Self-consistent bounces in two dimensions

Self - consistent mean field electrodynamics in two and three dimensions

Self-consistent nonperturbative anomalous dimensions

A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted non-perturbatively by solving and suitably truncating the topologies of the full Dyson-Schwinger set of equations. The first step requires a sensible ansatz for the full vertex part, which c...

A Characterization of Consistent Digital Line Segments in Two Dimensions

Our concern is the digitalization of line segments in Z as considered by Chun et al. [5] and Christ et al. [4]. The key property that differentiates the research of Chun et al. and Christ et al. from other research in digital line segment construction is that the intersection of any two segments must be connected. Such a system of segments is called a consistent digital line segments system (CD...

Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions

This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled methods exhibit large errors on the atomistic/continuum interface (which are often attributed to spurious forces called “ghost forces”). There are only few existi...

Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effec...