Probing spatial homogeneity with LTB models: a detailed discussion

Do current observational data confirm the assumptions of the cosmological principle, or is there statistical evidence for deviations from spatial homogeneity on large scales? To address these questions, we developed a flexible framework based on spherically symmetric, but radially inhomogeneous Lemaitre-Tolman-Bondi (LTB) models with synchronous Big Bang. We expanded the (local) matter density profile in terms of flexible interpolation schemes and orthonormal polynomials. A Monte Carlo technique in combination with recent observational data was used to systematically vary the shape of these profiles. In the first part of this article, we reconsider giant LTB voids without dark energy to investigate whether extremely fine-tuned mass profiles can reconcile these models with current data. While the local Hubble rate and supernovae can easily be fitted without dark energy, however, model-independent constraints from the Planck 2013 data require an unrealistically low local Hubble rate, which is strongly inconsistent with the observed value; this result agrees well with previous studies. In the second part, we explain why it seems natural to extend our framework by a non-zero cosmological constant, which then allows us to perform general tests of the cosmological principle. Moreover, these extended models facilitate explorating whether fluctuations in the local matter density profile might potentially alleviate the tension between local and global measurements of the Hubble rate, as derived from Cepheid-calibrated type Ia supernovae and CMB experiments, respectively. We show that current data provide no evidence for deviations from spatial homogeneity on large scales. More accurate constraints are required to ultimately confirm the validity of the cosmological principle, however.Comment: 18 pages, 12 figures, 2 tables; accepted for publication in A&

An exactly solvable quantum-lattice model with a tunable degree of nonlocality

An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose spectrum is known as equal to the set of zeros of the N-th Laguerre polynomial. The two key problems (viz., the one of the ambiguity and the one of the closed-form construction of all of the eligible inner products which make $H$ Hermitian in the respective {\em ad hoc} Hilbert spaces) are discussed. Then, for illustration, the first four simplest, $k-$parametric definitions of inner products with $k=0,k=1,k=2$ and $k=3$ are explicitly displayed. In mathematical terms these alternative inner products may be perceived as alternative Hermitian conjugations of the initial N-plet of Laguerre polynomials. In physical terms the parameter $k$ may be interpreted as a measure of the "smearing of the lattice coordinates" in the model.Comment: 35 p

A Wiener-Laguerre model of VIV forces given recent cylinder velocities

Slender structures immersed in a cross flow can experience vibrations induced by vortex shedding (VIV), which cause fatigue damage and other problems. VIV models in engineering use today tend to operate in the frequency domain. A time domain model would allow to capture the chaotic nature of VIV and to model interactions with other loads and non-linearities. Such a model was developed in the present work: for each cross section, recent velocity history is compressed using Laguerre polynomials. The compressed information is used to enter an interpolation function to predict the instantaneous force, allowing to step the dynamic analysis. An offshore riser was modeled in this way: Some analyses provided an unusually fine level of realism, while in other analyses, the riser fell into an unphysical pattern of vibration. It is concluded that the concept is promissing, yet that more work is needed to understand orbit stability and related issues, in order to further progress towards an engineering tool

Stochastic model for the 3D microstructure of pristine and cyclically aged cathodes in Li-ion batteries

It is well-known that the microstructure of electrodes in lithium-ion batteries strongly affects their performance. Vice versa, the microstructure can exhibit strong changes during the usage of the battery due to aging effects. For a better understanding of these effects, mathematical analysis and modeling has turned out to be of great help. In particular, stochastic 3D microstructure models have proven to be a powerful and very flexible tool to generate various kinds of particle-based structures. Recently, such models have been proposed for the microstructure of anodes in lithium-ion energy and power cells. In the present paper, we describe a stochastic modeling approach for the 3D microstructure of cathodes in a lithium-ion energy cell, which differs significantly from the one observed in anodes. The model for the cathode data enhances the ideas of the anode models, which have been developed so far. It is calibrated using 3D tomographic image data from pristine as well as two aged cathodes. A validation based on morphological image characteristics shows that the model is able to realistically describe both, the microstructure of pristine and aged cathodes. Thus, we conclude that the model is suitable to generate virtual, but realistic microstructures of lithium-ion cathodes

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetised, turbulent plasma---and, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion discs around black holes. In the context of discs, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfv\'enic turbulence: collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, $\beta_\mathrm{i}$: it ranges from $\sim0.05$ at $\beta_\mathrm{i}=0.1$ to at least $30$ for $\beta_\mathrm{i} \gtrsim 10$. This energy partition is approximately insensitive to the ion-to-electron temperature ratio $T_\mathrm{i}/T_\mathrm{e}$. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfv\'enic turbulence will tend towards a nonequilibrium state in which one of the species is significantly hotter than the other, viz., hotter ions at high $\beta_\mathrm{i}$, hotter electrons at low $\beta_\mathrm{i}$. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high $\beta_i$ and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when $\beta_\mathrm{i}\lesssim1$ and by linear phase mixing (Landau damping) when $\beta_\mathrm{i}\gg1