A rigorous formulation of the cosmological Newtonian limit without averaging

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein-Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System

It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for this matter model as many families of this type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweighted Sobolev spaces for a wave equation satisfied by the second fundamental form of a maximal foliation.Comment: 24 pages, plain TE

REE, Uranium (U) and Thorium (Th) contents in Betula pendula leaf growing around Komsomolsk gold concentration plant tailing (Kemerovo region, Western Siberia, Russia)

The article deals with the research findings of peculiarities of REE, Uranium and Thorium distribution in the territory surrounding the tailing of former Komsomolsk gold concentration plant according to the data from Betula pendula leaf testing. In the leaf element composition the slight deficiency of MREE and substantial excess of HREE are presented. In the nearest impacted area around the tailing, La, Yb, U and Th content, and Th/U ratio are lower than in the distant buffer area. It is shown, that value of Th/U ratio and REE can be an indicator for geochemical transformations of technogenic landscapes in mining districts. The results of the research can be used for biomonitoring of the territory around the tailing

Theory of the "honeycomb chain-channel" reconstruction of Si(111)3x1

First-principles electronic-structure methods are used to study a structural model for Ag/Si(111)3x1 recently proposed on the basis of transmission electron diffraction data. The fully relaxed geometry for this model is far more energetically favorable than any previously proposed, partly due to the unusual formation of a Si double bond in the surface layer. The calculated electronic properties of this model are in complete agreement with data from angle-resolved photoemission and scanning tunneling microscopy.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett (the ugly postscript error on page 4 has now been repaired

Existence of families of spacetimes with a Newtonian limit

J\"urgen Ehlers developed \emph{frame theory} to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter $\lambda$, which can be thought of as $1/c^2$, where $c$ is the speed of light. By construction, frame theory is equivalent to general relativity for $\lambda >0$, and reduces to Newtonian gravity for $\lambda =0$. Moreover, by setting \ep=\sqrt{\lambda}, frame theory provides a framework to study the Newtonian limit \ep \searrow 0 (i.e. $c\to \infty$). A number of ideas relating to frame theory that were introduced by J\"urgen have subsequently found important applications to the rigorous study of both the Newtonian limit and post-Newtonian expansions. In this article, we review frame theory and discuss, in a non-technical fashion, some of the rigorous results on the Newtonian limit and post-Newtonian expansions that have followed from J\"urgen's work

False friends in the Fanfanyu

In the present article, a remarkable phenomenon is brought to the attention of those interested in early Chinese translations of Buddhist texts: false friends in the Fanfanyu (T54n2130). Baochang's Sanskrit-Chinese lexicon that was compiled as early as 517 AD reveals some curious examples of faux amis. In the present contribution, this case will be illustrated with references from the Shanjian lü piposha (T24n1462), a fifth century Chinese translation of the Samantapāsādikā, Buddhaghosa's commentary on the Pāli Vinaya. The fact that Baochang did not realise that this text was not translated from Sanskrit, inadvertently gave rise to some interesting jeux de mots

Relaxor ferroelectricity and colossal magnetocapacitive coupling in ferromagnetic CdCr2S4

Multiferroic materials, which reveal magnetic and electric order, are in the focus of recent solid state research. Especially the simultaneous occurrence of ferroelectricity and ferromagnetism, combined with an intimate coupling of magnetization and polarization via magneto-capacitive effects, could pave the way for a new generation of electronic devices. Here we present measurements on a simple cubic spinel with unusual properties: It shows ferromagnetic order and simultaneously relaxor ferroelectricity, i.e. a ferroelectric cluster state, reached by a smeared-out phase transition, both with sizable ordering temperatures and moments. Close to the ferromagnetic ordering temperature the magneto-capacitive coupling, characterized by a variation of the dielectric constant in an external magnetic field, reaches colossal values of nearly 500%. We attribute the relaxor properties to geometric frustration, which is well known for magnetic moments, but here is found to impede long-range order of the structural degrees of freedom.Comment: 4 pages, 3 figure