Massive fields tend to form highly oscillating self-similarly expanding shells

Highly Oscillating Conductivities with Jumps

We study the regularized, oscillatory, multiscale, quasilinear, elliptic problem in divergence form − div(Qη(x, x , u)∇u) = f, in Ω, (0.1) u = g, on ∂Ω, (0.2) assuming that the conductivity has the form Qη(x, y, r) = a−(x) + (a+(x)− a−(x))βη(r − ψ(x, y)), (0.3) for some domain Ω ⊂ Rn, n ≥ 1, a regularization βη of the Heaviside step function and a locally periodic function ψ(x, y), Y -periodic ...

Kink Drift in Oscillating Fields.

NORMAL FORM SOLUTION OF REDUCED ORDER OSCILLATING SYSTEMS

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

Quantum Squeezing and Late Time Classical Behavior of Massive Fields in Expanding Robertson-walker Universe

A Schroedinger picture analysis of time dependent quantum oscillators, in a manner of Guth and Pi, clearly identifies two physical mechanisms for possible decoherence of vacuum fluctuations in early universe: turning of quantum oscillators upside-down, and rapid squeezing of upside-right oscillators so that certain squeezing factor diverges. In inflationary cosmology the former mechanism explai...

Structural Optimization of Free-Form Grid Shells

In the 21 st century, as free-form design gains popularity, free-form grid shells are becoming a universal structural solution, enabling merger of structure and façade into a single layer – a skin [1]. This paper shows some of the results of a research project concerned with the optimization of grid structures over some predefined free form shape, with the goal of generating a stable and static...