# Chris Budd, OBE

## Profile

I have broad research interests in interdisciplinary industrial and applied mathematics with a particular interest in complex nonlinear problems arising in real applications. Typically these involve the solution (analytically or numerically) of partial differential equations. A large amount of my work for the last ten years has been in numerical weather prediction and data assimilation in close collaboration with the Met Office (which I visit very frequently). My algorithms are now incorporated into the Met Office operational weather forecasting code where they have made a significant difference to their accuracy and received a Knowledge Transfer Award. I am also working on climate modelling using modern mathematical and computational methods and am actively involved in a number of international climate modelling networks, including CliMathNet which I co-direct and the Maths of Planet Earth programme. I also collaborate with the energy industry, the aerospace industry, the telecommunications industry and the food industry. Anywhere that maths can be applied is of interest to me.

#### Public Understanding of Science and Engagement

I believe very strongly indeed that the excitement and importance of mathematics and science should be communicated to as wide an audience as possible. I am actively involved in doing this, both in developing programmes with young people through my positions of Prof of Mathematics at the Royal Institution and my vice-presidentship of the Institute of Mathematics and its Applications, and in directing the Bath Taps Into Science Festival. My recent projects include two Citizen Science Projects in Climate Science and I am also working closely with Policy Makers involved in climate science. The latter has involved regular discussion/policy meetings with senior civil servants through the CliMathNet network, and also in running programmes on climate science with the British Science Association, the Science Museum and the Royal Institution

### Publications

Aouaichia, M., McCullen, N., Bowen, C., Almond, D., Budd, C. and Bouamrane, R., 2017. Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks. *European Physical Journal B*, 90 (3), 39.

Budd, C. J., Chakhchoukh, A. N., Dodwell, T. J. and Kuske, R., 2016. Chevron folding patterns and heteroclinic orbits. *Physica D: Nonlinear Phenomena*

Budd, C. J. and Stockie, J. M., 2016. Multilayer asymptotic solution for wetting fronts in porous media with exponential moisture diffusivity. *Studies in Applied Mathematics*, 136 (4), pp. 424-458.

Weller, H., Browne, P., Budd, C. and Cullen, M., 2016. Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation. *Journal of Computational Physics*, 308, pp. 102-123.

Budd, C., Cullen, M. and Piccolo, C., 2016. Improving weather forecasting accuracy by using r-adaptive methods coupled to data assimilation algorithms. *In*: Aston, P. J., Mulholland, A. J. and Tant, K. M. M., eds. *UK Success Stories in Industrial Mathematics.* Springer International Publishing AG, pp. 11-18.

Jenkins, S., Smith, N., Budd, C. and Freitag, M., 2015. The effect of numerical model error on data assimilation. *Journal of Computational and Applied Mathematics*, 290, pp. 567-588.

Budd, C. J., Dold, J. W. and Galaktionov, V. A., 2015. Global blow-up for a semilinear heat equation on a subspace. *Proceedings of the Royal Society of Edinburgh Section A - Mathematics*, 145 (5), 893 - 923.

Budd, C., Walsh, E. and Russell, R., 2015. The geometry of r-adaptive meshes generated using optimal transport methods. *Journal of Computational Physics*, 282, pp. 113-137.

Mora, K., Budd, C., Glendinning, P. and Keogh, P., 2014. Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery. *Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*, 470 (2171), p. 20140490.

Zhang, Z., Li, J., Li, F., Budd, C. and Hamidi, V., 2014. Assessment of DG security contribution on transmission levels. *In*: *PES General Meeting/ Conference & Exposition, 2014 IEEE*, 2014-07-27 - 2014-07-31. IEEE.

Browne, P. A., Budd, C. J., Piccolo, C. and Cullen, M., 2014. Fast three dimensional r-adaptive mesh redistribution. *Journal of Computational Physics*, 275, pp. 174-196.

Amodio, P., Budd, C. J., Koch, O., Settanni, G. and Weinmüller, E., 2014. Asymptotical computations for a model of flow in saturated porous media. *Applied Mathematics and Computation*, 237, pp. 155-167.

Freitag, M. A., Nichols, N. K. and Budd, C. J., 2013. Resolution of sharp fronts in the presence of model error in variational data assimilation. *Quarterly Journal of the Royal Meteorological Society*, 139 (672), pp. 742-757.

Budd, C. J., Cullen, M. J. P. and Walsh, E. J., 2013. Monge–Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem. *Journal of Computational Physics*, 236, pp. 247-270.

Almond, D. P., Budd, C. J., Freitag, M. A., Hunt, G. W., McCullen, N. J. and Smith, N. D., 2013. The origin of power-law emergent scaling in large binary networks. *Physica A: Statistical Mechanics and its Applications*, 392 (4), pp. 1004-1027.

Browne, P. A., Budd, C., Gould, N. I. M., Kim, H. A. and Scott, J. A., 2012. A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints. *International Journal for Numerical Methods in Engineering*, 92 (12), pp. 1026-1043.

Dodwell, T. J., Hunt, G. W., Peletier, M. A. and Budd, C. J., 2012. Multi-layered folding with voids. *Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences*, 370 (1965), pp. 1740-1758.

Hunt, G., Butler, R. and Budd, C., 2012. Geometry and mechanics of layered structures and materials. *Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences*, 370 (1965), pp. 1723-1729.

Budd, C., 2012. *Improving the Forecasting of Storms.* University of Bath.

Dodwell, T. J., Peletier, M. A., Budd, C. J. and Hunt, G. W., 2012. Self-similar voiding solutions of a single layered model of folding rocks. *SIAM Journal on Applied Mathematics*, 72 (1), pp. 444-463.

Budd, C., Freitag, M. A. and Nichols, N. K., 2011. Regularization techniques for ill-posed inverse problems in data assimilation. *Computers and Fluids*, 46 (1), pp. 168-173.

Budd, C., Champneys, A., Lord, G. and Virgin, L., 2011. Introduction to special issue on reflections in nonlinear mechanics. *IMA Journal of Applied Mathematics*, 76 (1), p. 1.

Pring, S. R. and Budd, C. J., 2011. The dynamics of a simplified pinball machine. *IMA Journal of Applied Mathematics*, 76 (1), pp. 67-84.

Budd, C. J. and Hill, A. D. C., 2011. A comparison of models and methods for simulating the microwave heating of moist foodstuffs. *International Journal of Heat and Mass Transfer*, 54 (4), pp. 807-817.

Soleimani, M., Stewart, V. and Budd, C., 2011. Crack detection in dielectric objects using electrical capacitance tomography imaging. *Insight: Non-Destructive Testing and Condition Monitoring*, 53 (1), pp. 21-24.

Green, S. C., Budd, C. J. and Hunt, G. W., 2011. Breathers in a pinned mechanical lattice. *SIAM Journal on Applied Dynamical Systems*, 10 (1), pp. 66-91.

Almond, D., Budd, C. J. and McCullen, N. J., 2011. Emergent behaviour in large electrical networks. *In*: Georgoulis, E. H., Iske, A. and Levesley, J., eds. *Approximation Algorithms for Complex Systems.* Springer, pp. 3-26.

Freitag, M. A., Nichols, N. K. and Budd, C. J., 2010. L1-regularisation for ill-posed problems in variational data assimilation. *PAMM - Proceedings in Applied Mathematics and Mechanics*, 10 (1), 665 -668.

Smith, N. D., Pokhotelov, D., Mitchell, C. N. and Budd, C., 2010. Image-model coupling:application to an ionospheric storm. *Nonlinear Processes in Geophysics*, 17 (4), pp. 361-369.

Budd, C. J. and Williams, J. F., 2010. How to adaptively resolve evolutionary singularities in differential equations with symmetry. *Journal of Engineering Mathematics*, 66 (1-3), pp. 217-236.

Pring, S. R. and Budd, C. J., 2010. The dynamics of regularized discontinuous maps with applications to impacting systems. *SIAM Journal on Applied Dynamical Systems*, 9 (1), pp. 188-219.

Stewart, V. J., Budd, C. J., Dorn, S. and Soleimani, M., 2010. Crack detection in dielectric objects using electrical capacitance tomography. *In*: *6th World Congress on Industrial Process Tomography (WCIPT6)*, 2010-09-06 - 2010-09-09. International Society for Industrial Process Tomography, pp. 876-883.

Budd, C. J., Huang, W. and Russell, R. D., 2009. Adaptivity with moving grids. *Acta Numerica*, 18, pp. 111-241.

Smith, N. D., Mitchell, C. N. and Budd, C. J., 2009. Image-model coupling:a simple information theoretic perspective for image sequences. *Nonlinear Processes in Geophysics*, 16 (2), pp. 197-210.

Budd, C. J. and Williams, J. F., 2009. Moving mesh generation using the parabolic Monge–Ampère equation. *SIAM Journal on Scientific Computing*, 31 (5), pp. 3438-3465.

di Bernardo, M., Budd, C. J., Champneys, A. R., Kowalczyk, P., Nordmark, A. B., Tost, G. O. and Piiroinen, P. T., 2008. Bifurcations in Nonsmooth Dynamical Systems. *Siam Review*, 50 (4), pp. 629-701.

di Bernardo, M., Budd, C. J., Champneys, A. R. and Kowalczyk, P., 2008. *Piecewise-smooth dynamical systems:theory and applications.* Springer.

Mccullen, N. J., Almond, D. P., Budd, C. J. and Hunt, G. W., 2008. The robustness of the emergent scaling property of random RC network models of complex materials. *Journal of Physics D: Applied Physics*, 42 (6), 064001.