The dynamical properties of an optical parametric amplifier with an added fourth-order (Kerreffect term) nonlinearity are studied by means of a computer simulation of a semiclassical nonlinear Langevin formulation. The transient statistics above threshold are analyzed in detail, and the relevance of the present results for the production of squeezed light in traveling-wave devices is finally di...

The Newtonian limit of fourth-order gravity is worked out discussing its viability with respect to the standard results of General Relativity. We investigate the limit in the metric approach which, with respect to the Palatini formulation, has been much less studied in the recent literature, due to the higherorder of the field equations. In addition, we refrain from exploiting the formal equiva...

This article presents a revised formulation of the color gradient method to model immiscible two-phase flows in lattice Boltzmann framework. Thanks this formulation, color-gradient is generalized an arbitrary Equation State under form p=f(?,?), relieving nonphysical limitation between density and sound speed ratios present original formulation. A fourth-order operator for equilibrium function i...

In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. Some new positive periodic criteria are given.  

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtai...

this paper presents the bending analysis of annular plates by the indirect trefftz boundary approach. the formulation for thin and thick plates is based on the kirchhoff plate theory and the reissner plate theory. the governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. the trefftz method employs the complete set of solu...

in this paper, we investigate some problems which can be reduced to the goursat problem for afourth order equation. some results and theorems are given concerning the existence and uniqence for thesolution of the suggested problem.