Cyclical Features of Uzawa-Lucas Endogenous Growth Model

This paper analyzes the cyclical properties of a generalized version of Uzawa-Lucas endogenous growth model. We study the dynamic features of different cyclical components of this model characterized by a variety of decomposition methods. The decomposition methods considered can be classified in two groups. On the one hand, we consider three statistical filters: the Hodrick-Prescott filter, the Baxter-King filter and Gonzalo-Granger decomposition. On the other hand, we use four model-based decomposition methods. The latter decomposition procedures share the property that the cyclical components obtained by these methods preserve the log-linear approximation of the Euler-equation restrictions imposed by the agent’s intertemporal optimization problem. The paper shows that both model dynamics and model performance substantially vary across decomposition methods. A parallel exercise is carried out with a standard real business cycle model. The results should help researchers to better understand the performance of Uzawa-Lucas model in relation to standard business cycle models under alternative definitions of the business cycle.

Litter dynamics and phenology of Melaleuca quinquenervia in south Florida

We monitored litterfall biomass at six different sites of melaleuca (Melaleuca quinquenervia (Cav.) S.T. Blake) forested wetlands in South Florida from July 1997 to June 1999. Annual litterfall of melaleuca varied between sites from 6.5 to 9.9 t dry wt ha(-1) yr(1) over the two-year period. Litterfall was significantly higher (p < 0.0001) in scasonally flooded habitats (9.3 t ha(-1) yr(1)) than in non-flooded (7.5 t ha(-1) yr(1)) and permanently flooded habitats (8.0 t ha(-1) yr(1)). Leaf fall was the major component forming 70% of the total litter, woody material 16%, and reproductive material 11%. Phenology of flowering and leaf flush was investigated by examination of the timing and duration of the fall of different plant parts in the litter traps, coupled with monthly field observations during the two-year study. In both years, flowering began in October and November, with peak flowers production around December, and was essentially completed by February and March. New shoot growth began in mid winter after peak flowering, and extended into the spring. Very little new growth was observed in melaleuca forests during the summer months, from May to August, in South Florida. In contrast, the fall of leaves and small wood was recorded in every month of the year, but generally increased during the dry season with higher levels observed from February to April. Also, no seasonality was recorded in the fall of seed capsules, which apparently resulted from the continual self-thinning of small branches and twigs inside the forest stand. In planning management for perennial weeds, it is important to determine the period during its annual growth cycle when the plant is most susceptible to control measures. These phenological data suggest that the appropriate time for melaleuca control in South Florida might be during late winter and early spring, when the plant is most active.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

Long-Term Growth and Persistence with Endogenous Depreciation: Theory and Evidence

Previous research has shown a strong positive correlation between short-term persistence and long-term output growth as well as between depreciation rates and long-term output growth. This evidence, therefore, contradicts the standard predictions from traditional neoclassical or AK-type growth models with exogenous depreciation. In this paper, we first confirm these findings for a larger sample of 101 countries. We then study the dynamics of growth and persistence in a model where both the depreciation rate and growth are endogenous and procyclical. We find that the model s predictions become consistent with the empirical evidence on persistence, long-term growth and depreciation rates.

Effects of Thermocapillary Convection on the Growth Process in Industrial 8-inch Silicon Czochralski Growth

Czochralski (CZ) crystal growth process is a widely used technique in manufacturing of silicon crystals and other semiconductor materials. The ultimate goal of the IC industry is to have the highest quality substrates, which are free of point defect, impurities and micro defect clusters. The scale up of silicon wafer size from 200 mm to 300 mm requires large crucible size and more heat power. Transport phenomena in crystal growth processes are quite complex due to melt and gas flows that may be oscillatory and/or turbulent, coupled convection and radiation, impurities and dopant distributions, unsteady kinetics of the growth process, melt crystal interface dynamics, free surface and meniscus, stoichiometry in the case of compound materials. A global model has been developed to simulate the temperature distribution and melt flow in an 8-inch system. The present program features the fluid convection, magnetohydrodynamics, and radiation models. A multi-zone method is used to divide the Cz system into different zones, e.g., the melt, the crystal and the hot zone. For calculation of temperature distribution, the whole system inside the stainless chamber is considered. For the convective flow, only the melt is considered. The widely used zonal method divides the surface of the radiation enclosure into a number of zones, which has a uniform distribution of temperature, radiative properties and composition. The integro-differential equations for the radiative heat transfer are solved using the matrix inversion technique. The zonal method for radiative heat transfer is used in the growth chamber, which is confined by crystal surface, melt surface, heat shield, and pull chamber. Free surface and crystal/melt interface are tracked using adaptive grid generation. The competition between the thermocapillary convection induced by non-uniform temperature distributions on the free surface and the forced convection by the rotation of the crystal determines the interface shape, dopant distribution, and striation pattern. The temperature gradients on the free surface are influenced by the effects of the thermocapillary force on the free surface and the rotation of the crystal and the crucible.

Modeling of Ammonothermal Growth of Gallium Nitride Single Crystals

Ammonothermal growth of GaN crystals with a retrograde solubility has been modeled and simulated here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow in the porous charge is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. For the case of retrograde solubility, the charge is put above the baffle. The temperature difference between the dissolving zone and growth zone is found smaller than that applied on the sidewall of autoclave. The baffle opening has a strong effect on the nutrient transport and supersaturation of GaN species in the growth zone.

Transport Phenomena in Ammonothermal Growth of Gallium Nitride

GaN can be used to fabricate blue/green/UV LEDs and high temperature, high power electronic devices. Ideal substrates are needed for high quality III-nitride epitaxy, which is an essential step for the manufacture of LEDs. GaN substrates are ideal to be lattice matched and isomorphic to nitride-based films. Bulk single crystals of GaN can be grown from supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. In this process, a mineralizer such as amide, imide or azide is used to attack a bulk nitride feedstock at temperatures from 200 - 500癈 and pressures from 1 - 4 kbar. Baffle design is essential for successful growth of GaN crystals. Baffle is used to separate the dissolving zone from the growth zone, and to maintain a temperature difference between the two zones. For solubility curve with a positive coefficient with respect to temperature, the growth zone is maintained at a lower temperature than that in the dissolving zone, thus the nutrient becomes supersaturated in the growth zone. The baffle opening is used to control the mixing of nutrients in the two zones, thus the transfer of nutrient from the lower part to the upper part. Ammonothermal systems have been modeled here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. We investigated the effects of baffle opening and position on the transport phenomena of nutrient from dissolving zone to the growth zone. Simulation data have been compared qualitatively with experimental data.

The Politics of Internet Regulation in Brazil : dynamics, factors, and actors in broadband policy

In May 2010, Brazil joined the roll of nations with a National Broadband Plan. The Decree nº 7,175/2010 had implemented a program that aimed to offer 30 million permanent broadband accesses until 2014 and established its main goals, such as accelerating economic and social development, promoting digital inclusion, reducing social and regional inequalities, promoting a generation of employment and income, and expanding electronic government services. However, the broadband access in Brazil is limited, expensive, and centralized in the main urban centres. Despite the fast growth in the past years due to mobile internet access, the market is still concentrated in the local incumbent operators that currently provide mobile services, landline services and Paid-TV services, resulting in a high level of market verticalization. The following dissertation investigates the constraint of broadband access development, the dynamics, the actors, and the factors that have delayed the roll-out of broadband services in Brazil. The study also promotes reflections about the challenge posed by the media, by costumers associations and by public opinion as critical observers of the policy making process. This research examines on the political influence towards regulation to determine the way policy will benefit interest groups. Many interviews have been conducted in order to understand the forces which have been acting in the telecommunications in Brazil after privatization, in 1998. This study aims to provide a better understanding of telecommunications regulatory process in Brazil, in order to help the country finding an adequate policy which can lead to the implementation of a broadband roll-out. The universal broadband access is the only way to benefit the whole society in Brazil with a satisfactory level of education and create more jobs and economic development regarding the plenty use of Information and Communications Technology (ICT).

Economic Effects of Global Warming under Stock Growth Uncertainty: The European Sardine Fishery

Global warming of the oceans is expected to alter the environmental conditions that determine the growth of a fishery resource. Most climate change studies are based on models and scenarios that focus on economic growth, or they concentrate on simulating the potential losses or cost to fisheries due to climate change. However, analysis that addresses model optimization problems to better understand of the complex dynamics of climate change and marine ecosystems is still lacking. In this paper a simple algorithm to compute transitional dynamics in order to quantify the effect of climate change on the European sardine fishery is presented. The model results indicate that global warming will not necessarily lead to a monotonic decrease in the expected biomass levels. Our results show that if the resource is exploited optimally then in the short run, increases in the surface temperature of the fishery ground are compatible with higher expected biomass and economic profit.

Population dynamics of the anchoveta, Cetengraulis mysticetus, in the Gulf of Panama, as determined by tagging experiments

ENGLISH: The anchoveta is the major constituent of the important bait and reduction fisheries of the Gulf of Panama. It is a short-lived species, the great majority of the catch consisting of fish in their first year of life. Fish for reduction are caught chiefly in the Isla Verde area, between Punta Chame and the entrance of the Panama Canal. In 1960 and 1961 anchovetas were tagged with metal internal tags and released in the major areas of occurrence of this species. The tags were recovered from the meal in the reduction plants with magnets. From the 53,380 fish tagged in 1960, 745 tags were returned during the 1960 season, 246 during the 1961 season, and 8 during the 1962 season. From the 113,202 tagged in 1961, 373 tags were returned during the 1961 season and 48 during the 1962 season. Complete catch statistics are available, and length-frequency and length-weight data were used to convert these from pounds to numbers of fish of each year class. The annual survival rate for the fish of the 1959 year class in the Isla Verde area was estimated to be 0.086 by the Chapman-Robson method, 0.102 by the year-class method, and 0.088 by the Jackson positive method. The first method is considered to give the best estimate. Six estimates of the population of fish of the 1959 year class in the Isla Verde area were obtained from the sample tag ratios of six experiments conducted in that area in 1960. The estimates differed due to the temporal decrease in the population, but the downward trend corresponded fairly well to what was expected from the total annual mortality rate. It was estimated that the population of 1959-year class fish was about 818 million on March 8, 1960, and about 70 million on March 8, 1961. As the population of anchovetas decreases during the season the effort increases sufficiently that the catch remains roughly constant. This is described as the "constant absolute catch" type fishery. Of the original population of fish in the Isla Verde area at the beginning of the 1960 season, about 11 per cent were caught and 81 per cent died of natural causes. Evaluation of growth and mortality data demonstrated that beginning the fishery for the youngest age group later than March 8 (the date it began in 1960) would reduce the yield per recruit, while increasing the fishing effort would greatly increase it. Further, it is believed unlikely that increases in the catch in the Isla Verde area alone would noticeably decrease the number of recruits to that area. Therefore there is no foreseeable need for regulation of the fishery. SPANISH: El principal constituyente de la importante pesquería para carnada y para reducción en el Golfo de Panamá es la anchoveta. Es una especie de vida corta cuya pesca, en su mayor parte, está constituida por peces que se encuentran en su primer año de vida. Para la industria de reducción los peces son capturados principalmente en el área de Isla Verde, entre Punta Chame y la entrada del Canal de Panamá. En 1960 y 1961 las anchovetas fueron marcadas con marcas metálicas internas y liberadas en las áreas más importantes en que se encuentra esta especie. Las marcas fueron recobradas de la harina en las plantas de reducción por medio de magnetos. De los 53,380 peces marcados en 1960, fueron devueltas 745 marcas durante la temporada pesquera de 1960, 246 durante la de 1961, y 8 durante la de 1962. De los 113,202 marcados en 1961, 373 marcas fueron devueltas durante la temporada pesquera de 1961 y 48 durante la de 1962. Se dispone de estadísticas completas de captura, y los datos de frecuencia-longitud y de longitud-peso fueron usados para convertir éstos de libras a números de peces de cada clase anual. La tasa anual de supervivencia correspondiente a la clase anual de 1959 en el área de Isla Verde estimó en 0.086 por medio del método Chapman-Robson; en 0.102 por método de la clase anual; y en 0.088 por el método positivo de Jackson. Se considera que el primer método dé la mejor estimación. Seis estimaciones de la población de peces de la clase anual 1959 en el área de Isla Verde fueron obtenidas según la proporción de marcas halladas en las muestras correspondientes a seis experimentos efectuados en aquella área en 1960. Las estimaciones variaron debido a la disminución temporal de la población, pero esta tendencia descendente correspondió bastante bien a lo que se esperaba según la tasa total de mortalidad anual. Se estimó que la población de peces de la clase anual de 1959 era de unos 818 millones el 8 de marzo de 1960, y aproximadamente de unos 70 millones el 8 de marzo de 1961. Conforme a que la población de anchovetas disminuye durante la temporada pesquera, el esfuerzo aumenta lo suficientemente como para que la pesca se mantenga más o menos constante. Este es el tipo de pesquería descrito como de "captura absoluta constante". De la población original de peces en el área de Isla Verde al comienzo de la temporada pesquera de 1960, cerca del 11 por ciento fue capturada y el 81 por ciento murió por causas naturales. La evaluación de los datos del crecimiento mortalidad demostraron que al comenzar la pesquería a explotar grupo de edad más joven en una fecha posterior al 8 de marzo (la fecha en que comenzó en 1960) se reduciría el rendimiento por recluta, mientras que al aumentar el esfuerzo de pesca lo aumentaría considerablemente. Más aún, se cree improbable que el aumento en la pesca en el área de Isla Verde de por sí disminuyera perceptiblemente el número de reclutas en esa área. En consecuencia no se prevé la necesidad de una reglamentación de la pesquería. (PDF contains 172 pages.)

Fishery dynamics and present status of the yellowfin tuna population of the Eastern Pacific Ocean

ENGLISH: From morphometric data, tagging results and reaction of the stock to fishing, it is inferred that the yellowfin tuna of the Eastern Pacific form a distinct population which intermingles little, if at all, with populations to the westward. Excellent statistics of catch and effort, and records of total catch, available since 1934, during rapid growth of the fishery, have made possible application of a generalized mathematical predator-prey model to estimate the effect of fishing on the population, and the average abundance and yield corresponding to different amounts of fishing effort, and also to estimate the rate of fishing mortality per unit of effort. From serial samples of size composition of catches, and from tagging experiments, it has been possible to determine rates of growth and of total mortality. These kinds of information permit application of the catch-per-recruit model of Beverton and Holt. Combination of the results of application of the Beverton and Holt model and of the generalized predator-prey model, leads to inference of the relationship between stock size and recruitment. The form of the relationship is remarkably similar to the theoretical model developed by W. E. Ricker. These studies, based on the data of the near-surface fishery by baitboats and purse seiners, indicate clearly that the increased intensity of fishing has caused diminution of the stocks to the point where they are somewhat "overfished"-that is, incapable of supporting the maximum sustainable average harvest. SPANISH: De los datos morfométricos, de los resultados de las marcaciones y de la reacción del stock a la pesca, se infiere que el atún aleta amarilla del Pacífico oriental forma una población diferente que se mezcla poco, si es que llega a mezclarse, con las poblaciones del oeste. Las excelentes estadísticas de la captura y el esfuerzo y los registros de la pesca global disponibles desde 1934, durante el rápido crecimiento de la pesquería, han hecho posible la aplicación de un modelo matemático generalizado depredador-presa para estimar el efecto de la pesca en la población y el promedio de la abundancia y del rendimiento correspondientes a los diferentes valores del esfuerzo de pesca, y también para estimar la tasa de la mortalidad de pesca por unidad de esfuerzo. Gracias a las muestras en serie de la composición de tamaños de las capturas y a los experimentos de marcación, ha sido posible determinar las tasas del crecimiento y de la mortalidad total. Estos tipos de información permiten la aplicación del modelo de la captura-porrecluta de Beverton y Holt. La combinación de los resultados de la aplicación del modelo de Beverton y Holt y del modelo generalizado depredador-presa, conduce a la inferencia de la relación entre el tamaño del stock y el reclutamiento. La forma de la relación es notoriamente similar al modelo teórico desarrollado por W. E. Ricker. Estos estudios, basados en los datos de la pesquería cerca de la superficie efectuada por barcos de carnada y rederos, indican claramente que el aumento de la intensidad de la pesca ha causado la disminución de los stocks hasta el punto de dejarlos algo "superexplotados", o sea, incapacitados para mantener una producción máxima promedio. (PDF contains 50 pages.)

Population dynamics of the skipjack tuna (Katsuwonus pelamis) of the Eastern Pacific Ocean

ENGLISH: Catches of skipjack tuna supporting major fisheries in parts of the western, central and eastern Pacific Ocean have increased in recent years; thus, it is important to examine the dynamics of the fishery to determine man's effect on the abundance of the stocks. A general linear hypothesis model was developed to standardize fishing effort to a single vessel size and gear type. Standardized effort was then used to compute an index of abundance which accounts for seasonal variability in the fishing area. The indices of abundance were highly variable from year to year in both the northern and southern areas of the fishery but indicated a generally higher abundance in the south. Data from 438 fish tagged and recovered in the eastern Pacific Ocean were used to compute growth curves. A least-squares technique was used to estimate the parameters of the von Bertalanffy growth function. Two estimates of the parameters were made by analyzing the same data in different ways. For the first set of estimates, K= 0.819 on an annual instantaneous basis and L= 729 mm; for the second, K = 0.431 and L=881. These compared well with estimates derived using the Chapman-Richards growth function, which includes the von Bertalanffy function as a special case. It was concluded that the latter function provided an adequate empirical fit to the skipjack data since the more complicated function did not significantly improve the fit. Tagging data from three cruises involving 8852 releases and 1777 returns were used to compute mortality rates during the time the fish were in the fishery. Two models were used in the analyses. The best estimates of the catchability coefficient (q) in the north and south were 8.4 X 10- 4 and 5.0 X 10- 5 respectively. The other loss rate (X), which included losses due to emigration, natural mortality and mortality due to carrying a tag, was 0.14 on an annual instantaneous basis for both areas. To detect the possible effect of fishing on abundance and total yield, the relation between abundance and effort and between total catch and effort was examined. It was found that at levels of intensity observed in the fishery, fishing does not appear to have had any measurable effect on the stocks. It was concluded therefore that the total catch could probably be increased by substantially increasing total effort beyond the present level, and that the fluctuations in abundance are fishery-independent. The estimates of growth, mortality and fishing effort were used to compute yield-per-recruitment isopleths for skipjack in both the northern and southern areas. For a size at first entry of about 425 mm, the yield per recruitment was calculated at 3 pounds in the north and 1.5 pounds in the south. In both areas it would be possible to increase the yield per recruitment by increasing fishing effort. It was not possible to assess potential production of the skipjack stocks fished in the eastern Pacific, except to note that the fishery had not affected their abundance and that they were certainly under-exploited. It was concluded that the northern and southern stocks could support increased harvests, especially the latter. SPANISH: Las capturas de atún barrilete que sostienen las pesquerías principales de la parte occidental, central y oriental del Océano Pacífico han aumentado en los últimos años; así que es importante examinar la dinámica de la pesquería para determinar el efecto que pueda tener sobre la abundancia de los stocks. Se desarrolló un modelo hipotético, lineal para standardizar el esfuerzo de pesca a un solo tamaño de barco y tipo de arte. Luego se usó el esfuerzo standardizado para computar un índice de la abundancia que pueda dar razón de la variabilidad estacional en el área de pesca. Los índices de la abundancia variaron mucho de un año a otro tanto en el área septentrional como en el área meridional de la pesquería, pero indicaron una abundancia generalmente superior en el sur. Se emplearon los datos de 438 peces marcados y recuperados en el Océano Pacífico oriental para computar las curvas de crecimiento. Una técnica de mínimos cuadrados fue usada para estimar los parámetros de la función de crecimiento de van Bertalanffy. Se hicieron dos estimativos de los parámetros mediante el análisis de los mismos datos, de diferente manera. Para el primer juego de estimativos, K=0.819 sobre una base anual instantánea y L∞=729 mm; para el segundo, K=0.431 y L∞=881. Estos se correlacionaron bien con los estimativos obtenidos usando la función de crecimiento de Chapman-Richards, que incluye la de von Bertalanffy como un caso especial. Se decidió que la última función proveía un ajuste empírico, adecuado a los datos del barrilete, ya que la función más complicada no mejoró significativamente el ajuste. Los datos de marcación de tres cruceros incluyendo 8852 liberaciones y 1777 retornos, fueron usados para computar las tasas de mortalidad durante el tiempo en que los peces estuvieron en la pesquería. Se usaron dos modelos en los análisis. Los mejores estimativos del coeficiente de capturabilidad (q) en el norte y en el sur fueron 8.4 X 10-4 y 5.0 X 10-5 , respectivamente. La otra tasa de pérdida (X), la cual incluyó pérdidas debidas a la emigración, mortalidad natural y mortalidad debida a llevar una marca, fue 0.14 sobre una base anual instantánea para las dos áreas. Con el fin de descubrir el efecto que posiblemente pueda tener la pesca sobre la abundancia y el rendimiento total, se examinó la relación entre la abundancia y el esfuerzo y entre la captura total y el esfuerzo. Se encontró que a los niveles de la intensidad observada en la pesquería, la pesca no parece haber tenido ningún efecto perceptible en los stocks. Por lo tanto se decidió que mediante un aumento substancial del esfuerzo total, más allá del nivel actual, la captura total probablemente podría aumentarse, y que las fluctuaciones de la abundancia son independientes de la pesquería. Los estimativos del crecimiento, mortalidad y esfuerzo de pesca fueron usados para computar las isopletas del rendimiento por recluta del barrilete, tanto en las áreas del norte como del sur. Para una talla de primera entrada de unos 425 mm, el rendimiento por recluta fue calculado en 3 libras en el norte y 1.5 libras en el sur. En ambas áreas sería posible aumentar el rendimiento por recluta mediante un aumento del esfuerzo de pesca. No fue posible determinar la producción potencial de los stocks del barrilete pescado en el Pacífico oriental, excepto para observar que la pesquería no ha afectado su abundancia y que ciertamente se encuentran subexplotados. Se concluyó que los stocks norte y sur pueden soportar un aumento en el rendimiento, especialmente este último. (PDF contains 274 pages.)

Growth of deformation twins in room-temperature rolled nanocrystalline nickel

Deformation twinning has been observed in room-temperature rolled nanocrystalline Ni. The growth of the deformation twins via the emission of partial dislocations from a grain boundary has been examined in detail. Partial dislocations on neighboring slip planes may migrate for different distances and then remain in the grain interior, leading to the formation of a steplike twin boundary TB . With continued twin growth, the TBs become gradually distorted and lose their coherent character due to accumulated high stresses. Moreover, we propose that microtwins may form near such TBs due to the emission of partial dislocations from the TB.

Periodic solutions of integro-differential equations which arise in population dynamics

The problem of the existence and stability of periodic solutions of infinite-lag integra-differential equations is considered. Specifically, the integrals involved are of the convolution type with the dependent variable being integrated over the range (- ∞,t), as occur in models of population growth. It is shown that Hopf bifurcation of periodic solutions from a steady state can occur, when a pair of eigenvalues crosses the imaginary axis. Also considered is the existence of traveling wave solutions of a model population equation allowing spatial diffusion in addition to the usual temporal variation. Lastly, the stability of the periodic solutions resulting from Hopf bifurcation is determined with aid of a Floquet theory.

The first chapter is devoted to linear integro-differential equations with constant coefficients utilizing the method of semi-groups of operators. The second chapter analyzes the Hopf bifurcation providing an existence theorem. Also, the two-timing perturbation procedure is applied to construct the periodic solutions. The third chapter uses two-timing to obtain traveling wave solutions of the diffusive model, as well as providing an existence theorem. The fourth chapter develops a Floquet theory for linear integro-differential equations with periodic coefficients again using the semi-group approach. The fifth chapter gives sufficient conditions for the stability or instability of a periodic solution in terms of the linearization of the equations. These results are then applied to the Hopf bifurcation problem and to a certain population equation modeling periodically fluctuating environments to deduce the stability of the corresponding periodic solutions.

Dynamics of cell–matrix mechanical interactions in three dimensions

The forces cells apply to their surroundings control biological processes such as growth, adhesion, development, and migration. In the past 20 years, a number of experimental techniques have been developed to measure such cell tractions. These approaches have primarily measured the tractions applied by cells to synthetic two-dimensional substrates, which do not mimic in vivo conditions for most cell types. Many cell types live in a fibrous three-dimensional (3D) matrix environment. While studying cell behavior in such 3D matrices will provide valuable insights for the mechanobiology and tissue engineering communities, no experimental approaches have yet measured cell tractions in a fibrous 3D matrix.

This thesis describes the development and application of an experimental technique for quantifying cellular forces in a natural 3D matrix. Cells and their surrounding matrix are imaged in three dimensions with high speed confocal microscopy. The cell-induced matrix displacements are computed from the 3D image volumes using digital volume correlation. The strain tensor in the 3D matrix is computed by differentiating the displacements, and the stress tensor is computed by applying a constitutive law. Finally, tractions applied by the cells to the matrix are computed directly from the stress tensor.

The 3D traction measurement approach is used to investigate how cells mechanically interact with the matrix in biologically relevant processes such as division and invasion. During division, a single mother cell undergoes a drastic morphological change to split into two daughter cells. In a 3D matrix, dividing cells apply tensile force to the matrix through thin, persistent extensions that in turn direct the orientation and location of the daughter cells. Cell invasion into a 3D matrix is the first step required for cell migration in three dimensions. During invasion, cells initially apply minimal tractions to the matrix as they extend thin protrusions into the matrix fiber network. The invading cells anchor themselves to the matrix using these protrusions, and subsequently pull on the matrix to propel themselves forward.

Lastly, this thesis describes a constitutive model for the 3D fibrous matrix that uses a finite element (FE) approach. The FE model simulates the fibrous microstructure of the matrix and matches the cell-induced matrix displacements observed experimentally using digital volume correlation. The model is applied to predict how cells mechanically sense one another in a 3D matrix. It is found that cell-induced matrix displacements localize along linear paths. These linear paths propagate over a long range through the fibrous matrix, and provide a mechanism for cell-cell signaling and mechanosensing. The FE model developed here has the potential to reveal the effects of matrix density, inhomogeneity, and anisotropy in signaling cell behavior through mechanotransduction.