Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model

The special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transtion dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reductionSpecial functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics

Global dynamics and imbalance effects in the Lucas-Uzawa model: further results

In this paper we use a new analytical approach to the Lucas-Uzawa model (Boucekkine and Ruiz Tamarit, 2007) to extend the existing results on the dynamics, and notably on the imbalance effects arising in the model. The approach does not only allow to extend the traditional analysis to any initial conditions and for all variables in level, but it also permits a more general investigation of imbalance effects.Lucas-Uzawa, hypergeometric functions, imbalance effects, global dynamics

A note on global dynamics and imbalance effects in the Lucas-Uzawa model

In the traditional literature on the Lucas-Uzawa model, it is proved that in the neighborhood of the long-run balanced growth path, human capital stock grows at a rate greater than its long-run counterpart when the ratio physical to human capi- tal is above its long run value if and only if the capital share in the production of physical good is lower than the inverse of the elasticity of intertemporal substitution in consumption. We first prove that the claim is true outside the neighborhood of balanced growth paths. More importantly, we identify a crucial asymmetry: what- ever the position of the capital share with respect to the inverse of the elasticity of intertemporal substitution, physical capital stock always grows at a rate lower than its long-run counterpart when the ratio physical to human capital is above its long run value.Lucas-Uzawa, hypergeometric functions, imbalance e®ects, global dynamics.

Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms

This paper studies the different mechanisms and the dynamics through which demography is channelled to the economy. We analyze the role of demographic changes in the economic development process by studying the transitional and the long-run impact of both the rate of population growth and the initial population size on the levels of per capita human capital and income. We do that in an enlarged Lucas-Uzawa model with intergenerational altruism. In contrast to the existing theoretical literature, the long-run level effects of demographic changes, i.e. their impact on the levels of the variables along the balanced growth path, are deeply characterized in addition to the more standard long-run growth effects. We prove that the level effect of the population rate of growth is non-negative (positive in the empirically most relevant case) for the average level of human capital, but a priori ambiguous for the level of per capita income due to the interaction of three transmission mechanisms of demographic shocks, a standard one (dilution) and two non-standard (altruism and human capital accumulation). Overall, the sign of the level effects of population growth depend on preference and technology parameters, but numerically we show that the joint negative effect of dilution and altruism is always stronger than the finduced positive human capital effect. The growth effect of population growth depends basically on the attitude to intergenerational altruism and intertemporal substitution. Moreover, we also prove that the long-run level effects of population size on per capita human capital and income may be negative, nil, or positive, depending on the relationship between preferences and technology, while its growth effect is zero. Finally, we show that the model is able to replicate complicated time relationships between economic and demographic changes. In particular, it entails a negative effect of population growth on per capita income, which dominates in the initial periods, and a positive effect which restores a positive correlation between population growth and economic performance in the long term.Human Capital, Population Growth, Population Size, Endogenous Growth, Level Effect, Growth Effect

Characterizing and testing a thermally isolating superconducting link for SAFIRE-like missions

The discovery of a new class of ceramic superconductors with transition temperatures above the boiling point of liquid nitrogen has opened the doors for several space applications. One important space application is the fabrication of an electrically conducting and thermally isolating link to replace manganin wires used in connecting IR detectors to data acquisition electronics on remote sensing platforms like SAFIRE and SIRTF. These NASA platforms designed to monitor the earth's atmosphere from space use infrared detectors which operate at liquid helium temperature (4.2K) for optimum performance. The SAFIRE mission employs hybrid dewars which combine both mechanical and cryogenic liquid cooling. The lifetime of such a mission is limited by the heat conducted through sensor array leads that connect the electronics (at approximately 80 K) to the sensors (at approximately 4 K). Currently these remoter sensing systems use manganin wires to connect the IR detectors to the data acquisition electronics. This link between a detector operating at 4 K and electronics operating at 80 K must be made of material that has high electrical conductivity and high thermal resistance. The YBCO superconductor with a transition temperature, Tc, of 93 K can achieve these conflicting requirements. A link with these characteristics will improve the thermal isolation of IR detectors and will increase the lifetime of the cryogen. The fabrication of an electrically conducting and thermally isolating link that replaces the manganin wires is an important application that will improve thermal isolation of IR detectors and will increase the lifetime of the cryogen. The link is made by screen printing superconducting lines on a low thermal conductivity ceramic substrate. Developing, modeling, and testing this high temperature superconducting link is a collaborative effort among NASA-Langley Research Center, Christopher Newport University (CNU), Clemson University and the industrial companies that have joined the Commercialization of Space Program for the purpose of developing and testing this link. CNU's effort in the development of this superconducting link included the following major efforts: (1) Development of a thermal conductivity measurement system for high temperature superconductors and ceramic materials which are potential candidates for use as substrates in this link. (2) Development of a mathematical model for the superconducting link that studies the effect of materials and geometry on the heat load and life time of missions. (3) Characterization of high Tc materials and assemblies made for space applications. Properties studied include humidity effects and aging effects on high Tc materials. This report summarizes the results of the research studies that were completed. Copies of publications detailing these findings are attached to this report

Dynamic Modeling and Simulation of a STATCOM/SMES Compensator in Power Systems

The advent of Flexible AC Transmission Systems (FACTS) is giving rise to a new family of electronic equipment emerging to controlling and optimizing the performance of power system, e.g. STATCOM. Static synchronous compensator (STATCOM) is one of the most widely used FACTS devices. This paper presents the integration of STATCOM coupled with superconducting magnetic energy storage (SMES) device in order to provide power oscillation damping in power systems. The additional of energy storage allows the combined compensator to exchange both reactive and active power with the ac network and also capability of the STATCOM is enhanced. This paper describes the structure and characteristics of STATCOM/SMES. In addition, using a proper control scheme, STATCOM/SMES is tested on an IEEE 3-bus system and more effective performance of the presented STATCOM/SMES compensator is evaluated with alone STATCOM through the dynamic simulation by using PSCAD/EMTDC software

Dynamic Modeling and Simulation of a STATCOM/SMES Compensator in Power Systems

The advent of Flexible AC Transmission Systems (FACTS) is giving rise to a new family of electronic equipment emerging to controlling and optimizing the performance of power system, e.g. STATCOM. Static synchronous compensator (STATCOM) is one of the most widely used FACTS devices. This paper presents the integration of STATCOM coupled with superconducting magnetic energy storage (SMES) device in order to provide power oscillation damping in power systems. The additional of energy storage allows the combined compensator to exchange both reactive and active power with the ac network and also capability of the STATCOM is enhanced. This paper describes the structure and characteristics of STATCOM/SMES. In addition, using a proper control scheme, STATCOM/SMES is tested on an IEEE 3-bus system and more effective performance of the presented STATCOM/SMES compensator is evaluated with alone STATCOM through the dynamic simulation by using PSCAD/EMTDC software

Experimental Benefits of Sex Hormones on Vascular Function and the Outcome of Hormone Therapy in Cardiovascular Disease

Cardiovascular disease (CVD) is more common in men and postmenopausal women than premenopausal women, suggesting vascular benefits of female sex hormones. Experimental data have shown beneficial vascular effects of estrogen including stimulation of endothelium-dependent nitric oxide, prostacyclin and hyperpolarizing factor-mediated vascular relaxation. However, the experimental evidence did not translate into vascular benefits of hormone replacement therapy (HRT) in postmenopausal women, and HERS, HERS-II and WHI clinical trials demonstrated adverse cardiovascular events with HRT. The lack of vascular benefits of HRT could be related to the hormone used, the vascular estrogen receptor (ER), and the subject’s age and preexisting cardiovascular condition. Natural and phytoestrogens in small doses may be more beneficial than synthetic estrogen. Specific estrogen receptor modulators (SERMs) could maximize the vascular benefits, with little side effects on breast cancer. Transdermal estrogens avoid the first-pass liver metabolism associated with the oral route. Postmenopausal decrease and genetic polymorphism in vascular ER and post-receptor signaling mechanisms could also modify the effects of HRT. Variants of cytosolic/nuclear ER mediate transcriptional genomic effects that stimulate endothelial cell growth, but inhibit vascular smooth muscle (VSM) proliferation. Also, plasma membrane ERs trigger not only non-genomic stimulation of endothelium-dependent vascular relaxation, but also inhibition of [Ca2+]i, protein kinase C and Rho kinase-dependent VSM contraction. HRT could also be more effective in the perimenopausal period than in older postmenopausal women, and may prevent the development, while worsening preexisting CVD. Lastly, progesterone may modify the vascular effects of estrogen, and modulators of estrogen/testosterone ratio could provide alternative HRT combinations. Thus, the type, dose, route of administration and the timing/duration of HRT should be customized depending on the subject’s age and preexisting cardiovascular condition, and thereby make it possible to translate the beneficial vascular effects of sex hormones to the outcome of HRT in postmenopausal CVD