Geoffrey M. Vasil
YOU?
Author Swipe
View article: Itô calculus meets the Hubble tension: effects of small-scale electron density fluctuations on the CMB anisotropies
Itô calculus meets the Hubble tension: effects of small-scale electron density fluctuations on the CMB anisotropies Open
We develop a novel formalism to include the effect of electron density fluctuations at ultra small scales (well below the sound horizon at last scattering) on the observed anisotropies of the Cosmic Microwave Background (CMB). We treat the…
View article: Rapidly rotating wall-mode convection
Rapidly rotating wall-mode convection Open
In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode …
View article: Ito calculus meets the Hubble tension: Effects of small-scale electron density fluctuations on the CMB anisotropies
Ito calculus meets the Hubble tension: Effects of small-scale electron density fluctuations on the CMB anisotropies Open
In this work, we develop a novel formalism to include the effect of electron density fluctuations at ultra small scales (well below the sound horizon at last scattering) on the observed anisotropies of the Cosmic Microwave Background (CMB)…
View article: Clifford algebras and liquid crystalline fermions
Clifford algebras and liquid crystalline fermions Open
We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section c…
View article: A Potential Mushy Source for the Geysers of Enceladus and Other Icy Satellites
A Potential Mushy Source for the Geysers of Enceladus and Other Icy Satellites Open
Enceladus is a target for astrobiology due to the plume ejecta measured by the Cassini spacecraft and the inferred subsurface ocean that could be the source of the geysers. Here we explore an alternative where shear heating along tiger str…
View article: Rescaled Equations for Well-Conditioned Direct Numerical Simulations of Rapidly Rotating Convection
Rescaled Equations for Well-Conditioned Direct Numerical Simulations of Rapidly Rotating Convection Open
Convection is a ubiquitous process driving geophysical/astrophysical fluid flows, which are typically strongly constrained by planetary rotation on large scales. A celebrated model of such flows, rapidly rotating Rayleigh-Bénard convection…
View article: Rapidly Rotating Wall-Mode Convection
Rapidly Rotating Wall-Mode Convection Open
In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode …
View article: The solar dynamo begins near the surface
The solar dynamo begins near the surface Open
The magnetic dynamo cycle of the Sun features a distinct pattern: a propagating region of sunspot emergence appears around 30° latitude and vanishes near the equator every 11 years (ref. 1 ). Moreover, longitudinal flows called torsional o…
View article: The solar dynamo begins near the surface
The solar dynamo begins near the surface Open
The Sun's magnetic dynamo cycle features a distinct pattern: a propagating region of sunspot emergence appears around 30 degrees latitude and vanishes near the equator every 11 years. Moreover, longitudinal flows called "torsional oscillat…
View article: Iterative Methods for Navier--Stokes Inverse Problems
Iterative Methods for Navier--Stokes Inverse Problems Open
Even when the partial differential equation underlying a physical process can be evolved forward in time, the retrospective (backward in time) inverse problem often has its own challenges and applications. Direct Adjoint Looping (DAL) is t…
View article: Rational function approximation with normalized positive denominators
Rational function approximation with normalized positive denominators Open
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionall…
View article: Force balances in strong-field magnetoconvection simulations
Force balances in strong-field magnetoconvection simulations Open
We study force balances in two-dimensional Rayleigh-Benard simulations with a large range of imposed background magnetic fields. We find two main regimes, a magnetically constrained regime where the linear Lorentz force dominates, and a ma…
View article: Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: The Puzzling Structure of Solar Convection: Window into the Dynamo
The Puzzling Structure of Solar Convection: Window into the Dynamo Open
Whitepaper #105 in the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. Main topics: basic research; infrastructure/workforce/other programmatic. Additional topics: solar physics; research tools and infrastructure.
View article: The photometric variability of massive stars due to gravity waves excited by core convection
The photometric variability of massive stars due to gravity waves excited by core convection Open
Massive stars die in catastrophic explosions that seed the interstellar medium with heavy elements and produce neutron stars and black holes. Predictions of the explosion’s character and the remnant mass depend on models of the star’s evol…
View article: The photometric variability of massive stars due to gravity waves excited by core convection
The photometric variability of massive stars due to gravity waves excited by core convection Open
Massive stars die in catastrophic explosions, which seed the interstellar medium with heavy elements and produce neutron stars and black holes. Predictions of the explosion's character and the remnant mass depend on models of the star's ev…
View article: The Puzzling Structure of Solar Convection: Window into the Dynamo
The Puzzling Structure of Solar Convection: Window into the Dynamo Open
The operation of the solar dynamo, with all of its remarkable spatio-temporal ordering, remains an outstanding problem of modern solar physics. A number of mechanisms that might plausibly contribute to its operation have been proposed, but…
View article: Convex optimization over a probability simplex
Convex optimization over a probability simplex Open
We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…
View article: Code, Data, and Supplemental Materials for "The photometric variability of massive stars due to gravity waves excited by core convection"
Code, Data, and Supplemental Materials for "The photometric variability of massive stars due to gravity waves excited by core convection" Open
This repository backs up the code, data, and supplemental materials required to reproduce the analyses and figures in "The photometric variability of massive stars due to gravity waves excited by core convection" (Anders et al. 2023). In t…
View article: Code, Data, and Supplemental Materials for "The photometric variability of massive stars due to gravity waves excited by core convection"
Code, Data, and Supplemental Materials for "The photometric variability of massive stars due to gravity waves excited by core convection" Open
This repository backs up the code, data, and supplemental materials required to reproduce the analyses and figures in "The photometric variability of massive stars due to gravity waves excited by core convection" (Anders et al. 2023). In t…
View article: Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: A continuum limit for dense spatial networks
A continuum limit for dense spatial networks Open
Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at th…
View article: Mathematica code to generate figure 3 from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Mathematica code to generate figure 3 from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: Mathematica code to generate figure 1 from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Mathematica code to generate figure 1 from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: Mathematica code to generate figure 2 from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Mathematica code to generate figure 2 from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: Mathematica derivation of signed-distance coordinates around curves from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Mathematica derivation of signed-distance coordinates around curves from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: Mathematica derivation of signed-distance coordinates for surfaces from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Mathematica derivation of signed-distance coordinates for surfaces from Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces Open
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and co…
View article: Corner cases of the tau method: symmetrically imposing boundary conditions on hypercubes
Corner cases of the tau method: symmetrically imposing boundary conditions on hypercubes Open
Polynomial spectral methods produce fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions is well understood. However, automating extensions to doma…
View article: The Stability of Prendergast Magnetic Fields
The Stability of Prendergast Magnetic Fields Open
Convection in massive main sequence stars generates large scale magnetic fields in their cores which persists as they evolve up the red giant branch. The remnants of these fields may take the form of the Prendergast magnetic field, a combi…
View article: A mushy source for the geysers of Enceladus
A mushy source for the geysers of Enceladus Open
Enceladus is a primary target for astrobiology due to the $\rm H_2O$ plume ejecta measured by the Cassini spacecraft and the inferred subsurface ocean sustained by tidal heating. Sourcing the plumes via a direct connection from the ocean t…