Recurrence plots for the analysis of complex systems

Solar driven catalysis on semiconductors to produce clean chemical fuels, such as hydrogen, is widely considered as a promising route to mitigate environmental issues caused by the combustion of fossil fuels and to meet increasing worldwide demands for energy. The major limiting factors affecting the efficiency of solar fuel synthesis include; (i) light absorption, (ii) charge separation and transport and (iii) surface chemical reaction; therefore substantial efforts have been put into solving these problems. In particular, the loading of co-catalysts or secondary semiconductors that can act as either electron or hole acceptors for improved charge separation is a promising strategy, leading to the adaptation of a junction architecture. Research related to semiconductor junction photocatalysts has developed very rapidly and there are a few comprehensive reviews in which the strategy is discussed (A. Kudo and Y. Miseki, Chemical Society Reviews, 2009, 38, 253–278, K. Li, D. Martin, and J. Tang, Chinese Journal of Catalysis, 2011, 32, 879–890, R. Marschall, Advanced Functional Materials, 2014, 24, 2421–2440). This critical review seeks to give an overview of the concept of heterojunction construction and more importantly, the current state-of-the art for the efficient, visible-light driven junction water splitting photo(electro)catalysts reported over the past ten years. For water splitting, these include BiVO4, Fe2O3, Cu2O and C3N4, which have attracted increasing attention. Experimental observations of the proposed charge transfer mechanism across the semiconductor/semiconductor/metal junctions and the resultant activity enhancement are discussed. In parallel, recent successes in the theoretical modelling of semiconductor electronic structures at interfaces and how these explain the functionality of the junction structures is highlighted.

/pdf/visible-light-driven-heterojunction-photocatalysts-for-water-33q4busijg.pdf

Visible-light driven heterojunction photocatalysts for water splitting – a critical review

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.

https://arxiv.org/pdf/physics/0201064.pdf

Recurrence-plot-based measures of complexity and their application to heart-rate-variability data.

Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

/pdf/nonlinear-vibrations-and-stability-of-shells-and-plates-4zhg0tiabh.pdf

Nonlinear Vibrations and Stability of Shells and Plates

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.

The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

Nonlinear vibrations of suspended cables—Part I: Modeling and analysis

Continuum non-linear equations of free motion of a heavy elastic cable about a deformed initial configuration are developed. Referring to an assumed mode technique one ordinary equation for the cable planar motion is obtained via a Galerkin procedure, an approximate solution of which is pursued through a perturbation method. Suitable nondimensional results are presented for the vibrations in the first symmetric mode with different values of the cable properties. Which procedure is the proper one to account consistently for the non-linear kinematical relations of the cable in one ordinary equation of motion is discussed.

/pdf/planar-non-linear-free-vibrations-of-an-elastic-cable-52jsawkps2.pdf

Planar non-linear free vibrations of an elastic cable

Approximations of the resonant non-linear normal modes of a general class of weakly non-linear one-dimensional continuous systems with quadratic and cubic geometric non-linearities are constructed for the cases of two-to-one, one-to-one, and three-to-one internal resonances. Two analytical approaches are employed: the full-basis Galerkin discretization approach and the direct treatment, both based on use of the method of multiple scales as reduction technique. The procedures yield the uniform expansions of the displacement field and the normal forms governing the slow modulations of the amplitudes and phases of the modes. The non-linear interaction coefficients appearing in the normal forms are obtained in the form of infinite series with the discretization approach or as modal projections of second-order spatial functions with the direct approach. A systematic discussion on the existence and stability of coupled/uncoupled non-linear normal modes is presented. Closed-form conditions for non-linear orthogonality of the modes, in a global and local sense, are discussed. A mechanical interpretation of these conditions in terms of virtual works is also provided.

/pdf/resonant-non-linear-normal-modes-part-i-analytical-treatment-43is8zpobm.pdf

Giuseppe Rega

Papers

Nonlinear vibrations of suspended cables—Part I: Modeling and analysis

Planar non-linear free vibrations of an elastic cable

Resonant non-linear normal modes. Part I: analytical treatment for structural one-dimensional systems

Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions

Nonlinear vibrations of suspended cables—Part II: Deterministic phenomena