The geometry of a vorticity model equation

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$.Comment: 24 page

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle

In this paper, we study the geodesic flow of a right-invariant metric induced by a general Fourier multiplier on the diffeomorphism group of the circle and on some of its homogeneous spaces. This study covers in particular right-invariant metrics induced by Sobolev norms of fractional order. We show that, under a certain condition on the symbol of the inertia operator (which is satisfied for the fractional Sobolev norm $H^{s}$ for $s \ge 1/2$), the corresponding initial value problem is well-posed in the smooth category and that the Riemannian exponential map is a smooth local diffeomorphism. Paradigmatic examples of our general setting cover, besides all traditional Euler equations induced by a local inertia operator, the Constantin-Lax-Majda equation, and the Euler-Weil-Petersson equation.Comment: 40 pages. Corrected typos and improved redactio

Glycogen synthase 2 is a novel target gene of peroxisome proliferator-activated receptors

Glycogen synthase 2 (Gys-2) is the ratelimiting enzyme in the storage of glycogen in liver and adipose tissue, yet little is known about regulation of Gys-2 transcription. The peroxisome proliferator-activated receptors (PPARs) are transcription factors involved in the regulation of lipid and glucose metabolism and might be hypothesized to govern glycogen synthesis as well. Here, we show that Gys-2 is a direct target gene of PPARα, PPARβ/δ and PPARγ. Expression of Gys-2 is significantly reduced in adipose tissue of PPARα-/-, PPARβ/δ-/- and PPARγ+/- mice. Furthermore, synthetic PPARβ/δ, and γ agonists markedly up-regulate Gys-2 mRNA and protein expression in mouse 3T3-L1 adipocytes. In liver, PPARα deletion leads to decreased glycogen levels in the refed state, which is paralleled by decreased expression of Gys-2 in fasted and refed state. Two putative PPAR response elements (PPREs) were identified in the mouse Gys-2 gene: one in the upstream promoter (DR-1prom) and one in intron 1 (DR-1int). It is shown that DR-1int is the response element for PPARs, while DR-1prom is the response element for Hepatic Nuclear Factor 4 alpha (HNF4α). In adipose tissue, which does not express HNF4α, DR-1prom is occupied by PPARβ/δ and PPARγ, yet binding does not translate into transcriptional activation of Gys-2. Overall, we conclude that mouse Gys-2 is a novel PPAR target gene and that transactivation by PPARs and HNF4α is mediated by two distinct response elements

Entanglement-enhanced probing of a delicate material system

Quantum metrology uses entanglement and other quantum effects to improve the sensitivity of demanding measurements. Probing of delicate systems demands high sensitivity from limited probe energy and has motivated the field's key benchmark-the standard quantum limit. Here we report the first entanglement-enhanced measurement of a delicate material system. We non-destructively probe an atomic spin ensemble by means of near-resonant Faraday rotation, a measurement that is limited by probe-induced scattering in quantum-memory and spin-squeezing applications. We use narrowband, atom-resonant NOON states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and per-damage basis. This demonstrates quantum enhancement with fully realistic loss and noise, including variable-loss effects. The experiment opens the way to ultra-gentle probing of single atoms, single molecules, quantum gases and living cells.Comment: 7 pages, 8 figures; Nature Photonics, advance online publication, 16 December 201

Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200

Does plant diversity affect the water balance of established grassland systems like in manipulative biodiversity experiments?

Land-use intensification and biodiversity loss are known drivers of the water cycle but their interactions are unclear. We investigated how evapotranspiration (ETa), downward water flux (DF), and capillary rise (CR) in topsoil and subsoil are related to land-use and plant diversity in established, commercially managed grassland and compared these results to findings from an experiment in which plant diversity was manipulated. In three Central European regions (“Biodiversity Exploratories”), we studied 29 grassland plots (50 m x 50 m; 9-11 plots per region). Land-use intensity increases in the order, pasture < mown pasture < meadow. In 2010-2015, we measured soil moisture, meteorological conditions, plant species richness, number of species in the functional groups of grasses, herbs, and legumes, and root biomass. ETa, DF, and CR were calculated for two soil layers with a soil water balance model. Land-use and biodiversity effects on water fluxes were analyzed with repeated-measures analysis of variance. Land-use intensity did not affect water fluxes. Species richness did not influence DF and CR. ETa from topsoil decreased with increasing species richness while ETa from subsoil increased. Opposing effects on ETa in the two soil layers were also observed for the number of herbs and legumes. In manipulative biodiversity experiments, such opposing effects were explained by higher biomass in species-rich mixtures, which increases shading of topsoil and reduces evaporation. In subsoil, deeper roots in species-rich mixtures increased transpiration. In the commercially managed grasslands, biomass and species richness correlated negatively because fertilizer application increased biomass and decreased species richness. Thus, similar effects of biodiversity on water fluxes in commercially managed and experimentally manipulated grassland had different reasons. We speculate that improved infiltration and enhanced bioturbation in species-rich grassland explained our observations

Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66

Predicting Concentrations of Organic Chemicals in Fish by Using Toxicokinetic Models

Quantification of chemical toxicity continues to be generally based on measured external concentrations. Yet, internal chemical concentrations have been suggested to be a more suitable parameter. To better understand the relationship between the external and internal concentrations of chemicals in fish, and to quantify internal concentrations we compared three. toxicokinetic (TK) models with each other and with literature data of measured concentrations of 39 chemicals. Two one, compartment models, together with the physiologically based toxicokinetic (PBTK) model, in which we improved the treatment of lipids, were used to predict concentrations of organic chemicals in two fish species: rainbow trout (Oncorhynchus mykiss) and fathead minnow (Pimephales promelas). All models predicted the measured internal concentrations in fish within I order of magnitude for at least 68% of the chemicals. Furthermore, the PBTK model outperformed the one-compartment models with respect to simulating chemical concentrations in the whole body (at least 88% of internal concentrations were predicted within 1 order of magnitude using the PBTK model). All the models can be used to predict concentrations in different fish species without additional experiments. However, further development of TK models is required for polar, ionizable, and easily biotransformed compounds

Measuring multipartite entanglement via dynamic susceptibilities

Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments.Comment: 5+5 pages, 3+2 figure