1,721,289 research outputs found
Noisy one-dimensional maps near a crisis .2. General uncorrelated weak noise
No full textThe escape rate for one-dimensional noisy maps near a crisis is investigated. A previously introduced perturbation theory is extended to very general kinds of weak uncorrelated noise, including multiplicative white noise as a special case. For single-humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law for the rate is derived. It predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum of the map is of sufficiently large order. A simple heuristic explanation of this effect is given. The escape rate is discussed in detail for noise distributions of Levy, dichotomous, and exponential type. In the latter case, the rate is dominated by an exponentially leading Arrhenius factor in the deep precritical regime. However, the preexponential factor may still depend more strongly than any power law on the noise strength
Noisy one-dimensional maps near a crisis : I. Weak Gaussian white and colored noise
No full textWe study one-dimensional single-humped maps near the boundary crisis at fully developed chaos in the presence of additive weak Gaussian white noise. By means of a new perturbation-like method the quasi-invariant density is calculated from the invariant density at the crisis in the absence of noise. In the precritical regime, where the deterministic map may show periodic windows, a necessary and sufficient condition for the validity of this method is derived. From the quasi-invariant density we determine the escape rate, which has the form of a scaling law and compares excellently with results from numerical simulations. We find that deterministic transient chaos is stabilized by weak noise whenever the maximum of the map is of order z > 1. Finally, we extend our method to more general maps near a boundary crisis and to multiplicative as well as colored weak Gaussian noise. Within this extended class of noises and for single-humped maps with any fixed order z > 0 of the maximum, in the scaling law for the escape rate both the critical exponents and the scaling function are universal
Escape rates for noisy maps with anomalous prefactors
No full textEscape rates for noisy maps with anomalous prefactors / Peter Reimann ; Eddy Lootens. - In: Europhysics letters. 34. 1996. S. 1-
Examining System Dynamics Models Together: Using Variation Theory to Identify
No full textThis study applies variation theory to examine the discourse of three online groups learning about the structure and behavior of simple population models. Students’ discussions were examined to reveal whether the discussions provided opportunities to become aware of possible variations corresponding to those critical dimensions. The findings indicated that only in Group 1 did the discussion open variations corresponding to critical dimensions of the model structure and growth patterns. We propose that variation theory is useful as an analytic lens for researchers interested in collaborative learning particularly in online environments, and also as an instructional design tool for teachers in designing collaborative tasks
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Designing for disruption: Remodelling a blended course in technology in (language) teacher education
Full text linkThis study employs a case study model to documenting the evolution over three semesters of a Masters course in technology and language learning for in-service teachers using a social constructivist pedagogical approach (Felix, 2002) within an ecological framework, from completely face-to-face (f2f) to predominantly online. The focus is on teachers’ acceptance of change in the form of integration of technology into firstly their learning and secondly their teaching, as well as their adaptability to self-managing their learning. The design of the modified course took an experiential modelling approach in which all of the tools and processes that were taught in the course were modelled and experienced by students (teachers) during the semester. These tools include reflective and social computing tools such as chat, blogs, wikis and e-portfolios, as well as lesson and task templating software such as Swarthmore Makers, Hot Potatoes, and WebQuests, and webpage creation software such as Dreamweaver. Based on grounded research methods, techniques such as surveys, problem-based focus groups and short answer responses were used to ascertain the values of the changes. The information collected from these instruments is presented and compared to the reflective pieces produced by students in their blogs, and the projects they created
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