102 research outputs found
Structures in magnetohydrodynamic turbulence: detection and scaling
We present a systematic analysis of statistical properties of turbulent
current and vorticity structures at a given time using cluster analysis. The
data stems from numerical simulations of decaying three-dimensional (3D)
magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic
field; the magnetic Prandtl number is taken equal to unity, and we use a
periodic box with grids of up to 1536^3 points, and with Taylor Reynolds
numbers up to 1100. The initial conditions are either an X-point configuration
embedded in 3D, the so-called Orszag-Tang vortex, or an
Arn'old-Beltrami-Childress configuration with a fully helical velocity and
magnetic field. In each case two snapshots are analyzed, separated by one
turn-over time, starting just after the peak of dissipation. We show that the
algorithm is able to select a large number of structures (in excess of 8,000)
for each snapshot and that the statistical properties of these clusters are
remarkably similar for the two snapshots as well as for the two flows under
study in terms of scaling laws for the cluster characteristics, with the
structures in the vorticity and in the current behaving in the same way. We
also study the effect of Reynolds number on cluster statistics, and we finally
analyze the properties of these clusters in terms of their velocity-magnetic
field correlation. Self-organized criticality features have been identified in
the dissipative range of scales. A different scaling arises in the inertial
range, which cannot be identified for the moment with a known self-organized
criticality class consistent with MHD. We suggest that this range can be
governed by turbulence dynamics as opposed to criticality, and propose an
interpretation of intermittency in terms of propagation of local instabilities.Comment: 17 pages, 9 figures, 5 table
Approaches to scaling phenomena in space and laboratory plasma
Many laboratory and space plasma phenomena exhibit scaling, i.e., no characteristic spatial and/or temporal scale can be identified in their dynamics. This lack of a characteristic scale makes the dynamics of these systems extremely complex and intractable to analytical approaches. Their statistical features, however, appear to be simple and exhibit a degree of universality. We will explore two approaches to scaling in plasma systems, one based on avalanching sandpile model and the second one based on turbulence.
The avalanching model developed here exhibits a wide range of dynamic behavior and incorporates other established models as limiting cases. A single control parameter that specifies the length scale over which the redistribution rule operates compared to the finite system size, allows us to explore different regimes of the model's dynamics close to and away from the existing fixed points. An advanced Virtual Reality visualization technique was employed to gain a better qualitative understanding of the sandpile behavior in the parameter space. This sandpile model was used to simulate features found in the fusion plasma in both low and high confinement modes. Because of the simplicity of this model, it was possible to formally characterize and explain the mechanisms underlying steep gradients formation and appearance of internal transport barriers, and to identify links to tokamak plasma behavior.
The solar wind is a supersonic, super-Alfvenic flow of compressible and inhomogeneous plasma from the Sun. The solar wind provides a natural laboratory for observations of MHD turbulence over extended temporal scales. In this case a generic and model independent method of differencing and rescaling was applied to identify self-similarity in the Probability Density Functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. The single curve, which we found to describe the fluctuations PDF of some quantities, is non-Gaussian. We model this PDF with two approaches-Fokker-Planck, for which we derived the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade. The technique was also used to quantify the statistical properties of fluctuations in the coupled solar wind-magnetosphere system. These quantitative and model-independent results place important constraints on models for the coupled solar wind-magnetosphere system
Tackling the subsampling problem to infer collective properties from limited data
Complex systems are fascinating because their rich macroscopic properties
emerge from the interaction of many simple parts. Understanding the building
principles of these emergent phenomena in nature requires assessing natural
complex systems experimentally. However, despite the development of large-scale
data-acquisition techniques, experimental observations are often limited to a
tiny fraction of the system. This spatial subsampling is particularly severe in
neuroscience, where only a tiny fraction of millions or even billions of
neurons can be individually recorded. Spatial subsampling may lead to
significant systematic biases when inferring the collective properties of the
entire system naively from a subsampled part. To overcome such biases, powerful
mathematical tools have been developed in the past. In this perspective, we
overview some issues arising from subsampling and review recently developed
approaches to tackle the subsampling problem. These approaches enable one to
assess, e.g., graph structures, collective dynamics of animals, neural network
activity, or the spread of disease correctly from observing only a tiny
fraction of the system. However, our current approaches are still far from
having solved the subsampling problem in general, and hence we conclude by
outlining what we believe are the main open challenges. Solving these
challenges alongside the development of large-scale recording techniques will
enable further fundamental insights into the working of complex and living
systems.Comment: 20 pages, 6 figures, review articl
Fluctuation properties in random walks on networks and simple integrate and fire models
In questa tesi si è studiato l’insorgere di eventi critici in un semplice modello neurale del tipo Integrate and Fire, basato su processi dinamici stocastici markoviani definiti su una rete. Il segnale neurale elettrico è stato modellato da un flusso di particelle. Si è concentrata l’attenzione sulla fase transiente del sistema, cercando di identificare fenomeni simili alla sincronizzazione neurale, la quale può essere considerata un evento critico. Sono state studiate reti particolarmente semplici, trovando che il modello proposto ha la capacità di produrre effetti "a cascata" nell’attività neurale, dovuti a Self Organized Criticality (auto organizzazione del sistema in stati instabili); questi effetti non vengono invece osservati in Random Walks sulle stesse reti. Si è visto che un piccolo stimolo random è capace di generare nell’attività della rete delle fluttuazioni notevoli, in particolar modo se il sistema si trova in una fase al limite dell’equilibrio. I picchi di attività così rilevati sono stati interpretati come valanghe di segnale neurale, fenomeno riconducibile alla sincronizzazione
Order out of Randomness : Self-Organization Processes in Astrophysics
Self-organization is a property of dissipative nonlinear processes that are
governed by an internal driver and a positive feedback mechanism, which creates
regular geometric and/or temporal patterns and decreases the entropy, in
contrast to random processes. Here we investigate for the first time a
comprehensive number of 16 self-organization processes that operate in
planetary physics, solar physics, stellar physics, galactic physics, and
cosmology. Self-organizing systems create spontaneous {\sl order out of chaos},
during the evolution from an initially disordered system to an ordered
stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical
resonances, or gyromagnetic resonances. The internal driver can be gravity,
rotation, thermal pressure, or acceleration of nonthermal particles, while the
positive feedback mechanism is often an instability, such as the
magneto-rotational instability, the Rayleigh-B\'enard convection instability,
turbulence, vortex attraction, magnetic reconnection, plasma condensation, or
loss-cone instability. Physical models of astrophysical self-organization
processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra
equation systems.Comment: 61 pages, 38 Figure
Sandpile-simulation-based graph data model for MVD generative design of shield tunnel lining using information entropy
BIM standard development is central to the performance and behavior of BIM model application across transmission, visualization, and information management perspectives. Tremendous effort has been made to ease the implementation of IFC data model in practice. Yet, the complexity of IFC data model hurdles the implementation of the import and export functionality by software vendors. To overcome this, buildingSMART introduced the concept of Model View Definitions to define which parts of an IFC data model need to be implemented for a specific data exchange scenario. With such, the certification of compatibility for software products with the IFC standard is formed. The Model View Definition is use case orientated to determine whether the specific information should be included in an IFC partial model. With the creation of ad-hoc, project-specific Exchange Requirements increasing, associated MVD development requires much more work to incorporate standard development. To resolve this issue, this paper attempts to exploit the potential of information entropy which has proven itself extremely crucial in many other industries in terms of information management, and then integrates it with sandpile simulation to propose a Top-down hierarchy to structure as well as interpret IFC partial model via Model View Definition. The proposed information entropy shifted MVD development approach would manage to unify the MVD development process that enables the reduction on confusion for various end users, specific organization, or project needs. Moreover, to better translate the BIM standard topology into sandpile simulations, a new notion system is proposed. Sandpile simulations are further implemented to prove their applicability, during the simulation, self-organized criticality is identified, and the existence of chaos is observed
Open Source Software Evolution and Its Dynamics
This thesis undertakes an empirical study of software evolution by analyzing open source software (OSS) systems. The main purpose is to aid in understanding OSS evolution. The work centers on collecting large quantities of structural data cost-effectively and analyzing such data to understand software evolution dynamics (the mechanisms and causes of change or growth). We propose a multipurpose systematic approach to extracting program facts (e. g. , function calls). This approach is supported by a suite of C and C++ program extractors, which cover different steps in the program build process and handle both source and binary code. We present several heuristics to link facts extracted from individual files into a combined system model of reasonable accuracy. We extract historical sequences of system models to aid software evolution analysis. We propose that software evolution can be viewed as Punctuated Equilibrium (i. e. , long periods of small changes interrupted occasionally by large avalanche changes). We develop two approaches to study such dynamical behavior. One approach uses the evolution spectrograph to visualize file level changes to the implemented system structure. The other approach relies on automated software clustering techniques to recover system design changes. We discuss lessons learned from using these approaches. We present a new perspective on software evolution dynamics. From this perspective, an evolving software system responds to external events (e. g. , new functional requirements) according to Self-Organized Criticality (SOC). The SOC dynamics is characterized by the following: (1) the probability distribution of change sizes is a power law; and (2) the time series of change exhibits long range correlations with power law behavior. We present empirical evidence that SOC occurs in open source software systems
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