# Area M: Mathematics, new concepts and methods

Area M represents the foundation of our project. The scientists in that area work on new mathematical concepts and numerical methods to be tested in the other project areas. Thus, it forms the basis for future work.

## Objectives

### Interdisciplinary approach

Applied mathematicians and experts from geo sciences are working together in area M, to foster an exchange with the other research areas and to transfer knowledge between the different disciplines. By working on consistent model formulation, new and consistent parameterisations and numerics for both atmosphere and ocean, the mathematicians can help climate scientists improve their models and thus enhance climate projections.

### Specific research questions in Research Area M are:

- What is a mathematically and physically consistent model formulation for the different dynamical regimes and their interaction?
- Can we formulate better and physically consistent sub-grid scale parameterisations for the interaction between different dynamical regimes?
- Can we develop better numerical schemes?

## Publications

**Ovsyannikov, I. I.**, & Turaev, D. V. (2016). Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model.*Nonlinearity*, 30(1), 115.**Franzke, C. L.**, and O'Kane, T. J. (Eds.). (2017). Nonlinear and Stochastic Climate Dynamics.*Cambridge University Press.***Franzke, C. L.**(2017). Extremes in dynamic-stochastic systems.(1), 012101.*Chaos: An Interdisciplinary Journal of Nonlinear Science*,*27*Graves, T.,

**Franzke, C. L.**, Watkins, N. W., Gramacy, R. B., and Tindale, E. (2017). Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models.*Physica A: Statistical Mechanics and its Applications*,*473*, 60-71.Gonchenko, M. , Gonchenko, S.,

**Ovsyannikov, I. (2017)**. Bifurcations of Cubic Homoclinic Tangencies in Two-dimensional Symplectic Maps.*Math. Model. Nat. Phenom. , Vol. 12, No. 1,*2017, pp. 41-61. doi: 10.1051/mmnp/20171210.**Blender, R.**, &**Badin, G.**(2017). Viscous dissipation in 2D fluid dynamics as a symplectic process and its metriplectic representation.*The European Physical Journal Plus*,*132*(3), 137.Gonchenko, S. V., and

**Ovsyannikov, I. I.**(2017). Homoclinic tangencies to resonant saddles and discrete Lorenz attractors.*Discrete and Continuous Dynamical Systems Series*, Vol 10 (2), p. 273-288, doi: 10.3934/dcdss.2017013.**Carpenter, J. R.**, Guha, A., & Heifetz, E. (2017). A physical interpretation of the wind-wave instability as interacting waves.*Journal of Physical Oceanography*.**Franzke, C. L.**(2017). Impacts of a changing climate on economic damages and insurance.*Economics of Disasters and Climate Change*,*1*(1), 95-110.**Kutsenko, A. A.,**Nagy, A. J., Su, X., Shuvalov, A. L. , Norris, A. N. (2017). Wave Propagation and Homogenization in 2d and 3d Lattices: A Semi-Analytical Approach.*Q J Mechanics Appl Math (2017) 70 (2): 131-151.*doi: 10.1093/qjmam/hbx002