The Physical Tourist

I provide a tour of Edinburgh focusing on famous contributors to the history of physics and related sciences, using them as a way to write about particular parts of Edinburgh. I proceed chronologically, from the seventeenth century to the Scottish Enlightenment of the eighteenth century and on to the nineteenth and twentieth centuries. Among the notable individuals I discuss are John Napier (1550–1617), James Gregory (1638–1675), George Sinclair (ca. 1625–1696), Colin Maclaurin (1698–1746), Joseph Black (1728–1799), James Hutton (1726–1797), John James Waterston (1811–1883), William J. Macquorn Rankine (1820–1872), David Brewster (1781–1868), Peter Guthrie Tait (1831–1901), James Clerk Maxwell (1831–1879), Charles Piazzi Smyth (1819–1900), Charles Glover Barkla (1877–1944), Max Born (1882–1970), Edward Victor Appleton (1892–1965), Charles T.R. Wilson (1869–1959), and Peter Higgs (b. 1929).     

Time-resolved PIV investigation on the unsteadiness of a low reynolds number confined impinging jet

The flow characteristics in a confined slot jet impinging on a flat plate were investigated in low Reynolds number regime by using time-resolved Particle Image Velocimetry technique. The jet Reynolds number was varied from 404 to 1026, where it is presumed that the transient regime exists. We found that the vortical structures in the shear layer are developed with increase of Reynolds number and that the jet becomes remains steady at the Reynolds number of 404. Vortical structures and their temporal evolution are verified and the results were compared with previous numerical studies.     

A novel three-dimensional system to study interactions between endothelial cells and neural cells of the developing central nervous system

Background  

During angiogenesis in the developing central nervous system (CNS), endothelial cells (EC) detach from blood vessels growing on the brain surface, and migrate into the expanding brain parenchyma. Brain angiogenesis is regulated by growth factors and extracellular matrix (ECM) proteins secreted by cells of the developing CNS. In addition, recent evidence suggests that EC play an important role in establishing the neural stem cell (NSC) niche. Therefore, two-way communication between EC and neural cells is of fundamental importance in the developing CNS. To study the interactions between brain EC and neural cells of the developing CNS, a novel three-dimensional (3-D) murine co-culture system was developed. Fluorescent-labelled brain EC were seeded onto neurospheres; floating cellular aggregates that contain NSC/neural precursor cells (NPC) and smaller numbers of differentiated cells. Using this system, brain EC attachment, survival and migration into neurospheres was evaluated and the role of integrins in mediating the early adhesive events addressed.     

Amyloid-like aggregates of neuronal tau induced by formaldehyde promote apoptosis of neuronal cells

Background  

The microtubule associated protein tau is the principle component of neurofibrillar tangles, which are a characteristic marker in the pathology of Alzheimer's disease; similar lesions are also observed after chronic alcohol abuse. Formaldehyde is a common environmental contaminant and also a metabolite of methanol. Although many studies have been done on methanol and formaldehyde intoxication, none of these address the contribution of protein misfolding to the pathological mechanism, in particular the effect of formaldehyde on protein conformation and polymerization.     

Thermal modeling of laser sintering of two-component metal powder on top of sintered layers via multi-line scanning

Laser sintering of a two-component metal powder layer on top of sintered layers, with a moving circular Gaussian laser beam is modeled numerically. The overlap between the adjacent scanning lines, as well as the binding between the newly sintered layer and existing sintered layers underneath through melting, are also considered. The governing equation is formulated by a temperature-transforming model, with partial shrinkage induced by melting taken into account. The liquid flow of the molten low melting point metal powders driving by capillary and gravity forces is formulated by Darcy’s law. The effects of the dominant processing parameters, including the moving laser beam intensity, scanning speed, and the number of the existing sintered layers underneath on the shape of the heat affected zone (HAZ) are investigated. PACS 44.05.+e; 81.20.Ev     

Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

The problem of studying the quantum Hall effect on manifolds with non constant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well. PACS numbers: 73.43.-f, 02.30.Jr.     

Properties of Generalized Univariate Hypergeometric Functions

Based on Spiridonov’s analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E ₇ (elliptic, hyperbolic) and of type E ₆ (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars’ relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.     

Bound-State Solutions of the Klein-Gordon Equation for the Generalized <Emphasis Type="Italic">PT</Emphasis>-Symmetric Hulthén Potential

The one-dimensional Klein-Gordon equation is solved for the PT-symmetric generalized Hulthén potential in the scalar coupling scheme. The relativistic bound-state energy spectrum and the corresponding wave functions are obtained by using the Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. PACS numbers: 03.65.Fd, 03.65.Ge     

Localization of Non-Relativistic Particles

This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2) to show that the rigged Hilbert space incorporates particle localization in a natural manner.