Physics Commons^™

Melting And Solidification Study Of As-Deposited And Recrystallized Bi Thin Films, M. K. Zayed, H. E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

Melting and solidification of as-deposited and recrystallized Bi crystallites, deposited on highly oriented 002-graphite at 423 K, were studied using reflection high-energy electron diffraction (RHEED). Films with mean thickness between 1.5 and 33 ML (monolayers) were studied. Ex situ atomic force microscopy was used to study the morphology and the size distribution of the formed nanocrystals. The as-deposited films grew in the form of three-dimensional crystallites with different shapes and sizes, while those recrystallized from the melt were formed in nearly similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting …

Monodomain Dynamics For Rigid Rod And Platelet Suspensions In Strongly Coupled Coplanar Linear Flow And Magnetic Fields. Ii. Kinetic Theory, M. Gregory Forest, Sarthok Sircar, Qi Wang, Ruhai Zhou

Mathematics & Statistics Faculty Publications

We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional …

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by …

A Structure Theorem For Stationary Perfect Fluids, Brendan Guilfoyle

Preprints

It is proven that, under mild physical assumptions, an isolated stationary relativistic perfect fluid consists of a finite number of cells fibred by invariant annuli or invariant tori. For axially symmetric circular flows it is shown that the fluid consists of cells fibred by rigidly rotating annuli or tori.

Developing A B -Tagging Algorithm Using Soft Muons At Level-3 For The Dø Detector At Fermilab, Mayukh Das

Doctoral Dissertations

The current data-taking phase of the DØ detector at Fermilab, called Run II, is designed to aid the search for the Higgs Boson. The neutral Higgs is postulated to have a mass of 117 GeV. One of the channels promising the presence of this hypothetical particle is through the decay of b-quark into a muon. The process of identifying a b-quark in a jet using muon as a reference is b-tagging with a muon tag.

At the current data taking and analysis rate, it will take long to reach the process of identifying valid events. The triggering mechanism of the …

The Straggling Green's Function Method For Ion Transport, Steven Andrew Walker

Mathematics & Statistics Theses & Dissertations

For many years work has been conducted on developing a concise theory and method for HZE ion transport capable of being validated in the laboratory. Previous attempts have ignored dispersion and energy downshift associated with nuclear fragmentation and energy and range straggling. Here we present a Green's function approach to ion transport that incorporates these missing elements. This work forms the basis for a new version of GRNTRN, a Green's function transport code. Comparisons of GRNTRN predictions and laboratory results for an ⁵⁶Fe ion beam with average energy at the target of one GeV/amu or more are presented for …

The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses `kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor …

Quantum Quasi-Paradoxes And Quantum Sorites Paradoxes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

There can be generated many paradoxes or quasi-paradoxes that may occur from the combination of quantum and non-quantum worlds in physics. Even the passage from the micro-cosmos to the macro-cosmos, and reciprocally, can generate unsolved questions or counter-intuitive ideas. We define a quasi-paradox as a statement which has a prima facie self-contradictory support or an explicit contradiction, but which is not completely proven as a paradox. We present herein four elementary quantum quasi-paradoxes and their corresponding quantum Sorites paradoxes, which form a class of quantum quasi-paradoxes.

Kinetic Structure Simulations Of Nematic Polymers In Plane Couette Cells. Ii: In-Plane Structure Transitions, M. Gregory Forest, Ruhai Zhou, Qi Wang

Mathematics & Statistics Faculty Publications

Nematic, or liquid crystalline, polymer (LCP) composites are composed of large aspect ratio rod-like or platelet macromolecules. This class of nanocomposites exhibits tremendous potential for high performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. Fibers made from nematic polymers have set synthetic materials performance standards for decades. The current target is to engineer multifunctional films and molded parts, for which processing flows are shear-dominated. Nematic polymer films inherit anisotropy from collective orientational distributions of the molecular constituents and develop heterogeneity on length scales that are, as yet, not well understood and thereby uncontrollable. Rigid LCPs in …

Vector Operations In Superscalar Architectures, Nathan Daniel Flinn

Electrical & Computer Engineering Theses & Dissertations

Vector calculations are very prevalent today. Though the vector-processing computer is quite an old concept, superscalar processors lack hardware support for vector operations. This thesis investigates whether an ordinary superscalar computer architecture can be designed to include hardware support for improved vector operations without drastically changing the existing superscalar design and behavior. A computer architecture design was created and implemented that included the vector multiply (dot product) operation. The design includes a Vector Operations Unit that captures incoming vector operations and generates the necessary set of machine instructions to complete the vector operation internally. It then delivers these instructions to …

An Experimental Study Of Micron-Scale Droplet Aerosols Produced Via Ultrasonic Atomization, Thomas D. Donnelly, J. Hogan '03, A. Mugler '04, N. Schommer '04, M. Schubmehl '02, Andrew J. Bernoff, B. Forrest '02

All HMC Faculty Publications and Research

In the last 10 years, laser-driven fusion experiments performed on atomic clusters of deuterium have shown a surprisingly high neutron yield per joule of input laser energy. Results indicate that the optimal cluster size for maximizing fusion events should be in the 0.01–μm diameter range, but an appropriate source of droplets of this size does not exist. In an attempt to meet this need, we use ultrasonic atomization to generate micron-scale droplet aerosols of high average density, and we have developed and refined a reliable droplet sizing technique based on Mie scattering. Harmonic excitation of the fluid in …

Blowup And Dissipation In A Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, Andrea L. Bertozzi

All HMC Faculty Publications and Research

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.

Objectivity, Information, And Maxwell's Demon, Steven Weinstein

Dartmouth Scholarship

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell's Demon.

Complex Multiplication Symmetry Of Black Hole Attractors, Monika Lynker, Vipul Periwal, Rolf Schimmrigk

Faculty Articles

We show how Moore’s observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications with finite fundamental groups. This generalization leads to an alternative general framework in terms of motives associated to a Calabi-Yau variety in which it is possible to address the arithmetic nature of the attractor varieties in a universal way via Deligne’s period conjecture.

Aspects Of Conformal Field Theory From Calabi-Yau Arithmetic, Rolf Schimmrigk

Faculty Articles

This paper describes a framework in which techniques from arithmetic algebraic geometry are used to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and aspects of the underlying conformal field theory. As an application the algebraic number field determined by the fusion rules of the conformal field theory is derived from the number theoretic structure of the cohomological Hasse-Weil L-function determined by Artin's congruent zeta function of the algebraic variety. In this context a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.

Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite

Articles

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational …

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …

Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite

Articles

We verify the Generalised Moonshine conjectures for some irrational modular functions for theMonster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.

Like A Bridge Over Colored Water: A Mathematical Review Of The Rainbow Bridge: Rainbows In Art, Myth, And Science, John A. Adam

Mathematics & Statistics Faculty Publications

Commenting on a recent book, the author discusses various views of the rainbow: its role in culture, its scientific description, and its mathematical theory.

Analytically Continued Hypergeometric Expression Of The Incomplete Beta Function, Jack C. Straton

Physics Faculty Publications and Presentations

The Incomplete Beta Function is rewritten as a Hypergeometric Function that is the analytic continuation of the conventional form, a generalization of the finite series, which simpifies the Stieltjes transform of powers of a monomial divided by powers of a binomial.

Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin

All HMC Faculty Publications and Research

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum l_F is replaced by l_B =l_F − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …

Unsteady Flow Model For An Irrigation Canal Network, Talaat Taher El Gamel

Civil & Environmental Engineering Theses & Dissertations

A mathematical model is developed to route unsteady flow through an irrigation canal network. The model is designed to handle branches, lateral inflow and outflow, sluice gates, and various boundary conditions. The model is developed for use on a personal computer. A specific irrigation canal network in Egypt is used as a case study to verify the model, and the results are presented. Full documentation is included in the appendix.

Transient Anomalous Diffusion In Poiseuille Flow, Marco Latini '01, Andrew J. Bernoff

All HMC Faculty Publications and Research

We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [double less-than sign] D^−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [dbl greater-than sign] D⁻¹), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with …

Scintillation Behind The Collecting Lens Of A Receiver, Clarissa A. Fleming Russell

Retrospective Theses and Dissertations

One of the negative effects that a laser beam experiences as it propagates through the atmosphere is intensity fluctuations or scintillation. Because scintillation-- as it pertains to laser radar and laser satellite communication systems-- is the main subject of this research, the assumption of an optical element ( such as a Gaussian lens) along the propagation path in front of the detector is valid. The mathematical addition of optical elements to the propagation path is treated using the ABCD ray matrix method. The expression for scintillation is derived, analyzed, and numerically calculated for positions to the left and right of …

Eddy Structures Induced Within A Wedge By A Honing Circular Arc, C. P. Hills

Articles

In this paper we outline an expeditious numerical procedure to calculate the Stokes flow in a corner due to the rotation of a scraping circular boundary. The method is also applicable to other wedge geometries. We employ a collocation technique utilising a basis of eddy (similarity) functions introduced by Moffatt (1964) that allows us to satisfy automatically the governing equations for the streamfunction and all the boundary conditions on the surface of the wedge. The circular honing problem thereby becomes one-dimensional requiring only the satisfaction of conditions on the circular boundary. The advantage of using the Moffatt eddy functions as …

Eddies Induced In Cylindrical Containers By A Rotating End Wall, Christopher Hills

Articles

The flow generated in a viscous liquid contained in a cylindrical geometry by a rotating end wall is considered. Recent numerical and experimental work has established several distinct phases of the motion when fluid inertia plays a significant role. The current paper, however, establishes the nature of the flow in the thus far neglected low Reynolds number regime. Explicitly, by employing biorthogonality relations appropriate to the current geometry, it is shown that a sequence of exponentially decaying eddies extends outward from the rotating end wall. The cellular structure is a manifestation of the dominance of complex eigensolutions to the homogeneous …

Mathematical Models Of Quiescent Solar Prominences, Iain Mckaig

Mathematics & Statistics Theses & Dissertations

Magnetic fields in the solar atmosphere suspend and insulate dense regions of cool plasma known as prominences. The convection zone may be the mechanism that both generates and expels this magnetic flux through the photosphere in order to make these formations possible. The connection is examined here by modeling the convection zone as both one-dimensional, then more realistically, two-dimensional.

First a Dirichlet problem on a semi-infinite strip is solved using conformal mapping and the method of images. The base of the strip represents the photosphere where a current distribution can be given as a boundary condition, and the strip extends …

Rotary Honing: A Variant Of The Taylor Paint-Scraper Problem, Christopher Hills, H. Moffatt

Articles

The three-dimensional Row in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the 'Taylor' …

Distribution Of Petrogenic Hydrocarbons In Water, Sediment And Cockles (Anadara Granosa) From Kuala Sungai Sepetang And Kuala Sungai Selangor, Mohd Hilmi Jaafar

Student Works (2000-2009)

In order to assess the level of oil pollution in the cockle culture areas along the Straits of Malacca, water, sediment and cockle samples were collected from the culture beds of Kuala Sepetang and Kuala Selangor, two of the largest cockle producing areas of Malaysia. The samples were analysed for petrogenic hydrocarbons by employing a spectrofluorometric technique which measures the content of polycyclic aromatic hydrocarbons (PAH) in oil. The content of aliphatic straight chain hydrocarbons were measured by using gas chromatography􀀐mass spectrometry (GCMS) which also allowed for the estimation of carbon preference indices and hence providing a means of estimating …

Development Of Multiple Channels Edf Lasers, Muhammad Zamzuri Abdul Kadir

Student Works (2000-2009)

This thesis presents the research work carried out on the development and analysis of single wavelength EDFL and multiple wavelength EDFL. Two types of single wavelength EDF ring laser were studied namely a fixed signal wavelength system and a tuneable signal wavelength system. However, emphasis was given to the first case. The analyses made, were based on the following parameters: pump and signal stability, pump power, reflectivity, EDF length and cavity loss. The influence of each cavity component such as isolator, polarisation controller, attenuator and tuneable filter were also investigated and reported here. Only one type of multiple wavelength EDFL …