Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces

We consider an inverse problem associated with some 2-dimensional non-compact surfaces with conical singularities, cusps and regular ends. Our motivating example is a Riemann surface ℳ = Γ∖ℍ2 associated with a Fuchsian group of the first kind Γ containing parabolic elements. The surface ℳ is then non-compact, and has a finite number of cusps and elliptic singular points, which is regarded as a hyperbolic orbifold. We introduce a class of Riemannian surfaces with conical singularities on its finite part, having cusps and regular ends at infinity, whose metric is asymptotically hyperbolic. By observing solutions of the Helmholtz equation at the cusp, we define a generalized S-matrix. We then show that this generalized S-matrix determines the Riemannian metric and the structure of conical singularities

Inviscid incompressible limits of the full Navier-Stokes-Fourier system

We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on the three dimensional Euclidean space. The Euler-Boussinesq approximation is identified as the limit system

Formation of superfluid liquid pocket in aerogel and its solidification by cooling

Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport process are discussed

Formation of superfluid liquid pocket in aerogel and its solidification by cooling

Formation of superfluid liquid pockets of ⁴He surrounded by ⁴He crystals were observed in an aerogel of 96% porosity. The liquid pockets did not crystallize by application of pressure but crystallized via avalanche by cool-ing below a particular temperature. The crystallization by cooling was also observed when crystals occupied a smaller portion of the aerogel. Driving force for the crystallization by cooling and possible mass transport process are discussed

Provenance changes of eolian dust at Lingtai section in the Chinese Loess Plateau since 7 Ma and its implication for desert development in East Asia

International audienceIt is suggested that the uplift of Himalaya-Tibetan Plateau enhanced interior aridity in East Asia and resulted in development of middle latitude gobi and sandy deserts and accumulation of the eolian sediments in the Chinese Loess Plateau. Therefore, estimation of the provenance for eolian sediments in the Chinese Loess Plateau is critical to reconstruct the environmental changes in East Asia and their relation to the Himalaya-Tibetan Plateau uplift. We recently developed a new provenance tracing method by using a combination of Electron Spin Resonance (ESR) signal intensity and Crystallinity Index (CI) of quartz, and demonstrated that fine fraction of the surface sediments from nine major deserts in East Asia could be distinguished one another on the ESR signal intensity versus CI diagram. Here, we measured ESR signal intensity and CI of quartz in fine fractions of samples covering the last 7 Ma obtained from Lingtai section in the central Chinese Loess Plateau, and compared the results with those of the surface samples from nine major deserts in East Asia. The results suggest that the provenance of fine fraction of the eolian sediment in Lingtai section changed at 4.3, 2.1, 1.4, 1.1, 0.8 and 0.4 Ma. During 7 to 4.3 Ma, the dust might be have been supplied from Precambrian to Paleozoic metamorphic and granitic rocks and granite exposed in the present central to eastern part of the Tian Shan Mountains. The contribution from the Taklimakan desert appeared at 4.3 Ma, increased drastically at 1.1 Ma, and persisted till 0.8 Ma, whereas the main source of detrital material to the Taklimakan desert might have changed from eastern part of the Kunlun and the Altyn Mountains to western part of the Kunlun and the Tian Shan Mountains. During 0.8 to 0.4 Ma, contribution from the Badain Juran desert gradually increased. Finally, contribution from the Tengger desert appeared from 0.4 to 0 Ma. Together with tectonic evidences from literatures, the provenance changes from 4.3 to 0.8 Ma seem to reflect uplift of the Tian Shan and the Kunlun Mountains and consequent formation of the Taklimakan desert, whereas the change at 0.4 Ma may reflect uplift of the Qilian Mountains although formation of mountain glaciers could be an alternative possibility. These provenance changes will provide important constraints not only on the development of arid areas and evolution of monsoon but also on the uplift and erosion of mountains in East Asia

Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

ADAM‐10 is overexpressed in rheumatoid arthritis synovial tissue and mediates angiogenesis

Objective To examine the expression of ADAM‐10 in rheumatoid arthritis (RA) synovial tissue (ST) and the role it plays in angiogenesis. Methods ADAM‐10 expression was determined using immunohistology, Western blotting, and quantitative polymerase chain reaction. In order to examine the role of ADAM‐10 in angiogenesis, we performed in vitro Matrigel tube formation and chemotaxis assays using human microvascular endothelial cells (HMVECs) transfected with control or ADAM‐10 small interfering RNA (siRNA). To determine whether ADAM‐10 plays a role in angiogenesis in the context of RA, we performed Matrigel assays using a coculture system of HMVECs and RA synovial fibroblasts. Results Endothelial cells and lining cells within RA ST expressed high levels of ADAM‐10 compared with cells within osteoarthritis ST and normal ST. ADAM‐10 expression was significantly elevated at the protein and messenger RNA levels in HMVECs and RA synovial fibroblasts stimulated with proinflammatory mediators compared with unstimulated cells. ADAM‐10 siRNA–treated HMVECs had decreased endothelial cell tube formation and migration compared with control siRNA–treated HMVECs. In addition, ADAM‐10 siRNA–treated HMVECs from the RA synovial fibroblast coculture system had decreased endothelial cell tube formation compared with control siRNA–treated HMVECs. Conclusion These data show that ADAM‐10 is overexpressed in RA and suggest that ADAM‐10 may play a role in RA angiogenesis. ADAM‐10 may be a potential therapeutic target in inflammatory angiogenic diseases such as RA.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94711/1/37755_ftp.pd

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

Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment

In this paper, we study inverse scattering of massless Dirac fields that propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a stationary approach we determine precisely the leading terms of the high-energy asymptotic expansion of the scattering matrix that, in turn, permit us to recover uniquely the mass of the black hole and its charge up to a sign

Inhibitor of DNA binding 1 as a secreted angiogenic transcription factor in rheumatoid arthritis

Abstract Introduction Rheumatoid arthritis (RA) is characterized by enhanced blood vessel development in joint synovium. This involves the recruitment of endothelial progenitor cells (EPCs), allowing for de novo vessel formation and pro-inflammatory cell infiltration. Inhibitor of DNA Binding 1 (Id1) is a transcription factor characteristic of EPCs that influences cell maturation. Method Enzyme-linked immunosorbant assay (ELISA) and polymerase chain reaction (PCR) were used to examine Id1 levels in synovial fluid (SF) and endothelial cells (ECs), respectively. Immunohistology was used to determine the expression of Id1 in synovial tissue (ST). Human dermal microvascular EC (HMVEC) migration and tube forming assays were used to determine if recombinant human Id1 (rhuId1) and/or RA SF immunodepleted Id1 showed angiogenic activity. We also utilized the RA ST severe combined immunodeficient (SCID) mouse chimera to examine if Id1 recruits EPCs to RA synovium. Results ST samples immunostained for Id1 showed heightened expression in RA compared to osteoarthritis (OA) and normal (NL) ST. By immunofluorescence staining, we found significantly more Id1 in RA compared to OA and NL vasculature, showing that Id1 expressing cells, and therefore EPCs, are most active in vascular remodeling in the RA synovium. We also detected significantly more Id1 in RA compared to OA and other arthritis SFs by ELISA, which correlates highly with Chemokine (C-X-C motif) ligand 16 (CXCL16) levels. In vitro chemotaxis assays showed that Id1 is highly chemotactic for HMVECs and can be attenuated by inhibition of Nuclear Factor κB and phosphoinositide 3-kinase. Using in vitro Matrigel assays, we found that HMVECs form tubes in response to rhuId1 and that Id1 immunodepleted from RA SF profoundly decreases tube formation in Matrigel in vitro. PCR showed that Id1 mRNA could be up-regulated in EPCs compared to HMVECs in response to CXCL16. Finally, using the K/BxN serum induced arthritis model, we found that EC CXCR6 correlated with Id1 expression by immunohistochemistry. Conclusions We conclude that Id1 correlates highly with CXCL16 expression, EPC recruitment, and blood vessel formation in the RA joint, and that Id1 is potently angiogenic and can be up-regulated in EPCs by CXCL16.http://deepblue.lib.umich.edu/bitstream/2027.42/110805/1/13075_2013_Article_4258.pd