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Reunión de Usuarios y Desarrolladores de Métodos de Simulación de Aragón

Granular and Active Fluids

Prof. Javier Brey, Universidad de Sevilla
Prof. Eric Clement, ESPCI-Pierre et Marie Curie
Prof. Rodrigo Soto, Universidad de Chile

DATE OF EVENT : 12/09/2011       DURATION : 4 day(s)

LOCATION : ZCAM Campus Actur C/ Mariano Esquillor s/n Edificio I+D 50018 Zaragoza


SUMMARY :

The emergence of collective and cooperative phenomena in non-equilibrium particulate systems normally takes place when a large number of constituents are present. Besides, the large fluctuations developed by these systems (anomalously large in the case of nematic flocking) need also a large numbers of particles in order to extract statistically relevant information. In absence of validated continuous models for granular and active fluids (analogous to the hydrodynamic equations), it is necessary to make numerical simulations that solve the dynamics of all the individual particles. It is similar to the molecular dynamics method, widely used in the study of liquids and solids. However, some important differences appear that need for specific developments.

In the case of granular matter, the most used model consists on considering grains as hard particles that interact only at contact (normally, instantaneous contacts). Event driven algorithms have been successfully used but still they are not able to efficiently treat the effect of the interstitial fluid, non-spherical grain shapes (needed for realistic flows) or the multiple contacts that develop in dense flows. Soft sphere models, where grains can overlap, allow for multiple contacts, but considering realistic values of the elastic moduli make simulations extremely expensive. In addition, in many cases the system exhibits a wide range of densities, making it hard to use approximations which in principle only apply in well defined density ranges.

Active matter presents also interesting computational challenges in order to include the self-propulsion in a realistic way, while preserving computational efficiency. Several regimes are present with various complexities. First, in active grains, rotational symmetry must be broken, having therefore the complexity of simulating non-spherical grains. Microscopic active matter in fluids (e.g. bacteria, algae, spermatozoids, and chemically activated nano-motors) normally lives in the low Reynolds regime. In this regime, the hydrodynamic interactions are long ranged, and special numerical methods need to be developed similar to the Ewald sum, fast multipoles and treecode approaches. Finally, the computational modelling of active matter with some level of consciousness (e.g. fishes, birds, and locusts) needs radically new strategies beyond the basic Viscek model.

Also, the novel type of non-equilibrium dynamics, phase transitions and cooperative motion that these systems show, need also the development of new tools to analyse the experimental and computational results. These tools must provide relevant information to characterize the emergence of the phenomena and still be computationally efficient. An example of these tools is the four-point susceptibilities that characterize the effect of disorder and heterogeneity. In highly fluctuating systems, fluctuation-dissipation relations can be used to obtain the response laws. This would require that much more efficient computational methods be developed for non-equilibrium systems.

In summary, the computational challenges in the study of granular and active fluids are related to the efficient simulation of particulate systems and fast on-the-fly statistical analysis that provide with reliable and relevant information of their dynamics, for a large amount of raw data.

The main objective is to bring together two communities, to interchange the ideas and methods developed during the last 25 years in the context of granular flows with the experimental and theoretical challenges that are recently arising in the study of active matter.

Some specific objectives are:

1. To blend the discussion on theoretical and numerical approaches, with some experimental contributions on real active matter and vibrated granular matter.
2. At the end we seek to transfer the theoretical methods develop to handle collective motion.
3. To test those methods from basic principle of kinetic theory.
4. To present the first steps towards a rigorous approach for “active granular fluids”.
5. To discuss the applicability in active and granular fluids of the recently proposed fluctuation and dissipation theorems, focusing in their numerical tests.