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Sunday, August 2, 2020 | History

3 edition of A renormalization group model for the stick-slip behavior of faults found in the catalog.

A renormalization group model for the stick-slip behavior of faults

# A renormalization group model for the stick-slip behavior of faults

Written in English

Subjects:
• Faults (Geology),
• Renormalization group.,
• Coefficient of friction.,
• Earthquakes.,
• Fault tolerance.,
• Geological faults.,
• Seismic waves.,
• Statistical distributions.

• Edition Notes

Microfiche. [Washington, D.C. : National Aeronautics and Space Administration], 1984. 1 microfiche.

The Physical Object ID Numbers Statement R.F. Smalley, Jr. and D.L. Turcotte and Sara A. Solla. Series NASA CR -- 173362., NASA contractor report -- NASA CR-173362. Contributions Turcotte, Donald Lawson., Solla, Sara A., Cornell University., United States. National Aeronautics and Space Administration. Format Microform Pagination 1 v. Open Library OL17727252M

Such a simple model is successful because using tools from the theory of phase transitions such as the renormalization group, one can show that in this case, the long-range interactions are so long range that mean-field theory, which assumes infinite-range interactions, gives the correct scaling behavior for the slip statistics [23, 26] on. In physics, self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves.

Renormalization Group: Stress F Failure stress Arrest stress Weakened Same scaling behavior and phase diagram as single earthquake fault zone model of Ben-Zion and Rice. strain Strain-rate v F c strain stress stress Stress F Stick-slip + mode switching Power law. • Ultra-violet divergences and their renormalization. • Anomalous scaling in high momentum limits; the renormalization group. • Asymptotic behavior as some momenta get large; the operator product expansion (OPE). • How these ideas, after being developed in a simple theory (φ4 theory), apply to the standard model and other ﬁeld theories.

Open Library is an open, editable library catalog, building towards a web page for every book ever published. Read, borrow, and discover more than 3M books for free. The model we calculated is the restricted solid -on-solid model with a point-contact -type step- step attraction (p-RSOS model) [2]. The polar graph of the surface tension (the Wulff figure) is calculated by using the density matrix renormalization group (DMRG) method.

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### A renormalization group model for the stick-slip behavior of faults Download PDF EPUB FB2

Using a renormalization group (RG) method, we investigate the properties of a scale invariant hierarchical model for the stochastic growth of fault breaks through induced failure by stress transfer. An extrapolation to arbitrarily large scales shows the existence of a critical applied stress at which the solutions by: Get this from a library.

A renormalization group model for the stick-slip behavior of faults. [R F Smalley; Donald Lawson Turcotte; Sara A Solla; Cornell University.; United States. National Aeronautics and Space Administration.]. The stick-slip behavior of faults is a natural consequence of the renormalization group approach to the statistical model presented here for asperity failure.

Using a renormalization group (RG) method, the properties of a scale invariant hierarchical model are investigated for the stochastic growth of fault breaks through induced failure by stress transfer. An extrapolation to arbitrarily large scales shows the existence of a critical applied stress at which the solutions by: A renormalization group model for the stick-slip behavior of faults - NASA/ADS A fault which is treated as an array of asperities with a prescribed statistical distribution of strengths is described.

For a linear array the stress is transferred to a single adjacent asperity and for a two dimensional array to three ajacent by: 2.

fault, a model for the stick-slip behavior of a fault must be applicable to this depth. Taking f=p = x 10 3 kg m -3, •/ = 10 m s -2, and z = 15 km, we find • = MPa.

Any stress associated with fracture and rehealing must be larger than the. A renormalization group model for the stick-slip behavior of faults. By Jr. Smalley, It is found that the stick slip behavior of most faults can be attributed to the distribution of asperities on the fault.

The observation of stick slip behavior on faults rather than stable sliding, why the observed level of seismicity on a locked.

A renormalization group approach to the stick-slip behavior of faults - NASA/ADS We treat a fault as an array of asperities with a prescribed statistical distribution of strengths. When an asperity fails, the stress on the failed asperity is transferred to one or more adjacent asperities.

Smalley R, Turcotte D, Solla S () A renormalization group approach to the stick-slip behavior of faults. J Geophys Res Solid Earth 90(B2)– Article. "A renormalization group approach to the stick-slip behavior of faults".

Journal of Geophysical Journal of Geophysical Binder parameter ( words) [view diff] exact match in snippet view article find links to article.

A systematic way for deriving fundamental earthquake scaling relationships in their size-frequency distribution and high-frequency spectrum falloff based on the renormalization group method is presented for the model earthquakes.

It is known that faults populations are broadly scale-invariant over several orders of magnitude. A renormalization group model is developed with a new stress transfer mechanism. The crack damage stress threshold, σcd, is equivalent to a phase transition point.

The σcd/σucsratio may be an intrinsic property of low-porosity rocks. A quantitative criterion for the failure prediction of rock samples is established. A systematic way for deriving fundamental earthquake scaling relationships in their size-frequency distribution and high-frequency spectrum falloff based on the renormalization group method.

Abstract. Applying the idea of renormalization group and fractal theory, we analyzed seismic hierarchy feature detailed. Based on the seismogenic model of “fracture penetration”, we built a model of seismic critical instability, deduced its recursion relationship of renormalization, and estimated the probability of its critical instability P.

My question is somehow related to: The relation between critical surface and the (renormalization) fixed point but there is another problem: The problem is that if we accept that all points on the critical surfaceare critical in the manner that their corresponding correlation length is infinite, then according to scaling hypothesis a system whose parameters lie on the critical.

The renormalization group (RG) as a geometric flow (like the Ricci flow) is a very special case of the RG, namely, the one corresponding to the nonlinear sigma-model (NLSM) in two dimensions with values in a Riemannian manifold.

Now the RG is much more general and applies to all sorts of models, not just the NLSM. The modern theory of phase transitions occupies a central place in this book.

A separate, largely rewritten, chapter is devoted to the renormalization group approach to critical phenomena, with detailed discussion of the basic concepts of this important technique and examples of both exact and approximate calculations given.

Creep is analogous to slow and permanent deformation, while stick-slip movement along seismic faults is highly discontinuous in time. Transient slip rate have been recorded along creeping fault segments, and, most of the time, it can be related to changes in seismicity (Murray & Segall ).

Considering the scale invariance of the renormalization group theory, we where % 0' % 0 b ; b is the scale factor, which is obtained by b = Nd–1; N is the block number of initial level in the renormalization transformation; and d is the spatial dimension.

According to Fig. 3, the value of b is 2. Combining Eqs. 16 w one v ln b / ln). group method. Our first study applied the renormalization group method to the problem of the stick-slip behavior of faults.

It was hypothesized that the distribution of asperitites on a fault is a fractal. The interaction of failed asperitites was modeled as a fractal tree. The resulting model showed that the failure of only a few asperitites would. The simplest and earliest example I know regarding the renormalization group idea is the following.

Suppose we want to study some feature $\mathcal{Z}(\vec{V})$ of some object $\vec{V}$ which is in a set $\mathcal{E}$ of similar objects.

Suppose that unfortunately this question is too hard.Renormalization group approach to fragmentation Fractal behaviors during the process of rock rupture.

12 Fractal Pores and Particles of Rocks and Soils Fractal models of porous media Fractal pores Fractal particles Fractal capillary tube model in soil water retention estimation.

13 Fractal Models of Rock Micro.Our first study applied the renormalization group method to the problelll of the stick-slip behavior of faults. It was hypothesized that the distribution of asperitites on a fault is a fractal.