We studied a method of using symplectic integrator to simulate incoherent synchrotron radiation in an electron storage ring. The simulation includes both classical radiation and its quantum uctuations. We found that the emission process of photon using a compound Poisson process cannot be applied to the fourth-order integrator because it has negative path length which implies a negative n umber...

We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, 〈∆H2〉1/2, is about 10 times smaller than that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increa...

Central to the theoretical description of a chemical reaction is the reaction pathway. The intrinsic reaction coordinate is defined as the steepest descent path in mass weighted Cartesian coordinates that connects the transition state to reactants and products. In this work, a new integrator for the steepest descent pathway is presented. This method is a Hessian based predictor-corrector algori...

In this paper, we present a novel Lagrangian formulation of the equations of motion for point vortices on the unit 2-sphere. We show first that no linear Lagrangian formulation exists directly on the 2-sphere but that a Lagrangian may be constructed by pulling back the dynamics to the 3-sphere by means of the Hopf fibration. We then use the isomorphism of the 3-sphere with the Lie group SU(2) t...

We present a receding horizon control scheme that utilizes a discrete time version of a nonlinear, iterative, projection-based optimization routine. The routine utilizes a projection operator to ensure feasible system trajectories at each iteration of the optimization resulting in valid control signals even when constraints on computation time prevent full convergence. An additional feature of ...

A new explicit time-reversible orbit integrator for the equations of motion in a static homogeneous magnetic field —called Cyclotronic integrator— is presented. Like Spreiter and Walter’s Taylor expansion algorithm, for sufficiently weak electric field gradients this second order method does not require a fine resolution of the Larmor motion; it has however the essential advantage of being symp...

Modelling neutral beam injection (NBI) in fusion reactors requires computing the trajectories of large ensembles particles. Slowing down times up to one second combined with nanosecond time steps make these simulations computationally very costly. This paper explores performance BGSDC, a new numerical stepping method, for tracking ions generated by NBI DIII-D and JET reactors. BGSDC is high-ord...

The Brockett integrator is a 3-dimensional system with a non-holonomic constraint and the non-holonomic constraint makes the stabilization and control of the system challenging. The 3-dimensional non-holonomic integrator can be generalized in more than one way and this work looks into the time-optimal control of the generalized Brockett integrator which evolves on R × Skewm(R). The problem has ...

in this paper, a new approach for solving the second order fuzzy differential equations (fde) with fuzzy initial value, under strongly generalized h-differentiability is presented. solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...