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1.
Allawala, Altan Turowicz.
Direct Statistical Simulation of Chaos and
Turbulence.
Degree: Department of Physics, 2017, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:792604/ 
► Statistical descriptions are well-suited for chaotic systems and turbulent flows. A common strategy for studying the statistics of such systems is Direct Numerical Simulation (DNS).…
(more)
▼ Statistical descriptions are well-suited for chaotic
systems and turbulent flows. A common strategy for studying the
statistics of such systems is Direct Numerical Simulation (DNS).
However accumulating statistics via DNS can be inefficient because
convergence to a statistically steady-state is slow, especially in
systems with rare but large deviations as are often found in
chaotic systems and turbulent flows. Another drawback of DNS is
that it is difficult to extract the physics from the computed
numbers. In this thesis I present two alternative strategies to
directly solve for the statistics. In the first part, a
Fokker-Planck description is used to study the equal-time
statistics of the stochastically-forced Lorenz attractor. In
particular, the steady-state probability distribution of the
attractor is solved for directly by computing the zero mode of a
Fokker-Planck operator. I also investigate a perturbative expansion
in the equal-time cumulants of the system, tested on the Lorenz
attractor and on two idealized barotropic models. Since low-order
statistics tend to be spatially smoother than the corresponding
dynamical fields, this method can capture the macroscopic features
of turbulent flows using fewer degrees of freedom. An added benefit
of such a cumulant expansion scheme is that the small-scale modes
are integrated out, leaving only large-scale modes containing
information about the coherent structures of interest. These modes
are associated with the low-order statistics of the system and
might be described by a fixed point or slow manifold, allowing for
quicker convergence to a statistically steady state. Since this
perturbative expansion suffers from the "curse of dimensionality",
I detail my efforts to resolve this issue via a dimensional
reduction scheme that uses a type of unsupervised machine learning
technique known as Proper Orthogonal Decomposition. This involves
rotating into a new coordinate system spanned by the eigenvectors
of the vorticity second cumulants of the system and retaining only
the most energetic modes. A substantial basis reduction with order
of magnitude computational gains is demonstrated, providing an
accurate alternative to directly accessing the low-order statistics
of turbulent flows.
Advisors/Committee Members: Marston, Brad (Advisor), Pelcovits, Robert (Reader), Mandre, Shreyas (Reader).
Subjects/Keywords: Computational fluid dynamics
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APA (6th Edition):
Allawala, A. T. (2017). Direct Statistical Simulation of Chaos and
Turbulence. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792604/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Allawala, Altan Turowicz. “Direct Statistical Simulation of Chaos and
Turbulence.” 2017. Thesis, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:792604/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Allawala, Altan Turowicz. “Direct Statistical Simulation of Chaos and
Turbulence.” 2017. Web. 22 Jan 2021.
Vancouver:
Allawala AT. Direct Statistical Simulation of Chaos and
Turbulence. [Internet] [Thesis]. Brown University; 2017. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:792604/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Allawala AT. Direct Statistical Simulation of Chaos and
Turbulence. [Thesis]. Brown University; 2017. Available from: https://repository.library.brown.edu/studio/item/bdr:792604/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
2.
Li, Feifei.
Transport in Low Dimensional Strongly Correlated Electronic
System.
Degree: PhD, Physics, 2009, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:203/
► This thesis presents two theoretical investigations on transport in low dimensional strongly correlated electronic systems. In the study of one dimensional system, we demonstrate that…
(more)
▼ This thesis presents two theoretical investigations on
transport in low dimensional strongly correlated electronic
systems. In the study of one dimensional system, we demonstrate
that spin current can be generated by an ac voltage in a
one-channel quantum wire with strong repulsive electron
interactions in the presence of a non-magnetic impurity and uniform
static magnetic field. We show that in a certain range of voltages,
the spin current can exhibit a power dependence on the ac voltage
bias with a negative exponent. The spin current expressed in units
of \hbar/2 per second can become much larger than the charge
current in units of the electron charge per second. The spin
current generation requires neither spin-polarized particle
injection nor time-dependent magnetic fields. In the study of
on-Abelian statistics in two dimensional quantum Hall system, we
suggest an experiment which can determine the physical state for
the ν=5/2 quantum Hall plateau. The proposal involves transport
measurements in the geometry with three quantum Hall edges
connected by two quantum point contacts. In contrast to
interference experiments, this approach can distinguish the
Pfaffian and anti-Pfaffian states as well as different states with
identical Pfaffian or anti-Pfaffian statistics. In addition, the
transport is not sensitive to the fluctuations of the number of the
quasiparticles trapped in the system.
Advisors/Committee Members: Feldman, Dima (director), Marston, Brad (reader), Valles, James (reader).
Subjects/Keywords: Luttinger Liquid
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Manager
APA (6th Edition):
Li, F. (2009). Transport in Low Dimensional Strongly Correlated Electronic
System. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:203/
Chicago Manual of Style (16th Edition):
Li, Feifei. “Transport in Low Dimensional Strongly Correlated Electronic
System.” 2009. Doctoral Dissertation, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:203/.
MLA Handbook (7th Edition):
Li, Feifei. “Transport in Low Dimensional Strongly Correlated Electronic
System.” 2009. Web. 22 Jan 2021.
Vancouver:
Li F. Transport in Low Dimensional Strongly Correlated Electronic
System. [Internet] [Doctoral dissertation]. Brown University; 2009. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:203/.
Council of Science Editors:
Li F. Transport in Low Dimensional Strongly Correlated Electronic
System. [Doctoral Dissertation]. Brown University; 2009. Available from: https://repository.library.brown.edu/studio/item/bdr:203/
3.
Liu, Wencong.
NMR Study of Materials with Significant Spin-Orbit Coupling
and Transparent Oxide Films.
Degree: Department of Physics, 2017, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:792641/
► Spin-orbit coupling (SOC) refers to the interaction between the orbital angular momentum and electron spin, which is typically a small perturbation in relative light elements.…
(more)
▼ Spin-orbit coupling (SOC) refers to the interaction
between the orbital angular momentum and electron spin, which is
typically a small perturbation in relative light elements. However,
such interaction is proportional to the fourth order of the atomic
number and could be quite significant for heavy elements. Exotic
physics arising from significant SOC include the emergent phases in
Mott insulators with strong SOC and the exploded works on
topological insulators (TI). For the first research thread, the
combined effects of strong electronic correlations with SOC can
lead to a plethora of emergent novel quantum states. The second
research thread which also involves strong SOC and correlated
electrons lies at the intersection of topological insulator and
Kondo insulator. In this thesis, we first present an extensive
nuclear magnetic resonance (NMR) study of 23Na in Ba2NaOsO6, a
typical Mott insulator with SOC. We measured 23Na NMR spectra as a
function of temperature in different magnetic fields. The NMR
measurements reveals a paramagnetic at high temperatures, a broken
local point symmetry (BLPS) phase at intermediate temperatures and
a canted ferromagnetic phase at low temperatures. Most importantly,
we determine the field-temperature phase diagram of Ba2NaOsO6 which
shows that the intermediate BLPS phase extends to wider range in
high fields. Furthermore, by adopting numerical calculation, we
confirm that the breaking of local point symmetry is not due to
trivial intrinsic structure instability but is due to multipolar
interaction. Next, angle dependence of NMR spectra show that the
canted ferromagnetic order is suppressed along certain direction at
low temperatures. Secondly, we performed NMR measurements of
spin-lattice relaxation (T1) on 11B of Kondo insulator SmB6 at
ultra-low temperatures in various magnetic fields. We observed
constant low-energy density-of-states (DOS) which corresponds to
gapless excitation.
Advisors/Committee Members: Mitrovic, Vesna (Advisor), Valles, James (Reader), Marston, Brad (Reader).
Subjects/Keywords: Nuclear magnetic resonance
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CSE |
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Manager
APA (6th Edition):
Liu, W. (2017). NMR Study of Materials with Significant Spin-Orbit Coupling
and Transparent Oxide Films. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792641/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Liu, Wencong. “NMR Study of Materials with Significant Spin-Orbit Coupling
and Transparent Oxide Films.” 2017. Thesis, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:792641/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Liu, Wencong. “NMR Study of Materials with Significant Spin-Orbit Coupling
and Transparent Oxide Films.” 2017. Web. 22 Jan 2021.
Vancouver:
Liu W. NMR Study of Materials with Significant Spin-Orbit Coupling
and Transparent Oxide Films. [Internet] [Thesis]. Brown University; 2017. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:792641/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Liu W. NMR Study of Materials with Significant Spin-Orbit Coupling
and Transparent Oxide Films. [Thesis]. Brown University; 2017. Available from: https://repository.library.brown.edu/studio/item/bdr:792641/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
4.
Hu, Rongwei.
Investigation of a d-electron Kondo insulator FeSb2.
Degree: PhD, Physics, 2009, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:185/
► FeSb2 is a narrow band semiconductor, whose magnetic susceptibility strongly resembles that of FeSi, an archetype example of Kondo insulator. The unusual spectral weight transfer…
(more)
▼ FeSb2 is a narrow band semiconductor, whose magnetic
susceptibility strongly resembles that of FeSi, an archetype
example of Kondo insulator. The unusual spectral weight transfer in
the optical conductivity measurement and ab initio LDA+U
calculations imply that FeSb2 is an unconventional semiconductor
with strong electron correlations. In order to study the anisotropy
and probe the electronic structure of FeSb2, single crystals are
grown by high temperature flux method and carriers are introduced
into FeSb2 by substituting Fe and Sb with Co/Cr and Te
respectively. We investigated the magnetic and electrical
properties of FeSb2 and the doping effects. Hall measurement on
FeSb2 reveals that multiple band carriers with very large mobility
difference are involved in the electrical transport. This can be
explained by the orbital selective hybridization of the Fe
d-orbitals with Sb-p electrons in FeSb2 involving only one
electronic subsystem. Band structure calculation suggests that
FeSb2 is close to a magnetic instability. Indeed, various magnetic
orders are experimentally observed in doped FeSb2. For example, the
activated Pauli paramagnetism of FeSb2 evolves into a weak
ferromagnetism in Fe1-xCoxSb2 and a complex canted
antiferromagnetic structure in Fe1-xCrxSb2 and Fe(Sb1-xTex)2.
Metallic states are readily induced by doping FeSb2 as a result of
band filling. Positive colossal magnetoresistance mainly attributed
to quasi 1D weak localization is observed in Co doped FeSb2. With
Te substitution, FeSb2 evolves from a strongly correlated
semiconductor into a moderate heavy fermion metal. Most of the
Kondo insulator materials are cubic, with the exception of CeRhSb
and CeNiSn, and 4f intermetallics. An important question is that if
the Kondo insulator scenario can be applied to 3d materials, e.g.
FeSi and FeSb2. FeSb2 can be obtained in single crystal form with
high quality and can be readily doped with carriers, thus it
represents a model system with only 3d elements to study this
physics. Our results indicate that the underling physics of FeSb2
can be well described by the Kondo insulator picture and FeSb2
resembles FeSi in many ways as a prototypical example of a
nonrare-earth containing Kondo insulator.
Advisors/Committee Members: Mitrovic, Vesna (director), Petrovic, Cedomir (director), Marston, Brad (reader), Valles, James (reader).
Subjects/Keywords: Kondo Insulator
Record Details
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Record Details
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APA ·
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MLA ·
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CSE |
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Manager
APA (6th Edition):
Hu, R. (2009). Investigation of a d-electron Kondo insulator FeSb2. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:185/
Chicago Manual of Style (16th Edition):
Hu, Rongwei. “Investigation of a d-electron Kondo insulator FeSb2.” 2009. Doctoral Dissertation, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:185/.
MLA Handbook (7th Edition):
Hu, Rongwei. “Investigation of a d-electron Kondo insulator FeSb2.” 2009. Web. 22 Jan 2021.
Vancouver:
Hu R. Investigation of a d-electron Kondo insulator FeSb2. [Internet] [Doctoral dissertation]. Brown University; 2009. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:185/.
Council of Science Editors:
Hu R. Investigation of a d-electron Kondo insulator FeSb2. [Doctoral Dissertation]. Brown University; 2009. Available from: https://repository.library.brown.edu/studio/item/bdr:185/
. 
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