Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.

Polynomial Structure of the (Open) Topological String Partition Function

Abstract: In this paper we show that the polynomial structure of the topological string partition function found by Yamaguchi and Yau for the quintic holds for an arbitrary Calabi-Yau manifold with any number of moduli. Furthermore, we generalize these results to the open topological string partition function as discussed recently by Walcher and reproduce his results for the real quintic.

An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity

Abstract: This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrodinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing NLSs in two dimensions with a linear, cubic, or quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter ${\delta}$ is larger than a threshold value ${\delta}_{\rm th}$. We note that our method can also be applied to solve the three-dimensional Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).

Solitons with cubic and quintic nonlinearities modulated in space and time.

Abstract: This work deals with soliton solutions of the nonlinear Schr\"odinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent paper [J. Belmonte-Beitia et al., Phys. Rev. Lett. 100, 164102 (2008)], and we solve the equation in the presence of a linear background and cubic and quintic interactions which are modulated in space and time. As a result, we show how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential and the cubic and quintic nonlinearities.

Quintic G/sup 2/-splines for the iterative steering of vision-based autonomous vehicles

Abstract: This paper presents a new motion planning primitive to be used for the iterative steering of vision-based autonomous vehicles. This primitive is a parameterized quintic spline, denoted as /spl eta/-spline, that allows interpolating an arbitrary sequence of points with overall second-order geometric (G/sup 2/-) continuity. Issues such as completeness, minimality, regularity, symmetry, and flexibility of these G/sup 2/-splines are addressed in the exposition. The development of the new primitive is tightly connected to the inversion control of nonholonomic car-like vehicles. The paper also exposes a supervisory strategy for iterative steering that integrates feedback vision data processing with the feedforward inversion control.