The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.
In this paper we study a generalization of the Hubbard model by considering spin-spin interactions described by the exchange constant J. An external magnetic field his also taken into account. In the narrowband limit and for the 1D case, we present the exact solution obtained in the framework of the Green’s function formalism, using the Composite Operator Method. We report the T = 0 phase diagram for both ferro (J > 0) and anti-ferro (J < 0) couplings. The competition of the different energy scales (U, J, and h; being U the local charge interaction) generates a variety of phases and different charge and spin orderings.
In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.
In this paper, the AKNS isospectral problem and its corresponding time evolution are generalized by embedding three coefficient functions. Starting from the generalizedAKNS isospectral problem, a mixed spectralAKNS hierarchy with variable coefficients is derived. Thanks to the selectivity of these coefficient functions, the mixed spectral AKNS hierarchy contains not only isospectral equations but also nonisospectral equations. Based on a systematic analysis of the related direct and inverse scattering problems, exact solutions of the mixed spectral AKNS hierarchy are obtained through the inverse scattering transformation. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. This paper shows that the AKNS spectral problem being nonisospectral is not a necessary condition to construct a nonisospectral AKNS hierarchy and that the inverse scattering transformation can be used for solving some other variable-coefficient mixed hierarchies of isospectral equations and nonisospectral equations.
The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.