Adaptive control and noise suppression by a variable-gain gradient algorithm

An adaptive control system based on normalized LMS filters is investigated. The finite impulse response of the nonparametric controller is adaptively estimated using a given reference model. Specifically, the following issues are addressed: The stability of the closed loop system is analyzed and heuristically established. Next, the adaptation process is studied for piecewise constant plant parameters. It is shown that by introducing a variable-gain in the gradient algorithm, a substantial reduction in the LMS adaptation rate can be achieved. Finally, process noise at the plant output generally causes a biased estimate of the controller. By introducing a noise suppression scheme, this bias can be substantially reduced and the response of the adapted system becomes very close to that of the reference model. Extensive computer simulations validate these and demonstrate assertions that the system can rapidly adapt to random jumps in plant parameters

Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature

This investigation extends earlier studies of a shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. My main purpose here is to explore the possibility that the configurational degrees of freedom of such systems fall out of thermodynamic equilibrium with the heat bath during persistent mechanical deformation, and that the resulting state of configurational disorder may be characterized by an effective temperature. The further assumption that the population of STZ's equilibrates with the effective temperature allows the theory to be compared directly with experimentally measured properties of metallic glasses, including their calorimetric behavior. The coupling between the effective temperature and mechanical deformation suggests an explanation of shear-banding instabilities.Comment: 29 pages, 11 figure

Glassy dynamics in granular compaction

Two models are presented to study the influence of slow dynamics on granular compaction. It is found in both cases that high values of packing fraction are achieved only by the slow relaxation of cooperative structures. Ongoing work to study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter, proceedings of the Trieste workshop on 'Unifying concepts in glass physics

Performance characteristics of an adaptive controller based on least-mean-square filters

A closed loop, adaptive control scheme that uses a least mean square filter as the controller model is presented, along with simulation results that demonstrate the excellent robustness of this scheme. It is shown that the scheme adapts very well to unknown plants, even those that are marginally stable, responds appropriately to changes in plant parameters, and is not unduly affected by additive noise. A heuristic argument for the conditions necessary for convergence is presented. Potential applications and extensions of the scheme are also discussed

Density-functional theory for fermions in the unitary regime

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the free Fermi gas with a proportionality constant $\xi$. We use a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employ Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi=0.42$ and a rather large effective mass. Our approach is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.Comment: 5 pages, 2 figure

Competition and cooperation:aspects of dynamics in sandpiles

In this article, we review some of our approaches to granular dynamics, now well known to consist of both fast and slow relaxational processes. In the first case, grains typically compete with each other, while in the second, they cooperate. A typical result of {\it cooperation} is the formation of stable bridges, signatures of spatiotemporal inhomogeneities; we review their geometrical characteristics and compare theoretical results with those of independent simulations. {\it Cooperative} excitations due to local density fluctuations are also responsible for relaxation at the angle of repose; the {\it competition} between these fluctuations and external driving forces, can, on the other hand, result in a (rare) collapse of the sandpile to the horizontal. Both these features are present in a theory reviewed here. An arena where the effects of cooperation versus competition are felt most keenly is granular compaction; we review here a random graph model, where three-spin interactions are used to model compaction under tapping. The compaction curve shows distinct regions where 'fast' and 'slow' dynamics apply, separated by what we have called the {\it single-particle relaxation threshold}. In the final section of this paper, we explore the effect of shape -- jagged vs. regular -- on the compaction of packings near their jamming limit. One of our major results is an entropic landscape that, while microscopically rough, manifests {\it Edwards' flatness} at a macroscopic level. Another major result is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction

Analysis of the separated boundary layer flow on the surface and in the wake of blunt trailing edge airfoils

The viscous flow phenomena associated with sharp and blunt trailing edge airfoils were investigated. Experimental measurements were obtained for a 17 percent thick, high performance GAW-1 airfoil. Experimental measurements consist of velocity and static pressure profiles which were obtained by the use of forward and reverse total pressure probes and disc type static pressure probes over the surface and in the wake of sharp and blunt trailing edge airfoils. Measurements of the upper surface boundary layer were obtained in both the attached and separated flow regions. In addition, static pressure data were acquired, and skin friction on the airfoil upper surface was measured with a specially constructed device. Comparison of the viscous flow data with data previously obtained elsewhere indicates reasonable agreement in the attached flow region. In the separated flow region, considerable differences exist between these two sets of measurements

Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment

We present and analyse in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the `bare' interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the `bare' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.Comment: 17 pages and 26 figures. Submitted to Physical Review

Probability density of determinants of random matrices

In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the matrices