"This
paper (pdf) was recently published in Switzerland, and provides an
interesting look at
our recent topic--default cascades. Although these papers are mathematically
dense, they are worth working through sometimes as they may give some
foreshadowing of future economic policy.
Block-slider model of earthquakes
Battiston et al. (2011) have presented a model of the financial system which might look like one of Turcotte's slider-block models of earthquakes, which are comprised of numerous blocks of (possibly varying) masses, connected by springs, having to slide across a surface with a limited (and possibly variable) friction. Motion in one block can change the stress field across the model, possibly triggering slip in one or more other blocks.
The original slider-block model consisted of two blocks connected by a spring, both of which sat on a somewhat rough surface (so there would be friction between it and the blocks). If block A moves some small distance, then it will add to the forces on block B. That force may be enough to overcome the friction which kept block B stable. If both blocks move together, we have a larger earthquake. The simple two-block slider model exhibits chaotic behaviour (Turcotte, 1997). I remember attending a conference a few years before the above volume was published when Turcotte presented a more advanced model that looked something like the one below.
We are looking at a plan view of several interconnected blocks. The frictional forces vary for each block, and each block has its own driver. Once again, the slippage of a single block may trigger slippages in one or more blocs--the more blocks that slip, the larger the earthquake. We might expect such models to satisfy the Gutenberg-Richter law which is an observed distribution of earthquake sizes through time that is consistent with a system at self-organized criticality (SOC). But I'm not sure because I've never seen the results although comments on similar models used to study avalanches were consistent with SOC (there are those avalanches again)..."
at http://www.zerohedge.com/news/guest-post-another-view-default-cascades?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+zerohedge%2Ffeed+%28zero+hedge+-+on+a+long+enough+timeline%2C+the+survival+rate+for+everyone+drops+to+zero%29
Block-slider model of earthquakes
Battiston et al. (2011) have presented a model of the financial system which might look like one of Turcotte's slider-block models of earthquakes, which are comprised of numerous blocks of (possibly varying) masses, connected by springs, having to slide across a surface with a limited (and possibly variable) friction. Motion in one block can change the stress field across the model, possibly triggering slip in one or more other blocks.
The original slider-block model consisted of two blocks connected by a spring, both of which sat on a somewhat rough surface (so there would be friction between it and the blocks). If block A moves some small distance, then it will add to the forces on block B. That force may be enough to overcome the friction which kept block B stable. If both blocks move together, we have a larger earthquake. The simple two-block slider model exhibits chaotic behaviour (Turcotte, 1997). I remember attending a conference a few years before the above volume was published when Turcotte presented a more advanced model that looked something like the one below.
We are looking at a plan view of several interconnected blocks. The frictional forces vary for each block, and each block has its own driver. Once again, the slippage of a single block may trigger slippages in one or more blocs--the more blocks that slip, the larger the earthquake. We might expect such models to satisfy the Gutenberg-Richter law which is an observed distribution of earthquake sizes through time that is consistent with a system at self-organized criticality (SOC). But I'm not sure because I've never seen the results although comments on similar models used to study avalanches were consistent with SOC (there are those avalanches again)..."
at http://www.zerohedge.com/news/guest-post-another-view-default-cascades?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+zerohedge%2Ffeed+%28zero+hedge+-+on+a+long+enough+timeline%2C+the+survival+rate+for+everyone+drops+to+zero%29
