Victor Smirnov

The fractality of sea-ice drift dynamics as revealed from the ‘North Pole 32’ monitoring

The O(n) vector model with logarithmic action on a lattice of coordination 3 is related to a gas of self-avoiding loops on the lattice. This formulation allows for analytical continuation in n: critical behaviour is found in the real interval [-2,2]. The solution of the model on random planar lattices, recovered by random matrices, also involves an analytic continuation in the number n of auxiliary matrices. Here we show that, in the two cases n=-1, -2, a combinatorial reformulation of the loop gas problem allows to achieve the random matrix solution with no need of this analytical continuation.

Hierarchy of non-extensive mechanical processes in fracturing sea ice

The fracture-induced oscillations in sea ice were detected by seismographs and seismic tiltmeters established on the Arctic ice pack. Field observations were supplemented with a laboratory experiment. The energy distributions in elastic waves generated during: (i) large-scale ice pack fragmentation over area of about 105 km2, (ii) local crack propagation in ice floe, and (iii) laboratory ice crashing were constructed and analyzed using principles of the Tsallis statistics. The energy release regimes at different stages of fracturing were characterized by the parameter of nonextensivity q. In terms of the non-extensive statistical mechanics, q > 1 evidences the correlated (non-extensive) dynamics of the process in nonequilibrium system, q = 1 responds to the additivity of events occurring in equilibrium system, and q < 1 takes place when the energy release is additive and limited by an upper cut-off. All these scenarios were revealed in fracture processes occurring at three hierarchic levels. The variation of the q-value demonstrates high thermodynamic changeability of the fracture process driven by irregular external source. The role of energy conservation in fracturing sea ice is discussed in connection with the observed reversible transitions between extensive and non-extensive modes of fracture.

Nonextensive Dynamics of Drifting Sea Ice

Cycles of ice pack fragmentation in the Arctic Ocean are caused by the irregular drift dynamics. In February 2004, the Russian ice-research camp North Pole 32 established on a floe in the Arctic Ocean ceased its working activity and was abandoned after a catastrophic icequake. In this communication, the data collected during the last month of the field observations were used for calculating the changes in the kinetic energy of the ice floe. The energy distribution functions corresponding to periods of different drift intensity were analyzed using the Tsallis statistics, which allow one to assess a degree of deviation of an open dynamic system, such as the drifting ice, from its equilibrium state. The obtained results evidenced that the above-mentioned critical fragmentation has occurred in the period of substantially nonequilibrium dynamics of the system of ice floes. The determination of the state of the pack (in the sense of its equilibrium/nonequilibrium) could provide some useful information on forthcoming icequakes.