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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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  • 12 2015

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Items (1-12) out of 12 results

Analysis and Simulation of Molecular Systems: Memory Function Approach and Uncertainty Quantification

Description:
The mesoscopic description of molecular systems is investigated by using the memory function approach, and uncertainty quantification methods are developed for the evaluation of time …
Year:
2015
Contributor:
Kim, Changho (creator)
Karniadakis, George (Director)
Matzavinos, Anastasios (Reader)
Stratt, Richard (Reader)
Borodin, Oleg (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Generalized Langevin equation
Brownian motion
Molecular dynamics simulation
Brownian motion processes
Molecular dynamics--Simulation methods
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Combinatorial and Geometric Structure in the Self-Assembly of Polyhedra

Description:
We consider a discrete attachment model for the self-assembly of polyhedra called the Building Game. The combinatorial configuration space of the model is computed for …
Year:
2015
Contributor:
Johnson, Daniel C (creator)
Menon, Govind (Director)
Gidas, Basilis (Reader)
Holmes-Cerfon, Miranda (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Self-Assembly
Polyhedra
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Compatible high-order meshless schemes for viscous flows through l2 optimization

Description:
Meshless methods provide an ideal framework for scalably simulating Lagrangian hydrodynamics in domains undergoing large deformation. For these schemes, interfaces can easily be treated without …
Year:
2015
Contributor:
Trask, Nathaniel A (creator)
Maxey, Martin (Director)
Karniadakis, George (Reader)
Shu, Chi-Wang (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
compatible discretization
numerical pde
meshless method
mimetic method
Meshfree methods (Numerical analysis)
Graph theory
Computational fluid dynamics
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Data-Driven Parallel Scientific Computing: Multi-Fidelity Information Fusion Algorithms and Applications to Physical and Biological Systems

Description:
This thesis takes aim at two directions. The first direction involves setting the foundations for a new type of data-driven scientific computing, essentially creating a …
Year:
2015
Contributor:
Perdikaris, Paris (creator)
Karniadakis, George (Director)
Royset, Johannes (Reader)
Venturi, Daniele (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Multi-fidelity modeling
High performance scientific computing
Design optimization
Uncertainty quantification
Arterial biomechanics
Inverse problems
Machine learning
Big data
Blood flow
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Existence and Stability of Spatially Localized Planar Patterns

Description:
Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been …
Year:
2015
Contributor:
Makrides, Elizabeth (creator)
Sandstede, Bjorn (Director)
Beck, Margaret (Reader)
Menon, Govind (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
dynamical systems
pattern formation
PDEs
spatial dynamics
Evans function
Dynamics
Pattern formation (Physical sciences)
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit

Description:
In this dissertation, we mainly discuss two topics of partial differential equations in fluid dynamics and kinetic theory: viscous surface wave and diffusive limit. With …
Year:
2015
Contributor:
Wu, Lei (creator)
Guo, Yan (Director)
Shu, Chi-Wang (Director)
Dong, Hongjie (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
free surface
Milne problem
geometric correction
Interpolation
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

High-Dimensional Response-Excitation PDF Methods for Uncertainty Quantification and Stochastic Modeling

Description:
The probability density approach based on the response-excitation theory is developed for stochastic simulations of non-Markovian systems. This approach provides the complete probabilistic configuration of …
Year:
2015
Contributor:
Cho, Heyrim (creator)
Karniadakis, George (Director)
Rozovsky, Boris (Reader)
Venturi, Daniele (Reader)
Sapsis, Themistoklis (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Uncertainty quantification
Numerical PDE
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Moderate Deviations and Subsolution-Based Importance Sampling for Recursive Stochastic Algorithms

Description:
We prove a moderate deviations principle for the continuous time linear interpolation of discrete time recursive stochastic processes, and then investigate importance sampling schemes based …
Year:
2015
Contributor:
Johnson, Dane Michael (creator)
Dupuis, Paul (Director)
Ramanan, Kavita (Reader)
Budhiraja, Amarjit (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Weak Convergence
Importance Sampling
Large deviations
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Numerical methods for stochastic systems subject to generalized Levy noise

Description:
In this thesis, we aim to improve the accuracy and efficiency in uncertainty quantification (UQ) of stochastic partial differential equations (SPDEs) driven by Levy jump …
Year:
2015
Contributor:
Zheng, Mengdi (creator)
Karniadakis, George (Director)
Wang, Hui (Reader)
Wan, Xiaoliang (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
uncertainty quantification
Levy jump process
gPC
fractional dynamics
Fokker-Planck equation
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

On Numerical Models of Calcium-Induced Calcium Release

Description:
In this thesis, we examine hybrid numerical models of calcium-induced calcium release using deterministic PDEs for the diffusion of cytosolic calcium and a stochastic process …
Year:
2015
Contributor:
Nixon, Andrew T L (creator)
Sandstede, Björn (Director)
Matzavinos, Anastasios (Reader)
Maxey, Martin (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
calcium-induced calcium release
Calcium channels
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Spectral and Spectral Element Methods for Fractional PDEs

Description:
We develop a new spectral theory of fractional Sturm-Liouville problems and further generalize it to a tempered class of eigen-problems. Our theory fractionalizes and then …
Year:
2015
Contributor:
Zayernouri, Mohsen (creator)
Karniadakis, George (Director)
Ainsworth, Mark (Reader)
Hesthaven, Jan (Reader)
Meerschaert, Mark (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Fractional PDEs
Fractional Sturm-Liouville Problems
Jacobi Polyfractonomials
Petrov-Galerkin Spectral Methods
DG Spectral Element Methods
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

The Incidental Parameter Problem in Network Analysis for Neural Spiking Data

Description:
The spiking electrical activity of simultaneously recorded neurons is often modeled as a multivariate binary time series. Inference about the fast temporal correlation structure of …
Year:
2015
Contributor:
Nadkarni, Dahlia (creator)
Harrison, Matthew (Director)
Geman, Stuart (Reader)
Amarasingham, Asohan (Reader)
Brown University. Applied Mathematics (sponsor)
Genre:
theses
Subject:
Incidental parameter problems
Conditional inference
Language:
English
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-12) out of 12 results