Trajectory Generation for Stair Ascent Walking using Rayleigh Oscillator

This paper describes a trajectory generation technique for stair-ascent walking. The knee, hip and ankle joint trajectory during stair ascent are generated using mutually coupled, nonlinear oscillators. The parameters of the oscillators are tuned using the harmonic balance method, which converts the nonlinear differential equations to a set of algebraic equations. Fourier analysis of data generated by stair-ascent walking is performed to extract the amplitude and the phase of the dominant frequency components for each joint trajectory. The solution for the oscillator is assumed to be a sinusoidal wave and then by harmonic balance method the parameters of the oscillator are found. Each oscillator is responsible for generating a single frequency component with a specific phase and amplitude. The complete trajectory is obtained by summing the output of the oscillators that are relevant to one joint and the coupling maintains the phase relationship between the oscillators

An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs. This integral representation is a suitable starting point for a detailed analysis of the long-time dynamics of scalar waves in the Kerr geometry.Comment: 41 pages, 4 figures, minor correction

Xenopus NM23-X4 regulates retinal gliogenesis through interaction with p27Xic1

Background. In Xenopus retinogenesis, p27Xic1, a Xenopus cyclin dependent kinase inhibitor, functions as a cell fate determinant in both gliogenesis and neurogenesis in a context dependent manner. This activity is essential for co-ordination of determination and cell cycle regulation. However, very little is known about the mechanism regulating the context dependent choice between gliogenesis versus neurogenesis. Results. We have identified NM23-X4, a NM23 family member, as a binding partner of p27Xic1. NM23-X4 is expressed at the periphery of the ciliary marginal zone of the Xenopus retina and the expression overlaps with p27Xic1 at the central side. Our in vivo functional analysis in Xenopus retina has shown that knockdown of NM23-X4 activates gliogenesis. Furthermore, co-overexpression of NM23-X4 with p27Xic1 results in the inhibition of p27Xic1-mediated gliogenesis, through direct interaction of NM23-X4 with the amino-terminal side of p27Xic1. This inhibitory effect on gliogenesis requires serine-150 and histidine-148, which correspond to the important residues for the kinase activities of NM23 family members. Conclusion. This study demonstrates that NM23-X4 functions as an inhibitor of p27Xic1-mediated gliogenesis in Xenopus retina and suggests that this activity contributes to the proper spatio-temporal regulation of gliogenesis

Hall plateaus at magic angles in bismuth beyond the quantum limit

We present a study of the angular dependence of the resistivity tensor up to 35 T in elemental bismuth complemented by torque magnetometry measurements in a similar configuration. For at least two particular field orientations a few degrees off the trigonal axis, the Hall resistivity was found to become field-independent within experimental resolution in a finite field window corresponding to a field which is roughly three times the frequency of quantum oscillations. The Hall plateaus rapidly vanish as the field is tilted off theses magic angles. We identify two distinct particularities of these specific orientations, which may play a role in the emergence of the Hall plateaus.Comment: 5 pages, 5 figure

Error bound analysis of the stochastic parareal algorithm

Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a predictor-corrector (PC) scheme. The key difference is that carefully chosen random perturbations are added to the PC to try to accelerate the location of a stochastic solution to the ODE. In this paper, we derive superlinear and linear mean-square error bounds for SParareal applied to nonlinear systems of ODEs using different types of perturbations. We illustrate these bounds numerically on a linear system of ODEs and a scalar nonlinear ODE, showing a good match between theory and numerics

Retained stones in the common bile duct: results of management

Seventeen patients underwent treatment for retained common bile duct stones. In 7 patients the stones were removed via a T-tube tract using steerable catheters while 5 patients underwent ERCP and sphincterotomy and 5 underwent surgical re-exploration. Considering morbidity, mortality, success rate and patients\u27 stay in the hospital, non-operative modalities should be the treatment of choice for retained common bile duct stones

Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences

The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the classical transformations in the scalar case. It is demonstrated that Laplace transformations can be pulled back to the transformations of the corresponding hydrodynamic type systems. We discuss periodic Laplace sequences of with the emphasize on the simplest nontrivial case of period 2. For 3-component systems in Riemann invariants a complete discription of closed quadruples is proposed. They turn to be related to a special quadratic reduction of the (2+1)-dimensional 3-wave system which can be reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of the Lame and rotation coefficients Laplace transformations have a natural interpretation as the symmetries of the Dirac operator, associated with the (2+1)-dimensional n-wave system. The 2-component Laplace transformations can be interpreted also as the symmetries of the (2+1)-dimensional integrable equations of Davey-Stewartson type. Laplace transformations of hydrodynamic type systems originate from a canonical geometric correspondence between systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late

Analysis of metallurgical aspects and their role in processing and performance of superalloys: A review

Metallurgical processing factors like kinetic and thermodynamic parameters which are essential for modeling of γ′ phase precipitation have been studied. These parameters include γ′ solvus temperature, Gibbs free energy of dissociation of the γ matrix to form γ′, nucleation rate, effective diffusivity and interfacial energy. Nucleation methods and effect of cooling rate on the final phase structure have been analyzed. Co based  superalloys have been studied as a potential and promising material for aerospace applications. Effect of microporosity on the mechanical properties of Superalloys has also been analyzed.Keywords: Superalloys, Precipitation, Solidification, Gamma prime, Microsegregation, Microporosity

Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations

It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented.Comment: 4 pages, conference proceeding of Spanish Relativity Meeting (ERE 2009, Bilbao