Linda Cummings works on a variety of physically-motivated free boundary problems, mostly fluid-dynamical in nature, many of which arise in industrial or biological applications. On the biological side her current work includes studies of fluid flow, nutrient transport and cell growth in tissue engineering applications; flow dynamics and bacterial biofilm formation in prosthetic devices such as urethral catheters and ureteric stents; and dynamics of lipids in cell membranes.
Her current industrially-relevant projects include modeling and analysis of "bistable" nematic liquid crystal display devices; modeling of bubble dynamics in the manufacture of glass fibers; and the flow of thin liquid films (both Newtonian and non-Newtonian). She also works on classical low Reynolds number free boundary flows, such as Stokes flows and Hele-Shaw flows. Her mathematical approaches are wide-ranging, encompassing skills of mathematical modeling, discrete and continuum mechanics, complex analysis, and asymptotic and numerical methods.
PhD, Applied Mathematics, University of Oxford (UK)
Much of my research is concerned with physically-arising free boundary problems.
My current work ranges from classical low Reynolds number fluid dynamical problems (such as Hele-Shaw flows and Stokes flows with free boundaries), through industrial problems (such as bistable nematic liquid crystal displays, directly motivated by the need for low energy consumption "electronic paper"; and flows of thin liquid films), to biological applications (including dynamics in cell membranes, tissue engineering applications, and flow dynamics in the catheterized or stented urinary tract).
In such applied problems, mathematical models can provide new insights that complement those obtained by experimental methods. The mathematical approaches are wide-ranging, encompassing skills of mathematical modeling, discrete and continuum mechanics, complex analysis, and asymptotic and numerical methods.
"Comparison of methods for evaluating functions of a matrix exponential" (with H.A. Ashi, P.C. Matthews), to appear in Appl. Num. Math. (2008).
"Ureteric stents: Investigating flow and encrustation" (with S.L. Waters, K. Heaton, J.H. Siggers, R. Bayston, M. Bishop, D.M. Grant, J.M. Oliver, J.A.D. Wattis), to appear in J. Eng. Med. (2008).
"Liquid film dynamics in horizontal and tilted tubes: dry spots and sliding drops" (with A.A. King and O.E. Jensen), Phys. Fluids. 19, 042101 (2007).
"Towards a mathematical model of the assembly and disassembly of membrane microdomains: comparison with experimental models" (with G.W. Richardson, H.J. Harris, P. O´Shea), Biophys. J. 92, 4145-4156 (2007).
"Tissue growth in a rotating bioreactor: Part II: fluid flow and nutrient transfer problems" (with S.L. Waters), Math. Med. Biol. 24, 169-208 (2007).
"Bistable nematic liquid crystal device with flexoelectric switching" (with G.W. Richardson), Europ. J. Appl. Math. 17, 435-463 (2006).
"Tissue growth in a rotating bioreactor: Part I: mechanical stability" (with S.L. Waters, K.M. Shakesheff, F.R.A.J. Rose), Math. Med. Biol. 23, 311-337 (2006).
"Capillary drainage of an annular film: the dynamics of collars and lobes" (with J. Lister, J.M. Rallison, A.A. King, O.E. Jensen), J. Fluid Mech. 552, 311-343 (2006).
"Evolution of a thin film of nematic liquid crystal with anisotropic surface energy", Europ. J. Appl. Math. 15, 651-677 (2004).
"Hele-Shaw flow with a point sink: generic solution breakdown" (with J.R. King), Europ. J. Appl. Math. 15, 1-37 (2004).
"Transition of a moving contact line from smooth to angular" (with M. Ben Amar, Y. Pomeau), Phys. Fluids 15, 2949-2960 (2003).