Matching Items (4)
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- All Subjects: Dynamical Systems
- Creators: Platte, Rodrigo
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
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.
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.
ContributorsYalim, Jason (Author) / Welfert, Bruno D. (Thesis advisor) / Lopez, Juan M. (Thesis advisor) / Jones, Donald (Committee member) / Tang, Wenbo (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2019
Description
The three-dimensional flow contained in a rapidly rotating circular
split cylinder is studied numerically solving the Navier--Stokes
equations. The cylinder is completely filled with fluid
and is split at the midplane. Three different types of boundary
conditions were imposed, leading to a variety of instabilities and
complex flow dynamics.
The first configuration has a strong background rotation and a small
differential rotation between the two halves. The axisymmetric flow
was first studied identifying boundary layer instabilities which
produce inertial waves under some conditions. Limit cycle states and
quasiperiodic states were found, including some period doubling
bifurcations. Then, a three-dimensional study was conducted
identifying low and high azimuthal wavenumber rotating waves due to
G’ortler and Tollmien–-Schlichting type instabilities. Over most of
the parameter space considered, quasiperiodic states were found where
both types of instabilities were present.
In the second configuration, both cylinder halves are in exact
counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic
is dominated by the shear layer created
in the midplane. By changing the speed rotation and the aspect ratio
of the cylinder, the flow loses symmetries in a variety of ways
creating static waves, rotating waves, direction reversing waves and
slow-fast pulsing waves. The bifurcations, including infinite-period
bifurcations, were characterized and the flow dynamics was elucidated.
Additionally, preliminary experimental results for this case are
presented.
In the third set up, with oscillatory boundary conditions, inertial
wave beams were forced imposing a range of frequencies. These beams
emanate from the corner of the cylinder and from the split at the
midplane, leading to destructive/constructive interactions which
produce peaks in vorticity for some specific frequencies. These
frequencies are shown to be associated with the resonant Kelvin
modes. Furthermore, a study of the influence of imposing a phase
difference between the oscillations of the two halves of the cylinder
led to the interesting result that different Kelvin
modes can be excited depending on the phase difference.
split cylinder is studied numerically solving the Navier--Stokes
equations. The cylinder is completely filled with fluid
and is split at the midplane. Three different types of boundary
conditions were imposed, leading to a variety of instabilities and
complex flow dynamics.
The first configuration has a strong background rotation and a small
differential rotation between the two halves. The axisymmetric flow
was first studied identifying boundary layer instabilities which
produce inertial waves under some conditions. Limit cycle states and
quasiperiodic states were found, including some period doubling
bifurcations. Then, a three-dimensional study was conducted
identifying low and high azimuthal wavenumber rotating waves due to
G’ortler and Tollmien–-Schlichting type instabilities. Over most of
the parameter space considered, quasiperiodic states were found where
both types of instabilities were present.
In the second configuration, both cylinder halves are in exact
counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic
is dominated by the shear layer created
in the midplane. By changing the speed rotation and the aspect ratio
of the cylinder, the flow loses symmetries in a variety of ways
creating static waves, rotating waves, direction reversing waves and
slow-fast pulsing waves. The bifurcations, including infinite-period
bifurcations, were characterized and the flow dynamics was elucidated.
Additionally, preliminary experimental results for this case are
presented.
In the third set up, with oscillatory boundary conditions, inertial
wave beams were forced imposing a range of frequencies. These beams
emanate from the corner of the cylinder and from the split at the
midplane, leading to destructive/constructive interactions which
produce peaks in vorticity for some specific frequencies. These
frequencies are shown to be associated with the resonant Kelvin
modes. Furthermore, a study of the influence of imposing a phase
difference between the oscillations of the two halves of the cylinder
led to the interesting result that different Kelvin
modes can be excited depending on the phase difference.
ContributorsGutierrez Castillo, Paloma (Author) / Lopez, Juan M. (Thesis advisor) / Herrmann, Marcus (Committee member) / Platte, Rodrigo (Committee member) / Welfert, Bruno (Committee member) / Tang, Wenbo (Committee member) / Arizona State University (Publisher)
Created2017
DescriptionUnderstanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.
ContributorsWeber, Dylan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicolas (Committee member) / Platte, Rodrigo (Committee member) / Armbruster, Dieter (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2021