A Spectral Method for Elliptic Equations: The Neumann Problem

Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving an elliptic partial differential equation $-\Delta u+\gamma u=f$ over $\Omega$ with a Neumann boundary condition. The problem is converted to an equivalent elliptic problem over the unit ball $B$, and then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials $u_{n}$ of degree $\leq n$ that is convergent to $u$. The transformation from $\Omega$ to $B$ requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For $u\in C^{\infty}(\overline{\Omega})$ and assuming $\partial\Omega$ is a $C^{\infty}$ boundary, the convergence of $\Vert u-u_{n}\Vert_{H^{1}}$ to zero is faster than any power of $1/n$. Numerical examples in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ show experimentally an exponential rate of convergence.Comment: 23 pages, 11 figure

P53 is active in murine stem cells and alters the transcriptome in a manner that is reminiscent of mutant p53

Since it was found that p53 is highly expressed in murine embryonic stem cells, it remained a mystery whether p53 is active in this cell type. We show that a significant part of p53 is localised in the nucleus of murine embryonic stem cells and that the majority of this nuclear p53 is bound to DNA. According to its nuclear localisation, we show that p53 alters the transcriptional program of stem cells. Nevertheless, the anti-proliferative activity of p53 is compromised in stem cells, and this control is due, at least in part, to the high amount of MdmX that is present in embryonic stem cells and bound to p53. Instead of the anti-proliferative activity that p53 has in differentiated cells, p53 controls transcription of pro-proliferative genes in embryonic stem cells including c-myc and c-jun. The impeded anti-proliferative activity of p53 and the induction of certain proto-oncogenes by p53 in murine embryonic stem cells can explain why stem cells proliferate efficiently despite having high levels of p53

Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

Scattering series in mobility problem for suspensions

The mobility problem for suspension of spherical particles immersed in an arbitrary flow of a viscous, incompressible fluid is considered in the regime of low Reynolds numbers. The scattering series which appears in the mobility problem is simplified. The simplification relies on the reduction of the number of types of single-particle scattering operators appearing in the scattering series. In our formulation there is only one type of single-particle scattering operator.Comment: 11 page

Comparison of ultracold neutron sources for fundamental physics measurements

Ultracold neutrons (UCNs) are key for precision studies of fundamental parameters of the neutron and in searches for new CP violating processes or exotic interactions beyond the Standard Model of particle physics. The most prominent example is the search for a permanent electric dipole moment of the neutron (nEDM). We have performed an experimental comparison of the leading UCN sources currently operating. We have used a 'standard' UCN storage bottle with a volume of 32 liters, comparable in size to nEDM experiments, which allows us to compare the UCN density available at a given beam port.Comment: 20 pages, 30 Figure

A spectral method for elliptic equations: the Dirichlet problem

An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method is applied to the reformulated problem, using multivariate polynomials as the approximants. For a smooth boundary and smooth problem parameter functions, the method is proven to converge faster than any power of 1/n with n the degree of the approximate Galerkin solution. Examples in two and three variables are given as numerical illustrations. Empirically, the condition number of the associated linear system increases like O(N), with N the order of the linear system.Comment: This is latex with the standard article style, produced using Scientific Workplace in a portable format. The paper is 22 pages in length with 8 figure

Theory for the ultrafast ablation of graphite films

The physical mechanisms for damage formation in graphite films induced by femtosecond laser pulses are analyzed using a microscopic electronic theory. We describe the nonequilibrium dynamics of electrons and lattice by performing molecular dynamics simulations on time-dependent potential energy surfaces. We show that graphite has the unique property of exhibiting two distinct laser induced structural instabilities. For high absorbed energies (> 3.3 eV/atom) we find nonequilibrium melting followed by fast evaporation. For low intensities above the damage threshold (> 2.0 eV/atom) ablation occurs via removal of intact graphite sheets.Comment: 5 pages RevTeX, 3 PostScript figures, submitted to Phys. Re

Identification of Novel Fibrosis Modifiers by In Vivo siRNA Silencing.

Fibrotic diseases contribute to 45% of deaths in the industrialized world, and therefore a better understanding of the pathophysiological mechanisms underlying tissue fibrosis is sorely needed. We aimed to identify novel modifiers of tissue fibrosis expressed by myofibroblasts and their progenitors in their disease microenvironment through RNA silencing in vivo. We leveraged novel biology, targeting genes upregulated during liver and kidney fibrosis in this cell lineage, and employed small interfering RNA (siRNA)-formulated lipid nanoparticles technology to silence these genes in carbon-tetrachloride-induced liver fibrosis in mice. We identified five genes, Egr2, Atp1a2, Fkbp10, Fstl1, and Has2, which modified fibrogenesis based on their silencing, resulting in reduced Col1a1 mRNA levels and collagen accumulation in the liver. These genes fell into different groups based on the effects of their silencing on a transcriptional mini-array and histological outcomes. Silencing of Egr2 had the broadest effects in vivo and also reduced fibrogenic gene expression in a human fibroblast cell line. Prior to our study, Egr2, Atp1a2, and Fkbp10 had not been functionally validated in fibrosis in vivo. Thus, our results provide a major advance over the existing knowledge of fibrogenic pathways. Our study is the first example of a targeted siRNA assay to identify novel fibrosis modifiers in vivo