Matching Items (8)
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- All Subjects: Quantum Mechanics
- All Subjects: WENO
- Creators: Gardner, Carl
- Creators: Comfort, Joseph
- Resource Type: Text
- Status: Published
Description
In 2010, two gamma-ray /x-ray bubbles were detected in the center of the Milky Way Galaxy. These bubbles extend symmetrically ≈ 30, 000 light years above and below the Galactic Center, with a width of ≈ 27, 000 light years. These bubbles emit gamma-rays at energies between 1 and 100 giga-electronvolts, have approximately uniform surface brightness, and are expanding at ≈ 30, 000 km/s. We believe that these Fermi Bubbles are the result of an astrophysical jet pulse that occurred millions of years ago. Utilizing high-performance computing and Euler’s Gas Dynamics Equations, we hope to find a realistic simulation that will tell us more about the age of these Fermi Bubbles and better understand the mechanism that powers the bubbles.
ContributorsWagner, Benjamin Leng (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Computing and Informatics Program (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The longstanding issue of how much time it takes a particle to tunnel through quantum barriers is discussed; in particular, the phenomenon known as the Hartman effect is reviewed. A calculation of the dwell time for two successive rectangular barriers in the opaque limit is given and the result depends on the barrier widths and hence does not lead to superluminal tunneling or the Hartman effect.
ContributorsMcDonald, Scott (Author) / Davies, Paul (Thesis director) / Comfort, Joseph (Committee member) / McCartney, M. R. (Committee member) / Barrett, The Honors College (Contributor)
Created2009-05
Description
This project discusses simulation results of star formation by Active Galactic Nuclei (AGN) jets using the WENO method. A typical AGN jet with velocity uj=0.3c, density ρj=10^(-2) H/cm3, and temperature Tj=10^(7) K was injected into a 425 light years square region. The jet passes through a stationary inhomogeneous ambient background of temperature Ta=5x10^4 K and density ρa= 2 H/cm^3 to test if AGN jets, by creating bow shocks propagating through the interstellar medium and molecular clouds, can form stars in the densest regions. According to the star formation criteria for gravitational collapse of Cen and Ostriker, the resulting simulations indicate the presence of star formation via AGN jets (1992). The parameters are tuned to match Centaurs A to identify star formation in this galaxy. The simulations will also be run in three dimensions in the future and for longer time intervals to gain a better understanding of the star formation process via AGN jets.
ContributorsFindley, Christina Marie (Author) / Gardner, Carl (Thesis director) / Scannapieco, Evan (Committee member) / Barrett, The Honors College (Contributor) / School of Earth and Space Exploration (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
ContributorsLanfear, Nathan A (Author) / Suslov, Sergei (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Platte, Rodrigo (Committee member) / Matyushov, Dmitry (Committee member) / Kuiper, Hendrik (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016
Description
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This project attempts to create an accurate numerical simulation of the eastern limb of the HH 901 jet in the Mystic Mountain formation located in the Carina Nebula. Using a 3rd order accurate WENO numerical scheme in space, and a 3rd order accurate RK method in time, the temperature, density, radiative cooling, length, and average jet velocity of this astrophysical phenomenon were simulated based on observations made by Hubble Space Telescope and the work of Reiter and Smith (2013) and (2014). The results of this simulation are displayed in three figures, one each for temperature, radiative cooling, and density, which show a jet displaying morphology consistent with that of the HH 901 eastern limb without adjustment for stellar wind. Also discussed are the effects of different jet speeds, initial conditions, and pulse parameters on the shape and behavior of the simulated jets, as well as continuing work to be done on the simulation to enhance its accuracy and usefulness.
ContributorsKreitzer, Kyle (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Glioblastoma brain tumors are among the most lethal human cancers. Treatment efforts typically involve both surgical tumor removal, as well as ongoing therapy. In this work, we propose the use of deuterium magnetic resonance imaging (MRI) to delineate tumor boundaries based on spatial distributions of deuterated leucine, as well as resolve the metabolism of leucine within the tumor. Accurate boundary identification contributes to effectiveness of tumor removal efforts, while amino acid metabolism information may help characterize tumor malignancy and guide ongoing treatment. So, we first examine the fundamental mechanisms of deuterium MRI. We then discuss the use of spin-echo and gradient recall echo sequences for mapping spatial distributions of deuterated leucine, and the use of single-voxel spectroscopy for imaging metabolites within a tumor.
ContributorsCostelle, Anna (Author) / Beeman, Scott (Thesis director) / Kodibagkar, Vikram (Committee member) / Barrett, The Honors College (Contributor) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05
Description
The purpose of this thesis is to accurately simulate in 3D the HH901 jet in the Mystic Mountain Formation of the Carina Nebula. Astronomers present a narrow-band Wide Field Camera image of Carina and the morphology of some astrophysical jets, including HH901. The simulation attempts to replicate features of the jet, among which are pulses, bow shock, terminal Mach disk, and Kelvin-Helmholtz rollup. We use the gas dynamical equations to solve for density, velocity, and temperature. The numerical methods used to solve the equations are third-order WENO (weighted essentially non-oscillatory) and third-order Runge-Kutta. Graphs of density and radiative cooling demonstrate the effect of adding wind (nonzero ambient velocity). The paper discusses the altering of the ambient velocity and final time to fit the shape of the jet in the Hubble image. The suggested next steps are simulating the other HH901 jet and comparing the jets’ atomic makeups to advance understanding of astrophysical jets.
ContributorsBuyer, Michael (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05