# A Short Course in General Relativity by James Foster, J. D. Nightingale

By James Foster, J. D. Nightingale

This textbook offers a very good advent to a subject that's tremendous effortless to get slowed down in. I took a one semester path that used this article as an undergraduate, in which i presumed the e-book used to be in basic terms respectable, yet then whilst I took a gradute direction that used Carroll's Spacetime and Geometry is while i actually got here to understand the practise this publication gave me (not that Carroll's booklet is undesirable, I simply would not suggest it for a primary reading). let alone the booklet is beautiful reasonable so far as physics texts move.

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Phillips et al. (1992) also discussed the possibility of the effect of spatially varying viscosity that arises from spatially varying particle concentration. Namely, since the apparent viscosity is larger in the higher concentration region than in the lower concentration region, the resistance to migration into larger concentration region is larger than that into smaller concentration region. 77. These conditions correspond to the flume experiment and the actual debris flow at Jiangjia gully, respectively, which will be referred to below.

Especially in this stage, the granular temperature is low and particles are moving in order with continuous contact; the skeleton stress that is independent of velocity is dominant. Herein, such quasi-static pressure and shearing stress are considered as similar to the snow avalanche case described by Eqs (11), (13) and (14). 5 (Takahashi & Tsujimoto, 1997a). Uniform particle concentration is assumed in considering the dynamic stress, τc and τk. Then, from Eqs (6), (11), (13), (14) and the balance of force equation (19), the cross-sectional mean veloc- velocity, Hf the depth of the flow, u = * f1 = 4εF 2go, f2 = 8εF 2go /( 5 π ), f22 = 1/( 3go π ), f5 = F = Cst− ε)F 2g / ;θ ≤ φ⎫ and ε = (1 + e)/2.

Flow material is comprised of a wide range of particle sizes from very fine clay to large stones, it is a difficult problem to decide up to what size particles can be considered to form the interstitial slurry. The typical viscous debris flow that occurs at Jiangjia gully, Yunnan, China has a wide sediment size distribution (the maximum size is, however, about 10 cm) and it passes over a gently sloping reach having a very high solids concentration; it must therefore have small ε value. It is possible that particles larger than the clay size effectively form part of the interstitial slurry.