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b0f1f22e74dc68701b63b7b4303b63857d0e77e9 | subsection | 142 | 153 | Symmetric products | Then there is an isomorphism of \Lambda _{/2}-modules\operatorname{HF}_*(\kappa _{k,\lambda }(\phi ) )\cong \bigoplus _{\langle c_1(\mathfrak {s} ),[\Sigma ] \rangle = 2(n+1-g)}{\mathrm {HM}_*(T_\phi , \mathfrak {s}; c_\lambda )} \quad (\lambda >0),where on the right-hand side, a representative ofc_\lambda :=-8\pi ^2 (... | {
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63f7bec5725edc89aa7f610568ba2150bd14fb4a | subsection | 143 | 153 | Symmetric products | Write \widehat{V}^k for the component of \widehat{V}_\gamma that lies over \operatorname{Sym}^k(\Sigma _1)\times \operatorname{Sym}^{n-1-k} (\Sigma _2). It was shown in that strong negativity for \widehat{V}^k in \operatorname{Sym}^n(\Sigma )_-
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790ed49200d4006ac55df9b7fcdf1eb1aa06dab8 | subsection | 144 | 153 | Symmetric products | (We work over \Lambda _{/2} for convenient comparison with symplectic Floer homology.) The cobordism X induces a homomorphism HM_*(X)\colon HM_*(Y_1)\otimes _{\Lambda _{/2}} HM_*(Y_2)\rightarrow HM_*(Y_1 \# Y_2 ), and the composite HM_*(X)\circ (U\otimes 1 - 1\otimes U) is nullhomotopic because the basepoints in Y_1 an... | {
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78fa55eb2759cef9b7454832e035f820dd387a22 | subsection | 145 | 153 | Symmetric products | Salamon , but it can also be described in elementary terms .When \mu =\kappa _{\lambda ,n}(\phi ) for some area-preserving diffeomorphism \phi \in \operatorname{Aut}(\Sigma ), the fixed-point Floer homology \operatorname{HF}(\mu ) was conjectured by D. Salamon to be isomorphic to a version of Seiberg–Witten monopole Fl... | {
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72080cdfd03a2334a1c4b09b9cf62197f3692687 | subsection | 146 | 153 | Symmetric products | Thus there is an S^1-bundle\rho \colon V_\gamma \rightarrow N ; \quad \rho ^*\bar{\omega }_\lambda = \omega _\lambda |_{V_\gamma }.The Euler class e(V) is Poincaré dual to the difference of the divisors p+\operatorname{Sym}^{n-2}(\Sigma _\gamma ) and q+\operatorname{Sym}^{n-2}(\Sigma _\gamma ), where p and q lie in the... | {
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cdb57af85cde3d4d6fdcd7bb455f8eec5328a6d8 | subsection | 147 | 153 | Symmetric products | Then there is an isomorphism\operatorname{HF}(\widehat{V},(\mathrm {id}\times \mu )\widehat{V}) \cong \bigoplus _{c_1(\mathfrak {t} ) = 2(n+1-g)}{\mathrm {HM}_*(Y_1 \# Y_2, \mathfrak {t}; \tilde{c}_\lambda )},where \tilde{c}_\lambda is the class on Y_1 \# Y_2 induced by the c_\lambda -classes on the Y_i.We invoke an un... | {
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21abf6fc125230b957a6c371e78b7dbb13474093 | subsection | 148 | 153 | Non-separating circles | A simpler situation occurs when \gamma \subset \Sigma is a non-separating circle. Since n+ \chi (\Sigma )/2 = (n-1) + \chi (\Sigma _\gamma )/2, N is (anti-)monotone precisely when M is. The product M_- \times N is also (anti-)monotone, with monotonicity constant n+\chi (\Sigma )/2, when this constant is positive (negat... | {
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74720ad9fc7cf3bad643291baf0b6b38da7ce136 | subsection | 149 | 153 | Non-separating circles | Since n+ \chi (\Sigma )/2 = (n-1) + \chi (\Sigma _\gamma )/2, N is (anti-)monotone precisely when M is. The product M_- \times N is also (anti-)monotone, with monotonicity constant n+\chi (\Sigma )/2, when this constant is positive (negative), and its minimal Chern number isc_1^{\min } (M_-\times N )= |n+ \frac{\chi (\... | {
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9857114836d1763eca486a07d304950d4ded625f | subsection | 150 | 153 | Flat connections | Just as symplectic geometry of symmetric products mimics Seiberg–Witten theory, so symplectic geometry of moduli spaces of flat connections models instanton Floer homology (cf. Dostoglou–Salamon ), at least in cases where reducible flat connections can be avoided.Consider the twisted character variety M_g of a puncture... | {
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c2a223cf29d26d84242a1cb66d2200b6ec41c788 | subsection | 151 | 153 | Flat connections | Thus \operatorname{HF}_*(\widehat{V}, \theta (\phi )\widehat{V}) is either always (i.e., for all \phi ) zero, or else it is always isomorphic, as a relatively graded module, to \operatorname{HF}_*(\theta (\phi ))\oplus \operatorname{HF}_*(\theta (\phi ))[3].However, \operatorname{HF}_*(\widehat{V},\widehat{V}) is non-z... | {
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8695c8505064702c29bb5c643125a38f0f6af907 | subsection | 152 | 153 | Flat connections | It is easily verified to be the reduction map of an S^3-fibred coisotropic submanifold (to see this one can use either the Atiyah–Bott symplectic structure, thinking of the A_i and B_i as holonomies of flat connections, or Goldman's finite-dimensional reformulation of it).Because M_g and M_{g-1} are simply connected, o... | {
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79f399d054d8078dac958686113ddd0db0e6ec96 | abstract | 0 | 30 | Abstract | We present an analysis of the foreground emission present in the WMAP 3-year
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a118515a845dee7f043489d96993b6a9811c41f3 | subsection | 1 | 30 | Introduction | Measurements of the Cosmic Microwave Background (CMB) provide
cosmological information by probing the early universe
some 380,000 years after the Big Bang.
However their precision is limited by the
contamination of the cosmological signal due to emission from
local astrophysical sources such as our own Galaxy.
In parti... | {
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1e831f21ef283574cb9ff300ee6f5e487a12e1ec | subsection | 2 | 30 | Introduction | Sections and
then attempt to improve our knowledge of the spectral and physical
properties of the foreground components based on the scaling
properties of the templates.
An assessment of the efficiency of
the method is then afforded by studying the power spectrum of the cleaned
CMB data, whilst a final iterative appl... | {
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f3812faf10bc5835f7f0854c28eb2709e84e1549 | subsection | 3 | 30 | Body | ICA is a blind component separation method: it
works without any knowledge about the spectral and spatial properties
of the components to be
recovered. A particular application of this method is fastica
as originally proposed by ,
and applied to the analysis of CMB total intensity data in
and more recently to polariz... | {
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f700f6d8309008e6a4b1403b2e5100693299b869 | subsection | 4 | 30 | Body | These functions depend on the statistics of the
independent signals which are assumed to be unknown.
Generally, p,
which corresponds to the kurtosis, should be used for sub-Gaussian
components but it is strongly sensitive to outliers in the distributions;
g is for super-Gaussian signals while t is a general purpose fun... | {
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b144abdc027248b7008b0def2c75cb0301bf2944 | subsection | 5 | 30 | Body | In general, the cross–correlation measure,
\alpha , between a data vector {\bf d} and a template vector {\bf t} can be measured by minimising:\chi ^2 = ({\bf d}-\alpha {\bf t})^T \cdot {\bf M}^{-1}_{SN}\cdot ({\bf d}-\alpha {\bf t}) = {\bf \tilde{d}}^T \cdot {\bf M}^{-1}_{SN}\cdot {\bf \tilde{d}}where {\bf M}_{SN} is t... | {
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cd47ceeada84021adc116e32ff54d11296648556 | subsection | 6 | 30 | Body | The corresponding sky map data are available on the LAMBDA
websiteLegacy Archive for Microwave Background Data
Analysis – http://lambda.gsfc.nasa.gov/.
in a HEALPixhttp://healpix.jpl.nasa.gov.
pixelisation scheme, with a pixel resolution parameter of N_{side}=512.We have smoothed each of the sky maps to an effective re... | {
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2823abeebf46864ee311b7a21c612574118fdd4b | subsection | 7 | 30 | Body | The templates were scaled using the weights from
Table 3 of , where for the Q-, V- and W-
bands we have considered the average values.The distribution of coefficients determined by fastica when
utilising the t function is clearly unsatisfactory – the
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s... | {
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149414775aab6480a5e4b72a74db2a37f5f22acd | subsection | 8 | 30 | Body | Some care should then be exercised in interpreting the coefficients for
the former two components.
[Figure: Scatter plots of the coupling coefficients obtainedby fastica with the p-function using the simulations performed with the K-Ka map as synchrotrontemplate.We show as an example the results in the Q-band.There is ... | {
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ac2787455ebe4f876e1f671c41c26fc3ba46a8a6 | subsection | 9 | 30 | DATA USED IN THE ANALYSIS | The current analysis seeks to
clean the WMAP data from the main Galactic foreground
emissions by applying the fastica algorithm
to the observed WMAP sky signal at each frequency together with
appropriate templates for each component.
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ce061536d78efb1d58f84d6eb24910f28aac82a6 | subsection | 10 | 30 | Synchrotron templates | Synchrotron emission arises from the acceleration of cosmic ray electrons in the
magnetic field of our Galaxy.
This is the dominant Galactic emission at frequencies lower than 10~GHz,
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5efbbe820c11f55ac6ee20d36f080721a899df47 | subsection | 11 | 30 | H | The free-free emission arises from electron-ion scattering. Its
spectrum is
generally described by a power law T_A\sim \nu ^{-\beta _{ff}}
with \beta _{ff}=2.15 at high-frequency (\nu > 10 GHz) and \beta _{ff}=2
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2aaca7d3ab34739fc30d137710c747322d35c23e | subsection | 12 | 30 | Dust templates | Thermal dust emission is the dominant foreground component at frequencies
in the range \sim 100 – 1000 GHz.
Its emissivity is generally approximated by a modified black body lawI(\nu ) \sim \nu ^{\alpha _d}B_{\nu }(T_d)where \alpha _d is the emissivity index and B_{\nu }(T_d) the
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45f3459e9317418ba1e11ea3434212c060f59896 | subsection | 13 | 30 | MONTE CARLO SIMULATIONS AND CALIBRATION OF METHOD | As the first step of our analysis, we have tested fastica
using realistic simulations of the WMAP observations
to calibrate the accuracy of the method for template fitting.
Specifically, we performed 1000 simulations of the microwave sky
at each of the 5 WMAP frequencies, each containing a realisation of
the CMB signal... | {
"cite_spans": []
} | 0807.1865 | Foreground analysis of the WMAP three-year data with FASTICA | [
"M. Bottino",
"A. J. Banday",
"D. Maino"
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f000eefa94c892ef6aac97414746a81e702de18b | subsection | 14 | 30 | ANALYSIS WITH THE HASLAM MAP AS SYNCHROTRON TEMPLATE. | For our initial analysis we consider template fits to the WMAP data
for all five frequency bands using fastica and the Haslam map as
the model for the synchrotron emission.
Table REF summarises the results determined
using both p- and g-functions for the Kp2 and Kp0 sky
coverages. The corresponding Kp2 results based on... | {
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c0cda58546073f9048bbc50772cc034cb50867f4 | subsection | 15 | 30 | ANALYSIS WITH THE HASLAM MAP AS SYNCHROTRON TEMPLATE. | The free-free amplitudes are also
typically 1-\sigma higher for the fastica analysis.Similarly, the constrained fits from are of
comparable amplitude for the synchrotron and dust coefficients. These
values were derived by fixing the synchrotron spectral index at a
value of 2.7, and the free-free to 2.15 for frequencies... | {
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... | 0807.1865 | Foreground analysis of the WMAP three-year data with FASTICA | [
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0815ff044678247daccfcd1d1b3810b3601edaa4 | subsection | 16 | 30 | Spectral index of foreground emissions. | We utilise the derived frequency dependence of the scaling factors to
parameterise the spectral behavior of the foreground emission
components. For each component, we fit the corresponding coefficients
with a power law model of the form
A_{norm}(\nu /\nu _{0})^{-\beta }. A_{norm} is the amplitude of the
emission of a s... | {
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b4a5e20f8fd25d4288f863c8f4cb5ca9d95709f1 | subsection | 17 | 30 | Spectral index of foreground emissions. | As with the synchrotron component, the
amplitude of the emission drops for the Kp0 mask, and consequently
the spectral index steepens noticeably. One might speculate that this is
related to the differing properties of the anomalous component closer
to the Galactic plane flattening the index of the Kp2 results. In
the c... | {
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3dc8ca3ddd04672c3b3dd7c5067b2896916a12f5 | subsection | 18 | 30 | Spectral index of foreground emissions. | In our analysis, no such
subtraction is necessary, since the coefficients are essentially
determined as part of the process of deriving the best CMB estimate
from the data. In fact, our Kp2 amplitudes show more extreme
behaviour at high frequencies, and indicate a systematically rising
spectrum, although the best-fit i... | {
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0102f98a0044b964029c9fac83f823e1c0c03ba9 | subsection | 19 | 30 | Single Year Analysis | In order to test the stability of the coupling coefficients between
the foreground templates and the WMAP data to potential systematics,
eg. annual instrumental or calibration variations,
we have performed the same fastica analysis for the yearly sky maps.
These results are plotted in
Figure REF
together with the 3-ye... | {
"cite_spans": []
} | 0807.1865 | Foreground analysis of the WMAP three-year data with FASTICA | [
"M. Bottino",
"A. J. Banday",
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32283d46a96d6be2959577edd06eea87707e0dcb | subsection | 20 | 30 | Analysis with the K-Ka map as synchrotron template. | One of the limitations of the previous foreground analysis is that the
Haslam map used as template for the synchrotron emission is unlikely
to be completely representative of the foreground morphology at the
WMAP frequencies due to spectral index variations across the sky.
Therefore, we repeated the analysis using the ... | {
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7895080e4a1d8f78012319d3c0c2f9bb8eb3d801 | subsection | 21 | 30 | Analysis with the K-Ka map as synchrotron template. | We have also made a
more detailed study using simulations, with the same results. Of
course, this does not imply that the K-Ka template is not a
significant improvement on the Haslam map, but that the gross features
of the two foreground models are in agreement. The quality of the two
synchrotron templates will be cons... | {
"cite_spans": []
} | 0807.1865 | Foreground analysis of the WMAP three-year data with FASTICA | [
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6e303e2a6ab0e564d1cf3679cabd80d0ca6835a7 | subsection | 22 | 30 | Spectral properties of foreground emissions. | A study of the spectral index of the returned K-Ka coefficients would
be unphysical, or at least difficult to interpret, since the template
is a mix of synchrotron, free-free and anomalous dust emission.
Moreover, the interpretation of the spectral behaviour of the returned
dust and free-free coefficients is similarly ... | {
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9372cb4a1a90c13744e2629727c494c41deaf75c | subsection | 23 | 30 | EVALUATION OF THE Q-, V- AND W-BAND SKY MAPS AFTER FOREGROUND
CLEANING | One of the main aims of the foreground analysis performed thus far
with fastica is to promote the possibility of cleaning the WMAP data sufficiently to allow its use for cosmological purposes.
Therefore, adopting the coupling coefficients derived for various
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} | 0807.1865 | Foreground analysis of the WMAP three-year data with FASTICA | [
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47f8b3577c7dcbb0e4101c9fe716675391980f25 | subsection | 24 | 30 | EVALUATION OF THE Q-, V- AND W-BAND SKY MAPS AFTER FOREGROUND
CLEANING | This structure is seen clearly in both the fastica and WMAP residual plots. Also seen is evidence of a negative residual
associated with a well-known feature in the low frequency template – the North Polar
Spur – plus other residuals around the edge of the Galactic plane
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7f1f4942a3873f6142b8a8a9ab19798effde69a4 | subsection | 25 | 30 | AN `ITERATIVE' BLIND COMPONENT SEPARATION STUDY USING | As demonstrated in the previous section, the WMAP data cleaned by
foreground templates still show evidence of contamination due to
either the inability of the templates to describe real spectral
variations in the foreground emission on the sky, or other emission
mechanisms not identified with the standard Galactic
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"M. Bottino",
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36aeac9001d6a2050b16865562e2cc65f4963529 | subsection | 26 | 30 | Foreground residuals | The upper row of Figure REF shows the output maps
from fastica that we identify with foreground residuals when using
the Haslam template for synchrotron emission.The leftmost figure presents results from analysing the five WMAP frequency bands
after cleaning using the coefficients previously derived in this paper
(see ... | {
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db3391db24288154d73a056f8b9512e678026113 | subsection | 27 | 30 | CMB component | In order to quantify
the improvement connected to the
iterative processing step,
we have studied
the CMB components returned by fastica when working
on the data pre-cleaned with a template analysis stage. They are
very similar, as shown in Figure REF .
This is also confirmed by the plot of the power spectrum for
the CM... | {
"cite_spans": []
} | 0807.1865 | Foreground analysis of the WMAP three-year data with FASTICA | [
"M. Bottino",
"A. J. Banday",
"D. Maino"
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d243deefd7931d5511fec8303e0b4169550d7b1e | subsection | 28 | 30 | DISCUSSION | In this paper, we have utilised a blind component separation algorithm
– fastica – to address the issue of the Galactic foreground
emission in the WMAP 3-year data. In particular, we have adapted the
technique to allow three Galactic foreground templates (that trace
synchrotron, free-free and thermal dust emission) to ... | {
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5392dc223d15b148996630d9a0336969b0cee5dc | subsection | 29 | 30 | DISCUSSION | In this manner, we have confirmed the existence of a
component spatially distributed along the Galactic plane, with pronounced
emission near the Galactic center.
This is the emission previously noted in the SMICA analysis
of , and is the `WMAP haze' of .
However, the amplitude and extent of the emission is less when
th... | {
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5e0cb0215ab1096625eb126374d470591548454c | abstract | 0 | 7 | Abstract | We study accelerating Universes with power-law scale-factors. We include
shear and vorticity, a cosmological "constant" term, and spin from torsion, as
in Einstein-Cartan's theory when a scalar-field of Brans-Dicke type acts in the
model. We find a "no-hair" result, for shear and vorticity; we also make
contact with th... | {
"cite_spans": []
} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
Torsion | [
"Marcelo Samuel Berman"
] | [
"physics.gen-ph"
] | 2,008 | en | Physics | [
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fc02d447fd11cc007cec06b328cf9b5251b626a5 | subsection | 1 | 7 | Body | 30
SHEAR AND VORTICITY IN AN ACCELERATING BRANS-DICKE
LAMBDA-UNIVERSE WITH TORSION
Marcelo Samuel Berman^{1}
^{1}Instituto Albert Einstein / Latinamerica - Av. Candido Hartmann, 575 -
# 17
80730-440 - Curitiba - PR - Brazil - email: msberman@institutoalberteinstein.org
Cosmology; Einstein; Brans-D... | {
"cite_spans": []
} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
Torsion | [
"Marcelo Samuel Berman"
] | [
"physics.gen-ph"
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b154e85e27236159835224f04d06fc9bafccf0ce | subsection | 2 | 7 | Body | Afterwards, we shall proceed to the conversion
to the Jordan-frame, i.e., in the conventional set of units.Consider now Robertson-Walker's metric,ds^{2}=dt^{2}-\frac{R^{2}(t)}{\left[ 1+\left( \frac{kr^{2}}{4}\right)
\right] ^{2}}d\sigma ^{2} , (1)where k=0 and d\sigma ^{2}=dx^{2}+dy^{2}+dz^{2} .When we include a cosmol... | {
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} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
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1e5ca31efd5d0426c2f63877ed0a7cdcea6405ec | subsection | 3 | 7 | Body | (6)Raychaudhuri's equation (Raychaudhuri, 1979), as derived by Berman,
becomes, when we include shear and vorticity,3\dot{H}+3H^{2}=\dot{u}_{;\alpha }^{\alpha }+2\left( \varpi ^{2}-\sigma ^{2}\right) -4\pi G\left( \rho +3p+4\rho _{\lambda }\right) +\Lambda
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for Hubb... | {
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} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
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63fe8e010ed955c557ffe8374e8151ff8fa6f3e2 | subsection | 4 | 7 | Body | (12)When we go back to Jordan's frame, we find:\bar{R}=R\phi ^{\frac{1}{2}} ;\bar{\rho }=\rho \phi ^{-2} ;\bar{p}=p\phi ^{-2}=\left[ \frac{p_{0}}{\rho _{0}}\right] \bar{\rho } ;(13)\bar{\varpi }=\varpi \phi ^{-\frac{1}{2}} ;\bar{\sigma }=\sigma \phi ^{-\frac{1}{2}} ;\bar{\Lambda }=\Lambda _{0}\phi ^{-1} ;\bar{\phi }=\p... | {
"cite_spans": []
} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
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"Marcelo Samuel Berman"
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384004f51ea0ecb4d6956ee0226d8b255d87b6df | subsection | 5 | 7 | Body | (16)It must be clear that the spin density term must be included in the resulting
Raychaudhuri's equation, whereby, from the relation (7) we obtain the new one
by making the substitution below,\Lambda \longrightarrow \left[ \Lambda +128\pi ^{2}S^{2}\right]
. (16a)We can check, that in the given model for the BD case,... | {
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} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
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5097ced4603dcf834a92ef29b621305abcae79e6 | subsection | 6 | 7 | Body | (1923) - Ann. Ec. Norm. Sup., 40, 325.Dicke, R.H. (1962) - Physical Review, 125, 2163.Faraoni, V. (2004) - Cosmology in Scalar-Tensor Gravity, Kluwer, Dordrecht.Fujii, Y.; Maeda, K-I. (2003) - The Scalar-Tensor Theory of
Graviation, CUP, Cambridge.Raychaudhuri, A. K. (1979) - Theoretical Cosmology, Oxford
University Pr... | {
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} | 10.1007/s10509-008-9879-3 | 0807.1866 | Shear and Vorticity in an Accelerating Brans-Dicke Lambda-Universe with
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25457e783fdfd3b434beb943b4aafea9d94c2b09 | abstract | 0 | 18 | Abstract | Swimming and pumping at low Reynolds numbers are subject to the "Scallop
theorem", which states that there will be no net fluid flow for time reversible
motions. Living organisms such as bacteria and cells are subject to this
constraint, and so are existing and future artificial "nano-bots" or
microfluidic pumps. We st... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
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"cond-mat.soft"
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6d4262e37bd7f2130b4d7dff29bca88072521aa7 | subsection | 1 | 18 | Introduction | Insight into swimming of microorganisms and bacteria can
be gained by studying the motion at low Reynolds numbers of
experimental and theoretical model
systems , . Compared to the macroscopic world, a
striking feature of propulsion of these micron-scale objects, for
which inertia is typically negligible, is that a body... | {
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... | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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0a5d672e37d414089fdb6073787c541665aa4c22 | subsection | 2 | 18 | Optical tweezers | The optical tweezers setup used in this work consists of a laser (IPG Photonics,
PYL-1-1064-LP, \lambda =1064nm, P_{max}=1.1W) focused through a
water immersion objective (Zeiss, Achroplan IR 63x/0.90 W), trapping
from below. The laser beam is steered via a pair of acousto-optic
deflectors (AA Opto-Electronic, AA.DTS.X... | {
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... | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
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"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
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c74ae04a80c370f7b6e0bcc6cea9006213765bb8 | subsection | 3 | 18 | Experimental protocol | The experimental protocol is composed of two parts. In the first
calibration stage all the traps are kept at rest, and the beads
undergo only Brownian motion confined by the traps. The driven
dynamics occurs only during the second stage. Data is acquired at
48.79 frames per second, with exposure time 19\times 10^{-3}s.... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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d37c0b6d5bcf61b6524553438d4a1f0c4985f199 | subsection | 4 | 18 | Numerical simulations | Numerical simulations were performed by integrating directly the
equation of motion of the three beads with Taylor's
method . We considered both simulations that included
thermal motion (i.e. adding a white noise term to the equations) and
deterministic ones, finding no relevant differences. The results in
the body of ... | {
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} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
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"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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17eee354605d2a5b44a3bd0a9ce60843965fcd44 | subsection | 5 | 18 | Experimental | We study a swimmer composed of three beads immersed in a high
viscosity Newtonian liquid. The beads are controlled by an optical
tweezer , and interact with each other through the
fluid. The laser traps are set-up following the scheme of
figure REF (a,b). The central trap is kept at rest,
holding the central bead in a ... | {
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... | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
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b39c0f7f7f12df42f345665a60145ecd0e959cd5 | subsection | 6 | 18 | Quantifying displacements | Trapping lasers act with good approximation as harmonic potentials on
each bead. Thus, the average displacement \langle \Delta x
\rangle _{t} of the central bead from the position of the central trap
can be converted using Hooke's law into the mean force exerted on the
fluid by the whole system. However, a direct measu... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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d75f88454ea3206b5edecd9c9c32f7c3e8d54de9 | subsection | 7 | 18 | Quantifying displacements | We also define a third observable (3) s:= |p_1| + |p_2|
+ |p_3| + |p_4|, the sum of absolute values of the peaks. s is
always positive, and quantifies the amplitude of the swimmer's
motion. | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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b4a86a5c4bc01e3d3b9e253a024a97195498e8d7 | subsection | 8 | 18 | Comparison of experiments with simulations | We compare the measured flow to simple numerical simulations (see
methods). The hydrodynamic interaction between the spheres is
described by the Oseen tensor , corresponding to the limit
of point force, or far field. Along the \hat{x} axis of the swimmer,
the equation of motion for bead n is\dot{x}_n &=& \frac{1}{\gamm... | {
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"J. Kotar",
"B. Bassetti",
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b50de441989d8b782502df0ce1dc2013e3c9de2e | subsection | 9 | 18 | Comparison of experiments with simulations | A mapping between each of
the observables (2, inv) and the temporal
average x t is obtained by means of
simulations. Here, sampling problems are not present and x t is quantifiable directly by time averaging with
arbitrary accuracy; 2 and inv are obtained from
the steady-state mean cycle, similarly to experiments. For ... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
"cond-mat.soft"
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bb3fd9ec68734ab1c95d523c23c3ad394e56cd13 | subsection | 10 | 18 | Discussion | Our first result is that the system is able to generate flow. This is
qualitatively visible in the distribution of position of the central
bead (figure REF (c)). This effective potential is
composed of two contributions: the harmonic potential exerted by the
tweezer, and the configurational bias induced by the interact... | {
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"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
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c80338c44cbee0e6f8eaee4d9bcab60e8bfaab8a | subsection | 11 | 18 | Comparison with other model systems | It is instructive to compare our swimmer
with the closely related theoretical model originally proposed in the
literature by Najafi and Golestanian, and the variants
that have been recently explored , . There are two
main features characterizing our model.
Firstly, beads are subject to the compliance of the trapping
p... | {
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"P. Cicuta",
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f3c2a42e424e364e5cedfbd90d62c0e9c0369cd8 | subsection | 12 | 18 | Comparison with other model systems | In our case, using simulations of an analogous
intrinsic swimmer actuated by two-body two-state springs, we find that
the differences are mostly quantitative, the intrinsic variant being
slightly faster and more efficient (Supplementary Figure S3).Finally, it may be of interest to compare this pump to other
engines. We... | {
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e523a1d50a7e50c95635f359d28a4b610bd31551 | subsection | 13 | 18 | Comparison with other model systems | (c) Close up and complete cycle showing relaxation of a single bead
in a switching trap, with no interacting partners.
Fig. 3
Quantitative characterisation of the swimmer.
The main observable is the mean force felt by the central bead,
measured by its mean displacement in the optical trap. The mean
force is studied her... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
"cond-mat.soft"
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bcdae3ad541ba547dfbbfed74b9615f7b9a45e1d | subsection | 14 | 18 | Scaling with | We present here a simple argument for the scaling of the amplitude s
with distance d, explaining the scaling seen for experiments and simulations in figure 3(d).To estimate the d-dependency of the amplitude during a cycle, it is
sufficient to describe the displacement of the central bead in one of
the four sub-phases. ... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
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56d1bfa0d434f1b67d34390d170bda6b4223a1d1 | subsection | 15 | 18 | Scaling with | The argument has the advantage of
showing how the hydrodynamic interaction tensor comes into play
explicitly after a trap switches its position.In the
same linear approximation, the coupled equations (eq.1) from the main text
can even be solved directly in a straightforward way, and the
resulting maximum displacement i... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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43973f086799922904fa17023e67a9dd335e3577 | subsection | 16 | 18 | Relating the observables | We summarise here how the procedure to relate the experimental data to the induced flow.
[Figure: Converting observables into mean force. This schemeillustrates the procedure used to obtain the mean force from theexperiments, by means of simulations. Step 1: Because of thedifferent shapes of the mean cycles for differe... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
"M. Leoni",
"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
] | [
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6e0085374ae49b6614ff5c6a45a04451bf9643e0 | subsection | 17 | 18 | Intrinsic Swimmer | Figure REF shows a comparison of our model with
simulations of an analogous intrinsic swimmer.
[Figure: Comparison of the propulsive forces for extrinsic andintrinsic swimmers. The extrinsic swimmer is studiedexperimentally and numerically in this work, whereas we can onlystudy the intrinsic swimmer, actuated by two-st... | {
"cite_spans": []
} | 10.1039/b812393d | 0807.1867 | A basic swimmer at low Reynolds number | [
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"J. Kotar",
"B. Bassetti",
"P. Cicuta",
"M. Cosentino Lagomarsino"
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1b646d3299484409a9f0adfe4bcdf8e5358b78e7 | abstract | 0 | 7 | Abstract | Quantum rings can be characterized by a specific radius and ring width. For
this rich class of physical systems, an accurate approximation for the
exchange-hole potential and thus for the exchange energy is derived from first
principles. Excellent agreement with the exact-exchange results is obtained
regardless of the ... | {
"cite_spans": []
} | 0807.1868 | Electronic exchange in quantum rings | [
"E. Rasanen",
"S. Pittalis",
"C. R. Proetto",
"E. K. U. Gross"
] | [
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075834060a06760d7cda013cb0a70a2b549f9a0e | subsection | 1 | 7 | Body | Electronic exchange in quantum rings
E. Räsänen
[Electronic address:]esa.rasanen@jyu.fi
Institut für Theoretische Physik,
Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
Nanoscience Center, Department of Physics,
University of Jyväskylä, B.O.Box 35,
FI-40014 Jyväskylä, Finland
European Theoretical Spec... | {
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9adacd1bd671e5e9cacee80b782f1cf74a8537c8 | subsection | 2 | 7 | Body | Our derivation follows
the strategy originally proposed for atoms by Becke and Roussel,
in which the averaged exchange hole of a suitable single-electron
wavefunction is adapted to a general N-electron system by
examining the short-range behavior of the exchange hole.
Recently, a similar approach has been used to deve... | {
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005e8e1984882515c4a8e340f529fcbb1b23282d | subsection | 3 | 7 | Body | ()]and the single-electron ring radius r_0 and width \Delta r (see the inset).The curves correspond to fixed values of M.]we show explicitly the relation between the single-electron
radius and width of the QR (r_0,\Delta r) and the parameters
(M,\alpha ) in the external confining potential given in Eq. (REF ).The exact... | {
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"C. R. Proetto",
"E. K. U. Gross"
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ecfa57c8f17bfe378cf235a8bd31535d2071acf3 | subsection | 4 | 7 | Body | To summarize our method, the calculation of the
exchange energy of an N-electron QR consists of the following steps:(1)
Use the KS orbitals \psi _{k,\sigma } to
calculate the spin densities \rho _{\sigma },
the local curvature of the exchange hole C^{\sigma }_x from
Eq. (REF ), and to estimate M^*.
(2)
Compute y(r) num... | {
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"C. R. Proetto",
"E. K. U. Gross"
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aae7091d5155c817536200ece17e34176189fc16 | subsection | 5 | 7 | Body | The
inability of the LSDA to yield the correct shape of the curve
is due to the simple density-dependent expression of the
exchange energy per particle in the LSDA,
i.e., \epsilon ^{\rm LSDA}_{x,\sigma }\propto \rho _{\sigma }^{1/2},
leading to differences also in the exchange energy.
In the case of Fig. REF (a), we fi... | {
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"E. Rasanen",
"S. Pittalis",
"C. R. Proetto",
"E. K. U. Gross"
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4f9e3431df9bfe8d82fc6a1a73cc540f32be4832 | subsection | 6 | 7 | Body | We find that in
the latter case the agreement with the EXX is better.To conclude, we have derived, from first principles, an accurate
and general approximation
for the exchange-hole potential and hence for the exchange energy
in quantum rings.
Excellent agreement with the exact-exchange results is obtained
regardless o... | {
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c3285018a8fa11119f2fc34049c8fdf15ae3aed3 | abstract | 0 | 11 | Abstract | We study the chaotic behavior of the synchronization phase transition in the
Kuramoto model. We discuss the relationship with analogous features found in
the Hamiltonian Mean Field (HMF) model. Our numerical results support the
connection between the two models, which can be considered as limiting cases
(dissipative an... | {
"cite_spans": []
} | 10.1209/0295-5075/85/10007 | 0807.1870 | Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators | [
"G. Miritello",
"A. Pluchino",
"A. Rapisarda"
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b5be075dbb3418b2bebe9f870724c5c67ff7b4c7 | subsection | 1 | 11 | Introduction | Long-range interacting systems have been intensively studied
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One of the most promising directions is the combination of
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9ce36ac49132058edacde1207e3445875ee93d39 | subsection | 2 | 11 | Phase transition and chaos in the HMF model | The Hamiltonian Mean Field model describes the dynamics of N classical spins or rotators,
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0a54a1a0cb3069f37a8ec1ef48dd6b374d118a48 | subsection | 3 | 11 | Phase transition and chaos in the HMF model | It is well known that in classical many-particle systems macroscopic collective behavior
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8de0bb172881355e169241c66943cae308b15dd2 | subsection | 4 | 11 | Phase transition and chaos in the Kuramoto model | The Kuramoto model , , is considered one of the simplest models
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399f5b89a10b7193f892071a2eaa8f636ca8923e | subsection | 5 | 11 | Phase transition and chaos in the Kuramoto model | For a given value of K, as the population becomes more coherent, r grows and the effective
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2e19c7984c1ccb39453d2a4b0b9c0c8c39cb7efe | subsection | 6 | 11 | Phase transition and chaos in the Kuramoto model | One immediately recognizes a different kind of transition: a continuous (2nd-order-like) one, for the Gaussian g(\omega ) (Fig.2) and an abrupt (1st-order-like) one, for the uniform g(\omega ) (Fig.3). Correspondingly,
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0701ffb56baf6c756274b6b45f1291eee19a1410 | subsection | 7 | 11 | Phase transition and chaos in the Kuramoto model | On the other hand, compared with those of Fig.1, the plots of Fig.2 seem to indicate
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3a062c61bea61d62c439e1a70e759b89fafb455e | subsection | 8 | 11 | Phase transition and chaos in the Kuramoto model | In the insets, the bounded g(\omega ) distributions (with \omega \in [-3,3]) used in the simulations are plotted for three increasing values of \sigma .See text.]We conclude this section by showing that, although it is believed that for strictly unimodal g(\omega )
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7273429e19103a2cf159258b81d2d367f90e5824 | subsection | 9 | 11 | Phase transition and chaos in the Kuramoto model | Despite the different context, we think that this analogy
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4683e3fa8588404d2bf0bb7ffc22564fa50ef3dc | subsection | 10 | 11 | Conclusions | We presented new numerical evidence of the presence of chaotic behavior
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5eaeb1eb04459c085755ef027ce49ea607b7a355 | subsection | 1 | 19 | Introduction | Stronger regulations concerning pollutant emissions led to the development of new generations of swirl burners stabilizing lean premixed flames well suited to reach low NOx levels .
Swirling motion permits to improve the mixing rate between fuel and oxidant streams and to control the flame stabilization through the swi... | {
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"raw": "S. Correa. Power generation and aeropropulsion gas turbines: From combustion science to combustion technology. Proceedings of the Combustion Institute, 27:1793–1807, 1998.",
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injector using high frequency PIV | [
"Séverine Barbosa",
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"Sébastien Ducruix"
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faee9f6c080590c08f131796d507042d79c77175 | subsection | 2 | 19 | Introduction | For the last 20 years, the development and improvement of PIV have proceeded in several stages, related to the technical progresses successively achieved in the fields of lasers (double-pulsed solid-state lasers), cameras (now holding two images recorded in rapid succession) and computers (for post-processing) . The st... | {
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injector using high frequency PIV | [
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afeb3dd0676998989fe1dd3be6a8fc5abfa6370b | subsection | 3 | 19 | Experimental Configuration | Figure REF shows a schematic diagram of the experimental injector. The setup is composed of a two-staged swirled injector, representative of a gas turbine injector, supplied with propane and air and a rectangular combustion chamber.
[Figure: Schematic view of the experimental injector.]The primary stage consists in a c... | {
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} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
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f8e41b549e73cdcbaefd4839e4bc5aca8ae42c56 | subsection | 4 | 19 | HFPIV measurements | A High Frequency Particle Image Velocimetry (HFPIV) system is used to measure velocity flow fields in the combustion chamber. A schematic view of the experimental burner and the PIV system are reported on figure REF .
[Figure: Schematic view of the experimental combustor and the PIV system.]For such experiments, the to... | {
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"source_ref... | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
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"Sébastien Ducruix"
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0f879c16d735f7519c8f99b9c0367851416d10f3 | subsection | 5 | 19 | Post-processing | For each experiment, a continuous acquisition of N = 12 000 image pairs (24 000 raw images) corresponding to a physical time of 1 second has been performed. The instantaneous velocity fields associated with the N image pairs are processed to determine the mean velocity components U_{mean} and V_{mean} and the RMS veloc... | {
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injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
] | [
"physics.flu-dyn"
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b107516e075807e5f426b19f61f55bf5a65e1ede | subsection | 6 | 19 | Post-processing | As {S}^2 + {\Omega }^2 is symmetric, it has only real eigenvalues ordered as follows \lambda 1 > \lambda 2 > \lambda 3. According to this criterion, a local minimum of the \lambda 2 field is associated with the local pressure minimum that is met in the vortex core. The study of the \lambda 2 field permits to discrimina... | {
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... | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
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"Sébastien Ducruix"
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12d6ca4a7e978a7fc453b080386ebe2800189f6a | subsection | 7 | 19 | Post-processing | The detection algorithm provides the center of the vortices that are detected, assuming that each vortex center coincides with a local maximum of |W|. This makes it possible to estimate the velocity distribution around the vortices and their convection speed. The convection (or transport) velocity of a structure (u_{c}... | {
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... | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
] | [
"physics.flu-dyn"
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bcd2813a6bacdbd5647819215a64e35e92c02b40 | subsection | 8 | 19 | Operating conditions | The HFPIV diagnostic is tested for the operating conditions reported in table REF .
[Table: Operating Conditions. \bf {(\textrm {Q}_{C3H8})_{prim}} and \bf {(\textrm {Q}_{C3H8})_{sec}} are the fuel flow rates injected respectively in the primary and the secondary stages, while \bf {\textrm {Q}_{air}} is the global air ... | {
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injector using high frequency PIV | [
"Séverine Barbosa",
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400ebef9708261a503ebaa1067d847aa1af5d1ca | subsection | 9 | 19 | Operating conditions | It is expected from PIV measurements to gain insight into the dynamical coupling leading to combustion instabilities.Once the flow reaches a steady state and the flame is well stabilized in the combustion chamber, PIV images are acquired in the combustion chamber downstream the injection plane.
Two complementary region... | {
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... | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
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5e283662081a512c08a33f3a2d79db3ce9d3f385 | subsection | 10 | 19 | Mean flow field | The mean axial and radial velocities, measured in a plane placed on the chamber axis, are reported on figure REF . The top of this vertical observation area is at the distance y^*= 0.87, while the top (resp. the bottom) of the chamber is at a distance of y^* =1 (resp. y^* = -1) and the edges of the injector are situate... | {
"cite_spans": []
} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
] | [
"physics.flu-dyn"
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1d263edd63bfde0d924ecd4a6b79a11684280cca | subsection | 11 | 19 | Mean flow field | Profiles of U_{rms}, plotted in figure REF , are symmetric around y^* = 0. U_{rms} presents maxima on each side of the chamber at y^*\approx \pm 0.43, i.e where the mixing region between the central recirculation zone and the positive streamwise velocity flow is located. Two secondary peaks, which are associated with a... | {
"cite_spans": []
} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
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1e80f7148724629916dd73632c1c2679d1bcb08a | subsection | 12 | 19 | Mean flow field | Profiles obtained with the vertical observation area ("region 1") are plotted in gray and the ones obtained with the horizontal observation area ("region 2") are plotted in black.]Using this recording, the evolution of the maximum of U_{mean} in each vertical cut is plotted in figure REF as a function of the reduced ax... | {
"cite_spans": []
} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
] | [
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b447eff6342d642cc43e6dc3c657999a9b7b23bf | subsection | 13 | 19 | Calculation of the flow rate injected | In order to check the coherence of the experimental results, the fluid flow rate in the combustion chamber is calculated using the axial velocity measured experimentally using HFPIV. The fluid flow rate is estimated using the radial distribution of Umean, taken at a distance of x^* = 0.06, so that the result is less di... | {
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} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
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d0b26ad553efd9088c74d01e087a261f95a33641 | subsection | 14 | 19 | Analysis of instantaneous flow fields | A temporal analysis of the velocity field is carried out in the regime defined in table REF . A serie of six successive instantaneous velocity vectors and their associated vorticity field are displayed in figure REF . The views are taken on the vertical symmetry axis of the combustion chamber (y^* = 0). A time delay of... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 2122,
"openalex_id": "",
"raw": "J. Jeong and F. Hussain. On the identification of a vortex. J. Fluid. Mech, 285:69–94, 1995.",
"source_ref_id": "abd365f09c882d4092dcafcd4a9cad79e8115737",
"start": 1979
}
]
} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
] | [
"physics.flu-dyn"
] | 2,008 | en | Physics | [
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20218fa065da2980382d7e7d08284405d55e0a34 | subsection | 15 | 19 | Vortex detection | Figure REF shows the \lambda 2 fields, analyzed with the wavelet transform, for the six velocity fields of figure REF . The \lambda 2 criterion is not sensitive to shear regions, on the contrary to vorticity. Several peaks of \lambda 2 are detected and the structure cited in the previous paragraph (figure REF ) is visi... | {
"cite_spans": []
} | 0807.1871 | Characterization of the reactive flow field dynamics in a gas turbine
injector using high frequency PIV | [
"Séverine Barbosa",
"Philippe Scouflaire",
"Sébastien Ducruix"
] | [
"physics.flu-dyn"
] | 2,008 | en | Physics | [
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