Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting

Full potential unsteady computations including aeroelastic effects

A unified formulation is presented based on the full potential framework coupled with an appropriate structural model to compute steady and unsteady flows over rigid and flexible configurations across the Mach number range. The unsteady form of the full potential equation in conservation form is solved using an implicit scheme maintaining time accuracy through internal Newton iterations. A flux biasing procedure based on the unsteady sonic reference conditions is implemented to compute hyperbolic regions with moving sonic and shock surfaces. The wake behind a trailing edge is modeled using a mathematical cut across which the pressure is satisfied to be continuous by solving an appropriate vorticity convection equation. An aeroelastic model based on the generalized modal deflection approach interacts with the nonlinear aerodynamics and includes both static as well as dynamic structural analyses capability. Results are presented for rigid and flexible configurations at different Mach numbers ranging from subsonic to supersonic conditions. The dynamic response of a flexible wing below and above its flutter point is demonstrated

Full potential methods for analysis/design of complex aerospace configurations

The steady form of the full potential equation, in conservative form, is employed to analyze and design a wide variety of complex aerodynamic shapes. The nonlinear method is based on the theory of characteristic signal propagation coupled with novel flux biasing concepts and body-fitted mapping procedures. The resulting codes are vectorized for the CRAY XMP and the VPS-32 supercomputers. Use of the full potential nonlinear theory is demonstrated for a single-point supersonic wing design and a multipoint design for transonic maneuver/supersonic cruise/maneuver conditions. Achievement of high aerodynamic efficiency through numerical design is verified by wind tunnel tests. Other studies reported include analyses of a canard/wing/nacelle fighter geometry

Myxoid Neurothekeoma of the Nipple

Neurothekeomas are rare benign cutaneous neoplasms of nerve sheath origin. They are primarily found in the superficial soft tissue and are also known as dermal nerve sheath myxomas. They are commonly found on the upper extremities, head and neck followed by trunk. Here is an unusual presentation of neurothekeoma occurring as a polypoidal lesion of the nipple in a young female patient

On two theta function identities of Ramanujan

On page 310 of his second notebook, Ramanujan recorded two theta function identities. B. C. Berndt proved them by the method of parameterization. The purpose of this article is to give an elementary proof for those two identities and also we have obtained two theta function identities which are analogues to the identities of Ramanujan. Further, we establish two distinct formula for 3-core partitions in terms of divisor function

Identification and biochemical characterisation of genes involved in mycobacterial cell wall assembly

The cell wall of $Mycobacterium$ $tuberculosis$ has a very complex ultrastructure, consisting of mycolic acids, an array of polysaccharides and surface exposed antigenic glycolipids. These cell wall components play a vital role in pathogenicity and virulence and hence, are attractive drug targets. Recent advances in TB drug discovery have produced a plethora of candidate drug molecules, many of them, affect mycolic acid biosynthesis and transport. A major part of the thesis work consists of biochemical and structural characterisation of proteins involved in mycolic acids biosynthesis and transport using a combination of genetic and biophysical tools. Through deletion of $fabH$, its non-essentiality for growth and survival of mycobacteria was demonstrated, and suggested the possibility of a functional substitute. The latter part of the thesis deals with the identification and characterisation of glycosyltransferases involved in the biosynthesis of lipooligosaccharides (LOS) in $M.$ $kansasii.$ LOS’s are surface exposed, highly polar antigenic glycolipids, present in several mycobacterial species. Using targeted gene deletion, mutant strain defective in LOS production was obtained that has provided the first insights into LOS biosynthesis in $M.$ \(kansasii.\

Efficient Parallel Circuits and Algorithms for Division

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / ECS 8404866Semiconductor Research Corporation / SRC 86-12-109Joint Services Electronics Program / N00014-84-C-014

Generalized BCS Equations: A Review and a Detailed Study of the Superconducting Features of Ba₂Sr₂CaCu₂O₈

High-Tc superconductors (SCs) are most widely studied via the multiband approach (MBA) based on the work of Suhl et al. and the Nambu-Eliashberg-McMillan extension of the BCS theory. Complementing MBA and presented in a recent monograph is an approach based on the generalized BCS equations (GBCSEs), which too has been applied to a significant number of SCs. GBCSEs are obtained via a Bethe-Salpeter equation and the Matsubara technique. One of the key features of this approach is the characterization of a composite SC by Cooper pairs with different binding energies—each of which is identified with a gap (Δ) of the SC—depending on whether pairing is due to phonon exchanges with one, two, or more ion species. Another feature is the incorporation of chemical potential in the GBCSEs, which enables one to calculate the critical current density j0 of an SC using the same parameters that determine its Tc and Δ. Following a review of the concepts of this approach, given herein, for the first time, is a detailed explanation of the multitude of reported empirical values of {Tc, Δ, j0} of Bi2Sr2CaCu2O8. Also discussed are the currently topical issues of s±-superconductivity and the isotope-like effect for high-Tc SCs

A High-Order Ultra-Weak Variational Formulation for Electromagnetic Waves Utilizing Curved Elements

The Ultra Weak Variational Formulation (UWVF) is a special Trefftz discontinuous Galerkin method, here applied to the time-harmonic Maxwell's equations. The method uses superpositions of plane waves to represent solutions element by element on a finite element mesh. We discuss the use of our parallel UWVF implementation called ParMax, and concentrate on methods for obtaining high order solutions in the presence of scatterers with piecewise smooth boundaries. In particular, we show how curved surface triangles can be incorporated in the UWVF. This requires quadrature to assemble the system matrices. We also show how to implement a total field and scattered field approach, together with the transmission conditions across an interface to handle resistive sheets. We note also that a wide variety of element shapes can be used, that the elements can be large compared to the wavelength of the radiation, and that a matrix free version is easy to implement (although computationally costly). Our contributions are illustrated by several numerical examples showing that curved elements can improve the efficiency of the UWVF, and that the method accurately handles resistive screens as well as PEC and penetrable scatterers. Using large curved elements and the matrix free approach, we are able to simulate scattering from an aircraft at X-band frequencies. The innovations here demonstrate the applicability of the UWVF for industrial examples