Energy avalanches in a rice-pile model

We investigate a one-dimensional rice-pile model. We show that the distribution of dissipated potential energy decays as a power law with an exponent $\alpha=1.53$. The system thus provides a one-dimensional example of self-organized criticality. Different driving conditions are examined in order to allow for comparison with experiments.Comment: 8 pages, elsart sty files (provided

Steady State and Relaxation Spectrum of the Oslo Rice-pile

We show that the one-dimensional Oslo rice-pile model is a special case of the abelian distributed processors model. The exact steady state of the model is determined. We show that the time evolution operator W for the system satisfies the equation W^{n+1} = W^n where n = L(L+1)/2 for a pile with L sites. This is used to prove that W has only one eigenvalue 1 corresponding to the steady state, and all other eigenvalues are exactly zero. Also, all connected time-dependent correlation functions in the steady state of the pile are exactly zero for time difference greater that n. Generalization to other abelian critical height models where the critical thresholds are randomly reset after each toppling is briefly discussed.Comment: 11 pages, latex, no figure

Tracer Dispersion in a Self-Organized Critical System

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a $1D$ cellular automaton modeling the experiment.Comment: 4 pages, RevTex, 1 Encapsulated PostScript and 4 PostScript available upon request, Submitted to Phys. Rev. Let

A Heavenly Example of Scale Free Networks and Self-Organized Criticality

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower energy configurations when they are overly stressed. Our recent analysis of observational data reveals that the loops (links) and footpoints (nodes), where they attach on the photosphere, embody a scale free network. The statistics of the avalanches and of the network structure are unified through a simple dynamical model where the avalanches and network co-generate each other into a complex, critical state. This particular example points toward a general dynamical mechanism for self-generation of complex networks.Comment: Submitted to proceedings for the Latin American Workshop on Nonlinear Phenomena, Salvador, Brazil (2003

Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to $r^{-\rho}$, $r$ being the distance traveled by a grain in a single topling event. The exponent $\rho$ controls the average rolling distance. We have shown that the crossover from power law to stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for $1<\rho<2$ where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short range regime for $\rho>2$, where the average rolling distance is independent of the system size.Comment: 5 pages, 3 figure

Lærarerfaringar i møte med elever i risikogruppa for fråfall – korleis finne vegen inn?

Samandrag I dagens samfunn står vi overfor utfordringar knytt til fråfall i skulen og talet på unge som står utan tilbod, arbeid og utdanning er altfor høgt. Det er difor nødvendig å undersøkja korleis vi kan finna vegen inn til elevar i risikosona for å bli ein del av denne statistikken. Korleis få ned fråfallet i vidaregåande skule har gjennom dei seinare åra vore gjenstand for mykje forsking og fokus. I NIFO-rapporten: «…respekten for forskjelligheten…» (Markussen, Carlsten, Grøgaard, & Smedsrud, 2019), kjem det blant anna fram at fleirtalet av elevar med lave inntakspoeng frå ungdomskulen går på yrkesfag. Resultatet av at desse elevane søker seg til yrkesfaga, er at det i nokon av utdanningsprogramma vil det vere elevar som treng stor grad av tilrettelegging og tilpassing i sin undervisningssituasjon. Dette kan stille ekstra høge krav til lærarar som skal møte og undervise desse elevane. Målet for denne studien har vore å kunne kome nærare inn på kva refleksjonar og handlingar som går før seg i praksisfeltet til dei som står elevane nærast i opplæringa, nemleg læraren. Med utgangspunkt i grunntanken om at kunnskapen om dette finst, men at kunnskapen på eit vis er «skjult» fordi det ikkje er ei enkelt handling eller ei «oppskrift» som utgjer dette. Det har det vore interessant å lytte til kva som vart trekt fram som viktige «nøklar» inn til læring og trivsel hjå elevar som har behov for ekstra tilrettelegging i skulekvardagen sin gjennom relasjonsbygging og pedagogisk tilrettelegging innafor ramma av ordinær undervisning på yrkesfaglege utdanningsprogram. Med utgangspunkt i dette er følgande problemstilling formulert: Lærarerfaringar i møte med elever i risikogruppa for fråfall – korleis finne vegen inn