Publications & Other Projects

Publications and Preprints

[6] Dynamics of tethered membranes in inviscid flow arXiv, Journal
C. Mavroyiakoumou, S. Alben, J. Fluids Struct., 107:103384 (2021)

We investigate the dynamics of membranes that are held by freely-rotating tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations in terms of deflection amplitudes, dominant periods, and numbers of deflection extrema along the membranes across the parameter space of membrane mass density, stretching modulus, pretension, and tether length. We determine the region of instability and the small-amplitude behavior by solving a nonlinear eigenvalue problem. We also consider an infinite periodic membrane model, which yields a regular eigenvalue problem, analytical results, and asymptotic scaling laws. We find qualitative similarities among all three models in terms of the oscillation frequencies and membrane shapes at small and large values of membrane mass, pretension, and tether length/stiffness.
[5] Eigenmode analysis of membrane stability in inviscid flow arXiv, Journal
C. Mavroyiakoumou, S. Alben, Phys. Rev. Fluids, 6, 043901-1--32 (2021)

We study the stability of a thin membrane (of zero bending rigidity) with a vortex sheet as a nonlinear eigenvalue problem in the parameter space of membrane mass (R1) and pretension (T0). With both ends fixed light membranes become unstable by a divergence instability and heavy membranes lose stability by flutter and divergence for a T0 that increases with R1. With the leading edge fixed and trailing edge free, or both edges free, membrane eigenmodes transition in shape across the stability boundary. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.
[4] Large-amplitude membrane flutter in inviscid flow arXiv, Journal
C. Mavroyiakoumou, S. Alben, Journal of Fluid Mechanics, 891, A23-1--34 (2020)

    Fixed-free membranes: R1=0.31623, R3=3.1623, T0=0.01,   R1=1, R3=3.1623, T0=0.01,   R1=1, R3=10, T0=0.01
    Free-free membranes: R1=0.31623, R3=3.1623, T0=0.01,   R1=1, R3=10, T0=0.01,   R1=3.1623, R3=10, T0=0.01

We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex sheet wakes in two-dimensional inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free to move in the transverse direction, the membranes flutter periodically at intermediate values of mass density. As mass density increases, the motions are increasingly aperiodic, and the amplitudes increase and spatial and temporal frequencies decrease. As mass density decreases from the periodic regime, the amplitudes decrease and spatial and temporal frequencies increase until the motions become difficult to resolve numerically. With both edges free to move in the transverse direction, the membranes flutter similarly to the fixed–free case, but also translate vertically with steady, periodic or aperiodic trajectories, and with non-zero slopes that lead to small angles of attack with respect to the oncoming flow.
[3] Collinear interaction of vortex pairs with different strengths - criteria for leapfrogging PDF, Journal
C. Mavroyiakoumou, F. Berkshire, Physics of Fluids, 32, 023603 (2020) *Editor's pick*

We formulate a system of equations that describes the motion of four vortices made up of two interacting vortex pairs, where the absolute strengths of the pairs are different. Each vortex pair moves along the same axis in the same sense. In much of the literature, the vortex pairs have equal strength. The vortex pairs can either escape to infinite separation or undergo a periodic leapfrogging motion. We determine an explicit criterion in terms of the initial horizontal separation of the vortex pairs given as a function of the ratio of their strengths, to describe a periodic leapfrogging motion when interacting along the line of symmetry. In an appendix we also contrast a special case of interaction of a vortex pair with a single vortex of the same strength in which a vortex exchange occurs.
[2] Mathematical modelling of a viscida network PDF, Journal
C. Mavroyiakoumou, I. M. Griffiths, P. D. Howell, Journal of Fluid Mechanics, 872, 147-176 (2019)

We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly, and then considering the limit as the smoothing tends to zero. The analysis is generalized to derive a simple model for the behaviour at a junction between an arbitrary number of viscidas, which is then coupled to the governing equation for each viscida. We thus obtain a general theory, consisting of N partial differential equations and 3J algebraic conservation laws, for a system of N viscidas connected at J junctions. This approach provides a framework to understand the fabrication of microstructured optical fibres containing closely spaced holes separated by interconnected thin viscous struts. We show sample solutions for simple networks with J=2 and N=2 or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses.
[1] The QRD and SVD of matrices over a real algebra arXiv, Journal
P. Ginzberg, C. Mavroyiakoumou, Linear Algebra and its Applications, 504, 27-47 (2016)

Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD to a wide class of real algebras, including all finite-dimensional semi-simple algebras, (twisted) group algebras and Clifford algebras. Two approaches are described for computing the QRD/SVD: one Jacobi method with a generalised Givens rotation, and one based on the Artin–Wedderburn theorem.


[1] Optimizing the performance of a conical ceramic membrane PDF, Report
C. Mavroyiakoumou et al., Proc. 146th European Study Group with Industry (2019)

Other projects

[8] Mathematical Modelling of Microstructured Optical Fibres
C. Mavroyiakoumou, Prof. Ian Griffiths and Prof. Peter Howell, MSc Thesis (Trinity Term and Summer 2017)

[7] Solving Non-linear Elasticity BVPs in FEniCS: Bifurcations and Buckling of Beams PDF
C. Mavroyiakoumou, Prof. Patrick Farrell, Python in Scientific Computing (Trinity Term 2017)

[6] Stokes Flow and Free Boundaries PDF
C. Mavroyiakoumou, Prof. Peter Howell, Applied Complex Variables (Hilary Term 2017)

[5] Modelling Soil Erosion and Bed Formation in Shallow Overland Flow PDF
C. Mavroyiakoumou, Prof. Graham Sander, Case Study for Mathematical Modelling (Hilary Term 2017)

[4] Numerical Linear Algebra: Comparison of Several Numerical Methods used to solve Poisson's Equation PDF
C. Mavroyiakoumou, Dr. Kathryn Gillow, Case Study for Scientific Computing (Hilary Term 2017)

[3] Sliding Glaciers and Cavitation PDF
C. Mavroyiakoumou, Prof. Ian Hewitt, Mathematical Geoscience (Michaelmas Term 2016)

[2] Dynamics of Interacting Vortices - the restricted three vortex problem and leapfrogging of vortex pairs
C. Mavroyiakoumou, Dr. Frank Berkshire, UROP research project (Summer 2015)

[1] A Network of Mathematical Theorems PDF
C. Mavroyiakoumou, Dr. Nick Jones, Second year group project (June 2015)