Extensible-pendulum and double-pendulum problems: damping & periodic forcing, chaos & fractals
(2024)
Presentation / Conference
Christian, J., Jafari, M., & Horne, D. (2024, April). Extensible-pendulum and double-pendulum problems: damping & periodic forcing, chaos & fractals. Poster presented at 65th British Applied Mathematics Colloquium (BAMC 2024), University of Newcastle, UK
Outputs (171)
Julia sets in relaxed Schröder and Newton-Raphson maps: periodic points, escape points, symmetry-breaking (2024)
Presentation / Conference
Christian, J., Elsby, D., & Alali, S. (2024, April). Julia sets in relaxed Schröder and Newton-Raphson maps: periodic points, escape points, symmetry-breaking. Presented at 65th British Applied Mathematics Colloquium (BAMC 2024), University of Newcastle, UK
The Newton-Raphson fractal (2023)
Other
Christian, J. M., & Jensen, G. S. (2023). The Newton-Raphson fractal
A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion (2023)
Journal Article
Elatrash, L., Chadwick, E., El-Mazuzi, R., Christian, J. M., Wang, Y., Adamu, H. A., & Chadwick, E. (in press). A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion. Computers and Fluids, 266, https://doi.org/10.1016/j.compfluid.2023.106064The problem studied was the non-reciprocal cyclic swimming motion of three spheres linked with axially aligned retractable arms in Stokes flow. The arms are assumed to be able to retract at a steady speed to half their length, and then at a later tim... Read More about A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion.
Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems (2023)
Journal Article
Huo, K., Yang, R., Jia, H., He, Y., & Christian, J. (2023). Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems. Nonlinear Dynamics, https://doi.org/10.1007/s11071-023-08574-9Seeking analytical solutions of nonlinear Schrödinger (NLS)-like equations remains an open topic. In this paper, we revisit the general inhomogeneous nonautonomous NLS (inNLS) equation and report on exact similaritons under generic constraint relati... Read More about Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems.
Vector cnoidal waves in spatiotemporal propagation: exact solutions beyond slowly-varying envelopes (2023)
Presentation / Conference
Christian, J., & McAteer, É. (2023, April). Vector cnoidal waves in spatiotemporal propagation: exact solutions beyond slowly-varying envelopes. Presented at 64th British Applied Mathematics Colloquium (BAMC 2023), University of the West of England and University of Bristol, UKCnoidal waves are periodic solutions to certain classes of nonlinear partial differential equations (PDEs). They are fundamental excitations in theories of waves and their more familiar localized counterparts––solitons––typically emerge as limits.... Read More about Vector cnoidal waves in spatiotemporal propagation: exact solutions beyond slowly-varying envelopes.
Dynamics on ₵ with generalized Newton-Raphson maps: Julia sets, uncertainty dimension, and periodic orbits (2023)
Presentation / Conference
Christian, J., & Jensen, G. (2023, April). Dynamics on ₵ with generalized Newton-Raphson maps: Julia sets, uncertainty dimension, and periodic orbits. Poster presented at 64th British Applied Mathematics Colloquium (BAMC 2023), University of the West of England and University of Bristol, UKThe Newton-Raphson (NR) method is a well-known iterative scheme for approximating the roots of functions. Deployed on the complex plane, ₵, perhaps its most famous application is to finding the cube roots of –1. One often regards any specific outco... Read More about Dynamics on ₵ with generalized Newton-Raphson maps: Julia sets, uncertainty dimension, and periodic orbits.
The effect of coherent coupling nonlinearity on modulation instability and rogue wave excitation (2022)
Journal Article
and rogue wave excitation. Communications in Nonlinear Science and Numerical Simulation, 106246. https://doi.org/10.1016/j.cnsns.2021.106246We study modulation instability (MI) in both anomalous and normal dispersion regimes of a coherently coupled system. It is found that there exist three types of MI spectra with distinct characteristics termed baseband, passband, and zero-baseband b... Read More about The effect of coherent coupling nonlinearity on modulation instability and rogue wave excitation.
Chaotic scattering : uncertainty and fractals from reflections (2020)
Journal Article
Christian, J. (2020). Chaotic scattering : uncertainty and fractals from reflections. Chalkdust (Online), 12, 11-18James M Christian reflects on chaos
On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson (2020)
Journal Article
Christian, J., & Middleton-Spencer, H. (2020). On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson. College Mathematics Journal, 51(2), 95-114. https://doi.org/10.1080/07468342.2020.1703452We consider a systematic generalization of the well-known cube roots of -1 problem to include the Nth roots. The associated fractal basin boundaries are computed, and we also explore how sensitive this class of systems is to fluctuations at its input... Read More about On the Nth roots of -1 and complex basin boundaries : fractals from Newton-Raphson.