Hyperbolic positive energy theorem with electromagnetic fields

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

An Expansion Theorem for Electromagnetic Fields

Low energy electromagnetic fields and immunity

Recent rapid development of electromagnetic field (EMF) emitters (mobile phones, microwave broadcast stations, radiolocation, microwave sources in household devices) increased the environmental level of electromagnetic radiation. This, in turn, increased the interest on the possible risk of harmful influence of exposure to EMF. On the other hand, the low energy EMF of both low (homogenous magne...

Energy transfer performance of mechanical nanoresonators coupled with electromagnetic fields

: We study the energy transfer performance in electrically and magnetically coupled mechanical nanoresonators. Using the resonant scattering theory, we show that magnetically coupled resonators can achieve the same energy transfer performance as for their electrically coupled counterparts or even outperform them within the scale of interest. Magnetic and electric coupling are compared in the na...

A poor man’s positive energy theorem

We show that positivity of energy for stationary, asymptotically flat, non-singular domains of outer communications is a simple corollary of the Lorentzian splitting theorem. A milestone in mathematical general relativity is the positive energy theorem [8, 10]. It is somewhat surprising that the standard proofs of this result do not have anything to do with Lorentzian geometry. In this note we ...