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A. Allison

Publications and source records attributed to A. Allison.

6 recordsLinked to original sources
arXiv2012

A variational approach to the analysis of non-conservative mechatronic systems

We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles that are strictly variational. We do not use any ad hoc features that are added on after the analysis has been completed, such as the Rayleigh dissipation function. We generalise the concept of potential, and define generalised potentials for dissipative lumped system elements. Our innovation offers a unified approach to the analysis of mechatronic systems where there are energy and power terms in both the mechanical and electrical parts of the system. Using our novel technique, we can take advantage of the analytic approach from mechanics, and we can apply these pow- erful analytical methods to electrical and to mechatronic systems. We can analyse systems that include non-conservative forces. Our methodology is deterministic and does does require any special intuition, and is thus suitable for automation via a computer-based algebra package.

physics.class-ph↗
arXiv2004

Efficiency of discrete-time ratchets

Recently there has been much interest in discrete forms of Brownian ratchets, using a game-theoretic formalism. Using the approach pioneered by Parrondo, we develop a new method for obtaining the stationary probabilities and probability current for the case of discrete-time and discrete-space ratchets. We then use this result to calculate the Parrondian ratchet efficiency in two cases: firstly, for Parrondo's original system and, secondly, for a set of probabilities derived from a discretized ratchet potential.

cond-mat.stat-mech↗
arXiv2004

Parrondo's games with chaotic switching

This paper investigates the different effects of chaotic switching on Parrondo's games, as compared to random and periodic switching. The rate of winning of Parrondo's games with chaotic switching depends on coefficient(s) defining the chaotic generator, initial conditions of the chaotic sequence and the proportion of Game A played. Maximum rate of winning can be obtained with all the above mentioned factors properly set, and this occurs when chaotic switching approaches periodic behavior.

cs.GT↗
arXiv2003

Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.

cond-mat.stat-mech↗
arXiv2002

State-Space Visualisation and Fractal Properties of Parrondo's Games

In Parrondo's games, the apparently paradoxical situation occurs where individually losing games combine to win. The basic formulation and definitions of Parrondo's games are described in Harmer et al.. These games have recently gained considerable attention as they are physically motivated and have been related to physical systems such as the Brownian ratchet, lattice gas automata and spin systems. Various authors have pointed outinterest in these games for areas as diverse as biogenesis, political models, small-world networks, economics and population genetics. In this chapter, we will first introduce the relevant properties of Markov transition operators and then introduce some terminology and visualisation techniques from the theory of dynamical systems. We will then use these tools, later in the chapter, to define and investigate some interesting properties of Parrondo's games.

cond-mat.stat-mech↗