arXiv subjects

Igor S. Aranson

Publications and source records attributed to Igor S. Aranson.

40 records · Page 3Linked to original sources

arXiv2000

Continuum description of avalanches in granular media

We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation which describes the transition between flowing and static components of the granular system. This theory captures important phenomenology recently observed in experiments with granular flows on rough inclined planes (Daerr and Douady, Nature (London) v. 399, 241 (1999)): layer bistability, and transition from triangular avalanches propagating downhill at small inclination angles to balloon-shaped avalanches also propagating uphill for larger angles.

cond-mat.soft↗

arXiv2000

Nonequilibrium dislocation dynamics and instability of driven vortex lattices in two dimensions

We consider dislocations in a vortex lattice that is driven in a two-dimensional superconductor with random impurities. The structure and dynamics of dislocations is studied in this genuine nonequilibrium situation on the basis of a coarse-grained equation of motion for the displacement field. The presence of dislocations leads to a characteristic anisotropic distortion of the vortex density that is controlled by a Kardar-Parisi-Zhang nonlinearity in the coarse-grained equation of motion. This nonlinearity also implies a screening of the interaction between dislocations and thereby an instability of the vortex lattice to the proliferation of free dislocations.

cond-mat.stat-mech↗

arXiv1999

Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".

cond-mat.supr-con↗

arXiv1999

Crystallization Kinetics in the Swift--Hohenberg Model

It is shown numerically and analytically that the front propagation process in the framework of the Swift-Hohenberg model is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of the corresponding linear problem. We derive the evolution equation for this mode using asymptotic analysis, and evaluate the time interval between nucleation events, and hence the front speed. In the presence of noise, we derive the velocity exponent of ``thermally activated'' front propagation (creep) beyond the pinning threshold.

patt-sol↗