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70a29dab0deca9a5e390081ae09b28475f05f207 | subsection | 30 | 38 | Proof of the statement | \left(
\Gamma (v_L,\Omega _R)-\Gamma (v_R,\Omega _L)
+
P_{\text{ct}}(v_L^{\Omega ^{-1}_R},v_R^{\Omega ^{-1}_L})
\right)\Big |_{\Omega _R=1,\Omega _L=m_{RL}^{-1}}
\right]
\\
&=&
\frac{1}{2}\left[
\Gamma (v_R,m_{RL}^{-1})-\Gamma (v_L,m_{LR}^{-1})
+
P_{\text{ct}}(v_R,v_L^{m_{LR}})
-
P_{\text{ct}}(v_L,v_R^{m_{RL}})
\right]... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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8e94e9874afd2ac523bee90da2ba69f05f3ac357 | subsection | 31 | 38 | Explicit Klein-Gordon form | The operators K_{R,L} can be brought to a manifest Klein-Gordon form
if desired. Indeed,K_R
&=&
m_{RL}m_{LR}- \mathrel {\mathop {\!\!\!/}}_R m_{LR}^{-1} \mathrel {\mathop {\!\!\!/}}_L m_{LR}\\
&=&
m_{RL}m_{LR}- \mathrel {\mathop {\!\!\!/}}_R^{\,\,2}
-\mathrel {\mathop {\!\!\!/}}_Rm_{LR}^{-1}(\mathrel {\mathop {\!\!\!/}... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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3de8b6462db544de44bf3eb85059054f04e2cbf8 | subsection | 32 | 38 | Explicit Klein-Gordon form | This
gives (using (REF ))W^+
&=&
-\frac{1}{4}{\rm Tr}\log ({\tilde{M}}_R - ({\tilde{D}}^R_\mu )^2 )
-\frac{1}{4}{\rm Tr}\log ({\tilde{M}}_L - ({\tilde{D}}^L_\mu )^2 )
,
\\
W^-_c
&=&
\frac{1}{4}{\rm Tr}\left(\gamma _5\log ({\tilde{M}}_R - ({\tilde{D}}^R_\mu )^2 ) \right)
-\frac{1}{4}{\rm Tr}\left(\gamma _5\log ({\tilde{... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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bfe856b74e7f6592a3faaf94fd4c593015127c3a | subsection | 33 | 38 | Direct computation of the leading order in two dimensions | In this section we carry out explicitly the computation of W_c^- in
two dimensions to LO in the derivative expansion. This verifies the
identification (REF ) in this case and illustrates its use.To this end we apply the convenient method of Chan
to compute the trace of the logarithm of K_R. This takes the form{\rm Tr}... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 292,
"openalex_id": "",
"raw": "L.-H. Chan, Phys. Rev. Lett. 57, 1199 (1986).",
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"start": 195
}
]
} | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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0... |
53602f6429f594cd26b87068a2e5a28958895e33 | subsection | 34 | 38 | Direct computation of the leading order in two dimensions | IntroducingN_R= (p^2+m_{RL}m_{LR})^{-1}one finds-{\rm tr \,}\left(\gamma _5\log ({\tilde{N}}_R)\right)
&=&
-{\rm tr \,}(\gamma _5\log N_R)
+{\rm tr \,}\!\left(
\gamma _5 \,N_R\left(
-\frac{1}{2}\sigma _{\mu \nu } F^R_{\mu \nu }
+ (B^R_\mu )^2 -[D^R_\mu , B^R_\mu ]
\right)\right)
+{\mathcal {O}}(D^4)
,
\\
{}[{\tilde{D}}... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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c529c6af478c1b0915aa47ee63b8020b06077e5f | subsection | 35 | 38 | Direct computation of the leading order in two dimensions | Similarly, the
identity\int d^2x\epsilon _{\mu \nu }{\rm tr \,}\!\left(
\frac{1}{2}N_R F^R_{\mu \nu }-\frac{1}{2}N_L F^L_{\mu \nu }
\right)
=
\int d^2x\epsilon _{\mu \nu }{\rm tr \,}\!\Big (
-N_R(D_\mu m)_{RL}N_L(D_\nu m)_{LR}
\Big )allows to bring the second term to an UV convergent form (up to terms
which are symmetr... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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2e95c9169d9e5d87572c13f930ea2413fcdf7217 | subsection | 36 | 38 | Direct computation of the leading order in two dimensions | One can now take matrix
elements to compute the trace in (REF ). In doing so
m_{RL}m_{LR} and m_{LR}m_{RL} are replaced by their eigenvalues and the
momentum integral becomes straightforward. This givesThe
limit m_j^2\rightarrow m_i^2 is finite and it correctly reproduces the
contribution from diagonal matrix elements.... | {
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"doi... | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
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] | 2,008 | en | Physics | [
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11355d099ae69d11a8d50ac78553e648a55da4c5 | subsection | 37 | 38 | Conclusions | In this work we have found a remarkable result, namely, there is a
local operator, {\bf K}, which correctly reproduces the non-trivial
chiral invariant factor of {\rm Det\,}{\bf D}. Moreover, such operator is
explicitly constructed. This allows to address a direct non
perturbative definition of the chiral determinant a... | {
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"doi"... | 10.1140/epjc/s10052-008-0782-4 | 0807.1696 | The invariant factor of the chiral determinant | [
"L. L. Salcedo"
] | [
"hep-th"
] | 2,008 | en | Physics | [
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4bf56581303c668701c608875e8bc79c8a1c201b | abstract | 0 | 16 | Abstract | Since the order of elliptic type model equation (Laplace equation) is two
[1], [2], then it is natural the order of composite type model equation must be
[3] [4] [5] three. At each point of the domain under consideration these
equations have both real and complex characteristics. Notice that a boundary
value problem fo... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0... | |
6aba910f27eee46707ac4a9ec44a11f1c08d7f04 | subsection | 1 | 16 | Introduction. | The paper is devoted to the investigation of boundary value problems for a composite type equation of second order.This was possible as earlier we investigated an elliptic type boundary value problem of first order ( Cauchy-Riemann equation) for which the boundary is a carrier of boundary conditions [7]. Notice that in... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0.... | |
b4c7536e9cb58c49ab6340c2a3444c8bf5c0d240 | subsection | 2 | 16 | Problem statement | Let's consider the following boundary value problem:\ell \, u\equiv \frac{\partial ^{2} u(x)}{\partial x_{2}^{2} } +i\frac{\partial ^{2} u(x)}{\partial x_{1} \, \partial x_{2} } =0,\, \, \, \, \, x\in D,\ell _{k} u\equiv \left. \frac{\partial u(x)}{\partial \, x_{2} } \right|_{x_{2} =\gamma _{k} (x_{1} )} +\alpha _{k} ... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0.0... | |
9a619742ca210c85f52eef2c7784e08f29f58c42 | subsection | 3 | 16 | Fundamental solution. | Applying the Fourier transform to equation (REF ) we get a fundamental solution in the formU(x-\xi )=\frac{-1}{4\pi ^{2} } \int _{R^{2} }\frac{e^{i(\alpha ,\, x-\xi )} }{\alpha _{2} (\alpha _{2} +i\, \alpha _{1} )} d\alpha ,where(\alpha _{1} x-\xi )=\sum _{j=1}^{2}\alpha _{j} (x_{j} -\xi _{j} ) .Further, since\frac{1}{... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
-0.044481340795755386,
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0.002028812887147069,
0.0... | |
be4a7cce6d047c205eb8fa8130fc7228f588e19e | subsection | 4 | 16 | Necessary conditions. | Multiplying equation (REF ) by fundamental solution (REF ) and integrating if in domain D, applying Ostrogradskii-Gauss formula [8], we get formula similar to Green's second formula that after application of fundamentality properties of function (REF ) get the form:\int _{a_{1} }^{b_{1} }\left. \left[u(x)\frac{\partial... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0.0249... | |
79ee10d33eb5239d05f83ad48c7fb4a8d3f6fc95 | subsection | 5 | 16 | Necessary conditions. | \frac{\partial u(x)}{\partial x_{2} } \right|_{x_{2} =\gamma _{1} (x_{1} )} U(x_{1} -\xi _{1} ,\gamma _{1} (x_{1} )-\gamma _{1} (\xi _{1} ))\left[1-i\gamma ^{\prime }_{1} (x_{1} )\right]dx_{1}In exactly the same way to [9] and [10], we get the following necessary conditions:\left. \frac{\partial u(\xi )}{\partial \xi _... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0.010... | |
872b9166a9f1f75571531edd73a03a2a9ec13c78 | subsection | 6 | 16 | Necessary conditions. | \frac{\partial U(x-\xi )}{\partial x_{2} } \right|_{\begin{array}{l} {x_{2} =\gamma _{2} (x_{1} )} \\ {\xi _{2} =\gamma _{1} (\xi _{1} )} \end{array}} \left[1-i\gamma ^{\prime }_{2} (x_{1} )\right]dx_{1} --2\int _{a_{1} }^{b_{1} }\left. \frac{\partial u(x)}{\partial x_{2} } \right|_{x_{2} =\gamma _{1} (x_{1} )} \left. ... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0... | |
aecc112a9bda6ee5dda480ec50eb718e18722eb4 | subsection | 7 | 16 | Necessary conditions. | \frac{\partial U(x-\xi )}{\partial x_{2} } \right|_{\begin{array}{l} {x_{2} =\gamma _{2} (x_{1} )} \\ {\xi _{2} =\gamma _{2} (\xi _{1} )} \end{array}} \left[1-i\gamma ^{\prime }_{2} (x_{1} )\right]dx_{1} ,\left. \frac{\partial u(\xi )}{\partial \xi _{2} } \right|_{\xi _{2} =\gamma _{2} (\xi _{1} )} =2\int _{a_{1} }^{b_... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0... | |
97c325ea2502b6340918481c1e4e0253defc7393 | subsection | 8 | 16 | Regularization. | As it was said above, necessary conditions (REF )–(REF ) contain singular addends.Considering (REF ), we have:\left. \frac{\partial U(x-\xi )}{\partial x_{2} } \right|_{\begin{array}{l} {x_{2} =\gamma _{k} (x_{1} )} \\ {\xi _{2} =\gamma _{k} (\xi _{1} )} \end{array}} =\frac{1}{2\pi } \cdot \frac{1}{\gamma _{k} (x_{1} )... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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... | |
6ccb213bd22bea9c40479b793d7736bedcbf2fe6 | subsection | 9 | 16 | Regularization. | \frac{\partial u(\xi )}{\partial \xi _{1} } \right|_{\xi _{2} =\gamma _{1} (\xi _{1} )} +i\left. \frac{\partial u(\xi )}{\partial \xi _{2} } \right|_{\xi _{2} =\gamma _{1} (\xi _{1} )} ==\frac{1}{\pi } \int _{a_{1} }^{b_{1} }\left. \frac{\partial u(x)}{\partial x_{2} } \right|_{x_{2} =\gamma _{2} (x_{1} )} \frac{dx_{1}... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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080113fcec30157dfe99cea4d3eafc3204e1da19 | subsection | 10 | 16 | Regularization. | \frac{\partial u(x)}{\partial x_{2} } \right|_{x_{2} =\gamma _{2} (x_{1} )} \frac{dx_{1} }{x_{1} -\xi _{1} } + ......where the sum of non-singular addends are denoted by dots.Considering boundary conditions (REF ), from necessary conditions (REF ) for boundary values of the unknown function we get the following regular... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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1539e7594cd9714ff2826593286cebf7055dc4b8 | subsection | 11 | 16 | Regularization. | Thus we proved the following statement:Theorem 3. When fulfilling the conditions of Theorem 2
if \varphi _{k} (x_{1} ), k=1,\, 2 are continuously
differentiable functions vanishing at the end of the interval
(a_{1} ,\, b_{1} ), then (REF ) are regular
relations. | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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ee21f2dced80a6cc6539b183d308ad848deb45d3 | subsection | 12 | 16 | Fredholm property. | Considering boundary conditions (REF ), the first necessary condition (REF ) not containing singular integrals leads to regular relation (REF ).Further, proceeding from boundary conditions, after regularizing two necessary conditions given in (REF ), that contain singular integrals, we get a relation that has no singul... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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0... | |
e0db709ee841f02e3b4f1956f92507a65bcd2b10 | subsection | 13 | 16 | The inverse problem in Tikhonov-Lavrent'ev sense. | Let's consider the problem\frac{\partial ^{2} u(x)}{\partial x_{2}^{2} } +i\frac{\partial ^{2} u(x)}{\partial x_{1} \partial x_{2} } =0,\, \, \, \, x\in D,\left. \frac{\partial u(x)}{\partial x_{2} } \right|_{x_{2} =\gamma _{k} (x_{1} )} +\alpha _{k} u(x_{1} ,\gamma _{k} (x_{1} ))=\varphi _{k} (x_{1} ),\, \, \, \, k=1,... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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36bdc82585754660d642303b2d36f3374ce0783d | subsection | 14 | 16 | Stephan's inverse problem. | The above mentioned boundary value problem (REF ),(REF ), is given provided \alpha _{k} ,\, \, \varphi _{k} (x_{1} ), k=1,\, 2, \gamma _{1} (x_{1} ), \alpha _{k} (x_{1} ), k=\overline{1,\, 4} è \varphi _{3} (x_{1} ) - are the known, u(x), x\in D è \gamma _{2} (x_{1} ), x_{1} \in [a_{1} ,\, b_{1} ] are the unknown funct... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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7b923f809dbe64fd4e25c2085dbc3390f6043179 | subsection | 15 | 16 | Reference | 1. Courant, R. and Hilbert, D. Methods of mathematical physics, 1-2
Interscience,
1953 - 19622. Bitsadze, A.V. Boundary value problems for second order elliptic equations, North -
Holland, 19683. Hadamard, Tohoku, Math., J., vol. 37, pp. 133-150, 19334. Hadamard, L'Enseignement Math. Vol. 35, pp. 5 -42, 19365. Jurayev ... | {
"cite_spans": []
} | 0807.1697 | Investigation of solutions of boundary value problems for a composite
type equation with non-local boundary conditions | [
"N. A. Aliev",
"A. M. Aliev"
] | [
"math.AP"
] | 2,008 | en | Mathematics | [
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3e8f4de458bfce8181dce49a7f8c0bef133f22b1 | abstract | 0 | 15 | Abstract | We present optical time series spectroscopy of the pulsating white dwarf star
G29-38 taken at the Very Large Telescope (VLT). By measuring the variations in
brightness, Doppler shift, and line shape of each spectrum, we explore the
physics of pulsation and measure the spherical degree ($\ell$) of each stellar
pulsation... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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7baf64268e69ca604d861fa4737777610765cf49 | subsection | 1 | 15 | Introduction | DAVs, or ZZ Cetis, are variable white dwarf stars with hydrogen atmospheres. They are the coolest known white dwarf pulsators and reside in an instability strip near 12,000 K. Their pulsations are multi-periodic with amplitudes as high as 5 per cent and periods between 70 s and 1100 s. In the past few years the number ... | {
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"raw": "Voss, B., Koester, D., Østensen, R., Napiwotzki, R., Homeier, D., & Reimers, D. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 372, 15th European Workshop on White Dwarfs, ed. ... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
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04e49e9b82cb94ad72a97246409d9f26d3d4abe1 | subsection | 2 | 15 | Introduction | It has an abundance of modes, but they are not all excited simultaneously and many observation runs are necessary to measure them all. compiled 10 years of photometric observations and found a possible series of \ell =1 modes on G 29-38. Time series spectroscopy taken at the Keck Observatory with the LRIS spectrograph ... | {
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... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.06660240143537521,
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c0829c5773a06f58fdf0243d18100f0675cfb844 | subsection | 3 | 15 | Observations | We present a 6.14 hour spectral series (604 spectral images) of G29-38 from the VLT, observed with the FORS1 spectrograph on August 27, 1999 starting at 03:00:19.67 UT. The average exposure time on each image is 16.0 s with a readout time of 16.0 s. We perform a standard reduction on each image using routines in IRAF. ... | {
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{
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Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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c970a8c63c41204f75ddbfef4f94cb4df8d82c76 | subsection | 4 | 15 | Periodicities | Time series spectroscopy of pulsating white dwarfs provides the opportunity to measure both the variations in brightness of the star and the radial velocity of the gas along the surface of the star. We find periodic variations in our measurements of both the light and velocity curves. We create a light curve by averagi... | {
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... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
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c84b67a8c38df2aa1b98c97b8c2ab5e75a295b67 | subsection | 5 | 15 | Periodicities | However, since the light curve fixes the frequency, for a velocity mode to have less than 0.1 per cent chance of being due to noise it simply needs an amplitude greater than 1.47 km s^{-1}. Only the modes F1, F2 and the combination of F1+F2 have velocity amplitudes greater than this limit.We compare the observed veloci... | {
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Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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ea294e1148364e6b15776522e07d2484208c53e9 | subsection | 6 | 15 | Periodicities | Since we have not resolved rotational splitting of our modes, use of combination modes to determine \ell is very uncertain. We only note that the first harmonic of F4 shows a larger value than the other harmonics.One curious feature in these time series is the modestly significant peak in the velocity FT at 2858\mu Hz ... | {
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"open... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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ae02cc2d330a2dde5c4dff66fe8602734b544f5f | subsection | 7 | 15 | Mode identification of G 29-38 | Due to differences in limb darkening across the spectral lines, the hydrogen spectral line shapes change according to the distribution of the pulsation across the surface of the star. As a result, chromatic amplitudes, wavelength dependent amplitude variations across the Balmer lines, have characteristic shapes that re... | {
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"end": 1... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0715ec3c0d77e2d0e93a41fb88be6e8974bbb4fa | subsection | 8 | 15 | How to measure spherical degree | We follow the procedure outlined by for fitting each spectral line with the combination of a Gaussian and a Lorentzian superimposed on a linear continuum. We fit each spectrum only allowing the area of the Gaussian and Lorentzian to vary along with the slope and intercept of the linear continuum. Prior to fitting we es... | {
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... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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434a2f5e91668cbc42dc8f50a7ca816b08ab6f0f | subsection | 9 | 15 | How to measure spherical degree | The amplitude of the Gaussian EW corresponds to the central bump seen in the chromatic amplitudes, while the Lorentzian EW corresponds to the wings of the chromatic amplitudes. With only two parameters, the EW variation plot simplifies the comparison between observed pulsations and the models. In this paper we use the ... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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e23c59fd498204a69a828063c5a3dd8b69be4b4a | subsection | 10 | 15 | Measured EW variations | We measure the periodic changes in the normalized EWs for the six largest modes of the VLT observations and perform the same analysis on the Keck time series spectroscopy of G 29-38 (VK00). With a consistent analysis we can compare the data sets to the models as well as to each other. Figures 5 and 6 show analysis of b... | {
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Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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570c882a2994acd8de9f4445c8212416f5156591 | subsection | 11 | 15 | Noise simulations | To better understand how noise affects our measurement of spherical degree, we perform Monte Carlo simulations of model spectral series. Gaussian noise was introduced to both the overall brightness of the spectra and across the individual wavelengths of the model spectrum to match the noise observed in the VLT data. Th... | {
"cite_spans": []
} | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
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6e95507f3a330ac9eeb2bdef532a1e399267c6ba | subsection | 12 | 15 | Discussion | Due to the limb-darkening variation across the spectral lines, periodic changes in the line shape reveal the distribution of the pulsation across the surface of the star. The observations of the line shape do not explicitly agree with the model, as seen in previous chromatic amplitudes (C00). However, the trends betwee... | {
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... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
"Susan E. Thompson",
"M. H. van Kerkwijk",
"J. C. Clemens"
] | [
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929267ce503338f270aaeaeb60f53d5a6e492607 | subsection | 13 | 15 | Discussion | This could be the reason we observe line shape variations similar to \ell =4 modes, but not \ell =3; nonlinear mixing distorts the mode identification. In addition to our F4, these nonlinearities may be responsible for the unusual chromatic amplitudes seen on G 117-B15A by . Luckily, knowing that the mode is high \ell ... | {
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... | 10.1111/j.1365-2966.2008.13591.x | 0807.1698 | Deciphering the Pulsations of G 29-38 with Optical Time Series
Spectroscopy | [
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"J. C. Clemens"
] | [
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20b2eaf8942fd2424185b6b187967644b56941f6 | subsection | 14 | 15 | Conclusions | Time series spectroscopy has proven to be a useful tool to measure white dwarf pulsation. For G 29-38, it has revealed the physical motion of the pulsation through Doppler shifts and \ell through the variations of line shape. The three sets of spectroscopy on G 29-38, the VLT time series presented here, the Keck time s... | {
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"J. C. Clemens"
] | [
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99b03282798322b03c7eb9608ce5be6e79adb7b4 | abstract | 0 | 16 | Abstract | We explore how inherent flexibility of a protein molecule influences the
mechanism controlling the kinetics of allosteric transitions using a
variational model inspired from work in protein folding. The striking
differences in the predicted transition mechanism for the opening of the two
domains of calmodulin (CaM) emp... | {
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} | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
"John J. Portman"
] | [
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890d3f92c79b3b7509eef788f27ba8ad31b9d7e2 | subsection | 1 | 16 | INTRODUCTION | To understand protein function, it is often essential to characterize
large conformational changes that occur upon ligand binding. Within
the population-shift mechanism of allosteric conformational
change, the bound complex is formed
when a ligand selects and stabilizes a weakly populated conformational
ensemble from t... | {
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... | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
"John J. Portman"
] | [
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34c52745e3078594ae35fb99937e5d7e7ec61cb7 | subsection | 2 | 16 | INTRODUCTION | Aside from
general theoretical implications, the results presented in this paper
are interesting from the point of view of understanding the well-known
and intensely studied thermodynamic differences between the two
domains of CaM., Our approach is based on a coarse-grained variational model previously
developed to cha... | {
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EF-hands of Calmodulin | [
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] | [
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d1c193bca202feed2cd74219908e42efcd64cde7 | subsection | 3 | 16 | RESULTS | Conformational Flexibility of the CaM Domains. We first
compare the inherent flexibility of the two domains of CaM by
calculating the mean-square fluctuations \mathcal {B}_i for each
residue in the nCaM and cCaM for the open/closed conformational
transitions of each domain. Fig. REF (a) shows
\mathcal {B}_i along the ... | {
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} | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
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] | [
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7bb4ff2e95e82e5265c7a6787a3ee6439ff6baea | subsection | 4 | 16 | RESULTS | REF (a) and
REF (a).] Residue Asp118 of the F/G helix-linker from
cCaM shows very different behavior relative to the rest of the
residues in Fig. REF . Residue Asp118 shows highest
\mathcal {B}_i near the transition state at \alpha _0 = 0.4 whereas
\mathcal {B}_i of all the other residues shown decrease monotonically ... | {
"cite_spans": []
} | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
"John J. Portman"
] | [
"q-bio.QM",
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30758a4500f8af5d5b9280634505fd6a798589e6 | subsection | 5 | 16 | RESULTS | The engineered “even-odd" EF-hands paired CaM2/3 fragment (composed
of EF-hands 2 and 3) has been shown recently to have distinct
transition characteristics from the “odd-even" EF-hands paired nCaM
and cCaM. NMR spectroscopy
has shown that Ca^{2+}-free (apo) CaM2/3 does not have a stable
folded structure but rather sh... | {
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]... | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
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6971833dd5cf714f3dfe66237e5b9ba2b3ea017e | subsection | 6 | 16 | RESULTS | The local unfolding
of the domain linker enhances the flexibility of this linker region
dramatically, first relaxing in structure and then stabilized in
the holo-CaM2/3 structure as a rigid \alpha -helix conformation.
This local unfolding signaled by increase and decrease in flexibility
is similar to the cracking exhib... | {
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"... | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
"John J. Portman"
] | [
"q-bio.QM",
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81a27500a786df2835c2c18c34a16ce9993a1162 | subsection | 7 | 16 | DISCUSSION | CaM, a small (148-residue) Ca^{2+}-binding protein with very high
plasticity, may be an ideal system to demonstrate flexibility influenced
conformational transitions. The
protein consists of structurally similar N- and C-terminal globular
domains connected by a flexible tether also known as central or interdomain
linke... | {
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... | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
"John J. Portman"
] | [
"q-bio.QM",
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] | 2,008 | en | Quantitative Biology | [
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95722b29d3649f603f801dddea71a101af01fe00 | subsection | 8 | 16 | DISCUSSION | The mechanism controlling the open/closed
transition does not involve cracking for the relatively flexible nCaM
whereas the mechanism controlling the conformation transition of the
more rigid cCaM exhibits transient partial local unfolding in its
helix-linker between the binding loops.
This partial local unfolding or c... | {
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}... | 10.1073/pnas.0806872106 | 0807.1699 | Inherent flexibility determines the transition mechanisms of the
EF-hands of Calmodulin | [
"Swarnendu Tripathi",
"John J. Portman"
] | [
"q-bio.QM",
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] | 2,008 | en | Quantitative Biology | [
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9c12065e3e78395393128641d9f64a01d3dc7e00 | subsection | 9 | 16 | DISCUSSION | On the other hand, in
Ca^{2+}-bound (holo) CaM structure
this same central linker adopts a more stable \alpha -helix
conformation which requires cracking in the conformational transition from its apo-CaM
structure. | {
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EF-hands of Calmodulin | [
"Swarnendu Tripathi",
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] | [
"q-bio.QM",
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4995ae87f1b52a7659bb8b94308b2b9339cbfc61 | subsection | 10 | 16 | METHODS | Preparation of Structures. The structures of the two
conformations of the transition are rotated to have the same center of
mass and minimum root-mean square deviation of the C_{\alpha }
positions. In nCaM, EF-hands 1 and 2 are consist of helices A/B and
C/D (Fig. REF (a)), respectively, whereas helices E/F
and G/H in... | {
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EF-hands of Calmodulin | [
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"John J. Portman"
] | [
"q-bio.QM",
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] | 2,008 | en | Quantitative Biology | [
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6fdbfb8c088016ce6c4bac6e346e2a26daa9a0a7 | subsection | 11 | 16 | METHODS | The probability
for a particular configurational ensemble specified by the variational
parameters \lbrace C_i,\alpha _i\rbrace at temperature T is given by the
variational free energy F(\lbrace C\rbrace ,\lbrace \alpha \rbrace ) = E(\lbrace C\rbrace ,\lbrace \alpha \rbrace ) -
TS(\lbrace C\rbrace ,\lbrace \alpha \rbrac... | {
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EF-hands of Calmodulin | [
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ea69a658a7d11996027367db843b1a34dc138260 | subsection | 12 | 16 | METHODS | These natural order
parameters for the reference Hamiltonian \mathcal {H}_0, \mathcal {B}_i =
\langle \delta \mathbf {r}_i^2\rangle _0,
contains information about the degree of structural order of each
residue. , Conformational Transition Mechanism. The main-chain dynamics
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EF-hands of Calmodulin | [
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8a47c51db2e3b76656339b94ec6f21fa210cfaf6 | subsection | 13 | 16 | METHODS | This difference shifts the relative degree of
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\Delta \overline{\rho _i}(0) =-1 corresponding to the apo and holo
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af0df5de31965a13608f3613c1f5a5c556371dda | subsection | 14 | 16 | Figure | Three dimensional structures of calmodulin (CaM) domains and EF-hands 2 and
3 fragment. The apo-CaM and holo-CaM structures shown here
are correspond to human CaM with PDB code 1cfd and 1cll respectively.
(a) The closed, apo and open, holo conformations of N-terminal domains of CaM (nCaM)
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4f35358700e006e836f60edd4dc4c4eab9da5278 | subsection | 15 | 16 | Figure | Residue Glu45 and Asp118 are from the nCaM and cCaM,
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df439270ce55c72b049036eb38f3f78e44136c6e | abstract | 0 | 6 | Abstract | Interface dynamics in two-dimensional systems with a maximal number of
conservation laws gives an accurate theoretical model for many physical
processes, from the hydrodynamics of immiscible, viscous flows (zero
surface-tension limit of Hele-Shaw flows, [1]), to the granular dynamics of
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446ab50bd18b1191ace3e1893ac3196618bab790 | subsection | 1 | 6 | Body | Optimal approximation of harmonic growth clusters by orthogonal polynomialsFerenc Balogh^{{\sharp },{\ddagger }}
Razvan Teodorescu^{\sharp }
^{\sharp }Center for Nonlinear Studies, LANL
^{\ddagger }Concordia University, MontréalInterface dynamics in two-dimensional systems with a maximal number of conservation
laws giv... | {
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c0e3ac514795ac1bebdd4415e99e3a5945d229d8 | subsection | 3 | 6 | Body | To that
end, we define the following family of orthogonal polynomials:
consider the domain specified by the exterior harmonic moments
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bfdddb46903ee83a1c2b8d7a705c4e0a059011d4 | subsection | 4 | 6 | Body | Since f(\zeta ) is a rational function of order two, the Cauchy transform C_{D_+} (z) (REF ) in the exterior domain D_- satisfies a quadratic equationwith rational coefficients in z depending on the parameters of f(\zeta ). As an algebraic function, C_{D_+} (z) can be analytically continued on a plane with a branch cut... | {
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2cd23ee911de23ca94654c26c67a6a7cba6d8495 | subsection | 5 | 6 | Body | For example, such
(reduced) representations arise in satellite imaging data
compression . Shape reconstruction algorithms are
then needed to find the boundary \Gamma , given the set of
moments t_0, \lbrace t_k\rbrace , with particular emphasis on good convergence
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75c14e8f6dc9d243f4d09e9d5c9f833c4056de12 | abstract | 0 | 22 | Abstract | We discuss the theoretical modelling of x-ray photoelectron diffraction (XPD)
with hard x-ray excitation at up to 20 keV, using the dynamical theory of
electron diffraction to illustrate the characteristic aspects of diffraction
patterns resulting from such localized emission sources in a multi-layer
crystal.
We show ... | {
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} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
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"F. Javier Garcia de Abajo"
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15b62eeb361b8efea81e8f6c63e64f9ba0717394 | subsection | 1 | 22 | Introduction | The method of x-ray photoelectron diffraction (XPD) is a powerful tool for the analysis of surface atomic structure, including adsorbates and overlayer growth. By measuring the angular intensity of photoelectrons excited by x-rays and comparing the experimental data with simulations, element-specific information on the... | {
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b852e612905804475b8c11535c554d65b68ccbb2 | subsection | 2 | 22 | Introduction | This poses considerable calculational difficulties as the photoelectron kinetic energies become larger than approximately 1 keV. Beyond this, the clusters sizes needed at these energies also become larger due to the greater inelastic mean free paths, which roughly go as E_{kin}^{0.75} and can be as large as 5-15 nm for... | {
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df9e6d71bf182dc4ef26c05d99cac6d38d367fc1 | subsection | 3 | 22 | Introduction | It was shown that this theory can not only explain the formation of Kikuchi bands but also reproduces features like forward-scattering directions and ring-shaped interference maxima around these directions.
Such features can also be explained in the intuitive forward scattering picture of
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de0d6b858ce3bc5e030b08bbb2e152a54665d1b7 | subsection | 4 | 22 | Theory | Although the full details of our long-range-order dynamical approach have been presented elsewhere, we introduce the essentials briefly here.
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d91dfd32c96d6994a9ac5c0cf6e29ae8607334f4 | subsection | 5 | 22 | Theory | After this, the wave function (REF ) is known and can be used to calculate the probability density inside the crystal for a plane wave moving in the \mathbf {k}^{\alpha }_{out} direction.
The modulation of this probability at the photoemitter positions describes the diffraction
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4875b3398656d9cdc8bd9f218f573faf16cb5b6a | subsection | 6 | 22 | Theory | This leads to coefficients of the form
\mu _{\mathbf {g},\mathbf {h}}= \exp (-M_{\mathbf {g}-\mathbf {h}}^n) \exp [ i (\mathbf {g}-\mathbf {h})\cdot \mathbf {r}_n ]
and results in the cross section formula which we have used in our previous simulations for quasi-elastic backscattering of electrons and XPD , :I_{DYN} \p... | {
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baee21e894f90e33000559348cce826859dd43f7 | subsection | 7 | 22 | Results | In this section, we will first show that the dynamical electron diffraction
approach is able to reproduce published experimental data for XPD at kinetic energies near 1 keV from diamond C(111) and from silicon Si(111) with very good agreement.
We then calculate the corresponding XPD patterns at kinetic energies ranging... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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0... |
90e972dd09dc24cf5533ce3705576da05f42d6dd | subsection | 8 | 22 | XPD from Diamond and Silicon near 1 keV | In Fig. REF a, we show the experimental data of , for C1s photoemission in diamond C(111) observed at a kinetic energy of 964 eV.
In part b of Fig. REF , the result of an XPD simulation using dynamical electron diffraction theory for point sources in a crystal is shown.
We assumed a lattice constant of 3.57Å and isotr... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 131,
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"raw": "J. Osterwalder, R. Fasel, A. Stuck, P. Aebi, and L. Schlapbach, Journal of Electron Spectroscopy and Related Phenomena 68, 1 (1994).",
"source_ref_id": "32c2cd11ecb158d02af330956d538fcc319469e... | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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cf5c203b4bc9acba9a81a3efe82c302d35f94dfd | subsection | 9 | 22 | XPD from Diamond and Silicon near 1 keV | REF . We will demonstrate below
that a rather complicated fine structure of dark lines exists at high kinetic
energies and that this is very sensitive to the crystal geometry.
From this fine structure, valuable information should be obtainable in a way which is qualitatively different from the low energy regime.Summari... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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... |
9976c67dadb84bb0873d81a966ddc0ab2c1f884a | subsection | 10 | 22 | Energy dependent full-hemispherical patterns | Having convinced ourselves that our calculational approach is able to describe
the XPD patterns of diamond and silicon at around 1 keV kinetic energy, we
will now show the results of calculations at systematically higher energies up to 20 keV. In Figures REF and REF we show calculations for the same two cases C(111) an... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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0.... |
fd8879643b36faffa7a38827e236d8d71b92336a | subsection | 11 | 22 | Simple interpretation of the photoelectron diffraction process at high energies | We see from the simulation that the photoelectron diffraction patterns become
dominantly characterized by a network of Kikuchi bands as energy is increased. These have the
general property of being symmetric with respect to a projected lattice
plane and they appear either with increased intensity in the middle of the b... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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f86b39dc08275357c4224a6dc3b2ccac3f782acf | subsection | 12 | 22 | Simple interpretation of the photoelectron diffraction process at high energies | At the position of the dark Kikuchi line, marked by the red solid square (a), we see
that the probability density is concentrated between the photoemitters, so that
it is more unlikely for photoelectrons to be diffracted in the direction of the red square, which is then manifested by the lower photoelectron intensity. ... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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664a8e2b22f6c2b96edd0fde94c798ce35c2bc5b | subsection | 13 | 22 | Experimental implications and possible applications | Based on the simulations above, we consider some implications for future HXPD
experiments. First of all, this concerns the angular width of the features to be observed and the necessary angular resolution. | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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d9af98d5b64d4bef42a1f2d98723b593d0d0613d | subsection | 14 | 22 | Angular resolution | In figure REF , we compare
two simulated HXPD patterns of C(111) which are blurred according to an angular
resolution of \pm 1 degree (comparable to resolutions used in existing XPD
experiments). One immediately notices the strongly reduced angular range over which the
variations occur at 10 keV photoelectron energy. T... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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0.0... |
5f8991ef23d4b3252ec8659aaf11dc2787ec5b1c | subsection | 15 | 22 | Sensitivity to lattice distortions: tetragonal example | We have demonstrated above that the high energy XPD patterns are dominated
by the crystallographic symmetries. The angular scales on which relevant changes
are visible are considerably reduced. This also means that it might not be necessaryily useful in all cases to measure large angular ranges at these high energies. ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 576,
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"raw": "B. Krömker, M. Escher, D. Funnemann, D. Hartung, H. Engelhard, and J. Kirschner, Review of Scientific Instruments 79, 053702 (2008).",
"source_ref_id": "3e360839b6650077376c774672256b9f922963c... | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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fa5cfe5d6c77a34d4e1cea77440173abc832e02a | subsection | 16 | 22 | Impurity or Dopant Site Determination | Another possible application of high energy XPD concerns the determination of
the crystallographic position of impurities in an otherwise perfect crystal.
A similar problem appears in the context of fluorescence radiation from impurities under excitation of crystals by either x-rays or electrons while changing the inci... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 334,
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"e... | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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29c83af0568b95041d0b3525310365a378202371 | subsection | 17 | 22 | Effects beyond the inelastic mean free path picture | Compared to the elastic interference effects that lead to changing Kikuchi band profiles of impurities occupying different positions in the unit cell, the qualitatively different contrast reversal effect of Kikuchi bands described below could allow measurements of localized absorption effects.
In photoelectron spectros... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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07775a97d2c787737cb2091a498dee9c8842eb91 | subsection | 18 | 22 | Effects beyond the inelastic mean free path picture | We illustrate this effect by calculations for Si(111) at 6 keV in Figure REF , placing the emitters in starting depths of 5nm, 10nm, and 30nm. The Figure REF clearly shows
how the contrast is reversing with increasing thickness. A similar effect is known
in transmission electron microscopy and is termed "anomalous abso... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 586,
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"raw": "D. M. Bird and Q. A. King, Acta Cryst. A 46, 202 (1990).",
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... | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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d8eb93a9869067bb2e0e2650e952bf4c08a87b29 | subsection | 19 | 22 | Spin-dependent effects and magnetic dichroism | In complete analogy to the lower energy case, in HXPD it should also be possible to observe diffraction effects that depend on the
photoelectron spin and magnetic dichroism.
Although the difference in purely exchange scattering of spin-up and spin-down electrons is expected to decrease as energy is increased , the spin... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 174,
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"raw": "M. A. Van Hove, A. P. Kaduwela, H. Xiao, W. Schattke, and C. S. Fadley, Journal of Electron Spectroscopy and Related Phenomena 80, 137 (1996).",
"source_ref_id": "e5e3790b290a1d664c19971dca0f8... | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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d11e5554fbd14bed3aed4091204f22397715a3c6 | subsection | 20 | 22 | Comparison to Cluster Model Calculations | In Fig. REF , we now show calculations for s-wave emission from C(111) based on a cluster model whose methodology is described in detail elsewhere . These calculations were carried out in single scattering (SS) and for emission from emitters in a cluster containing about 13,000 atoms and extending to about 30 Å below ... | {
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"raw": "F. J. Garcia de Abajo, M. A. Van Hove, and C. S. Fadley, Phys. Rev. B 63, 075404 (2001).",
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} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
"cond-mat.mtrl-sci"
] | 2,008 | en | Physics | [
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1b2f6a13733a9580bc05c50d6f6951a9b9a3bdd2 | subsection | 21 | 22 | Summary | We have presented a long-range order dynamical scattering approach for simulating photoelectron diffraction patterns
at high kinetic energies. The approach is based on exploiting the quasi
three-dimensional translational symmetry of the scattering potential
that the photoelectron experiences at high energies. The predi... | {
"cite_spans": []
} | 10.1088/1367-2630/10/11/113002 | 0807.1701 | High energy photoelectron diffraction: model calculations and future
possibilities | [
"Aimo Winkelmann",
"Charles S. Fadley",
"F. Javier Garcia de Abajo"
] | [
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bd1e064b42e3b70e1265cbd0fde1cde124733896 | abstract | 0 | 31 | Abstract | A joint spectral analysis of some Chandra ACIS X-ray data and Molonglo
Observatory Synthesis Telescope radio data was performed for 13 small regions
along the bright northeastern rim of the supernova remnant SN 1006. These data
were fitted with a synchrotron radiation model. The nonthermal electron
spectrum used to com... | {
"cite_spans": []
} | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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5c37cb889607aa054e53d30c3b1e607a2495b7bb | subsection | 1 | 31 | Introduction | Several observational and theoretical clues support the suggestion that
Galactic cosmic rays, up to an energy of 100 TeV or more
, , , are accelerated predominantly in the shocks of
supernova remnants. If Galactic supernovae occur at an average rate of one
event every 30 years, then an average supernova remnant must tr... | {
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"end... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
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6050c3651f3bcae71c2ff45df8c7d9140e60e450 | subsection | 2 | 31 | Introduction | Similarly, report that for the
southeastern rim of SN 1006 the ratio varies from a value of
0.91^{+0.03}_{-0.02} (i.e., r = 4.0^{+2.2}_{-0.5}) between the bright
X-ray synchrotron–emitting filaments to a value of 1 (i.e., r = \infty )
along the filaments. The mean value between the filaments is 0.96 \pm 0.03
(i.e., r =... | {
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... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
5fc0ee1b478026888ebcedb060bff805377d7e1b | subsection | 3 | 31 | Data and analysis | X-ray spectra of the filaments along the northeastern rim of SN 1006 were
obtained by analyzing 68 ks of data from the 2000 July 10–11 ChandraFor more information about the Chandra X-ray
Observatory refer to the Chandra Proposers' Observatory Guide, which
is available at http://asc.harvard.edu/proposer/POG/index.html. ... | {
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... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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d3cd6e5ed35ac1d0f00423efc96c80c885e80e46 | subsection | 4 | 31 | Data and analysis | As displayed in Figure (and
as originally reported by Koyama et al. 1995), the high-energy nonthermal
emission is concentrated along the rim. The second reason is that the ACIS
detectors are not well calibrated at energies below about 0.7 keV. The last
reason is that the absorption column density can be frozen at some... | {
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"... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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d8a1e98fe8a155154d1fd5c0666f2e01464b5652 | subsection | 5 | 31 | Data and analysis | Although both sets
of flux densities represent local averages because the half-power beamwidth
associated with the 843 MHz MOST image (44^{\prime \prime } \times 66^{\prime \prime }; see
Fig. ) is comparable to the size of the regions (49^{\prime \prime } \times 49^{\prime \prime }), they are reasonable estimates of th... | {
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"doi": "",
"end": 943,
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"raw": "Houck, J. C., & DeNicola, L. A. 2000, in ASP Conf. Ser. 216, Astronomical Data Analysis Software and Systems IX, ed. N. Manset, C. Veillet, & D. Crabtree (San Francisco: ASP), 591",
"source_re... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.... |
b46132a302c80ee012c0be074383614470c53d71 | subsection | 6 | 31 | Data and analysis | Note that ,
, , and use a more general form for
the cutoff (exp[- \left( p / p_{m} \right)^{s} ], where s = {1}{4},
{1}{2}, 1, or 2) and that performed a detailed study of
the shape of the cutoff for particles experiencing diffusive shock
acceleration.The synchrotron spectrum is computed by evaluating the following int... | {
"cite_spans": [
{
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"doi": "",
"end": 254,
"openalex_id": "",
"raw": "Ellison, D. C., Slane, P., & Gaensler, B. M. 2001, , 563, 191",
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"start": 0
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{
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"doi": ""... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.024319816380739212,
0.008673661388456821,
0.01... |
ddf832f5c2c2ddb1d0bc94a2c1820b998b7aa970 | subsection | 7 | 31 | Data and analysis | In this case, the mean value of \sin \theta in equation (REF ) is about \pi / 4,\nu _{m}
=
1.26 \times 10^{17}
\left( \frac{p_{m}}{10\ {\rm TeV}\ c^{-1}} \right)^{2}
\left( \frac{B}{100\ \mu {\rm G}} \right)\ {\rm Hz},andh \nu _{m}
=
0.522
\left( \frac{p_{m}}{10\ {\rm TeV}\ c^{-1}} \right)^{2}
\left( \frac{B}{100\ \mu ... | {
"cite_spans": [
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... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.021244700998067856,
0.00... |
1d0f194f268045aec8e9c9f834b3ef35b4dfa393 | subsection | 8 | 31 | Data and analysis | The
best-fit model for region 6, the region with the largest number of counts,
is plotted in Figures and . | {
"cite_spans": []
} | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.032402265816926956,
-0.0011422409443184733... |
07091a2961cae955e92dee80bd5275b58c5c8bc5 | subsection | 9 | 31 | Discussion | It is not immediately obvious whether the cospatial or peak radio fluxes
yield results that are more accurate, because the X-ray and radio
synchrotron morphologies are not the same. For example, along 49^{\prime \prime }-wide
strips that pass through the 13 X-ray regions toward the center of the
remnant, one finds that... | {
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{
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"doi": "",
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} | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.018489349633455276,
-0.042623139917850494,
-... |
64548ad5e870ce826eb3f9aad1a63681aa4d1ddb | subsection | 10 | 31 | Curvature | While the values of \chi ^{2} per degree of freedom (dof) are acceptable
for each of the four sets of fits, a comparison of Tables and
(and of Tables and ) reveals that the values
are uniformly lower when curvature is included as a free parameter. For
example, Figure shows the 1, 2, and 3 \sigma confidence
contours... | {
"cite_spans": []
} | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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0.02079271338880062,
-0.009... |
8cc4387db675fa2ef9cfb1cd968424d015d5e8a1 | subsection | 11 | 31 | Curvature | The use of a curved source
model is also compelling in the sense that the values of the best-fit
indices and curvature parameters are consistent with the expected values.
One expectation is that the best-fit index should be consistent with the
radio spectral index. That is, the best-fit model should fit the radio
spect... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1507,
"openalex_id": "",
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"arxiv_id": "",
"doi": "",
"end": 1507,
"o... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
-0.038481373339891434,
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0.034239571541547775,
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0.021209003403782845,
-0.02612216956913471... |
cfe0c4d361a16d4044bc8e3731f0145f2dc86f9e | subsection | 12 | 31 | Curvature | This index and the index obtained
using the uncurved model (\Gamma = 2.031^{+0.017}_{-0.016}) are both
consistent with the idea that the highest-energy electrons in SN 1006 have a
spectral index of 2.0.If the effective spectral index of the X-ray synchrotron–producing
electrons \Gamma _{X} = 2 (aside from the exponenti... | {
"cite_spans": []
} | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
82b1a2befb0e2af581bad27731c3ddb37f03f70e | subsection | 13 | 31 | Curvature | If
the uncertainty associated with the radio flux leads to an uncertainty in
the amount of curvature comparable to the statistical uncertainty, then the
amount of curvature is most likely 0.05 \pm 0.01.Not only is the best-fit amount of curvature consistent with
equation (REF ), it is also consistent with the amount of... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 793,
"openalex_id": "",
"raw": "Ellison, D. C., Berezhko, E. G., & Baring, M. G. 2000, , 540, 292",
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"do... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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8381840d3ef31efb0becc0528b3fc51033155a4d | subsection | 14 | 31 | Curvature | Unfortunately, these kinds of data are not available for SN 1006.Evidence of curvature in the synchrotron spectra of supernova remnants has
been reported previously. analyzed the remnant-integrated
radio spectra of Kepler, Tycho, and SN 1006. They find hints of curvature for
Tycho and Kepler. Unfortunately, a careful s... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 243,
"openalex_id": "",
"raw": "Reynolds, S. P., & Ellison, D. C. 1992, , 399, L75",
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"doi": "",
"e... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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-... |
a8611f6d2c9ec69819293113549154c2d925b3d2 | subsection | 15 | 31 | Cutoff Frequency and Diffusion Coefficient | In addition to providing evidence of curvature, fits to the synchrotron
spectral data provide a measure of the frequency at which the synchrotron
spectrum is cut off (eq. [REF ]). The results for the cutoff
critical frequency are listed in Tables –. A
comparison of Tables and (and of Tables and
) reveals that the fre... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 954,
"openalex_id": "",
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"arxiv_id": "",
"doi... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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... |
9d8533ac0a7e220f404293672d914822732e7f24 | subsection | 16 | 31 | Cutoff Frequency and Diffusion Coefficient | For these reasons, we believe that the
cut-off frequencies reported here are relatively accurate.The frequencies listed in Tables and are plotted in
Figure as a function of the position angles of the regions. This
angle is measured relative to the location of the center of the remnant
(Fig. ) and is expressed in degr... | {
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{
"arxiv_id": "",
"doi": "",
"end": 714,
"openalex_id": "",
"raw": "Rothenflug, R., Ballet, J., Dubner, G., Giacani, E., Decourchelle, A., & Ferrando, P. 2004, , 425, 121",
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... | 10.1086/589628 | 0807.1702 | Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN
1006 | [
"G. E. Allen",
"J. C. Houck",
"S. J. Sturner"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
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