The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-li...

We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the transition, parametrized by cumulants, is the only available information about the system. We present an analytical method for reconstructing generators of the t...

In this paper, we extend the operational matrix method to solve tempered fractional differential equation, via shifted Legendre polynomial. Although is widely used in solving various calculus problems, it yet apply equations defined derivatives. We first derive analytical expression for derivative x p</...

A review of novel method of numerical Fourier transform spectroscopy of non-stationary signals and its applications to the time-frequency waveforms analysis of the electroencephalogram (EEG). The method uses the similar basis function (SBF) algorithm supported by classical methods of numerical estimation of trigonometric integrals based on the polynomial expansion of the function to be transfor...

Here, we are concerned with a new, highly precise, numerical solution to the one-dimensional neutron transport equation based on Case’s analytical, singular eigenfunction expansion (SEE). While considerable number of solutions currently exist, understandably, because its complexity even in one dimension, there only few truly analytical equation. In 1960, Case introduced consistent theory SEE fo...

A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve a collection of basic flow problems based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, two half-space problems, Kramers and thermal creep, and three problems defined by flow in a plane-parallel channel, Poiseuille, thermalcreep and Couette fl...

The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the ge...

In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...

Polynomial expansion procedures, along with an analytical discrete-ordinates method, are used to solve the temperature-jump problem based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, the temperature and density perturbations and the temperature-jump coe5cient are obtained (essentially) analytically in terms of a modern version of the d...