Correction to “Continuum Microkinetic Rate Theory of Lattice Systems: Formalization, Current Limitations, and a Possible Basis for Continuum Rate Theory”

Continuum methods in lattice perturbation theory

We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Usi...

History of Continuum Theory

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 2 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 3 The Jordan Curve Theorem and the concept of a curve . . . . . . . . . . . . . . . . . 707 4 Local connectedness; plane continua.. . . . . ....

Continuum Theory of Fracture

We present a continuum theory of fracture which describes the fast propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore the selection of the steady state tip radius and velocity. Two different numerical approaches are presented to solve this problem. A sharp interface a...

Continuum Theory for Liquid Crystals

Refined plate theory for free vibration analysis of FG nanoplates using the nonlocal continuum plate model

In this article, the free vibration behavior of nanoscale FG rectangular plates is studied within the framework of the refined plate theory (RPT) and small-scale effects are taken into account. Using the nonlocal elasticity theory, the governing equations are derived for single-layered FG nanoplate. The Navier’s method is employed to obtain closed-form solutions for rectangular nanoplates assum...