Implementation of the Combined--Nonlinear Condensation Transformation

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press

Local sensory control of a dexterous end effector

A numerical scheme was developed to solve the inverse kinematics for a user-defined manipulator. The scheme was based on a nonlinear least-squares technique which determines the joint variables by minimizing the difference between the target end effector pose and the actual end effector pose. The scheme was adapted to a dexterous hand in which the joints are either prismatic or revolute and the fingers are considered open kinematic chains. Feasible solutions were obtained using a three-fingered dexterous hand. An algorithm to estimate the position and orientation of a pre-grasped object was also developed. The algorithm was based on triangulation using an ideal sensor and a spherical object model. By choosing the object to be a sphere, only the position of the object frame was important. Based on these simplifications, a minimum of three sensors are needed to find the position of a sphere. A two dimensional example to determine the position of a circle coordinate frame using a two-fingered dexterous hand was presented

Numerical evaluation of multiple polylogarithms

Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for arbitrary complex arguments and without any restriction on the weight. We have implemented these algorithms with arbitrary precision arithmetic in C++ within the GiNaC framework.Comment: 23 page

Numerical Evaluation of Harmonic Polylogarithms

Harmonic polylogarithms $\H(\vec{a};x)$, a generalization of Nielsen's polylogarithms ${S}_{n,p}(x)$, appear frequently in analytic calculations of radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of harmonic polylogarithms of arbitrary real argument. This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt hplog} to compute harmonic polylogarithms up to weight 4.Comment: 16 pages, LaTeX, minor changes, to appear in Comp. Phys. Com

Hamiltonian description and traveling waves of the spatial Dysthe equations

The spatial version of the fourth-order Dysthe equations describe the evolution of weakly nonlinear narrowband wave trains in deep waters. For unidirectional waves, the hidden Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. A highly accurate Fourier-type spectral scheme is developed to solve for the equations and validate the new conservation laws, which are satisfied up to machine precision. Further, traveling waves are numerically investigated using the Petviashvili method. It is found that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.Comment: Research report. 17 pages, 7 figures, 38 references. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh/ . arXiv admin note: substantial text overlap with arXiv:1110.408