Particle conservation in numerical models of the tokamak plasma edge

The test particle Monte-Carlo models for neutral particles are often used in the tokamak edge modelling codes. The drawback of this approach is that the self-consistent solution suffers from random error introduced by the statistical method. A particular case where the onset of nonphysical solutions can be clearly identified is violation of the global particle balance due to non-converged residuals. There are techniques which can reduce the residuals - such as internal iterations in the code B2-EIRENE - but they may pose severe restrictions on the time-step and slow down the computations. Numerical diagnostics described in the paper can be used to unambiguously identify when the too large error in the global particle balance is due to finite-volume residuals, and their reduction is absolutely necessary. Algorithms which reduce the error while allowing large time-step are also discussed.Comment: Link to journal publication: http://aip.scitation.org/doi/full/10.1063/1.498085

How Changing Investment Climate Impacts on the Foreign Investors Investment Decision: Evidence from FDI in Germany

In the paper we have analysed how the changing investment climate influences investment decisions of German investors. The basic idea of our concept is a treatment of investment climate conditions as a number of factors which negatively contribute to the foreign investors’ decisions. Using statistics on FDI and aggregate indicators describing the institutional (level of corruption, protection of property rights) and macro-economical (foreign exchange rates and consumer prices dynamics) environment for the period from 1998 to 2005 we have examined the impact of the investment climate conditions on FDI inflows from Germany to the countries of BRIC, G8 and some members of EU. By controlling for FDI in BRIC countries we have shown that these states represent less attractive investment destinations for German FDI despite being viewed as the future’s most promising economies. German investors still prefer exporting rather than investing in BRIC emerging markets.Investment Climate, FDI, BRIC, G8

Dirac equation for quasi-particles in graphene and quantum field theory of their Coulomb interaction

There is evidence for existence of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points. It is shown that parity operator in (1+2) dimensions play an interesting role and can be used for defining "conserved" currents resulting from the underlying Lagrangian for Dirac quasi-particles in graphene which is shown to have U_{A}(1)*U_{B}(1) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self energy and the renormalization of the effective coupling g of this interaction and Fermi velocity $v_{f}$ which has important implications in the renormalization group analysis of g and v_{f}.Comment: 10 pages, some typos have been corrected, some references have been adde

Curving Yang-Mills-Higgs Gauge Theories

Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like those mediated by photons and gluons. In the present article, we permit non-zero curvature also on the internal space, the target of the field map. The action functional and the symmetries are constructed in such a way that they reduce to those of standard Yang-Mills-Higgs (YMH) gauge theories precisely when the curvature on the target of the fields is turned off. For curved targets one obtains a new theory, a curved YMH gauge theory. It realizes in a mathematically consistent manner an old wish in the community: replacing structures constants by functions depending on the scalars of the theory. In addition, we provide a simple 4d toy model, where the gauge symmetry is abelian, but turning off the gauge fields, no rigid symmetry remains---another possible manifestation of target curvature. It now remains to be seen, if internal curvature in the above sense is realized in nature. Curvature of space-time is proven, but still negligible in particle physics, except for the very early universe where quantum gravity must have played an essential role. An important question therefore is, if glimpses of target curvature can be visible in accelerator physics. We know that at contemporary energy scales, the usual (flat) standard model describes nature to a very high accuracy. Could it be that the alleged deviations in the B to D-star-tau-nu decay reported by BaBar in 2012 and recently also by LHCb are already a manifestation of target curvature? What kind of effects does target curvature have on a YMH theory in general, for what kind of effects do we need to look out for so as to detect it?Comment: 5 pages. Presented by T.S. on several occasions during the first half of 2015. Preprint finished and submitted to Phys. Rev. in July 201

Lie algebroids, gauge theories, and compatible geometrical structures

The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular compatibility conditions. This paper analyzes these compatibilities from a mathematical perspective. In particular, we show that the compatibility of a connection with a Lie algebroid that one finds is the Cartan condition, introduced previously by A. Blaom. For the metric on the base M of a Lie algebroid equipped with any connection, we show that the compatibility suggested from gauge theories implies that the (possibly singular) foliation induced by the Lie algebroid becomes a Riemannian foliation. Building upon a result of del Hoyo and Fernandes, we prove furthermore that every Lie algebroid integrating to a proper Lie groupoid admits a compatible Riemannian base. We also consider the case where the base is equipped with a compatible symplectic or generalized metric structure.Comment: 25 pages. This is the first part of the original preprint that was split into two parts for publication, with a new title, abstract, and introduction. The second, somewhat extended part, entitled 'Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries' is published at Journal of Geometry and Physics 135 (2019) 1-6 and can be found under arXiv:1904.0580