Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Ant Colony Optimization Algorithms for Shortest Path Problems

We propose four variants of recently proposed multi-timescale algorithm in [1] for ant colony optimization and study their application on a multi-stage shortest path problem. We study the performance of the various algorithms in this framework. We observe, that one of the variants consistently outperforms the algorithm [1].

Problems of Proto-Slavic Historical Nominal Morphology : On the Basis of Old Church Slavic

In this study I offer a diachronic solution for a number of difficult inflectional endings in Old Church Slavic nominal declensions. In this context I address the perhaps most disputed and the most important question of the Slavic nominal inflectional morphology: whether there was in Proto-Slavic an Auslautgesetz (ALG), a law of final syllables, that narrowed the Proto-Indo-European vowel */o/ to */u/ in closed word-final syllables. In addition, the work contains an exhaustive morphological classification of the nouns and adjectives that occur in canonical Old Church Slavic. I argue that Proto-Indo-European */o/ became Proto-Slavic */u/ before word-final */s/ and */N/. This conclusion is based on the impossibility of finding credible analogical (as opposed to phonological) explanations for the forms supporting the ALG hypothesis, and on the survival of the neuter gender in Slavic. It is not likely that the */o/-stem nominative singular ending */-u/ was borrowed from the accusative singular, because the latter would have been the only paradigmatic form with the stem vowel */-u-/. It is equally unlikely that the ending */-u/ was borrowed from the */u/-stems, because the latter constituted a moribund class. The usually stated motivation for such an analogical borrowing, i.e. a need to prevent the merger of */o/-stem masculines with neuters of the same class, is not tenable. Extra-Slavic, as well as intra-Slavic evidence suggests that phonologically-triggered mergers between two semantically opaque genders do not tend to be prevented, but rather that such mergers lead to the loss of the gender opposition in question. On the other hand, if */-os/ had not become */-us/, most nouns and, most importantly, all adjectives and pronouns would have lost the formal distinction between masculines and neuters. This would have necessarily resulted in the loss of the neuter gender. A new explanation is given for the most apparent piece of evidence against the ALG hypothesis, the nominative-accusative singular of the */es/-stem neuters, e.g. nebo 'sky'. I argue that it arose in late Proto-Slavic dialects, replacing regular nebe, under the influence of the */o/- and */yo/-stems where a correlation had emerged between a hard root-final consonant and the termination -o, on the one hand, and a soft root-final consonant and the termination -e, on the other.

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiff ened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.

Temperature characteristics of the billet and the dies in a small batch forging production

The work reported herein is part of an on-going programme to develop a computer code which, given the geometrical, process and material parameters of the forging operation, is able to predict the die and the billet cooling/heating characteristics in forging production. The code has been experimentally validated earlier for a single forging cycle and is now validated for a small batch production. To facilitate a step-by-step development of the code, the billet deformation has so far been limited to its surface layers, a situation akin to coining. The code has been used here to study the effects of die preheat-temperature, machine speed and rate of deformation the cooling/heating of the billet and the dies over a small batch of 150 forgings. The study shows: that there is a pre-heat temperature at which the billet temperature changes little from one forging to the next; that beyond a particular number of forgings, the machine speed ceases to have any pronounced influence on the temperature characteristics of the billet; and that increasing the rate of deformation reduces the heat loss from the billet and gives the billet a stable temperature profile with respect to the number of forgings. The code, which is simple to use, is being extended to bulk-deformation problems. Given a practical range of possible machine, billet and process specifics, the code should be able to arrive at a combination of these parameters which will give the best thermal characteristics of the die-billet system. The code is also envisaged as being useful in the design of isothermal dies and processes.

Impedance tube technology for flow acoustics

Acoustic impedance of a termination, or of a passive subsystem, needs to be measured not only for acoustic lining materials but also in the exhaust systems of flow machinery, where mean flow introduces peculiar problems. Out of the various methods of measurement of acoustic impedance, the discrete frequency, steady state, impedance tube method [1] is most reliable, though time consuming, and requires no special instrumentation.

Public Open Spaces in Kathmandu Valley: A Review of Contemporary Problems and Historic Precedents

The current growth of Kathmandu Valley has been malignant in many ways which suggests a decline of public realm in the city. As the current efforts for planning and design of public open space exhibit numerous problems related to both physical and social aspects of city building, this book examines the shortcomings with contemporary urban development from urban planning and design point of view and attempts to suggest methods to overcome such shortcomings based on the study of historic urban squares. This book identifies the inherent urban design qualities of the historic urban squares in order to learn from them and also attempts to put forward the principles and guidelines for contemporary public space design based on such findings.

Hybrid game strategies for MO problems in aerospace design

Game strategies have been developed in past decades and used in the field of economics, engineering, computer science and biology due to their efficiency in solving design optimisation problems. In addition, research on Multi-Objective (MO) and Multidisciplinary Design Optimisation (MDO) has focused on developing robust and efficient optimisation method to produce quality solutions with less computational time. In this paper, a new optimisation method Hybrid Game Strategy for MO problems is introduced and compared to CMA-ES based optimisation approach. Numerical results obtained from both optimisation methods are compared in terms of computational expense and model quality. The benefits of using Game-strategies are demonstrated.

A large orthotropic plate with misfit pin under arbitrarily oriented biaxial loading

The problem of misfit (interference or clearance) pin in a large orthotropic plate was solved earlier by the authors for biaxial loading in the principal directions of orthotropy. Here, a more general case of arbitrarily oriented loading is considered. The most important aspect of the problem studied is the partial contact at the pin-hole interface. The solution is obtained by extending the use of ‘inverse technique’ which was successfully applied earlier by the authors to problems of pins in isotropic and orthotropic domains. The loss of symmetry because of the arbitrary orientation of loading makes the problem more complex. Additional parameters are then involved in the inversion of the problem for the solution. Numerical results are presented primarily for a smooth interference fit pin in a typical orthotropic plate.

Algebraic design techniques for reliable stabilization

In this paper we study two problems in feedback stabilization. The first is the simultaneous stabilization problem, which can be stated as follows. Given plantsG_{0}, G_{1},..., G_{l}, does there exist a single compensatorCthat stabilizes all of them? The second is that of stabilization by a stable compensator, or more generally, a "least unstable" compensator. Given a plantG, we would like to know whether or not there exists a stable compensatorCthat stabilizesG; if not, what is the smallest number of right half-place poles (counted according to their McMillan degree) that any stabilizing compensator must have? We show that the two problems are equivalent in the following sense. The problem of simultaneously stabilizingl + 1plants can be reduced to the problem of simultaneously stabilizinglplants using a stable compensator, which in turn can be stated as the following purely algebraic problem. Given2lmatricesA_{1}, ..., A_{l}, B_{1}, ..., B_{l}, whereA_{i}, B_{i}are right-coprime for alli, does there exist a matrixMsuch thatA_{i} + MB_{i}, is unimodular for alli?Conversely, the problem of simultaneously stabilizinglplants using a stable compensator can be formulated as one of simultaneously stabilizingl + 1plants. The problem of determining whether or not there exists anMsuch thatA + BMis unimodular, given a right-coprime pair (A, B), turns out to be a special case of a question concerning a matrix division algorithm in a proper Euclidean domain. We give an answer to this question, and we believe this result might be of some independent interest. We show that, given twon times mplantsG_{0} and G_{1}we can generically stabilize them simultaneously provided eithernormis greater than one. In contrast, simultaneous stabilizability, of two single-input-single-output plants, g0and g1, is not generic.

Development of special fastener elements

A special finite element (FASNEL) is developed for the analysis of a neat or misfit fastener in a two-dimensional metallic/composite (orthotropic) plate subjected to biaxial loading. The misfit fasteners could be of interference or clearance type. These fasteners, which are common in engineering structures, cause stress concentrations and are potential sources of failure. Such cases of stress concentration present considerable numerical problems for analysis with conventional finite elements. In FASNEL the shape functions for displacements are derived from series stress function solutions satisfying the governing difffferential equation of the plate and some of the boundary conditions on the hole boundary. The region of the plate outside FASNEL is filled with CST or quadrilateral elements. When a plate with a fastener is gradually loaded the fastener-plate interface exhibits a state of partial contact/separation above a certain load level. In misfit fastener, the extent of contact/separation changes with applied load, leading to a nonlinear moving boundary problem and this is handled by FASNEL using an inverse formulation. The analysis is developed at present for a filled hole in a finite elastic plate providing two axes of symmetry. Numerical studies are conducted on a smooth rigid fastener in a finite elastic plate subjected to uniaxial loading to demonstrate the capability of FASNEL.

Problems Connected with the Rhombus

Abstract is not available.

Visual search and eye movements: Studies of perceptual span

In visual search one tries to find the currently relevant item among other, irrelevant items. In the present study, visual search performance for complex objects (characters, faces, computer icons and words) was investigated, and the contribution of different stimulus properties, such as luminance contrast between characters and background, set size, stimulus size, colour contrast, spatial frequency, and stimulus layout were investigated. Subjects were required to search for a target object among distracter objects in two-dimensional stimulus arrays. The outcome measure was threshold search time, that is, the presentation duration of the stimulus array required by the subject to find the target with a certain probability. It reflects the time used for visual processing separated from the time used for decision making and manual reactions. The duration of stimulus presentation was controlled by an adaptive staircase method. The number and duration of eye fixations, saccade amplitude, and perceptual span, i.e., the number of items that can be processed during a single fixation, were measured. It was found that search performance was correlated with the number of fixations needed to find the target. Search time and the number of fixations increased with increasing stimulus set size. On the other hand, several complex objects could be processed during a single fixation, i.e., within the perceptual span. Search time and the number of fixations depended on object type as well as luminance contrast. The size of the perceptual span was smaller for more complex objects, and decreased with decreasing luminance contrast within object type, especially for very low contrasts. In addition, the size and shape of perceptual span explained the changes in search performance for different stimulus layouts in word search. Perceptual span was scale invariant for a 16-fold range of stimulus sizes, i.e., the number of items processed during a single fixation was independent of retinal stimulus size or viewing distance. It is suggested that saccadic visual search consists of both serial (eye movements) and parallel (processing within perceptual span) components, and that the size of the perceptual span may explain the effectiveness of saccadic search in different stimulus conditions. Further, low-level visual factors, such as the anatomical structure of the retina, peripheral stimulus visibility and resolution requirements for the identification of different object types are proposed to constrain the size of the perceptual span, and thus, limit visual search performance. Similar methods were used in a clinical study to characterise the visual search performance and eye movements of neurological patients with chronic solvent-induced encephalopathy (CSE). In addition, the data about the effects of different stimulus properties on visual search in normal subjects were presented as simple practical guidelines, so that the limits of human visual perception could be taken into account in the design of user interfaces.

Development and Simulation of a Variable Rate Controller for an Air search and Air Sampling Unmanned Aerial System

This report describes the development and simulation of a variable rate controller for a 6-degree of freedom nonlinear model. The variable rate simulation model represents an off the shelf autopilot. Flight experiment involves risks and can be expensive. Therefore a dynamic model to understand the performance characteristics of the UAS in mission simulation before actual flight test or to obtain parameters needed for the flight is important. The control and guidance is implemented in Simulink. The report tests the use of the model for air search and air sampling path planning. A GUI in which a set of mission scenarios, in which two experts (mission expert, i.e. air sampling or air search and an UAV expert) interact, is presented showing the benefits of the method.

Griggs' Folly: An Essay on the Theory, Problems, and Origin of the Adverse Impact Definition of Employment Discrimination and a Recommendation for Reform

This Article examines the adverse impact theory of employment discrimination under Title VII. The author begins by discussing the development of adverse impact in the case law, and by scrutinizing its theoretical underpinnings. He demonstrates that Congress did not intend to mandate adoption of adverse impact theory when it established Title VII. The author then argues that the Courts have exceeded their authority under Title VII by embracing the theory of adverse impact. He concludes that the courts should therefore return to a narrower theory of employment discrimination, namely, a theory based on the legal concept of “intent.”