Student Publications

Note to MASDOC students, the following acknowledgement must apear on any papers resulting from research done while in the MASDOC program:

This work is supported by EPSRC as part of the MASDOC DTC at the University of Warwick. Grant No. EP/HO23364/1.

2015 Cohort

 Kamil Kosiba Dynamical poroplasticity model with mixed boundary conditions – Theory for LM-type nonlinearity With K. Kisiel. 443(1), 187–229, 2016 Katharina Hopf Aggregation equations with fractional diffusion: preventing concentration by mixing with J. Rodrigo

2014 Cohort

 Wojciech Ożański Równania różniczkowe cząstkowe (Partial differential equations). With K. Chelminski. Warsaw University of Technology Publishing House (2015) 978-83-7814-405-2 A generalised comparison principle for the Monge-Ampère equation and the pressure in 2D fluid flows arxiv:1611.06157 The Lagrange multiplier and the stationary Stokes equations On weak solutions to the Navier-Stokes inequality with internal singularities Leray's fundamental work on the Navier-Stokes equations: a modern review of “Sur le mouvement d’un liquide visqueux emplissant l’espace” with B. Pooley Pavlos Tsatsoulis Spectral Gap for the Stochastic Quantization Equation on the 2-dimensional Torus. With H. Weber. arxiv:1609.08447 Theodoros Assiotis Interlacing Diffusions With N. O'Connell and J. Warren arxiv:1607.07182 Intertwinings for general β Laguerre and Jacobi processes arxiv:1609.03764 Hua-Pickrell diffusions and Feller processes on the boundary of the graph of spectra arxiv:1703.01813

2013 Cohort

 Adam Bowditch Escape regimes of biased random walks on Galton-Watson trees. Early access online: Probab. Theory Relat. Fields Central limit theorems for biased randomly trapped random walks on $\mathbb{Z}$ A quenched central limit theorem for biased random walks on supercritical Galton-Watson trees Jake Dunn The Klein-Gordon equation on the toric adS-Schwarzschild black hole. With C. Warnick. Classical and Quantum Gravity 33(12) 125010. Yulong Lu A Bayesian level set method for geometric inverse problems. With M.Iglesias and A. Stuart. Interfaces and Free Boundaries, 18 (2016) Gaussian approximations for transition paths in molecular dynamics. With A. Stuart and H. Weber. arXiv:1604.06594 Gaussian Approximations for Probability Measures on $\mathbb{R}^d$ With A. Stuart and H. Weber. arxiv:1611.08642 On the Bernstein-Von Mises Theorem for High Dimensional Nonlinear Bayesian Inverse Problems arxiv:1706.00289 Jamie Lukins Multi-point correlations for two dimensional coalescing random walks With R. Tribe and O. Zaboronski arxiv:1707.06250 Jack Skipper A simple integral condition for energy conservation in the 3D Euler equations With J. Robinson and J. Rodrigo arxiv:1611.00181 Approach and separation of quantum vortices with balanced cores With C. Rorai, R. Kerr and K. Sreenivasan arxiv:1410.1259 John Sylvester Random walk hitting times and effective resistance in sparsely connected Erdős-Rényi random graphs arxiv:1612.00731

2012 Cohort

 Matthew Dunlop The Bayesian Formulation of EIT: Analysis and Algorithms. With A. M. Stuart. Inverse Problems and Imaging Volume 10, No. 4, 2016, 1007-1036 MAP Estimators for Piecewise Continuous Inversion. With A. M. Stuart. Inverse Problems 32 ( 2016 ) 105003 ( 50pp ) Hierarchical Bayesian Level Set Inversion. With M. A. Iglesias and A. M. Stuart. Statistics and Computing 2016 Adam Griffin Simulation from quasi-stationary distributions on reducible state spaces With P. Jenkins, G. Roberts and S. Spencer Graham Hobbs A Variational Approach to Particles in Lipid Membranes. With C. M. Elliott, C. Gräser, R. Kornhuber and M. Wolf. Arch Rational Mech Anal (2016) 222: 1011. doi:10.1007/s00205-016-1016-9. Jere Koskela Computational inference beyond Kingman's coalescent. With P Jenkins and D. Spano. Journal of Applied Probability 52.2 (2015), 519-537 Consistency of Bayesian nonparametric inference for discretely observed jump diffusions. With P. A. Jenkins and D. Spanò arXiv:1506.04709 Bayesian non-parametric inference for Lambda-coalescents: consistency and a parametric method. With P. A. Jenkins and D. Spano. arXiv:1512.00982 Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo. With P. A. Jenkins and D. Spano. Early access online: Statistics and Computing, 2017, 1-14. DOI: 10.1007/s11222-017-9722-1 Benjamin Lees Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loops. Comm. Math. Phys., 347(1), 83-101 (2016) Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction. Journal of Mathematics and Physics. 55, 093303 (2014) Correlation inequalities for the quantum XY model. With C. Benassi and D. Ueltschi. J. Stat. Phys., 164(5), 1157-1166 (2016) Staggered long-range order for diluted quantum spin models. With R Kotecký. arXiv:1605.06279 Felipe Medina-Aguayo Stability of Noisy Metropolis-Hastings. With A. Lee and G. Roberts. Statistics and Computing November 2016, Volume 26, Issue 6, pp 1187–1211 Faizan Nazar Locality of the Thomas-Fermi-von Weizsäcker Equations. With C. Ortner. arXiv:1509.06753 Convergence Rates from Yukawa to Coulomb Interaction in the Thomas-Fermi-von Weizsäcker Model. arXiv:1601.01187 David O'Connor The Cahn-Hilliard equation on an evolving surface. With B. Stinner arXiv:1607.05627 Daniel Sanz-Alonso Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators. With K. Law, A. Shukla and A. Stuart. Physica D: Nonlinear Phenomena, 325, 1-13 (2016). Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems. With A. Stuart. SIAM/ASA J. Uncertainty Quantification, 3(1), 1200-1220 (2015) Importance sampling: Computational complexity and intrinsic dimension. With S. Agapiou, O. Papaspiliopoulos and A. Stuart. To appear in Statistical Science. Gaussian approximations of small noise diffusions in Kullback-Leibler divergence. With A. Stuart. To appear in Communications in Mathematical Sciences. Huan Wu Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. With A. Dedner and C. Ortner To appear in ESAIM: Mathematical Modelling and Numerical Analysis.

2011 Cohort

 Amal Alphonse An abstract framework for parabolic PDEs on evolving spaces. With C. M. Elliott and B. Stinner. Port. Math. 72 (2015), 1-46 A Stefan problem on an evolving surface. With C. M. Elliott. Phil. Trans. R. Soc. A 373:20140279 (2015) On some linear parabolic PDEs on moving hypersurface. With C. M. Elliott and B. Stinner. Interfaces Free Bound. 17 (2015), 157-187 Well-posedness of a fractional porous medium equation on an evolving surface. With C. M. Elliott. Nonlinear Analysis: Theory, Methods & Applications 137, 3-42 Barnaby Garrod Interacting particle systems on $\mathbb{Z}$ as Pfaffian point processes I - annihilating and coalescing random walks With R. Tribe and O. Zaboronski Examples of interacting particle systems on $\mathbb{Z}$ as Pfaffian point processes II - coalescing branching random walks and annihilating random walks with immigration With M. Poplavskiy, R. Tribe and O. Zaboronski arxiv:1605.09668 Alexander Kister Sample path large deviations for Laplacian models in $(1+1)$-dimensions With S. Adams and H. Weber. Electron. J. Probab. 21 (2016), no. 62, 1–36. Yuchen Pei A q-weighted version of the Robinson-Schensted algorithm. With N. O'Connell. Electronic Journal of Probability, 18 (2013), 95, 1-25 A symmetry property for q-weighted Robinson-Schensted and other branching insertion algorithms. J. Algebr. Comb. 40(3) 743-770(2014) On a causal quantum double product integral related to Lévy stochastic area. With R. Hudson. arXiv:1506.04294 Unitary causal quantum stochastic double products as universal interactions I. With R. Hudson. Vol. 46 (2015) ACTA PHYSICA POLONICA B No 9. Abhishek Shukla Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model. With K. Law and A. Stuart. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume 34 , Number 3 , March 2014 Matthew Thorpe Convergence of the k-means minimization problem using Gamma convergence. With F. Theil, A. Johansen and N. Cade. SIAM Journal on Applied Mathematics, (2015) Self-reinforced Meta Learning for Belief Generation. With A. Gkiokas and A. Cristea. Research and Development in Intelligent Systems XXXI, Springer International Publishing, (2014) Convergence and Rates for Fixed-Interval Multiple-Track Smoothing Using k-Means Type Optimization. With A. Johansen. Electronic Journal of Statistics 10(2):3693-3722, 2016. Weak Convergence of General Smoothing Splines. With A. Johansen. arXiv:1506:08450

2010 Cohort

 Charles Brett Accuracy and Stability of Filters for Dissipative PDEs. With K. Lam, K Law, D. McCormick, M. Scott and A. Stuart. Physica D245 (15 February 2013), 34-45 Mesh adaptivity in optimal control of elliptic variational inqualities with point-tracking of the state. With C.M. Elliott, M. Hintermuller and C. Lobhard Interfaces and Free Boundaries Vol 17 (2015) 21-53 Phase diagrams for knotted and unknotted ring polymers. Phys. Rev. E 85, 031804 (2012) Phase field methods for binary recovery. With A. Dedner and C. M. Elliott. LNCSE Optimization with PDE constraints, Vol 101, (2014) 25-63 Optimal control of elliptic PDEs at points. With A. Dedner and C. M. Elliot. IMA J. Numer. Anal. 36 (2016), no. 3, 1015–1050. Optimal control of elliptic PDEs on surfaces of codimension 1. With A. Dedner and C. M. Elliot. arXiv:1411.4974 Michael Eyers Phase Transitions in Delaunay Potts Models With S. Adams Journal of Statistical Physics 161, No. 4, DOI10.1007/s10955-015-1393-8 (2015) Adam Hall Pharmacokinetic modelling of derivatives of the anti-malerial drug artemisinin. Biological and Medical Systems 8 (2013) 266-271 Kei Fong Lam Analysis of the diffuse domain approach for a bulk-surface coupled PDE system. With H. Abels, K. Lam and B. Stinner SIAM J Math Analysis 47 (2015), 3687--3725. Accuracy and Stability of Filters for Dissipative PDEs. With C. Brett, K. Law, D. McCormick, M. Scott and A. Stuart. Physica D245 (15 February 2013), 34-45 Diffuse interface modelling of soluble surfactants in two-phase flow. With H. Garcke and B. Stinner Communications in Mathematics, Vol 12, Number 8, pages 1475-1522 Pravin Madhavan Adaptive discontinuous Galerkin methods on surfaces. With A. Dedner Numerische Mathematik (2015) DOI 10.1007/s00211-015-0719-4 Analysis of the discontinuous Galerkin method for elliptic problems on surfaces. With A. Dedner and B. Stinner IMA Journal of Numerical Analysis 33, No 3(2013), 952-973 Discontinuous Galerkin methods for hyperbolic and advection-dominated problems on surfaces. With A. Dedner arXiv:1505.06752 High Order discontinuous Galerkin Methods on Surfaces. With P. Antonietti, A. Dedner, S. Stangalino, B. Stinne and M. Verani. SIAM Journal on Numerical Analysis 53 (2), 1145-1171 David McCormick Accuracy and Stability of Filters for Dissipative PDEs. With C. Brett, K. Lam, K. Law, M. Scott and A. Stuart. Physica D245 (15 February 2013), 34-45 Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation. With J. Robinson and J. Rodrigo. Arch. Rational Mech. Anal., 214(2):503–523, (2014) Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO. With J. Robinson and J. Rodrigo. Milan J. Math., 81(2):265–289, (2013) Local existence for the non-resistive MHD equations in Besov spaces. With J. Chemin, J. Robinson and J. Rodrigo Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. With C. Fefferman, J. Robinson and J. Rodrigo J. Funct. Anal., 267(4):1035–1056, (2014) Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in $\overdot{H}^{3/2}$, $\overdot{H}^{5/2}$, and $\overdot{B}^{5/2}_{2,1}$. With E. Olson, J. Robinson, J. Rodrigo, A. Vidal-Lopez and Y. Zhou Michael Scott Accuracy and Stability of Filters for Dissipative PDEs. With C. Brett, K. Lam, K. Law, D. McCormick and A. Stuart. Physica D245 (15 February 2013), 34-45 Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds. With C. M. Elliott and M. Hairer arXiv:1208.5958 Maria Veretennikova Controlled Continuous Time Random Walks and Fractional Hamilton Jacobi Bellman Equations. With V. Kolokoltsov arXiv:1203.6333 A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled Continuous Time Random Walks With V. Kolokoltsov Communications in Applied and Industrial Mathematics, 6 (1) - CAIM Special Issue hosted in the journal Communications in Applied and Industrial Mathematics published by SIMAI. Wellposedness and regularity of the Cauchy problem for nonlinear fractinal in time and space equations. With V. Kolokoltsov Fractional Differential Calculus, Volume 4, Number 1 (2014), 1–30