固体地球科学特論IV

The class opens in S1 term, starting Apr 9th and ending May 28th. 1. Dimensional analysis 1.1 Methodology 1.2 Examples 2. Diffusion 2.1 infinite domain: scaling, self-similarity; point source and Green’s function; finite-sized source, long-time asymptotics, multipole expansion, moments, and memory 2.2 finite domain separation of scales; definition and asymptotics of “early” and “late” times; 2.3 self-similarity and anomalous diffusion example: leaky one-dimensional diffusion; Newton-cooling/membrane diffusion and improvements using Green’s function; passing from instantaneous time derivatives to longer-term memory; short- and long-range interactions in space; example from fault mechanics: viscous fault 3. Time-dependent instability 3.1 linear stability analysis 3.2 nonlinear instabilities: physical examples and their models across various fields 3.3 self-similar asymptotics of finite-time instabilities 3.4 focus on relevance for problems in fluid and fault mechanics 4. Time-independent instability 4.1 Illustrative model: thin-slab with basal friction 4.2 Slip-weakening friction, external forcing, and the unstable growth of sliding 4.3 Critical points, linear eigenvalue problems, and instability 4.4 Energy considerations 5. (if time permits) Essentials of fracture mechanics 5.1 Integral equation formulation 5.2 Stress intensity factors and weight functions 5.3 Cohesive zone models of strength 5.4 Small-scale-yielding as a boundary layer problem 5.5 Singular perturbations and matched asymptotic expansions

In-person lecture

In-class participation, presentation

Undergraduate-level courses in multivariable calculus, differential equations, and continuum, fluid, or solid mechanics