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1 
Lagrangian methods of cosmic web classificationFisher, Justin David January 2016 (has links)
A Research Report submitted to the Department of Physics, Faculty of Science, University
of the Witwatersrand, Johannesburg, in partial ful lment of the requirements for the degree
of Master of Science.
Signed on the 24th March 2016 in Johannesburg. / This research report uses cosmological Nbody simulations to examine the the large
scale mass distribution of the Universe, known as the cosmic web. The cosmic web can be
classi ed into nodes, laments, sheets and voids  each with its own characteristic density
and velocity elds. In this work, the author proposes a new Lagrangian cosmic web classi
cation algorithm, based on smoothed particle hydrodynamics. This scheme o ers adaptive
resolution, resolves smaller substructure and obeys similar statistical properties with existing
Eulerian methods. Using the new classi cation scheme, halo clustering dependence on cosmic
web type is examined. The author nds halo clustering is signi cantly correlated with
web type. Consequently, the mass dependence of halo clustering may be explained by the
fractions of web types found for a particular halo mass. Finally, an analysis of dark matter
halo spin, shape and fractional anisotropy is presented per web type to suggest avenues for
future work.

2 
Equivalent lagrangians and transformation maps for differential equationsWilson, Nicole 09 January 2013 (has links)
A dissertation submitted to the Faculty of Science, University of the
Witwatersrand, in fulflment of the requirements for the degree of
Master of Science. / The Method of Equivalent Lagrangians is used to find the solutions of a given
differential equation by exploiting the possible existence of an isomorphic Lie
point symmetry algebra and, more particularly, an isomorphic Noether point
symmetry algebra. Applications include ordinary differential equations such
as the Kummer Equation and the Combined GravityInertialRossby Wave
Equation and certain classes of partial differential equations related to the
(1 + 1) linear wave equation. We also make generalisations to the (2 + 1) and
(3 + 1) linear wave equations.

3 
Constructing special Lagrangian cones /Haskins, Mark, January 2000 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 8591). Available also in a digital version from Dissertation Abstracts.

4 
Finding the sweetspot of a cricket bat using a mathematical approachRogers, Langton 13 September 2016 (has links)
University Of The Witwatersrand
Department Of Computational And Applied Mathematics
Masters’ Dissertation
2015 / The ideal hitting location on a cricket bat, the ‘sweetspot’, is taken to be
defined in two parts: 1) the Location of Impact on a cricket bat that transfers
the maximum amount of energy into the batted ball and 2) the Location
of Impact that transfers the least amount of energy to the batsman’s
hands postimpact with the ball; minimizing the unpleasant stinging sensation
felt by the batsman in his hands. An analysis of di↵erent hitting
locations on a cricket bat is presented with the cricket bat modelled as a
one dimensional beam which is approximated by the EulerLagrange Beam
Equation. The beam is assumed to have uniform density and constant flexural
rigidity. These assumptions allow for the EulerLagrange Beam Equation
to be simplified considerably and hence solved numerically. The solution is
presented via both a Central Time, Central Space finite di↵erence scheme
and a CrankNicolson scheme. Further, the simplified EulerLagrange Beam
Equation is solved analytically using a Separation of Variables approach.
Boundary conditions, initial conditions and the framework of various collision
scenarios between the bat and ball are structured in such a way that the
model approximates a batsman playing a defensive cricket shot in the first
two collision scenarios and an aggressive shot in the third collision scenario.
The first collision scenario models a pointlike, impulsive, perpendicular collision
between the bat and ball. A circular Hertzian pressure distribution is
used to model an elastic, perpendicular collision between the bat and ball in
the second collision scenario, and an elliptical Hertzian pressure distribution
does similarly for an elastic, oblique collision in the third collision scenario.
The pressure distributions are converted into initial velocity distributions
through the use of the Lagrange Field Equation. The numerical solution via
the CrankNicolson scheme and the analytical solution via the Separation
of Variables approach are analysed. For di↵erent Locations of Impact along
the length on a cricket bat, a postimpact analysis of the displacement of
points along the bat and the strain energy in the bat is conducted. Further,
through the use of a Fourier Transform, a postimpact frequency analysis
of the signals travelling in the cricket bat is performed. Combining the results
of these analyses and the twopart definition of a ‘sweetspot’ allows
for the conclusion to be drawn that a Location of Impact as close as possible
to the fixedend of the cricket bat (a point just below the handle of the
bat) results in minimum amount of energy transferred to the hands of the
batsman. This minimizes the ‘stinging’ sensation felt by the batsman in his
hands and satisfies the second part of the definition of a sweetspot. Due to
the heavy emphasis of the frequency analysis in this study, the conclusion
is drawn that bat manufacturers should consider the vibrational properties
of bats more thoroughly in bat manufacturing. Further, it is concluded that
the solutions from the numerical CrankNicolson scheme and the analytical
Separation of Variables approach are in close agreement.

5 
Embeddings of Lorentzian manifolds by solutions of the d'Alembertian equations /Kim, JongChul. January 1980 (has links)
Thesis (Ph. D.)Oregon State University, 1980. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

6 
Existence of a solution to a variational data assimilation method in twodimensional hydrodynamics /Hagelberg, Carl R. January 1992 (has links)
Thesis (Ph. D.)Oregon State University, 1992. / Typescript (photocopy). Includes bibliographical references (leaves 6870). Also available on the World Wide Web.

7 
Friction stir welding (FSW) simulation using an arbitrary LagrangianEulerian (ALE) moving mesh approachZhao, Hua, January 1900 (has links)
Thesis (Ph. D.)West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains x, 166 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 154161).

8 
A survey on constructions of special Lagrangian submanifolds. / CUHK electronic theses & dissertations collectionJanuary 2013 (has links)
本論文旨在討論複空間上的特殊拉格朗日子流行的各種建構方法。這些方法主要自R. Harvey, B. Lawson, D. Joyce, R. Bryanl 以及M. Haskins這幾位數學家發展及研究. 本文側重於擁有不同類型對稱位的特殊拉格朗日子流行的結構方法, 其中包指於n維環面群及特殊正交群不變的例子，以及直紋特殊拉格朗日子流行。除此之外,本論文也會討論以上建構方法所給出的具體制子。最後, 本文亦會討論一種可以建構擁有高虧格鏈的特殊拉格朗日子流行的方法。 / This thesis gives a survey on constructions of special Lagrangian submanifolds in C[superscript n]. These construction methods are mainly studied by Harvey and Lawson, D. Joyce, R. Bryant and M. Haskins. We mainly focus on special Lagrangian submanifolds with different kinds of symmetries. These include local constructions of T[superscript n] and SO(n)invariant examples, and ruled examples. We also discuss explicit examples arose from those constructions. Besides local constructions, a global gluing construction of special Lagrangian submanifolds with high genus links is also discussed. / Detailed summary in vernacular field only. / Lam, Yi Chun. / Thesis (M.Phil.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 9799). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1  Introduction  p.6 / Chapter 2  Preliminaries  p.17 / Chapter 2.1  Special Lagrangian Geometry  p.17 / Chapter 2.2  Special Legendrian Links  p.23 / Chapter 2.3  Harmonic Maps  p.25 / Chapter 2.4  Moment Maps  p.28 / Chapter 2.5  Evolution Equation  p.30 / Chapter 2.6  Background Materials from Analysis  p.33 / Chapter 3  T[superscript n] invariant Special Lagrangian Submanifolds  p.36 / Chapter 3.1  Basic Example  p.36 / Chapter 3.2  U(1)[superscript n2] invariant Special Lagrangian Cones in C[superscript n]  p.37 / Chapter 3.2.1  General Construction  p.37 / Chapter 3.2.2  Reduction of O.D.E. System  p.40 / Chapter 3.2.3  The 3dimensional Case  p.48 / Chapter 4  SO(n)invariant Special Lagrangian Submanifolds  p.52 / Chapter 4.1  Basic Example  p.52 / Chapter 4.2  Special Lagrangian Submanifolds with Fixed Loci  p.54 / Chapter 4.2.1  Reduction to P.D.E  p.55 / Chapter 4.2.2  The 3Dimensional Case  p.63 / Chapter 5  Ruled Special Lagrangian Submanifolds  p.65 / Chapter 5.1  Normal Bundle of a Submanifold  p.65 / Chapter 5.2  Twisted Normal Bundles  p.69 / Chapter 5.3  The 3Dimensional Case  p.72 / Chapter 5.3.1  Construction of Special Lagrangian Ruled 3folds  p.71 / Chapter 5.3.2  Explicit Examples  p.75 / Chapter 5.4  Twisted Special Lagrangian Cones  p.78 / Chapter 6  Other Constructions  p.81 / Chapter 6.1  Analysis on U(1)invariant Special Lagrangian submanifolds  p.81 / Chapter 6.1.1  Nonsingular Solutions  p.83 / Chapter 6.1.2  Existence of Singular Solutions  p.84 / Chapter 6.1.3  Properties of Singular Solutions  p.86 / Chapter 6.2  Harmonic Maps and Minimal Immersions  p.87 / Chapter 6.3  Construction of Special Lagrangian 3folds with High Genus Links  p.92 / Bibliography  p.97

9 
Discrete Lagrange equations for reacting thermofluid systemsHean, Charles Robert, 1960 16 October 2012 (has links)
The application of Lagrange's equations to nonequilibrium reacting compressible thermofluid systems yields a modeling methodology for thermofluid dynamics compatible with the discrete energy methods used extensively in other energy domains; examples include mechanical systems simulations and molecular dynamics modeling. The introduction of internal energies as generalized coordinates leads to a thermomechanical model with a simple but general form. A finite element interpolation is used to formulate the ODE model in an ALE reference frame, without reference to any partial differential equations. The formulation is applied to highly nonlinear problems without the use of any timesplitting or shocktracking methods. The method is verified via the solution of a set of example problems which incorporate a variety of reference frames, both open and closed control volumes, and moving boundaries. The example simulations include transient detonations with complex chemistry, pistoninitiated detonations, canonical unstable overdriven detonations, highresolution inductionzone species evolution within a pulsating hydrogenair detonation, and the detonation of a solid explosive due to highvelocity impact. / text

10 
Analysis of the rolling motion of loaded hoops /Theron, Willem Frederick Daniel. January 2008 (has links)
Dissertation (PhD)University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

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