Self-Organized Criticality Theory Model of Thermal Sandpile

A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.

The Taylor Rule and the Sandpile: The Taylor Contribution and Other Matters

The author of the Taylor Rule has provided new evidence about the application of the Sandpile model to his rule. The same findings of the Sandpile model are described in the Taylor paper in agreement with the conclusions of the Sandpile model. That is, that keeping interest rates too low for too long penalizes the economic recovery. On top of that the Sandpile also provides a metric for the severity of the crisis. The same law (Power Law) applies to the size and the duration of the crisis just modifying the order of the distribution paving thus a way for measuring the size of the crisis. According to the NBER data, the length is already determined for the US crisis, if the model holds on, we can also assess the severity.

Sandpile Dynamics Driven by Degree on Scale-Free Networks

We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld （BTW） model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation.

An Anisotropic Model of Sandpile

An anisotropic model of sandpile has been proposed with different topping in different directions taken in consideration. Simulation results show that no significant differences exist between this anisotropic model and the isotropic one.

A Lecture of the Taylor Rule from the Sandpile Model

Sandpile phenomena in dynamic systems in the vicinity of criticality always appeal to a sudden break of stability with avalanches of different sizes due to minor perturbations. We can view the intervention of the Central Banks on the rate of interest as a perturbation of the economic system. It is an induced perturbation to a system that fare in vicinity of criticality according to the conditions of stability embedded in the equations of the neoclassical model. An alternative reading of the Taylor Rule is proposed in combination with the Sandpile paradigm to give an account of the economic crisis as an event like an avalanche, that can be triggered by a perturbation, as is the intervention of the Central Bank on the interest rate.

The Taylor Rule and the Sandpile: A Former Paper’s Review

Looking for ways to establish solid links between Complexity Sciences and Economics, new evidence comes in form of studies that can serve to validate models as the Sandpile and the phenomenon of punctuated equilibrium, when considering the portability of the theories and models from the Complexity Sciences to Economics. This is a review of a former paper on the Taylor Rule and the Sandpile in the light of new findings regarding the recent US Housing Bubble.

Growing Sandpile Problem with Local and Non-Local Boundaries Conditions

In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see [1]). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our theoretical results.