Browsing by Subject "equilibria"

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    Birth Rates Determine Life Expectancy in Theoretical Equilibrium Populations: Implications for political demography and conflict early warning
    (American Intelligence Journal, 2018-04) Andregg, Michael M.
    Executive Summary This paper examines implications for political demography of a theoretical population that is in complete equilibrium. By “complete equilibrium,” we mean that the population neither grows nor shrinks, there is neither immigration to nor emigration from it, and that the age structure has stabilized so that it no longer changes over time. These are all important elements of complete equilibrium, as opposed to stability in just absolute numbers. This condition is found in some natural populations of animals and plants, but it has not obtained in most human populations in recorded history. Reduced to basics, this theoretical population has the following characteristics: 1. In complete equilibrium populations, birth rates will equal death rates so the population neither grows nor shrinks. 2. In a complete equilibrium population, death rates determine life expectancy, expressible as: LE = 1000/DR. 3. Since, in a complete equilibrium population, birth rates equal death rates, this can also be expressed as: LE = 1000/BR. 4. This implies that fundamentally, birth rates determine life expectancy in complete equilibrium populations. This paper has two goals. The first is simply to check the accuracy of the theoretical formulas identified above. Since they are quite simple and likely accurate, I invite others to identify any errors. The second goal is at least as important. How do human populations evade this limiting outcome? Or do they really? I fear the short answer to these questions is a) genocide and war, and b) no, they do not really escape an iron law of biology. However, they often do displace the high death rates to marginal or weaker populations. If correct, this has significant implications for conflict early warning as illustrated by several real-world examples.
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    A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
    (2008-11-26) Lewicka, Marta
    We prove that the critical points of the $3$d nonlinear elasticity functional over a thin shell of arbitrary geometry and of thickness $h$, as well as the weak solutions to the static equilibrium equations (formally the Euler Lagrange equations associated to the elasticity functional) converge, in the limit of vanishing thickness $h$, to the critical points of the generalized von Karman functional on the mid-surface, recently derived in [14]. This holds provided the elastic energy of the $3$d deformations scale like $h^4$ and the magnitude of the body forces scale like $h^3$.