# Paul Milewski

## Profile

My research interests are in fluid mechanics, numerical computation and mathematical biology.

My fluid mechanics work is mainly focussed on wave propagation at many scales, from a few centimetres on the surface of a pond (gravity-capillary waves) to planetary scale motions. An example of the latter are equatorial atmospheric waves propagating around the globe. This research has applications to physical oceanography, climate modelling and an understanding of physical processes of energy transfer and mixing.

In mathematical biology, I have interests in spatio-temporal dynamics of population level models, and how these population models can be derived from the behaviour of individuals in the population. For example I study how bacterial signalling and movement result in larger scale aggregations, and the equations describing the population density.

I approach these problems with a combination of dynamical systems methods, mathematical analysis, asymptotic approximations and numerical computations.

### Publications

Milewski, P. A. and Wang, Z., 2016. Self-focusing dynamics of patches of ripples. *Physica D: Nonlinear Phenomena*

Milewski, P. A., Galeano-Rios, C. A., Nachbin, A. and Bush, J. W. M., 2015. Faraday pilot-wave dynamics:modelling and computation. *Journal of Fluid Mechanics*, 778, pp. 361-388.

Milewski, P. A. and Tabak, E. G., 2015. Conservation law modelling of entrainment in layered hydrostatic flows. *Journal of Fluid Mechanics*, 772, pp. 272-294.

Wang, Z., Vanden-Broeck, J. M. and Milewski, P. A., 2014. Asymmetric gravity-capillary solitary waves on deep water. *Journal of Fluid Mechanics*, 759, R2.

Wang, Z., Pãrãu, E. I., Milewski, P. A. and Vanden-Broeck, J.-M., 2014. Numerical study of interfacial solitary waves propagating under an elastic sheet. *Proceedings of the Royal Society A*, 470 (2168), 20140111.

Boonkasame, A. and Milewski, P. A., 2014. A model for strongly nonlinear long interfacial waves with background shear. *Studies in Applied Mathematics*, 133 (2), pp. 182-213.

Watras, C.J., Morrison, K.A., Mather, J., Milewski, P. and Hanson, P.C., 2014. Correcting CDOM fluorescence measurements for temperature effects under field conditions in freshwaters. *Limnology and Oceanography: Methods*, 12 (1), pp. 23-24.

Milewski, P. A. and Wang, Z., 2014. Transversally periodic solitary gravity-capillary waves. *Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, 470 (2161), 20130537.

Wang, Z., Milewski, P. A. and Vanden-Broeck, J.-M., 2014. Computation of three-dimensional flexural-gravity solitary waves in arbitrary depth. *Procedia IUTAM*, 11, pp. 119-129.

Dutykh, D., Clamond, D., Milewski, P. and Mitsotakis, D., 2013. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. *European Journal of Applied Mathematics*, 24 (5), pp. 761-787.

Milewski, P. and Papageorgiou, D., 2013. Editorial:Special Issue: Analysis and Computation of Complex Wave and Free Boundary Problems: a celebration of Professor Jean-Marc Vanden-Broeck’s 60th Birthday. *IMA Journal of Applied Mathematics*, 78 (4), p. 651.

Milewski, P. A. and Wang, Z., 2013. Three dimensional flexural–gravity waves. *Studies in Applied Mathematics*, 131 (2), pp. 135-148.

Wang, Z., Vanden-Broeck, J.-M. and Milewski, P. A., 2013. Two-dimensional flexural-gravity waves of finite amplitude in deep water. *IMA Journal of Applied Mathematics*, 78 (4), pp. 750-761.

Milewski, P. A., Vanden-Broeck, J.-M. and Wang, Z., 2013. Steady dark solitary flexural gravity waves. *Proceedings of the Royal Society A*, 469 (2150), 20120485.

Wang, Z. and Milewski, P. A., 2012. Dynamics of gravity-capillary solitary waves in deep water. *Journal of Fluid Mechanics*, 708, pp. 480-501.

Wang, Z. and Milewski, P. A., 2012. Dynamics of gravity–capillary solitary waves in deep water. *Journal of Fluid Mechanics*, 708, pp. 480-501.

Kim, B., Dias, F. and Milewski, P. A., 2012. On weakly nonlinear gravity–capillary solitary waves. *Wave Motion*, 49 (2), pp. 221-237.

Boonkasame, A. and Milewski, P. A., 2012. The stability of large-amplitude shallow interfacial non-Boussinesq flows. *Studies in Applied Mathematics*, 128 (1), pp. 40-58.

Milewski, P. A., Vanden-Broeck, J.-M. and Wang, Z., 2011. Hydroelastic solitary waves in deep water. *Journal of Fluid Mechanics*, 679, pp. 628-640.

Milewski, P. A. and Tabak, E. G., 2011. The diurnal cycle and the meridional extent of the tropics. *Physica D: Nonlinear Phenomena*, 240 (2), pp. 233-240.

Simons, J. E. and Milewski, P. A., 2011. The volcano effect in bacterial chemotaxis. *Mathematical and Computer Modelling*, 53 (7-8), pp. 1374-1388.

Milewski, P. A., Vanden-Broeck, J.-M. and Wang, Z., 2010. Dynamics of steep two-dimensional gravity-capillary solitary waves. *Journal of Fluid Mechanics*, 664, pp. 466-477.

Dias, F. and Milewski, P., 2010. On the fully-nonlinear shallow-water generalized Serre equations. *Physics Letters A*, 374 (8), pp. 1049-1053.

Akers, B. and Milewski, P. A., 2010. Dynamics of three-dimensional gravity-capillary solitary waves in deep water. *SIAM Journal on Applied Mathematics*, 70 (7), pp. 2390-2408.

Akers, B. and Milewski, P. A., 2009. A model equation for wavepacket solitary waves arising from capillary-gravity flows. *Studies in Applied Mathematics*, 122 (3), pp. 249-274.

Chumakova, L., Menzaque, F. E., Milewski, P. A., Rosales, R. R., Tabak, E. G. and Turner, C. V., 2009. Shear instability for stratified hydrostatic flows. *Communications on Pure and Applied Mathematics*, 62 (2), pp. 183-197.

Chumakova, L., Menzaque, F. E., Milewski, P. A., Rosales, R. R., Tabak, E. G. and Turner, C. V., 2009. Stability properties and nonlinear mappings of two and three-layer stratified flows. *Studies in Applied Mathematics*, 122 (2), pp. 123-137.

Akers, B. and Milewski, P. A., 2008. A stability result for solitary waves in nonlinear dispersive equations. *Communications in Mathematical Sciences*, 6 (3), pp. 791-797.

Milewski, P. A. and Yang, X., 2008. A simple model for biological aggregation with asymmetric sensing. *Communications in Mathematical Sciences*, 6 (2), pp. 397-416.

Jacobson, T., Milewski, P. A. and Tabak, E. G., 2008. Mixing closures for conservation laws in stratified flows. *Studies in Applied Mathematics*, 121 (1), pp. 89-116.

Akers, B. and Milewski, P. A., 2008. Model equations for gravity-capillary waves in deep water. *Studies in Applied Mathematics*, 121 (1), pp. 49-69.

Raupp, C. F. M., Silva Dias, P. L., Tabak, E. G. and Milewski, P. A., 2008. Resonant wave interactions in the equatorial waveguide. *Journal of the Atmospheric Sciences*, 65 (11), pp. 3398-3418.