3D Dune Skeleton Model as a Coupled Dynamical System of 2D Cross-Sections

To analyze theoretically the stability of the shape and the migration process of transverse dunes and barchans, we propose a {\it skeleton model} of 3D dunes described with coupled dynamics of 2D cross-sections. First, 2D cross-sections of a 3D dune parallel to the wind direction are extracted as elements of a skeleton of the 3D dune, hence, the dynamics of each and interaction between them is considered. This model simply describes the essential dynamics of 3D dunes as a system of coupled ordinary differential equations. Using the model we study the stability of the shape of 3D transversal dunes and their deformation to barchans depending on the amount of available sand in the dune field, sand flow in parallel and perpendicular to wind direction.Comment: 6 pages, 6 figures, lette

Coherent control of mesoscopic superpositions in a diatomic molecule

A phase controlled wave packet, recently used in experiment of wave packet interferometry of adiatomic molecule, is investigated to obtain mesoscopic superposition structures, useful in quantum metrology. This analysis provides a new way of obtaining sub-Planck scale structures at smaller time scale of revival dynamics. We study a number of situations for delineating the smallest interference structures and their control by tailoring the relative phase between two subsidiary wave packets. We also find the most appropriate state, so far, for high precision parameter estimation in a system of diatomic molecule.Comment: 9 pages, 3 figure

Development of laser guided deep-hole measurement system: adjustment to a smaller size hole

Deep holes are bored with the meter, millimeter, and micrometer level diameters in engineering. Examples of such holes with large 100-millimeter-level diameters and meter-level lengths are the rotation shafts of jet engines, generators and cannons. Holes with normal 10-millimeter-level diameters and lengths of several hundred millimeters are used for the main spindles of machines, the small cylinder in plastic injection molding, the tube sheet for heat exchanger, and guns. To measure such components the proposed measurement system consists of a measurement head in order to scan hole wall, a laser interferometer for measuring surface parameters of the hole and an optical device at the backside for detecting attitude of the measurement head. As a result of experimental analysis, it is observed that deephole having small diameter and longlength can be measured automatically by the new developed measurement system

Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test