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599de1455628b2be733c0b65d651a1f89691b829 | subsection | 23 | 41 | On bracket polynomials | The coordinate function \psi : G \rightarrow \mathbb {R}^3 is then given by the formula\psi \left(\left(\begin{} 1 & x & z \\ 0 & 1 & y \\ 0 & 0 & 1\end{}\right)\right) = (x,y,z - xy),and the element written here is equivalent, under right multiplication by an element of \Gamma , to the element with coordinates(\lbrace... | {
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69e172349906403fabb8f22ff9ec9440976127cc | subsection | 24 | 41 | On bracket polynomials | From Proposition (\ref {equi-prop}) we have
\mathbb {E}_{n \in [N]} \mu (n) F_1(g(n)\Gamma ) \ll N^{-c}, and the uniform distribution of (g(n))n [N] implies that
\mathbb {E}_{n \in [N]} F_2(g(n)\Gamma ) \leqslant \varepsilon + O(\varepsilon ^{-O(1)}N^{-c}). Now we have the bounds
\begin{align*}
|\mathbb {E}_{n \in [N... | {
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aae4f16bfa3a94afc95c3c036c17dd0747d165fc | subsection | 25 | 41 | On bracket polynomials | This may be used to “explain” the observation that n\sqrt{2}\lfloor n\sqrt{2}\rfloor is not uniformly distributed modulo one; see for further details.Inside G/\Gamma , G^{\prime }/\Gamma ^{\prime } may be identified with the union of two segments\lbrace \left(\begin{} 1 & x & x^2/2 \\ 0 & 1 & x \\ 0 & 0 & 1\end{}\right... | {
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9e1985532652dfed4d272f01b1e9231f9e8531f5 | subsection | 26 | 41 | On bracket polynomials | Suppose for simplicity that \varepsilon = \gamma = \operatorname{id}_G (this was, in fact, the case in the two examples above).Choose a Mal'cev basis for G^{\prime }/\Gamma ^{\prime } with coordinate map \psi ^{\prime } : G^{\prime } \rightarrow \mathbb {R}^{m^{\prime }}. Then G^{\prime }/\Gamma ^{\prime } may be ident... | {
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9ebabb4b1ced3185512c0e8699ec7c5da3999ed9 | subsection | 27 | 41 | On bracket polynomials | One then works with the conjugated sequences \gamma _j^{-1}g^{\prime }(n)\gamma _j as we did at the end of §.We conclude by remarking on some variants and generalizations of Theorem REF . If p_1,\dots ,p_M are bracket polynomials and F : (\mathbb {R}/\mathbb {Z})^M \rightarrow is a smooth function then one could establ... | {
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344872dde00e485003493c12915782d90b13cde2 | subsection | 28 | 41 | The Liouville function | Everything we have proved for the Möbius function also holds for the Liouville function \lambda : \mathbb {N}\rightarrow \lbrace -1,1\rbrace , defined to be the unique completely multiplicative function such that \lambda (p) = -1 for all primes p. This function is related to the Möbius function via the identity\lambda ... | {
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eefd46ff419fdc6dd80c3ade6ceb2be9162ef502 | subsection | 29 | 41 | A recurrence result along the primes | In this section we derive the following result. Here p_1,p_2,p_3,\dots is the sequence of primes.Theorem 1 (Prime return times on a nilmanifold)
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2c62de70732a0f4ae25392b47261bdc4ded9a1e4 | subsection | 30 | 41 | A recurrence result along the primes | The contribution from the first piece is bounded using the machinery of Gowers norms, and here one must estimate the dual Gowers norm of the nilsequence F(g^nx\Gamma ) as well as the Gowers norm of objects related to \Lambda ^{\sharp }. This is a substantial amount of work.Let us return to the proof at hand. Since (REF... | {
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7af04acac552b803b76cfe4a6c38c72748de51f8 | subsection | 31 | 41 | A recurrence result along the primes | Doing so, we obtain\lim _{N \rightarrow \infty } \mathbb {E}_{n \in [N]}\Lambda ^{\prime }(n) F(g^n x \Gamma ) = \int _{G/\Gamma } F.An easy argument using the prime number theorem, noting that \Lambda ^{\prime }(p_n) is essentially \log N for almost all primes p_n, n \leqslant N, concludes the proof.Very straightforwa... | {
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ebe2a689403a3b7aa609bafd696f240bd2c91fa2 | subsection | 32 | 41 | Möbius and periodic functions | In this appendix we give the proof of Proposition REF . The argument is, quite apart from being completely standard, already contained in . We nonetheless take the opportunity to recall it here, as we wish to emphasise the fact that the main input to this part of the argument is information on the zeros of L-functions.... | {
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e4818d2aef314fc1d884ff3f2c8ba7d575c63b5b | subsection | 33 | 41 | Möbius and periodic functions | Applying Proposition REF and the triangle inequality, we conclude\mathbb {E}_{n \in [N]} \mu (n) \overline{f(n)} \ll _A q^{1/2} \log ^{-A} N \big (\sum _\chi |\hat{f}(\chi )|\big ).But from Cauchy-Schwarz and Plancherel we have\sum _\chi |\hat{f}(\chi )| \leqslant \phi (q)^{1/2} (\sum _\chi |\hat{f}(\chi )|^2)^{1/2}
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d55e3abb951a3f21fc03c5b119afbc6812887ef2 | subsection | 34 | 41 | On total equidistribution of nilsequences | During the proof that Proposition REF implies Theorem REF (specifically, in the claim towards the end of §), we implicitly used the following technical factWe note that this fact was absent in our original posting of this paper on the ArXiV in 2008; we apologize for this oversight..Lemma 1
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567c2640cddd78a6b090fb0275fb326bc2e48d9b | subsection | 35 | 41 | On total equidistribution of nilsequences | This follows from the fact that [\Gamma : \Gamma \cap \gamma ^{-1}\Gamma \gamma ] \leqslant Q^{O_{m,d}(1)}, which may in turn be proven by noting that the \mathcal {X} coordinates of every element in \gamma ^{-1}\Gamma \gamma are rationals over some fixed denominator Q^{O_{m,d}(1)}, as follows from .Lemma 2 Suppose tha... | {
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53f41026b9545691eca09c3b006a75dced29cd7b | subsection | 36 | 41 | On total equidistribution of nilsequences | Applying the quantitative Leibman dichotomy, namely , this may be further reduced to the corresponding abelian statement. Indeed that result immediately implies that (g(n)\Gamma )_{n \in [N]} is totally \delta -equidistributed if and only if (\pi (g(n)\Gamma )_{n \in [N]} is totally \delta ^{\prime }-equidistributed in... | {
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3427fa899d2d98c0770ec1ebf08ad4ead75e01db | subsection | 37 | 41 | On total equidistribution of nilsequences | This implies that \Vert k^{\prime } \cdot g^{\prime }\Vert _{C^{\infty }[N]} \leqslant \delta ^{\prime -O_{m,d}(1)}, where k^{\prime } :=( \det A) k A^{-1}; note that k^{\prime } \in \mathbb {Z}^m and that |k^{\prime }| \leqslant \delta ^{\prime -O_{m,d}(1)}. Recalling the definition of \Vert \cdot \Vert _{C^{\infty }[... | {
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1b811c9f03dc5fbb7d9d25700b1230be98d95c04 | subsection | 38 | 41 | On total equidistribution of nilsequences | The conjugate G^{\prime }_{\gamma } := \gamma ^{-1}G^{\prime }\gamma is a rational subgroup of G which comes together with a Mal'cev basis \mathcal {X}^{\prime }_{\gamma } for G^{\prime }_{\gamma }/\Gamma ^{\prime }_{\gamma } (where \Gamma ^{\prime }_{\gamma } := G^{\prime }_{\gamma } \cap \Gamma ), in which element is... | {
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2f841a3b0177869cb9f753cc79f9e5b230b63a4e | subsection | 39 | 41 | On total equidistribution of nilsequences | Then there is a Mal'cev basis \mathcal {X}_2 for G/\Gamma _2, each element of which is a \delta ^{-O_{m,d}(1)}-rational combination of the elements of \mathcal {X}_1, and such that (g(n)\Gamma _2)_{n \in [N]} is totally \delta ^{c_{m,d}}-equidistributed with respect to the metric d_{\mathcal {X}_2}.Remark. This lemma w... | {
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dbfe5064a93367d93d12908725a20d46401ab1d4 | subsection | 40 | 41 | On total equidistribution of nilsequences | We have reduced matters, then, to the following assertion.Lemma 3 Let m \geqslant 1 be a positive integer and suppose that A \in \operatorname{GL}_m(\mathbb {Z}) is invertible and has entries bounded by \frac{1}{\delta }. Let g : \mathbb {Z}\rightarrow \mathbb {R}^m be a polynomial of degree d, and write g^{\prime } :=... | {
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} | 10.1103/PhysRevA.79.035801 | 0807.1736 | The Mobius function is strongly orthogonal to nilsequences | [
"Ben Green",
"Terence Tao"
] | [
"math.NT"
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3996081ab7515bcb776527a47ad0cb988c0c582d | abstract | 0 | 8 | Abstract | We consider zero temperature solutions to the Abelian Higgs model coupled to
gravity with a negative cosmological constant. With appropriate choices of
parameters, the geometry contains two copies of anti-de Sitter space, one
describing conformal invariance in the ultraviolet, and one in the infrared.
The effective spe... | {
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} | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
breaking | [
"Steven S. Gubser",
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] | [
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1351096911f8db773d63c928f2ed6b7f0f110e8d | subsection | 1 | 8 | Body | PUPT-2275The gravity dual to a quantum critical point with spontaneous symmetry breakingSteven S. Gubserssgubser@Princeton.EDU
Fábio D. Rochafrocha@Princeton.EDU
Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544We consider zero temperature solutions to the Abelian Higgs model coupled to gravity with ... | {
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... | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
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715f4600bea286d4a64031e75723cf8861485128 | subsection | 2 | 8 | Body | (This region is generally understood to correspond to infrared physics in a gravity dual.) In order for SO(3,2) conformal symmetry to emerge, one must also have A approach a linear function of r in the infrared region, so that the geometry is asymptotically AdS_4. Similar remarks apply in the ultraviolet region, where ... | {
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} | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
breaking | [
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62a5d3e736d836903bbe5f974ac88fe538cf7e21 | subsection | 3 | 8 | Body | The scalar provides such a deformation: if we assume that \psi is real everywhere, then
psiSet
(r) = IR + ae(IR-3)r/LIR
solves the linearized equation of motion for \psi around the background dsIR, where \Delta _{\rm IR} is the larger root of
DeltaIR
IR (IR - 3) =
1 2 V”(IR) LIR2
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04773033f4a87340c9712ec9cb88cf6604d5447c | subsection | 4 | 8 | Body | We can formally solve heom in terms of s(r):
FoundH
h(r) = 1 + -r dr1 e-3A(r1)
-r1 dr2 e3A(r2) s(r2) .
There are no free integration constants in FoundH because we assume h \rightarrow 1 in the infrared, which implies e^{3A(r)} h^{\prime }(r) \rightarrow 0 there as well. We learn from FoundH that h(r), and hence ... | {
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} | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
breaking | [
"Steven S. Gubser",
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e1772c5d2647b8375a4d0273130fcd712179ce4d | subsection | 5 | 8 | Body | If there is a stable solution, it represents a quantum critical point.To give an explicit example, we used the potential ChooseV and made the following choice of parameters:
ChooseParams
L = 1 q = 2 m2 = -2 u = 3 0 = 1 .
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} | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
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73afd64908afc47a866c89ef822530cda48f67a9 | subsection | 6 | 8 | Body | First, \Im \tilde{\sigma }\sim 1/\omega , because this is what Kramers-Kronig requires based on the existence of a delta function in \Re \tilde{\sigma } at \omega =0 Our first technical assumption is that the continuous part of \Re \tilde{\sigma } is integrable at \omega =0. This can be checked a posteriori.. In other ... | {
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} | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
breaking | [
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e6da681fce8dba3c88ec1cc38f0e858961e38341 | subsection | 7 | 8 | Body | So we conclude
axZeroScaling
ax(0) = r ax(r) -+1/2 ,
where the constant of proportionality involves \lim _{r\rightarrow \infty } Z_x(r), which encodes all the physics at high scales that we can access only through numerical methods. Plugging axZeroScaling into ReSigma, one obtains \Re \tilde{\sigma }\sim \omega ^\del... | {
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} | 10.1103/PhysRevLett.102.061601 | 0807.1737 | The gravity dual to a quantum critical point with spontaneous symmetry
breaking | [
"Steven S. Gubser",
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79c682d415a7c226579ba8596356f886a6f92a99 | abstract | 0 | 34 | Abstract | We consider resonant absorption in a spectral line in the outflowing plasma
within several tens of Schwarzschild radii from a compact object. We take into
account both Doppler and gravitational shifting effects and re-formulate the
theory of P-Cygni profiles in these new circumstances. It is found that a
spectral line ... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
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9bf9241c21fd5dbf3e2df4bd2e379b6bfb8173c2 | subsection | 1 | 34 | Introduction | It is widely accepted that radiation produced in the vicinity of
compact objects can bear an imprint of the strong
gravitational field, of either a stellar mass black hole (BH) or a
neutron star (NS) in Galactic X-ray binary systems, or of a
super-massive BH in case of active galactic nuclei
(AGN).
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... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
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51259b692b27c8c991a34a881527e9ce403c05a1 | subsection | 2 | 34 | Introduction | The data suggest these features are formed in a flow moving with velocity, v\sim 0.15-0.2\,c, or/and being gravitationally red-shifted.Much smaller astrophysical objects which may potentially demonstrate
gravitationally red-shifted lines are neutron stars.
It is widely believed that X-ray bursts are produced as neutron... | {
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... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
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fd3dcdabb684566d9335de1fba767f21d2a64891 | subsection | 3 | 34 | Introduction | Expecting that the gravitational red-shifting may introduce some characteristic distortion to the P-Cygni profile, we wish to investigate what kind of the distortion is made and whether it can be used to deduce information about the
wind and compact object system itself.The plan of the
paper is as follows: in Sect.2 ba... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
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c63ce32f6a5dc03db8412a3dae0d85a91a86a697 | subsection | 4 | 34 | Assumptions | As mentioned above, the problem we address in this paper may be
relevant to various astrophysical objects.
Physical conditions in the wind driven from the accretion disk in AGN are different from
those in the out-flowing plasma during an X-ray burst. At the same time we would like to elucidate some new features
which m... | {
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1985ce6d6e8c72561c8cf0228111afb32424c9ab | subsection | 5 | 34 | Assumptions | Taking into
account bending of photon trajectories would introduce
a significant complication in the solution the radiation
transfer problem and would require frequency dependent Monte-Carlo
simulations of the radiation transfer in the frame of the General Relativity (GR for short), which is beyond the scope of the cur... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
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9cc1f9bb0f6ec981d96f7ca64f9344208c892e9f | subsection | 6 | 34 | optical depth | We associate an observer situated at infinity, O^\infty with the laboratory frame (”lab”- frame for short).
The fluid is moving with the velocity v. It is most convenient to measure absorption and emission
coefficients in the co-moving frames, O_{\rm com}, coinciding instantaneously with the fluid at
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553831e5ed23dfce0dadc47b23f7f941ecb83088 | subsection | 7 | 34 | optical depth | In order to allow for moderately high terminal velocities we will write all equations out to the second order, i.e. retain terms \beta , \beta ^2, and \phi /c^2. | {
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} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
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49122adf5e48292e0bda665df0f2fff77183fac0 | subsection | 8 | 34 | optical depth | Taking into account that \nu _{\rm loc}(s_0)\sqrt{g_{00}(s_0)}=\nu ^\infty , where \nu ^\infty is the frequency measured by the observer O^\infty , we obtain:\tilde{\nu }(s)=\nu ^\infty \left(1-\mu (s)\beta (s)-\frac{\phi (s)}{c^2}+
\frac{\beta (s)^2}{2}\right)\mbox{.}The probability to emit a photon within
a frequency... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
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47c09b25d8bf49443f535dbc354fcdb1002f8687 | subsection | 9 | 34 | optical depth | Given the Sobolev approximation we assume that a photon, after being scattered in a line at a point s_0, can further interact with matter only in the immediate vicinity of this point. Due to gradients of the velocity and gravitational potential, such a photon is quickly shifted out of the resonance with the line.
We ex... | {
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objects | [
"A. V. Dorodnitsyn"
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-0.01537279598414898,
-0.0025996428448706865,
-0.01113097183406353,
0.011... |
dd61dae1619bd1e9aa13386af1c8d4782cc7c0cf | subsection | 10 | 34 | optical depth | The second factor in (REF ), \zeta (\tilde{\nu }) reads:\zeta (\tilde{\nu })=\int _{\nu _0-1/2}^{\tilde{\nu }} \,\Psi (\tilde{\nu }-\nu _0)\,d\tilde{\nu }\mbox{.}For simplicity we assume that the line absorption coefficient is zero outside the frequency interval
(\nu _0-\Delta \nu /2,\nu _0+\Delta \nu /2)
i.e. in terms... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.05129415541887283,
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-0.028301801532506943,
-0.013998330570757389,
0.005061521660536528,
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-0.004504639655351639,
-0.02634890004992485,
-0... |
79c1e04c9138b3961a467138d42bfe4fdd6abf78 | subsection | 11 | 34 | optical depth | \\
&+&\left.\mu \left( \frac{1}{\beta \,c^2} \frac{d\phi }{d \ln r} -\beta \frac{d\ln \beta }{d\ln r}
\right) \right] \mbox{.}Similarly, after some algebra we find:-({\nu ^\infty })^{-1}\frac{d^2 \tilde{\nu }}{d s^2}&=&
\left[ \frac{1-\mu ^2}{r}\left( \frac{2\mu \beta }{r}+\beta ^{\prime }(\beta -2\mu )-\frac{\phi ^{\p... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1762,
"openalex_id": "",
"raw": "Jeffery, D.J. 1995, ApJ, 440, 810J",
"source_ref_id": "6f213f2217185747b0022ebf00422309e5e8efc5",
"start": 1650
}
]
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.0707261860370636,
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0.015027026645839214,
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-0.009527287445962429,
0.007948305457830429,
0... |
e8a432ae3443cd347a4ff7c94d0208578515ee90 | subsection | 12 | 34 | optical depth | A wind moves radially with the velocity V(r).Corresponding projections of the radial velocityon the direction of the ray at points s_0 and s determine the relative Doppler shifting.For certain cases the latter can compensate for the gravitational shifting between these two points (see e.g. the discussion before and aft... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1888,
"openalex_id": "",
"raw": "Kuan, P., Kuhi, L.V. 1975, ApJ, 199, 148",
"source_ref_id": "74a640ec30e6ede655e0ff25ed71604fc5452a4a",
"start": 1754
},
{
"arxiv_id": "",
"doi": "",
"end": 18... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.08063849806785583,
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0.004280677065253258,
-0.02139575593173504,
0... |
18a21a5cac5bd775cc92db25571f3e6382510399 | subsection | 13 | 34 | Surfaces of equal frequency | It is convenient to
introduce a non - dimensional frequency variable which measures a displacement
of the frequency from that of the line center in terms of Doppler line width,
\Delta \nu :y= (\nu -\nu _0)/\Delta \nu \mbox{.}Similarly, a co-moving version of this variable reads:
{\displaystyle \tilde{y}= (\tilde{\nu }-... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.02573796547949314,
0.0029006702825427055,
0.0058... |
2a86380ca77ac6ec9fb149c4b8cab0c568e0e686 | subsection | 14 | 34 | Surfaces of equal frequency | A non-dimensional parameter,
g_0= R^*/r_g determines the relative
importance of gravitational red-shifting (i.e. by equating
g_0\rightarrow \infty one completely neglects the influence of the
gravitational field on the energy of a photon).
Equation (REF ) may have multiple roots, z_{0i} depending on the
values of y^\i... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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3a1c710f59514368842877237a3e3be718f4a12b | subsection | 15 | 34 | Surfaces of equal frequency | For a given y^\infty , the EFS has the shape of a sphere of radius, x(y^\infty )=g_0^{-1}(1-\zeta /(2y^\infty )).
{v}={\rm const}.
An example would be the outer part of a stellar wind in which the flow is
approaching
terminal velocity moves at almost constant speed. Alternatively, considering a spectrum from a thin, m... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.07856757193803787,
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0.005227154586464167,
0.002588776871562004,
... |
9f27f04aaf1544506a9aaf3168f4fc1c22cb1d5d | subsection | 16 | 34 | Surfaces of equal frequency | There are two equal red-shift surfaces: an ellipsoid-like
surface at small r and a plane-like at larger radii (Fig. REF , left panel). At larger
red-shift, y^\infty =0.3 \,y_{\rm min} the inner surface shrinks to
smaller r, where the gravitational potential is stronger, while the
outer surface shifts to larger r, to th... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.10588594526052475,
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0.015089510940015316,
0.00... |
4bae698b0234d5ac586aab043c3f94e86c390645 | subsection | 17 | 34 | Surfaces of equal frequency | A ray with impact parameter, p and frequency, y^\infty may
cross resonant surfaces several times depending on the velocity law and on the relative importance of gravity, i.e. proximity
to the compact object.Physical conditions (i.e. ionization
balance, radiation field) which affect the formation of a
particular portion... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.023632019758224487,
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0.017071807757019997,
-0.01509611494839191... |
e2b92b634579d5e2252031fb5bb802c543eae515 | subsection | 18 | 34 | Radiation field in a line | The mean radiation field J at any point on the Equal Frequency Surface consists of photons
emitted by atoms in the immediate vicinity of this point: a
local contribution, J_{\rm loc}, and a contribution from
distant points, J_{\rm dist}. The latter consist of photons
emitted by the core, J_{\rm core}, and photons which... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 719,
"openalex_id": "",
"raw": "Grachev, S.I., Grinin, V.P., 1975, Astrophysics, 11, 20",
"source_ref_id": "3a241627ac013d0a2c33a41171e9b3856024089e",
"start": 639
},
{
"arxiv_id": "",
"doi": "",
... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.029467139393091202,
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0.03131360560655594,
-0.024980688467621803,
0.... |
4ea5d9ad8e80bd9ef84a1ce3b2d2766f5887b169 | subsection | 19 | 34 | Radiation field in a line | In a general case it should be calculated separately for
each point where J is calculated. The same remains true about
all other possible branches of EFSs which can contribute to the
mean radiation field at a given point. Generally speaking Fig.
REF only shows that screening is possible. The goal of taking all these ge... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1745,
"openalex_id": "",
"raw": "Grachev, S.I., Grinin, V.P., 1975, Astrophysics, 11, 20",
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"start": 1580
},
{
"arxiv_id": "",
"doi": "",
... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
0.010816318914294243,
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0.015926992520689964,
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0.0001411155826644972,
-0.017788192257285118,
... |
f1b02ef74d6d396070c0dbb21aaabb44e4d4655a | subsection | 20 | 34 | Radiation field in a line | The intensity of the radiation at r\rightarrow \infty at a given impact parameter
p and with a given frequency y^\infty isI^\infty (y^\infty ,p)&=&I_{c}e^{-\tau (\Sigma ^{+})}
+S(\Sigma ^{+})(1-e^{-\tau (\Sigma ^{+})})\\
&+& S(\Sigma ^{-}_1)(1-e^{-\tau (\Sigma ^{-}_1)})
e^{-\tau (\Sigma ^{+})}\\
&+& S(\Sigma ^{-}_2)(1-... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1584,
"openalex_id": "",
"raw": "Hutsemekers, D., Surdej, J. 1990, ApJ, 361, 367",
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"start": 1476
},
{
"arxiv_id": "",
"doi": "",
"e... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.04056158661842346,
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0.0... |
2424f96dff61d6e3e3bb22483bd20d6071fc5c55 | subsection | 21 | 34 | Radiation field in a line | The penetration probability in the frame of Sobolev approximation reduces to\beta _{\rm pen}=\frac{1}{2}\int _{\mu _c}^1
\, \beta ^\mu _{\rm loc}\,d\mu \mbox{.}where \mu _c=\cos \theta _c, so that
{\displaystyle \theta _c=\arccos {\sqrt{1-\frac{1}{x^2}}}} is the maximum angle at which the core is seen from the point x.... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1125,
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"raw": "Hutsemekers, D., Surdej, J. 1990, ApJ, 361, 367",
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},
{
"arxiv_id": "",
"doi": "",
"e... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.04771958291530609,
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0.020945968106389046,
... |
b9e888c5cd4d0f9606a53caf6c8c348477845ed3 | subsection | 22 | 34 | Radiation field in a line | That is we ignore both negative \sim e^{-\tau } and positive
\sim S(1-e^{-\tau }) contributions which may arise from resonant points on the
line to the point where J is calculated.After the intensity, I^\infty (y^\infty , p) has been calculated from (REF ),
the normalized flux that is registered by the observer at inf... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 798,
"openalex_id": "",
"raw": "Marti, F., Noerdlinger, P. D. 1977, ApJ, 215, 247",
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"start": 719
}
]
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.053065698593854904,
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0... |
1e34c914059960326347cced70eebb6dcea821ab | subsection | 23 | 34 | Calculation of line profiles | Before we proceed to closer examination of line profiles we need to make several assumptions about physical conditions existing in the flow.
It is assumed that a spherically-symmetric wind originates
at the photosphere which emits radiation in continuum. The radius of the photosphere is R^*.
The radiation emitted by th... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 767,
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"raw": "Castor, J.I., Lamers, H.J.G.L.M. 1979, ApJ, 39, 481",
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"start": 632
}
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} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
2a11f92564c927651e70d745834e0eba4e040fee | subsection | 24 | 34 | Calculation of line profiles | Velocity law () with w_c=0.01.Opacity curves: solid line: equation (); dashed: equation (), k=-2;dot-dashed: equation (), k=2.Curves are marked by pairs of \alpha _1,\alpha _2 from().][Figure: Profiles for R^*=25 r_g, V^{\rm \infty }=0.01\,c (upper left),R^*=25 r_g, V^{\rm \infty }=0.2\,c (upper right),R^*=10 r_g, V^{\... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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4909ee044e75907432813456383d9afad81e591e | subsection | 25 | 34 | Body | In Sect. 3 it has been established that in the case of linear velocity law (REF ), the EFS (the red-shifted part) may have two disconnected branches if
the influence of strong gravity is taken into account and provided parameter g_0 is small enough (c.f. Fig. REF ).
This is easily understood from the following argument... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.012201070785522461... |
154b7efdcc2bc4ac3fc8bfdb820a15e380b83c7b | subsection | 26 | 34 | More realistic | First we
calculate line profiles for parameters of the flow relevant to those of a wind from a normal star. These provide a good test of our results against those of .
Results are shown in Fig.REF .
They are calculated for different values of T_0. The terminal velocity is
V^{\infty }\simeq 1897\,{\rm km\, s^{-1}}.The ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 168,
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"raw": "Castor, J.I., Lamers, H.J.G.L.M. 1979, ApJ, 39, 481",
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"doi": "",
... | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.0... |
1ccd3ebced0ff32505106775ce59006223b50dd8 | subsection | 27 | 34 | More realistic | In most cases, the narrow absorption is superimposed on the blue-shifted emission. For k=-3 and k=-2, profiles look similar to those obtained from the linear law (c.f. Fig. REF ). | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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55c6036a8e4c31ab2cd64528a3b62a0e4853b142 | subsection | 28 | 34 | Shielding by the disk | Our method, as presented in this paper, does not allow to consider
anisotropic radiation field
of an
accretion disk or some additional attenuation of the emission. However, we can gain some insight by considering a wind that is viewed face on (i.e. perpendicular to the disk plane) and accounting for the blocking of tho... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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516543ab040d0ae5f92ce1969c0a31a0a060acfa | subsection | 29 | 34 | Discussion | The strongest double absorption profile is found for the v\sim r velocity
law.
The superposition of
the gravitational red-shift and Doppler shift easily produces two pronounced absorption features if the velocity
law is not steep (as in the case of linear law) or the maximum velocity within the line forming region is s... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
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28d2267eec6311e1c7b38b9f849440d779459926 | subsection | 30 | 34 | Discussion | Results show that the centroid energy of the blue-shifted absorption depends, on the distribution of the opacity, and
can be seen at significantly smaller shifts.
If the gravitational red-shift effect is significant but smaller than the pure Doppler effect, there exists some maximum red-shift at which the
EFS has a com... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
objects | [
"A. V. Dorodnitsyn"
] | [
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aebf14d24b94461d7bf8733e6d4d83fcad7a3ed5 | subsection | 31 | 34 | Conclusions | Our goal in this paper has been to study shapes of spectral lines from plasma which is rapidly
moving in the vicinity of a neutron star or a black hole. The
latter case can account for both stellar (Galactic Black Hole Candidates) and supper-massive BHs (AGN). In the well studied
case of winds from normal hot stars, a ... | {
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"A. V. Dorodnitsyn"
] | [
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7212f5ed6926faca583956be28064e375e7d86a3 | subsection | 32 | 34 | Conclusions | Some branches of the EFSs in the red-shifted part of the spectra are found to be in front of the
core, meaning the possibility for the absorption component to be
observed as red-shifted, with respect to the emission.From numerical calculations, which are second order accurate in v/c,
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1326457bd1e1f7e5466898130bf3acfcdc55699c | subsection | 33 | 34 | Conclusions | Surprisingly enough, no W-shape profiles are found for a v\sim \sqrt{1-1/x} law. In this case
the red-shifted absorption almost exactly compensates for the blue-ward emission peak, producing a sharp edge in the emission
(Fig. REF ).However, in many other cases of different \alpha _1,\alpha _2,
W-shape profiles are also... | {
"cite_spans": []
} | 10.1142/S0218271808013364 | 0807.1738 | Gravitationally distorted P-Cygni profiles from outflows near compact
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a3fd044baad68974de010d3f821d4b2380d3163b | abstract | 0 | 6 | Abstract | The instanton-antiinstnton contributions to the $q\overline{q}$ bound state
pole in the four-point Green function in the Schwinger Model are calculated. It
is shown that these configurations, thanks to the cancellation of all unwanted
terms, are responsible for the restoration of the perfect factorizability of
the resi... | {
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} | 0807.1739 | Restoration of the residue factorizability in the bound-state pole by
instanton-antiinstanton configurations | [
"Tomasz Radozycki"
] | [
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600c7ace8f37e4ec92196c4546f38c6fd7ff2aa6 | subsection | 1 | 6 | Body | Restoration of the residue factorizability in the bound-state pole by instanton-antiinstanton configurations
Tomasz Radożycki
Department of Mathematical Methods in
Physics, Warsaw University, Hoża 74, 00-682 Warsaw,
Poland
torado@fuw.edu.plThe instanton-antiinstnton contributions to the q\overline{q} bound state pole i... | {
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c4249644776f0fa748d702816db054c0cd1dd15e | subsection | 2 | 6 | Body | One can then make instanton-antiinstanton separation arbitrarily large.Following , we substitute into the path integral in the generating functionalthe following form of the gauge potentialwith \varepsilon ^{\mu \nu } being the antisymmetric symbol.
The integration, which will be led in euclidean space, is now performe... | {
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"... | 0807.1739 | Restoration of the residue factorizability in the bound-state pole by
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fa80a03257dd9e85c84c5f4939d279910790b74c | subsection | 3 | 6 | Body | Obviously, for finite R they are not exact.They are eigenfunctions (with eigenvalues \pm 1) of the chirality operator \gamma ^5 (our conventions as to the \gamma matrices are given in ).Now our previous calculation can be applied with only obvious modifications and with the additional difference that our formulae will ... | {
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741e6b300311ca1ac3dd95e31d6c24b0714a6b52 | subsection | 4 | 6 | Body | Because we are interested in the t-channel singularity, the pole corresponding to the bound state should be found in the complex plane of P^2, where P is the two-momentum canonically conjugated to Z. The Z dependence of the expression is then crucial.Let us begin with the first term in the square brackets in (REF ). It... | {
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63e39754da93b9cca9a1599f62e1c69f77f1232d | subsection | 5 | 6 | Body | The straightforward calculation leads to the similar result as above only with the modification in the \gamma matrices structure, which actually might be predicted. The two modes (REF ) and () exchange their roles, so the matrical structure is changed into (+\gamma ^5)\otimes (-\gamma ^5) and the rest of the expression... | {
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] | [
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44620d81aa6666e93963b197df339369e7f9e93d | abstract | 0 | 6 | Abstract | Ultrafast two-color pump-probe measurements, involving coherent acoustic
phonon (CAP) waves, have provided information simultaneously on the mechanical
properties and on the electronic structure of ferromagnetic GaMnAs. The elastic
constant C11 of Ga1-xMnxAs (0.03<x<0.07) are observed to be systematically
smaller than ... | {
"cite_spans": []
} | 10.1103/PhysRevB.81.115208 | 0807.1740 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using
Ultrafast Coherent Acoustic Phonons | [
"J. Qi",
"J. A. Yan",
"H. Park",
"A. Steigerwald",
"Y. Xu",
"S. N. Gilbert",
"X. Liu",
"J. K. Furdyna",
"S. T. Pantelides",
"N. Tolk"
] | [
"cond-mat.mtrl-sci"
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e9931dca23aa1bf3ad1d82a9b05823c6063bc43c | subsection | 1 | 6 | Body | Ultrafast Dynamics of Coherent Acoustic Phonons in the Ferromagnetic Ga_{1-x}Mn_xAs/GaAs SystemJ. Qi, Y. Xu, A. Steigerwald, and N. Tolk
Department of
Physics and Astronomy, Vanderbilt University, Nashville, TN, 37235X. Liu and J. K. Furdyna
Department of Physics, University of Notre Dame, Notre
Dame, IN 46556T. V. Sha... | {
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... | 10.1103/PhysRevB.81.115208 | 0807.1740 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using
Ultrafast Coherent Acoustic Phonons | [
"J. Qi",
"J. A. Yan",
"H. Park",
"A. Steigerwald",
"Y. Xu",
"S. N. Gilbert",
"X. Liu",
"J. K. Furdyna",
"S. T. Pantelides",
"N. Tolk"
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c8611e627db4aed9323948e206a0edb3c6826104 | subsection | 2 | 6 | Body | Both pump and probe beams were focused
onto the sample at the same spot with a diameter of around 100 \mu m and an intensity ratio of 10:1. The pump light typically had a
fluence of 1.7 \mu J/cm^2.
[Figure: Pump-probe response ofGa_{0.976}Mn_{0.024}As/GaAs at 10 K for 830 nm. Inset: thesubtracted oscillatory response d... | {
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"arxiv_i... | 10.1103/PhysRevB.81.115208 | 0807.1740 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using
Ultrafast Coherent Acoustic Phonons | [
"J. Qi",
"J. A. Yan",
"H. Park",
"A. Steigerwald",
"Y. Xu",
"S. N. Gilbert",
"X. Liu",
"J. K. Furdyna",
"S. T. Pantelides",
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0ee4ede578ad0cf2ed7e9350daa0356e7ced5f5b | subsection | 3 | 6 | Body | We estimate that it takes about \Delta t
(\approx 210 ps) for the strain wave to reach GaAs layer if
assuming that V_{s(\text{GaMnAs})} is approximately equal to
V_{s(\text{GaAs})} (4.78 \times 10^3 m/s at 10 K
). It can be seen from experimental results that 210
ps is around the transition region between the two disti... | {
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{
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... | 10.1103/PhysRevB.81.115208 | 0807.1740 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using
Ultrafast Coherent Acoustic Phonons | [
"J. Qi",
"J. A. Yan",
"H. Park",
"A. Steigerwald",
"Y. Xu",
"S. N. Gilbert",
"X. Liu",
"J. K. Furdyna",
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ed36e5a288c3e01d93461c123ce327cce1c32fdb | subsection | 4 | 6 | Body | Solid straight line is a linear fitof experimental data for Ga_{0.976}Mn_{0.024}As. (b) Absorptioncoefficient \alpha as a function of photon energy forGa_{0.976}Mn_{0.024}As (line+dot) and GaAs (line+opentriangle).]Another experimental result is that the absorption coefficient ¦Á
can be directly obtained from our measu... | {
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... | 10.1103/PhysRevB.81.115208 | 0807.1740 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using
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"H. Park",
"A. Steigerwald",
"Y. Xu",
"S. N. Gilbert",
"X. Liu",
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2eae932c33338c5b814b0dd55656168630203010 | subsection | 5 | 6 | Body | According to Eq.(REF ), in the vicinity
of the bandgap the amplitude A for GaAs manifests itself a strong
peak in REF . As also discussed above, the optical
properties for Ga_{1-x}Mn_xAs are very different with GaAs, e.g.
the absorption coefficient ¦Á for ferromagnetic Ga_{1-x}Mn_xAs
varies smoothly in the wavelength r... | {
"cite_spans": []
} | 10.1103/PhysRevB.81.115208 | 0807.1740 | Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using
Ultrafast Coherent Acoustic Phonons | [
"J. Qi",
"J. A. Yan",
"H. Park",
"A. Steigerwald",
"Y. Xu",
"S. N. Gilbert",
"X. Liu",
"J. K. Furdyna",
"S. T. Pantelides",
"N. Tolk"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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0446ebf184fcf47a856a3b88c52686b4cab18644 | abstract | 0 | 9 | Abstract | Building a \BBz experiment with the ability to probe neutrino mass in the
inverted hierarchy region requires the combination of a large detector mass
sensitive to \BBz, on the order of 1-tonne, and unprecedented background
levels, on the order of or less than 1 count per year in the \BBz signal
region. The MAJORANA Col... | {
"cite_spans": []
} | 10.1088/1742-6596/173/1/012007 | 0807.1741 | The Majorana Project | [
"S. R. Elliott"
] | [
"nucl-ex"
] | 2,008 | en | Physics | [
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9b1753a386fcbcaa441ad841be86fa523560ef06 | subsection | 1 | 9 | Introduction | This is an exciting time in our quest to understand
neutrinos — fundamental particles that play key roles in the early
universe, in cosmology and astrophysics, and in nuclear and particle
physics. Recent results from atmospheric, solar, and reactor-based
neutrino oscillation experiments (Super-Kamiokande, SNO, and
KamL... | {
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"end"... | 10.1088/1742-6596/173/1/012007 | 0807.1741 | The Majorana Project | [
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f4ff2ac24b53e9ec78a0fa54e03c3bd90235600e | subsection | 2 | 9 | Introduction | The predicted half-life for 0 \nu \beta \beta with an effective mass in this region is greater than 10^{27} years. An experiment will
require approximately 1 tonne of isotope
to be sensitive to such a long half-life, and it will require a background level of 1 count/tonne-year or better. | {
"cite_spans": []
} | 10.1088/1742-6596/173/1/012007 | 0807.1741 | The Majorana Project | [
"S. R. Elliott"
] | [
"nucl-ex"
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21d2c24899b97f2ff57c69c344bfb1d8cc780c06 | subsection | 3 | 9 | The | The objective of the first experimental phase of Majorana is to build a 60-kg module of high-purity Ge, of which 30 kg will be enriched to 86% in ^{76}Ge,
to search 0 \nu \beta \beta . This module is referred to by the collaboration as the Demonstrator. The physics goals
for this first phase are to:Probe the neutrino m... | {
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672a6209d1aa649a9e98ce0f48eb80bce4131f8a | subsection | 4 | 9 | The | Right: A conceptual design of a two N-SC detector string.]The efficient commercial production of Ge detectors depends strongly
on the yields for producing high-purity single crystals of Ge and
for producing p-n junction diodes from these crystals. Single-crystal
boules naturally favor right circular cylindrical geometr... | {
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692df04cfc7b4d641d5f54f83af02ee5b2d37177 | subsection | 5 | 9 | The | (Earlier attempts employing n-type material exhibited poor energy
resolution at hight energies due to increased charge trapping.)
This in turn results in an increased range
of drift times and a distinct electric signal marking the arrival
of the charge cloud at the central electrode. Figure REF
illustrates the p-type ... | {
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262e3f242b1fe87a374552c9dc432cb8e35f5dfb | subsection | 6 | 9 | The | The cryostats themselves are situated within a
thick layer of electroformed Cu comprising the innermost
passive shielding layers, so extra cryostat wall and coldplate
thickness is not a concern from the standpoint of backgrounds.
However, thicker cryostat walls do reduce the potential for
inter-cryostat granularity rej... | {
"cite_spans": []
} | 10.1088/1742-6596/173/1/012007 | 0807.1741 | The Majorana Project | [
"S. R. Elliott"
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"nucl-ex"
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01f3177899beef27eca1012e49d8816766dd0db2 | subsection | 7 | 9 | The | This high-Z shielding
enclosure will be contained inside a gas-tight Rn exclusion box
made of stainless-steel sheet. Outside this bulk high-Z shielding
will be a layer of hydrogenous material, some of which will be doped
with a neutron absorber such as boron, intended to reduce the neutron
flux. Finally, active cosmic-... | {
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e15e494b0c222f41ff279a10b5877b765d0c0ef3 | subsection | 8 | 9 | Conclusion | The Majorana collaboration is carrying out R&D to develop a 1-tonne 0 \nu \beta \beta experiment based on enriched ^{76}Ge. The Ge detectors will be housed in a classic cryostat design that is constructed from ultra low-radioactivity materials. The cryostats will be contained within a passive shield, and active veto sy... | {
"cite_spans": []
} | 10.1088/1742-6596/173/1/012007 | 0807.1741 | The Majorana Project | [
"S. R. Elliott"
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912b064b0387cbecd9509f6c341a67b8986f7b33 | abstract | 0 | 20 | Abstract | We present a light and fast, public available, ray-tracer {\tt Splotch}
software tool which supports the effective visualization of cosmological
simulations data. We describe the algorithm it relies on, which is designed in
order to deal with point-like data, optimizing the ray-tracing calculation by
ordering the parti... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
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adcb919d9f5228172b72f65417fd3ea31aa29528 | subsection | 1 | 20 | Introduction | According to the standard theory of the Big Bang,
our universe came into existence as a singularity
around 13.7 billion years ago. After its initial appearance, it
inflated from a very dense, hot and
homogeneous state to the expanded, cooled and very structured state of
our current universe. During its evolution, plane... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
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df4f4f4ad5712ea5001577ea37f78ae276f50580 | subsection | 2 | 20 | Introduction | We will describe methods used to generate the data used for the Splotch rendering
and the technique adopted to create the stereographic
version of the movie. | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
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] | [
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db67725ecbf11ed1ab2699994852f9e318e1f024 | subsection | 3 | 20 | Splotch | The underlying visualization algorithm is a derivate of what in
general is called volumetric ray castinghttp://en.wikipedia.org/wiki/Volume_ray_casting
and uses an approximation of the radiative transfer equation,
which – together with the application of perspective – gives the
produced images a very realistic appearan... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
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8040ca845513244da6ed45cad495149abcba07fe | subsection | 4 | 20 | Physical motivation of the algorithm | The rendering algorithm of Splotch is generally designed to handle
point-like particle distributions. We especially have Smoothed
Particle Hydrodynamic
,
simulations in mind, where the density of
the fluid is described by spreading tracer particles by a kernel, most
commonly the B_2-SplineW(x,h)=\frac{8}{\pi h^3}\left... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
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05a480ca4c144cbd068c5b7f292ae71bb2e960aa | subsection | 5 | 20 | Physical motivation of the algorithm | The mapping between the scalar
property and the three components of \bf {E} and \bf {A} (for red, green and blue)
is typically achieved via a colour look-up table or palette, which can
be provided to the ray-tracer as an external file to allow a maximum of flexibility.Assuming that absorption and emission are homogeneo... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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cd5ed4971ad885f8c24bf25bbe78b0d2bf6cbeaf | subsection | 6 | 20 | Implementation of the algorithm | The rendering algorithm now proceeds as follows:A camera position \vec{c}, a look-at point \vec{l} (e.g. the
position of the object of interest) and a sky
vector \vec{s} are specified by the user. The latter just defines the up-direction
for the scene, and the first two define the viewing direction \vec{v}, i.e. \vec{v... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
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e1c2a4b532f0d7bc6cbbd11651ce1ac1297bc225 | subsection | 7 | 20 | Public version of the algorithm | Besides various internal optimisations, Splotch uses OpenMPhttp://openmp.org/
to generate different regions of the image distributed over several
cores on shared memory platforms. The algorithm requires 30
bytes per particle, which allows to render more than 70 million
particles on a standard PC with 2 GByte of main me... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
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70ad8b0f0d938129fef98e30f9a48476560f2775 | subsection | 8 | 20 | Performance of the algorithm | The CPU time consumption of splotch to render individual frames
depends on the frame size, the number of particles to visualize as well as
their apparent size, e.g. over how many pixels they get spread. For a
typical setup we find T_\mathrm {CPU} \propto n_\mathrm {pixel}
and T_\mathrm {CPU} \propto -0.5 \varphi , e.g.... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
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"C. Gheller",
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5a925edd2955ed6896be91ef3b6cc118deea899d | subsection | 9 | 20 | Application to cosmological simulations | Clusters of galaxies are ideal cosmological probes . They are the
largest collapsed objects in the Universe and so are very sensitive to
the structure formation process. The evolution of the diffuse cluster
baryons (the so-called intra cluster medium, ICM)
has a nontrivial interplay with the cosmological
environment, a... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.0005856285570189357,
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... |
5f6fb72ab3888c0154c0db91fc4b9cd3e733ed9b | subsection | 10 | 20 | Visualisations using flat projection | For visualising cosmological structures it is often useful to adopt a
flat projection to obtain the equivalent of a map as obtained from a
very distant object. In this case, the raytracing – due to handling
of absorption – still can lead to some three-dimensional impression,
as becomes apparent in figure REF . Especial... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.... |
5c2fe8b5ba3608ac360698542c38cdca70deb391 | subsection | 11 | 20 | Animations of evolving galaxy clusters | To display the dynamics characterising the formation of galaxy clusters,
the realistic, 3D impression obtained when rendering with Splotch results in amazing animations, as shown in Figure
REF . This movie is based on processing nearly 250
outputs (each \approx 1GB in size) of a high resolution, “zoomed”
galaxy cluster... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
3a01269d9ea6d5fcad9e61ff8a5aabe2fee49988 | subsection | 12 | 20 | Animations of evolving galaxy clusters | Thereby, it produces one
frame for every entry in the file, without having to reload the
cosmological simulation every time. This can be quite handy, especially
when the simulation data are huge (several GB or more). It is
also useful to pre-process the data to emphasise different aspects of
a cosmological simulation. ... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.05394739285111427,
-0.01833845116198063,
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-0.020001422613859177,
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b9b847ee78d1575c153600f1eb7e4c84d9d55687 | subsection | 13 | 20 | The 4D Universe | The visual rendering of the universe and its evolution can
represent a spectacular approach toward the intuitive explanation of
the complex phenomena that are at the bases of our incredibly
fascinating theory of cosmology, for both scientists and common people.
Unfortunately, an effective
implementation of this approac... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.02493681013584137,
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0.04... |
cc590e402e9a15ab91fcc78d5e3cdd3d71954731 | subsection | 14 | 20 | Body | The realisation of such a complex visualisation project required
to properly fine-tune the usage of Splotch. Colours, transparencies,
smoothing lengths adapt to the represented environment
and objects, which continuosly change following the evolution of cosmological
structures and the movements of the camera.The movie ... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.01458948478102684,
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... |
4af989c009fd226f70ea34228bb5a0b3331a6225 | subsection | 15 | 20 | The Big Bang | The representation of the first few instants after the Big Bang is an
incredibly difficult task. Nothing that we can conceive is able to
properly describe what happened in that initial time frame. We have adopted
an abstract geometric representation, in which
a spherical symmetric mesh represents the expanding space-ti... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
0.002832694910466671,
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-0.020113086327910423,
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0... |
c5b3a9a24cefac62b3fb939577d777406775b5a2 | subsection | 16 | 20 | The evolution of the Universe | For a project like the 4D Universe, it is necessary to create the images
making use of data from an extremely high resolution simulation.
We used a simulation of a large
cosmic structure which connects 4 very massive galaxy clusters
.
The high resolution region in this simulation is
more than one order of magnitude lar... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.018374359235167503,
0.04315837845206261,
-0.01600888930261135,
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-0.00850806012749672,
0.007378739304840565,
0.0... |
e3eff67ad2769db543ddc243eefe2312a6459c00 | subsection | 17 | 20 | The Galaxy | Galaxies, and in particular spiral galaxies, are amongst the most spectacular
objects in the universe. For many galaxies, high resolution images have been
caught (e.g. by the Hubble Space Telescope, http://heritage.stsci.edu/2005/12a/big.html), which provide a detailed
description of their structure and morphological f... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.0352165512740612,
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-0.011199717409908772,
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0.027449989691376686,
-0.0007681686547584832,
... |
1c0754566336fb2e67b8bdbc1c482a3f61871ba1 | subsection | 18 | 20 | The Galaxy | This results in a purely kinematic approach (no dynamics considered).\bullet The stars in the bulge and in the globular clusters rotate around the
galaxy center, each with its own constant velocity, calculated in order to
balance the gravitational attraction of the matter distributed inside the orbit.\bullet Equations ... | {
"cite_spans": []
} | 10.1088/1367-2630/10/12/125006 | 0807.1742 | Splotch: Visualizing Cosmological Simulations | [
"K. Dolag",
"M. Reinecke",
"C. Gheller",
"S. Imboden"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.012693991884589195,
0.011336100287735462,
0.0... |
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