Mathematical models of martensitic microstructure

Martensitic microstructures are studied using variational models based on nonlinear elasticity. Some relevant mathematical tools from nonlinear analysis are described, and applications given to austenite-martensite interfaces and related topics

B->gamma e nu Transitions from QCD Sum Rules

B->gamma e nu transitions have recently been studied in the framework of QCD factorization. The attractiveness of this channel for such an analysis lies in the fact that, at least in the heavy quark limit, the only hadron involved is the B meson itself, so one expects a very simple description of the form factor in terms of a convolution of the B meson distribution amplitude with a perturbative kernel. This description, however, does not include contributions suppressed by powers of the b quark mass. In this letter, we calculate corrections to the factorized expression which are induced by the ``soft'' hadronic component of the photon. We demonstrate that the power-suppression of these terms is numerically not effective for physical values of the $b$ quark mass and that they increase the form factor by about 30% at zero momentum transfer. We also derive a sum rule for lambda_B, the first negative moment of the B meson distribution amplitude, and find lambda_B = 0.6 GeV (to leading order in QCD).Comment: 13 pages, 5 figure

A method for putting chiral fermions on the lattice

We describe a method to put chiral gauge theories on the lattice. Our method makes heavy use of the effective action for chiral fermions in the continuum, which is in general complex. As an example we discuss the chiral Schwinger model.Comment: 4 pages, HLRZ 92-8

Ben Bernanke and the Zero Bound

From 2000 to 2003, when Ben Bernanke was a professor and then a Fed Governor, he wrote extensively about monetary policy at the zero bound on interest rates. He advocated aggressive stimulus policies, such as a money-financed tax cut and an inflation target of 3-4%. Yet, since U.S. interest rates hit zero in 2008, the Fed under Chairman Bernanke has taken more cautious actions. This paper asks when and why Bernanke changed his mind about zero-bound policy. The answer, at one level, is that he was influenced by analysis from the Fed staff that was presented at the FOMC meeting of June 2003. This answer raises another question: why did the staff's views influence Bernanke so strongly? I seek answers to this question in the social psychology literature on group decision-making.

Partial regularity and smooth topology-preserving approximations of rough domains

For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good directions defined in a suitable neighbourhood of $\partial\Omega$, in terms of which a corresponding flow can be defined. Using this flow it is shown that $\Omega$ can be approximated from the inside and the outside by diffeomorphic domains of class $C^\infty$. Whether or not the image of a general continuous field of good directions (pseudonormals) defined on $\partial\Omega$ is the whole of $\mathbb{S}^{m-1}$ is shown to depend on the topology of $\Omega$. These considerations are used to prove that if $m=2,3$, or if $\Omega$ has nonzero Euler characteristic, there is a point $P\in\partial\Omega$ in the neighbourhood of which $\partial\Omega$ is Lipschitz. The results provide new information even for more regular domains, with Lipschitz or smooth boundaries.Comment: Final version appeared in Calc. Var PDE 56, Issue 1, 201

Quasistatic nonlinear viscoelasticity and gradient flows

We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is $\lambda$-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the deformation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium state as time $t \to \infty$ and prove convergence to equilibrium under a nondegeneracy condition. We show that this condition is satisfied in particular for any real analytic cubic-like stress-strain function.Comment: 40 pages, 1 figur