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Partial Differential Equations Commons™
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Articles 1 - 30 of 66
Full-Text Articles in Partial Differential Equations
Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della
Modeling Seiche Oscillations Using Damped Vibration Differential Equations, Sharjeel Malik, Justin Della
Discovery Day - Daytona Beach
Combustion instability in liquid rocket engines is driven by coupling acoustic pressure oscillations and unsteady heat release. To achieve specific desired outcomes, small perturbations can be made to either decay or grow, depending on system dynamics and artificial parameters. Using a linearized eigenvalue framework, where eigenvalues determine growth/decay rates and frequencies, and eigenvectors describe spatial mode shapes and couplings between pressure, velocity, and heat release, a mathematical model can be derived to describe said behavior for a cross-section of the rocket engine. The Rayleigh criterion is used to identify conditions under which energy is added to oscillations, while flame transfer …
A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie
A Differential Equation Approach To Heat Flow In A Thin Rod, Alexandria Krol, David Cardona, Collin Petrie
Discovery Day - Daytona Beach
A Differential Equation Approach to Heat Flow in a Thin Rod examines how differential equations can be used to model and understand heat conduction in a fundamental physical system. Heat transfer in solids is a key concept in physics and engineering, particularly in systems where temperature changes over time. A thin rod provides a useful one-dimensional model for studying how heat moves through a material and how temperature varies along the rod as time passes. The primary objective is to develop a mathematical description of this process using differential equations. The analysis begins with physical principles such as conservation of …
Dynamics Of A Two-Stage Epidemiological Model With Post-Infection Mortality And Transmission Heterogeneity, B Sagar
Biology and Medicine Through Mathematics Conference
No abstract provided.
A Multiscale Computational Framework Coupling Pulmonary Arterial Blood Flow And Lung Tissue Perfusion, Nigar Sultana, Hangjie Ji, Mette Sofie Olufsen
A Multiscale Computational Framework Coupling Pulmonary Arterial Blood Flow And Lung Tissue Perfusion, Nigar Sultana, Hangjie Ji, Mette Sofie Olufsen
Biology and Medicine Through Mathematics Conference
No abstract provided.
Eigenvalue Bound Preservation: Numerical Experiments On The 2d Q-Tensor Flow, Marcel C. Deguzman
Eigenvalue Bound Preservation: Numerical Experiments On The 2d Q-Tensor Flow, Marcel C. Deguzman
Knowledge and Creativity Expo
We study the evolution of nematic liquid crystals in two dimensions using the Q-tensor model, a continuum framework that describes the orientational order of rod-like molecules via symmetric, traceless matrices. Focusing on the Landau-de Gennes energy and its associated gradient flow, we consider a reduced two-dimensional formulation in which the Q-tensor is fully described by two scalar functions. This reduction simplifies the system to a nonlinear, coupled PDE for the scalars, while preserving essential physical features. A key question is whether the eigenvalues of the Q-tensor remain within the physically admissible range under this flow. Building on a theoretical result …
Computational Models For Pre-Lens Tear Film Drug Concentration Dynamics With Drug Supply From A Contact Lens And Drug Exchange During Blinking, Mazen A. Althobaiti
Computational Models For Pre-Lens Tear Film Drug Concentration Dynamics With Drug Supply From A Contact Lens And Drug Exchange During Blinking, Mazen A. Althobaiti
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Model Of Ovarian Cancer Tumor Growth In Mice, Jessica A. Hoffman
Mathematical Model Of Ovarian Cancer Tumor Growth In Mice, Jessica A. Hoffman
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Can We End The Hiv Epidemic In The U.S.? Linking Clinical And National Surveillance Data Through Multiscale Modeling From Patients To Populations, Necibe Tuncer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Quantification Of Parameters To Predict The Rupture Of Intracranial Saccular Aneurysms Using Physics Informed Neural Networks, Alonso Gabriel Ogueda, Padmanabhan Seshaiyer
Quantification Of Parameters To Predict The Rupture Of Intracranial Saccular Aneurysms Using Physics Informed Neural Networks, Alonso Gabriel Ogueda, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Properties Of Eigenvalues Of The Fractal Laplacian, Eric Stachura, Andrew Chincea
Properties Of Eigenvalues Of The Fractal Laplacian, Eric Stachura, Andrew Chincea
Symposium of Student Scholars
We investigate the properties of the eigenvalues of the fractal Laplacian. We begin by defining the fractal Laplacian operator in one dimension and formulate the corresponding Dirichlet eigenvalue problem. Analytical solutions are obtained for specific fractal parameters, and computational results illustrate the structure of eigenvalues and their associated eigenfunctions. We extend our analysis to two dimensions using separation of variables. Our findings contribute to a deeper understanding of how fractal geometry affects the spectral characteristics of differential operators.
A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes
A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes
Biology and Medicine Through Mathematics Conference
No abstract provided.
Reaction-Diffusions System Simulated On Irregular Shapes And Surfaces Model Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons, Arielle M. Cooley, Joshua R. Puzey, Gregory D. Conradi Smith
Reaction-Diffusions System Simulated On Irregular Shapes And Surfaces Model Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons, Arielle M. Cooley, Joshua R. Puzey, Gregory D. Conradi Smith
Biology and Medicine Through Mathematics Conference
No abstract provided.
Exploring The Evolution Of Altruistic Punishment Using A Pde Model For Multilevel Selection, Daniel Cooney
Exploring The Evolution Of Altruistic Punishment Using A Pde Model For Multilevel Selection, Daniel Cooney
Biology and Medicine Through Mathematics Conference
No abstract provided.
Identifiability For Pde Models Of Fluorescence Microscopy Experiments, Veronica Ciocanel
Identifiability For Pde Models Of Fluorescence Microscopy Experiments, Veronica Ciocanel
Biology and Medicine Through Mathematics Conference
No abstract provided.
Chemoattractant Distribution In The Drosophila Egg Chamber, Lara Scott
Chemoattractant Distribution In The Drosophila Egg Chamber, Lara Scott
Biology and Medicine Through Mathematics Conference
No abstract provided.
Sperm-Egg Interaction For Fertilization Success, Prajakta P. Bedekar
Sperm-Egg Interaction For Fertilization Success, Prajakta P. Bedekar
Biology and Medicine Through Mathematics Conference
No abstract provided.
Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.
Computational Modeling Using A Novel Continuum Approach Coupled With Pathway-Informed Neural Networks To Optimize Dynein-Mediated Centrosome Positioning In Polarized Cells, Arkaprovo Ghosal, Padmanabhan Seshaiyar Dr., Adriana Dawes Dr., General Genomics Inc.
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Lnksc Method On Pde-Constrained Optimization For Mcf-7 Breast Cancer Cell Growth Predictions And Treatment Response With Gold Nanoparticles, Widodo Samyono, Shakhawat Bhuiyan
Lnksc Method On Pde-Constrained Optimization For Mcf-7 Breast Cancer Cell Growth Predictions And Treatment Response With Gold Nanoparticles, Widodo Samyono, Shakhawat Bhuiyan
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Helices In Fluids And Applications To Modeling In Biology, Eva M. Strawbridge
Helices In Fluids And Applications To Modeling In Biology, Eva M. Strawbridge
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Effects Of Slip On Highly Viscous Thin-Film Flows Inside A Vertical Tube Of Constant Radius, Mark S. Schwitzerlett
Effects Of Slip On Highly Viscous Thin-Film Flows Inside A Vertical Tube Of Constant Radius, Mark S. Schwitzerlett
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Pde Model For Protocell Evolution And The Origin Of Chromosomes Via Multilevel Selection, Daniel B. Cooney, Fernando W. Rossine, Dylan H. Morris, Simon A. Levin
Pde Model For Protocell Evolution And The Origin Of Chromosomes Via Multilevel Selection, Daniel B. Cooney, Fernando W. Rossine, Dylan H. Morris, Simon A. Levin
Biology and Medicine Through Mathematics Conference
No abstract provided.
Reaction-Diffusion System On Irregular Boundaries Reproduces Multiple Generations Of Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons
Reaction-Diffusion System On Irregular Boundaries Reproduces Multiple Generations Of Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons
Biology and Medicine Through Mathematics Conference
No abstract provided.
Helices In Fluids And Their Applications, Eva M. Strawbridge
Helices In Fluids And Their Applications, Eva M. Strawbridge
Biology and Medicine Through Mathematics Conference
No abstract provided.
On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini
On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
De-Coupling Cell-Autonomous And Non-Cell-Autonomous Fitness Effects Allows Solution Of The Fokker-Planck Equation For The Evolution Of Interacting Populations, Steph J. Owen
Biology and Medicine Through Mathematics Conference
No abstract provided.
Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki
Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki
Biology and Medicine Through Mathematics Conference
No abstract provided.
Spatial Patterning Of Predator-Prey Distributions Arising From Prey Defense, Evan C. Haskell, Jonathan Bell
Spatial Patterning Of Predator-Prey Distributions Arising From Prey Defense, Evan C. Haskell, Jonathan Bell
Biology and Medicine Through Mathematics Conference
No abstract provided.
Genetically Explicit Model May Explain Multigenerational Control Of Emergent Turing Patterns In Hybrid Mimulus, Emily Simmons
Genetically Explicit Model May Explain Multigenerational Control Of Emergent Turing Patterns In Hybrid Mimulus, Emily Simmons
Biology and Medicine Through Mathematics Conference
No abstract provided.
Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations., Quinnlan Paul Aiken
Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations., Quinnlan Paul Aiken
ONU Student Research Colloquium
Approximation of the functions which are the solutions of complex or difficult problems is a worthwhile endeavor. This has resulted in many ways to effectively approximate the solution of the partial differential equations. One such way to approximate the solution of the partial differential equation is Oscillatory radial basis function method. This method can approximate the solution of the partial differential equation well however relies heavily on a “shape parameter” to achieve acceptable error. Choosing this parameter was traditionally done through a trial-and-error method. Selecting shape parameters in a more analytical way has been desired. One such method is the …
Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney
Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.