Vlasov simulation in multiple spatial dimensions

A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010, http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown promising results, in this paper we present an alternative, the Vlasov Multi Dimensional (VMD) model, that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone, as may be the case for stimulated Raman scatter in large optic f# laser beams. Perpendicular grid spacing large compared to a Debye length is then possible without instability, enabling an order 10 decrease in required computational resources compared to standard particle in cell (PIC) methods in 2D, with another reduction of that order in 3D. Further advantage compared to PIC methods accrues in regimes where particle noise is an issue. VMD and PIC results in a 2D model of localized Langmuir waves are in qualitative agreement

A correspondence of modular forms and applications to values of L-series

An interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two applications to values of L-series and values of their derivatives

Standard Model with Cosmologically Broken Quantum Scale Invariance

We argue that scale invariance is not anomalous in quantum field theory, provided it is broken cosmologically. We consider a locally scale invariant extension of the Standard Model of particle physics and argue that it fits both the particle and cosmological observations. The model is scale invariant both classically and quantum mechanically. The scale invariance is broken cosmologically producing all the dimensionful parameters. The cosmological constant or dark energy is a prediction of the theory and can be calculated systematically order by order in perturbation theory. It is expected to be finite at all orders. The model does not suffer from the hierarchy problem due to absence of scalar particles, including the Higgs, from the physical spectrum.Comment: 13 pages, no figures significant revisions, no change in results or conclusion

Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity

The Turaev-Viro state sum invariant is known to give the transition amplitude for the three dimensional BF theory with cosmological term, and its deformation parameter hbar is related with the cosmological constant via hbar=sqrt{Lambda}. This suggests a way to find the expectation value of the spacetime volume by differentiating the Turaev-Viro amplitude with respect to the cosmological constant. Using this idea, we find an explicit expression for the spacetime volume in BF theory. According to our results, each labelled triangulation carries a volume that depends on the labelling spins. This volume is explicitly discrete. We also show how the Turaev-Viro model can be used to obtain the spacetime volume for (2+1) dimensional quantum gravity.Comment: 13 pages, Revtex, figure

A Spin-Statistics Theorem for Certain Topological Geons

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with nontrivial spin and statistics. In a theory without topology change there is no obstruction to ``anomalous'' spin-statistics pairings for geons. However, in a sum-over-histories formulation including topology change, we show that non-chiral abelian geons do satisfy a spin-statistics correlation if they are described by a wave function which is given by a functional integral over metrics on a particular four-manifold. This manifold describes a topology changing process which creates a pair of geons from $R^3$.Comment: 21 pages, Plain TeX with harvmac, 3 figures included via eps

Vortex core size in interacting cylindrical nanodot arrays

The effect of dipolar interactions among cylindrical nanodots, with a vortex-core magnetic configuration, is analyzed by means of analytical calculations. The cylinders are placed in a N x N square array in two configurations - core oriented parallel to each other and with antiparallel alignment between nearest neighbors. Results comprise the variation in the core radius with the number of interacting dots, the distance between them and dot height. The dipolar interdot coupling leads to a decrease (increase) of the core radius for parallel (antiparallel) arrays

Do contaminants originating from state-of-the-art treated wastewater impact the ecological quality of surface waters?

Since the 1980s, advances in wastewater treatment technology have led to considerably improved surface water quality in the urban areas of many high income countries. However, trace concentrations of organic wastewater-associated contaminants may still pose a key environmental hazard impairing the ecological quality of surface waters. To identify key impact factors, we analyzed the effects of a wide range of anthropogenic and environmental variables on the aquatic macroinvertebrate community. We assessed ecological water quality at 26 sampling sites in four urban German lowland river systems with a 0–100% load of state-of-the-art biological activated sludge treated wastewater. The chemical analysis suite comprised 12 organic contaminants (five phosphor organic flame retardants, two musk fragrances, bisphenol A, nonylphenol, octylphenol, diethyltoluamide, terbutryn), 16 polycyclic aromatic hydrocarbons, and 12 heavy metals. Non-metric multidimensional scaling identified organic contaminants that are mainly wastewater-associated (i.e., phosphor organic flame retardants, musk fragrances, and diethyltoluamide) as a major impact variable on macroinvertebrate species composition. The structural degradation of streams was also identified as a significant factor. Multiple linear regression models revealed a significant impact of organic contaminants on invertebrate populations, in particular on Ephemeroptera, Plecoptera, and Trichoptera species. Spearman rank correlation analyses confirmed wastewater-associated organic contaminants as the most significant variable negatively impacting the biodiversity of sensitive macroinvertebrate species. In addition to increased aquatic pollution with organic contaminants, a greater wastewater fraction was accompanied by a slight decrease in oxygen concentration and an increase in salinity. This study highlights the importance of reducing the wastewater-associated impact on surface waters. For aquatic ecosystems in urban areas this would lead to: (i) improvement of the ecological integrity, (ii) reduction of biodiversity loss, and (iii) faster achievement of objectives of legislative requirements, e.g., the European Water Framework Directive

Thermally assisted magnetization reversal in the presence of a spin-transfer torque

We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin transfer torques. Since the spin transfer torque can pump a magnetic energy into the magnetic system, the equilibrium temperature of the magnetic system is ill-defined. We introduce an effective temperature based on a stationary solution of the Fokker-Planck equation. In the limit of high energy barriers, the law of thermal agitation is derived. We find that the N\'{e}el-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent of the spin torque. We carry out the numerical integration of the stochastic Landau-Lifshitz equation to support our theory. Our results agree with existing experimental data.Comment: 5 figure