Butterfly catastrophe for fronts in a three-component reaction–diffusion system

We study the dynamics of front solutions in a three-component reaction–diffusion system via a combination of geometric singular perturbation theory, Evans function analysis, and center manifold reduction. The reduced system exhibits a surprisingly complicated bifurcation structure including a butterfly catastrophe. Our results shed light on numerically observed accelerations and oscillations and pave the way for the analysis of front interactions in a parameter regime where the essential spectrum of a single front approaches the imaginary axis asymptotically.

Scaling law characterizing the dynamics of the transition of HIV-1 to error catastrophe

Increasing the mutation rate, mu, of viruses above a threshold, mu(c), has been predicted to trigger a catastrophic loss of viral genetic information and is being explored as a novel intervention strategy. Here, we examine the dynamics of this transition using stochastic simulations mimicking within-host HIV-1 evolution. We find a scaling law governing the characteristic time of the transition: tau approximate to 0.6/(mu - mu(c)). The law is robust to variations in underlying evolutionary forces and presents guidelines for treatment of HIV-1 infection with mutagens. We estimate that many years of treatment would be required before HIV-1 can suffer an error catastrophe.

Experimental Evidence of Critical Sensitivity in Catastrophe

The paper presents an experimental study on critical sensitivity in rocks. Critical sensitivity means that the response of a system to external controlling variable may become significantly sensitive as the system approaches its catastrophic rupture point. It is found that the sensitivities measured by responses on three scales (sample scale, locally macroscopic scales and mesoscopic scale) display increase prior to catastrophic transition point. These experimental results do support the concept that critical sensitivity might be a common precursory feature of catastrophe. Furthermore, our previous theoretical model is extended to explore the fluctuations in critical sensitivity in the rock tests.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

Evolution-induced catastrophe and its predictability

Both earthquake prediction and failure prediction of disordered brittle media are difficult and complicated problems and they might have something in common. In order to search for clues for earthquake prediction, the common features of failure in a simple nonlinear dynamical model resembling disordered brittle media are examined. It is found that the failure manifests evolution-induced catastrophe (EIC), i.e., the abrupt transition from globally stable (GS) accumulation of damage to catastrophic failure. A distinct feature is the significant uncertainty of catastrophe, called sample-specificity. Consequently, it is impossible to make a deterministic prediction macroscopically. This is similar to the question of predictability of earthquakes. However, our model shows that strong stress fluctuations may be an immediate precursor of catastrophic failure statistically. This might provide clues for earthquake forecasting.

Damage Localization, Sensitivity of Energy Release and the Catastrophe Transition

Large earthquakes can be viewed as catastrophic ruptures in the earth’s crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.

Numerical simulation of evolution-induced catastrophe

A numerical simulation of damage evolution in a two-dimensional system of micocracks is presented. It reveals that the failure is induced by a cascade of coalescences of microcracks, and the fracture surface appears fractal. A model of evolution-induced catastrophe is introduced. The fractal dimension is found to be a function of evolution rule only. This result could qualitatively explain the correlation of fractal dimension and fracture toughness discovered in experiments.

Evolution induced catastrophe

Fracture due to coalescence of microcracks seems to be catalogued in a new model of evolution induced catastrophe (EIC). The key underlying mechanism of the EIC is its automatically enlarging interaction of microcracks. This leads to an explosively evolving catastrophe. Most importantly, the EIC presents a fractal dimension spectrum which appears to be dependent on the interaction.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

Experimental Evidence of Critical Sensitivity in Catastrophe

The paper presents an experimental study on critical sensitivity in rocks. Critical sensitivity means that the response of a system to external controlling variable may become significantly sensitive as the system approaches its catastrophic rupture point. It is found that the sensitivities measured by responses on three scales (sample scale, locally macroscopic scales and mesoscopic scale) display increase prior to catastrophic transition point. These experimental results do support the concept that critical sensitivity might be a common precursory feature of catastrophe. Furthermore, our previous theoretical model is extended to explore the fluctuations in critical sensitivity in the rock tests.

Politicians, elections and catastrophe: the general election of 1847

Over the last decade, much new research has appeared on the subject of the Great Irish Famine but, remarkably, a major political event during the famine - the 1847 general election - has received virtually no mention. Recent work on politics in this period has tended to concentrate on political reaction in Britain rather than Ireland. The aim of this article is to examine the response of Irish politicians to the famine during the general election of 1847. The main source has been the political addresses and nomination speeches of most of the 140 candidates. The evidence from this material shows that, although the famine was an important matter in many constituencies, it was not the dominant issue countrywide. Various proposals to deal with the famine emerged, but there was an absence of agreed, practical measures to deal with immediate problems. The parties in Ireland failed to create a common platform to challenge the government over its efforts. Ideological constraints played an important part in these failures. The general election of 1847 represents a lost opportunity to tackle some of the effects of the famine.

Suppressing mitotic catastrophe: identifying mcs3 in Schizosaccharomyces pombe

In Schizosaccharomyces pombe (fission yeast), the transition from G2 phase of the cell cycle to mitosis is under strict regulation. The activation of Cdc2, a cyclin dependent serine/threonine protein kinase, is the critical control step in this process. The Cdc2/Cyclin-B (Cdc13) complex is regulated by Wee1 tyrosine kinase and Cdc25 tyrosine phosphatase, which work antagonistically to control progression into mitosis. Hyperactivation of the Cdc2/Cdc13 complex by phosphorylation results in premature mitosis, and as a consequence leads to genome instability. This is referred to as mitotic catastrophe, a lethal phenotype associated with chromosomal segregation abnormalities including chromosome breakage. Six mitotic catastrophe loci were found, five of which have been characterized and identified as various activators and repressors of the core mitotic control. The locus for mcs3 remains unknown. I used tetrad analysis in this study to determine the linkage distance between three genes suspected of flanking the region in which mcs3 is located. Linkage distances obtained in this study confirm that the SPBC428.10 and met17, as well as SPBC428.10 and wpl1 are tightly linked, suggesting this is an area of low recombination. Further linkage analysis should be conducted to determine the precise location of mcs3-12.