|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).
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 >>.