Search results for "moment"

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On shape differentiation of discretized electric field integral equation

2013

Abstract This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.

ta113Discretizationta213Automatic differentiationApplied MathematicsMathematical analysista111General EngineeringFinite differenceBasis functionMethod of moments (statistics)Electric-field integral equationComputational MathematicsShape optimizationSensitivity (control systems)AnalysisMathematicsEngineering Analysis with Boundary Elements
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"Figure 9c-2" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN) …

2023

The quark-number-scaled $v_2$ ($v_2/n_q$) of identified hadrons are shown as a function of the kinetic energy per quark, KE$_T/n_q$ in 0–10% centrality [panel (a)] in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The error bars (shaded boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown are type A and B only.

transverse kinetic energyAu Au —> $K^+$ $K^-$midrapiditycentralityppg123transverse momentum200.0
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"Figure 8b-2" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN) …

2023

Identified hadron $v_2$ in central (0–20% centrality, left panels) Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Panels (a) and (b) show $v_2$ as a function of transverse momentum $p_T$. The $v_2$ of all species for centrality 0–20% has been scaled up by a factor of 1.6 for better comparison with results of 20–60% centrality. The error bars (shaded boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown are type A and B only.

transverse kinetic energyAu Au —> $K^+$ $K^-$midrapiditycentralityppg123transverse momentum200.0
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"Figure 10b-2" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN)…

2023

The quark-number-scaled $v_2$ ($v_2/n_q$) of identified hadrons are shown as a function of the kinetic energy per quark, KE$_T/n_q$ in 10–40% centrality [panel (b)] in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The $v_2$ of $\Lambda$ and K$^0_S$ are measured by STAR collaboration [21]. The error bars (open boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown on the results from this study are type A and B only.

transverse kinetic energyAu Au —> $K^+$ $K^-$midrapiditycentralityppg123transverse momentum200.0
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"Figure 10b-1" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN)…

2023

The quark-number-scaled $v_2$ ($v_2/n_q$) of identified hadrons are shown as a function of the kinetic energy per quark, KE$_T/n_q$ in 10–40% centrality [panel (b)] in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The $v_2$ of $\Lambda$ and K$^0_S$ are measured by STAR collaboration [21]. The error bars (open boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown on the results from this study are type A and B only.

transverse kinetic energyAu Au —> $\pi^+$ $\pi^-$midrapiditycentralityppg123transverse momentum200.0
researchProduct

"Figure 8b-1" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN) …

2023

Identified hadron $v_2$ in central (0–20% centrality, left panels) Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Panels (a) and (b) show $v_2$ as a function of transverse momentum $p_T$. The $v_2$ of all species for centrality 0–20% has been scaled up by a factor of 1.6 for better comparison with results of 20–60% centrality. The error bars (shaded boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown are type A and B only.

transverse kinetic energyAu Au —> $\pi^+$ $\pi^-$midrapiditycentralityppg123transverse momentum200.0
researchProduct

"Figure 9a-1" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN) …

2023

The quark-number-scaled $v_2$ ($v_2/n_q$) of identified hadrons are shown as a function of the kinetic energy per quark, KE$_T/n_q$ in 10–20% centrality [panel (b)] in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The error bars (shaded boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown are type A and B only.

transverse kinetic energyAu Au —> $\pi^+$ $\pi^-$midrapiditycentralityppg123transverse momentum200.0
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"Figure 9c-3" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN) …

2023

The quark-number-scaled $v_2$ ($v_2/n_q$) of identified hadrons are shown as a function of the kinetic energy per quark, KE$_T/n_q$ in 0–10% centrality [panel (a)] in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The error bars (shaded boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown are type A and B only.

transverse kinetic energyAu Au —> $p$ $\bar p$midrapiditycentralityppg123transverse momentum200.0
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"Figure 10b-3" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN)…

2023

The quark-number-scaled $v_2$ ($v_2/n_q$) of identified hadrons are shown as a function of the kinetic energy per quark, KE$_T/n_q$ in 10–40% centrality [panel (b)] in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The $v_2$ of $\Lambda$ and K$^0_S$ are measured by STAR collaboration [21]. The error bars (open boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown on the results from this study are type A and B only.

transverse kinetic energyAu Au —> $p$ $\bar p$midrapiditycentralityppg123transverse momentum200.0
researchProduct

"Figure 8b-3" of "Deviation from quark-number scaling of the anisotropy parameter v_2 of pions, kaons, and protons in Au+Au collisions at sqrt(s_NN) …

2023

Identified hadron $v_2$ in central (0–20% centrality, left panels) Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Panels (a) and (b) show $v_2$ as a function of transverse momentum $p_T$. The $v_2$ of all species for centrality 0–20% has been scaled up by a factor of 1.6 for better comparison with results of 20–60% centrality. The error bars (shaded boxes) represent the statistical (systematic) uncertainties. The systematic uncertainties shown are type A and B only.

transverse kinetic energyAu Au —> $p$ $\bar p$midrapiditycentralityppg123transverse momentum200.0
researchProduct