6,452 research outputs found
All order covariant tubular expansion
We consider tubular neighborhood of an arbitrary submanifold embedded in a
(pseudo-)Riemannian manifold. This can be described by Fermi normal coordinates
(FNC) satisfying certain conditions as described by Florides and Synge in
\cite{FS}. By generalizing the work of Muller {\it et al} in \cite{muller} on
Riemann normal coordinate expansion, we derive all order FNC expansion of
vielbein in this neighborhood with closed form expressions for the curvature
expansion coefficients. Our result is shown to be consistent with certain
integral theorem for the metric proved in \cite{FS}.Comment: 27 pages. Corrected an error in a class of coefficients resulting
from a typo. Integral theorem and all other results remain unchange
Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows
Rotating shear flows, when angular momentum increases and angular velocity
decreases as functions of radiation coordinate, are hydrodynamically stable
under linear perturbation. The Keplerian flow is an example of such systems
which appears in astrophysical context. Although decaying eigenmodes exhibit
large transient energy growth of perturbation which could govern nonlinearity
into the system, the feedback of inherent instability to generate turbulence
seems questionable. We show that such systems exhibiting growing
pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the
logarithmic norm of the involved nonnormal operators, thus exhibiting feedback
of inherent instability. This supports the existence of turbulence of
hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence,
this enlightens the mismatch between the linear theory and
experimental/observed data and helps in resolving the outstanding question of
origin of turbulence therein.Comment: 12 pages including 4 figures; to appear in New Journal of Physic
Behaviour of spin-1/2 particle around a charged black hole
Dirac equation is separable in curved space-time and its solution was found
for both spherically and axially symmetric geometry. But most of the works were
done without considering the charge of the black hole. Here we consider the
spherically symmetric charged black hole background namely Reissner-Nordstrom
black hole. Due to presence of the charge of black-hole charge-charge
interaction will be important for the cases of incoming charged particle (e.g.
electron, proton etc.). Therefore both gravitational and electromagnetic gauge
fields should be introduced. Naturally behaviour of the particle will be
changed from that in Schwarzschild geometry. We compare both the solutions. In
the case of Reissner-Nordstrom black hole there is a possibility of
super-radiance unlike Schwarzschild case. We also check this branch of the
solution.Comment: 8 Latex pages and 4 Figures; RevTex.style; Accepted for Publication
in Classical and Quantum Gravit
Dynamics of electromagnetic waves in Kerr geometry
Here we are interested to study the spin-1 particle i.e., electro-magnetic
wave in curved space-time, say around black hole. After separating the
equations into radial and angular parts, writing them according to the black
hole geometry, say, Kerr black hole we solve them analytically. Finally we
produce complete solution of the spin-1 particles around a rotating black hole
namely in Kerr geometry. Obviously there is coupling between spin of the
electro-magnetic wave and that of black hole when particles propagate in that
space-time. So the solution will be depending on that coupling strength. This
solution may be useful to study different other problems where the analytical
results are needed. Also the results may be useful in some astrophysical
contexts.Comment: 15 Latex pages, 4 Figures; Accepted for publication in Classical and
Quantum Gravit
Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior
We propose a model of a heterogeneous glass forming liquid and compute the
low-temperature behavior of a tagged molecule moving within it. This model
exhibits stretched-exponential decay of the wavenumber-dependent, self
intermediate scattering function in the limit of long times. At temperatures
close to the glass transition, where the heterogeneities are much larger in
extent than the molecular spacing, the time dependence of the scattering
function crosses over from stretched-exponential decay with an index at
large wave numbers to normal, diffusive behavior with at small
wavenumbers. There is a clear separation between early-stage, cage-breaking
relaxation and late-stage relaxation. The spatial
representation of the scattering function exhibits an anomalously broad
exponential (non-Gaussian) tail for sufficiently large values of the molecular
displacement at all finite times.Comment: 9 pages, 6 figure
Holography of Gravitational Action Functionals
Einstein-Hilbert (EH) action can be separated into a bulk and a surface term,
with a specific ("holographic") relationship between the two, so that either
can be used to extract information about the other. The surface term can also
be interpreted as the entropy of the horizon in a wide class of spacetimes.
Since EH action is likely to just the first term in the derivative expansion of
an effective theory, it is interesting to ask whether these features continue
to hold for more general gravitational actions. We provide a comprehensive
analysis of lagrangians of the form L=Q_a^{bcd}R^a_{bcd}, in which Q_a^{bcd} is
a tensor with the symmetries of the curvature tensor, made from metric and
curvature tensor and satisfies the condition \nabla_cQ^{abcd}=0, and show that
they share these features. The Lanczos-Lovelock lagrangians are a subset of
these in which Q^{abcd} is a homogeneous function of the curvature tensor. They
are all holographic, in a specific sense of the term, and -- in all these cases
-- the surface term can be interpreted as the horizon entropy. The
thermodynamics route to gravity, in which the field equations are interpreted
as TdS=dE+pdV, seems to have greater degree of validity than the field
equations of Einstein gravity itself. The results suggest that the holographic
feature of EH action could also serve as a new symmetry principle in
constraining the semiclassical corrections to Einstein gravity. The
implications are discussed.Comment: revtex 4; 17 pages; no figure
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Fluorescent amplification for next generation sequencing (FA-NGS) library preparation.
BACKGROUND:Next generation sequencing (NGS) has become a universal practice in modern molecular biology. As the throughput of sequencing experiments increases, the preparation of conventional multiplexed libraries becomes more labor intensive. Conventional library preparation typically requires quality control (QC) testing for individual libraries such as amplification success evaluation and quantification, none of which occur until the end of the library preparation process. RESULTS:In this study, we address the need for a more streamlined high-throughput NGS workflow by tethering real-time quantitative PCR (qPCR) to conventional workflows to save time and implement single tube and single reagent QC. We modified two distinct library preparation workflows by replacing PCR and quantification with qPCR using SYBR Green I. qPCR enabled individual library quantification for pooling in a single tube without the need for additional reagents. Additionally, a melting curve analysis was implemented as an intermediate QC test to confirm successful amplification. Sequencing analysis showed comparable percent reads for each indexed library, demonstrating that pooling calculations based on qPCR allow for an even representation of sequencing reads. To aid the modified workflow, a software toolkit was developed and used to generate pooling instructions and analyze qPCR and melting curve data. CONCLUSIONS:We successfully applied fluorescent amplification for next generation sequencing (FA-NGS) library preparation to both plasmids and bacterial genomes. As a result of using qPCR for quantification and proceeding directly to library pooling, the modified library preparation workflow has fewer overall steps. Therefore, we speculate that the FA-NGS workflow has less risk of user error. The melting curve analysis provides the necessary QC test to identify and troubleshoot library failures prior to sequencing. While this study demonstrates the value of FA-NGS for plasmid or gDNA libraries, we speculate that its versatility could lead to successful application across other library types
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