We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh’s SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, ...

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the Itˆo stochastic differential equation with an anti-persistent fractional ...

A two-dimensional stochastic–diffusive energy balance model (EBM) formulated on a sphere by G. R. North et al. is explored and generalized. Instantaneous and frequency-dependent spatial autocorrelation functions and local temporal power spectral densities are computed for local sites and for spatially averaged surface temperature signals up to the global scale. On time scales up to the relaxation ...

We show that in order to have a scaling description of the climate system that is not inherently non-stationary, the rapid shifts between stadial and interstadial conditions during the last glaciation cannot be included in the scaling law. The same is true for the 5 shifts between the glacial and interglacial states in the quaternary climate. When these events are omitted from a scaling analysis ...

A simple conceptual model for the global mean surface temperature (GMST) response to CO2 emissions is presented and analysed. It consists of linear long-memory models for the GMST anomaly response ∆T to radiative forcing and atmospheric CO2 - 5 concentration response ∆C to emission rate. The responses are connected by the standard logarithmic relation between CO2 concentration and its radiative ...

Multiple, linear regression is employed to attribute variability in the global surface temperature to various forcing components and prominent internal climatic modes. The purpose of the study is to assess how sensitive attribution is to long-range memory (LRM) in the model for the temperature response. The model response to a given forcing component is its fingerprint and is different for a zero ...

A linearized energy-balance model for global temperature is formulated, featuring a scale-invariant longrange memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parameterized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface ...

In a toroidal plasma confined by a purely toroidal magnetic field the plasma transport is governed by electrostatic turbulence driven by the flute interchange instability on the low-field side of the torus cross section. In this paper we revisit experimental data obtained from the Blaamann torus at the University of Tromso. On time-scales shorter than the poloidal rotation time, the time series of ...

There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this paper we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some ...