Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Temperature chaos in 3D Ising spin glasses is driven by rare events

Temperature chaos has often been reported in the literature as a rare-event–driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a largedeviations functional that allows to discuss the size dependences. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

Chemical Reactors. Problem 1: A simple ODE (chaos in the atmosphere) (2011-2012 Course)

Wording of problem 1: A simple ODE (chaos in the atmosphere).

Dynamic Visual Servoing With Chaos Control for Redundant Robots

This paper presents a new dynamic visual control system for redundant robots with chaos compensation. In order to implement the visual servoing system, a new architecture is proposed that improves the system maintainability and traceability. Furthermore, high performance is obtained as a result of parallel execution of the different tasks that compose the architecture. The control component of the architecture implements a new visual servoing technique for resolving the redundancy at the acceleration level in order to guarantee the correct motion of both end-effector and joints. The controller generates the required torques for the tracking of image trajectories. However, in order to guarantee the applicability of this technique, a repetitive path tracked by the robot-end must produce a periodic joint motion. A chaos controller is integrated in the visual servoing system and the correct performance is observed in low and high velocities. Furthermore, a method to adjust the chaos controller is proposed and validated using a real three-link robot.

Descent from banking union to political chaos. CEPS Commentary, 24 January 2014

To counteract the powerful anti-Europe sentiments swirling throughout the EU today and to motivate EU citizens to vote in a constructive spirit in the upcoming European elections, Karel Lannoo argues in this commentary that the functioning of the EU institutions needs to be openly discussed and proposals need to be aired for improving the decision-making process to render it more transparent and democratic. This process would encompass, in his view, the proper role and functioning of the European Commission, the European Parliament and the member states in the EU Council and the interrelationships between these institutions.

Bosniacki chaos. Zrodla kryzysu politycznego we wspolczesnej Bosni i Hercegowinie. Prace OSW 31/2009. = Bosnia's chaos. Causes of the political crisis in Bosnia and Herzegovina today. OSW Study 31/2009

A new form of 'transformational crisis' has been observed in Bosnia and Herzegovina since at least 2005. Politicians representing the three major ethno-political communities (Bosnians, Croats and Serbs) have successively been raising disputes and have employed various political tools to preserve the conflicts instead of resolving them. As a result, the central state institutions and organisations have been weakened and attempts to replace them with narrower ethnic structures have been made. This is increasingly paralysing the state, thus impeding its everyday operation and preventing its structures and legislation from being modernised; had this been achieved, it would have resulted in a real acceleration of the process of Bosnia's integration with the EU and NATO. The present crisis is also an effect of the disagreement between the key international players - the European Union, the United States and Russia - over the 'plan for Bosnia' and the role and duties of the Office of the High Representative, who acts on behalf of the international community in the country.

The debt, the stock market and the state-owned enterprises. The sources of chaos on the Chinese financial markets. OSW Commentary NUMBER 201/16.03.2016

The government’s extensive programme for stimulating the economy has enabled China to maintain high economic growth after the global financial crisis in 2008. However, this success has come at the price of a number of negative economic phenomena and the consequences they have had are the major challenge for the government today. The vast programme of investments in infrastructure, construction and fixed assets, which has been the main source of economic growth over the past few years, has caused a rapid increase in China’s debt from 158% of GDP in 2007 to 282% in 2014. Along with the local governments in charge of implementing the programme, the Chinese sector of state-owned enterprises (SOEs) has been heavily burdened by the stimulation policy. The sector’s profitability has fallen, its indebtedness has increased and management problems have been revealed.

Europe in limbo while the UK descends into chaos. EPC Post-Summit Commentary, 30 June 2016

The EU Summit and the separate meeting of the EU27 without the UK on 28/29 June 2016 demonstrated that the EU is in limbo. Following the initial shock, frustration and anger after the unexpected result of the UK ‘in/out’ referendum, the future relationship between the European Union (EU) and the United Kingdom (UK) monopolised the meetings of EU leaders. The EU has entered uncharted waters and leaders are struggling to figure out how exactly to deal with the manifold (potential) consequences of the ‘Brexit crisis’. Despite the many uncertainties, the EU27 managed to reach some common lines, trying to convey four key messages, although the final outcome of the crisis and its effects on the Union’s overall future are still very unclear:

Fault development and interaction in distributed strike-slip shear zones: an experimental approach

Analogue model experiments using both brittle and viscous materials were performed to investigate the development and interaction of strike-slip faults in zones of distributed shear deformation. At low strain, bulk dextral shear deformation of an initial rectangular model is dominantly accommodated by left-stepping, en echelon strike-slip faults (Riedel shears, R) that form in response to the regional (bulk) stress field. Push-up zones form in the area of interaction between adjacent left-stepping Riedel shears. In cross sections, faults bounding push-up zones have an arcuate shape or merge at depth. Adjacent left-stepping R shears merge by sideways propagation or link by short synthetic shears that strike subparallel to the bulk shear direction. Coalescence of en echelon R shears results in major, through-going faults zones (master faults). Several parallel master faults develop due to the distributed nature of deformation. Spacing between master faults is related to the thickness of the brittle layers overlying the basal viscous layer. Master faults control to a large extent the subsequent fault pattern. With increasing strain, relatively short antithetic and synthetic faults develop mostly between old, but still active master faults. The orientation and evolution of the new faults indicate local modifications of the stress field. In experiments lacking lateral borders, closely spaced parallel antithetic faults (cross faults) define blocks that undergo clockwise rotation about a vertical axis with continuing deformation. Fault development and fault interaction at different stages of shear strain in our models show similarities with natural examples that have undergone distributed shear.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

Stick to reality and a dream : celebrating America's young readers : a lecture for the Year of the Young Reader, presented on November 17, 1988 at the Library of Congress /

"Children's Literature Center lecture series, no. 3"--T.p. verso.

Men of chaos,

Mode of access: Internet.