arXiv subjects

Christopher J. Winfield

Publications and source records attributed to Christopher J. Winfield.

4 recordsLinked to original sources

arXiv2025

On the Cowling Approximation: A Verification of Ansatz via Methods of Functional and Asymptotic Analysis

We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic degree and high oscillation frequency. Our methods involve a reformulation of the system in terms of an integro-differential equation for which certain Hilbert-space methods apply. By way of a more complete asymptotic study, we extend our results to certain fundamental solution sets, characterized according to certain multi-point boundary-value problems: Such asymptotics further enable us to produce sharp estimates as confirmation of our general results.

math-ph↗

arXiv2016

Continuum Eigenmodes in Some Linear Stellar Models

We apply parallel approaches in the study of continuous spectra to adiabatic stellar models. We seek continuum eigenmodes for the LAWE formulated as both finite difference and linear differential equations. In particular, we apply methods of Jacobi matrices and methods of subordinancy theory in these respective formulations. We find certain pressure-density conditions which admit positive-measured sets of continuous oscillation spectra under plausible conditions on density and pressure. We arrive at results of unbounded oscillations and computational or, perhaps, dynamic instability.

math-ph↗

arXiv2011

Local Solvability on H_1: Non-homogeneous Operators

Local solvability and non-solvability are classified for left-invariant differential operators on the Heisenberg group H_1 of the form L=P_n(X,Y)+Q(X,Y) where the P_n are certain homogeneous polynomials of order n greater than or equal to 2 and Q is of lower order with X= \partial_x, Y=\partial_y+x\partial_w on R^3. We extend previous studies of operators of the form P_n(X,Y) via representations involving ordinary differential operators with a parameter.

math.AP↗

arXiv2011

Asymptotic Methods of ODEs: Exploring Singularities of the Second Kind

We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and higher-order scalar equations where growth behavior is expressed in terms of elementary functions. We then recast our equations in mollified form - thereby obtaining stability.

cs.SC↗