Distributed Periodic Steady State Kalman Filter

In this paper a distributed implementation for the periodic steady state Kalman filter is proposed. The distributed algorithm has parallel structure and can be implemented using processors in parallel without idle time. The number of processors is equal to the model period. The resulting speedup is also derived. The Finite Impulse Response (FIR) form of the periodic steady state Kalman filter is derived.

Near-resonant dynamics, period doubling and chaos of a 3-DOF vibro-impact system

A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part is a vibro-impact unit composed of a linear oscillator with an internally colliding small block. This block is coupled with the secondary part being a damped linear oscillator. The mathematical model of the system has been presented in a non-dimensional form. The analytical studies are restricted to the case of a periodic steady-state motion with two symmetric impacts per cycle near 1:1 resonance. The multiple scales method combined with the sawtooth-function-based modelling of the non-smooth dynamics is employed. A conception of the stability analysis of the periodic motions suited for this theoretical approach is presented. The frequency–response curves and force–response curves with stable and unstable branches are determined, and the interplay between various model parameters is investigated. The theoretical predictions related to the motion amplitude and the range of stability of the periodic steady-state response are verified via a series of numerical experiments and computation of Lyapunov exponents. Finally, the limitations and extensibility of the approach are discussed.

Non-Markovian quantum Otto refrigerator

Based on a recently developed non-perturbative platform designed to simulate the full quantum dynamics of quantum thermal machines, the situation of a quantum refrigerator operating according to an Otto cycle is studied. The periodic steady-state dynamics is discussed in detail as well as the key thermodynamic quantities work, heat, and entropy. A particular benefit of the formulation is that it allows to access explicitly the work required for switching on and off the interaction with the respective thermal reservoirs in a consistent way. The domains in which the device operates in refrigerator mode are characterized.

Near-resonant dynamics, period doubling and chaos of a 3-DOF vibro-impact system

A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part is a vibro-impact unit composed of a linear oscillator with an internally colliding small block. This block is coupled with the secondary part being a damped linear oscillator. The mathematical model of the system has been presented in a non-dimensional form. The analytical studies are restricted to the case of a periodic steady-state motion with two symmetric impacts per cycle near 1:1 resonance. The multiple scales method combined with the sawtooth-function-based modelling of the non-smooth dynamics is employed. The approximate analytical solutions allow for stability analysis of the periodic motions. Moreover, the frequency-response curves and force-response curves with stable and unstable branches are determined, and the interplay between various model parameters is investigated. The theoretical predictions related to the motion amplitude and the range of stability of the periodic steady-state response is verified via a series of numerical experiments and computation of Lyapunov exponents.