Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

Analysis of Rectangular Folded-Waveguide Millimeter-Wave Slow-wave Structures using Conformal Transformations

An analysis of rectangular folded-waveguide slow-wave structure was developed using conformal mapping technique through Schwarz's polygon transformation and closed form expressions for the lumped capacitance and inductance per period of the slow-wave structure were derived in terms of the physical dimensions of the structure, incorporating the effects of the beam hole in the lumped parameters. The lumped parameters were subsequently interpreted for obtaining the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures, one operating in Ka-band and the other operating in Q-band, against measurement and 3D electromagnetic modeling using MAFIA.

Stresses around reinforced curvilinear holes in spherical shells

A perturbation technique is used to determine the stress concentration around reinforced curvilinear holes in thin pressurized spherical shells. Starting from the governing differential equations for thin shallow spherical shells, a solution is first obtained for a circular hole. The solution for an arbitrary shaped curvilinear hole is then obtained as a first-order perturbation over the circular hole solution using the conformal mapping technique. The effects of a large number of parameters involved in the design of a reinforcement around cutouts in shells are studied. The problems of symmetric and eccentric reinforcements are also considered. The results obtained would be very helpful in the design of an efficient reinforcement for elliptical and square holes in thin shallow spherical shells.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

A simple method for potential flow simulation of cascades

A simple method using a combination of conformal mapping and vortex panel method to simulate potential flow in cascades is presented. The cascade is first transformed to a single body using a conformal mapping, and the potential flow over this body is solved using a simple higher order vortex panel method. The advantage of this method over existing methodologies is that it enables the use of higher order panel methods, as are used to solve flow past an isolated airfoil, to solve the cascade problem without the need for any numerical integrations or iterations. The fluid loading on the blades, such as the normal force and pitching moment, may be easily calculated from the resultant velocity field. The coefficient of pressure on cascade blades calculated with this methodology shows good agreement with previous numerical and experimental results.

Analysis of multi-conductor coupled microstrip lines with an aperture in the ground plane for the design of a broadband filter

Closed-form expressions for the propagation characteristics of coupled microstrip lines with a symmetrical aperture in the ground plane are derived. Expressions for the regular microstrip coupled lines have been modified using physical insights to incorporate the effect of the aperture. The accuracy of these expressions has been verified by full-wave simulations and compared with conformal mapping analysis. These expressions are accurate within 5% for a substrate whose thickness varies from 0.2 to 1.6mm and permittivity in the range of 210. Designing a broadband filter based on planar multi-conductor coupled lines with aperture in the ground plane is demonstrated in this paper using the proposed expressions for its practical use.

Analysis of modified microstrip line and its application

Analysis of a microstrip line with a symmetrically located aperture in its ground plane is reported in this paper. The solution is based on conformal mapping technique. Conformal mapping has been used to determine the characteristic impedance and effective permittivity of the line. The accuracy of results is within 5% error. An low pass filter has been designed based on the electrical parameters obtained using the proposed method.

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

Immunochemical approach to the mapping of an assembled epitope of human chorionic gonadotropin: Proximity of CTP-alpha to the receptor binding region of the beta-subunit

A single-step solid-phase RIA (SS-SPRIA) developed in our laboratory using hybridoma culture supernatants has been utilised for the quantitation of epitope-paratope interactions. Using SS-SPRIA as a quantitative tool for the assessment of epitope stability, it was found that several assembled epitopes of human chorionic gonadotropin (hCG) are differentially stable to proteolysis and chemical modification. Based on these observations an approach has been developed for identifying the amino acid residues constituting an epitopic region. This approach has now been used to map an assembled epitope at/near the receptor binding region of the hormone. The mapped site forms a part of the seat belt region and the cystine knot region (C34-C38-C88-C90-H106). The carboxy terminal region of the alpha-subunit forms a part of the epitope indicating its proximity to the receptor binding region. These results are in agreement with the reported receptor binding region identified through other approaches and the X-ray crystal structure of hCG.

Defect-selective photothermal imaging: a sensitive tool for damage mapping in optical coatings

A defect-selective photothermal imaging system for the diagnostics of optical coatings is demonstrated. The instrument has been optimized for pump and probe parameters, detector performance, and signal processing algorithm. The imager is capable of mapping purely optical or thermal defects efficiently in coatings of low damage threshold and low absorbance. Detailed mapping of minor inhomogeneities at low pump power has been achieved through the simultaneous action of a low-noise fiber optic photothermal beam defection sensor and a common-mode-rejection demodulation (CMRD) technique. The linearity and sensitivity of the sensor have been examined theoretically and experimentally, and the signal to noise ratio improvement factor is found to be about 110 compared to a conventional bicell photodiode. The scanner is so designed that mapping of static or shock sensitive samples is possible. In the case of a sample with absolute absorptance of 3.8 x 10(-4), a change in absorptance of about 0.005 x 10(-4) has been detected without ambiguity, ensuring a contrast parameter of 760. This is about 1085% improvement over the conventional approach containing a bicell photodiode, at the same pump power. The merits of the system have been demonstrated by mapping two intentionally created damage sites in a MgF2 coating on fused silica at different excitation powers. Amplitude and phase maps were recorded for thermally thin and thick cases, and the results are compared to demonstrate a case which, in conventional imaging, would lead to a deceptive conclusion regarding the type and location of the damage. Also, a residual damage profile created by long term irradiation with high pump power density has been depicted.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Isolation, characterization and mapping of temperature-sensitive mutants of mycobacteriophage I3

Eighteen temperature-sensitive mutants of mycobacteriophage I3 have been isolated and partially characterized. All the mutants were defective in vegetative replication. Based on temperature shift experiments with the temperature sensitive mutants, the thermosensitive phase of the phage development period has been characterized for each mutant. The genes have been mapped by recombination analysis. The early, continuous and middle genes seem to cluster on the genetic map

Liquefaction Hazard Mapping of Bangalore, South India

his paper presents identification and mapping of vulnerable and safe zones for liquefaction hazard. About 850 bore logs data collected from geotechnical investigation reports have been used to estimate the liquefaction factor of safety for Bangalore Mahanagara palike (BMP) area of about 220 km(2). Liquefaction factor of safety is arrived based on surface level peak ground acceleration presented by Anbazhagan and Sitharam(5) and liquefaction resistance, using corrected standard penetration test (SPT) N values. The estimated factor of safety against liquefaction is used to estimate liquefaction potential index and liquefaction severity index. These values are mapped using Geographical information system (GIS) to identify the vulnerable and safe zones in Bangalore. This study shows that more than 95% of the BMP area is safe against liquefaction potential. However the western part of the BMP is not safe against liquefaction, as it may be subjected to liquefaction with probability of 35 to 65%. Three approaches used in this study show that 1) mapping least factor of safety irrespective of depth may be used to find liquefiable area for worst case. 2) mapping liquefaction potential index can be used to assess the liquefaction severity of the area by considering layer thickness and factor of safety and 3) mapping of liquefaction severity index can be used to access the probability of liquefaction of area.

DNase I Site Mapping and Micrococcal Nuclease Digestion of Pachytene Chromatin Reveal Novel Structural Features

A comparison of the DNase I digestion products of the 32P-5’-end-labeled pachytene nucleosome core particles (containing histones H2A, TH2A, X2, H2B, THPB, H3a, nd H4) and liver nucleosome core particles (containing somatic histones H2A, H2B, H3, and H4) revealed that the cleavage sites that are 30, 40, and 110 nucleotidesa way from the 5’-enda re significantly more accessiblei n the pachytene core particles than in the liver core particles. These cleavage sites correspond to the region wherein H2B interacts with the nucleosome core DNA. These results, therefore, suggest that the histone-DNA interactiona t these sites in the pachytene core particles is weaker, possibly because of the presence of the histone variant THBB interacting at similar topological positions in the nucleosome core as that of its somatic counterpart H2B. Such a loosened structumrea y also be maintainede ven in the native pachytene chromatin since micrococcal nuclease digestion of pachytene nuclei resulted in a higher ratio of subnucleosomes (SN4 + SN?) to mononucleosomes than that observed liinv er chromatin

Gauging the conformal group

It is demonstrated that Kibble’s method of gauging the Poincaré group can be applied to the gauging of the conformal group. The action of the gauge transformations is the action of general spacetime diffeomorphisms (or coordinate transformations) combined with a local action of an 11-parameter subgroup of SO(4,2). Because the translational subgroup is not an invariant subgroup of the conformal group the appropriate generalisation of the derivative of a physical field is not a covariant derivative in the usual sense, but this does not lead to any inconsistencies.