Development in a biologically inspired spinal neural network for movement control

In two phases, we develop neural network models of spinal circuitry which self-organises into networks with opponent channels for the control of an antagonistic muscle pair. The self-organisation is enabled by spontaneous activity present in the spinal cord. We show that after the process of self-organisation, the networks have developed the possibility to independently control the length and tension of the innerated muscles. This allows the specification of joint angle independent from the specification of joint stiffness. The first network comprises only motorneurons and inhibitory interneurons through which the two channels interact. The inhibitory interneurons prevent saturation of the motorneuron pools, which is a necessary condition for independent control. In the second network, however, the neurons in the motorneuron pools obey the size-principle, which is a threat to the desired invariance of joint angle for varying joint stiffness, because of the different amplification of inputs in the case these inputs are not equal. To restore the desired invariance the second network ha.s been expanded with Renshaw cells. The manner in which they are included in the circuitry corrects the problem caused by the addition of the size-principle. The results obtained from the two models compare favourably with the FLETE-model for spinal circuitry (Bullock & Grossberg, 1991; Bullock et al., HJ93; Bullock & Contreras-Vidal, 1993) which has been successful in explaining several phenomena related to motor control.Fulbright Scholarship; Office of Naval Research (N00014-92-J-1309, N00014-95-1-0409

A model for vortical plumes in rotating convection

In turbulent rotating convection a typical flow structuring in columnar vortices is observed. In the internal structure of these vortices several symmetries are approximately satisfied. A model for these columnar vortices is derived by prescribing these symmetries. The symmetry constraints are applied to the Navier¿Stokes equations with rotation in the Boussinesq approximation. It is found that the application of the symmetries results in a set of linearized equations. An investigation of the linearized equations leads to a model for the columnar vortices and a prediction for the heat flux (Nusselt number) that is very appropriate compared to the results from direct numerical simulations of the full governing equation

The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-B\'enard convection

When the classical Rayleigh-B\'enard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large scale circulation (LSC) is the dominant feature of the flow. In regime II (moderate rotation) the LSC is replaced by vertically aligned vortices. Regime III (strong rotation) is characterized by suppression of the vertical velocity fluctuations. Using results from experiments and direct numerical simulations of RB convection for a cell with a diameter-to-height aspect ratio equal to one at $Ra \sim 10^8-10^9$ ($Pr=4-6$) and $0 \lesssim 1/Ro \lesssim 25$ we identified the characteristics of the azimuthal temperature profiles at the sidewall in the different regimes. In regime I the azimuthal wall temperature profile shows a cosine shape and a vertical temperature gradient due to plumes that travel with the LSC close to the sidewall. In regime II and III this cosine profile disappears, but the vertical wall temperature gradient is still observed. It turns out that the vertical wall temperature gradient in regimes II and III has a different origin than that observed in regime I. It is caused by boundary layer dynamics characteristic for rotating flows, which drives a secondary flow that transports hot fluid up the sidewall in the lower part of the container and cold fluid downwards along the sidewall in the top part.Comment: 21 pages, 12 figure

A model for vortical plumes in rotating convection

In turbulent rotating convection a typical flow-structuring in columnar vortices is observed. In the internal structure of these vortices several symmetries are approximately satisfied. A model for these columnar vortices is derived by prescribing these symmetries. The symmetry constraints are applied to the Navier-Stokes equations with rotation in the Boussinesq approximation. It is found that the application of the symmetries results in a set of linearized equations. An investigation of the linearized equations leads to a model for the columnar vortices, and a prediction for the heat flux (Nusselt number) that is very appropriate compared with results from direct numerical simulations of the full governing equations

The Okubo-Weiss Criteria in Two-Dimensional Hydrodynamic and Magnetohydrodynamic Flows

The Okubo [2]-Weiss [3] criterion is recast by using the 2D hydrodynamic Beltrami condition (Shivamoggi et al.[13]) that approximates the slow flow-variation ansatz imposed in its derivation. This turns out to provide an interesting interpretation of the Okubo-Weiss criterion very logically in terms of the topological properties of the underlying vorticity manifold. These developments are then extended to 2D quasi-geostrophic flows (via the potential divorticity framework), magnetohydrodynamic flows and electron magnetohydrodynamic flows (via the generalized magnetic flux framework) and the Okubo-Weiss criteria for these cases are considered.Comment: 13 page

Ground state of a resonantly interacting Bose gas

We show that a two-channel mean-field theory for a Bose gas near a Feshbach resonance allows for an analytic computation of the chemical potential, and therefore the universal constant \beta, at unitarity. To improve on this mean-field theory, which physically neglects condensate depletion, we study a variational Jastrow ansatz for the ground-state wave function and use the hypernetted-chain approximation to minimize the energy for all positive values of the scattering length. We also show that other important physical quantities such as Tan's contact and the condensate fraction can be directly obtained from this approach.Comment: Replaced with published version; 11 pages, 7 figure