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DTSTAMP:20261020T161629Z
LAST-MODIFIED:20160314T151409Z
DTSTART:20160407T193000Z
DTEND:20160407T203000Z
UID:event1569@bu.edu
URL:http://physics.bu.edu/internal/events/show/1569
SUMMARY:The Role of Heterogeneity in Long_Range Interacting Systems:  From 
	Nucleation to Earthquake Fault Systems
DESCRIPTION:Featuring James Silva\n\nPart of the PhD Final Oral Exams.\n\nD
	issertation:  William Klein\, Pankaj Mehta\,James Miller\, Harvey Gould\n\n
	Abstract:\n\nIn this dissertation the role heterogeneity in two long-range 
	systems will be explored.\nThe first will be the heterogeneous Ising model 
	with long-range interactions.\nEarthquake fault systems under long-range st
	ress transfer with varying types of heterogeneity\nwill be the second syste
	m of interest.\nFirst I will review the use of the intervention method used
	 to determine the\ntime and place of nucleation and extend its use in a nov
	el method that can be\nused as an indicator for spinodal nucleation. The he
	terogeneous Ising model with\nfixed magnetic sites will then be reformulate
	d as a dilute random field Ising model.\nThis reformulation will allow for 
	the application of spinodal nucleation theory to the\nheterogeneous Ising m
	odel by correcting the spinodal field and the critical exponent\nσ describ
	ing the critical behavior of clusters described in spinodal nucleation theo
	ry.\nThe applicability of this correction is shown through the use of simul
	ation work that\nobtains the percolation cluster scaling of snapshots of th
	e Ising spin system. Having\nobtained a reasonable definition of the saddle
	 point object describing the nucleation\ndroplet the density profile of the
	 nucleating droplet is measured and deviations from\nthe homogeneous spinod
	al nucleation begin to occur due to an excess amount of sparseness in the n
	ucleating droplet. \n\nEarthquake fault systems are then introduced and a c
	onnection is drawn connecting\ntwo such earthquake models. Heterogeneity is
	 introduced to this model in\nthe form of asperities with the intent of mod
	eling the effect such hard rocks have\non the earthquake faults. These aspe
	rities are observed to be a crucial element in\nexplaining the behavior of 
	aftershocks resulting in Omori’s law. A second form of\nheterogeneity is 
	introduced by coupling the Olami - Feder - Christensen model to an\ninvasio
	n percolation model for the purpose of modeling an earthquake fault system\
	nundergoing hydraulic fracturing. The ergodicty and event size statistics a
	re explored\nin this extended model. The robustness of the event size stati
	stics results are explored\nby allowing for the dissipation parameter in th
	e Olami - Feder - Christensen\nmodel to vary. Lastly the dissertation is su
	mmarized and new directions of research\nin each of these systems is deline
	ated.\n\n![Silva](/resources/event-image/1569/bf1ac93_small)
LOCATION:SCI 328\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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