Daniel Spirn
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View article: Tetrahedral frame fields via constrained third order symmetric tensors
Tetrahedral frame fields via constrained third order symmetric tensors Open
Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal vect…
View article: On the regularity of the flow map for the gravity-capillary equations
On the regularity of the flow map for the gravity-capillary equations Open
We prove via explicitly constructed initial data that solutions to the gravity-capillary wave system in R3R3 representing a 2d air–water interface immediately fail to be C3C3 with respect to the initial data if the initial data (h0,ψ0)∈Hs+…
View article: A Variational Method for Generating $n$-Cross Fields Using Higher-Order $Q$-Tensors
A Variational Method for Generating $n$-Cross Fields Using Higher-Order $Q$-Tensors Open
An $n$-cross field is a locally-defined orthogonal coordinate system invariant with respect to the cubic symmetry group. Cross fields are finding wide-spread use in mesh generation, computer graphics, and materials science among many appli…
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: The profile decomposition for the hyperbolic Schrödinger equation
The profile decomposition for the hyperbolic Schrödinger equation Open
In this note, we prove the profile decomposition for hyperbolic Schrödinger (or mixed signature) equations on $\mathbb{R}^2$ in two cases, one mass-supercritical and one mass-critical. First, as a warm up, we show that the profile decompos…
View article: Quench detection on a superconducting radio-frequency cavity
Quench detection on a superconducting radio-frequency cavity Open
We study quench detection in superconducting accelerator cavities cooled with He-II. A rigorous mathematical formula is derived to localize the quench position from dynamical data over a finite time interval at a second sound detector.
View article: Well-posedness and global behavior of the Peskin problem of an immersed elastic filament in Stokes flow
Well-posedness and global behavior of the Peskin problem of an immersed elastic filament in Stokes flow Open
We consider the problem of a one dimensional elastic filament immersed in a two dimensional steady Stokes fluid. Immersed boundary problems in which a thin elastic structure interacts with a surrounding fluid are prevalent in science and e…
View article: Gross-Pitaevskii vortex motion with critically scaled inhomogeneities
Gross-Pitaevskii vortex motion with critically scaled inhomogeneities Open
We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation iδtu = Δu + 1/ε²(ρ² ε(ᵡ) - |u|²). For a unique scaling regime |ρε(ᵡ) - 1 = O(logε¯¹), it is shown that vortices can interact both with the background perturba…
View article: Gross--Pitaevskii Vortex Motion with Critically Scaled Inhomogeneities
Gross--Pitaevskii Vortex Motion with Critically Scaled Inhomogeneities Open
We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation $i \partial_t u = Δu + {1\over \varepsilon^2} (p_\varepsilon^2(x) - |u|^2)$. For a unique scaling regime $|p_\varepsilon(x) - 1 | = O(|\log \varepsilon|^{-1})$…