Biomedical subjects
Publications and source records attributed to D B Abraham.
An exact derivation of the surface magnetizations of the two phases m(1)I and m(1)II coexisting below the bulk critical temperature for the semi-infinite two-dimensional Ising ferromagnet subject to a surface field is given. The surface critical behavior of the difference m(1)I - m(1)II is that of the ordinary transition only in a limit of a weak surface field below the wetting temperature.
An exact statistical mechanical derivation of corner filling in the two-dimensional Ising ferromagnet is given. The surface fields on the edges that meet at the corner are not required to be the same in the solution. Both thermodynamic results and microscopic structure are obtained.
In this article we introduce, develop, and discuss the theoretical calculations required for the exact solution of a recently reported phase transition, the geodesic to zigzag transition. In this scenario the interfacial transition emerges from geometric competition between a geodesic, shortest path, configuration and a zigzag configuration which is able to reduce its energy by binding to a centrally positioned defect line. From a technical point of view the transition is unusual as it is described by a change from saddle dominated behavior to pole dominated behavior of the integral representing the partition function ratio. We also establish the precise fluctuation behavior of the interface by computing the spin magnetization at any point in the system.
Recently an interesting phase transition scenario in the context of a planar Ising system with a grain boundary was revealed [Phys. Rev. Lett. 93, 076101 (2004)]]. In this paper we study in more detail the relaxation dynamics of this system and show how the grain boundary acts as a guide spatially confining matter transport. This is done by performing simulations using the continuous time Monte Carlo algorithm with Kawasaki dynamics. We also set up the problem as a solid-on-solid model and formulate corresponding Langevin equations for the dynamics in two cases, with and without matter conservation.
We consider a tier of weakened bonds along the center line of a two-dimensional Ising ferromagnet strip as a model of a grain boundary. When an interface traverses such a strip at an angle, whether or not there is a continuous pinning-depinning transition at subcritical temperature depends on this angle and the degree of bond weakening. We also study the relaxation of such a system to its equilibrium state using continuous time Monte Carlo simulation with Kawasaki dynamics; this reveals a matter transport mechanism confined to the grain boundary.
We obtain the exact solution for a two-dimensional rectangular Ising ferromagnet forming a corner with a surface field applied to the spins on edges. We establish the existence of the filling transition and give the condition for the filling temperature. We discuss the basic properties of the transition.