Geodesics on Lie groups: Euler equations and totally geodesic subgroup

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing

Production of high concentrations of H2O2 in a bioelectrochemical reactor fed with real municipal wastewater

Bioelectrochemical systems can be used to energy-efficiently produce hydrogen peroxide (H2O2) from wastewater. Organic compounds in the wastewater are oxidized by microorganisms using the anode as electron acceptor. H2O2 is produced by reduction of oxygen on the cathode. In this study, we demonstrate for the first time production of high concentrations of H2O2 production from real municipal wastewater. A concentration of 2.26g/L H2O2 was produced in 9h at 8.3kWh/kgH(2)O(2). This concentration could poTENTially be useful for membrane cleaning at membrane bioreactor wastewater treatment plants. With an acetate-containing nutrient medium as anode feed, a H2O2 concentration of 9.67g/L was produced in 21h at an energy cost of 3.0kWh/kgH(2)O(2). The bioelectrochemical reactor used in this study suffered from a high internal resistance, most likely caused by calcium carbonate deposits on the cathode-facing side of the cation exchange membrane separating the anode and cathode compartments

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

Diffeomorphic random sampling using optimal information transport

In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-Rao metric on the space of probability densities and the right-invariant information metric on the group of diffeomorphisms. The resulting sampling algorithm is a promising alternative to OMT, in particular as our formulation is semi-explicit, free of the nonlinear Monge--Ampere equation. Compared to Markov Chain Monte Carlo methods, we expect our algorithm to stand up well when a large number of samples from a low dimensional nonuniform distribution is needed.Comment: 8 pages, 3 figure

The key role of nitric oxide in hypoxia: hypoxic vasodilation and energy supply-demand matching

Significance: a mismatch between energy supply and demand induces tissue hypoxia with the potential to cause cell death and organ failure. Whenever arterial oxygen concentration is reduced, increases in blood flow - 'hypoxic vasodilation' - occur in an attempt to restore oxygen supply. Nitric oxide is a major signalling and effector molecule mediating the body's response to hypoxia, given its unique characteristics of vasodilation (improving blood flow and oxygen supply) and modulation of energetic metabolism (reducing oxygen consumption and promoting utilization of alternative pathways). Recent advances: this review covers the role of oxygen in metabolism and responses to hypoxia, the hemodynamic and metabolic effects of nitric oxide, and mechanisms underlying the involvement of nitric oxide in hypoxic vasodilation. Recent insights into nitric oxide metabolism will be discussed, including the role for dietary intake of nitrate, endogenous nitrite reductases, and release of nitric oxide from storage pools. The processes through which nitric oxide levels are elevated during hypoxia are presented, namely (i) increased synthesis from nitric oxide synthases, increased reduction of nitrite to nitric oxide by heme- or pterin-based enzymes and increased release from nitric oxide stores, and (ii) reduced deactivation by mitochondrial cytochrome c oxidase. Critical issues: several reviews covered modulation of energetic metabolism by nitric oxide, while here we highlight the crucial role NO plays in achieving cardiocirculatory homeostasis during acute hypoxia through both vasodilation and metabolic suppression Future directions: we identify a key position for nitric oxide in the body's adaptation to an acute energy supply-demand mismatc

Middleborns disadvantaged? testing birth-order effects on fitness in pre-industrial finns

Parental investment is a limited resource for which offspring compete in order to increase their own survival and reproductive success. However, parents might be selected to influence the outcome of sibling competition through differential investment. While evidence for this is widespread in egg-laying species, whether or not this may also be the case in viviparous species is more difficult to determine. We use pre-industrial Finns as our model system and an equal investment model as our null hypothesis, which predicts that (all else being equal) middleborns should be disadvantaged through competition. We found no overall evidence to suggest that middleborns in a family are disadvantaged in terms of their survival, age at first reproduction or lifetime reproductive success. However, when considering birth-order only among same-sexed siblings, first-, middle-and lastborn sons significantly differed in the number of offspring they were able to rear to adulthood, although there was no similar effect among females. Middleborn sons appeared to produce significantly less offspring than first-or lastborn sons, but they did not significantly differ from lastborn sons in the number of offspring reared to adulthood. Our results thus show that taking sex differences into account is important when modelling birth-order effects. We found clear evidence of firstborn sons being advantaged over other sons in the family, and over firstborn daughters. Therefore, our results suggest that parents invest differentially in their offspring in order to both preferentially favour particular offspring or reduce offspring inequalities arising from sibling competition

Elucidation of the liquid-liquid distribution behavior of ion associates of metal-halogeno complex anions with quaternary ammonium counter cations and its application to separation and analysis

第四級アンモニウムイオンを対イオンとする一価, 二価金属ハロゲノ錯陰イオンのイオン会合抽出挙動を把握し, 分離・分析的応用を図るために, 炭素数及び形状の異なる第四級アンモニウム陽イオンを用いて, 水-各種抽出溶媒 {1,2-ジクロロエタン, クロロホルム (CF), クロロベンゼン (Cl-B), ベンゼン (B), トルエン (T) 及び四塩化炭素 (CTC)} 系での抽出定数を求めた. 得られた抽出定数から次の知見を得た. (1) 配位子の抽出性に及ぼす影響 : 配位子がCl-, Br-, I-と変わるにつれ, この順に抽出性は良くなる. (2) 配位子数の影響 : 配位子数が多くなるに従い, 抽出性も良くなる. (3) 中心金属の影響 : 配位子数が同じ場合には, 抽出性はほぼ中心金属イオンの大きさの順となる. (4) 金属錯陰イオンの電荷の影響 : 一般に二価陰イオンよりも一価陰イオンのほうが抽出されやすい. (5) 対陽イオンのアルキル鎖のメチレン基の寄与 : メチレン基一つ当たり, 大体0.4～0.8の抽出定数 (log K(ex)) の増大となる. (6) 抽出溶媒の影響 : 抽出溶媒の抽出能は次の順となる : CTC<T<B<Cl-B<CF. (7) 金属ハロゲノ錯陰イオンの配位子の違いによる抽出定数の差 (Δlog K(ex)) は溶媒によらず, ほぼ一定である. これらの知見を基に, 金属ハロゲノ錯陰イオンと疎水性陽イオンとのイオン会合抽出を利用する幾つかの金属の分離・定量法を開発した.The distribution behavior of ion associates of both monovalent and divalent metal-halogeno complex anions with various quaternary ammonium cations between the aqueous phase and several organic phases {1,2-dichloroethane, chloroform (CF), chlorobenzene (Cl-B), benzene (B), toluene (T) and carbon tetrachloride (CTC)} was examined, and the extraction constants (log Kex) were determined. The larger is the size of the ligand (Cl-<Br-<I-) and the coordination number, the greater is the ion associability. For the same coordination number, in general, the larger is the size of the metal ion, the greater is the ion associability. In general, the extractability of monovalent metal-halogeno complex anions is larger than that of divalent metal-halogeno complex anions. A linear relationship was obtained between log Kex and the number of carbon atoms in quaternary ammonium ion, and the contribution of a methylene group to the extraction constant (Δlog K(ex)/-CH(2-)) was found to be about 0.4∼0.8. Among the ion associates examined, the order of the extractability of the extracting solvent was generally CTC<T<B<Cl-B<CF. Also, the order of the extractability of the ion associates for dihalogenocuprate (I), tetrahalogenoaurate (III) and tetrahalogenothallate (III) complex ions was as follows, respectively : CuCl(2)-<CuBr(2)-<CuI(2)- ; AuCl(4)-<AuBr(4)- ; TlCl(4)-<TlBr(4)-<TlI(4-). The values of Δlog K(ex) between the complex anions were almost equal, even though the extracting solvents were changed. From these results, several extraction-spectrophotometric methods for the determination of metal based on the formation of an ion associate of metal-halogeno complex anion with hydrophobic cations were developed

‘‘Beet-ing’’ the Mountain: A Review of the Physiological and Performance Effects of Dietary Nitrate Supplementation at Simulated and Terrestrial Altitude

Exposure to altitude results in multiple physiological consequences. These include, but are not limited to, a reduced maximal oxygen consumption, drop in arterial oxygen saturation, and increase in muscle metabolic perturbations at a fixed sub-maximal work rate. Exercise capacity during fixed work rate or incremental exercise and time-trial performance are also impaired at altitude relative to sea-level. Recently, dietary nitrate (NO3-) supplementation has attracted considerable interest as a nutritional aid during altitude exposure. In this review, we summarise and critically evaluate the physiological and performance effects of dietary NO3- supplementation during exposure to simulated and terrestrial altitude. Previous investigations at simulated altitude indicate that NO3- supplementation may reduce the oxygen cost of exercise, elevate arterial and tissue oxygen saturation, improve muscle metabolic function, and enhance exercise capacity/ performance. Conversely, current evidence suggests that NO3- supplementation does not augment the training response at simulated altitude. Few studies have evaluated the effects of NO3- at terrestrial altitude. Current evidence indicates potential improvements in endothelial function at terrestrial altitude following NO3- supplementation. No effects of NO3- supplementation have been observed on oxygen consumption or arterial oxygen saturation at terrestrial altitude, although further research is warranted. Limitations of the present body of literature are discussed, and directions for future research are provided

Metal recovery by microbial electro-metallurgy

Raw metals are fundamental to the global economy as they are essential to maintain the quality of our life as well as industrial performance. A number of metal-bearing aqueous matrices are appealing as alternative supplies to conventional mining, like solid industrial and urban waste leachates, wastewaters and even some natural extreme environments (e.g. deep marine sediments, geothermal brines). Some of these sources are already managed for recovery, while others are not suitable either because they are too low in content of recoverable metals or they contain too many impurities that would interfere with classical recovery processes or would be cost-prohibitive. Microbial electro-metallurgy, which results from the interactions between microorganisms, metals and electrodes, in which the electron transfer chain associated with microbial respiration plays a key role, can contribute to overcome these challenges. This review provides the state of the art on this subject, and summarizes the general routes through which microbes can catalyse or support metal recovery, leading to nano- and macro-scale materials. Competing sorption and electrochemical technologies are briefly revisited. The relevant sources of metals are highlighted as well as the challenges and opportunities to turn microbial electro-metallurgy into a sustainable industrial technology in the near future. Finally, an outlook to pursue functional materials through microbial electrometallurgy is provided

Profiling social, emotional and behavioural difficulties of children involved in direct and indirect bullying behaviours

Being involved in bullying places a child at risk of poor psychosocial and educational outcomes. This study aimed to examine the profile of behavioural, emotional and social functioning for two subtypes of bullying; direct and indirect (relational). Pupils aged between seven and eleven years old completed sociometric measures of social inclusion and bullying behaviour to identify 192 pupils considered to be involved in either direct, indirect, both or neither types of bullying. These pupils and their teachers completed a battery of assessments relating to behaviour, social competence and self-perception. All bully-groups experienced similar levels of significant social rejection. ‘Direct’ and ‘both’ groups showed the greatest number of behavioural, emotional and social difficulties, while the ‘indirect’ group showed weaknesses in self-perception, but no teacher-rated problems. Understanding the behavioural, emotional and social correlates of bullying is of particular importance for early identification of children at risk of becoming bullies and for developing targeted interventions