Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions

The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect product ${\rm Diff}\circledS{\cal F}$, where $\mathcal{F}$ denotes the space of scalar functions. This paper generalizes the second construction to consider geodesic motion on ${\rm Diff} \circledS\mathfrak{g}$, where $\mathfrak{g}$ denotes the space of scalar functions that take values on a certain Lie algebra (for example, $\mathfrak{g}=\mathcal{F}\otimes\mathfrak{so}(3)$). Measure-valued delta-like solutions are shown to be momentum maps possessing a dual pair structure, thereby extending previous results for the EPDiff equation. The collective Hamiltonians are shown to fit into the Kaluza-Klein theory of particles in a Yang-Mills field and these formulations are shown to apply also at the continuum PDE level. In the continuum description, the Kaluza-Klein approach produces the Kelvin circulation theorem.Comment: 22 pages, 2 figures. Submitted to Proc. R. Soc.

The effect of breed and feed-type on the sensory profile of breast meat in male broilers reared in an organic free-range system

1. Studies on the sensory profiling of male broiler breast meat were carried out to evaluate the effect of two very different broiler breeds (JA757 and New Hampshire), two different feed types (broiler and grower feed) and age at slaughter (82 and 110 d). 2. The sensory profiling consisted of a pilot study, 4 training sessions, and finally the assessment. During the training session a panel of 9 assessors defined 17 attributes, which were used to describe the smell, texture and flavour of the breast fillets. Each attribute was evaluated on a 15-cm unstructured line scale. 3. The breast meat became significantly less hard, and more juicy and tender in the New Hampshire at 110 d of age, whereas the opposite was found in JA757, which also acquired a more ‘‘sourish’’ flavour with age. The smell of ‘‘sweet/maize’’ and ‘‘bouillon’’ became weaker with age in JA757, but not in New Hampshire. 4. Several significant differences in relation to the main factors of breed and age were found. The traditional broiler hybrid JA757 did best for most smell and flavour attributes, whereas New Hampshire did best for the texture attributes. Age had a negative effect on the flavours and smell attributes ‘‘fresh chicken’’, ‘‘neck of pork’’ and ‘‘sweet maize’’, but a positive effect on the texture attribute ‘‘crumbly’’. In addition meat was more ‘‘stringy’’ at 110 d of age. 5. The flavours ‘‘neck of pork’’ and ‘‘umami’’ were significantly improved when JA757 was fed on the broiler feed and when New Hampshire was given the grower feed. The meat smelt more ‘‘sourish’’ at 82 d of age and less ‘‘sourish’’ at 110 d of age when the grower feed was consumed. Meat was significantly harder and stringier when JA757 was fed on the grower feed. This was not the case for New Hampshire. In general, the meat was significantly less crumbly and stringier with the grower feed. 6. Overall a very distinct difference in sensory profile was found between the two breeds. In addition different slaughter ages and feeding strategies should be taken into consideration in a niche production based on alternative genotypes

Produktion af kyllinger i frugtplantage kan give større spiseoplevelse

Produktion af slagtekyllinger i frugtplantage åbner en spændende mulighed for større spiseoplevelse for den kvalitetsbevidste forbruger. Sensorikbedømmelser af brystkødet fra to typer slagtekyllinger, JA757 og New Hampshire viste en markant forskellig sensorisk profil. Hvor JA757 fik bedre score i visse lugt og smagsegenskaber, opnåede New Hampshire bedre score i teksturegenskaber som f.eks. mørhed og saftighed. For begge afstamninger var smagen og lugten af frisk kylling lavere ved højere slagtealder

Generalized Euler-Poincar\'e equations on Lie groups and homogeneous spaces, orbit invariants and applications

We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar\'e equations on Lie groups and homogeneous spaces. Orbit invariants play an important role in this context and we use these invariants to prove global existence and uniqueness results for a class of PDE. This class includes Euler-Poincar\'e equations that have not yet been considered in the literature as well as integrable equations like Camassa-Holm, Degasperis-Procesi, $\mu$CH and $\mu$DP equations, and the geodesic equations with respect to right invariant Sobolev metrics on the group of diffeomorphisms of the circle

Frontotemporal Dementia Caused by CHMP2B Mutations

CHMP2B mutations are a rare cause of autosomal dominant frontotemporal dementia (FTD). The best studied example is frontotemporal dementia linked to chromosome 3 (FTD-3) which occurs in a large Danish family, with a further CHMP2B mutation identified in an unrelated Belgian familial FTD patient. These mutations lead to C-terminal truncations of the CHMP2B protein and we will review recent advances in our understanding of the molecular effects of these mutant truncated proteins on vesicular fusion events within the endosome-lysosome and autophagy degradation pathways. We will also review the clinical features of FTD caused by CHMP2B truncation mutations as well as new brain imaging and neuropathological findings. Finally, we collate the current data on CHMP2B missense mutations, which have been reported in FTD and motor neuron disease

GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc

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

The Dynamics of a Rigid Body in Potential Flow with Circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte

Euler-Poincar\'e approaches to nematodynamics

Nematodynamics is the orientation dynamics of flowless liquid-crystals. We show how Euler-Poincar\'e reduction produces a unifying framework for various theories, including Ericksen-Leslie, Luhiller-Rey, and Eringen's micropolar theory. In particular, we show that these theories are all compatible with each other and some of them allow for more general configurations involving a non vanishing discination density. All results are also extended to flowing liquid crystals.Comment: 26 pages, no figure