|School of Computing Science and Engineering, Newton Building (Office 272), University of Salford, Greater Manchester, United Kingdom, M5 4WT.|
|0161 295 5383|
MATHEMATICAL FLUID DYNAMICS
• Diffuse wakes and viscous flow problems. Calculation of flow fields around bluff bodies; Green’s boundary integral formulation of fluidic and aerodynamic problems; D’Alembert’s paradox; development of Eulerlet methods for predicting lift and drag characteristics.
• Non-Newtonian effects in Maxwellian fluids. Perturbation theory applied to peristaltic wave propagation; Maxwellian rheology (compressible fluids, viscoelasticity, finite-time response); finite-slip boundary conditions.
FRACTALS & COMPLEXITY
• Scattering of electromagnetic fields. Mathematical descriptions of scattered waves (Kirchhoff, Rayleigh-Sommerfeld, Fresnel); circulation and edge-wave formulations; computation of diffraction patterns; complex domains (fractal apertures and screens); scattering problems with fractal waves; boundary element methods.
• Fractal lasers. Virtual-source modelling of unstable-cavity lasers; role of transverse symmetry and kaleidoscope / fractal boundary conditions; computation of fractal dimension.
• Spontaneous pattern formation. Reaction-diffusion systems (dispersive & absorptive nonlinearities); thin-slice geometries (single feedback-mirror, ring cavity, Fabry-Pérot); propagation in bulk nonlinear media (counter-propagating beams, filled ring cavities); discrete nonlinear equations (Schrödinger and Ablowitz-Ladik) with ring cavity and counter-propagation boundary conditions; incoherent patterns and video-feedback systems.
• Spatiotemporal solitons. Spatially-dispersive systems (exact spatiotemporal solitons & stability); multi-component models (vector solutions & modulational instabilities); complex Ginzburg-Landau models and dissipative waves; nonlinear Klein-Gordon equations (exact solutions & stability); pulse propagation in nonlinear metamaterials.
• Nonparaxial spatial solitons. Fundamentals: geometrical aspects of beam propagation (exact analytical solitons of nonlinear Helmholtz equations, simulations of nonlinear wave phenomena, internal modes, stability & bistability); weakly-nonlinear analysis for Helmholtz equations; delocalized solutions (boundary solitons, cnoidal waves); multi-component solitons (coupled equations, vector solutions, stability); modelling ultranarrow optical beams. Applications: single interfaces (soliton refraction & Goos-Hänchen shifts); nonlinear surface waves (exact solutions & stability); solitons in patterned systems (waveguide arrays, photonic crystals).
• Ultra-broadband multi-frequency Raman generation. Exact solutions of UMRG equations; gain suppression analyses; detuning effects (linear and nonlinear); computational modelling of transient dynamics; novel cavity applications (ultrashort pulse generation, spontaneous self-synchronization).
Andrew King, MSc by Research thesis (Physics) "The utilisation of commercial off-the-shelf carbon nanotube fibre in individual metamaterial antennas to enble a reduction in operating frequencies."
Bwebum C. Dang, PhD thesis (Applied Mathematics) "A novel boundary element method for low Reynolds number external flow of biological fluid dynamics."
Rabeea M. H. Darghoth, PhD thesis (Applied Mathematics) "An investigation of the Oseen differential equations for the boundary layer."
Internal award of £2,000 for Research Support
Internal award of £2,000 for Research Support
Collaborations with other national and international reserach institutions evidenced by joint co-authorship of publications and conference contributions from 2005 - date:
Shanxi University, Taiyuan, China
U... more >>.
Optics Express (2015 - present)
Europhysics Letters (2014 - present)
Zeitschrift fuer Natrurforschung A: Journal of Physical ... more >>.
Prof. Rongcao Yang, Shanxi University, China. 4-month academic visit funded by Scholarship Council of China (November 2014 – March 2015).
£500 AWARDED: funding from University of Salford PGR conference fund to contribute to costs associated with presenting six papers at 3rd Annual Student Conference on Complexity Sci... more >>.
£1,200 AWARDED: funding from University of Salford ICF to contribute to costs associated with presenting four papers at Nonlinear Optics 2013 Topical Meeting, Kohala Coast, Hawaii, U... more >>.
£195 AWARDED: funding from Rank Prize Bursary Fund (Optoelectronics Committee) to contribute to costs associated with PhD student (Christopher Bostock) presenting papers at Photon12 (htt... more >>.
£1,240 AWARDED: School Research Funds (to support conference costs).
Main supervisor for students: Christopher Bostock (GTA, 01/10/2011-present) and Emily A McCoy (DTA, 01/10/2010-present). Also Timothy J. Ashcroft (DTA, 01/10/08-25/09/09)<... more >>.
£2,500 AWARDED: EPSRC Vacation Bursary: Self-sustaining light pulses arising from novel seminconductor material effects (awarded to Timothy F.Hodgkinson, 22/06/09 - 30/08/09).
Co-sup... more >>.
£800 AWARDED: funding from University of Salford ICF to contribute to costs associated with presenting two papers at Nonlinear Photonics 2007 Topical Meeting, Québec City, Canada (http://www.osa.or... more >>.