Near-wall reconstruction of higher order moments and length scales using the POD

An analysis of the near-wall behavior of the proper orthogonal decomposition (POD) eigenfunctions derived from direct numerical simulation (DNS) of channel flow is performed. Consistent with previous studies, a low order multi-mode reconstruction of the kinetic energy and Reynolds shear stress suffices. A similar reconstruction of the isotropic dissipation rate is shown to be insufficient, however. An analysis is performed of the multi-mode composition of the dissipation rate in the near-wall region, and it is shown that a significant number of higher-order modes are required to achieve the correct asymptotic consistency in the near-wall region. In an attempt to avoid this problem, a length scale definition is proposed in terms of an integration of the correlation tensor which factors in the presence of the wall. The wall is accounted for by only integrating out to 2y(+) and not over the entire domain. Viscous and inviscid estimates for the dissipation were used in the near-wall and core regions respectively, in conjunction with this length scale representation to obtain an estimate of the dissipation throughout the domain. The resulting dissipation exhibits the proper behavior near the wall and in the inertial layer. A 1 POD mode estimate of the length scale is computed and found to agree quite well with the length scale obtained when the entire correlation tensor is used

A nilpotent group without local functional equations for pro-isomorphic subgroups

The pro-isomorphic zeta function of a torsion-free finitely generated nilpotent group G enumerates finite index subgroups H such that H and G have isomorphic profinite completions. It admits an Euler product decomposition, indexed by the rational primes. We manufacture the first example of a torsion-free finitely generated nilpotent group G such that the local Euler factors of its pro-isomorphic zeta function do not satisfy functional equations. The group G has nilpotency class 4 and Hirsch length 25. It is obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable algebraic automorphism group Aut(L).Comment: 16 page

Green's functions for multiply connected domains via conformal mapping

A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz-Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K-1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations

A generalization of the Kostka-Foulkes polynomials

Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases. Conjecturally these polynomials coincide with the Poincare polynomials of isotypic components of certain graded GL(n)-modules supported in a nilpotent conjugacy class closure in gl(n).Comment: 37 page

Shuttle tethered operations: The effect on orbital trajectory and inertial navigation

The first full scale test of a large tethered satellite system is planned. The Orbiter will be linked to a 500 kg payload by a 20 km tether, an action with a profound effect on the trajectory of the Orbiter. For the first time in the history of the Shuttle program, the vehicle will conduct prolonged operations with the center of mass of the orbiting system a significant distance from the center of mass of the Space Shuttle Orbiter, a violation of the fundamental assumption made in both the Orbiter ground-based and onboard navigation software. Inertial navigation of tethered operations with the Shuttle is further complicated by the presence of non-conservative forces in the system: Reaction Control System (RCS) translational effects, atmospheric drag, and electro-magnetic dynamics. These can couple with the conservative tether dynamics effects, and degrade the navigation software performance. The primary effects are examined on the Orbiter's trajectory, coupling by conservative forces during tethered operations, and the impact of both on the ability to meet inertial navigation constraints. The impact of electrodynamics, different RCS control modes, commanded attitudes, and attitude deadbands are presented. Operational guidelines which optimize successful mission navigation, and necessary navigation constraints are discussed

Analysis of error propagation in particle filters with approximation

This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense $L_p$ error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node particle filter and present numerical experiments exploring its performance and the relationship to the error bounds.Comment: Published in at http://dx.doi.org/10.1214/11-AAP760 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On gait as a biometric: progress and prospects

There is increasing interest in automatic recognition by gait given its unique capability to recognize people at a distance when other biometrics are obscured. Application domains are those of any noninvasive biometric, but with particular advantage in surveillance scenarios. Its recognition capability is supported by studies in other domains such as medicine (biomechanics), mathematics and psychology which also suggest that gait is unique. Further, examples of recognition by gait can be found in literature, with early reference by Shakespeare concerning recognition by the way people walk. Many of the current approaches confirm the early results that suggested gait could be used for identification, and now on much larger databases. This has been especially influenced by DARPA’s Human ID at a Distance research program with its wide scenario of data and approaches. Gait has benefited from the developments in other biometrics and has led to new insight particularly in view of covariates. Equally, gait-recognition approaches concern extraction and description of moving articulated shapes and this has wider implications than just in biometrics

The way we walk

Mark Nixon and John Carter reveal how developments in biometrics could mean the increasing use of biometric evidence such ear shape and gait to identify defendants