Combining gravity with the forces of the standard model on a cosmological scale

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the underlying spacetime is a Friedman universe with flat spatial slices and where the matter fields are comprised of the strong interaction, with \SU(3) replaced by a general \SU(n), $n\ge 2$, and the electro-weak interaction. The wave functions are maps from $\R[4n+10]$ to a subspace of the antisymmetric Fock space, and one noteworthy result is that, whenever the electro-weak interaction is involved, the image of an eigenfunction is in general not one dimensional, i.e., in general it makes no sense specifying a fermion and looking for an eigenfunction the range of which is contained in the one dimensional vector space spanned by the fermion.Comment: 53 pages, v6: some typos correcte

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.Comment: 12 pages, REVTEX, 7 figures, submitted to Physical Review

Ultrafast circular polarization oscillations in spin-polarized vertical-cavity surface-emitting laser devices

Spin-polarized lasers offer new encouraging possibilities for future devices. We investigate the polarization dynamics of electrically pumped vertical-cavity surface-emitting lasers after additional spin injection at room temperature. We find that the circular polarization degree exhibits faster dynamics than the emitted light. Moreover the experimental results demonstrate a strongly damped ultrafast circular polarization oscillation due to spin injection with an oscillation frequency of approximately 11GHz depending on the birefringence in the VCSEL device. We compare our experimental results with theoretical calculations based on rate-equations. This allows us to predict undamped long persisting ultrafast polarization oscillations, which reveal the potential of spin-VCSELs for ultrafast modulation applications

Birefringence controlled room-temperature picosecond spin dynamics close to the threshold of vertical-cavity surface-emitting laser devices

We analyze the spin-induced circular polarization dynamics at the threshold of vertical-cavity surface-emitting lasers at room-temperature using a hybrid excitation combining electrically pumping without spin preference and spin-polarized optical injection. After a short pulse of spin-polarized excitation, fast oscillations of the circular polarization degree (CPD) are observed within the relaxation oscillations. A theoretical investigation of this behavior on the basis of a rate equation model shows that these fast oscillations of CPD could be suppressed by means of a reduction of the birefringence of the laser cavity

VEGF guides angiogenic sprouting utilizing endothelial tip cell filopodia

Vascular endothelial growth factor (VEGF-A) is a major regulator of blood vessel formation and function. it controls several processes in endothelial cells, such as proliferation, survival, and migration, but it is not known how these are coordinately regulated to result in more complex morphogenetic events, such as tubular sprouting, fusion, and network formation. We show here that VEGF-A controls angiogenic sprouting in the early postnatal retina by guiding filopodial extension from specialized endothelial cells situated at the tips of the vascular sprouts. The tip cells respond to VEGF-A only by guided migration; the proliferative response to VEGF-A occurs in the sprout stalks. These two cellular responses are both mediated by agonistic activity of VEGF-A on VEGF receptor 2. Whereas tip cell migration depends on a gradient of VEGF-A, proliferation is regulated by its concentration. Thus, vessel patterning during retinal angiogenesis depends on the balance between two different qualities of the extracellular VEGF-A distribution, which regulate distinct cellular responses in defined populations of endothelial cells

Intrinsic time gravity and the Lichnerowicz-York equation

We investigate the effect on the Hamiltonian structure of general relativity of choosing an intrinsic time to fix the time slicing. 3-covariance with momentum constraint is maintained, but the Hamiltonian constraint is replaced by a dynamical equation for the trace of the momentum. This reveals a very simple structure with a local reduced Hamiltonian. The theory is easily generalised; in particular, the square of the Cotton-York tensor density can be added as an extra part of the potential while at the same time maintaining the classic 2 + 2 degrees of freedom. Initial data construction is simple in the extended theory; we get a generalised Lichnerowicz-York equation with nice existence and uniqueness properties. Adding standard matter fields is quite straightforward.Comment: 4 page

Sexual selection and population divergence III : interspecific and intraspecific variation in mating signals

Funding: Orthopterists' Society, Natural Environment Research Council (Grant Number(s): NE/G00949X/1, NE/G014906/1, NE/L011255/1), ARC (Grant Number(s): DP180101708).A major challenge for studying the role of sexual selection in divergence and speciation is understanding the relative influence of different sexually selected signals on those processes in both intra‐ and interspecific contexts. Different signals may be more or less susceptible to co‐option for species identification depending on the balance of sexual and ecological selection acting upon them. To examine this, we tested three predictions to explain geographic variation in long‐ versus short‐range sexual signals across a 3,500 + km transect of two related Australian field cricket species (Teleogryllus spp.): (a) selection for species recognition, (b) environmental adaptation and (c) stochastic divergence. We measured male calling song and male and female cuticular hydrocarbons (CHCs) in offspring derived from wild populations, reared under common garden conditions. Song clearly differentiated the species, and no hybrids were observed suggesting that hybridization is rare or absent. Spatial variation in song was not predicted by geography, genetics or climatic factors in either species. In contrast, CHC divergence was strongly associated with an environmental gradient supporting the idea that the climatic environment selects more directly upon these chemical signals. In light of recently advocated models of diversification via ecological selection on secondary sexual traits, the different environmental associations we found for song and CHCs suggest that the impact of ecological selection on population divergence, and how that influences speciation, might be different for acoustic versus chemical signals.Publisher PDFPeer reviewe

Metamagnetism in the XXZ model with next-to-nearest-neighbor coupling

We investigate groundstate energies and magnetization curves in the one dimensional XXZ-model with next to nearest neighbour coupling $\alpha>0$ and anisotropy $\Delta$ ($-1 \le \Delta \le 1$) at T=0. In between the familiar ferro- and antiferromagnetic phase we find a transition region -- called metamagnetic phase -- where the magnetization curve is discontinuous at a critical field $B_c(\alpha,\Delta)$.Comment: LaTeX file (text) + 5 PS files (5 figures