On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed

Pieces of a Theory

A survey of theories of part, whole and dependence from Aristotle to the Gestalt psychologists, with special attention to Husserl’s Third Logical Investigation “On the Theory of Parts and Wholes”

Gauge Theories of Gravitation

During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincar\'e group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincar\'e gauge theory, encompasses Einstein's general relativity as well as the teleparallel theory of gravity as subcases. The spacetime structure is enriched by Cartan's torsion, and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions \`a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\'e gauge theory and its generalizations are explored and special topics, such as its Hamiltonian formulation and exact solutions, are studied. This guide to the literature on classical gauge theories of gravity is intended to be a stimulating introduction to the subject.Comment: 169 pages, pdf file, v3: extended to a guide to the literature on classical gauge theories of gravit

Development of Features for Recognition of Handwritten Odia Characters

In this thesis, we propose four different schemes for recognition of handwritten atomic Odia characters which includes forty seven alphabets and ten numerals. Odia is the mother tongue of the state of Odisha in the republic of India. Optical character recognition (OCR) for many languages is quite matured and OCR systems are already available in industry standard but, for the Odia language OCR is still a challenging task. Further, the features described for other languages can’t be directly utilized for Odia character recognition for both printed and handwritten text. Thus, the prime thrust has been made to propose features and utilize a classifier to derive a significant recognition accuracy. Due to the non-availability of a handwritten Odia database for validation of the proposed schemes, we have collected samples from individuals to generate a database of large size through a digital note maker. The database consists of a total samples of 17, 100 (150 × 2 × 57) collected from 150 individuals at two different times for 57 characters. This database has been named Odia handwritten character set version 1.0 (OHCS v1.0) and is made available in http://nitrkl.ac.in/Academic/Academic_Centers/Centre_For_Computer_Vision.aspx for the use of researchers. The first scheme divides the contour of each character into thirty segments. Taking the centroid of the character as base point, three primary features length, angle, and chord-to-arc-ratio are extracted from each segment. Thus, there are 30 feature values for each primary attribute and a total of 90 feature points. A back propagation neural network has been employed for the recognition and performance comparisons are made with competent schemes. The second contribution falls in the line of feature reduction of the primary features derived in the earlier contribution. A fuzzy inference system has been employed to generate an aggregated feature vector of size 30 from 90 feature points which represent the most significant features for each character. For recognition, a six-state hidden Markov model (HMM) is employed for each character and as a consequence we have fifty-seven ergodic HMMs with six-states each. An accuracy of 84.5% has been achieved on our dataset. The third contribution involves selection of evidence which are the most informative local shape contour features. A dedicated distance metric namely, far_count is used in computation of the information gain values for possible segments of different lengths that are extracted from whole shape contour of a character. The segment, with highest information gain value is treated as the evidence and mapped to the corresponding class. An evidence dictionary is developed out of these evidence from all classes of characters and is used for testing purpose. An overall testing accuracy rate of 88% is obtained. The final contribution deals with the development of a hybrid feature derived from discrete wavelet transform (DWT) and discrete cosine transform (DCT). Experimentally it has been observed that a 3-level DWT decomposition with 72 DCT coefficients from each high-frequency components as features gives a testing accuracy of 86% in a neural classifier. The suggested features are studied in isolation and extensive simulations has been carried out along with other existing schemes using the same data set. Further, to study generalization behavior of proposed schemes, they are applied on English and Bangla handwritten datasets. The performance parameters like recognition rate and misclassification rate are computed and compared. Further, as we progress from one contribution to the other, the proposed scheme is compared with the earlier proposed schemes

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 4: Maintenance document (version 3.0)

The Maintenance Document Version 3.0 is a guide to the PAN AIR software system, a system which computes the subsonic or supersonic linear potential flow about a body of nearly arbitrary shape, using a higher order panel method. The document describes the overall system and each program module of the system. Sufficient detail is given for program maintenance, updating, and modification. It is assumed that the reader is familiar with programming and CRAY computer systems. The PAN AIR system was written in FORTRAN 4 language except for a few CAL language subroutines which exist in the PAN AIR library. Structured programming techniques were used to provide code documentation and maintainability. The operating systems accommodated are COS 1.11, COS 1.12, COS 1.13, and COS 1.14 on the CRAY 1S, 1M, and X-MP computing systems. The system is comprised of a data base management system, a program library, an execution control module, and nine separate FORTRAN technical modules. Each module calculates part of the posed PAN AIR problem. The data base manager is used to communicate between modules and within modules. The technical modules must be run in a prescribed fashion for each PAN AIR problem. In order to ease the problem of supplying the many JCL cards required to execute the modules, a set of CRAY procedures (PAPROCS) was created to automatically supply most of the JCL cards. Most of this document has not changed for Version 3.0. It now, however, strictly applies only to PAN AIR version 3.0. The major changes are: (1) additional sections covering the new FDP module (which calculates streamlines and offbody points); (2) a complete rewrite of the section on the MAG module; and (3) strict applicability to CRAY computing systems