An analytic solution for the equal-mass banana graph

An Analytic Flow Solution for YSO Jets

We present an analytic solution for a jet flow from a young stellar object (YSO). This solution allows us to compute the speed, density, and magnetic field strength of the flow, but it is only true if YSO jet flows are powered by toroidal magnetic fields. We illustrate how the balance between centrifugal force and magnetic pressure provides the converging/diverging nozzle shape required to acce...

The analytic value of the sunrise self - mass with two equal masses and the external invariant equal to the third squared mass

We consider the two-loop self-mass sunrise amplitude with two equal masses M and the external invariant equal to the square of the third mass m in the usual d-continuous dimensional regularization. We write a second order differential equation for the amplitude in x = m/M and show as solve it in close analytic form. As a result, all the coefficients of the Laurent expansion in (d − 4) of the am...

An Analytic Motion Planning Solution for the Snakeboard

This paper provides a closed-form analytical solution to the motion planning problem for the Snakeboard. Given a desired planar trajectory in the fiber space, an explicit solution is computed for the gaits in the base space that locomote the Snakeboard along the desired trajectory. This is achieved by introducing a new momentum-like variable that simplifies the Snakeboard’s equations of motion ...

An analytic solution for the perspective 4-point problem

Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. Wi...