9,539 research outputs found
A Spectral Method for Elliptic Equations: The Neumann Problem
Let be an open, simply connected, and bounded region in
, , and assume its boundary is smooth.
Consider solving an elliptic partial differential equation over with a Neumann boundary condition. The problem is converted
to an equivalent elliptic problem over the unit ball , and then a spectral
Galerkin method is used to create a convergent sequence of multivariate
polynomials of degree that is convergent to . The
transformation from to requires a special analytical calculation
for its implementation. With sufficiently smooth problem parameters, the method
is shown to be rapidly convergent. For
and assuming is a boundary, the convergence of
to zero is faster than any power of .
Numerical examples in and 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
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