All Figures

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{4449fig1.eps}\end{figure}$ Figure 1: Solution to the Riemann problem with initial conditions $\rho _{\rm L}=1.0$ , $\rho _{\rm R}=0.5$ , $u_{\rm L}=0.5$ , and $u_{\rm R}=0.25$ . The solid line represents the dust density and the dots represent the gas density, both at t=0.5. For the gas, the speed of sound was set to 1.0.
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In the text

$\begin{figure} \par\includegraphics[width=15.8cm,clip]{4449fig2.eps}\end{figure}$ Figure 2: Numerical results for the Riemann problem of Fig. 1 for gas (dots) and dust (solid line). The top row shows the density, the bottom row the velocity. Left panels: no gas-dust interaction. Middle panels: $T_{\rm s}=0.5$ . Right panels: $T_{\rm s}=0.05$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.15cm,clip]{4449fig3.eps}\end{figure}$ Figure 3: Relative radial velocity of gas and dust (1 mm) in a disk without a planet. The dots represent the numerical solution, and the solid line represents Eq. (15).
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In the text

$\begin{figure} \par\includegraphics[width=7.65cm,clip]{4449fig4.eps}\end{figure}$ Figure 4: Close-up on a spiral density wave, with relative velocity arrows superimposed. Outside of the spiral wave, the dust drift is directed inward, according to Eq. (15). Close to the spiral, the particles move towards the centre of the wave. For 5 mm dust particles, as shown here, the maximum relative velocity is 2.6 $\times$ 10^-6, in units of the orbital velocity of the planet.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4449fig5.eps}\end{figure}$ Figure 5: Surface density of gas and dust (s=0.1 cm) after 500 orbits of a 0.1 ${{M}_{\rm J}}$ planet at $\phi =0$ (opposite to the planet). The dust density is multiplied by 100. The dots indicate the positions of the 2:3, the 3:2, and the 2:1 resonances.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4449fig6.eps}\end{figure}$ Figure 6: Azimuthally averaged radial acceleration a of dust particles after 100 orbits of a 0.1 ${{M}_{\rm J}}$ planet. The close-up shows a in the outer region of the disk. The 2:1 mean motion resonance is visible as a small bump in a.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{4449fig7.eps}\end{figure}$ Figure 7: Radial density cut opposite to the planet for four different particle sizes after 100 orbits of a 0.1 ${{M}_{\rm J}}$ planet. The dust densities are multiplied by 100.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{4449fig8.eps}\end{figure}$ Figure 8: Radial density cut opposite to the planet for four different planetary masses after 100 orbits and for a particle size of 1 mm. The dust densities are multiplied by 100, and the planetary masses are in units of ${{M}_{\rm J}}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{4449fig9.eps}\end{figure}$ Figure 9: Surface density of 1 mm dust particles after 100 orbits of a 0.5 ${{M}_{\rm J}}$ planet.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{4449fg10.eps}\end{figure}$ Figure 10: Azimuthal averages of the radial acceleration a (solid line) and gas surface density $\Sigma$ (dashed line, shown for $0.4 \le r \le 1.8$ ) for a 1 ${{M}_{\rm J}}$ planet after 400 orbits.
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In the text

$\begin{figure} \par\includegraphics[width=7.45cm,clip]{4449fg11.eps}\end{figure}$ Figure 11: Scatter plot of the relative velocity in the direction of a 0.1 ${{M}_{\rm J}}$ planet. The distance to the planet is in units of the Roche lobe ${R_{\rm R}}$ , and the unit of relative velocity is the Kepler velocity at the position of the planet. The size of the dust particles in this simulation is 2 mm.
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{4449fg12.eps}\end{figure}$ Figure 12: Accretion of gas and dust onto a 0.1 ${{M}_{\rm J}}$ planet. Left panel: gas and dust mass accreted on the planet. Right panel: relative accretion rate of dust with respect to the gas. For both panels, the dust mass is multiplied by 100 to compare it with the gas.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{4449fig1.eps}\end{figure}$	Figure 1: Solution to the Riemann problem with initial conditions $\rho _{\rm L}=1.0$ , $\rho _{\rm R}=0.5$ , $u_{\rm L}=0.5$ , and $u_{\rm R}=0.25$ . The solid line represents the dust density and the dots represent the gas density, both at t=0.5. For the gas, the speed of sound was set to 1.0.
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$\begin{figure} \par\includegraphics[width=15.8cm,clip]{4449fig2.eps}\end{figure}$	Figure 2: Numerical results for the Riemann problem of Fig. 1 for gas (dots) and dust (solid line). The top row shows the density, the bottom row the velocity. Left panels: no gas-dust interaction. Middle panels: $T_{\rm s}=0.5$ . Right panels: $T_{\rm s}=0.05$ .
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$\begin{figure} \par\includegraphics[width=7.15cm,clip]{4449fig3.eps}\end{figure}$	Figure 3: Relative radial velocity of gas and dust (1 mm) in a disk without a planet. The dots represent the numerical solution, and the solid line represents Eq. (15).
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$\begin{figure} \par\includegraphics[width=7.65cm,clip]{4449fig4.eps}\end{figure}$	Figure 4: Close-up on a spiral density wave, with relative velocity arrows superimposed. Outside of the spiral wave, the dust drift is directed inward, according to Eq. (15). Close to the spiral, the particles move towards the centre of the wave. For 5 mm dust particles, as shown here, the maximum relative velocity is 2.6 $\times$ 10^-6, in units of the orbital velocity of the planet.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4449fig5.eps}\end{figure}$	Figure 5: Surface density of gas and dust (s=0.1 cm) after 500 orbits of a 0.1 ${{M}_{\rm J}}$ planet at $\phi =0$ (opposite to the planet). The dust density is multiplied by 100. The dots indicate the positions of the 2:3, the 3:2, and the 2:1 resonances.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4449fig6.eps}\end{figure}$	Figure 6: Azimuthally averaged radial acceleration a of dust particles after 100 orbits of a 0.1 ${{M}_{\rm J}}$ planet. The close-up shows a in the outer region of the disk. The 2:1 mean motion resonance is visible as a small bump in a.
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{4449fig7.eps}\end{figure}$	Figure 7: Radial density cut opposite to the planet for four different particle sizes after 100 orbits of a 0.1 ${{M}_{\rm J}}$ planet. The dust densities are multiplied by 100.
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{4449fig8.eps}\end{figure}$	Figure 8: Radial density cut opposite to the planet for four different planetary masses after 100 orbits and for a particle size of 1 mm. The dust densities are multiplied by 100, and the planetary masses are in units of ${{M}_{\rm J}}$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{4449fig9.eps}\end{figure}$	Figure 9: Surface density of 1 mm dust particles after 100 orbits of a 0.5 ${{M}_{\rm J}}$ planet.
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$\begin{figure} \par\includegraphics[width=7.4cm,clip]{4449fg10.eps}\end{figure}$	Figure 10: Azimuthal averages of the radial acceleration a (solid line) and gas surface density $\Sigma$ (dashed line, shown for $0.4 \le r \le 1.8$ ) for a 1 ${{M}_{\rm J}}$ planet after 400 orbits.
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$\begin{figure} \par\includegraphics[width=7.45cm,clip]{4449fg11.eps}\end{figure}$	Figure 11: Scatter plot of the relative velocity in the direction of a 0.1 ${{M}_{\rm J}}$ planet. The distance to the planet is in units of the Roche lobe ${R_{\rm R}}$ , and the unit of relative velocity is the Kepler velocity at the position of the planet. The size of the dust particles in this simulation is 2 mm.
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$\begin{figure} \par\includegraphics[width=15.5cm,clip]{4449fg12.eps}\end{figure}$	Figure 12: Accretion of gas and dust onto a 0.1 ${{M}_{\rm J}}$ planet. Left panel: gas and dust mass accreted on the planet. Right panel: relative accretion rate of dust with respect to the gas. For both panels, the dust mass is multiplied by 100 to compare it with the gas.
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