Berwald spacetimes and very special relativity

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.Comment: 17 pages, example section updated, journal references adde

On the non metrizability of Berwald Finsler spacetimes

We investigate whether Szabo's metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern-Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi-Civita connection of some Riemannian metric. We show for the first time that this result does not extend to Finsler spacetimes. More precisely, we find a large class of Berwald spacetimes for which the Ricci tensor of the affine connection is not symmetric. The fundamental difference from positive definite Finsler spaces that makes such an asymmetry possible, is the fact that generally, Finsler spacetimes satisfy certain smoothness properties only on a proper conic subset of the slit tangent bundle. Indeed, we prove that when the Finsler Lagrangian is smooth on the entire slit tangent bundle, the Ricci tensor must necessarily be symmetric. For large classes of Finsler spacetimes, however, the Berwald property does not imply that the affine structure is equivalent to the affine structure of a pseudo-Riemannian metric. Instead, the affine structure is that of metric-affine geometry with vanishing torsion.Comment: 12 pages, contribution to the Special Issue "Finsler Modification of Classical General Relativity" in the Journal Univers

Identifying Berwald Finsler Geometries

Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type. Applied to $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces to a necessary and sufficient condition for the Levi-Civita covariant derivative of the defining $1$-form. We illustrate our results with novel examples of $(\alpha,\beta)$-Berwald geometries which represent Finslerian versions of Kundt (constant scalar invariant) spacetimes. The results generalize earlier findings by Tavakol and van den Bergh, as well as the Berwald conditions for Randers and m-Kropina resp. very special/general relativity geometries.Comment: 17 pages, results on $(\alpha,\beta)$-Finsler geometries extended, explicit examples added, updated to journal versio

Randers pp-waves

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer and Wohlfarth's vacuum field equation of Finsler gravity for this class. We show that in this case the field equation is equivalent to the vanishing of the Finsler Ricci tensor, analogously to Einstein gravity. This implies that the considered vacuum field equation and Rutz's equation coincide in this scenario. We also construct all exact solutions of Berwald-Randers type to vacuum Finsler gravity, which turn out to be composed of a CCNV (covariantly constant null vector) Lorentzian spacetime, commonly known as pp-wave, and a 1-form given by the pp-wave distinguished null vector. We therefore refer to the found solutions as \textit{Randers pp-waves}.Comment: 11 pagers, updated to journal versio

Chemischer Transport von Germanaten

[no abstract

A Cosmological Unicorn Solution to Finsler Gravity

We present a new family of exact vacuum solutions to Pfeifer and Wohlfarth's field equation in Finsler gravity, consisting of Finsler metrics that are Landsbergian but not Berwaldian, also known as unicorns due to their rarity. Interestingly we find that these solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. We furthermore find a promising analogy between our solutions and classical FLRW cosmology. One of our solutions in particular has cosmological symmetry, i.e. it is spatially homogeneous and isotropic, and it is additionally conformally flat, with conformal factor depending only on the timelike coordinate. We show that this conformal factor can be interpreted as the scale factor, we compute it as a function of cosmological time, and we show that it corresponds to a linearly expanding (or contracting) Finsler universe

Interaction between Experiment, Modeling and Simulation of Spatial Aspects in the JAK2/STAT5 Signaling Pathway

Fundamental progress in systems biology can only be achieved if experimentalists and theoreticians closely collaborate. Mathematical models cannot be formulated precisely without deep knowledge of the experiments while complex biological systems can often not be understood fully without mathematical interpretation of the dynamic processes involved. In this article, we describe how these two approaches can be combined to gain new insights on one of the most extensively studied signal transduction pathways, the Janus kinase (JAK)/ signal transducer and activator of transcription (STAT) pathway. We focus on the parameters of a model describing how STAT proteins are transported from the membrane to the nucleus where STATs regulate gene expression. We discuss which parameters can be measured experimentally in different cell types and how the unknown parameters are estimated, what the limits of these techniques and how accurate the determinations are

Model-based extension of high-throughput to high-content data

<p>Abstract</p> <p>Background</p> <p>High-quality quantitative data is a major limitation in systems biology. The experimental data used in systems biology can be assigned to one of the following categories: assays yielding average data of a cell population, high-content single cell measurements and high-throughput techniques generating single cell data for large cell populations. For modeling purposes, a combination of data from different categories is highly desirable in order to increase the number of observable species and processes and thereby maximize the identifiability of parameters.</p> <p>Results</p> <p>In this article we present a method that combines the power of high-content single cell measurements with the efficiency of high-throughput techniques. A calibration on the basis of identical cell populations measured by both approaches connects the two techniques. We develop a mathematical model to relate quantities exclusively observable by high-content single cell techniques to those measurable with high-content as well as high-throughput methods. The latter are defined as free variables, while the variables measurable with only one technique are described in dependence of those. It is the combination of data calibration and model into a single method that makes it possible to determine quantities only accessible by single cell assays but using high-throughput techniques. As an example, we apply our approach to the nucleocytoplasmic transport of STAT5B in eukaryotic cells.</p> <p>Conclusions</p> <p>The presented procedure can be generally applied to systems that allow for dividing observables into sets of free quantities, which are easily measurable, and variables dependent on those. Hence, it extends the information content of high-throughput methods by incorporating data from high-content measurements.</p

Glyoxylic acetals as electrolytes for Si/Graphite anodes in lithium-ion batteries

Using silicon-containing anodes in lithium-ion batteries is mainly impeded by undesired side reactions at the electrode/electrolyte interface leading to the gradual loss of active lithium. Therefore, electrolyte formulations are needed, which form a solid electrolyte interphase (SEI) that can accommodate to the volume changes of the silicon particles. In this work, we analyze the influence of two glyoxylic acetals on the cycling stability of silicon-containing graphite anodes, namely TMG (1 M LiTFSI in 1,1,2,2-tetramethoxyethane) and TEG (1 M LiTFSI in 1,1,2,2-tetraethoxyethane). The choice of these two electrolyte formulations was motivated by their positive impact on the thermal stability of LIBs. We investigate solid electrolyte decomposition products employing x-ray photoelectron spectroscopy (XPS). The cycling stability of Si/Gr anodes in each electrolyte is correlated to changes in SEI thickness, composition, and morphology upon formation and aging. This evaluation is completed by comparing the performance of TMG and TEG to two carbonate-based reference electrolytes (1 M LiTFSI in 1:1 ethylene carbonate: dimethyl carbonate and 1 M LiPF6 in the same solvent mixture). Cells cycled in TMG display inferior electrochemical performance to the two reference electrolytes. By contrast, cells cycled in TEG exhibit the best capacity retention with overall higher capacities. We can correlate this to better film-forming properties of the TEG solvent as it forms a smoother and more interconnected SEI, which can better adapt to the volume changes of the silicon. Therefore, TEG appears to be a promising electrolyte solvent for silicon-containing anodes