Past Research
Matthew J. Hancock, Ph.D.
Microfluidics Expert | MIT PhD, ACE
Partner at Veryst Engineering, LLC
hancock (at) alum.mit.edu
Fluid pipes. A combined theoretical and experimental investigation of laminar vertical jets impinging on a deep fluid reservoir. In the parameter regime of interest, in a pure water system, the jet is characterized by a stationary field of capillary waves at its base. When the reservoir is contaminated by surfactant, the base of the jet is void of capillary waves, cylindrical and quiescent: water enters the reservoir as if through a rigid pipe. A theoretical description of the resulting fluid pipe is deduced by matching extensional plug flow upstream of the pipe onto entry pipe flow within it. Theoretical predictions for the pipe height are found to be in excellent accord with our experimental results. An analogous theoretical description of the planar fluid pipe expected to arise on a falling fluid sheet is also presented. In collaboration with Prof. John Bush. More pictures can be found here.
Hancock MJ and Bush JWM. Fluid pipes. J. Fluid Mech. 2002, 466: 285-304 [pdf]
Sand bars generated by waves on beaches. Theoretical modeling and experimental investigation of sand bar formation under ocean surface waves, including effects of suspended sediment (fine grains) and bed load transport on a sloping mean seabed, in water of intermediate depth. Model predictions compared with available laboratory and field data. Sediment sorting under surface waves studied experimentally with colored sands. In collaboration with Prof. Chiang C. Mei (Ph.D. thesis advisor) and Blake J. Landry.
Landry BJ, Hancock MJ, Mei CC, García MH. WaveAR: A software tool for calculating parameters for water waves with incident and reflected components. Computers & Geosciences, 2012, 46 : 38-43. [pdf]
Hancock MJ, Landry BJ & Mei CC. Sandbar formation under surface waves: Theory and experiments, J. Geophys. Res. 2008, 113: C07022 [pdf]
Landry BJ, Hancock MJ & Mei CC. Note on sediment sorting in a sandy bed under standing water waves. Coast. Eng. 2007, 54: 694-699 [pdf]
Hancock, MJ. Generation of sand sand bars under surface waves. Ph.D. Thesis, Massachusetts Institute of Technology, 2005.
Wave propagation over a seabed with random roughness. We study the effects of multiple scattering of slowly modulated water waves by a weakly random bathymetry. The combined effects of weak nonlinearity, dispersion and random irregularities are treated together to yield a deterministic nonlinear Schrödinger equation with a complex damping term. Implications on localization and side-band instability are discussed. Transmission and nonlinear evolution of a wave packet past a finite strip of disorder is examined. In collaboration with Prof. Chiang C. Mei and Jørgen H. Pihl.
Mei CC & Hancock MJ. Weakly nonlinear surface waves over a random seabed. J. Fluid Mech. 2003, 475: 247-268 [pdf]
Pihl JH, Mei CC & Hancock MJ. Surface gravity waves over a two-dimensional random seabed. Phys. Rev. E 2002, 66: 016611 [pdf]
Nonlinear differential equations in cosmology. During my junior and senior years at the University of Waterloo, I worked with Prof. John Wainwright on a nonlinear dynamical system that modeled a class of cosmological models. My contribution was discovering a change of variable that allowed a five variable non-autonomous system with oscillating terms to be approximated by an autonomous "averaged" system. The averaged system was then analyzed using standard methods.
Horwood JT, Hancock MJ, The D, Wainwright J. Late-time asymptotic dynamics of Bianchi VIII cosmologies. Class. Quantum Grav. 2003, 20 : 1757 – 1777 [pdf]
Nilsson US, Hancock MJ, and Wainwright J. Non-tilted Bianchi VII0 models - the radiation fluid. Class. Quantum Grav. 2000, 17 : 3119 – 3134 [pdf]
Wainwright J, Hancock MJ and Uggla C. Asymptotic self-similarity breaking at late times in cosmology. Class. Quantum Grav. 1999, 16 : 2577 – 2598 [pdf]
Wainwright J, Coley AA, Ellis GFR and Hancock M. On the isotropy of the Universe : do Bianchi VIIh cosmologies isotropize? Class. Quantum Grav. 1998, 15 : 331 – 350 [pdf]
