Modelling The Polarization, Migration And Neuromast Deposition In The Zebrafish Posterior Lateral Line System,
2016
University of British Columbia
Modelling The Polarization, Migration And Neuromast Deposition In The Zebrafish Posterior Lateral Line System, Hildur Knutsdottir
Biology and Medicine Through Mathematics Conference
No abstract provided.
Spatial Patterning In The York River Tidal Marshes Through The Interaction Of Cordgrass, Mussels And Sediment,
2016
College of William and Mary
Spatial Patterning In The York River Tidal Marshes Through The Interaction Of Cordgrass, Mussels And Sediment, Sofya Zaytseva, Leah Shaw, Rom Lipcius, Junping Shi
Biology and Medicine Through Mathematics Conference
No abstract provided.
Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock.,
2016
Georgia Institute of Technology
Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry
Biology and Medicine Through Mathematics Conference
No abstract provided.
Explicitly Separating Growth And Motility In A Glioblastoma Tumor Model,
2016
Arizona State University
Explicitly Separating Growth And Motility In A Glioblastoma Tumor Model, Tracy Stepien, Erica Rutter, Meng Fan, Yang Kuang
Biology and Medicine Through Mathematics Conference
No abstract provided.
Force Generation And Contraction Of Random Actomyosin Bundles.,
2016
Courant Institute (NYU)
Force Generation And Contraction Of Random Actomyosin Bundles., Dietmar B. Oelz
Biology and Medicine Through Mathematics Conference
No abstract provided.
Nonlinear Dynamics Of Filaments In Free Space And Fluids,
2016
James Madison University
Nonlinear Dynamics Of Filaments In Free Space And Fluids, Victoria Kelley
Senior Honors Projects, 2010-2019
The purpose of this paper is to study a straight rod, held at both ends, with a known twist and tension or compression. We study the stability of this steady state when the system is dominated either by inertia or drag. In order to do this, we first replicate the work of Goriely and Tabor to look at the case with inertia, without drag. After conducting the analysis for that case, we then apply their framework to perform a linear stability analysis of a model that is without inertia, but with hydrodynamic drag. Our motivation is the study of locomotion …
General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay,
2016
West Chester University of Pennsylvania
General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay, Mark A. Mckibben
Mathematics Faculty Publications
Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t are established. The classical Lipschitz is replaced by a weaker so-called Caratheodory condition under which we still maintain uniqueness. The time-dependent case is discussed, as well as an extension of the theory to the case of a nonlocal …
Solution Techniques And Error Analysis Of General Classes Of Partial Differential Equations,
2016
Boise State University
Solution Techniques And Error Analysis Of General Classes Of Partial Differential Equations, Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe
Boise State University Theses and Dissertations
While constructive insight for a multitude of phenomena appearing in the physical and biological sciences, medicine, engineering and economics can be gained through the analysis of mathematical models posed in terms of systems of ordinary and partial differential equations, it has been observed that a better description of the behavior of the investigated phenomena can be achieved through the use of functional differential equations (FDEs) or partial functional differential equations (PFDEs). PFDEs or functional equations with ordinary derivatives are subclasses of FDEs. FDEs form a general class of differential equations applied in a variety of disciplines and are characterized by …
Performance Analysis Of Solar Adsorption Cooling System - Effect Of Position Of Heat Storage Tank,
2016
Independent University, Bangladesh
Performance Analysis Of Solar Adsorption Cooling System - Effect Of Position Of Heat Storage Tank, Rifat A. Rouf, K. C. Amanul Alam, M. A. Hakim Khan, Bidyut B. Saha, Ibrahim I. El-Sharkawy
Applications and Applied Mathematics: An International Journal (AAM)
An insulated storage tank has been added with adsorption cooling system run by solar heat collected by CPC panel. It has been expected and seen that the storage tank has a vital contribution in the performance of the chiller. The storage tank is connected with a solar heat driven single stage two bed basic adsorption chillers activated with silica gel-water pair in two ways. The tank is connected in such a way that (i) the solar collectors supply hot water to the desorption bed, the outflow of the desorber is collected in the reserve tank. The reserve tank supplies water …
Theoretical Modeling Of The Effect Of Polymer Chain Immobilization Rates On Holographic Recording In Photopolymers,
2016
Technological University Dublin
Theoretical Modeling Of The Effect Of Polymer Chain Immobilization Rates On Holographic Recording In Photopolymers, Dana Mackey, Paul O'Reilly, Izabela Naydenova
Articles
This paper introduces an improved mathematical model for holographic grating formation in an acrylamide-based photopolymer, which consists of partial differential equations derived from physical laws. The model is based on the two-way diffusion theory of \cite{izabela}, which assumes short polymer chains are free to diffuse, and generalizes a similar model presented in \cite{josab} by introducing an immobilization rate governed by chain growth and cross-linking. Numerical simulations were carried out in order to investigate the behaviour of the photopolymer system for short and long exposures, with particular emphasis on the effect of recording parameters (such as illumination frequency and intensity), as …
On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion,
2016
University of Richmond
On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion, Jeremy Lecrone, Gieri Simonett
Department of Math & Statistics Faculty Publications
We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially--unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π--axially--periodic perturbations if the radius r>1,and unstable if 0
Thermoelastic Waves In Microstructured Solids,
2016
Tallinn University of Technology
Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski
Publications
Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in …
Models Of Internal Waves In The Presence Of Currents,
2016
Technological University Dublin
Models Of Internal Waves In The Presence Of Currents, Alan Compelli, Rossen Ivanov
Conference papers
A fluid system consisting of two domains is examined. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. An internal wave propagating in one direction, driven by gravity, acts as a free common interface between the fluids. Various current profiles are considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are formulated. The presented models provide potential applications to modelling of internal geophysical …
The Global Stability Of The Solution To The Morse Potential In A Catastrophic Regime,
2016
Harvey Mudd College
The Global Stability Of The Solution To The Morse Potential In A Catastrophic Regime, Weerapat Pittayakanchit
HMC Senior Theses
Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single …
4. Dragging Along,
2016
Illinois Mathematics and Science Academy
Steady State Solutions For A System Of Partial Differential Equations Arising From Crime Modeling,
2016
Harvey Mudd College
Steady State Solutions For A System Of Partial Differential Equations Arising From Crime Modeling, Bo Li
HMC Senior Theses
I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate, hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model.
Homogenization Of Stokes Systems With Periodic Coefficients,
2016
University of Kentucky
Homogenization Of Stokes Systems With Periodic Coefficients, Shu Gu
Theses and Dissertations--Mathematics
In this dissertation we study the quantitative theory in homogenization of Stokes systems. We study uniform regularity estimates for a family of Stokes systems with rapidly oscillating periodic coefficients. We establish interior Lipschitz estimates for the velocity and L∞ estimates for the pressure as well as Liouville property for solutions in ℝd. We are able to obtain the boundary W{1,p} estimates in a bounded C1 domain for any 1 < p < ∞. We also study the convergence rates in L2 and H1 of Dirichlet and Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any regularity assumptions on the coefficients.
Controllability Of Neutral Stochastic Integro-Differential Evolution Equations Driven By A Fractional Brownian Motion,
2016
Universite Cadi Ayyad
Controllability Of Neutral Stochastic Integro-Differential Evolution Equations Driven By A Fractional Brownian Motion, El Hassan Lakhel, Mark A. Mckibben
Mathematics Faculty Publications
We establish sufficient conditions for the controllability of a certain class of neutral stochastic functional integro-differential evolution equations in Hilbert spaces. The results are obtained using semigroup theory, resolvent operators and a fixed-point technique. An application to neutral partial integro-differential stochastic equations perturbed by fractional Brownian motion is given.
A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows,
2016
West Chester University of Pennsylvania
A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou
Mathematics Faculty Publications
We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on the …
2. Population,
2016
Illinois Mathematics and Science Academy
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
