Prediction of stable walking for a toy that cannot stand

Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and which has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically-unstable mathematical model based loosely on the physical toy can predict stable limit-cycle walking motions. These calculations add to the repertoire of rigid-body mechanism behaviors as well as further implicating passive-dynamics as a possible contributor to stability of animal motions.Comment: Note: only corrections so far have been fixing typo's in these comments. 3 pages, 2 eps figures, uses epsf.tex, revtex.sty, amsfonts.sty, aps.sty, aps10.sty, prabib.sty; Accepted for publication in Phys. Rev. E. 4/9/2001 ; information about Andy Ruina's lab (including Coleman's, Garcia's and Ruina's other publications and associated video clips) can be found at: http://www.tam.cornell.edu/~ruina/hplab/index.html and more about Georg Bock's Simulation Group with whom Katja Mombaur is affiliated can be found at http://www.iwr.uni-heidelberg.de/~agboc

Functional Consequences of Compartmentalization of Synaptic Input

Intra-axonal recordings of stomatogastric nerve axon 1 (SNAX1) indicate that there are synaptic inputs onto the SNAX1 terminals in the stomatogastric ganglion (STG) of the crab Cancer borealis (Nusbaum et al., 1992b). To determine whether this synaptic input only influenced SNAX1 activity within the STG, we identified the SNAX1 soma in the commissural ganglion (CoG). We found that this neuron has a neuropilar arborization in the CoG and also receives synaptic inputs in this ganglion. Based on its soma location, we have renamed this neuron modulatory commissural neuron 1 (MCN1). While intracellular stimulation of MCN1soma and MCN1SNAX has the same excitatory effects on the STG motor patterns, MCN1 receives distinct synaptic inputs in the STG and CoG. Moreover, the synaptic input that MCN1 receives within the STG compartmentalizes its activity. Specifically, the lateral gastric (LG) neuron synaptically inhibits MCN1SNAX-initiated activity within the STG (Nusbaum et al., 1992b), and while LG did not inhibit MCN1soma- initiated activity in the CoG, it did inhibit these MCN1 impulses when they arrived in the STG. As a result, during MCN1soma-elicited gastric mill rhythms, MCN1soma is continually active in the CoG but its effects are rhythmically inhibited in the STG by LG neuron impulse bursts. One functional consequence of this local control of MCN1 within the STG is that the LG neuron thereby controls the timing of the impulse bursts in other gastric mill neurons. Thus, local synaptic input can functionally compartmentalize the activity of a neuron with arbors in distinct regions of the nervous system

The Values Grounded Learning Environment: Developing a Positive School Culture and Student Success

The Values Grounded Learning Environment training provides educators with a comprehensive positive behavior management model, including basic strategies for effective limit setting and positive reinforcement. It is a user friendly model that can be implemented in a variety of educational settings and provides a framework for thoughtfully responding to student behaviors and emphasizing student and staff accountability

Scale invariance and viscosity of a two-dimensional Fermi gas

We investigate the collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed at a frequency two times the dipole mode frequency for a large range of interaction strengths and temperatures, and the amplitude of the breathing mode is undamped. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence

The joint US/UK 1990 epoch world magnetic model

A detailed summary of the data used, analyses performed, modeling techniques employed, and results obtained in the course of the 1990 Epoch World Magnetic Modeling effort are given. Also, use and limitations of the GEOMAG algorithm are presented. Charts and tables related to the 1990 World Magnetic Model (WMM-90) for the Earth's main field and secular variation in Mercator and polar stereographic projections are presented along with useful tables of several magnetic field components and their secular variation on a 5-degree worldwide grid

Towards a High Energy Theory for the Higgs Phase of Gravity

Spontaneous Lorentz violation due to a time-dependent expectation value for a massless scalar has been suggested as a method for dynamically generating dark energy. A natural candidate for the scalar is a Goldstone boson arising from the spontaneous breaking of a U(1) symmetry. We investigate the low-energy effective action for such a Goldstone boson in a general class of models involving only scalars, proving that if the scalars have standard kinetic terms then at the {\em classical} level the effective action does not have the required features for spontaneous Lorentz violation to occur asymptotically $(t \to \infty)$ in an expanding FRW universe. Then we study the large $N$ limit of a renormalizable field theory with a complex scalar coupled to massive fermions. In this model an effective action for the Goldstone boson with the properties required for spontaneous Lorentz violation can be generated. Although the model has shortcomings, we feel it represents progress towards finding a high energy completion for the Higgs phase of gravity.Comment: 20 pages, 5 figures;fixed typos and added reference

Uniqueness of a Negative Mode About a Bounce Solution

We consider the uniqueness problem of a negative eigenvalue in the spectrum of small fluctuations about a bounce solution in a multidimensional case. Our approach is based on the concept of conjugate points from Morse theory and is a natural generalization of the nodal theorem approach usually used in one dimensional case. We show that bounce solution has exactly one conjugate point at $\tau=0$ with multiplicity one.Comment: 4 pages,LaTe

Chabauty-Coleman experiments for genus 3 hyperelliptic curves

We describe a computation of rational points on genus 3 hyperelliptic curves $C$ defined over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to compute the zero locus of two Coleman integrals and analyze the finite set of points cut out by the vanishing of these integrals. We run the algorithm on approximately 17,000 curves from a forthcoming database of genus 3 hyperelliptic curves and discuss some interesting examples where the zero set includes global points not found in $C(\mathbb{Q})$.Comment: 18 page