Minimum Energy Configurations in the NN-Body Problem and the Celestial Mechanics of Granular Systems

Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for $N=1,2,3$ and develops hypotheses on the relative equilibria and minimum energy configurations for $N\gg 1$ bodies.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd

Action selection and refinement in subcortical loops through basal ganglia and cerebellum

Subcortical loops through the basal ganglia and the cerebellum form computationally powerful distributed processing modules (DPMs). This paper relates the computational features of a DPM's loop through the basal ganglia to experimental results for two kinds of natural action selection. First, functional imaging during a serial order recall task was used to study human brain activity during the selection of sequential actions from working memory. Second, microelectrode recordings from monkeys trained in a step-tracking task were used to study the natural selection of corrective submovements. Our DPM-based model assisted in the interpretation of puzzling data from both of these experiments. We come to posit that the many loops through the basal ganglia each regulate the embodiment of pattern formation in a given area of cerebral cortex. This operation serves to instantiate different kinds of action (or thought) mediated by different areas of cerebral cortex. We then use our findings to formulate a model of the aetiology of schizophrenia

Mass Transport in Porous Media with Variable Mass

We present a theoretical and numerical study of mass transport in a porous medium saturated with a fluid and characterised by an evolving internal structure. The dynamics of the porous medium and the fluid as well as their reciprocal interactions are described at a coarse scale, so that the fundamental tools of Mixture Theory and Continuum Mechanics can be used. The evolution of the internal structure of the porous medium, which is here primarily imputed either to growth or to mass exchange with the fluid, is investigated by enriching the space of kinematic variables of the mixture with a set of structural descriptors, each of which is power-conjugate to generalised forces satisfying a balance law. Establishing the influence of the structural change of the porous medium on the transport properties of the mixture and, thus, on the quantities characterising fluid flow is the crux of our contribution