Hard transition to chaotic dynamics in Alfven wave fronts

The derivative nonlinear Schrodinger DNLS equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand LH polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about unstable wave frequency 2/4 x ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model different dampings of daughter waves,four-dimensional flow; both models differ in significant phase-space features but keep common features essential for the transition.

A generic, hard transition to chaos

A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive values of a parameter F, no matter how small, a fully developed chaotic attractor exists within some domain of additional parameters, whereas no chaotic behavior exists for F < 0. As F is made positive, an unstable fixed point reaches an invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic structure existing at F = 0 make the limits t --* +oc, F ~ +0 non-commuting, and allow an exact description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators in near-resonance at any 2 : q frequency ratio, with F representing linear excitation of the first oscillator) is fully analysed

Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

Sequences of bifurcations and transition to chaos in an optical processing element

Digital chaotic behaviour in an Optical-Processing Element is reported. It is obtained as the result of processing two fixed trains of bits. Period doublings in a Feigenbaum-like scenario have been obtained. A new method to characterize digital chaos is reported

Sudden transition to chaos in plasma wave interactions

The coherent three-wave interaction, with linear growth in the higher frequency wave and damping in the two other waves, is reconsidered; for equal dampings, the resulting three-dimensional (3-D) flow of a relative phase and just two amplitudes behaved chaotically, no matter how small the growth of the unstable wave. The general case of different dampings is studied here to test whether, and how, that hard scenario for chaos is preserved in passing from 3-D to four-dimensional flows. It is found that the wave with higher damping is partially slaved to the other damped wave; this retains a feature of the original problem an invariant surface that meets an unstable fixed point, at zero growth rate! that gave rise to the chaotic attractor and determined its structure, and suggests that the sudden transition to chaos should appear in more complex wave interactions.

Transition to a cyclable city: policies and variables affecting cycling commuting

The growing interest in achieving the objectives of cycling policies has increased the need to know the key variables that influence the use of the bicycle for daily mobility. This paper makes a contribution in this research line by examining a varying nature of variables – objective and psychological - and their influence on cycling commuting in the context of a “climber cycling city”: Vitoria-Gasteiz (Spain). Statistical differences of the variables were determined between cycling commuters and commuters by other modes. The objective variables analyzed allowed us to identify the cycling commuting profile in Vitoria-Gasteiz, but showed a small effect on cycling commuting. However, analyses on seven cycling psychological variables identified and defined, showed a higher influence, especially “Individual capacities” and “Non-commuting cycling habit”. Their results allowed recommending a wide et of policy initiatives. These policy recommendations were made considering that Vitoria-Gasteiz is a “city in transition” towards cycling: a high level of cycling share for the Spanish contex t and the safety issue not being the main barrier for cycling. However the psychological latent variable “Non-commuting cycling habit” indicates that normalization of the bicycle as a mode of transport needs more progress.

An approach to stakeholders involvement in the preparedness for nuclear and radiological emergency response & recovery in Spain

The elaboration of a generic decision-making strategy to address the evolution of an emergency situation, from the stages of response to recovery, and including a planning stage, can facilitate timely, effective and consistent decision making by the response organisations at every level within the emergency management structure and between countries, helping to ensure optimal protection of health, environment, and society. The degree of involvement of stakeholders in this process is a key strategic element for strengthening the local preparedness and response and can help a successful countermeasures strategy. A significant progress was made with the multi-national European project EURANOS (2004-2009) which brought together best practice, knowledge and technology to enhance the preparedness for Europe's response to any radiation emergency and long term contamination. The subsequent establishment of a European Technology Platform and the recent launch of the research project NERIS-TP ("Towards a self sustaining European Technology Platform (NERIS-TP) on Preparedness for Nuclear and Radiological Emergency Response and Recovery") are aimed to continue with the remaining tasks for gaining appropriate levels of emergency preparedness at local level in most European countries. One of the objectives of the NERIS-TP project is: Strengthen the preparedness at the local/national level by setting up dedicated fora and developing new tools or adapting the tools developed within the EURANOS projects (such as the governance framework for preparedness, the handbooks on countermeasures, the RODOS system, and the MOIRA DSS for long term contamination in catchments) to meet the needs of local communities. CIEMAT and UPM in close interaction with the Nuclear Safety Council will explore, within this project, the use and application in Spain of such technical tools, including other national tools and information and communication strategies to foster cooperation between local, national and international stakeholders. The aim is identify and involve relevant stakeholders in emergency preparedness to improve the development and implementation of appropriate protection strategies as part of the consequence management and the transition to recovery. In this paper, an overview of the "state of the art" on this area in Spain and the methodology and work Plan proposed by the Spanish group within the project NERIS to grow the stakeholder involvement in the preparedness to emergency response and recovery is presented.