Modelling and Simulation in Life and Materials Sciences (MSLMS) group at Basque Center for Applied Mathematics – BCAM

by Mario Fernández-Pendás, Simone Rusconi, Elena Akhmatskaya, BCAM

In the recent decades the widespread availability of powerful computers allowed to numerically solve problems arising in Materials Sciences, Biosciences, Geophysics, Economics, that will eventually contribute to public health, medicine, industry, environment and society.  Addressing these tasks has been the mission of Modelling and Simulation in Life and Materials Sciences (MSLMS) group http://www.bcamath.org/en/research/lines/MSLMS since its establishment in 2010 in the Basque Center for Applied Mathematics (BCAM).

The goal of MSLMS is to enable effective modelling and detailed simulations of extremely large, complex systems and phenomena, which are not possible with existing simulation methods and often without high performance computers. We are interested in both applications and methodology, to devise reliable predictive tools for material science, biomedical applications, and statistical inference. The focus is also on the use of high performance computers to problems currently beyond the capacity of existing methods.

MSLMS activities include the development of efficient computational models, algorithms, software and computational packages for simulations of complex systems with applications to real-life problems.

The defining features of the MSLMS group are multidisciplinary research, multitasking and active involvement of young researchers in the various scientific activities from the earliest stages of their career.

Development of novel sampling methods combining stochastic Markov Chain Monte Carlo with deterministic Hamiltonian Dynamics is one of our long-standing research interests. The methodologies, such as the Generalized Shadow Hybrid Monte Carlo (GSHMC) and Mix & Match Hamiltonian Monte Carlo, aim to overcome the deficiencies of conventional sampling techniques. We work on the extension of the methods to a range of simulation scales and statistical ensembles as well as on the further improvement of their efficiency through developing novel adaptive schemes, numerical integrators and parallel algorithms. As an illustration, the recently published Adaptive Integration Approach (AIA) and Modified AIA (MAIA) are the adaptive splitting numerical integrators developed for the molecular simulation sampling algorithms, which rely on Hamiltonian dynamics. AIA and MAIA improve the sampling efficiency by means of a better conservation of the (modified) Hamiltonian for a range of complex problems in life and materials sciences.

Polymer science and quantum measurement theory are another two applications of our interest. In particular, we have developed the mathematical tools for solving three long-standing problems in these fields. The question, “Why kinetic models cannot reproduce experimental observations in Controlled Radical Polymerization (CRP)?” has been answered by introducing in the kinetic model a delay and treating CRP as a non-Markovian process. An accurate prediction of a morphology development in multi-phase polymers is vital for the synthesis of new materials but still not feasible due to its complexity. Motivated by the lack of systematic modelling framework, we have designed an accurate and efficient method for the prediction of the morphology of interest. Finally, we have also designed a stochastic simulation framework for continuous measurements performed on quantum systems of theoretical and experimental interest, which helped us to re-examine the “fuzzy continuous measurements” theory by Audretsch and Mensky (1997), viewed by the date as a universal model-free approach to continuous quantum measurements.

Other group’s research project include mathematical modelling of chemical reactions, development of simulation methodologies for study of perspective materials for ion batteries, tracking development of resistance to therapy in cancer through mathematical modelling, metabolic flux analysis, history matching and reservoir simulation.

The derived methodologies are implemented in the in-house efficient highly parallelized simulation software packages allowing for optional simulation of complex high dimensional systems and rare events at quantum, atomistic, meso- and multi-scales as well as for parameters estimation in Bayesian statistics.

Olivine NaFePO₄ is a promising cathode material for Na-ion batteries. Intermediate phases such as Na_0.66FePO₄ govern phase stability during intercalation-deintercalation processes, yet little is known about Na⁺ diffusion in Na_xFePO (0 < x < 1). Here we use an advanced simulation technique, Randomized Shell Mass Generalized Shadow Hybrid Monte Carlo method (RSM-GSHMC) in combination with a specifically developed force field for describing NaFePO over the whole range of sodium compositions, to thoroughly examine Na⁺ diffusion in this material. We reveal a novel mechanism through which Na⁺/Fe²⁺ antisite defect formation halts transport of Na+ in the main diffusion direction [010], while simultaneously activating diffusion in the [001] channels. A similar mechanism was reported for Li+ in LiFePO4, suggesting that a transition from one- to two-dimensional diffusion prompted by antisite defect formation is common to olivine structures, in general. Picture taken from  https://pubs.acs.org/doi/abs/10.1021/acs.jpcc.8b00230