Recurrence quantification analysis of spatio-temporal chaotic transient in a closed unstirred Belousov-Zhabotinsky reaction

We analyse the transient spatio-temporal chaos that we observe in the Belousov-Zhabotinsky reaction performed in a closed unstirred batch reactor by recurrence quantification analysis (RQA). We characterize the chaotic transient by measuring the Lyapunov exponent and the Kaplan-Yorke dimension. The latter shows the fractality of the attractor. The importance of the coupling between hydrodynamics and kinetics for the onset of chaos is also shown

Bifurcations in spiral tip dynamics induced by natural convection in the Belousov–Zhabotinsky reaction

The transition to spatial-temporal complexity exhibited by spiral waves under the effect of gravitational field in the Belousov–Zhabotinsky reaction is numerically studied on the basis of spiral tip dynamics. Successive transformations in tip trajectories are characterized as a function of the hydrodynamical parameter and attributed to a Ruelle–Takens–Newhouse scenario to chaos. The analysis describes the emergence of complexity in terms of the interplay between the evolution of the velocity field and concentration waves. In particular, (i) by mapping the tip motion in relation to some hydrodynamical pseudopotentials, the general mechanism by which the velocity field affects the tip trajectory is pointed out, and, (ii) by comparing the dynamical evolutions of local and mean properties associated with the inhomogeneous structures and to the velocity field, a surprising correlation is found. The results suggest that the reaction-diffusion-convection (RDC) coupling addresses the system to some general regimes, whose nature is imposed by the hydrodynamical contribution. More generally, RDC coupling would be formalized as the phenomenon that governs the system and drives it to chaos

Ruelle–Takens–Newhouse scenario in reaction-diffusion-convection system

Direct numerical simulations of the transition process from periodic to chaotic dynamics are presented for two variable Oregonator-diffusion model coupled with convection. Numerical solutions to the corresponding reaction-diffusion-convection system of equations show that natural convection can change in a qualitative way, the evolution of concentration distribution, as compared with convectionless conditions. The numerical experiments reveal distinct bifurcations as the Grashof number is increased. A transition to chaos similar to Ruelle-Takens-Newhouse scenario is observed. Numerical results are in agreement with the experiments

Exome-wide Rare Variant Analysis Identifies TUBA4A Mutations Associated with Familial ALS

Exome sequencing is an effective strategy for identifying human disease genes. However, this methodology is difficult in late-onset diseases where limited availability of DNA from informative family members prohibits comprehensive segregation analysis. To overcome this limitation, we performed an exome-wide rare variant burden analysis of 363 index cases with familial ALS (FALS). The results revealed an excess of patient variants within TUBA4A, the gene encoding the Tubulin, Alpha 4A protein. Analysis of a further 272 FALS cases and 5,510 internal controls confirmed the overrepresentation as statistically significant and replicable. Functional analyses revealed that TUBA4A mutants destabilize the microtubule network, diminishing its repolymerization capability. These results further emphasize the role of cytoskeletal defects in ALS and demonstrate the power of gene-based rare variant analyses in situations where causal genes cannot be identified through traditional segregation analysis

Chemical Waves

In our paper we try to describe the basic concepts of chemical waves and spatial pattern formation in a simple way. We pay particular attention to self-organisation phenomena in extended excitable systems. These result in the appearance of travelling waves, spiral waves, target patterns, Turing structures or more complicated structures called scroll waves, which are three-dimensional systems. We describe the most famous oscillating reaction, the Belousov-Zhabotinsky (BZ) reaction, in greater detail. This is because it is of great interest in both physical chemistry and in studies on the evolution and sustenance of self-organising biological systems

Butterfly effect in a chemical oscillator

The strong sensitivity of aperiodic dynamics to initial conditions is one of the fingerprinting features of chaotic systems. While this dependence can be directly verified by means of numerical approaches, it is quite elusive and difficult to be isolated in real experimental systems. In this paper, we discuss a didactic and self-consistent method to show the divergent behaviour between two infinitesimally different solutions of the famous Belousov–Zhabotinsky oscillator simultaneously undergoing a transition to a chaotic regime. Experimental data are also used to give an intuitive visualization of the essential meaning of a Lyapunov exponent, which allows for a more quantitative characterization of the chaotic transient

On the origin of chaos in the Belousov-Zhabotinsky reaction in closed and unstirred reactors

We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations and spatial–temporal dynamics. In particular, numerical solutions to the corresponding reaction-diffusion-convection (RDC) problem show that natural convection can change the evolution of the concentration distribution as well as oscillation patterns. The results suggest a new way of perceiving the BZ reaction when it is conducted in CURs. In conflict with the common experience, chemical oscillations are no longer a mere chemical process. Within this framework the evolution of all dynamical observables are demonstrated to converge to the regime imposed by the RDC coupling: chemical and spatial–temporal chaos are genuine manifestations of the same phenomenon

On chaotic graphs: a different approach for characterizing aperiodic dynamics

Fractal worlds with limited connectivity are the topological result of growing graphs from chaotic series. We show how this model presents original characteristics which cannot be detected by means of the standard network descriptors. In detail, intrinsic inaccessibility to the fully connected configuration is demonstrated to be a universal feature associated with this family of graphs and strictly related to the fractality of a specific “chaotic source”. Here we discuss the potential of our model to be a generator of fractal graphs and also a self-consistent tool for differentiating chaotic dynamics from stochastic processes