EVEN in Aristotle’s day, there were some problems about the status of the "mixed sciences," mechanics, optics, astronomy, harmonics. They were mathematical in form, and depended on generalizations drawn from repeated and careful observation. In both respects they differed from "physics," as Aristotle saw it; he made them "the most physical part of mathematics," and thus inaugurated a long two-t...

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the ...

The Coherent Gradient Sensor (CGS) is extended to the optical differentiation of specular, diffracted wave fronts leading to the combined measurement of inand outof-plane displacement field gradients. A derivation of the underlying optical interference principles is presented along with an analysis of the effective instrument sensitivity. In order to demonstrate the capabilities of the techniqu...

Recently, based on a supersymmetric approach, new classes of conditionally exactly solvable problems have been found, which exhibit a symmetry structure characterized by non-linear algebras. In this paper the associated “nonlinear” coherent states are constructed and some of their properties are discussed in detail. PACS numbers: 03.65.Fd, 02.20.Qs, 42.50.-p

Coherent motions, which describe the collective movements of individuals in crowd, widely exist in physical and biological systems. Understanding their underlying priors and detecting various coherent motion patterns from background clutters have both scientific values and a wide range of practical applications, especially for crowd motion analysis. In this paper, we propose and study a prior o...

The original canonical coherent states could be defined in several ways. As applications for other sets of coherent states arose, the rules of definition were correspondingly changed. Among such rule changes were a change of group and relaxation of the analytic nature of the labels. Recent developments have done away with the group connections altogether and thereby allowed sets of coherent sta...

This paper takes a look at the visualization side of vector field analysis based on Lagrangian coherent structures. The Lagrangian coherent structures are extracted as height ridges of finite-time Lyapunov exponent fields. The resulting visualizations are compared to those from traditional instantaneous vector field topology of steady and unsteady vector fields. The examination is applied to th...

1 Introduction Coherent optical techniques contrast with those based on incoherent processes such as laser induced fluorescence or spontaneous Raman scattering by emitting a signal in a laser-like beam of radiation. For combustion diagnostics this presents obvious advantages for efficient collection of the signal and discrimination against background noise from scattered light or luminescence f...

Using spatial models as a shared common basis of information about the environment for different kinds of contextaware systems has been a heavily researched topic in the last years. Thereby the research focused on how to create, to update, and to merge spatial models so as to enable highly dynamic, consistent and coherent spatial models at large scale. In this paper however, we want to concentr...