Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- SelectedWorks (25)
- Illinois State University (9)
- Selected Works (4)
- University of Arkansas, Fayetteville (4)
- University of Tennessee, Knoxville (2)
-
- Arcadia University (1)
- California Polytechnic State University, San Luis Obispo (1)
- City University of New York (CUNY) (1)
- Georgia Southern University (1)
- Mississippi State University (1)
- Southern Methodist University (1)
- The Texas Medical Center Library (1)
- The University of Akron (1)
- University of Kentucky (1)
- University of New Hampshire (1)
- University of New Mexico (1)
- Virginia Commonwealth University (1)
- Western University (1)
- Keyword
-
- Informacje dla studentów (in Polish) (18)
- Prace ze studentami (in Polish) (8)
- Algorithms (3)
- Biogaz (2)
- Economy - Gospodarka (2)
-
- Energetyka (2)
- Matrices (2)
- 2001-2010 (1)
- Approximation (1)
- Asymptotic (1)
- Badania (1)
- Biogaz; oksy-reforming; wodór (1)
- Biomass (1)
- Bombay Phenotype (1)
- CFD (1)
- CO2 separation (1)
- COVID19 (1)
- Carbon Nanotubes (1)
- Carbonic anhydrase (1)
- Chaos (1)
- Classical memory (1)
- Coarse-graining (1)
- Coats-Redfern method (1)
- Commodity processors (1)
- Computational (1)
- Consultancy (1)
- Cooperation (1)
- Dense matrices (1)
- Dynamic scheduling (1)
- ETD (1)
- Publication Year
- Publication
-
- Wojciech Budzianowski (29)
- Annual Symposium on Biomathematics and Ecology Education and Research (9)
- Mathematical Sciences Spring Lecture Series (4)
- Biology and Medicine Through Mathematics Conference (1)
- Capstone Showcase (1)
-
- Chancellor’s Honors Program Projects (1)
- Dissertations & Theses (Open Access) (1)
- Dissertations, Theses, and Capstone Projects (1)
- Electronic Theses and Dissertations (1)
- Electronic Thesis and Dissertation Repository (1)
- Honors Theses and Capstones (1)
- Masters Theses (1)
- Mathematics Theses and Dissertations (1)
- Physics (1)
- Shared Knowledge Conference (1)
- Theses and Dissertations (1)
- Theses and Dissertations--Mechanical Engineering (1)
- Williams Honors College, Honors Research Projects (1)
- Publication Type
Articles 1 - 30 of 57
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley
Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley
Dissertations & Theses (Open Access)
The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and
several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept
for a high dose rate, high precision converging beam small animal irradiation platform.
In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for
high output and high directionality was designed and characterized. In the second aim, an
optimization algorithm was developed to customize a collimator geometry for this unique Xray
source to simultaneously maximize the irradiator’s intensity and precision. Then, a full
converging beam irradiator apparatus was fit with a multitude …
Physics-Informed Neural Networks For Agent-Based Epidemiological Model Calibration, Alvan C. Arulandu, Padmanabhan Seshaiyer
Physics-Informed Neural Networks For Agent-Based Epidemiological Model Calibration, Alvan C. Arulandu, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Application Of Physics Informed Neural Networks For Predicting Disease Dynamics, Alonso Gabriel Ogueda, Padmanabhan Seshaiyer
Application Of Physics Informed Neural Networks For Predicting Disease Dynamics, Alonso Gabriel Ogueda, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Data-Driven Exploration Of Coarse-Grained Equations: Harnessing Machine Learning, Elham Kianiharchegani
Data-Driven Exploration Of Coarse-Grained Equations: Harnessing Machine Learning, Elham Kianiharchegani
Electronic Thesis and Dissertation Repository
In scientific research, understanding and modeling physical systems often involves working with complex equations called Partial Differential Equations (PDEs). These equations are essential for describing the relationships between variables and their derivatives, allowing us to analyze a wide range of phenomena, from fluid dynamics to quantum mechanics. Traditionally, the discovery of PDEs relied on mathematical derivations and expert knowledge. However, the advent of data-driven approaches and machine learning (ML) techniques has transformed this process. By harnessing ML techniques and data analysis methods, data-driven approaches have revolutionized the task of uncovering complex equations that describe physical systems. The primary goal in …
Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer
Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
Theses and Dissertations
The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …
High-Order Flexible Multirate Integrators For Multiphysics Applications, Rujeko Chinomona
High-Order Flexible Multirate Integrators For Multiphysics Applications, Rujeko Chinomona
Mathematics Theses and Dissertations
Traditionally, time integration methods within multiphysics simulations have been chosen to cater to the most restrictive dynamics, sometimes at a great computational cost. Multirate integrators accurately and efficiently solve systems of ordinary differential equations that exhibit different time scales using two or more time steps. In this thesis, we explore three classes of time integrators that can be classified as one-step multi-stage multirate methods for which the slow dynamics are evolved using a traditional one step scheme and the fast dynamics are solved through a sequence of modified initial value problems. Practically, the fast dynamics are subcycled using a small …
Lecture 14: Randomized Algorithms For Least Squares Problems, Ilse C.F. Ipsen
Lecture 14: Randomized Algorithms For Least Squares Problems, Ilse C.F. Ipsen
Mathematical Sciences Spring Lecture Series
The emergence of massive data sets, over the past twenty or so years, has lead to the development of Randomized Numerical Linear Algebra. Randomized matrix algorithms perform random sketching and sampling of rows or columns, in order to reduce the problem dimension or compute low-rank approximations. We review randomized algorithms for the solution of least squares/regression problems, based on row sketching from the left, or column sketching from the right. These algorithms tend to be efficient and accurate on matrices that have many more rows than columns. We present probabilistic bounds for the amount of sampling required to achieve a …
Lecture 13: A Low-Rank Factorization Framework For Building Scalable Algebraic Solvers And Preconditioners, X. Sherry Li
Lecture 13: A Low-Rank Factorization Framework For Building Scalable Algebraic Solvers And Preconditioners, X. Sherry Li
Mathematical Sciences Spring Lecture Series
Factorization based preconditioning algorithms, most notably incomplete LU (ILU) factorization, have been shown to be robust and applicable to wide ranges of problems. However, traditional ILU algorithms are not amenable to scalable implementation. In recent years, we have seen a lot of investigations using low-rank compression techniques to build approximate factorizations.
A key to achieving lower complexity is the use of hierarchical matrix algebra, stemming from the H-matrix research. In addition, the multilevel algorithm paradigm provides a good vehicle for a scalable implementation. The goal of this lecture is to give an overview of the various hierarchical matrix formats, such …
Lecture 11: The Road To Exascale And Legacy Software For Dense Linear Algebra, Jack Dongarra
Lecture 11: The Road To Exascale And Legacy Software For Dense Linear Algebra, Jack Dongarra
Mathematical Sciences Spring Lecture Series
In this talk, we will look at the current state of high performance computing and look at the next stage of extreme computing. With extreme computing, there will be fundamental changes in the character of floating point arithmetic and data movement. In this talk, we will look at how extreme-scale computing has caused algorithm and software developers to change their way of thinking on implementing and program-specific applications.
Lecture 01: Scalable Solvers: Universals And Innovations, David Keyes
Lecture 01: Scalable Solvers: Universals And Innovations, David Keyes
Mathematical Sciences Spring Lecture Series
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the …
Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons
Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons
Honors Theses and Capstones
No abstract provided.
Personalized Immunotherapy Treatment Strategies For A System Of Chronic Myelogenous Leukemia, Paul Valle
Personalized Immunotherapy Treatment Strategies For A System Of Chronic Myelogenous Leukemia, Paul Valle
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce
Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce
Biology and Medicine Through Mathematics Conference
No abstract provided.
Modeling Gene Expression With Differential Equations, Madison Kuduk
Modeling Gene Expression With Differential Equations, Madison Kuduk
Capstone Showcase
Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in …
Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter
Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Period Drift In A Neutrally Stable Stochastic Oscillator, Kevin Sanft
Period Drift In A Neutrally Stable Stochastic Oscillator, Kevin Sanft
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera
Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera
Williams Honors College, Honors Research Projects
Coherency strains appear in interacting atomic monolayers due to differing bond lengths, which can arise from different materials or geometries. Examples include extended monolayers interacting with a substrate and the interacting walls of a multi-walled carbon nanotube. These strains can induce various equilibrium configurations, which we will analyze by means of a phenomenological model that incorporates forces from bond stretching and bending within each layer and the weak van der Waals interactions connecting the separate layers. We vary the strengths of each interaction to explore their effects on equilibrium structures, and the specific case of a two-walled carbon nanotube is …
Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski
Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe
Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe
Shared Knowledge Conference
Chemical Reaction Networks (CRNs) are a popular tool in the chemical sciences for providing a means of analyzing and modeling complex reaction systems. In recent years, CRNs have attracted attention in the field of molecular computing for their ability to simulate the components of a digital computer. The reactions within such networks may occur at several different scales relative to one another – at rates often too difficult to directly measure and analyze in a laboratory setting. To facilitate the construction and analysis of such networks, we propose a reduced order model for simulating such networks as a system of …
Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak
Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling And Simulation With Deep Learning Methods Of Cancer Growth For Patient-Specific Therapy, Vishal Kobla, Joshua P. Smith, Pranav Unni, Padmanabhan Seshaiyer
Mathematical Modeling And Simulation With Deep Learning Methods Of Cancer Growth For Patient-Specific Therapy, Vishal Kobla, Joshua P. Smith, Pranav Unni, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.
Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.
Dissertations, Theses, and Capstone Projects
This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).
Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.
These analytical solutions are …
Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, Kyle A. Gregory
Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, Kyle A. Gregory
Chancellor’s Honors Program Projects
No abstract provided.
C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski
Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski
Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang
A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang
Theses and Dissertations--Mechanical Engineering
Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model is …
Teaching Systems Biology Of The Circadian Clock With Journal Articles And Matlab, Stephanie R. Taylor
Teaching Systems Biology Of The Circadian Clock With Journal Articles And Matlab, Stephanie R. Taylor
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia
Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia
Physics
Methods of teaching numerical methods to solve ordinary differential equations in the context of galaxy mergers were explored. The research published in a paper by Toomre and Toomre in 1972 describing the formation of galactic tails and bridges from close tidal interactions was adapted into a project targeting undergraduate physics students. Typically undergraduate physics students only take one Computational Physics class in which various techniques and algorithms are taught. Although it is important to study computational physics techniques, it is just as important to apply this knowledge to a problem that is representative of what computational physics researchers are investigating …
Procesy Cieplne I Aparaty (Lab), Wojciech M. Budzianowski