Detection of unstable periodic orbits in mineralising geological systems

Feature-preserving synthesis of termite-mimetic spinodal nest morphology

Termite-built topology is complex due to group interactions and environmental feedback. Being interlinked with material characteristics and related to functionality, an accurate synthesis of termite mound topology has never been achieved. We scanned inner termite mound pieces via high-resolution micro-computed tomography. A wavelet scattering transform followed by optimization extracts features that are fed into a Gaussian Random Fields (GRFs) approach to synthesize termite-mimetic spinodal topology. Compared to natural structures the GRF topology is more regular. Irregularity is related to anisotropy, indicative of directionality caused by porous network connectivity of chambers and corridors. Since GRFs are related to diffusion, we assume that deterministic behavioral traits play a significant role in the development of these local differences. We pioneer a framework to reliably mimic termite mound spinodal features. Engineering termite-inspired structures will allow to inspect aspects of termite architectures and their behavior to manufacture novel material concepts with imprinted multi-functionality.

Interpolation and sampling effects on recurrence quantification measures

The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the dynamics, periodicity, regime changes, and many more. These methods are used in different fields of research, such as finance, engineering, life, and earth science. To use them, the data have usually to be uniformly sampled, posing difficulties in investigations that provide non-uniformly sampled data, as typical in medical data (e.g., heart-beat based measurements), paleoclimate archives (such as sediment cores or stalagmites), or astrophysics (supernova or pulsar observations). One frequently used solution is interpolation to generate uniform time series. However, this preprocessing step can introduce bias to the RQA measures, particularly those that rely on the diagonal or vertical line structure in the recurrence plot. Using prototypical model systems, we systematically analyze differences in the RQA measure average diagonal line length for data with different sampling and interpolation. For real data, we show that the course of this measure strongly depends on the choice of the sampling rate for interpolation. Furthermore, we suggest a correction scheme, which is capable of correcting the bias introduced by the prepossessing step if the interpolation ratio is an integer.

Submillimetre mechanistic designs of termite-built structures

Termites inhabit complex underground mounds of intricate stigmergic labyrinthine designs with multiple functions as nursery, food storage and refuge, while maintaining a homeostatic microclimate. Past research studied termite building activities rather than the actual material structure. Yet, prior to understanding how multi-functionality shaped termite building, a thorough grasp of submillimetre mechanistic architecture of mounds is required. Here, we identify for Nasutitermes exitiosus via granulometry and Fourier transform infrared spectroscopy analysis, preferential particle sizes related to coarse silts and unknown mixtures of organic/inorganic components. High-resolution micro-computed X-ray tomography and microindentation tests reveal wall patterns of filigree laminated layers and sub-millimetre porosity wrapped around a coarse-grained inner scaffold. The scaffold geometry, which is designed of a lignin-based composite and densely biocementitious stercoral mortar, resembles that of trabecula cancellous bones. Fractal dimension estimates indicate multi-scaled porosity, important for enhanced evaporative cooling and structural stability. The indentation moduli increase from the outer to the inner wall parts to values higher than those found in loose clays and which exceed locally the properties of anthropogenic cementitious materials. Termites engineer intricately layered biocementitious composites of high elasticity. The multiple-scales and porosity of the structure indicate a potential to pioneer bio-architected lightweight and high-strength materials.

Revisiting stigmergy in light of multi-functional, biogenic, termite structures as communication channel

Termite mounds are fascinating because of their intriguing composition of numerous geometric shapes and materials. However, little is known about these structures, or of their functionalities. Most research has been on the basic composition of mounds compared with surrounding soils. There has been some targeted research on the thermoregulation and ventilation of the mounds of a few species of fungi-growing termites, which has generated considerable interest from human architecture. Otherwise, research on termite mounds has been scattered, with little work on their explicit properties. This review is focused on how termites design and build functional structures as nest, nursery and food storage; for thermoregulation and climatisation; as defence, shelter and refuge; as a foraging tool or building material; and for colony communication, either as in indirect communication (stigmergy) or as an information channel essential for direct communication through vibrations (biotremology). Our analysis shows that systematic research is required to study the properties of these structures such as porosity and material composition. High resolution computer tomography in combination with nonlinear dynamics and methods from computational intelligence may provide breakthroughs in unveiling the secrets of termite behaviour and their mounds. In particular, the examination of dynamic and wave propagation properties of termite-built structures in combination with a detailed signal analysis of termite activities is required to better understand the interplay between termites and their nest as superorganism. How termite structures serve as defence in the form of disguising acoustic and vibration signals from detection by predators, and what role local and global vibration synchronisation plays for building are open questions that need to be addressed to provide insights into how termites utilise materials to thrive in a world of predators and competitors.

A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated.