21 citations · 30 across the 2 of their papers we have counts for
5 papers
Synchronization conditions in the Kuramoto model and their relationship to seminorms
Jared C. Bronski, Thomas E. Carty, Lee DeVille
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical resu…
A Matrix Valued Kuramoto Model
Jared C. Bronski, Thomas E. Carty, Sarah E. Simpson
Beginning with the work of Lohe [14,15] there have been a number of papers [3,5,8,9,11] that have generalized the Kuramoto model for phase-locking to a non-commuting situation. Her…
Configurational stability for the Kuramoto-Sakaguchi model
Jared Bronski, Thomas Carty, Lee DeVille
The Kuramoto--Sakaguchi model is a modification of the well-known Kuramoto model that adds a phase-lag paramater, or "frustration" to a network of phase-coupled oscillators. The Ku…
Elementary Solutions for a model Boltzmann Equation in one-dimension and the connection to Grossly Determined Solutions
Thomas E Carty
The Fourier-transformed version of the BGK model in one-dimension is solved in order to determine the general solution's asymptotics. The ultimate goal of this paper is to demonstr…
Grossly Determined Solutions for a Boltzmann-like Equation
Thomas E. Carty
In gas dynamics, the connection between the continuum physics model offered by the Navier-Stokes equations and the heat equation and the molecular model offered by the kinetic theo…