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Full-Text Articles in Physical Sciences and Mathematics
Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 4: Models Of N-Cov, Jyotirmoy Sarkar, Mamunur Rashid
Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 4: Models Of N-Cov, Jyotirmoy Sarkar, Mamunur Rashid
Mathematics Faculty Publications
What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, …
Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 3: Spherical Triangles, Jyotirmoy Sarkar, Mamunur Rashid
Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 3: Spherical Triangles, Jyotirmoy Sarkar, Mamunur Rashid
Mathematics Faculty Publications
What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, …
Mathematical Musings On The External Anatomy Of The Novel Coronavirus Part 2: Chasing After Quasi-Symmetry, Jyotirmoy Sarkar, Mamunur Rashid
Mathematical Musings On The External Anatomy Of The Novel Coronavirus Part 2: Chasing After Quasi-Symmetry, Jyotirmoy Sarkar, Mamunur Rashid
Mathematics Faculty Publications
What is the shape of the novel Coronavirus which has turned our world upside down? Even though it looks dull, unattractive, and even disgusting under a microscope, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning …
Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 1: The Overall Shape Of The N-Cov, Jyotirmoy Sarkar, Mamunur Rashid
Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 1: The Overall Shape Of The N-Cov, Jyotirmoy Sarkar, Mamunur Rashid
Mathematics Faculty Publications
What is the shape of the novel coronavirus which has turned our world upside down? Even though under a microscope it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still obeying the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others …
A Guide To Rbf-Generated Finite Differences For Nonlinear Transport: Shallow Water Simulations On A Sphere, Natasha Flyer, Erik Lehto, Sébastien Blaise, Grady Wright, Amik St-Cyr
A Guide To Rbf-Generated Finite Differences For Nonlinear Transport: Shallow Water Simulations On A Sphere, Natasha Flyer, Erik Lehto, Sébastien Blaise, Grady Wright, Amik St-Cyr
Mathematics Faculty Publications and Presentations
The current paper establishes the computational efficiency and accuracy of the RBF-FD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as Gibbs phenomena, sharp gradients, and complex vortical dynamics with rapid energy transfer from large to small scales over short time periods. The computations were possible as well as very competitive due to the implementation of hyperviscosity on large RBF stencil sizes (corresponding roughly to 6th …
Transport Schemes On A Sphere Using Radial Basis Functions, Natasha Flyer, Grady Wright
Transport Schemes On A Sphere Using Radial Basis Functions, Natasha Flyer, Grady Wright
Mathematics Faculty Publications and Presentations
The aim of this work is to introduce the physics community to the high performance of radial basis functions (RBFs) compared to other spectral methods for modeling transport (pure advection) and to provide the first known application of the RBF methodology to hyperbolic partial differential equations on a sphere. First, it is shown that even when the advective operator is posed in spherical coordinates (thus having singularities at the poles), the RBF formulation of it is completely singularity-free. Then, two classical test cases are conducted: 1) linear advection, where the initial condition is simply transported around the sphere and 2) …