A non-trained panel scored the atemoyas for overall eating quality and appearance. Fruits sealed in LDPE did not ripen, probably due to an injurious atmosphere developed inside the package. Atemoyas packaged in PD-955 film had a shelf-life of 17 days against 13 days of the control ones, both stored at 15°C, an increase of 30% on shelf-life.

Influence of the temperature in germination of seeds of jabuticaba tree

The jaboticaba tree (Myrciaria spp.) is originated from the center-south of Brazil and presents different types. It's a medium size tree, with tendency to form a crown with great number of branches. A characteristic considered as limitant for the commercial crop is the great juvenility, advicing producing good rootstocks of seedlings and graft wanted varieties, and other vegetative processes. With the purpose of evaluating the effect of temperature on germination of three clones of jaboticaba tree, was carried out a laboratorial research. It was observed influence of the temperature on germination. The highest percentage of germination was obtained at low temperature (15ºC and 20ºC). When it was used the temperature of 35ºC, two clones had only 8% of germination, while the other one was verified 35%. These values show the possibility of the ocurrence of variability among the clones of jaboticaba tree.

Integral cohomology of finite postnikov towers

Depuis le séminaire H. Cartan de 1954-55, il est bien connu que l'on peut trouver des éléments de torsion arbitrairement grande dans l'homologie entière des espaces d'Eilenberg-MacLane K(G,n) où G est un groupe abélien non trivial et n>1. L'objectif majeur de ce travail est d'étendre ce résultat à des H-espaces possédant plus d'un groupe d'homotopie non trivial. Dans le but de contrôler précisément le résultat de H. Cartan, on commence par étudier la dualité entre l'homologie et la cohomologie des espaces d'Eilenberg-MacLane 2-locaux de type fini. On parvient ainsi à raffiner quelques résultats qui découlent des calculs de H. Cartan. Le résultat principal de ce travail peut être formulé comme suit. Soit X un H-espace ne possédant que deux groupes d'homotopie non triviaux, tous deux finis et de 2-torsion. Alors X n'admet pas d'exposant pour son groupe gradué d'homologie entière réduite. On construit une large classe d'espaces pour laquelle ce résultat n'est qu'une conséquence d'une caractéristique topologique, à savoir l'existence d'un rétract faible X K(G,n) pour un certain groupe abélien G et n>1. On généralise également notre résultat principal à des espaces plus compliqués en utilisant la suite spectrale d'Eilenberg-Moore ainsi que des méthodes analytiques faisant apparaître les nombres de Betti et leur comportement asymptotique. Finalement, on conjecture que les espaces qui ne possédent qu'un nombre fini de groupes d'homotopie non triviaux n'admettent pas d'exposant homologique. Ce travail contient par ailleurs la présentation de la « machine d'Eilenberg-MacLane », un programme C++ conçu pour calculer explicitement les groupes d'homologie entière des espaces d'Eilenberg-MacLane. <br/><br/>By the work of H. Cartan, it is well known that one can find elements of arbitrarilly high torsion in the integral (co)homology groups of an Eilenberg-MacLane space K(G,n), where G is a non-trivial abelian group and n>1. The main goal of this work is to extend this result to H-spaces having more than one non-trivial homotopy groups. In order to have an accurate hold on H. Cartan's result, we start by studying the duality between homology and cohomology of 2-local Eilenberg-MacLane spaces of finite type. This leads us to some improvements of H. Cartan's methods in this particular case. Our main result can be stated as follows. Let X be an H-space with two non-vanishing finite 2-torsion homotopy groups. Then X does not admit any exponent for its reduced integral graded (co)homology group. We construct a wide class of examples for which this result is a simple consequence of a topological feature, namely the existence of a weak retract X K(G,n) for some abelian group G and n>1. We also generalize our main result to more complicated stable two stage Postnikov systems, using the Eilenberg-Moore spectral sequence and analytic methods involving Betti numbers and their asymptotic behaviour. Finally, we investigate some guesses on the non-existence of homology exponents for finite Postnikov towers. We conjecture that Postnikov pieces do not admit any (co)homology exponent. This work also includes the presentation of the "Eilenberg-MacLane machine", a C++ program designed to compute explicitely all integral homology groups of Eilenberg-MacLane spaces. <br/><br/>Il est toujours difficile pour un mathématicien de parler de son travail. La difficulté réside dans le fait que les objets qu'il étudie sont abstraits. On rencontre assez rarement un espace vectoriel, une catégorie abélienne ou une transformée de Laplace au coin de la rue ! Cependant, même si les objets mathématiques sont difficiles à cerner pour un non-mathématicien, les méthodes pour les étudier sont essentiellement les mêmes que celles utilisées dans les autres disciplines scientifiques. On décortique les objets complexes en composantes plus simples à étudier. On dresse la liste des propriétés des objets mathématiques, puis on les classe en formant des familles d'objets partageant un caractère commun. On cherche des façons différentes, mais équivalentes, de formuler un problème. Etc. Mon travail concerne le domaine mathématique de la topologie algébrique. Le but ultime de cette discipline est de parvenir à classifier tous les espaces topologiques en faisant usage de l'algèbre. Cette activité est comparable à celle d'un ornithologue (topologue) qui étudierait les oiseaux (les espaces topologiques) par exemple à l'aide de jumelles (l'algèbre). S'il voit un oiseau de petite taille, arboricole, chanteur et bâtisseur de nids, pourvu de pattes à quatre doigts, dont trois en avant et un, muni d'une forte griffe, en arrière, alors il en déduira à coup sûr que c'est un passereau. Il lui restera encore à déterminer si c'est un moineau, un merle ou un rossignol. Considérons ci-dessous quelques exemples d'espaces topologiques: a) un cube creux, b) une sphère et c) un tore creux (c.-à-d. une chambre à air). a) b) c) Si toute personne normalement constituée perçoit ici trois figures différentes, le topologue, lui, n'en voit que deux ! De son point de vue, le cube et la sphère ne sont pas différents puisque ils sont homéomorphes: on peut transformer l'un en l'autre de façon continue (il suffirait de souffler dans le cube pour obtenir la sphère). Par contre, la sphère et le tore ne sont pas homéomorphes: triturez la sphère de toutes les façons (sans la déchirer), jamais vous n'obtiendrez le tore. Il existe un infinité d'espaces topologiques et, contrairement à ce que l'on serait naïvement tenté de croire, déterminer si deux d'entre eux sont homéomorphes est très difficile en général. Pour essayer de résoudre ce problème, les topologues ont eu l'idée de faire intervenir l'algèbre dans leurs raisonnements. Ce fut la naissance de la théorie de l'homotopie. Il s'agit, suivant une recette bien particulière, d'associer à tout espace topologique une infinité de ce que les algébristes appellent des groupes. Les groupes ainsi obtenus sont appelés groupes d'homotopie de l'espace topologique. Les mathématiciens ont commencé par montrer que deux espaces topologiques qui sont homéomorphes (par exemple le cube et la sphère) ont les même groupes d'homotopie. On parle alors d'invariants (les groupes d'homotopie sont bien invariants relativement à des espaces topologiques qui sont homéomorphes). Par conséquent, deux espaces topologiques qui n'ont pas les mêmes groupes d'homotopie ne peuvent en aucun cas être homéomorphes. C'est là un excellent moyen de classer les espaces topologiques (pensez à l'ornithologue qui observe les pattes des oiseaux pour déterminer s'il a affaire à un passereau ou non). Mon travail porte sur les espaces topologiques qui n'ont qu'un nombre fini de groupes d'homotopie non nuls. De tels espaces sont appelés des tours de Postnikov finies. On y étudie leurs groupes de cohomologie entière, une autre famille d'invariants, à l'instar des groupes d'homotopie. On mesure d'une certaine manière la taille d'un groupe de cohomologie à l'aide de la notion d'exposant; ainsi, un groupe de cohomologie possédant un exposant est relativement petit. L'un des résultats principaux de ce travail porte sur une étude de la taille des groupes de cohomologie des tours de Postnikov finies. Il s'agit du théorème suivant: un H-espace topologique 1-connexe 2-local et de type fini qui ne possède qu'un ou deux groupes d'homotopie non nuls n'a pas d'exposant pour son groupe gradué de cohomologie entière réduite. S'il fallait interpréter qualitativement ce résultat, on pourrait dire que plus un espace est petit du point de vue de la cohomologie (c.-à-d. s'il possède un exposant cohomologique), plus il est intéressant du point de vue de l'homotopie (c.-à-d. il aura plus de deux groupes d'homotopie non nuls). Il ressort de mon travail que de tels espaces sont très intéressants dans le sens où ils peuvent avoir une infinité de groupes d'homotopie non nuls. Jean-Pierre Serre, médaillé Fields en 1954, a montré que toutes les sphères de dimension >1 ont une infinité de groupes d'homotopie non nuls. Des espaces avec un exposant cohomologique aux sphères, il n'y a qu'un pas à franchir...

Kumar's algorithm for solving Toeplitz systems of equations over finite fields

Adaptació de l'algorisme de Kumar per resoldre sistemes d'equacions amb matrius de Toeplitz sobre els reals a cossos finits en un temps 0 (n log n).

Dynamic Model of a Small Once-Through Boiler

In this study, a model for the unsteady dynamic behaviour of a once-through counter flow boiler that uses an organic working fluid is presented. The boiler is a compact waste-heat boiler without a furnace and it has a preheater, a vaporiser and a superheater. The relative lengths of the boiler parts vary with the operating conditions since they are all parts of a single tube. The present research is a part of a study on the unsteady dynamics of an organic Rankine cycle power plant and it will be a part of a dynamic process model. The boiler model is presented using a selected example case that uses toluene as the process fluid and flue gas from natural gas combustion as the heat source. The dynamic behaviour of the boiler means transition from the steady initial state towards another steady state that corresponds to the changed process conditions. The solution method chosen was to find such a pressure of the process fluid that the mass of the process fluid in the boiler equals the mass calculated using the mass flows into and out of the boiler during a time step, using the finite difference method. A special method of fast calculation of the thermal properties has been used, because most of the calculation time is spent in calculating the fluid properties. The boiler was divided into elements. The values of the thermodynamic properties and mass flows were calculated in the nodes that connect the elements. Dynamic behaviour was limited to the process fluid and tube wall, and the heat source was regarded as to be steady. The elements that connect the preheater to thevaporiser and the vaporiser to the superheater were treated in a special way that takes into account a flexible change from one part to the other. The model consists of the calculation of the steady state initial distribution of the variables in the nodes, and the calculation of these nodal values in a dynamic state. The initial state of the boiler was received from a steady process model that isnot a part of the boiler model. The known boundary values that may vary during the dynamic calculation were the inlet temperature and mass flow rates of both the heat source and the process fluid. A brief examination of the oscillation around a steady state, the so-called Ledinegg instability, was done. This examination showed that the pressure drop in the boiler is a third degree polynomial of the mass flow rate, and the stability criterion is a second degree polynomial of the enthalpy change in the preheater. The numerical examination showed that oscillations did not exist in the example case. The dynamic boiler model was analysed for linear and step changes of the entering fluid temperatures and flow rates.The problem for verifying the correctness of the achieved results was that there was no possibility o compare them with measurements. This is why the only way was to determine whether the obtained results were intuitively reasonable and the results changed logically when the boundary conditions were changed. The numerical stability was checked in a test run in which there was no change in input values. The differences compared with the initial values were so small that the effects of numerical oscillations were negligible. The heat source side tests showed that the model gives results that are logical in the directions of the changes, and the order of magnitude of the timescale of changes is also as expected. The results of the tests on the process fluid side showed that the model gives reasonable results both on the temperature changes that cause small alterations in the process state and on mass flow rate changes causing very great alterations. The test runs showed that the dynamic model has no problems in calculating cases in which temperature of the entering heat source suddenly goes below that of the tube wall or the process fluid.

Effect of temperature and moisture on the dormancy and activation pattern of Oxalis latifolia bulbs

Con objeto de buscar información para un mejor control de Oxalis latifolia Kunth, se ha estudiado el efecto que presentan la temperatura y la humedad sobre la activación de sus bulbos, tanto en la forma común como en la forma Cornwall de la misma. Los bulbos de la mala hierba se mantuvieron en un refrigerador a +4°C durante 13, 20, 27, 41, 48 y 55 días. Se sacaron tres grupos de 30 bulbos de cada forma en cada fecha de muestreo y se colocaron a 21°C; 15 de ellos se mantuvieron en condiciones de sequía —no se regaron— y otros 15 en condiciones de humedad —añadiendo el agua necesaria—. Los resultados muestran que la activación ocurre durante un período prolongado de tiempo en ambas formas, tanto en seco como en húmedo. También se observó que los bulbos secos se activaron antes que los húmedos y los de la forma común antes que los Cornwall. Se observaron dos patrones de activación: los bulbos secos de la forma común generalmente presentaron una activación que sigue un patrón logarítmico, mientras que sus bulbos humedecidos mostraron una tendencia linear; los bulbos Cornwall se activaron con una tendencia exponencial en la mayoría de los casos. El tiempo medio requerido para la activación después del almacenamiento en frío fue constante en la forma común, sin embargo la activación de Cornwall fue más rápida cuanto más tiempo permanecieron almacenados en frío.

Earliness per se and its dependence upon temperature in diploid wheat lines differing in the major gene Eps-Am1 alleles

Differences in development among wheat cultivars are not only restricted to photoperiod and vernalization responses. When both requirements are fully satisfied differences may still arise due to earliness per se. It is not clear at present to what extent this trait is ‘ intrinsically ’ expressed (a constitutive trait) independently of the environmental conditions so that it might be selected under any thermal condition or if it may be altered to the extent of showing a crossover interaction with temperature in which the ranking of wheat genotypes may be altered. The present study assessed the influence of temperature on the intrinsic earliness for lines of diploid wheat characterized for their differences in a major gene for intrinsic earliness, but also possibly differing in their genetic background for other factors controlling this polygenic trait. To do so the lines were grown individually in two temperature regimes (16 and 23 xC) under long days having previously been fully vernalized. Multiple comparisons analyses were carried out among lines of the same allelic group for the Eps-Am1 gene. Results indicated that within each group there were lines that did not differ in their earliness per se, others differed but without exhibiting any linertemperature interaction and finally different types of interaction were shown, including cases where the ranking of lines was altered depending on the growing temperature. It is thus possible that the selection of a genotype based on its earliness per se in an environment might not represent the same performance in another location where temperature varied significantly.

Effect of temperature and carpel size during pre-anthesis on potential grain weight in wheat

The effect of environmental conditions immediately before anthesis on potential grain weight was investigated in wheat at the experimental field of the Faculty of Agronomy (University of Buenos Aires, Argentina) during 1995 and 1996. Plants of two cultivars of wheat were grown in two environments (two contrasting sowing dates) to provide different background temperature conditions. In these environments, transparent boxes were installed covering the spikes in order to increase spike temperature for a short period (c. 6 days) immediately before anthesis, i.e. between ear emergence and anthesis. In both environments, transparent boxes increased mean temperatures by at least 3n8 mC. These increases were almost entirely due to the changes in maximum temperatures because minimum temperatures were little affected. Final grain weight was significantly reduced by higher temperature during the ear emergence–anthesis period. It is possible that this reduction could be mediated by the effect of the heat treatment on carpel weight at anthesis because a curvilinear association between final grain weight and carpel weight at anthesis was found. This curvilinear association may also indicate a threshold carpel weight for maximizing grain weight.

Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3

This paper is devoted to the study of the volcanoes of l-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the l-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case l = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided.

Base temperature and simulation model for nodes appearance in cape gooseberry (Physalis peruviana L.)

Data was analyzed on development of the solanaceen fruit crop Cape gooseberry to evaluate how well a classical thermal time model could describe node appearance in different environments. The data used in the analysis were obtained from experiments conducted in Colombia in open fields and greenhouse condition at two locations with different climate. An empirical, non linear segmented model was used to estimate the base temperature and to parameterize the model for simulation of node appearance vs. time. The base temperature (Tb) used to calculate the thermal time (TT, ºCd) for node appearance was estimated to be 6.29 ºC. The slope of the first linear segment was 0.023 nodes per TT and 0.008 for the second linear segment. The time at which the slope of node apperance changed was 1039.5 ºCd after transplanting, determined from a statistical analysis of model for the first segment. When these coefficients were used to predict node appearance at all locations, the model successfully fit the observed data (RSME=2.1), especially for the first segment where node appearance was more homogeneous than the second segment. More nodes were produced by plants grown under greenhouse conditions and minimum and maximum rates of node appearance rates were also higher.

Technical Note: Dissolved organic matter fluorescence a finite mixture approach to deconvolve excitation-emission matrices

The analysis of the shape of excitation-emission matrices (EEMs) is a relevant tool for exploring the origin, transport and fate of dissolved organic matter (DOM) in aquatic ecosystems. Within this context, the decomposition of EEMs is acquiring a notable relevance. A simple mathematical algorithm that automatically deconvolves individual EEMs is described, creating new possibilities for the comparison of DOM fluorescence properties and EEMs that are very different from each other. A mixture model approach is adopted to decompose complex surfaces into sub-peaks. The laplacian operator and the Nelder-Mead optimisation algorithm are implemented to individuate and automatically locate potential peaks in the EEM landscape. The EEMs of a simple artificial mixture of fluorophores and DOM samples collected in a Mediterranean river are used to describe the model application and to illustrate a strategy that optimises the search for the optimal output.