Computation and Applications of Mathieu Functions: A Historical Perspective
- MathematicsSIAM Rev.
This paper surveys and recapitulates the historical development of the theory and methods of computation for Mathieu functions and modified Mathieu function and identifies some gaps in current software capability, particularly to do with double eigenvalues of the Mathieu equation.
Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation
We construct a one-parameter family of generalized Mathieu functions, which are reduced quaternion-valued functions of a pair of real variables lying in an ellipse, and which we call λ-reduced…
Entropic analysis of optomechanical entanglement for a nanomechanical resonator coupled to an optical cavity field
- PhysicsSciPost Physics Core
We investigate entanglement dynamics for a nanomechanical resonator coupled to an optical cavity field through the analysis of the associated entanglement entropies. The effects of time variation of…
Gravitational waves in a closed spacetime via deviation equation
- PhysicsResults in Physics
Discrete Bessel and Mathieu Functions
The two-dimensional Helmholtz equation separates in elliptic coordinates based on two distinct foci, a limit case of which includes polar coordinate systems when the two foci coalesce. This equation…
A Compact, Passive Frequency-Hopping Harmonic Sensor Based on a Microfluidic Reconfigurable Dual-Band Antenna
- Computer ScienceIEEE Sensors Journal
It is demonstrated that the type of liquid mixture filling in the fluidic cavity can be clearly perceived by reading the peak received signal strength indicator (RSSI) in the spectrum of second harmonics.
Analytic baby skyrmions at finite density
We introduce a consistent ansatz for the baby Skyrme model in (2+1)-dimensions which is able to reduce the complete set of field equations to just one equation for the profile function in situations…
Metric preheating and radiative decay in single-field inflation
- PhysicsJournal of Cosmology and Astroparticle Physics
At the end of inflation, the inflaton oscillates at the bottom of its potential and these oscillations trigger a parametric instability for scalar fluctuations with wavelength λ comprised in the…
Almost Exact Computation of Eigenvalues in Approximate Differential Problems
- Mathematics, Computer ScienceMathematical and Computational Applications
This work presents a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools, allowing for high accuracy approximations of differential eigen values.