This paper presents a Lie-Trotter splitting for inertial Langevin equations (Geometric Langevin Algorithm) and analyzes its long-time statistical properties.The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting...

We derive an explicit second order reversible Poisson integrator for symmetric rigid bodies in space (i.e. without a fixed point). The integrator is obtained by applying a splitting method to the Hamiltonian after reduction by the S1 body symmetry. In the particular case of a magnetic top in an axisymmetric magnetic field (i.e. the Levitron) this integrator preserves the two momentum integrals....

A sigma delta modulator incorporating a linear phase integrator instead of a conventional voltage-domain integrator is described. The architecture allows achieving a quasi-second order noise shaping by using a passive SC low-pass filter in the first stage. Simulation results demonstrate that the circuit can operate with sampling frequencies of hundred of MHz while obtaining a figure of merit (F...

In this paper, we derive the impulse response of the distributed order integrator/ differentiator and its asymptotic property by using the complex path integral. Based on the derived analytical impulse response, we present a technique to perform the discretization of the above distributed order integrator/differentiator. The derived asymptotic property can be applied to verify the feasibility o...

This work introduces the high-order Boris-SDC method for integrating the equations of motion for electrically charged particles in an electric and magnetic fields. Boris-SDC relies on a combination of the Boris-integrator with spectral deferred corrections (SDC). SDC can be considered as preconditioned Picard iteration to compute the stages of a collocation method. In this interpretation, inver...

Corner detection is a critical component of many image analysis and understanding tasks, such as object recognition matching. Our research indicates that existing corner algorithms cannot properly depict the difference between edges corners this results in wrong detections. In paper, capability second-order generalized (isotropic anisotropic) Gaussian directional derivative filters to suppress ...

The energy dissipation law and the maximum bound principle (MBP) are two important physical features of well-known Allen--Cahn equation. While some commonly used first-order time stepping schemes have turned out to preserve unconditionally both MBP for equation, restrictions on step size still needed existing second-order or even higher order in such simultaneous preservation. In this paper, we...