Diffusive behavior of ergodic sums over rotations

For a rotation by an irrational [Formula: see text] on the circle and a BV function [Formula: see text], we study the variance of the ergodic sums [Formula: see text]. When [Formula: see text] is not of constant type, we construct sequences [Formula: see text] such that, at some scale, the ergodic sums [Formula: see text] satisfy an ASIP. Explicit non-degenerate examples are given with an application to the rectangular periodic billiard in the plane.

Effects of wiggler error in a free-electron laser oscillator with two electron beams

We have analyzed the effects of the wiggler error due to the electron beam's emittance, energy spreads, and higher-order modes in a free-electron laser (FEL) oscillator by using two electron beams of different energies based on the proposed FEL facility which is operated at a far-infrared and infrared regions. The three-dimensional (3D) effects in a FEL oscillator due to the wiggler error were calculated and an evaluation of the effect of the beam's emittance and energy spread was performed for the case of the coupled two-beam oscillator for phase shift errors and wiggler errors. The mode construction was studied on the higher-order modes of the wiggler for the various wiggler error parameters for FEL performance which is required for the high-quality electron beam. The radiation intensity at the fundamental mode was calculated for the rms phase shake in wiggler errors with sinus type, constant type, and parabolic type in the two-beam oscillator system using the 3D calculations. The results are compared with those of the fundamental modes without wiggler errors.

Perspectives on Constraining a Cosmological Constant-Type Parameter with Pulsar Timing in the Galactic Center

Independent tests aiming to constrain the value of the cosmological constant Λ are usually difficult because of its extreme smallness ( Λ ≃ 1 × 10 - 52 m - 2 , or 2 . 89 × 10 - 122 in Planck units ) . Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the ≃ 10 - 43 – 10 - 44 m - 2 ( 5 – 1 × 10 - 113 in Planck units ) level, but they may turn out to be optimistic since Λ has not yet been explicitly modeled in the planetary data reductions. Accurate ( σ τ p ≃ 1 – 10 μ s ) timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit Δ δ τ ¯ p Λ , an S2-like orbital configuration with e = 0 . 8839 , P b = 16 yr would permit a preliminarily upper bound of the order of Λ ≲ 9 × 10 - 47 m - 2 ≲ 2 × 10 - 116 in Planck units if only σ τ p were to be considered. Our results can be easily extended to modified models of gravity using Λ -type parameters.

Constant ratio timelike curves in pseudo-Galilean 3-space \mathbb{G}_{3}^{1}

In this paper, we consider unit speed timelike curves in pseudo-Galilean 3-space \mathbb{G}_{3}^{1} as curves whose position vectors can be written as linear combination of their Serret-Frenet vectors. We obtain some results of constant ratio curves and give an example of these curves. Further, we show that there is no T-constant curve and we obtain some results of N-constant type of curves in pseudo-Galilean 3-space \mathbb{G}_{3}^{1}.

Soft Computing Based Adaptive Error Optimisation for Control of Nonlinear System

This paper elaborates a novel hybrid learning approach for training error optimisation and control of highly dynamic triple-link inverted pendulum on cart. The study demonstrates a relationship between shape and number of membership functions (MFs) of both linear and constant type to determine training error tolerance of ANFIS controller. The results are plotted which clearly highlighted supremacy of constant type three triangular shape MFs. Mathematical model and simulink of proposed system has also been analysed. The learning ability and designing methodology of adaptive networks and robustness of PID controllers are briefly described. Finally, the study illustrates an offline mode comparison of PID based ANFIS and Neural controllers in terms of settling time, steady state error and overshoot.

Nonlinear State–Space Predictive Control with On–Line Linearisation and State Estimation

This paper describes computationally efficient model predictive control (MPC) algorithms for nonlinear dynamic systems represented by discrete-time state-space models. Two approaches are detailed: in the first one the model is successively linearised on-line and used for prediction, while in the second one a linear approximation of the future process trajectory is directly found on-line. In both the cases, as a result of linearisation, the future control policy is calculated by means of quadratic optimisation. For state estimation, the extended Kalman filter is used. The discussed MPC algorithms, although disturbance state observers are not used, are able to compensate for deterministic constant-type external and internal disturbances. In order to illustrate implementation steps and compare the efficiency of the algorithms, a polymerisation reactor benchmark system is considered. In particular, the described MPC algorithms with on-line linearisation are compared with a truly nonlinear MPC approach with nonlinear optimisation repeated at each sampling instant.

Sensorless Load Torque Estimation and Passivity Based Control of Buck Converter Fed DC Motor

Passivity based control of DC motor in sensorless configuration is proposed in this paper. Exact tracking error dynamics passive output feedback control is used for stabilizing the speed of Buck converter fed DC motor under various load torques such as constant type, fan type, propeller type, and unknown load torques. Under load conditions, sensorless online algebraic approach is proposed, and it is compared with sensorless reduced order observer approach. The former produces better response in estimating the load torque. Sensitivity analysis is also performed to select the appropriate control variables. Simulation and experimental results fully confirm the superiority of the proposed approach suggested in this paper.