A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.

Detecting and Predicting Tipping Points

Tipping points are sudden, and sometimes irreversible and catastrophic, changes in a system’s dynamical regime. Complex networks are now widely used in the analysis of time series from a complex system. In this paper, we investigate the scope of network methods to indicate tipping points. In particular, we verify that the permutation entropy of transition networks constructed from time series observations of the logistic map can distinguish periodic and chaotic regimes and indicate bifurcations. The permutation entropy of transition networks, the mean edge betweenness of visibility graphs and the number of code words in compression networks, are each shown to indicate the onset of transition of a pitchfork bifurcation system. Our study shows that network methods are effective in detecting transitions. Network-based forecasts can be applied to models of real systems, as we illustrate by considering a lake eutrophication model.

Energetics of the oxygen vacancy order-disorder transition in Ba2In2O5

The heat capacity and the enthalpy associated with the reported oxygen vacancy order-disorder transition in Ba2In2O5 were measured by high temperature step scanning calorimetry. The transition temperature is 1205 ± 2 K. The transition appears first order or nearly so. The enthalpy and entropy of transition are 1.3 kJ/mol and 1.1 J/mol K, respectively. The latter is only 4.8% of the configurational entropy, arising from mixing one vacancy and five oxygens per formula unit, 22.5 J/mol K. This suggests that the transition involves only a small fraction of the oxygen vacancies and implies extensive short-range order, SRO, in the high temperature phase.

Heat capacity and thermophysical properties of n-heptanoic cid from 5 to 350K

The sub-ambient heat capacity of heptanoic acid is characterized by a first order transition at 219.99 K which shows a Cp,m maximum greater than 400R and ΔtrsSm0 of 1.132R. The acid melts at the triple point 265.98 K and shows a Cp,m maximum greater than 8200R and ΔfusSm0 of 6.891R. At 298.15 K the values of ΔT0KK Sm0, ΔT0 KK Hm0, and Φm(T,0) are 38.89R, 6737R K, and 16.29R. Prior measurements by Adriaanse et al. (1964) with a micro calorimeter between 173 and the melting point did not reveal the transition, nor did the method-of-mixtures ("drop") calorimetry of Garner et al. (1924) between 213 K and the melting point although they claim to have confirmed the presence of both distinct crystalline phases. The somewhat greater measurement range of Schaake et al. (1982) — from 104 to 304 K — by adiabatic calorimetry on a characterized sample did reveal the transition albeit at a temperature 4.8 K higher and with 4% less entropy of transition (double the combined estimated standard deviation).Key words: n-heptanoic acid, heat capacity, transitions, triple point.

The derivation of the rotational potential function from atom–atom potentials. III. Borohydride compounds

The rotational potential functions for the borohydride ion embedded in potassium and rubidium halides are derived from atom–atom potentials of the Buckingham (exp-6) type. The librational frequencies computed from the potential functions are in good agreement with the observed frequencies. The potential functions for rubidium and potassium borohydrides derived from the atom–atom potentials yield librational frequencies that are about 10% higher than the observed values. Since the entropy of transition for potassium and rubidium borohydrides is less than expected, there is a possibility that there is some ordering of the borohydride ions above the transition temperature. An experimental method is presented for studying the ordering of the borohydride ions based on the difference in the ground level degeneracy of a tetrahedral ion in ordered and disordered states.