The inelastic hard dimer gas: a non-spherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution $\alpha<1$, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting non equilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalise to inelastic systems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat. Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres hold together by rigid bonds. Each dimer consists of two hard disks of diameter $d$, whose centers are separated by a fixed distance $a$. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law $t^{-2}$, describing how the kinetic energy of an inelastic hard sphere system with constant coefficient of restitution decreases in time, holds even in the case of these non spherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.Comment: 21 pages, 6 figures and 2 tables, submitted to JC

Reconstructions of deltaic environments from Holocene palynological records in the Volga delta, northern Caspian Sea

This article was made available through open access by the Brunel Open Access Publishing Fund.New palynological and ostracod data are presented from the Holocene Volga delta, obtained from short cores and surface samples collected in the Damchik region, near Astrakhan, Russian Federation in the northern Caspian Sea. Four phases of delta deposition are recognized and constrained by accelerated mass spectrometry (AMS) radiocarbon ages. Palynological records show that erosive channels, dunes (Baer hills) and inter-dune lakes were present during the period 11,500–8900 cal. BP at the time of the Mangyshlak Caspian lowstand. The period 8900–3770 cal. BP was characterized regionally by extensive steppe vegetation, with forest present at times with warmer, more humid climates, and with halophytic and xerophytic vegetation present at times of drought. The period 3770–2080 cal. BP was a time of active delta deposition, with forest or woodland close to the delta, indicating relatively warm and humid climates and variable Caspian Sea levels. From 2080 cal. BP to the present-day, aquatic pollen is frequent in highstand intervals and herbaceous pollen and fungal hyphae frequent in lowstand intervals. Soils and incised valley sediments are associated with the regional Derbent regression and may be time-equivalent with the ‘Medieval Warm Period’. Fungal spores are an indicator of erosional or aeolian processes, whereas fungal hyphae are associated with soil formation. Freshwater algae, ostracods and dinocysts indicate mainly freshwater conditions during the Holocene with minor brackish influences. Dinocysts present include Spiniferites cruciformis, Caspidinium rugosum, Impagidinium caspienense and Pterocysta cruciformis, the latter a new record for the Caspian Sea. The Holocene Volga delta is a partial analogue for the much larger oil and gas bearing Mio-Pliocene palaeo-Volga delta.Funding for the data collection and field work was provided from the following sources: 1 – IGCP-UNESCO 2003–2008 (Project 481 CASPAGE, Dating Caspian Sea Level Change); 2 – NWO, Netherlands Science Foundation and RFFI, Russian Science Foundation 2005–2008 (Programme: ‘VHR Seismic Stratigraphy and Paleoecology of the Holocene Volga Delta’); and 3 – BP Exploration (Caspian Sea) Sea Ltd. (Azeri-Chirag-Gunashli) 2005–2008 (‘Unravelling the Small-Scale Stratigraphy and Sediment Dynamics of the Modern Volga Delta Using VHR Marine Geophysics’). The palynological work was funded jointly by BP Exploration (Caspian Sea) Ltd., Delft University of Technology and KrA Stratigraphic Ltd. Ostracod analyses were funded by StrataData Ltd. and funding for two additional radiocarbon dates provided by Deltares