Tootfinder

Rheological Origin of Aging
Vikash Pandey
https://arxiv.org/abs/2506.06365 https://arxiv.org/pdf/2506.06365

Rheological Origin of Aging
Most materials of practical applications age, and their properties change with time. The aging of materials is reflected in their mechanical responses to external stress and strain, which exhibit ubiquity in the form of logarithms and power laws, respectively. Such responses are usually described using complicated phenomenological models, including fractional viscoelastic models, but they lack physical insights. In this Letter, we postulate a linear time-varying rheological property whose const…

This https://arxiv.org/abs/2403.14848 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Learning WENO for entropy stable schemes to solve conservation laws
Entropy conditions play a crucial role in the extraction of a physically relevant solution for systems of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions. TeCNO schemes (Fjordholm et al. 2012) form a class of arbitrary high-order entropy stable finite difference solvers, which require specialized reconstruction algorithms satisfying the sign property at each cell interface. Third-order weighted essentially non-osc…

The 'Brazil-nut effect' in bidisperse particle laden flow on an incline
Jack Luong, Sarah Cassie Burnett, Andrea L. Bertozzi
https://arxiv.org/abs/2505.24114

The 'Brazil-nut effect' in bidisperse particle laden flow on an incline
We study bidisperse suspensions -- suspensions where there are two particle species of the same density but different sizes -- of a viscous fluid on an incline. We use a lubrication theory/thin film model to form a hyperbolic system of three conservation laws for the height and particle volume fractions. The model predicts, over a range of parameters, that the larger particles rise to the top of the layer, consistent with the well-known `Brazil-nut effect' for granular media. The model predicts…

This https://arxiv.org/abs/2406.05694 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Low Rank Neural Representation of Entropy Solutions
We construct a new representation of entropy solutions to nonlinear scalar conservation laws with a smooth convex flux function in a single spatial dimension. The representation is a generalization of the method of characteristics and posseses a compositional form. While it is a nonlinear representation, the embedded dynamics of the solution in the time variable is linear. This representation is then discretized as a manifold of implicit neural representations where the feedforward neural netwo…

Does Newtonian dynamics need Euclidean space?
Alain Albouy
https://arxiv.org/abs/2506.00086 https://arxiv.org/pdf/2506.00086

Does Newtonian dynamics need Euclidean space?
We present an elementary deduction of the Newtonian force from Kepler's laws. We relate it to a generalization by Jacobi of the Keplerian motion, where the Euclidean form in the plane is replaced by some function with the same homogeneity. We show how several convexity properties of the generalized Keplerian orbits appear in this context. We describe the generalized hodographs.