Static- and dynamical-phase transition in one-dimensional reaction-diffusion systems with boundaries

Explicit Asymptotic Velocity of the Boundary between Particles and Antiparticles

“…In [3] the order of particles of the same type can be changed with time. There are no such simple formulae as (9) and (10) in this case. The result is however the same as in (8).…”

“…There are models of the market having similar type (but very different from ours, see [7,8,6]). In physical literature there are also other one-dimensional models of the boundary movement see in [9,10].…”

Static and dynamic phase transitions in multidimensional voting models on continua

“…If the space is one-dimensional, v ′ has only one acceptable value, as the parenthesis in (32) has only two values at most one of them can be zero.) If (33) holds, then there exists eigenvalues E for h, with E > −v • v/4. Otherwise, all of the eigenvalues of h are less than or equal to −v • v/4.…”

“…Based on the evolution of the one-point functions, it was shown there that the system exhibits two kinds of phase transitions: a static phase transition, corresponding to a discontinuous change in the stationary profile of the one-point function; and a dynamical one, corresponding to a discontinuous change in the behavior of the relaxation time of the system toward its stationary state. In [30][31][32][33][34], the phase structures of extensions of such systems on a one-dimensional lattice were investigated. All of these are restricted to the case of a one-dimensional lattice.…”