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View article: The slender body free boundary problem
The slender body free boundary problem Open
We consider the slender body free boundary problem describing the evolution of an inextensible, closed elastic filament immersed in a Stokes fluid in $\mathbb{R}^3$. The filament elasticity is governed by Euler-Bernoulli beam theory, and t…
View article: Rods in flows: the PDE theory of immersed elastic filaments
Rods in flows: the PDE theory of immersed elastic filaments Open
We investigate a family of curve evolution equations approximating the motion of a Kirchhoff rod immersed in a low Reynolds number fluid. The rod is modeled as a framed curve whose energy consists of the bending energy of the curve and the…
View article: A free boundary problem for an immersed filament in 3D Stokes flow
A free boundary problem for an immersed filament in 3D Stokes flow Open
We consider a simplified extensible version of a dynamic free boundary problem for a thin filament with radius $ε>0$ immersed in 3D Stokes flow. The 3D fluid is coupled to the quasi-1D filament dynamics via a novel type of angle-averaged N…
View article: On an angle-averaged Neumann-to-Dirichlet map for thin filaments
On an angle-averaged Neumann-to-Dirichlet map for thin filaments Open
We consider the Laplace equation in the exterior of a thin filament in $\mathbb{R}^3$ and perform a detailed decomposition of a notion of slender body Neumann-to-Dirichlet (NtD) and Dirichlet-to-Neumann (DtN) maps along the filament surfac…
View article: Well-posedness and applications of classical elastohydrodynamics for a swimming filament
Well-posedness and applications of classical elastohydrodynamics for a swimming filament Open
We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in . The hydrodynamics are described by resistive force theory, and the fibre elasticity is governed by Euler–Bernoulli beam theory…
View article: Well-posedness of a viscoelastic resistive force theory and applications to swimming
Well-posedness of a viscoelastic resistive force theory and applications to swimming Open
We propose and analyze a simple model for the evolution of an immersed, inextensible filament which incorporates linear viscoelastic effects of the surrounding fluid. The model is a closed-form system of equations along the curve only whic…
View article: Well-posedness and applications of classical elastohydrodynamics for a swimming filament
Well-posedness and applications of classical elastohydrodynamics for a swimming filament Open
We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in $\mathbb{R}^3$. The hydrodynamics are described by resistive force theory, and the fiber elasticity is governed by Euler-Bernoulli bea…
View article: Weakly nonlinear analysis of pattern formation in active suspensions
Weakly nonlinear analysis of pattern formation in active suspensions Open
We consider the Saintillan–Shelley kinetic model of active rod-like particles in Stokes flow (Saintillan & Shelley, Phys. Rev. Lett. , vol. 100, issue 17, 2008 a , 178103; Saintillan & Shelley, Phys. Fluids , vol. 20, issue 12, 2008 b , 12…
View article: On the stabilizing effect of swimming in an active suspension
On the stabilizing effect of swimming in an active suspension Open
We consider a kinetic model of an active suspension of rod-like microswimmers. In certain regimes, swimming has a stabilizing effect on the suspension. We quantify this effect near homogeneous isotropic equilibria $\overlineψ = \text{const…
View article: Remarks on Regularized Stokeslets in Slender Body Theory
Remarks on Regularized Stokeslets in Slender Body Theory Open
We remark on the use of regularized Stokeslets in the slender body theory (SBT) approximation of Stokes flow about a thin fiber of radius ϵ>0. Denoting the regularization parameter by δ, we consider regularized SBT based on the most common…
View article: Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations Open
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinea…
View article: An integral model based on slender body theory, with applications to curved rigid fibers
An integral model based on slender body theory, with applications to curved rigid fibers Open
We propose a novel integral model describing the motion of both flexible and rigid slender fibers in viscous flow and develop a numerical method for simulating dynamics of curved rigid fibers. The model is derived from nonlocal slender bod…
View article: An integral model based on slender body theory, with applications to\n curved rigid fibers
An integral model based on slender body theory, with applications to\n curved rigid fibers Open
We propose a novel integral model describing the motion of curved slender\nfibers in viscous flow, and develop a numerical method for simulating dynamics\nof rigid fibers. The model is derived from nonlocal slender body theory (SBT),\nwhic…
View article: Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations Open
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinea…
View article: Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid
Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid Open
We consider the accuracy of slender body theory in approximating the force exerted by a thin fiber on the surrounding viscous fluid when the fiber velocity is prescribed. We term this the slender body inverse problem, as it is known that s…
View article: Mathematical foundations of slender body theory
Mathematical foundations of slender body theory Open
University of Minnesota Ph.D. dissertation.May 2020. Major: Mathematics. Advisors: Yoichiro Mori, Daniel Spirn. 1 computer file (PDF); vii, 231 pages.
View article: A slender body model for thin rigid fibers: validation and comparisons
A slender body model for thin rigid fibers: validation and comparisons Open
In this paper we consider a computational model for the motion of thin, rigid fibers in viscous flows based on slender body theory. Slender body theory approximates the fluid velocity field about the fiber as the flow due to a distribution…
View article: Theoretical justification and error analysis for slender body theory
Theoretical justification and error analysis for slender body theory Open
Slender body theory facilitates computational simulations of thin fibers immersed in a viscous fluid by approximating each fiber using only the geometry of the fiber centerline curve and the line force density along it. However, it has bee…
View article: Model for breast cancer diversity and spatial heterogeneity
Model for breast cancer diversity and spatial heterogeneity Open
We present and analyze a growth model of an avascular tumor that considers the basic biological principles of proliferation, motility, death and genetic mutations of the cell. From a regulatory network analysis and an analysis of genomic d…