The Daisystat: A model to explore multidimensional homeostasis

The Homeostat was a physical device that demonstrated Ashby’s notion of ‘ultrastability’. The components interact in such a way as to maintain sets of essential variables to within critical ranges in the face of an externally imposed regime of perturbations. The Daisystat model is presented that bears a number of similarities to Ashby’s Homeostat but which can also be considered as a higher dimensional version of the Watson & Lovelock Daisyworld model that sought to explain how homeostasis operating at the planetary scale may arise in the absence of foresight or planning. The Daisystat model features a population of diverse individuals that affect and are affected by the environment in different ways. The Daisystat model extends Daisyworld in that homeostasis is observed with systems comprised of four environmental variables and beyond. It is shown that the behaviour of the population is analogous to the ‘uniselector’ in the Homeostat in that rapid changes in the population allows the system to ‘search’ for stable states. This allows the system to find and recover homeostatic states in the face of externally applied perturbations. It is proposed that the Daisystat may afford insights into the evolution of increasingly complex systems such as the Earth system

Entropy production in an energy balance Daisyworld model

Daisyworld is a simple mathematical model of a planetary system that exhibits self-regulation due to the nature of feedback between life and its environment. A two-box Daisyworld is developed that shares a number of features with energy balance climate models. Such climate models have been used to explore the hypothesis that non-equilibrium, dissipative systems such as planetary atmospheres are in a state of maximum entropy production with respect to the latitudinal flux of heat. When values for heat diffusion in the two-box Daisyworld are selected in order to maximize this rate of entropy production, the viability range of the daisies is maximized. Consequently planetary temperature is regulated over the widest possible range of solar forcing

The Maximum Entropy Production Principle: Its Theoretical Foundations and Applications to the Earth System

The Maximum Entropy Production (MEP) principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales

Pushing up the daisies

When components of an interacting dynamical system (such as organs within an organism, or daisies within the Daisyworld model) have a limited range of viability to changes in some essential variable, intuition suggests that increasing any individual range of viability will also increase viability in the context of the whole system. We show circumstances in which the reverse is true

The Daisyworld control system

The original Gaia Hypothesis proposed that life on Earth, along with the oceans, atmosphere and crust, forms a homeostatic system which reduces the effects of external perturbations, so that conditions are maintained to within the range that allows widespread life. Daisyworld is a simple mathematical model intended to demonstrate certain aspects of this planetary homeostasis. There have been a considerable number of extensions and developments to the original Daisyworld model. Some of this work has been produced in response to criticism of the Gaia Hypothesis and Daisyworld specifically and some has been produced by using Daisyworld as a testbed to explore a range of issues. This thesis examines the Daisyworld control system and in doing so explains how Daisyworld performs homeostasis. The control system is classified as a rein control system which is potentially applicable to a wide range of scenarios from physiological and environmental homeostasis to robotic control. A series of simple Daisyworld models are produced and aspects of the original Daisyworld are explained, in particular the inverse response to forcing: why temperature goes down on Daisyworld when the brightness of the star increases. The Daisyworld control system is evaluated within an evolutionary context. A key result is that environmental regulation emerges not despite of Darwinian evolution but because of it. Within an ecological context, it is found that increasing the complexity of a self-regulating ecosystem can increase its stability. An energy balance climate model is developed to assess the effects of non-equilibrium thermodynamic processes on the Daisyworld control system. Results are presented that support the hypothesis that when the system is in a state of maximum entropy production, homeostasis is maximised

Bragg spectroscopy of a strongly interacting Fermi gas

We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic $^6$Li using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterised these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.Comment: Replaced with published versio

Towards understanding how surface life can affect interior geological processes: a non-equilibrium thermodynamics approach

Life has significantly altered the Earth’s atmosphere, oceans and crust. To what extent has it also affected interior geological processes? To address this question, three models of geological processes are formulated: mantle convection, continental crust uplift and erosion and oceanic crust recycling. These processes are characterised as non-equilibrium thermodynamic systems. Their states of disequilibrium are maintained by the power generated from the dissipation of energy from the interior of the Earth. Altering the thickness of continental crust via weathering and erosion affects the upper mantle temperature which leads to changes in rates of oceanic crust recycling and consequently rates of outgassing of carbon dioxide into the atmosphere. Estimates for the power generated by various elements in the Earth system are shown. This includes, inter alia, surface life generation of 264 TW of power, much greater than those of geological processes such as mantle convection at 12 TW. This high power results from life’s ability to harvest energy directly from the sun. Life need only utilise a small fraction of the generated free chemical energy for geochemical transformations at the surface, such as affecting rates of weathering and erosion of continental rocks, in order to affect interior, geological processes. Consequently when assessing the effects of life on Earth, and potentially any planet with a significant biosphere, dynamical models may be required that better capture the coupled nature of biologically-mediated surface and interior processes

Thermodynamics of an attractive 2D Fermi gas

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behaviour.Comment: Contains minor revision

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2

Contact and sum-rules in a near-uniform Fermi gas at unitarity

We present an experimental study of the high-energy excitation spectra of unitary Fermi gases. Using focussed beam Bragg spectroscopy, we locally probe atoms in the central region of a harmonically trapped cloud where the density is nearly uniform, enabling measurements of the dynamic structure factor for a range of temperatures both below and above the superfluid transition. Applying sum-rules to the measured Bragg spectra, we resolve the characteristic behaviour of the universal contact parameter, ${\cal C}$, across the superfluid transition. We also employ a recent theoretical result for the kinetic (second-moment) sum-rule to obtain the internal energy of gases at unitarity.Comment: 5 pages, 4 figure