Compact spherical neutron polarimeter using high-T-c YBCO films

We describe a simple, compact device for spherical neutron polarimetry measurements at small neutron scattering angles. The device consists of a sample chamber with very low (<0.01 G) magnetic field flanked by regions within which the neutron polarization can be manipulated in a controlled manner. This allows any selected initial and final polarization direction of the neutrons to be obtained. We have constructed a prototype device using high-Tc superconducting films and mu-metal to isolate regions with different magnetic fields and tested device performance in transmission geometry. Finite-element methods were used to simulate the device’s field profile and these have been verified by experiment using a small solenoid as a test sample. Measurements are reported using both monochromatic and polychromatic neutron sources. The results show that the device is capable of extracting sample information and distinguishing small angular variations of the sample magnetic field. As a more realistic test, we present results on the characterization of a 10 μm thick Permalloy film in zero magnetic field, as well as its response to an external magnetic field

On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras

We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappings from $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation is continuous. We call such Lie algebras Fr\'echet Lie algebras. We introduce the notion of an integrable $\mathbb Z$-gradation of a Fr\'echet Lie algebra, and find all inequivalent integrable $\mathbb Z$-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.Comment: 26 page

Coulomb gap in a model with finite charge transfer energy

The Coulomb gap in a donor-acceptor model with finite charge transfer energy $\Delta$ describing the electronic system on the dielectric side of the metal-insulator transition is investigated by means of computer simulations on two- and three-dimensional finite samples with a random distribution of equal amounts of donor and acceptor sites. Rigorous relations reflecting the symmetry of the model presented with respect to the exchange of donors and acceptors are derived. In the immediate neighborhood of the Fermi energy $\mu$ the the density of one-electron excitations $g(\epsilon)$ is determined solely by finite size effects and $g(\epsilon)$ further away from $\mu$ is described by an asymmetric power law with a non-universal exponent, depending on the parameter $\Delta$.Comment: 10 pages, 6 figures, submitted to Phys. Rev.

Maximum solutions of normalized Ricci flows on 4-manifolds

We consider maximum solution $g(t)$, $t\in [0, +\infty)$, to the normalized Ricci flow. Among other things, we prove that, if $(M, \omega)$ is a smooth compact symplectic 4-manifold such that $b_2^+(M)>1$ and let $g(t),t\in[0,\infty)$, be a solution to (1.3) on $M$ whose Ricci curvature satisfies that $|\text{Ric}(g(t))|\leq 3$ and additionally $\chi(M)=3 \tau (M)>0$, then there exists an $m\in \mathbb{N}$, and a sequence of points $\{x_{j,k}\in M\}$, $j=1, ..., m$, satisfying that, by passing to a subsequence, $$(M, g(t_{k}+t), x_{1,k},..., x_{m,k}) \stackrel{d_{GH}}\longrightarrow (\coprod_{j=1}^m N_j, g_{\infty}, x_{1,\infty}, ...,, x_{m,\infty}),$$ $t\in [0, \infty)$, in the $m$-pointed Gromov-Hausdorff sense for any sequence $t_{k}\longrightarrow \infty$, where $(N_{j}, g_{\infty})$, $j=1,..., m$, are complete complex hyperbolic orbifolds of complex dimension 2 with at most finitely many isolated orbifold points. Moreover, the convergence is $C^{\infty}$ in the non-singular part of $\coprod_1^m N_{j}$ and $\text{Vol}_{g_{0}}(M)=\sum_{j=1}^{m}\text{Vol}_{g_{\infty}}(N_{j})$, where $\chi(M)$ (resp. $\tau(M)$) is the Euler characteristic (resp. signature) of $M$.Comment: 23 page

Galileo dust data from the jovian system: 2000 to 2003

The Galileo spacecraft was orbiting Jupiter between Dec 1995 and Sep 2003. The Galileo dust detector monitored the jovian dust environment between about 2 and 370 R_J (jovian radius R_J = 71492 km). We present data from the Galileo dust instrument for the period January 2000 to September 2003. We report on the data of 5389 particles measured between 2000 and the end of the mission in 2003. The majority of the 21250 particles for which the full set of measured impact parameters (impact time, impact direction, charge rise times, charge amplitudes, etc.) was transmitted to Earth were tiny grains (about 10 nm in radius), most of them originating from Jupiter's innermost Galilean moon Io. Their impact rates frequently exceeded 10 min^-1. Surprisingly large impact rates up to 100 min^-1 occurred in Aug/Sep 2000 when Galileo was at about 280 R_J from Jupiter. This peak in dust emission appears to coincide with strong changes in the release of neutral gas from the Io torus. Strong variability in the Io dust flux was measured on timescales of days to weeks, indicating large variations in the dust release from Io or the Io torus or both on such short timescales. Galileo has detected a large number of bigger micron-sized particles mostly in the region between the Galilean moons. A surprisingly large number of such bigger grains was measured in March 2003 within a 4-day interval when Galileo was outside Jupiter's magnetosphere at approximately 350 R_J jovicentric distance. Two passages of Jupiter's gossamer rings in 2002 and 2003 provided the first actual comparison of in-situ dust data from a planetary ring with the results inferred from inverting optical images.Comment: 59 pages, 13 figures, 6 tables, submitted to Planetary and Space Scienc

Epithelial p53 Status Modifies Stromal-Epithelial Interactions During Basal-Like Breast Carcinogenesis

Basal-like breast cancers (BBC) exhibit subtype-specific phenotypic and transcriptional responses to stroma, but little research has addressed how stromal-epithelial interactions evolve during early BBC carcinogenesis. It is also unclear how common genetic defects, such as p53 mutations, modify these stromal-epithelial interactions. To address these knowledge gaps, we leveraged the MCF10 progression series of breast cell lines (MCF10A, MCF10AT1, and MCF10DCIS) to develop a longitudinal, tissue-contextualized model of p53-deficient, pre-malignant breast. Acinus asphericity, a morphogenetic correlate of cell invasive potential, was quantified with optical coherence tomography imaging, and gene expression microarrays were performed to identify transcriptional changes associated with p53 depletion and stromal context. Co-culture with stromal fibroblasts significantly increased the asphericity of acini derived from all three p53-deficient, but not p53-sufficient, cell lines, and was associated with the upregulation of 38 genes. When considered as a multigene score, these genes were upregulated in co-culture models of invasive BBC with increasing stromal content, as well as in basal-like relative to luminal breast cancers in two large human datasets. Taken together, stromal-epithelial interactions during early BBC carcinogenesis are dependent upon epithelial p53 status, and may play important roles in the acquisition of an invasive morphologic phenotype

Mean Curvature Flow of Spacelike Graphs

We prove the mean curvature flow of a spacelike graph in $(\Sigma_1\times \Sigma_2, g_1-g_2)$ of a map $f:\Sigma_1\to \Sigma_2$ from a closed Riemannian manifold $(\Sigma_1,g_1)$ with $Ricci_1> 0$ to a complete Riemannian manifold $(\Sigma_2,g_2)$ with bounded curvature tensor and derivatives, and with sectional curvatures satisfying $K_2\leq K_1$, remains a spacelike graph, exists for all time, and converges to a slice at infinity. We also show, with no need of the assumption $K_2\leq K_1$, that if $K_1>0$, or if $Ricci_1>0$ and $K_2\leq -c$, $c>0$ constant, any map $f:\Sigma_1\to \Sigma_2$ is trivially homotopic provided $f^*g_2<\rho g_1$ where $\rho=\min_{\Sigma_1}K_1/\sup_{\Sigma_2}K_2^+\geq 0$, in case $K_1>0$, and $\rho=+\infty$ in case $K_2\leq 0$. This largely extends some known results for $K_i$ constant and $\Sigma_2$ compact, obtained using the Riemannian structure of $\Sigma_1\times \Sigma_2$, and also shows how regularity theory on the mean curvature flow is simpler and more natural in pseudo-Riemannian setting then in the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages: we replace the condition $K_1\geq 0$ by the the weaker one $Ricci_1\geq 0$. The proofs are essentially the same. We change the title to a shorter one. We add an applicatio

Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold

We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for x\in\RR^d, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension is $d\ge 3$ so that $m<1$, and even $m=-1$ for $d=3$. This case had been left open in the general study \cite{BBDGV} since it requires quite different functional analytic methods, due in particular to the absence of a spectral gap for the operator generating the linearized evolution. The linearization of this flow is interpreted here as the heat flow of the Laplace-Beltrami operator of a suitable Riemannian Manifold (\RR^d,{\bf g}), with a metric ${\bf g}$ which is conformal to the standard \RR^d metric. Studying the pointwise heat kernel behaviour allows to prove {suitable Gagliardo-Nirenberg} inequalities associated to the generator. Such inequalities in turn allow to study the nonlinear evolution as well, and to determine its asymptotics, which is identical to the one satisfied by the linearization. In terms of the rescaled representation, which is a nonlinear Fokker--Planck equation, the convergence rate turns out to be polynomial in time. This result is in contrast with the known exponential decay of such representation for all other values of $m$.Comment: 37 page