Controlled Multitype Branching Models: Geometric Growth

2000 Mathematics Subject Classi cation: 60J80, 60F25.

Interferência do método de previsão populacional no desempenho hidráulico de uma rede coletora de esgoto sanitário

The non existence of sewage services creates an unhealthy environmental, causing impact extremely prejudicial to the human health. In Brazil, this item represents the biggest deficit in the basic sanitation these days, and only about 50% of the population is attended. The sewage collection network is a needful system for the basic sanitation. Between the parameters of the project of a system of collection and sewage transportation, the definition of the population that will be attended is one of the most important variables, and that should be done based on criterion of population growth and in accordant to directrix presents in the comprehensive city plan. In this paper, were evaluated methods of growth based on the geometric growth rate, on the population density and on the number of residents per dwelling, and also mathematics models of growth prediction, emphasizing in the geometric growth and on the logistic curve method. That way, the goal of this paper were value the hydraulic performance in one of the watersheds delimited by the sewage network magnification work existent in the city of Cacoal–RO. Using simulation with different scenarios, the results pointed that the hydraulic performance of the system were strongly affected by the population determination method used. For the same drained area the diameters range from 150 to 250 mm as well as the trench’s deep, where some stretches exceeded the maximum values contained in the standard. Besides, the variation of the sewage contribution rate due the population variation estimated in different scenarios, led to alterations in others important project parameters, such as slope, shallow pool, tensile stress and spreading velocity

Effective energy conservation and management in the building sector : the answer to the energy predicament

Modern civilization has developed principally through man's harnessing of forces. For centuries man had to rely on wind, water and animal force as principal sources of power. The advent of the industrial revolution, electrification and the development of new technologies led to the application of wood, coal, gas, petroleum, and uranium to fuel new industries, produce goods and means of transportation, and generate the electrical energy which has become such an integral part of our lives. The geometric growth in energy consumption, coupled with the world's unrestricted growth in population, has caused a disproportionate use of these limited natural resources. The resulting energy predicament could have serious consequences within the next half century unless we commit ourselves to the philosophy of effective energy conservation and management. National legislation, along with the initiative of private industry and growing interest in the private sector has played a major role in stimulating the adoption of energy-conserving laws, technologies, measures, and practices. It is a matter of serious concern in the United States, where ninety-five percent of the commercial and industrial facilities which will be standing in the year 2000 - many in need of retrofit - are currently in place. To conserve energy, it is crucial to first understand how a facility consumes energy, how its users' needs are met, and how all internal and external elements interrelate. To this purpose, the major thrust of this report will be to emphasize the need to develop an energy conservation plan that incorporates energy auditing and surveying techniques. Numerous energy-saving measures and practices will be presented ranging from simple no-cost opportunities to capital intensive investments.

Optimal growth in a two-sector model without discounting: a geometric investigation

We characterize optimal policy in a two-sector growth model with xed coeÆcients and with no discounting. The model is a specialization to a single type of machine of a general vintage capital model originally formulated by Robinson, Solow and Srinivasan, and its simplicity is not mirrored in its rich dynamics, and which seem to have been missed in earlier work. Our results are obtained by viewing the model as a specific instance of the general theory of resource allocation as initiated originally by Ramsey and von Neumann and brought to completion by McKenzie. In addition to the more recent literature on chaotic dynamics, we relate our results to the older literature on optimal growth with one state variable: speci cally, to the one-sector setting of Ramsey, Cass and Koopmans, as well as to the two-sector setting of Srinivasan and Uzawa. The analysis is purely geometric, and from a methodological point of view, our work can be seen as an argument, at least in part, for the rehabilitation of geometric methods as an engine of analysis.

Body shape variation and colour change during growth in a protogynous fish

Protogynous sequential hermaphroditism is very common in marine fish. Despite a large number of studies on various aspects of sequential hermaphroditism in fish, the relationship between body shape and colour during growth in dichromatic species has not been assessed. Using geometric morphometrics, the present study explores the relationship between growth, body shape and colouration in Coris julis (L. 1758), a small protogynous labrid species with distinct colour phases. Results show that body shape change during growth is independent of change in colour phase, a result which can be explained by the biology of the species and by the social control of sex change. Also, during growth the body grows deeper and the head has a steeper profile. It is hypothesized that a deeper body and a steeper profile might have a function in agonistic interactions between terminal phase males and that the marked chromatic difference between colour phases allows the lack of strict interdependence of body shape and colour during growth.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Wallner lines, crack velocity and mechanisms of crack nucleation and growth in a brittle bulk metallic glass

Mode I fracture experiments were conducted on brittle bulk metallic glass (BMG) samples and the fracture surface features were analyzed in detail to understand the underlying physical processes. Wollner lines, which result from the interaction between the propagating crack front and shear waves emanating from a secondary source, were observed on the fracture surface and geometric analysis of them indicates that the maximum crack velocity is similar to 800 m s(-1), which corresponds to similar to 0.32 times the shear wave speed. Fractography reveals that the sharp crack nucleation at the notch tip occurs at the mid-section of the specimens with the observation of flat and half-penny-shaped cracks. On this basis, we conclude that the crack initiation in brittle BMGs is stress-controlled and occurs through hydrostatic stress-assisted cavity nucleation ahead of the notch tip. High magnification scanning electron and atomic force microscopies of the dynamic crack growth regions reveal highly organized, nanoscale periodic patterns with a spacing of similar to 79 nm. Juxtaposition of the crack velocity with this spacing suggests that the crack takes similar to 10(-10) s for peak-to-peak propagation. This, and the estimated adiabatic temperature rise ahead of the propagating crack tip that suggests local softening, is utilized to critically discuss possible causes for the nanocorrugation formation. Taylor's fluid meniscus instability is unequivocally ruled out. Then, two other possible mechanisms, viz. (a) crack tip blunting and resharpening through nanovoid nucleation and growth ahead of the crack tip and eventual coalescence, and (b) dynamic oscillation of the crack in a thin slab of softened zone ahead of the crack-tip, are critically discussed. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Modeling Ammonothermal Growth of GaN Single Crystals: The Role of Transport

Single crystal gallium nitride (GaN) is an important technological material used primarily for the manufacture of blue light lasers. An important area of contemporary research is developing a viable growth technique. The ammonothermal technique is an important candidate among many others with promise of commercially viable growth rates and material quality. The GaN growth rates are a complicated function of dissolution kinetics, transport by thermal convection and crystallization kinetics. A complete modeling effort for the growth would involve modeling each of these phenomena and also the coupling between these. As a first step, the crystallization and dissolution kinetics were idealized and the growth rates as determined purely by transport were investigated. The growth rates thus obtained were termed ‘transport determined growth rates’ and in principle are the maximum growth rates that can be obtained for a given configuration of the system. Using this concept, a parametric study was conducted primarily on the geometric and the thermal boundary conditions of the system to optimize the ‘transport determined growth rate’ and determine conditions when transport might be a bottleneck.

Diffusion dominated process for the crystal growth of a binary alloy

The pure diffusion process has been often used to study the crystal growth of a binary alloy in the microgravity environment. In the present paper, a geometric parameter, the ratio of the maximum deviation distance of curved solidification and melting interfaces from the plane to the radius of the crystal rod, was adopted as a small parameter, and the analytical solution was obtained based on the perturbation theory. The radial segregation of a diffusion dominated process was obtained for cases of arbitrary Peclet number in a region of finite extension with both a curved solidification interface and a curved melting interface. Two types of boundary conditions at the melting interface were analyzed. Some special cases such as infinite extension in the longitudinal direction and special range of Peclet number were reduced from the general solution and discussed in detail.

The age and growth of the tongue sole Cynoglossus canariensis (Steind 1882)

The geometric mean regression equation for the weight; length relationship of Cynoglossus canariensis was W = 0.0025 L super(3.1770). The Von Bertalanffy constants Woo, Loo, K, and to were 507.5852 g, 47.3683 cm, 0.3333 and 0.1397 for males and 839.0753 g, 54.4720 cm, 0.3062 and 0.1737 for females. Total mortality coefficient Z ranged from 0.6482 and 0.8021

Body shape variation and colour change during growth in a protogynous fish

Protogynous sequential hermaphroditism is very common in marine fish. Despite a large number of studies on various aspects of sequential hermaphroditism in fish, the relationship between body shape and colour during growth in dichromatic species has not been assessed. Using geometric morphometrics, the present study explores the relationship between growth, body shape and colouration in Coris julis (L. 1758), a small protogynous labrid species with distinct colour phases. Results show that body shape change during growth is independent of change in colour phase, a result which can be explained by the biology of the species and by the social control of sex change. Also, during growth the body grows deeper and the head has a steeper profile. It is hypothesized that a deeper body and a steeper profile might have a function in agonistic interactions between terminal phase males and that the marked chromatic difference between colour phases allows the lack of strict interdependence of body shape and colour during growth.

Nucleation and growth of glycine crystals with controllable sizes and polymorphs on Langmuir-Blodgett films

Control of crystal polymorph and size is very important in many application fields. Herein we demonstrate that Langmuir-Blodgett (LB) films of stearic acid (SA) and octadecylamine (ODA) can serve as templates and generate different polymorphs of glycine crystals. In the neutral aqueous solutions, gamma-glycine crystallizes on LB films of ODA while the polymorphic outcome becomes the (x-form on LB films of SA. These observed results could be explained by the electrostatic interactions and geometric lattice matching at the LB film/crystal interfaces, respectively. By keeping the appropriate supersaturation, we have successfully controlled the number of crystals grown on LB films; for example, in some certain cases, only one piece of crystal was grown on LB films in solution. Therefore, large crystals of centimeter size could be prepared. These experimental results suggest a new approach to produce an organic crystal with bulk scale.

Aflatoxin exposure in utero causes growth faltering in Gambian infants

Background Growth faltering in West African children has previously been associated with dietary exposure to aflatoxins, particularly upon weaning. However, in animal studies in utero exposure to low levels of aflatoxin also results in growth faltering.

Objective This study investigated the effect of in utero aflatoxin exposure on infant growth in the first year of life in The Gambia.

Methods Height and weight were measured for 138 infants at birth and at regular monthly intervals for one year. Aflatoxin-albumin (AF-alb) adduct level was measured in maternal blood during pregnancy, in cord blood and in infants at age 16 weeks.

Results The geometric mean AF-alb levels were 40.4pg/mg (range 4.82-60.8pg/mg), 10.1pg/mg (range 5.01-89.6pg/mg) and 8.7pg/mg (range 5.0-30.2pg/mg) in maternal, cord and infant blood, respectively. AF-alb in maternal blood was a strong predictor of both weight (P = 0.012) and height (P = 0.044) gain, with lower gain in those with higher exposure. A reduction of maternal AF-alb from 110pg/mg to 10pg/mg would lead to a 0.8kg increase in weight and 2cm increase in height within the first year of life.

Conclusions This study shows a strong effect of maternal aflatoxin exposure during pregnancy on growth in the first year of life and thus extends earlier observations of an association between aflatoxin exposure during infancy and growth faltering. The findings imply value in targeting intervention strategies at early life exposures.

A Prospective Study of Growth and Biomarkers of Exposure to Aflatoxin and Fumonisin during Early Childhood in Tanzania

BACKGROUND: Aflatoxin and fumonisin are toxic food contaminants. Knowledge about effects of their exposure and co-exposure on child growth is inadequate.

OBJECTIVE: To investigate the association between child growth and aflatoxin and fumonisin exposure in Tanzania.

METHODS: A total of 166 children were recruited at 6 to 14 months of age and studied at recruitment, and at the sixth and twelfth month following recruitment. Blood and urine samples were collected and analysed for plasma aflatoxin albumin adducts (AF-alb) using ELISA, and urinary fumonisin B1 (UFB1) using LC-MS, respectively. Anthropometric measurements were taken and growth index Z-scores were computed.

RESULTS: AF-alb geometric mean concentrations (95% confidence intervals) were 4.7 (3.9, 5.6), 12.9 (9.9, 16.7) and 23.5 (19.9, 27.7) pg/mg albumin at recruitment, six months, and 12 months from recruitment, respectively. At these respective sampling times, geometric mean UFB1 concentrations (95% CI) were 313.9 (257.4, 382.9), 167.3 (135.4, 206.7) and 569.5 (464.5, 698.2) pg/mL urine, and the prevalence of stunted children were 44%, 55% and 56%, respectively. UFB1 concentrations at recruitment were negatively associated with length for age Z-scores (LAZ) at six months (p = 0.016) and at 12 months from recruitment (p = 0.014). The mean UFB1 of the three sampling times (at recruitment, at six and 12 months from recruitment) in each child was negatively associated with LAZ (p < 0.001) and length velocity (p = 0.004) at 12 months from recruitment. The negative association between AF-alb and child growth did not reach statistical significance.

CONCLUSIONS: Exposure to fumonisin alone, or co-exposure with aflatoxins may contribute to child growth impairment.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.