Abstract
Inspired from the works of Baldassarri et al. [1] and Prados et al. [2], we formulated a granular lattice model to derive fluctuating hydrodynamics from microscopic ingredients under controlled assumptions, considering only shear modes on a granular linear chain [3]. The evolution of the system conserves momentum and dissipates energy, as in granular collisions. The new model is different from the previous proposals in a few crucial aspects. In [1], the velocity field evolved under the enforcement of the so-called kinematic constraint, which is disregarded here. In [2], only the energy field was considered, therefore momentum conservation was absent. The results I present especially focus on the hydrodynamic behavior of the model; the analysis of velocity distribution evolution and a detailed approach to a mesoscopic fluctuation theory of our model can be found respectively in [4,5,6].
Jusqu’ici tout va bien
(La Haine)
The material in this chapter is mostly directed adapted from the following Springer publication and is reproduced here with permission: Alessandro Manacorda, Carlos A. Plata, Antonio Lasanta, Andrea Puglisi, and Antonio Prados. Lattice models for granular-like velocity fields: Hydrodynamic description. J. Stat. Phys., 164(4):810–841, Aug 2016.
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- 1.
For the usual choice of an initial Gaussian distribution, see Sect. 4.3.1.
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Manacorda, A. (2018). Granular Lattice: Fluctuating Hydrodynamics. In: Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-95080-8_4
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