Non-monotonicity of the frictional bimaterial effect

Sliding along frictional interfaces separating dissimilar elastic materials is qualitatively different from sliding along interfaces separating identical materials due to the existence of an elastodynamic coupling between interfacial slip and normal stress perturbations in the former case. This bimaterial coupling has important implications for the dynamics of frictional interfaces, including their stability and rupture propagation along them. We show that while this bimaterial coupling is a monotonically increasing function of the bimaterial contrast, when it is coupled to interfacial shear stress perturbations through a friction law, various physical quantities exhibit a non-monotonic dependence on the bimaterial contrast. In particular, we show that for a regularized Coulomb friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is a non-monotonic function of the bimaterial contrast, and provide analytic insight into the origin of this non-monotonicity. We further show that for velocity-strengthening rate-and-state friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is also a non-monotonic function of the bimaterial contrast. Results from simulations of dynamic rupture along a bimaterial interface with slip-weakening friction provide evidence that the theoretically predicted non-monotonicity persists in non-steady, transient frictional dynamics.Comment: 14 pages, 5 figure

The configuration, sensitivity and rapid retreat of the Late Weichselian Icelandic ice sheet

The fragmentary glacial-geological record across the Icelandic continental shelf has hampered reconstruction of the volume, extent and chronology of the Late Weichselian ice sheet particularly in key offshore zones. Marine geophysical data collected over the last two decades reveal that the ice sheet likely attained a continental shelf-break position in all sectors during the Last Glacial Maximum, though its precise timing and configuration remains largely unknown. Within this context, we review the available empirical evidence and use a well-constrained three-dimensional thermomechanical model to investigate the drivers of an extensive Late Weichselian Icelandic ice-sheet, its sensitivity to environmental forcing, and phases of deglaciation. Our reconstruction attains the continental shelf break across all sectors with a total ice volume of 5.96×105km3 with high precipitation rates being critical to forcing extensive ice sheet flow offshore. Due to its location astride an active mantle plume, a relatively fast and dynamic ice sheet with a low aspect ratio is maintained. Our results reveal that once initial ice-sheet retreat was triggered through climate warming at 21.8 ka BP, marine deglaciation was rapid and accomplished in all sectors within c. 5 ka at a mean rate of 71 Gt of mass loss per year. This rate of ice wastage is comparable to contemporary rates observed for the West Antarctic ice sheet. The ice sheet subsequently stabilised on shallow pinning points across the near shelf for two millennia, but abrupt atmospheric warming during the Bølling Interstadial forced a second, dramatic collapse of the ice sheet onshore with a net wastage of 221 Gt a−1 over 750 years, analogous to contemporary Greenland rates of mass loss. Geothermal conditions impart a significant control on the ice sheet's transient response, particularly during phases of rapid retreat. Insights from this study suggests that large sectors of contemporary ice sheets overlying geothermally active regions, such as Siple Coast, Antarctica, and NE Greenland, have the potential to experience rapid phases of mass loss and deglaciation once initial retreat is initiated

Heterogeneity in Macroeconomics

In order to study aggregate issues, macroeconomists typically use representative agent models, in which aggregates are the choice of a fictitious average agent in the economy. By construction, these models ignore the tremendous heterogeneity across individual agents documented in microeconomic data. My dissertation addresses this gap by developing tools to incorporate micro heterogeneity into macro models, and using these tools to study an important aggregate issue. In the first chapter, I develop a new method to efficiently solve models with micro heterogeneity. The main challenge is that individual agents base their decisions on the entire distribution of agents, an infinite-dimensional object. I approximate this distribution using a finite-dimensional parametric family. I show how to easily implement the method using Dynare, a publicly available software package commonly used to solve representative agent models. In the second chapter, I use this method to incorporate realistic firm-level investment behavior into a model of aggregate investment. I find that including the extensive margin of whether a firm invests or not has important implications for business cycles and countercyclical stimulus policy. First, aggregate investment is less responsive to productivity shocks in recessions than in expansions, because in recessions fewer firms are likely to make an extensive margin investment. Second, the policy multiplier also falls in recessions. Third, a simple size-dependent policy, which targets extensive margin investment, is five times more cost effective than existing size-independent policies. In the third chapter, I develop a new method to solve heterogeneous agent models in continuous time. Continuous time models are promising in the heterogeneous agent context because they easily handle nonconvexities, like borrowing constraints or fixed costs, which are important for describing micro data. Following Achdou et al. (2015), I use a finite difference method, which approximates individual decisions and the distribution over a finite grid. I solve for the dynamics of these functions using local perturbation methods. I find that the method is very efficient at solving a continuous time version of Krusell & Smith (1998), suggesting that it is able to solve more complicated models which are intractable in discrete time

Financial Heterogeneity and the Investment Channel of Monetary Policy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163628/3/ecta200216.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163628/2/ecta200216-sup-0001-onlineappendix.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163628/1/ecta200216_am.pd

When inequality matters for macro and macro matters for inequality

We develop an efficient and easy to use computational method for solving a wide class of general equilibrium heterogeneous agent models with aggregate shocks together with an open source suite of codes that implement our algorithms in an easy to use toolbox. Our method extends standard linearization techniques and is designed to work in cases when inequality matters for the dynamics of macroeconomic aggregates. We present two applications that analyze a two asset incomplete markets model parameterized to match the distribution of income, wealth, and marginal propensities to consume. First, we show that our model is consistent with two key features of aggregate consumption dynamics that are difficult to match with representative agent models: (1) the sensitivity of aggregate consumption to predictable changes in aggregate income, and (2) the relative smoothness of aggregate consumption. Second, we extend the model to feature capital-skill complementarity and show how factor-specific productivity shocks shape dynamics of income and consumption inequality