Matching Items (13)

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Fluid flow in a temperature-stratified, parametrically forced regime

Description

This project is a synthesis of the author's learning over the semesters in working with the CFD Group at Arizona State University. The incompressible Navier-Stokes equations are overviewed, starting with

This project is a synthesis of the author's learning over the semesters in working with the CFD Group at Arizona State University. The incompressible Navier-Stokes equations are overviewed, starting with the derivation from the continuity equation, then non-dimensionalization, methods of solving and computing quantities of interest. The rest of this document is expository analysis of solutions in a confined fluid flow, building toward a parametrically forced regime that generates complex flow patterns including Faraday waves. The solutions come from recently published studies Dynamics in a stably stratified tilted square cavity (Grayer et al.) and Parametric instabilities of a stratified shear layer (Buchta et al).

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Date Created
  • 2021-05

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Comparison of MIMD and SIMT Parallel Iterative Solvers for Laplace's Equation

Description

A comparison of the performance of CUDA versus OpenMP for Jacobi, Gauss-Seidel, and S.O.R. iterative methods for Laplace's Equation with Dirichlet boundary conditions is presented. Both the number of cores

A comparison of the performance of CUDA versus OpenMP for Jacobi, Gauss-Seidel, and S.O.R. iterative methods for Laplace's Equation with Dirichlet boundary conditions is presented. Both the number of cores and the grid size were varied for the OpenMP program, while the grid size was varied for the CUDA program. CUDA outperforms the 8-core OpenMP program with the Jacobi and Gauss-Seidel schemes for all grid sizes, and is competitive with S.O.R for all grid sizes examined.

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Created

Date Created
  • 2013-05

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Optimal Sampling for Function Approximation

Description

This thesis project focuses on algorithms that generate good sampling points for function approximation. In one dimension, polynomial interpolation using equispaced points is unstable, with high Oscillations near the

This thesis project focuses on algorithms that generate good sampling points for function approximation. In one dimension, polynomial interpolation using equispaced points is unstable, with high Oscillations near the endpoints of the interpolated interval. On the other hand, Chebyshev nodes provide both stable and highly accurate points for polynomial interpolation. In higher dimensions, optimal sampling points are unknown. This project addresses this problem by finding algorithms that are robust in various domains for polynomial interpolation and least-squares. To measure the quality of the nodes produced by said algorithms, the Lebesgue constant will be used. In the algorithms, a number of numerical techniques will be used, such as the Gram-Schmidt process and the pivoted-QR process. In addition, concepts such as node density and greedy algorithms will be explored.

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Agent

Created

Date Created
  • 2021-05

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Two-Dimensional Stratified Cavity Flow Under Harmonic Forcing

Description

We study an idealized model of a wind-driven ocean, namely a 2-D lid-driven cavity with a linear temperature gradient along the side walls and constant hot and cold temperatures on

We study an idealized model of a wind-driven ocean, namely a 2-D lid-driven cavity with a linear temperature gradient along the side walls and constant hot and cold temperatures on the top and bottom boundaries respectively. In particular, we determine numerically the response on flow field and temperature stratification associated with the velocity of the lid driven by harmonic forcing using the Navier-Stokes equations with Boussinesq approximation in an attempt to gain an understanding of how variations of external forces (such as the wind over the ocean) transfer energy to a system by exciting internal modes through resonances. The time variation of the forcing, accounting for turbulence at the boundary is critical for allowing penetration of energy waves through the stratified medium in which the angles of the internal waves depend on these perturbation frequencies. Determining the results of the interaction of two 45 degree angle wave beams at the center of the cavity is of particular interest.

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Created

Date Created
  • 2015-05

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Design and Analysis of Algorithmic Trading Automation

Description

With the coming advances of computational power, algorithmic trading has become one of the primary strategies to trading on the stock market. To understand why and how these strategies have

With the coming advances of computational power, algorithmic trading has become one of the primary strategies to trading on the stock market. To understand why and how these strategies have been effective, this project has taken a look at the complete process of creating tools and applications to analyze and predict stock prices in order to perform low-frequency trading. The project is composed of three main components. The first component is integrating several public resources to acquire and process financial trading data and store it in order to complete the other components. Alpha Vantage API, a free open source application, provides an accurate and comprehensive dataset of features for each stock ticker requested. The second component is researching, prototyping, and implementing various trading algorithms in code. We began by focusing on the Mean Reversion algorithm as a proof of concept algorithm to develop meaningful trading strategies and identify patterns within our datasets. To augment our market prediction power (“alpha”), we implemented a Long Short-Term Memory recurrent neural network. Neural Networks are an incredibly effective but often complex tool used frequently in data science when traditional methods are found lacking. Following the implementation, the last component is to optimize, analyze, compare, and contrast all of the algorithms and identify key features to conclude the overall effectiveness of each algorithm. We were able to identify conclusively which aspects of each algorithm provided better alpha and create an entire pipeline to automate this process for live trading implementation. An additional reason for automation is to provide an educational framework such that any who may be interested in quantitative finance in the future can leverage this project to gain further insight.

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Agent

Created

Date Created
  • 2019-05

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Rotating split-cylinder flows

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

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.

Contributors

Agent

Created

Date Created
  • 2017

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Critical coupling and synchronized clusters in arbitrary networks of Kuramoto oscillators

Description

The Kuramoto model is an archetypal model for studying synchronization in groups

of nonidentical oscillators where oscillators are imbued with their own frequency and

coupled with other oscillators though a network of

The Kuramoto model is an archetypal model for studying synchronization in groups

of nonidentical oscillators where oscillators are imbued with their own frequency and

coupled with other oscillators though a network of interactions. As the coupling

strength increases, there is a bifurcation to complete synchronization where all oscillators

move with the same frequency and show a collective rhythm. Kuramoto-like

dynamics are considered a relevant model for instabilities of the AC-power grid which

operates in synchrony under standard conditions but exhibits, in a state of failure,

segmentation of the grid into desynchronized clusters.

In this dissertation the minimum coupling strength required to ensure total frequency

synchronization in a Kuramoto system, called the critical coupling, is investigated.

For coupling strength below the critical coupling, clusters of oscillators form

where oscillators within a cluster are on average oscillating with the same long-term

frequency. A unified order parameter based approach is developed to create approximations

of the critical coupling. Some of the new approximations provide strict lower

bounds for the critical coupling. In addition, these approximations allow for predictions

of the partially synchronized clusters that emerge in the bifurcation from the

synchronized state.

Merging the order parameter approach with graph theoretical concepts leads to a

characterization of this bifurcation as a weighted graph partitioning problem on an

arbitrary networks which then leads to an optimization problem that can efficiently

estimate the partially synchronized clusters. Numerical experiments on random Kuramoto

systems show the high accuracy of these methods. An interpretation of the

methods in the context of power systems is provided.

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Agent

Created

Date Created
  • 2018

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Robust experimental designs for fMRI with an uncertain design matrix

Description

Obtaining high-quality experimental designs to optimize statistical efficiency and data quality is quite challenging for functional magnetic resonance imaging (fMRI). The primary fMRI design issue is on the selection of

Obtaining high-quality experimental designs to optimize statistical efficiency and data quality is quite challenging for functional magnetic resonance imaging (fMRI). The primary fMRI design issue is on the selection of the best sequence of stimuli based on a statistically meaningful optimality criterion. Some previous studies have provided some guidance and powerful computational tools for obtaining good fMRI designs. However, these results are mainly for basic experimental settings with simple statistical models. In this work, a type of modern fMRI experiments is considered, in which the design matrix of the statistical model depends not only on the selected design, but also on the experimental subject's probabilistic behavior during the experiment. The design matrix is thus uncertain at the design stage, making it diffcult to select good designs. By taking this uncertainty into account, a very efficient approach for obtaining high-quality fMRI designs is developed in this study. The proposed approach is built upon an analytical result, and an efficient computer algorithm. It is shown through case studies that the proposed approach can outperform an existing method in terms of computing time, and the quality of the obtained designs.

Contributors

Agent

Created

Date Created
  • 2014

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Optimum Experimental Design Issues in Functional Neuroimaging Studies

Description

Functional magnetic resonance imaging (fMRI) is one of the popular tools to study human brain functions. High-quality experimental designs are crucial to the success of fMRI experiments as they allow

Functional magnetic resonance imaging (fMRI) is one of the popular tools to study human brain functions. High-quality experimental designs are crucial to the success of fMRI experiments as they allow the collection of informative data for making precise and valid inference with minimum cost. The primary goal of this study is on identifying the best sequence of mental stimuli (i.e. fMRI design) with respect to some statistically meaningful optimality criteria. This work focuses on two related topics in this research field. The first topic is on finding optimal designs for fMRI when the design matrix is uncertain. This challenging design issue occurs in many modern fMRI experiments, in which the design matrix of the statistical model depends on both the selected design and the experimental subject's uncertain behavior during the experiment. As a result, the design matrix cannot be fully determined at the design stage that makes it difficult to select a good design. For the commonly used linear model with autoregressive errors, this study proposes a very efficient approach for obtaining high-quality fMRI designs for such experiments. The proposed approach is built upon an analytical result, and an efficient computer algorithm. It is shown through case studies that our proposed approach can outperform the existing method in terms of computing time, and the quality of the obtained designs. The second topic of the research is to find optimal designs for fMRI when a wavelet-based technique is considered in the fMRI data analysis. An efficient computer algorithm to search for optimal fMRI designs for such cases is developed. This algorithm is inspired by simulated annealing and a recently proposed algorithm by Saleh et al. (2017). As demonstrated in the case studies, the proposed approach makes it possible to efficiently obtain high-quality designs for fMRI studies, and is practically useful.

Contributors

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Created

Date Created
  • 2017

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Parametrically forced rotating and/or stratified confined flows

Description

The dynamics of a fluid flow inside 2D square and 3D cubic cavities

under various configurations were simulated and analyzed using a

spectral code I developed.

This code was validated against known

The dynamics of a fluid flow inside 2D square and 3D cubic cavities

under various configurations were simulated and analyzed using a

spectral code I developed.

This code was validated against known studies in the 3D lid-driven

cavity. It was then used to explore the various dynamical behaviors

close to the onset of instability of the steady-state flow, and explain

in the process the mechanism underlying an intermittent bursting

previously observed. A fairly complete bifurcation picture emerged,

using a combination of computational tools such as selective

frequency damping, edge-state tracking and subspace restriction.

The code was then used to investigate the flow in a 2D square cavity

under stable temperature stratification, an idealized version of a lake

with warmer water at the surface compared to the bottom. The governing

equations are the Navier-Stokes equations under the Boussinesq approximation.

Simulations were done over a wide range of parameters of the problem quantifying

the driving velocity at the top (e.g. wind) and the strength of the stratification.

Particular attention was paid to the mechanisms associated with the onset of

instability of the base steady state, and the complex nontrivial dynamics

occurring beyond onset, where the presence of multiple states leads to a

rich spectrum of states, including homoclinic and heteroclinic chaos.

A third configuration investigates the flow dynamics of a fluid in a rapidly

rotating cube subjected to small amplitude modulations. The responses were

quantified by the global helicity and energy measures, and various peak

responses associated to resonances with intrinsic eigenmodes of the cavity

and/or internal retracing beams were clearly identified for the first time.

A novel approach to compute the eigenmodes is also described, making accessible

a whole catalog of these with various properties and dynamics. When the small

amplitude modulation does not align with the rotation axis (precession) we show

that a new set of eigenmodes are primarily excited as the angular velocity

increases, while triadic resonances may occur once the nonlinear regime kicks in.

Contributors

Agent

Created

Date Created
  • 2019