This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under...

We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED eeective Lagrangian in a constant magnetic eld. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop eeec...

This paper shows theoretically and empirically that an aggregate Euler equation relates the real interest rate to the growth rate of per capita consumption and the ratio of private and social security wealth plus asset income to consumption. Using the estimated Euler equation, the paper then calculates the steady-state effects of social security reform. Reforms that reduce the ratio of social s...

The "t-model" for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case, the model captures the rate of decay exactly, ...

Abstract We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of semi-linear stochastic differential equations (SDEs) where both the drift diffusion are not globally Lipschitz continuous. Numerical instability may arise either from stiffness linear operator or perturbation nonlinear under discretization, both. Typical applications space discretization...

This paper shows theoretically and empirically that an aggregate Euler equation relates the growth rate of per capita consumption to the real interest rate, the ratio of private wealth plus asset income to consumption, and the ratio of social security wealth to consumption. Using the estimated Euler equation, the paper then calculates the steady-state effects of social security reform. Reforms ...