Reduction, Symmetry and Phases in Mechanics

Various holonomy phenomena are shown to be instances of the reconstruction procedure for mechanical systems with symmetry. We systematically exploit this point of view for fixed systems (for example with controls on the internal, or reduced, variables) and for slowly moving systems in an adiabatic context. For the latter, we obtain the phases as the holonomy for a connection which synthesizes the Cartan connection for moving mechanical systems with the Hannay-Berry connection for integrable systems. This synthesis allows one to treat in a natural way examples like the ball in the slowly rotating hoop and also non-integrable mechanical systems

Spontaneous creation of non-zero angular momentum modes in tunnel-coupled two-dimensional degenerate Bose gases

We investigate the dynamics of two tunnel-coupled two-dimensional degenerate Bose gases. The reduced dimensionality of the clouds enables us to excite specific angular momentum modes by tuning the coupling strength, thereby creating striking patterns in the atom density profile. The extreme sensitivity of the system to the coupling and initial phase difference results in a rich variety of subsequent dynamics, including vortex production, complex oscillations in relative atom number and chiral symmetry breaking due to counter-rotation of the two clouds.Comment: 7 pages, 5 figure

Important factors in the maximum likelihood analysis of flight test maneuvers

The information presented is based on the experience in the past 12 years at the NASA Dryden Flight Research Center of estimating stability and control derivatives from over 3500 maneuvers from 32 aircraft. The overall approach to the analysis of dynamic flight test data is outlined. General requirements for data and instrumentation are discussed and several examples of the types of problems that may be encountered are presented

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

Design of experiments for non-manufacturing processes : benefits, challenges and some examples

Design of Experiments (DoE) is a powerful technique for process optimization that has been widely deployed in almost all types of manufacturing processes and is used extensively in product and process design and development. There have not been as many efforts to apply powerful quality improvement techniques such as DoE to improve non-manufacturing processes. Factor levels often involve changing the way people work and so have to be handled carefully. It is even more important to get everyone working as a team. This paper explores the benefits and challenges in the application of DoE in non-manufacturing contexts. The viewpoints regarding the benefits and challenges of DoE in the non-manufacturing arena are gathered from a number of leading academics and practitioners in the field. The paper also makes an attempt to demystify the fact that DoE is not just applicable to manufacturing industries; rather it is equally applicable to non-manufacturing processes within manufacturing companies. The last part of the paper illustrates some case examples showing the power of the technique in non-manufacturing environments

Viscous, resistive MHD stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow

Clarification on the generation of absolute and potential vorticity in mesoscale convective vortices

Atmos. Chem. Phys., 9, 7591-760

Effective buoyancy and CAPE: Some implications for tropical cyclones

We review the widely used concepts of buoyancy and convective available potential energy (CAPE) in relation to deep convection in tropical cyclones and discuss their limitations. A fact easily forgotten in applying these concepts is that the buoyancy force of an air parcel, as often defined, is non-unique because it depends on the arbitrary definition of a reference density field. However, when calculating CAPE, the buoyancy of a lifted air parcel is related to the specific reference density field along a vertical column passing through that parcel. Both concepts can be generalized for a vortical flow and to slantwise ascent of a lifted air parcel in such a flow. In all cases, the air parcel is assumed to have infinitely small dimensions. In this article, we explore the consequences of generalizing buoyancy and CAPE for buoyant regions of finite size that perturb the pressure field in their immediate environment. Quantitative calculations of effective buoyancy, defined as the sum of the conventional buoyancy and the static vertical perturbation pressure gradient force induced by it, are shown for buoyant regions of finite width. For a judicious choice of reference density, the effective buoyancy per unit mass is essentially a unique force, independent of the reference density, but its distribution depends on the horizontal scale of the buoyant region. A corresponding concept of effective CAPE is introduced and its relevance to deep convection in tropical cyclones is discussed. The study is conceived as a first step to understanding the decreasing ability of inner-core deep convection in tropical cyclones to ventilate the mass of air converging in the frictional boundary layer as the vortex matures and decays

The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem

This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noether theorem in terms of our formalism, and we give applications to Riemannian submanifolds, to Lagrangians of mechanical type, and to the determination of quadratic first integrals.Comment: 25 page

Stability and control derivative estimates obtained from flight data for the Beech 99 aircraft

Lateral-directional and longitudinal stability and control derivatives were determined from flight data by using a maximum likelihood estimator for the Beech 99 airplane. Data were obtained with the aircraft in the cruise configuration and with one-third flap deflection. The estimated derivatives show good agreement with the predictions of the manufacturer