Parametric Forcing of Confined and Stratified Flows

abstract: A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations. The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.Dissertation/ThesisSupplemental Materials Description Filezip file containing 10 mp4 formatted video animations, as well as a text readme and the previously submitted Supplemental Materials Description FileDoctoral Dissertation Mathematics 201

Dynamics of Barred Galaxies

Some 30% of disc galaxies have a pronounced central bar feature in the disc plane and many more have weaker features of a similar kind. Kinematic data indicate that the bar constitutes a major non-axisymmetric component of the mass distribution and that the bar pattern tumbles rapidly about the axis normal to the disc plane. The observed motions are consistent with material within the bar streaming along highly elongated orbits aligned with the rotating major axis. A barred galaxy may also contain a spheroidal bulge at its centre, spirals in the outer disc and, less commonly, other features such as a ring or lens. Mild asymmetries in both the light and kinematics are quite common. We review the main problems presented by these complicated dynamical systems and summarize the effort so far made towards their solution, emphasizing results which appear secure. (Truncated)Comment: This old review appeared in 1993. Plain tex with macro file. 82 pages 18 figures. A pdf version with figures at full resolution (3.24MB) is available at http://www.physics.rutgers.edu/~sellwood/bar_review.pd

ON THE STABILITY OF VARIABLE HELIX MILLING TOOLS

One of the main aims of the manufacturing industry has been to maximise the material removal rate of machining processes. However, this goal can be restricted by the appearance of regenerative chatter vibrations. In milling, one approach for regenerative chatter suppression is the implementation of variable-helix cutters. However, these tools can lead to isolated unstable regions in the stability diagram. Currently, variable-helix unstable islands have not been extensively researched in the literature. Therefore, the current thesis focuses on studying and experimentally validating these islands. For the validation, an experimental setup that scaled not only the structural dynamics but also the cutting force coefficients was proposed. Therefore, it was possible to attain larger axial depths of cut while assuming linear dynamics. The variable-helix process stability was modelled using the semi-discretization method and the multi-frequency approach. It was found that the variable helix tools can further stabilise a larger width of cut due to the distributed time delays that are a product of the tool geometry. Subsequently, a numerical study about the impact of structural damping on the variable-helix stability diagram revealed a strong relationship between the damping level and instability islands. The findings were validated by performing trials on the experimental setup, modified with constrained layer damping to recreate the simulated conditions. Additionally, a convergence analysis using the semi-discretization method (SDM) and the multi-frequency approach (MFA) revealed that these islands are sensitive to model convergence aspects. The analysis shows that the MFA provided converged solutions with a steep convergence rate, while the SDM struggled to converge. In this work, it is demonstrated that variable-helix instability islands only emerge at relatively high levels of structural damping and that they are particularly susceptible to model convergence effects. Meanwhile, the model predictions are compared to and validated against detailed experimental data that uses a specially designed configuration to minimise experimental error. To the authors' knowledge, this provides the first experimentally validated study of unstable islands in variable helix milling, while also demonstrating the importance of accurate damping estimates and convergence studies within the stability predictions

Self-consistent charge densities at isolated planar defects in metals

Imperial Users onl

Second harmonic generation in novel optical waveguides

Second Harmonic Generation has traditionally been restricted to crystals; however, due to the development of highly sophisticated fabrication technology, poling and phase matching techniques, it has now become feasible in glass fibres and waveguides which are widely used in nonlinear optics. For instance, silica glass based Photonic Crystal Fibres (PCF) exhibit long coherence lengths and controllable optical properties such as chromatic dispersion despite low second order nonlinearity. Given such benefits, the numerical modelling and analysis of optical waveguides accurately and efficiently has become vital for the advancement of nonlinear optics. Hence, this thesis focuses on enhancing the Second Harmonic Generation in optical waveguides through the use of different structures and different materials, and demonstrating the same by numerical simulations. In this thesis, the accurate and numerically efficient Finite Element based Beam Propagation Method has been employed to investigate the evolution of Second Harmonic Generation in highly nonlinear SF57 soft glass Equiangular Spiral PCFs. Further, the H-field based Finite Element Method has been employed for the stationary analysis of Photonic Crystal Fibres. It is shown here that the second harmonic output power in highly nonlinea

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Space-Angle Discontinuous Galerkin Finite Element Method for Radiative Transfer Equation

Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables, which are 3 dimensions in space and 2 dimensions in the angular direction. This high dimensionality and the presence of the integral term present serious challenges when solving the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation (RTE) have been introduced. These include, but are certainly not limited to, Monte Carlo methods, discrete-ordinate methods, spherical harmonics methods, spectral methods, finite difference methods, and finite element methods. Methods involving discrete ordinates and spherical harmonics have received particular attention in the literature. This work introduces a parallel space-angle discontinuous Galerkin (saDG) method to solve the steady-state RTEs. The objective-oriented design of the software allowed us to apply the saDG approach to a variety of RTEs with considerable ease, including 1x1s, 1x2s, and 2x2s. The direct solver can achieve high-order accuracy solutions for low-dimensional problems. However, for high-dimensional problems, the direct solver is time-consuming and requires significant memory usage that may exceed the computer\u27s RAM capacity. To address this issue, we employed the Angular Decomposition (AD) method in the iterative solver, which improves runtime efficiency and reduces memory usage. To handle large-scale problems, we developed a parallel solver based on AD and Domain Decomposition (DD) methods. Finally, we applied Reflective Boundary Conditions to 2-D Cartesian radiative transfer problems

Solar System Remote Sensing : September 20-21, 2002, Pittsburgh, Pennsylvania

This international meeting presents the current state of research over a wide range of topics including:; Photometric theory; Spectroscopic modeling; Laboratory exploration of scattering phenomena; Space weathering processes throughout the inner solar system; Photometric and spectroscopic studies of the Moon, Mars, Mercury, and asteroids; Photometric and spectroscopic studies of cold, icy places such as comets and outer planet satellites.This international meeting presents the current state of research over a wide range of topics including:; Photometric theory; Spectroscopic modeling; Laboratory exploration of scattering phenomena; Space weathering processes throughout the inner solar system; Photometric and spectroscopic studies of the Moon, Mars, Mercury, and asteroids; Photometric and spectroscopic studies of cold, icy places such as comets and outer planet satellites.sponsors, University of Pittsburgh ... [and others]conveners, William Cassidy, Deborah Domingue, Robert M. Nelson ; scientific organizing committee William Cassidy ... [and others].PARTIAL CONTENTS: Interpreting Photometry of Planetary Regoliths: Progress and Problems as Seen from Kharkov / Yu.G. Shkuratov--Toward an Improved Single-Particle Model for Large, Irregular Grains / W.M. Grundy, B. Schmitt, S. Doute--A New Method for Estimating the Single Scattering Phase Functions of Regolith Grains / P. Helfenstein--The Opposition Effect: A Very Unusual Case / R.M. Nelson--Coherent Backscattering by Random Particulate Media in the Solar System / K. Muinonen--The Diverse Surface Compositions of the Galilean Satellites / R.W. Carlso