Search for Stable Magnetohydrodynamic Equilibria in Barotropic Stars

It is now believed that magnetohydrodynamic equilibria can exist in stably stratified stars due to the seminal works of Braithwaite & Spruit (2004) and Braithwaite & Nordlund (2006). What is still not known is whether magnetohydrodynamic equilibria can exist in a barotropic star, in which stable stratification is not present. It has been conjectured by Reisenegger (2009) that there will likely not exist any magnetohydrodynamical equilibria in barotropic stars. We aim to test this claim by presenting preliminary MHD simulations of barotropic stars using the three dimensional stagger code of Nordlund & Galsgaard (1995).Comment: 4 pages, 2 figures, to appear in the proceedings of IAUS 302: "Magnetic Fields Throughout Stellar Evolution

On Nori's Fundamental Group Scheme

We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its \'etale and local parts. Pierre Deligne pointed out an error in the first version of this article. We profoundly thank him, in particular for sending us his enlightning example reproduced in Remark 2.4 2).Comment: 29 page

Oscillation results for Sturm–Liouville problems with an indefinite weight function

AbstractWe prove oscillation results for the real eigenvalues of Sturm–Liouville problems with an indefinite weight function. An essential role is played by the signature of an eigenvalue, which is shown to be related to the signs of the corresponding leading coefficients of the Titchmarsh–Weyl m-function and of the Prüfer angle at this eigenvalue

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case

Simply connected projective manifolds in characteristic p>0p>0 have no nontrivial stratified bundles

We show that simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker. The proof uses Hrushovski's theorem on periodic points.Comment: 16 pages. Revised version contains a more general theorem on torsion points on moduli, together with an illustration in rank 2 due to M. Raynaud. Reference added. Last version has some typos corrected. Appears in Invent.math

Scanning electron microscopy of Rydberg-excited Bose-Einstein condensates

We report on the realization of high resolution electron microscopy of Rydberg-excited ultracold atomic samples. The implementation of an ultraviolet laser system allows us to excite the atom, with a single-photon transition, to Rydberg states. By using the electron microscopy technique during the Rydberg excitation of the atoms, we observe a giant enhancement in the production of ions. This is due to $l$-changing collisions, which broaden the Rydberg level and therefore increase the excitation rate of Rydberg atoms. Our results pave the way for the high resolution spatial detection of Rydberg atoms in an atomic sample

Effect of Local Inhomogeneity on Nucleation; Case of Charge Density Wave Depinning

The spatial inhomogeneities are expected to affect nucleation process in an essential way. These effects are studied theoretically by considering the case of the depinning of the charge density wave as a typical example. The threshold field of the depinning of the one-dimensional commensurate charge density wave with one impurity has been examined classically based on the phase Hamiltonian at absolute zero. It is found that the threshold field is lowered by a finite amount compared to that in the absence of an impurity.Comment: pages 12, LaTeX, 9 figures, uses jpsj.sty, submitted to J. Phys. Soc. Jp

Dynamical density functional theory for the dewetting of evaporating thin films of nanoparticle suspensions exhibiting pattern formation

Recent experiments have shown that the striking structure formation in dewetting films of evaporating colloidal nanoparticle suspensions occurs in an ultrathin `postcursor' layer that is left behind by a mesoscopic dewetting front. Various phase change and transport processes occur in the postcursor layer, that may lead to nanoparticle deposits in the form of labyrinthine, network or strongly branched `finger' structures. We develop a versatile dynamical density functional theory to model this system which captures all these structures and may be employed to investigate the influence of evaporation/condensation, nanoparticle transport and solute transport in a differentiated way. We highlight, in particular, the influence of the subtle interplay of decomposition in the layer and contact line motion on the observed particle-induced transverse instability of the dewetting front.Comment: 5 pages, 5 figure

Ionized gas at the edge of the Central Molecular Zone

To determine the properties of the ionized gas at the edge of the CMZ near Sgr E we observed a small portion of the edge of the CMZ near Sgr E with spectrally resolved [C II] 158 micron and [N II] 205 micron fine structure lines at six positions with the GREAT instrument on SOFIA and in [C II] using Herschel HIFI on-the-fly strip maps. We use the [N II] spectra along with a radiative transfer model to calculate the electron density of the gas and the [C II] maps to illuminate the morphology of the ionized gas and model the column density of CO-dark H2. We detect two [C II] and [N II] velocity components, one along the line of sight to a CO molecular cloud at -207 km/s associated with Sgr E and the other at -174 km/s outside the edge of another CO cloud. From the [N II] emission we find that the average electron density is in the range of about 5 to 25 cm{-3} for these features. This electron density is much higher than that of the warm ionized medium in the disk. The column density of the CO-dark H$_2$ layer in the -207 km/s cloud is about 1-2X10{21} cm{-2} in agreement with theoretical models. The CMZ extends further out in Galactic radius by 7 to 14 pc in ionized gas than it does in molecular gas traced by CO. The edge of the CMZ likely contains dense hot ionized gas surrounding the neutral molecular material. The high fractional abundance of N+ and high electron density require an intense EUV field with a photon flux of order 1e6 to 1e7 photons cm{-2} s{-1}, and/or efficient proton charge exchange with nitrogen, at temperatures of order 1e4 K, and/or a large flux of X-rays. Sgr E is a region of massive star formation which are a potential sources of the EUV radiation that can ionize the gas. In addition X-ray sources and the diffuse X-ray emission in the CMZ are candidates for ionizing nitrogen.Comment: 12 pages, 9 figure