An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Spin-Orbit Coupling in LaAlO3_3/SrTiO3_3 interfaces: Magnetism and Orbital Ordering

The combination of Rashba spin-orbit coupling and electron correlations can induce unusual phenomena in the metallic interface between SrTiO$_3$ and LaAlO$_3$. We consider effects of Rashba spin-orbit coupling at this interface in the context of the recent observation of anisotropic magnetism. Firstly, we show how Rashba spin-orbit coupling in a system near a band-edge can account for the observed magnetic anisotropy. Secondly, we investigate the coupling between in-plane magnetic-moment anisotropy and nematicity in the form of an orbital imbalance between d$_{xz}$ / d$_{yz}$ orbitals. We estimate this coupling to be substantial in the low electron density regime. Such an orbital ordering can affect magneto transport

High-Resolution NIR Observations of the Circumstellar Disk System in the Bok Globule CB 26

We report on results of near-infrared and optical observations of the mm disk embedded in the Bok globule CB 26 (Launhardt & Sargent 2001). The near-infrared images show a bipolar reflection nebula with a central extinction lane which coincides with the mm disk. Imaging polarimetry of this object yielded a polarization pattern which is typical for a young stellar object surrounded by a large circumstellar disk and an envelope, seen almost edge-on. The strong linear polarization in the bipolar lobes is caused by single scattering at dust grains and allowed to locate the illuminating source which coincides with the center of the mm disk. The spectral energy distribution of the YSO embedded in CB 26 resembles that of a ClassI source with a luminosity of 0.5 L_sun.Using the pre-main-sequence evolutionary tracks and the stellar mass inferred from the rotation curve of the disk, we derive an age of the system of <10^6 yr. H_alpha and [SII] narrow-band imaging as well as optical spectroscopy revealed an Herbig-Haro object 6.15 arcmin northwest of CB 26 YSO 1, perfectly aligned with the symmetry axis of the bipolar nebula. This Herbig-Haro object (HH 494) indicates ongoing accretion and outflow activity in CB 26 YSO 1. Its excitation characteristics indicate that the Herbig-Haro flow is propagating into a low-density environment. We suggest that CB 26 YSO 1 represents the transition stage between embedded protostellar accretion disks and more evolved protoplanetary disks around T Tauri stars in an undisturbed environment.Comment: 21 pages, 6 figures (reduced resolution), ApJ accepte

Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

Spin-Glass Attractor on Tridimensional Hierarchical Lattices in the Presence of an External Magnetic Field

A nearest-neighbor-interaction Ising spin glass, in the presence of an external magnetic field, is studied on different hierarchical lattices that approach the cubic lattice. The magnetic field is considered as uniform, or random (following either a bimodal or a Gaussian probability distribution). In all cases, a spin-glass attractor is found, in the plane magnetic field versus temperature, associated with a low-temperature phase. The physical consequences of this attractor are discussed, in view of the present scenario of the spin-glass problem.Comment: Accepted for publication in Physical Review

Solute channels of the outer membrane: from bacteria to chloroplasts

Chloroplasts, unique organelles of plants, originated from endosymbiosis of an ancestor of today's cyanobacteria with a mitochondria-containing host cell. It is assumed that the outer envelope membrane, which delimits the chloroplast from the surrounding cytosol, was thus inherited from its Gram-negative bacterial ancestor. This plastid-specific membrane is thus equipped with elements of prokaryotic and eukaryotic origin. In particular, the membrane-intrinsic outer envelope proteins (OEPs) form solute channels with properties reminiscent of porins and channels in the bacterial outer membrane. OEP channels are characterised by distinct specificities for metabolites and a quite peculiar expression pattern in specialised plant organs and plastids, thus disproving the assumption that the outer envelope is a non-specific molecular sieve. The same is true for the outer membrane of Gram-negative bacteria, which functions as a permeability barrier in addition to the cytoplasmic membrane, and embeds different classes of channel pores. The channels of these prokaryotic prototype proteins, ranging from unspecific porins to specific channels to ligand-gated receptors, are exclusively built of P-barrels. Although most of the OEP channels are formed by P-strands as well, phylogeny based on sequence homology alone is not feasible. Thus, the comparison of structural and functional properties of chloroplast outer envelope and bacterial outer membrane channels is required to pinpoint the ancestral OEP `portrait gallery'

Correlated projection operator approach to non-Markovian dynamics in spin baths

The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated projection superoperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated projection operator technique significantly improves the standard methods and can be applied to many physical problems such as the hyperfine interaction in a quantum dot

Disentangling the near infrared continuum spectral components of the inner 500 pc of Mrk 573: two-dimensional maps

We present a near infrared study of the spectral components of the continuum in the inner 500$\times$500 pc$^2$ of the nearby Seyfert galaxy Mrk573 using adaptive optics near-infrared integral field spectroscopy with the instrument NIFS of the Gemini North Telescope at a spatial resolution of $\sim$50 pc. We performed spectral synthesis using the {\sc starlight} code and constructed maps for the contributions of different age components of the stellar population: young ($age\leq100$ Myr), young-intermediate ($100<age\leq700$ Myr), intermediate-old ($700$ Myr $2$ Gyr) to the near-IR K-band continuum, as well as their contribution to the total stellar mass. We found that the old stellar population is dominant within the inner 250 pc, while the intermediate age components dominate the continuum at larger distances. A young stellar component contributes up to $\sim$20% within the inner $\sim$70 pc, while hot dust emission and featureless continuum components are also necessary to fit the nuclear spectrum, contributing up to 20% of the K-band flux there. The radial distribution of the different age components in the inner kiloparsec of Mrk573 is similar to those obtained by our group for the Seyfert galaxies Mrk1066, Mrk1157 and NGC1068 in previous works using a similar methodology. Young stellar populations ($\leq$100 Myr) are seen in the inner 200-300 pc for all galaxies contributing with $\ge$20% of the K-band flux, while the near-IR continuum is dominated by the contribution of intermediate-age stars ($t=$100 Myr-2 Gyr) at larger distances. Older stellar populations dominate in the inner 250 pc

A Comparison of Phycocyanins from Three Different Species of Cyanobacteria Employing Resonance-Enhanced Coherent Anti-Stokes Raman Spectroscopy

Resonance-enhanced coherent anti-Stokes Raman spectra are recorded for monomers and trimers of phycocyanin from three different cyanobacteria: Westiellopsis prolifica, Mastigocladus laminosus and Spirulina platensis. It is shown that upon aggregation from monomer to trimer the electronic structures of both the α84 and β84 chromophores are changed. The spectra of the trimers originating from S. platensis and M. laminosus are very similar to each other, but distinctly different from the spectrum of W. prolifica