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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.2023.106064

The 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/s11071-023-08574-9

Seeking 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.

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, UK

The 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.

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, UK

Cnoidal 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.