Hawking radiation from "phase horizons" in laser filaments?

Belgiorno et al have reported on experiments aiming at the detection of (the analogue of) Hawking radiation using laser filaments [F. Belgiorno et al, Phys. Rev. Lett. 105, 203901 (2010)]. They sent intense focused Bessel pulses into a non-linear dielectric medium in order to change its refractive index via the Kerr effect and saw creation of photons orthogonal to the direction of travel of the pluses. Since the refractive index change in the pulse generated a "phase horizon" (where the phase velocity of these photons equals the pulse speed), they concluded that they observed the analogue of Hawking radiation. We study this scenario in a model with a phase horizon and a phase velocity very similar to that of their experiment and find that the effective metric does not quite correspond to a black hole. The photons created in this model are not due to the analogue of black hole evaporation but have more similarities to cosmological particle creation. Nevertheless, even this effect cannot explain the observations -- unless the pulse has significant small scale structure in both the longitudinal and transverse dimensions.Comment: 13 pages RevTeX, 2 figure

Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Huckel model

Based on infinite one-dimensional single-electron periodic models of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, albeit preserved in the molecular systems with only bound states, no longer generally held for the periodic systems. The overall permutation symmetry breakdown provides a fairly natural explanation to the widely observed large deviations of Kleinman symmetry for periodic systems in off-resonant regions. Physical conditions to experimentally test the overall permutation symmetry break are discussed.Comment: 7 pages, 1 figur

Long term minimum tillage investigations, Stubble management, Deep ripping

Direct drilling Long term minimum tillage investigations (1) Continuous cropping – 77A16, 77A18, 77MT15, 77WH17, 77WH13, 78M25. (2) Rotational cropping – 77A43, 77E52, 77M35, 77M56, 77MT51, 77WH8. Stubble management – 79M7, 79WH6, 82M34, 84M1, 82LG4, 82LG46 (82KD1). Deep ripping - 82M35 in Minimum Tillage Rotation section also contains a deep ripping treatment. 77WH17, 80A44, 80NO46, 81M45, 81NO3, 81NO4, 82GE37, 82GE38, 82M30, 82M46, 82M60, 82ME38, 82N32, 82WH49, 84E24, (84C42, 84C43, 84C44, 84C45, 84C46) Eradu Sandplain – ECRS, 84E23, 84E24, 84JE43, 84JE44, 84LG37, 84M38, 84NO58, 84WH2, 84WH3, 84WH39. Additional deep ripping research is included in summaries by W. Bowden, D. Tennant, J. Hamblin, J. Wilson

DIRK Schemes with High Weak Stage Order

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.Comment: 10 pages, 5 figure