Geometry, Scaling and Universality in the Mass Distributions in Heavy Ion Collisions

Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate the mass yields and the distribution of cluster sizes. Simple Malthusian dynamics and non-linear Verhulst dynamics are used to illustrate the approach. Nuclear cobwebbing, attractors of the dynamics, and Lyapanov exponents are discussed for the mass distribution. The self-similar property of the Malthusian orbit offers a new variable for the study of scale invariance using power moments of the mass distribution. Correlation lengths, exponents and dimensions associated with scaling relations are developed. Fourier transforms of the mass distribution are used to obtain power spectra which are investigated for a $1/f^{\beta}$ behavior.Comment: 29 pages in REVTEX, 9 figures (available from the authors), RU-92-0

STUDY OF THE POOR MAN\u27S NAVIER-STOKES EQUATION TURBULENCE MODEL

The work presented here is part of an ongoing effort to develop a highly accurate and numerically efficient turbulence simulation technique. The paper consists of four main parts, viz., the general discussion of the procedure known as Additive Turbulent Decomposition, the derivation of the synthetic velocity subgrid-scale model of the high wavenumber turbulent fluctuations necessary for its implementation, the numerical investigation of this model and a priori tests of said models physical validity. Through these investigations we have demonstrated that this procedure, coupled with the use of the Poor Mans Navier-Stokes equation subgrid-scale model, has the potential to be a faster, more accurate replacement of currently popular turbulence simulation techniques since: 1. The procedure is consistent with the direct solution of the Navier-Stokes equations if the subgrid-scale model is valid, i.e, the equations to be solved are never filtered, only solutions. 2. Model parameter values are set by their relationships to N.S. physics found from their derivation from the N.S. equation and can be calculated on the fly with the use of a local high-pass filtering of grid-scale results. 3. Preliminary studies of the PMNS equation model herein have shown it to be a computationally inexpensive and a priori valid model in its ability to reproduce high wavenumber fluctuations seen in an experimental turbulent flow

Synchronisation in dynamically coupled maps

The central aim of this thesis is to better understand the dynamics of a set of dynamically coupled map systems previously introduced by Ito & Kaneko in a series of papers (Phys. Rev. Lett. 88 (2002), no. 2, 028701 and Phys. Rev. E 67 (2003), no. 4, 046226). The current work extends Ito & Kaneko’s studies to clarify the changes in macrodynamics induced by the differences in microdynamics between the two systems. A third system is also introduced that has a minor change to the microdynamics from nonlinear to linear output function in the externally coupled system. The dynamics of these three dynamically-coupled maps is also compared with their simplified systems with static coupling. The previous studies of these dynamically-coupled maps showed a partitioning of the parameter space into regions of different macrodynamics. Here, an in-depth study is presented of the behaviour of the systems as they cross the boundary between one region and another. The behaviour across this boundary is shown to be much more complicated than suggested in the previous studies. These three systems of dynamically-coupled maps all differ in the form of their microscopic couplings, yet two of the systems are shown to produce similar macrodynamics, whereas the third differs dramatically by almost any measure of the macrodynamics. The time it takes for the systems to synchronise, both the dynamically-coupled and static-coupled systems, is investigated. It is shown that the introduction of dynamicalcouplings stops the systems from synchronising quasi-instantaneously. Details of potential consequences of this in the field of neuroscience are discussed. A brief study of the effect of driving the systems with external stimuli is presented. The different microscopic coupling forms cause different responses to the external stimuli. Some of the responses are similar to that observed by the visual cortex area of the brain

Testing the SOC hypothesis for the magnetosphere

As noted by Chang, the hypothesis of Self-Organised Criticality provides a theoretical framework in which the low dimensionality seen in magnetospheric indices can be combined with the scaling seen in their power spectra and the recently-observed plasma bursty bulk flows. As such, it has considerable appeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic to slowly-driven, interaction-dominated, thresholded systems rather than unique to the magnetosphere. In consequence, several recent numerical "sandpile" algorithms have been used with a view to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will require further work in the definition of a set of observable properties which are the unique "fingerprint" of SOC. This is because, for example, a scale-free power spectrum admits several possible explanations other than SOC. A more subtle problem is important for both simulations and data analysis when dealing with multiscale and hence broadband phenomena such as SOC. This is that finite length systems such as the magnetosphere or magnetotail will by definition give information over a small range of orders of magnitude, and so scaling will tend to be narrowband. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics can be described and contrasted. We then review existing observations which are indicative of SOC, and ask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need to be made?Comment: 29 pages, 0 figures. Based on invited talk at Spring American Geophysical Union Meeting, 1999. Journal of Atmospheric and Solar Terrestrial Physics, in pres

Quantity and Quality: Not a Zero-Sum Game

Quantification of existing theories is a great challenge but also a great chance for the study of language in the brain. While quantification is necessary for the development of precise theories, it demands new methods and new perspectives. In light of this, four complementary methods were introduced to provide a quantitative and computational account of the extended Argument Dependency Model from Bornkessel-Schlesewsky and Schlesewsky. First, a computational model of human language comprehension was introduced on the basis of dependency parsing. This model provided an initial comparison of two potential mechanisms for human language processing, the traditional "subject" strategy, based on grammatical relations, and the "actor" strategy based on prominence and adopted from the eADM. Initial results showed an advantage for the traditional subject" model in a restricted context; however, the "actor" model demonstrated behavior in a test run that was more similar to human behavior than that of the "subject" model. Next, a computational-quantitative implementation of the "actor" strategy as weighted feature comparison between memory units was used to compare it to other memory-based models from the literature on the basis of EEG data. The "actor" strategy clearly provided the best model, showing a better global fit as well as better match in all details. Building upon the success modeling EEG data, the feasibility of estimating free parameters from empirical data was demonstrated. Both the procedure for doing so and the necessary software were introduced and applied at the level of individual participants. Using empirically estimated parameters, the models from the previous EEG experiment were calculated again and yielded similar results, thus reinforcing the previous work. In a final experiment, the feasibility of analyzing EEG data from a naturalistic auditory stimulus was demonstrated, which conventional wisdom says is not possible. The analysis suggested a new perspective on the nature of event-related potentials (ERPs), which does not contradict existing theory yet nonetheless goes against previous intuition. Using this new perspective as a basis, a preliminary attempt at a parsimonious neurocomputational theory of cognitive ERP components was developed