The singular perturbation of surface tension in Hele-Shaw flows

Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid this extreme noise sensitivity, what is then the role played by small surface tension in the dynamic formation and selection of these patterns? What is the asymptotic behaviour of the interface in the limit as surface tension tends to zero? The ill-posedness of the zero-surface-tension problem and the singular nature of surface tension pose challenging difficulties in the investigation of these questions. Here, we design a novel numerical method that greatly reduces the impact of noise, and allows us to accurately capture and identify the singular contributions of extremely small surface tensions. The numerical method combines the use of a compact interface parametrization, a rescaling of the governing equations, and very high precision. Our numerical results demonstrate clearly that the zero-surface-tension limit is indeed singular. The impact of a surface-tension-induced complex singularity is revealed in detail. The singular effects of surface tension are first felt at the tip of the interface and subsequently spread around it. The numerical simulations also indicate that surface tension defines a length scale in the fingers developing in a later stage of the interface evolution

Integrated Educational Project of Theoretical, Experimental, and Computational Analyses

This research demonstrates how to design an integrated capstone project by including theoretical, experimental and computational analyses of a truss bridge. The project mainly focused on leading students to approach engineering problems with various methods and to understand the advantages and disadvantages of each method. The students applied three methods to acquire the values of stresses and deflections of members in the given truss bridge. First, they calculated the stresses and deformations theoretically. Second, they actually conducted an experiment of the truss bridge with electronic measuring equipment. Lastly, they built two simulation models with Autodesk Inventor and Dassault Systèmes SolidWorks. From the comparisons of above three methods, students were guided to the validation of assumptions of theories.Cockrell School of Engineerin

Flow field predictions for a slab delta wing at incidence

Theoretical results are presented for the structure of the hypersonic flow field of a blunt slab delta wing at moderately high angle of attack. Special attention is devoted to the interaction between the boundary layer and the inviscid entropy layer. The results are compared with experimental data. The three-dimensional inviscid flow is computed numerically by a marching finite difference method. Attention is concentrated on the windward side of the delta wing, where detailed comparisons are made with the data for shock shape and surface pressure distributions. Surface streamlines are generated, and used in the boundary layer analysis. The three-dimensional laminar boundary layer is computed numerically using a specially-developed technique based on small cross-flow in streamline coordinates. In the rear sections of the wing the boundary layer decreases drastically in the spanwise direction, so that it is still submerged in the entropy layer at the centerline, but surpasses it near the leading edge. Predicted heat transfer distributions are compared with experimental data

Interplay of the Chiral and Large N_c Limits in pi N Scattering

Light-quark hadronic physics admits two useful systematic expansions, the chiral and 1/N_c expansions. Their respective limits do not commute, making such cases where both expansions may be considered to be especially interesting. We first study pi N scattering lengths, showing that (as expected for such soft-pion quantities) the chiral expansion converges more rapidly than the 1/N_c expansion, although the latter nevertheless continues to hold. We also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of pi N scattering, finding that both fail if the large N_c limit is taken prior to the chiral limit.Comment: 10 pages, ReVTe

Order and Creep in Flux Lattices and CDWs Pinned by Planar Defects

The influence of randomly distributed point impurities \emph{and} planar defects on the order and transport in type-II superconductors and related systems is considered theoretically. For planar defects of identical orientation the flux line lattice exhibits a new glassy phase dominated by the planar defects with a finite compressibility, a transverse Meissner effect, large sample to sample fuctuations of the susceptibility and an exponential decay of translational long range order. The flux creep resistivity for currents $J$ parallel to the defects is $\rho(J)\sim \exp-(J_0/J)^{3/2}$ . Strong disorder enforces an array of dislocations to relax shear strain

Energy-level pinning and the 0.7 spin state in one dimension: GaAs quantum wires studied using finite-bias spectroscopy

We study the effects of electron-electron interactions on the energy levels of GaAs quantum wires (QWs) using finite-bias spectroscopy. We probe the energy spectrum at zero magnetic field, and at crossings of opposite-spin-levels in high in-plane magnetic field B. Our results constitute direct evidence that spin-up (higher energy) levels pin to the chemical potential as they populate. We also show that spin-up and spin-down levels abruptly rearrange at the crossing in a manner resembling the magnetic phase transitions predicted to occur at crossings of Landau levels. This rearranging and pinning of subbands provides a phenomenological explanation for the 0.7 structure, a one-dimensional (1D) nanomagnetic state, and its high-B variants.Comment: 6 pages, 4 figure

On the Universal Tachyon and Geometrical Tachyon

We study properties of non-BPS D(p+1)-brane in the background of k NS5-branes, with one transverse direction compactified on a circle, from the point of view of Dirac-Born-Infeld action. We present the analysis of two different embedding of non-BPS D(p+1)-brane in given background and study the classical solutions of given world-volume theory. We argue for the configuration of a non-BPS D(p+1)-brane which allows us to find solutions of the equations of motion that give unified descriptions of G and U-type branes.Comment: 24 pages, minor change