Generalised Compositional Theories and Diagrammatic Reasoning

This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G. Chirabella, R. Spekken

A new stellar mixing process operating below shell convection zones following off-center ignition

During most stages of stellar evolution the nuclear burning of lighter to heavier elements results in a radial composition profile which is stabilizing against buoyant acceleration, with light material residing above heavier material. However, under some circumstances, such as off-center ignition, the composition profile resulting from nuclear burning can be destabilizing, and characterized by an outwardly increasing mean molecular weight. The potential for instabilities under these circumstances, and the consequences that they may have on stellar structural evolution, remain largely unexplored. In this paper we study the development and evolution of instabilities associated with unstable composition gradients in regions which are initially stable according to linear Schwarzschild and Ledoux criteria. In particular, we explore the mixing taking place under various conditions with multi-dimensional hydrodynamic convection models based on stellar evolutionary calculations of the core helium flash in a 1.25 \Msun star, the core carbon flash in a 9.3\,\Msun star, and of oxygen shell burning in a star with a mass of 23\,\Msun. The results of our simulations reveal a mixing process associated with regions having outwardly increasing mean molecular weight that reside below convection zones. The mixing is not due to overshooting from the convection zone, nor is it due directly to thermohaline mixing which operates on a timescale several orders of magnitude larger than the simulated flows. Instead, the mixing appears to be due to the presence of a wave field induced in the stable layers residing beneath the convection zone which enhances the mixing rate by many orders of magnitude and allows a thermohaline type mixing process to operate on a dynamical, rather than thermal, timescale. We discuss our results in terms of related laboratory phenomena and associated theoretical developments.Comment: accepted for publication in Astrophysical Journal, 9 pages, 8 figure

Concentration fluctuations and phase transitions in coupled modulated bilayers

We consider the formation of finite-size domains in lipid bilayers consisting of saturated and hybrid lipids. First, we describe a monolayer model that includes a coupling between a compositional scalar field and a two-dimensional vectorial order-parameter. Such a coupling yields an effective two-dimensional microemulsion free-energy for the lipid monolayer, and its characteristic length of compositional modulations can be considered as the origin of finite-size domains in biological membranes. Next, we consider a coupled bilayer composed of two modulated monolayers, and discuss the static and dynamic properties of concentration fluctuations above the transition temperature. We also investigate the micro-phase separation below the transition temperature, and compare the micro-phase separated structures with statics and dynamics of concentration fluctuations above the transition.Comment: 14 pages, 12 figures, 1 tabl

Design of crystal-like aperiodic solids with selective disorder--phonon coupling

Functional materials design normally focuses on structurally-ordered systems because disorder is considered detrimental to many important physical properties. Here we challenge this paradigm by showing that particular types of strongly-correlated disorder can give rise to useful characteristics that are inaccessible to ordered states. A judicious combination of low-symmetry building unit and high-symmetry topological template leads to aperiodic "procrystalline" solids that harbour this type of topological disorder. We identify key classes of procrystalline states together with their characteristic diffraction behaviour, and establish a variety of mappings onto known and target materials. Crucially, the strongly-correlated disorder we consider is associated with specific sets of modulation periodicities distributed throughout the Brillouin zone. Lattice dynamical calculations reveal selective disorder-phonon coupling to lattice vibrations characterised by these same periodicities. The principal effect on the phonon spectrum is to bring about dispersion in energy rather than wave-vector, as in the poorly-understood "waterfall" effect observed in relaxor ferroelectrics. This property of procrystalline solids suggests a mechanism by which strongly-correlated topological disorder might allow new and useful functionalities, including independently-optimised thermal and electronic transport behaviour as required for high-performance thermoelectrics.Comment: 4 figure

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

Statistical mechanics characterization of spatio-compositional inhomogeneity

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical reference one that maximizes entropy. Two kinds of disorder compete: i) the spatial one connected with possible positions of pillars inside a cell (the first component of the measure), ii) the compositional one linked to compositions of each local sum of their integer heights into a number of pillars occupying the cell (the second component). As both the number of pillars and sum of their heights are conserved, the upper limit for a pillar height hmax occurs. If due to a further constraint there is the more demanding limit h <= h* < hmax, the exact number of restricted compositions can be then obtained only through the generating function. However, at least for systems with exclusively composition degrees of freedom, we show that the neglecting of the h* is not destructive yet for a nice correlation of the h*-constrained entropic measure and its less demanding counterpart, which is much easier to compute. Given examples illustrate a broad applicability of the measure and its ability to quantify some of the subtleties of a fractional Brownian motion, time evolution of a quasipattern [28,29] and reconstruction of a laser-speckle pattern [2], which are hardly to discern or even missed.Comment: 17 pages, 5 figure