Springer Science and Business Media LLC

We construct a model of a random walk in which the relation of space–time nonlocalities is defined by the structure of memory flow and a stochastic force model. The proposed model allows computing the parameters that characterize the nonlocality of the medium exposure and the particle memory.

We consider the modern state of a consistent kinetic theory of dusty plasmas. We present the derivation of equations for microscopic phase densities of plasma particles and grains. Such equations are suitable for extending the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy to the case of dusty plasmas and for deriving the kinetic equations with regard for both elastic and inelastic particle collisions. Moreover, we describe the effective grain-grain potentials kinetically.

We consider several models of non-Ising spin glass for which we can naturally formulate an analogue of spherical conditions well known for the Ising model. We calculate the partition functions of the obtained models exactly. The random matrix method and the replica method yield identical results.

This work is a continuation of our recent paper where we discussed numerical evidence that the numbers of the states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an even number of sites. We give two new conjectures related to different boundary conditions: we suggest and numerically verify that the numbers of the half-turn symmetric states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of open boundary conditions and an even number of sites.