Adaptable transition systems

We present an essential model of adaptable transition systems inspired by white-box approaches to adaptation and based on foundational models of component based systems. The key feature of adaptable transition systems are control propositions, imposing a clear separation between ordinary, functional behaviours and adaptive ones. We instantiate our approach on interface automata yielding adaptable interface automata, but it may be instantiated on other foundational models of component-based systems as well. We discuss how control propositions can be exploited in the specification and analysis of adaptive systems, focusing on various notions proposed in the literature, like adaptability, control loops, and control synthesis

Complex Network Approach for Recurrence Analysis of Time Series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix calculated from time series with the adjacency matrix of a complex network, and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potentials of these complex network measures for detecting dynamical transitions. Finally we apply the proposed approach to a marine palaeo-climate record and identify subtle changes of the climate regime.Comment: 23 pages, 7 figure

Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as ``non-normal''. If there is chaos in the invariant subspace that is not structurally stable, this has the effect of ``blurring out'' blowout bifurcations over a range of parameter values that we show can have positive measure in parameter space. Associated with such blowout bifurcations are bifurcations to attractors displaying a new type of intermittency that is phenomenologically similar to on-off intermittency, but where the intersection of the attractor by the invariant subspace is larger than a minimal attractor. The presence of distinct repelling and attracting invariant sets leads us to refer to this as ``in-out'' intermittency. Such behaviour cannot appear in systems where the transverse dynamics is a skew product over the system on the invariant subspace. We characterise in-out intermittency in terms of its structure in phase space and in terms of invariants of the dynamics obtained from a Markov model of the attractor. This model predicts a scaling of the length of laminar phases that is similar to that for on-off intermittency but which has some differences.Comment: 15 figures, submitted to Nonlinearity, the full paper available at http://www.maths.qmw.ac.uk/~eo

Staircase to Higher-Order Topological Phase Transitions

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairing interaction, which is parametrized by an algebraic decay with exponent $\alpha$. Remarkably, in the limit $\alpha = 1$ the order of the topological transition becomes infinite. We compute the critical exponents for the series of higher-order transitions in exact form and find that they fulfill the hyperscaling relation. We also study the critical behaviour at the boundary of the system and discuss potential experimental platforms of magnetic atoms in superconductors.Comment: 5+5pages, 7 figures. Accepted as a Rapid Communicatio

Novel magnetic phases in a Gd2Ti2O7 pyrochlore for a field applied along the [100] axis

We report on longitudinal and transverse magnetisation measurements performed on single crystal samples of Gd2Ti2O7 for a magnetic field applied along the [100] direction. The measurements reveal the presence of previously unreported phases in fields below 10 kOe in an addition to the higher-field-induced phases that are also seen for H//[111], [110], and [112]. The proposed H-T phase diagram for the [100] direction looks distinctly different from all the other directions studied previously.Comment: 4 pages, 5 figure

Adaptability Checking in Multi-Level Complex Systems

A hierarchical model for multi-level adaptive systems is built on two basic levels: a lower behavioural level B accounting for the actual behaviour of the system and an upper structural level S describing the adaptation dynamics of the system. The behavioural level is modelled as a state machine and the structural level as a higher-order system whose states have associated logical formulas (constraints) over observables of the behavioural level. S is used to capture the global and stable features of B, by a defining set of allowed behaviours. The adaptation semantics is such that the upper S level imposes constraints on the lower B level, which has to adapt whenever it no longer can satisfy them. In this context, we introduce weak and strong adaptabil- ity, i.e. the ability of a system to adapt for some evolution paths or for all possible evolutions, respectively. We provide a relational characterisation for these two notions and we show that adaptability checking, i.e. deciding if a system is weak or strong adaptable, can be reduced to a CTL model checking problem. We apply the model and the theoretical results to the case study of motion control of autonomous transport vehicles.Comment: 57 page, 10 figures, research papaer, submitte

Phase diagram and critical endpoint for strongly-interacting quarks

We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (\mu^E,T^E) ~ (1.0,0.9)T_c, where T_c is the critical temperature for chiral symmetry restoration at \mu=0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.Comment: 4 pages, 3 figure

Highly Confined Stacks of Graphene Oxide Sheets in Water

Since the discovery of graphene oxide (GO), the most accessible of the precursors of graphene, this material has been widely studied for applications in science and technology. In this work, we describe a procedure to obtain GO dispersions in water at high concentrations, these highly dehydrated dispersions being in addition fully redispersible by dilution. With the availability of such concentrated samples, it was possible to investigate the structure of hydrated GO sheets in a previously unexplored range of concentrations, and to evidence a structural phase transition. Tentatively applying models designed for describing the small-angle scattering curve in the Smectic A (or L$_{\alpha}$) phase of lyotropic systems, it was possible to extract elastic parameters characterising the system on the dilute side of the transition, thereby evidencing the relevance of both electrostatic and steric (Helfrich) interactions in stabilising aqueous lamellar stacks of GO sheetsComment: 11 pages, 10 figure