Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Dielectric screening in doped Fullerides

For conventional superconductors the electron-electron interaction is strongly reduced by retardation effects, making the formation of Cooper pairs possible. In the alkali-doped Fullerides, however, there are no strong retardation effects. But dielectric screening can reduce the electron-electron interaction sufficiently, if we assume that the random-phase approximation (RPA) is valid. It is not clear, however, if this assumption holds, since the alkali-doped Fullerides are strongly correlated systems close to a Mott transition. To test the validity of the RPA for these systems we have calculated the screening of a test charge using quantum Monte Carlo.Comment: 4 pages, 1 eps figure included; to be published in the proceedings of the International Winterschool on Electronic Properties of Novel Materials, Kirchberg/Tirol, 1998; additional information is available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene

Metal-Insulator transitions in generalized Hubbard models

We study the Mott transition in Hubbard models with a degenerate band on different 3-dimensional lattices. While for a non-degenerate band only the half-filled system may exhibit a Mott transition, with degeneracy there can be a transition for any integer filling. We analyze the filling dependence of the Mott transition and find that $U_c$ (the Hubbard interaction $U$ at which the transition takes place) decreases away from half-filling. In addition we can change the lattice structure of the model. This allows us to study the influence of frustration on the Mott transition. We find that frustration increases $U_c$, compared to bipartite systems. The results were obtained from fixed-node diffusion Monte Carlo calculations using trial functions which allow us to systematically vary the magnetic character of the system. To gain a qualitative understanding of the results, we have developed simple hopping arguments that help to rationalize the doping dependence and the influence of frustration on the Mott transition. Choosing the model parameters to describe the doped Fullerides, we can make contact with experiment and understand why some of the Fullerides are metals, while others, which according to density functional theory should also be metallic, actually are insulators.Comment: 4 pages LaTeX with 4 eps figures; submitted to Computer Physics Communications, Proceedings of the CPP'99/Centennial Meeting, Atlanta, GA; additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene

Filling dependence of the Mott transition in the degenerate Hubbard model

Describing the doped Fullerenes using a generalized Hubbard model, we study the Mott transition for different integer fillings of the t_1u band. We use the opening of the energy-gap E_g as a criterion for the transition. E_g is calculated as a function of the on-site Coulomb interaction U using fixed-node diffusion Monte Carlo. We find that for systems with doping away from half-filling the Mott transitions occurs at smaller U than for the half-filled system. We give a simple model for the doping dependence of the Mott transition.Comment: 7 pages RevTeX with 10 eps figures, additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene

The Effects on Stature of Poverty, Family Size and Birth Order: British Children in the 1930s

This paper examines effects of socio-economic conditions on the standardised heights and body mass index of children in Interwar Britain. It uses the Boyd Orr cohort, a survey of predominantly poor families taken in 1937-9, which provides a unique opportunity to explore the determinants of child health in the era before the welfare state. We examine the trade-off between the quality (in the form of health outcomes) and the number of children in the family at a time when genuine poverty still existed in Britain. Our results provide strong support both for negative birth order effects and negative family size effects on the heights of children. No such effects are found for the body mass index (BMI). We find that household income per capita positively influences the heights of children but, even after accounting for this, the number of children in the family still has a negative effect on height. This latter effect is closely associated with overcrowding and particularly with the degree of cleanliness or hygiene in the household, which conditions exposure to factors predisposing to disease. We also analyse evidence collected retrospectively, which indicates that the effects of childhood conditions on height persisted into adulthood.child health, heights, poverty

Fertility Decline and the Heights of Children in Britain, 1886-1938

In this paper we argue that the fertility decline that began around 1880 had substantial positive effects on the health of children, as the quality-quantity trade-off would suggest. We use microdata from a unique survey from 1930s Britain to analyze the relationship between the standardized heights of children and the number of children in the family. Our results suggest that heights are influenced positively by family income per capita and negatively by the number of children or the degree of crowding in the household. The evidence suggests that family size affected the health of children through its influence on both nutrition and disease. Applying our results to long-term trends, we find that rising household income and falling family size contributed significantly to improving child health between 1886 and 1938. Between 1906 and 1938 these variables account for nearly half of the increase in heights, and much of this effect is due to falling family size. We conclude that the fertility decline is a neglected source of the rapid improvement in health in the first half of the twentieth century.fertility decline, heights of children, health in Britain