Symplectic integrators do not, in general, reproduce all the features of the dynamics of the Hamiltonian systems which they approximate. For example, energy conservation is lost, and global features such as separatrices can be destroyed. We study these effects for a Hamiltonian system with a single degree of freedom and the simplest possible symplectic integrator. We look at a sequence of Hamil...

The exercise of market power by broiler processing firms (integrators) is plausible because local markets for growers are concentrated and because growers face hold-up risks arising from substantial investments in specific assets set against limited integrator purchase commitments. This article explores the links between local integrator concentration and grower compensation under production co...

A design method for PID controllers base on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) system for pure integrating process with time delay is proposed. Analytical expressions for PID controllers are derived for several common types of process models, including first order and second-order plus time delay models and an integrator plus time dela...

Effective Liouville operators of the firstand the second-order symplectic integrators are obtained for the one-dimensional harmonic-oscillator system. The operators are defined only when the time step is less than two. Absolute values of the coordinate and the momentum monotonically increase for large time steps. PACS numbers: 05.10.-a, 02.10.Hh

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...

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...