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f69cdd2cb42e9a5129b28218f98ce90ddc8d54a3 | subsection | 2 | 23 | Introduction | A warped disc makes it possible for the
radiation from the inner disc to reach the outer parts, enhancing
the reprocessing emission lines. Thus, this warping can solve the
long-standing energy-budget problem because the subtending angle of the
outer disc portion to the inner part has been increased by
the warp. It can ... | {
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... | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
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2859578638f9e501dbb2361820f5f09bb80f25d9 | subsection | 3 | 23 | Assumptions and Method of Calculation | In this paper, we will focus on how a warped disc affects the
optical emission-line profiles, such as H\alpha and H\beta .
A geometrically thin disc and a central point-like source of
ionizing radiation around a black hole are assumed. | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
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c065f0932742580de477e75dc35518e0b13f35ec | subsection | 4 | 23 | Geometrical considerations | The disc can be treated as being composed of a series of concentric
circular rings of increasing radii, and laying in different planes.
The rings interact with each other via viscous stresses. Each ring is
defined by two Eulerian angles \beta (R,t) and \gamma (R,t) (see Fig.1)
at radius R, where \beta (R,t) is the tilt... | {
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... | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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8cfaca05423cd31ac7bcbfa2d943e034bdc78cb1 | subsection | 5 | 23 | Geometrical considerations | The element of surface area is{\rm d}\mbox{$S$}=\left({{\partial \mbox{$R$}}\over {\partial R}}\,{\rm d}R\right)
\times \left({{\partial \mbox{$R$}}\over {\partial \phi }}\,{\rm d}\phi \right),by calculating these partial derivatives directly and after some
algebra which simplifies to{\rm d}\mbox{$S$}=\left[\mbox{$l$}+... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
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6f814f0244a412fc370bd8ce83d81c1d5179889b | subsection | 6 | 23 | Geometrical considerations | The two formalisms described
above can be related by the formulah(r,\varphi )&=&-R\sin \beta \cos \phi \\
&=&-R\sin \beta \cos \psi \big /\sqrt{1-\sin ^2\beta \sin ^2\psi }\\
&=& -r\tan \beta \cos \psi .Where \psi = \varphi -\gamma and satisfies\tan \phi \,=\,\tan \psi \cos \beta .Since it is difficult to calculate ana... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
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c8913b4146446fb853b7f8a71c7b3d4e822d118f | subsection | 7 | 23 | Photon motions in the background metric | The propagation of radiation from the disc around a Kerr
black hole and the particle kinematics in the disc were studied by many
authors , .
We review properties of the Kerr metric and formulae for
its particle orbits, and summarize here the basic equations relevant
to this paper. Throughout the paper we use units in w... | {
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... | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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f60016d2ae346b28c5db51d77a8fe46b12365cf2 | subsection | 8 | 23 | Photon motions in the background metric | The \phi coordinate along the trajectory is calculated by
, \int _{\phi _e}^{\phi }{\rm d}\phi =
\int _{\theta _e}^\theta \frac{\lambda {\rm d}\theta }{\sin ^2\theta \sqrt{\Theta (\theta )}} + \int _{r_e}^r \frac{(2ar-\lambda a^2){\rm d}r}{\Delta \sqrt{R(r)}}.Consider the orbit equation in the form\int _{r_{ms}}^r \fra... | {
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... | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
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ec3b07c827b8cde4288dd388d63816f1a75f3d03 | subsection | 9 | 23 | Photon motions in the background metric | Owing to a
spherically symmetric metric there is no favored direction for the black hole;
in this sense, \vartheta _{\rm o} can be acted as the angle between the
observer and the normal to the disc and is determined by taking the
dot-products of the unit vector \mbox{$l$} of the disc with the normalized
vector \mbox{$i... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
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049bef9332dd53b026112f3d21f493b9f2ba973f | subsection | 10 | 23 | Photon motions in the background metric | From this equation, the angle is determined by\tan \phi _{\rm o} = \frac{\sin \gamma \sin i}{\sin \beta \cos i -
\cos \beta \cos \gamma \sin i}.The photon motion equations are given by :\int _{r_e}^r \frac{dr}{\sqrt{R(r)}} = \pm \int _{\vartheta _e}^\vartheta \frac{d\vartheta }{\sqrt{\Theta (
\vartheta )}} \;,\int _{\p... | {
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... | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0764ca36a0093e6312b42747968bf5610691d735 | subsection | 11 | 23 | The observed line flux | Due to relativistic effects, the photon frequency will shift from
the emitted frequency \nu _{\rm e} to the observed one \nu _{\rm o}
received by a rest observer with the hole at infinity. We introduce
a g factor to describe the shift which is the ratio of observed
frequency to emitted one:g & = & \nu _{\rm o} / \nu _{... | {
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} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
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1c5046ed549f25891b9afe7efce65b270f722feb | subsection | 12 | 23 | The observed line flux | From
well-known transformation properties of \delta -functions we have
\delta (\nu _{\rm e}^{\prime }-\nu _{\rm e})=g\delta (\nu _{\rm o}-g\nu _{\rm e}),
using this in equation (REF ), we obtainF_{\rm o}(\nu _{\rm o}) = \int \varepsilon g^4 \delta (\nu _{\rm o} -
g\nu _{\rm e}) d\Omega _{\rm obs}\;.In order to calculat... | {
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"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
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baf498f338328bd2df7563ffac0f9f2f7ecb625c | subsection | 13 | 23 | The observed line flux | Here \cos \theta _i = h(r_i<r,\varphi _i)/r_i, \varphi _i
and \cos \theta (r_i,\varphi _i) are calculated by equations (REF )
and (REF ), respectively:\varphi _i = \varphi - \int _{r_i}^r \frac{2ar{\rm d}r}{\Delta \sqrt{R(r)}},\cos \theta (r_i,\varphi _i) = \mu _+{\rm cn}(a\sqrt{\mu _+^2 + \mu _-^2}P - K(m)|m) \;,Equat... | {
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"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
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3fb0898935862ecb3e364e3eff0bc197fd7fca3b | subsection | 14 | 23 | Method of calculation | With all of the preparation described in the previous section, we
now turn to how to calculate the line profiles numerically. We
divide the disc into a number of arbitrarily narrow rings, and
emission from each ring is calculated by considering its
axisymmetry. We shall denote by r_{\rm i} the radius of each
such emitt... | {
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"Sheng-Miao Wu",
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"Xiao-Bo Dong"
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7cce450702e2ac77cfaa042f8b7d44e33d3f5c78 | subsection | 15 | 23 | Method of calculation | The contribution of each element
denoted by (r_{\rm i},g) to the total line flux from the disc is calculated by
equation (REF ) only in the case that there does not exist another element with
\cos \theta _i > \cos \theta (r_i,\varphi _i) along the ray path, and is zero in the
opposite case. Here \cos \theta _i = h(r_i,... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
"Ting-Gui Wang",
"Xiao-Bo Dong"
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d97e471d979cbe5d18d1e36fc2da827d0fbfa5b1 | subsection | 16 | 23 | Results | In the accretion disc model, the double-peaked emission lines are
radiated from the disc region between around several hundred
gravitational radii to more than 2000r_g; here r_{\rm g} is the
gravitational radius and the widths of double-peaked lines range
from several thousand to nearly 40,000 \rm km\,s^{-1}
. In our m... | {
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"Sheng-Miao Wu",
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1b3d61ffeadd4aae3c6d30a4782068b9ec7f49ac | subsection | 17 | 23 | Line profiles from twisted warping discs | We extend the numerical code developed by to deal with
the warped discs. The images of the illuminated area and the
H\alpha line profiles computed by our code for a steady-state
twisted warping disc are shown in Figs REF and REF .
The disc zone is from R_{\rm in}=100r_{\rm g} to R_{\rm out}=
1000 r_{\rm g}, the other p... | {
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"Sheng-Miao Wu",
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"Xiao-Bo Dong"
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0bd1c03b45b3e4abdec9baf16556d199ca490545 | subsection | 18 | 23 | Line profiles from twisted warping discs | REF . The fraction reaches
27.3 per cent for a twisted warp disc n_1=2.0\pi , n_2=3.0, n_3=20^{\circ }.
[Figure: The fraction of light incident to the disc from the inner regionas a function of n_1 or n_3. The disc zone is from R_{\rm in}=250r_{\rm g}to R_{\rm out}= 1000 r_{\rm g}.] | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
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6488040b8e0967077827f356bfc85a82838644e3 | subsection | 19 | 23 | Comparison with the observations | As the first step, our main purpose in this paper is to demonstrate the
effect of disc warping on the line profiles, while the detailed fitting of
the observational data will be presented in a future paper. From the sample
of AGN with double-peaked Balmer lines drawn from the Sloan Digital Sky
Survey (SDSS) spectroscop... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
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"Xiao-Bo Dong"
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61e4da9270bf3a5818b8babba4e6f6789f87b4e1 | subsection | 20 | 23 | Comparison with the observations | The parametersare: i=10^{\circ },\; n_1=2.6\pi ,\;n_2=3.0,\;n_3=22^{\circ },\; \gamma _0 =88^{\circ }, the disc zone is from R_{\rm in}=250r_{\rm g}to R_{\rm out}= 1000 r_{\rm g} for a prograde disc.]A retrograde disc is needed to match the line profiles with the observations
for SDSS J094321.97+042412.0, J093653.84+53... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
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4ca7da0f995a9d6ba4f7676b641884439f90f257 | subsection | 21 | 23 | Comparison with the observations | REF the parameters of the disc are: i=10^{\circ },\; n_1 =
2.6\pi ,\; n_2=3.0,\; n_3=22^{\circ }, R_{\rm in}=250r_{\rm g}, R_{\rm out}
= 1000 r_{\rm g} for a prograde disc. The longitude of the observer
\gamma _0 from top left-hand side to bottom right-hand side takes steps
of 10^{\circ } from 30^{\circ } to 140^{\circ... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13538.x | 0807.1787 | Broad reprocessed Balmer emission from warped accretion discs | [
"Sheng-Miao Wu",
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f70b100448438c7a7433c1ba384c3406e326c73a | subsection | 22 | 23 | Summary | We compute the reprocessing emission-line profiles from a warped
relativistic accretion disc around a central black hole by including all
relativistic effects. A parametrized disc model is used to obtain an
insight into the impact of disc warping on the double-peaked Balmer
emission-line profiles. For simplicity, we as... | {
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ed26fb9ebd75c36f64a8940958e41385b1c91572 | abstract | 0 | 15 | Abstract | The water flow through the poly(acrylamide) gel under a constant water
pressure is measured by newly designed apparatus. The time evolution of the
water flow in the gel, is calculated based on the collective diffusion model of
the polymer network coupled with the friction between the polymer network and
the water. The ... | {
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"Yasuo Y. Suzuki",
"Masayuki Tokita",
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4e1c5266d5fe65fa62ff7227662f7d57ffb08243 | subsection | 1 | 15 | Introduction | The gel is an important state of matter that is found in a wide
variety of biological, chemical, and food systems . The polymer
gel consists of a cross-linked polymer network and a large amount of
solvent (typically water). Since the average mesh size (the distance between neighboring
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dc1a0dc2f6f35a2bebc926224e17670bcc7c5ec8 | subsection | 2 | 15 | Water flow measurements | The experimental setting of the water flow measurements is illustrated schematically in Figure 1.
[Figure: Experimental setting of water flow measurements]A thin circular slab gel of thickness, L, is set in a tube and the rim of the gel is glued to the tube.
The surface of the gel at the lower reaches side is
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b44f32cf8cd23de78dacf288244ddb6358cf462a | subsection | 3 | 15 | Mechanical response measurements | The mechanical response of the polymer gel relates
the friction coefficient to the collective diffusion coefficient of the polymer network
as D_{c}= \kappa /f where \kappa = K+ \frac{4\mu }{3} .
Here, \kappa is the longitudinal modulus of the gel
and K and \mu are the bulk modulus and the shear modulus
of the gel, resp... | {
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} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
"cond-mat.soft",
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21f9ed2121160e073e6b86885318dfe8b0742083 | subsection | 4 | 15 | Sample | The samples used in this paper are poly(acrylamide) gel that is obtained by the
radical co-polymerization of the main-chain component, acrylamide, and
the cross-linker, N,N'-methylene-bis-acrylamide. The concentration of
the gel used in this measurement is 1 M. Ammoniumpersulfate and
N,N,N',N'-tetramethyl-ethylenediami... | {
"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
"cond-mat.soft",
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de9e2647beaa6105024d6b6daa8858a3c5a855cb | subsection | 5 | 15 | Friction coefficient of gel | The experimental results of the measurement of water flow through
the gel are shown in Figure 3.
[Figure: Position of meniscus in capillary fit by equation () with a and bas adjusted parameters.]The position of the meniscus in
the capillary of 10 \mu l glass micro-pipette is plotted as a
function of the time elapsed af... | {
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} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
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cf0b1857730afdc07ee0837cff3f6ef5240f157b | subsection | 6 | 15 | Elastic modulus of gel | In Figure 4, we show the concentration dependence of the Young's
modulus and the Poisson's ratio of the gels used in our experiment.
[Figure: Concentration dependence of elastic moduli: (a) the upper graph shows Young's modulus, E, (b) the lower graph shows Poisson's ratio, \sigma .]The least-squares analysis of the re... | {
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... | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
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55a2f0c4a9ac6295b24420d293a4732fba4486c1 | subsection | 7 | 15 | Kinetics of water flow through gel | When the water flows in the gel (polymer network) by the application of the
mechanical pressure, the polymer network of gel deforms from the
initial position by the drag force of the water flow.
We introduce a function, u(x,t), that represents the
displacement of a point in the polymer network from its initial
position... | {
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"... | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
"cond-mat.soft",
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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96abcd417ae78e608384b5f474a2b62f1f729b1c | subsection | 8 | 15 | Kinetics of water flow through gel | In the equilibrium state, therefore, equations (REF ), (REF ), (REF ), (REF ) give\frac{\partial ^2 u(x, t= \infty )}{\partial x^2} = - \frac{P_0}{D_{c}Lf}.The displacement, u(x, t), satisfies the following boundary conditions:u(L,t) &=& 0,\\
\frac{\partial u(0, \infty )}{\partial x} &=& 0.Integration of equation (REF ... | {
"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
"cond-mat.soft",
"cond-mat.mtrl-sci"
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68fc0a9de6216922201031578d8747acc47547ae | subsection | 9 | 15 | Discussion | Now we compare the experimental results with the theoretical predictions
by equations (REF ) and (REF ). The values obtained by
the experimental measurements are, L = 1.0 \times 10^{-3} m, \kappa = 4.1 \times 10^{4} N/m^{2}, and f = 6.6 \times 10^{14}
Ns/m^{4}, respectively.By applying these values into
equation (REF )... | {
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... | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
"cond-mat.soft",
"cond-mat.mtrl-sci"
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5d0990dbd8502f389de0733efb87da45e594c911 | subsection | 10 | 15 | Conclusion | The kinetics of the water solvent flow through
the polymer network of gel is measured experimentally and described by a simple
phenomenological theory. The experiment shows that the equilibrium state is
reached after long time and that the friction of the gel shows a large value.
The time evolution of the velocity of t... | {
"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
] | [
"cond-mat.soft",
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61e7f1c519e800b6e50ea5a24f3afbc6a5093957 | subsection | 11 | 15 | APPENDIX A: Solution of the equation of motion | We define a function W(x, t) as a deviation from the equilibrium displacement:u(x, t) -\int v(t) dt \equiv W(x,t) + u(x, \infty ).We obtain an equation for W(x,t) from equation (REF ) as\frac{\partial W}{\partial t} = D_c \frac{\partial ^2 W}{\partial x^2}.By assuming W(x,t) = X(x)T(t), the equation (REF ) becomes\dot{... | {
"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
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"cond-mat.soft",
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0d13b403855035af0e9851f333889e4d1b3a315b | subsection | 12 | 15 | APPENDIX A: Solution of the equation of motion | \sum _{n=1}^\infty [A_n \cos \lambda _n x ](-\lambda _n^2 D_c) \exp (- \lambda _n^2 D_c t) \right|_{t=\infty } +A_0 \\
&=& v(\infty ).This indicates that the constant, \lambda _n^2, should be positive, \lambda _n^2 > 0 for n\ge 1 and A_0=v(\infty ).
Finally, the boundary condition () yieldsW(L, t) &=& \sum _{n=1}^\inft... | {
"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
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d08af1c82628ffbecaa8587a542ecf78630c4ac4 | subsection | 13 | 15 | APPENDIX A: Solution of the equation of motion | The following relationships for B_n, \lambda _n^2, and C_{nA} are obtained:B_n &=& 0, \\
\lambda _n^2 &>& 0, \\
C_{nA} &=& - \cos \lambda _n L.And W(x,t) becomesW(x,t) = \sum _{n=1}^{\infty } [A_n (\cos \lambda _n x + C_{nA})] \exp (-\lambda _n^2 D_c t).Substitution of this solution (REF ) into equation (REF ) yields& ... | {
"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
"Sata-atsu Mukai"
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02579ab9c96c553c028ee6596be6a451b8ca5eac | subsection | 14 | 15 | APPENDIX A: Solution of the equation of motion | \frac{1}{L} \sum _{n=1}^{\infty } (- \lambda _n^2 D_c) \frac{1}{\lambda _n} (A_n \sin \lambda _n x) \exp (-\lambda _n^2 D_c t) \right|_0^L\\
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"cite_spans": []
} | 10.1140/epje/i2009-10494-6 | 0807.1789 | Kinetics of water flow through polymer gel | [
"Yasuo Y. Suzuki",
"Masayuki Tokita",
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36d03f28e934f4dba7e75864392ffcce9e110837 | abstract | 0 | 4 | Abstract | The Fano-Snowflake, a specific $non$-unimodular projective lattice
configuration associated with the smallest ring of ternions $R_{\diamondsuit}$
(arXiv:0803.4436 and 0806.3153), admits an interesting partitioning with
respect to the Jacobson radical of $R_{\diamondsuit}$. The totality of 21 free
cyclic submodules gene... | {
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dd03bd8f35e2a28c6851be2af16cd17f2e1f1490 | subsection | 1 | 4 | Body | A Jacobson Radical Decomposition of the Fano-Snowflake
ConfigurationA Jacobson Radical Decompositionof the Fano-Snowflake
ConfigurationMetod SANIGA ^\dag and Petr PRACNA ^\ddagM. Saniga and P. Pracna^\dag Astronomical Institute, Slovak Academy of
Sciences,^\dag SK-05960 Tatranská Lomnica, Slovak Republic
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6818725d839b890650a6c93a73c11f3cbead8ab6 | subsection | 2 | 4 | Body | We consider an associative ring with unity 1 (\ne 0), R, and denote the free
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R(r_1, r_2,\dots , r_{n+1}), defined as followsis a left cyclic submodule of R^{n+1}. Any such submodule
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ef650834bce4782d4d1ff90540da044f201dfd43 | subsection | 3 | 4 | Body | Note a principalqualitative difference between the two factorizations, since the three sets (factors) are pairwise disjoint in the latter case but not in the former one.]The origin of the factorization of the Fano plane when related to
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03ce01443ed97938a6c12d5d2576d8b3fcf8ce4c | abstract | 0 | 26 | Abstract | We compare and contrast the computations that lead to the NMSGUT spectra and
Yukawa couplings that appeared\cite{nmsgut} in 2006 and a recent recalculation
of the same\cite{malinsky}. We argue that an explicit component based method of
computation jeopardizes the power of SO(10) and its sub-groups to organize, in
a uni... | {
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48b005a81c3113ddb6e24906aaa1c79c16787661 | subsection | 1 | 26 | Introduction | Since the discovery of neutrino mass in the late nineties, SO(10)
GUTs and particularly Supersymmetric SO(10) GUTs have become the
leading contenders for unification. We had
constructed the (renormalizable and
non-renormalizable) Minimal Supersymmetric Left Right
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820681a3fa761ca0c5da5156f4330595f4faacf0 | subsection | 2 | 26 | Introduction | Indeed
already the second version, in August 2003 , of our
manual on SO(10) decomposition (which we delayed sending to press
till 2005 in order that it retain as few calculational mistakes
and typos as possible) contained the Clebsches of the matter
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36b68708f873cea1dbeddb068c90b018aac58387 | subsection | 3 | 26 | Introduction | Indeed, using the very spectrum, Clebsch and Yukawa
couplings that we had computed in , we were able to
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359ad282fbf5c8034269423001a485f03f9f73e7 | subsection | 4 | 26 | Introduction | Due to the
importance of the basic framework for clarity in this complex
subject, we thought it behooved us to point out once again the
virtues of our method and the simple and correct prescription to
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2c1856747acac177dc07609a14300aa0739cff22 | subsection | 5 | 26 | Comparison of paper contents | Before proceeding let us first see the relation to our
previous work, and the notice he had of it, that author himself
gives in a Note Added at the end of his paper.“A day before finishing this manuscript the author's attention
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57764d1b1cbea23f4daeb81ea28358bb78aa2816 | subsection | 6 | 26 | Comparison of paper contents | The author also claims that “the current
study is certainly much more detailed ...... on top of that, a lot
of extra information provided in Sections IV)Higgs Sector Mass
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459443cb5e0fa496b30d1dac5fcea2d4b54415dd | subsection | 7 | 26 | Comparison of paper contents | As we shall explain below the
confusion in concerning the correct procedure to
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fb5abc01bf1b3e9b215fc41266444943266ba82c | subsection | 8 | 26 | Comparison of Methods and Results | The crux of the method used in and antecedent
papers can be appreciated by first quoting from
what he sees as the determining rationale of his method (our
italics and our text-compactifying interpolations in square
brackets): “For sake of illustration let us remark that there is
in total 13,321,010 terms in the sums i... | {
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"raw": "M. Malinsky, “Higgs sector of the next-to-minimal renormalizable SUSY SO(10),” arXiv:0807.0591 [hep-ph].",
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51a9e86727a67b7a509849437a81ba66cd5cad39 | subsection | 9 | 26 | Translation from SO(10) vector to PS labels | We have adopted the rule that
any submultiplet of an SO(10) field is always denoted by the
same symbol as its parent field, its identity being
established by the indices it carries or by supplementary indices,
if necessary. Our notation for indices is as follows : The indices
of the vector representation of SO(10) (som... | {
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} | 0807.1792 | Babel on the Petaplex site: On Rival Calculational methods in SO(10)
MSGUTs | [
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762cafb27ce194c51641f49fe9beeebe6db3c3e8 | subsection | 10 | 26 | SO(6) | Vector/Antisymmetric:The 6 dimensional vector representation of SO(6) denoted
by V_a
(a=1,2,..,6) transforms asV^{\prime }_a=(exp {{\frac{i}{2}}\omega ^{cd}J_{cd}})_{ab}V_bwhere the Hermitian generators J_{cd} have the explicit form(J_{cd})_{ef}=-i\delta _{c[e}\delta _{f]d}and thus satisfy the SO(6) algebra (square bra... | {
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422f5fffa1afc8bac9907af37c78430139110404 | subsection | 11 | 26 | SO(6) | In other words, if one
defines V_{\mu \nu }=\Theta _{\mu \nu }^{\hat{a}} V_{\hat{a}} with
\Theta _{{\bar{\mu }} 4}^{\hat{a}}=\delta ^{\hat{a}}_{\bar{\mu }},
\Theta _{{\bar{\mu }}{\bar{\nu }}}^{\hat{a}} =
\epsilon _{\bar{\mu }\bar{\nu }\bar{\lambda }}\delta ^{\hat{a}}_{\bar{\lambda }^*}, then since \Theta _{\mu \nu }^{\... | {
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} | 0807.1792 | Babel on the Petaplex site: On Rival Calculational methods in SO(10)
MSGUTs | [
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6e416b11de2f9732a862d665c13e81256c29b710 | subsection | 12 | 26 | Body | Vector/BidoubletWe use early
greek indices { \tilde{\alpha }, \tilde{\beta }=7,8,9,10} for the vector of SO(4)
corresponding to {i,j=7....10} of the 10-plet of SO(10). The
Hermitian generators of SO(4) have the usual SO(2N) vector
representation form :
{(J_{\tilde{\alpha }\tilde{\beta }})_{\tilde{\gamma }\tilde{\delta ... | {
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75f21a019e2be014c390b9b3bd24a71362a93cd3 | subsection | 13 | 26 | Body | Then one hasV_{\hat{7}}&=& V_{\bar{4}}= {{(V_7+iV_8)} \over \sqrt{2}}=V_{2\dot{2}}
~,~ V_{\hat{9}}= V_{\bar{5}}=
{{(V_9+iV_{10})}\over \sqrt{2}}=V_{1\dot{2}}\\
V_{\hat{8}}&=& V_{\bar{4}^*}={{(V_7-iV_8)} \over \sqrt{2}}=-V_{1\dot{1}}~,
~V_{\widehat{10}}\equiv V_{\hat{0}}= V_{\bar{5}^*}={{(V_9-iV_{10})}\over \sqrt{2}}=V_... | {
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6375b3117419df8098208b00f9bb49bf91348494 | subsection | 14 | 26 | SO(6) Spinors | The 4(\psi _\mu ) and \bar{4}(\widehat{\psi }^\mu ) of SU(4) may be
consistently identified with the 4_{-},4_{+} chiral spinor
multiplets of SO(6) by identifying components {\psi _\mu } of the
4 with the coefficients of the states
|\epsilon _1\epsilon _2\epsilon _3>_{-} in 4_{-}=|\psi >_{-} as|\psi >_{-}=\psi _{1}|-++>... | {
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70cbc011e48b899e21f8ef94085c5f64d20fdf92 | subsection | 15 | 26 | SO(6) Spinors | For example (we take \psi ,\chi to be non-chiral
8=4_{+}+4_{-} spinors to preserve generality)In this basis one has in the 8 dimensional spinor rep. of SO(6)exp({{i\omega ^{ab}J_{ab}}\over 2}) = Diag {\big (}
exp({{i\theta ^A \lambda ^A}\over 2}) , exp({{-i\theta ^A
\lambda ^{A*}}\over 2}){\big )}One finds
the followin... | {
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MSGUTs | [
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dc3ee36642b95f4aef7a7fcb7362f6aa1848f9d3 | subsection | 16 | 26 | SO(6) Spinors | See
the appendix of for useful translations of SO(6)
spinor-tensor invariants calculable from these identities . | {
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d7f0b057f33cf232348ffe2ced2f228791b932d5 | subsection | 17 | 26 | SO(4) Spinors | In the case of SO(4) the spinor representation is 4
dimensional and splits into 2_+\oplus 2_-. It is not hard to see
that with the definitions adopted for the generators of
SU(2)_{\pm } the chiral spinors 2_{\pm } may be identified with
the doublets {\psi _{\alpha },\psi _{\dot{\alpha }}} of
SU(2)_{-}=SU(2)_L and SU(2)... | {
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e6f4b58cd7bd5164a9ba46db202831c91392c4f2 | subsection | 18 | 26 | SO(4) Spinors | Then in that basisC_{2}=\left(\begin{array}{cc}
\epsilon ^{\alpha \beta } & 0_{2}\\ 0_{2} & -\epsilon ^{\dot{\alpha }\dot{\beta }}
\end{array}\right)~,~C_{1}=-\left(\begin{array}{cc}
\epsilon ^{\alpha \beta } & 0_{2}\\ 0_{2} &
\epsilon ^{\dot{\alpha }\dot{\beta }}\end{array}\right)~,
~[\gamma _{\rho \dot{\rho }}]=\sqrt... | {
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04b22cda29857314c4ae5dda742512bbfbd2446f | subsection | 19 | 26 | SO(10) Spinors | The spinor representation of SO(10) is 2^5 dimensional and
splits into chiral eigenstates with \gamma _F=\pm 1 as2^5&=&2^{4}_{+}+2^{4}_{-}=16_{+}+16_{-}\\
16&=&16_{+}=(4_{+},2_{+})+(4_{-},2_{-})=(\overline{4},1,2)+(4,2,1) \\
\overline{16}&=&16_{-}=(4_{+},2_{-})+(4_{-},2_{+})=(\overline{4},2,1)+
(4,1,2)Where the first e... | {
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a6024899ac3854e80c13611cc19daea1b1e9ae42 | subsection | 20 | 26 | SO(10) Spinors | Finally the standard PS embedding of a matter
fermion generation in the 16- plet completes the specification of
all normalizations and phases from the SO(10) down to the SM.(4,2,1) = (Q_{\alpha },L_{\alpha } ) \qquad \qquad ({\overline{4}},1,2) =
({\overline{Q}}_{\alpha },{\overline{L}}_{\alpha })withQ=\left({\begin{ar... | {
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bee904e35760970194fe5e77fb28d4e1e2c8a2e3 | subsection | 21 | 26 | Fermion Yukawa couplings | Since it is so simple let us summarize our prescription for
determining the MSSM couplings in terms of GUT ones. When we
rewrite the equations of in our notation the
non-holomorphic connection problem will become all too obvious.We call the (6 pairs of) EW type doublets contained in the SO(10)
fields, \lbrace \bar{h}_i... | {
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47445779284a6b4a7dda4a73def752623823d52f | subsection | 22 | 26 | Fermion Yukawa couplings | It is clear that the un-normalized Higgs fractions
\hat{\alpha }_i({\hat{\bar{\alpha }}}_i) are the
right and left null eigenvectors of {\cal H} and are
holomorphic in the vevs and couplings.The inverse transformations are obviously H=U^{\dagger }
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particu... | {
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af36116f232f81c275c7e2f88a0fa4f6413173bc | subsection | 23 | 26 | Fermion Yukawa couplings | Corresponding to the
equation (REF ) has :h_{u}&\propto &
w^{u}_{10}H^{u}+w^{u}_{\overline{126}}\overline{\Sigma }^{u}+w^{u}_{{126}}
{\Sigma }^{u}+w^{u}_{210}\Phi ^{u}+w^{u(1)}_{120}\Psi ^{u}_{(1)}+w^{u(2)}_{120}\Psi ^{u}_{(2)}\\
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\overlin... | {
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f1c8e8b265549860053798fe45f4408164d1a936 | subsection | 24 | 26 | Fermion Yukawa couplings | Conversely
when we examine the correspondents of the substitution
rule(REF ) we find that they are the equations (47,48)
of : “ Let us define the projections of the
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b6ce4e2f348ad2bd9a20951c7fdc2a7179b6a620 | subsection | 25 | 26 | Discussion | In this comment we have taken the trouble to deconstruct the
calculation of to make clear that there are
defects in the method of calculation. In our view use of group theoretic methods adequate
to conveniently, systematically and unambiguously encode the
complexities of the embeddings in SO(10) and the decomposition w... | {
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7c4630fbfe9a71ca69ed3b4e4545e8489f32f18f | abstract | 0 | 10 | Abstract | The peak amplitude of linear polarization detected recently from an
extrasolar hot giant planet HD 189733b, is a few times of $10^{-4}$, more than
an order of magnitude higher than all theoretical predictions. Rayleigh
scattering off $H_2$ and $He$ may although give rise to a planet-star flux
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4a5bc3db41ea780c99590580c6d65398ff517d5b | subsection | 1 | 10 | Introduction | Polarization has always been an efficient tool to probe the physical
properties in the environment of various astrophysical objects.
predicted detectable amount of
linear polarization from L dwarfs because of the presence of condensates in the
visible atmosphere. Subsequently, linear polarization attributed
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ed36ce8ec47349b2b35d092415fe0e08db3b301a | subsection | 2 | 10 | Theroetical Model | The state of polarization of light is described by the Stoke parameters, i, q, u and v.
The parameter i is the total scalar specific intensity of radiation.
It is the complete flux of radiant energy inside the unit intervals of
frequency, time, solid angle, and area perpendicular to the flux.
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293bffff6e9633d86cb2f2af089ed7e8d238cbcc | subsection | 3 | 10 | Theroetical Model | The harmonic co-efficients
are given by\left(\begin{array}{c} p_m \\ q_m \end{array}\right)=\frac{2\pi }{k^2}
\sum ^{\infty }_{l=M}F_{l2}(k)G^l_m(i)\left(\begin{array}{c} \eta _{lm} \\
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3a5cef30b774ce4d0f1747cffd9a9d51e907ac75 | subsection | 4 | 10 | Theroetical Model | Hence, the amount of polarization or the normalized Stokes parameters Q
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scatterers. It's worth mentioning here that the model does not calculate the reflected flux
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c84e940ed54b1b3901d38374c4a287df2234db56 | subsection | 5 | 10 | Dust Distribution and Location | The dust distribution in the atmosphere is calculated based on the one
dimensional cloud model of . The number density of cloud particles is given by
n(P)=3q_c\rho \mu _d/(4\pi r^3\mu \rho _d)
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3a319ef72199091b1b2c7b61f9d92324d6e9a8c0 | subsection | 6 | 10 | Results and Discussions | As mentioned in section 1, obtained a fit of the observed polarimetric data
by assumeing a perfectly reflecting Lambert sphere with the radius as large as 1.5-1.7
R_J. While a Lambert sphere does not yield any polarization, the argument in favour of
an unusually large Rayleigh scattering exosphere is somewhat premature... | {
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"arxiv_id":... | 10.1086/591733 | 0807.1794 | Cloudy Atmosphere of the Extra-solar Planet HD189733b : A Possible
Explanation of the Detected B-band Polarization | [
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27afbc9b87bc3c4c19cb37c18e18703b3b641650 | subsection | 7 | 10 | Results and Discussions | Under such situation and
in the absence of any signature obtained by any other method, it would highly be premature
to consider an extended exosphere of HD 189733b in order to explain the observed
polarimetric data.The re-binned polarization data shows negative value of Q at all phase angles. Because of
the large error... | {
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"end":... | 10.1086/591733 | 0807.1794 | Cloudy Atmosphere of the Extra-solar Planet HD189733b : A Possible
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c99d5318ff925f7308ed2a053faf85e332c72a7c | subsection | 8 | 10 | Results and Discussions | However, as estimated in section , the rotation induced oblateness
of the tidally locked planet HD 189733b is too small to yield any significant effect on the
polarization profile as comapred to the case of a perfectly spherical geometry. In fact, the
estimated oblateness of the planet increases the polarization by abo... | {
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} | 10.1086/591733 | 0807.1794 | Cloudy Atmosphere of the Extra-solar Planet HD189733b : A Possible
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735bf9345eaee3f3c39cdbd0374da5411858e216 | subsection | 9 | 10 | Conclusion | The relatively high peak amplitude of the detected polarization and the large 1-\sigma
errors in the data makes the reported polarization tentative and it remains to be confirmed
by further polarimetric observations with more accuracy. Until then, any interpretation
of the observation is only speculative. However, if ... | {
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9b3580a7c01e3e97cad9327cb2876c4babdc4899 | abstract | 0 | 13 | Abstract | A new formulation of the Yang-Mills theory which allows a manifestly
covariant gauge fixing accompanied by a gauge invariant ghost field interaction
is proposed. The gauge condition selects a unique representative in the class
of gauge equivalent configurations. | {
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47c5dc11c4a75c5bd55d567b6c34e81bdbb47ded | subsection | 1 | 13 | Introduction. | Quantization of the Yang-Mills theory involves fixing a gauge. A
Lorentz invariant gauge fixing in non-Abelian theories requires
introduction of additional anticommuting scalar fields,
Faddeev-Popov ghosts , with non gauge invariant
interaction. The ghost field interaction produces ultraviolet
divergencies which has to... | {
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6ed65e6bca2faf5816b18ebf79d8365b82a9719e | subsection | 2 | 13 | The model. | In this section I consider the SU(2) gauge model. Generalization to other compact
groups does not make serious problems.We start with the usual path integral representation for the S-matrix in the Coulomb
gaugeS=\int \exp \lbrace i\int [L_{YM}+\lambda ^a\partial _iA_i^a]dx\rbrace d\muwhereL_{YM}=- \frac{1}{4}F^a_{\mu \... | {
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70b2a27b7bc7a43c8526a7c61cb3c2e94e09c4e0 | subsection | 3 | 13 | The model. | Obviously due to the presence of
\delta (\partial _iA_i), \partial _i A_i=0 at any time.Performing explicitly the integration over the scalar fields in the eq.(REF ), we
get the factor (|D|^2)^{-2} from the integration over commuting fields \varphi and
\chi , and the factor (|D|^2)^2 from the integration over the antic... | {
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0d6d2bf1f3b815c4153950aef00418067b250010 | subsection | 4 | 13 | The model. | (Note that it is
impossible to integrate in the eq.(REF ) by parts, as \hat{a} is a constant
spinor.)The action in the exponent (REF ) is invariant with respect to "shifted" gauge
transformations\delta A_{\mu }^a=\partial _{\mu }\eta ^a-g \varepsilon ^{abc}A_{\mu }^b \eta ^c \\
\delta \varphi ^0= \frac{g}{2} \varphi ^a... | {
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cad6c3bf726d0072de659924863fb4671ee1e96c | subsection | 5 | 13 | The model. | One can see that to remove ultraviolet
infinities generated in the perturbative expansion of the integral (REF ) mass
renormalization of the type\delta m_g(e^*d+d^*e), \quad \delta m_{\varphi } \varphi ^* \varphi , \quad \delta m_{\chi } \chi ^* \chimay be needed, as well as new four point vertices\gamma (e^*b+b^*e)^2,... | {
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3549a8f6b4bf0688a32ee07da29cf86cde784821 | subsection | 6 | 13 | The model. | Being written in terms of creation and annihilation operators the
asymptotic charge looks as followsQ^0 \sim \int [a_b^{\alpha +}(a_{\chi }^{\alpha -}+a_{\varphi }^{\alpha -})+(a_{\chi }^{\alpha +}+a_{\varphi }^{\alpha +})a_b^{\alpha -}]d^3kwhere the operators a^{\pm } satisfy the following (anti)commutation relationsa... | {
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7e7e1f74f009c145b815a3cee08ddf462061f04c | subsection | 7 | 13 | The model. | Introducing the number operator for unphysical scalar modes\hat{N}=\int \lbrace a_{\varphi }^+(\textbf {k})a_{\varphi }^-(\textbf {k})-a_{\chi }^+(\textbf {k})a_{\chi }^-
((\textbf {k})+a_b^+(\textbf {k})a_e^-(\textbf {k})+a_e^+(\textbf {k})a_b^-(\textbf {k})\rbrace d^3kwe see that this operator may be presented as the... | {
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bb101047edb6bcb4c07003c916e3bb65a125c1bb | subsection | 8 | 13 | An unambiguous Lorentz covariant gauge with gauge invariant ghost interaction. | Up to now we considered the Yang-Mills theory in the Coulomb gauge and our
reformulation did not give any advantages in comparison with the standard one. In
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} | 10.1088/1126-6708/2008/08/047 | 0807.1795 | A Lorentz invariant formulation of the Yang-Mills theory with gauge
invariant ghost field Lagrangian | [
"A. A. Slavnov"
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"hep-ph"
] | 2,008 | en | Physics | [
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2fe58db1b46caf980d50ce2a4279f046b4338127 | subsection | 9 | 13 | An unambiguous Lorentz covariant gauge with gauge invariant ghost interaction. | We shall not analyze this cancelation in
details and assume that this integral is calculated by using a regularization similar
to the dimensional one, that is we omit all counterterms proportional to \delta (0)
or D_c(0).The free action determining the propagators for the perturbative expansion of the
integral (REF ) l... | {
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} | 10.1088/1126-6708/2008/08/047 | 0807.1795 | A Lorentz invariant formulation of the Yang-Mills theory with gauge
invariant ghost field Lagrangian | [
"A. A. Slavnov"
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8dcb1c6c6cc356f1d4ef7ccc7a1df16de5c1d7dc | subsection | 10 | 13 | An unambiguous Lorentz covariant gauge with gauge invariant ghost interaction. | The fields
\varphi ^a enter the complete lagrangian linearly:\int d^4x\lbrace [\varphi ^a [-a \partial _{\mu }A_{\mu }^a+
\frac{g}{2}A_{\mu }^a(\partial _{\mu }\varphi ^0-
\partial _{\mu }\chi ^0)]- \frac{g}{2}(\varphi ^0-\chi ^0)A_{\mu }^a \partial _{\mu }\varphi ^a\rbraceVariation of this expression with respect to \... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/08/047 | 0807.1795 | A Lorentz invariant formulation of the Yang-Mills theory with gauge
invariant ghost field Lagrangian | [
"A. A. Slavnov"
] | [
"hep-th",
"hep-ph"
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07a045510a75a65722006eae56f6934d22f01be0 | subsection | 11 | 13 | An unambiguous Lorentz covariant gauge with gauge invariant ghost interaction. | It is convenient to make further redefinitions:\lambda ^a(a+ \frac{g}{2}(\varphi ^0-\chi ^0))=\lambda ^{\prime a}\varphi ^a-\chi ^a= (\varphi ^a-\chi ^a)^{\prime }(a + \frac{g}{2}(\varphi ^0-\chi ^0))After such redefinition the eq.(REF ) acquires the form\int \exp \lbrace i \int [\tilde{L}(A_{\mu },(\varphi ^a+\chi ^a)... | {
"cite_spans": []
} | 10.1088/1126-6708/2008/08/047 | 0807.1795 | A Lorentz invariant formulation of the Yang-Mills theory with gauge
invariant ghost field Lagrangian | [
"A. A. Slavnov"
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cdc72216cf1951532c3795d86c4c76e7c5cc1880 | subsection | 12 | 13 | Discussion. | The main goal of this paper was to show that Yang-Mils theory allows a manifestly
Lorentz invariant formulation with gauge invariant ghost fields interaction. In this
formulation Yang-Mills theory demonstrates a remarkable similarity to QED. In
particular as in QED the gauge condition (REF ) does not lead to an ambigui... | {
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} | 10.1088/1126-6708/2008/08/047 | 0807.1795 | A Lorentz invariant formulation of the Yang-Mills theory with gauge
invariant ghost field Lagrangian | [
"A. A. Slavnov"
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266878722a317ad58367b03604cf5542ad7c5780 | abstract | 0 | 17 | Abstract | We have studied the characteristic timescales of 80 AGNs at 22, 37 and 90 GHz
examining the properties of the wavelet method and comparing them to
traditional Fourier-based methods commonly used in astronomy. We used the
continuous wavelet transform with the Morlet wavelet to study the
characteristic timescales. We als... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
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6ec75a8fe5ab53538f3651b63070ba4bafa9fc0d | subsection | 1 | 17 | Introduction | Wavelet methods have been used for the past 10 years to study
the variability timescales in different types of astronomical
objects , , .
Wavelets have properties superior to
Fourier based methods, the most useful being the locality of the
timescale.
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8394833cfbfaf63bec5ccb7a348bc649da795ebc | subsection | 2 | 17 | The sample and observations | We used the same sample of 80 AGNs selected from the Metsähovi monitoring
list that was used in Paper I. The
sample consists of 24 BL Lacertae Objects (BLOs), 23 Highly Polarised
Quasars (HPQs), 28 Low Polarisation Quasars (LPQs) and 5 Radio Galaxies
(GALs).
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f1aca1a300018df3e9621e98363425798e88feeb | subsection | 3 | 17 | The wavelet method | We have analysed the light curves using Morlet wavelets. They can be understood as local wave packets. The method is closely related to chirp analysis methods, Short Time Fourier Transform methods, Gabor transforms and also to the sonogram or spectrogram analysis used widely in audio signal processing. In wavelet analy... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
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4e7243ee5999f3d913d345c3dfff05d16e586dcd | subsection | 4 | 17 | The wavelet method | We then calculate a scalogram of normally distributed Gaussian white noise with a variance of unity sampled as was the original data. By repeating this 20 times we get a good estimate of the scalogram of this white noise. We then normalise our original scalogram by the white noise scalogram. If our data were pure noise... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
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14d717888b32e98aab8b7fa115031dd773bab01c | subsection | 5 | 17 | Interpretation | The advantage of wavelets is that in addition to finding the variability timescale in the frequency domain, we can see at what moments it has been present. This enables us to see whether the timescale is present during the whole observed time or is transient. In addition we can identify typical flare timescales i.e. fl... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
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30015b793ce87f3aff0b84eaaa6b2fa2fa02c48a | subsection | 6 | 17 | Long-term trends | We were able to determine a long-term timescale for 122 cases out of the
total 192 cases for which we calculated the wavelet transform. In
addition to the timescale, we determined how long it is present
in the flux curve. This way we were able to calculate how many times
the cycle has repeated itself. The timescales ar... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
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383d1b468fca41d3afe66c495410b6b4c2f41649 | subsection | 7 | 17 | Flare timescales | In addition to long-term trends we determined a flare timescale which
describes the duration or rise and decay times of flares.
These timescales are seen in the wavelet transform at the times
of the outbursts. We determined such a timescale in 53 cases.
They are also tabulated in Table .
We have taken into account case... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
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20ff1ae70d07bdb3e2e9813a1e5c7aea54622ced | subsection | 8 | 17 | Individual sources | Even though none of the sources studied here seems to show a strict periodicity
in radio frequencies, many of them show quasi-periodic behaviour. We are
interested in sources that have a variability timescale lasting four cycles
in at least two of the frequency bands.
There are eight such sources and their properties a... | {
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c898292c74e6bcbd9deba9d0ee835a195355b485 | subsection | 9 | 17 | Individual sources | At 90 GHz the timescale obtained is
2.7 years and it has been present for 73% of the time and continued for 4 cycles. This timescale is also very close to the DCF timescale of
2.9 years.Visual inspection of the flux curve at 37 GHz shows that indeed many of
the larger flares have approximately 4.5 to 5 years between th... | {
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"doi":... | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
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418d82bf23b464cd9381e5eb182c4cc69b866669 | subsection | 10 | 17 | Individual sources | They explained the modulations with a
shock-in-jet model in which the permanent timescale is associated with
the quiescent jet and the shorter timescale is due to the passage of a
shock.We found a timescale of 1.4 years at 22 and 90 GHz and 1.7 years at
37 GHz. Both of these can be considered to be very similar to the ... | {
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