All Figures

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{1507f1.eps} \end{figure}$ Figure 1: The intensity at gridpoint F is obtained by solving the transfer equation along the short characteristic $\overline {\rm EF}$ . The intensity at the upwind point E is interpolated from the (already known) intensity values at the surrounding gridpoints, A to D.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{1507f2.eps} \end{figure}$ Figure 2: The walking order of the short-characteristics method in a 2D grid for a ray direction pointing into the upper right quadrant. Black circles represent gridpoints on the upwind boundaries, where the intensity values are assumed to be given.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1507f3.eps} \end{figure}$ Figure 3: Geometrical setup of the simulation run. The vector ${\vec B}_0$ indicates the vertical homogeneous magnetic field introduced into the hydrodynamic convection at the beginning of the magnetic phase.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{1507f4.eps}\hspace*{4mm}\i... ...07f6.eps}\hspace*{4mm}\includegraphics[width=7.7cm,clip]{1507f7.eps}\end{figure}$ Figure 4: Map of (frequency-integrated) brightness ( lower right) and horizontal cuts at the the average geometrical height corresponding to optical depth unity of (clockwise from bottom left) temperature, vertical magnetic field and vertical velocity. The "mesoscale'' network of magnetic field structures is embedded in the network of granular downflows. Larger field concentrations appear dark while the brightness of small magnetic structures occasionally exceeds the brightness of granules. Most of the domain exhibits "abnormal'' granulation with small granules (compared to the "normal'' granules in the upper right corner). See also the movies provided as supplementary online material.
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In the text

$\begin{figure} \par\includegraphics[width=6.3cm,clip]{1507f8.eps}\hspace*{4mm}\i... ...10.eps}\hspace*{4mm}\includegraphics[width=6.1cm,clip]{1507f11.eps} \end{figure}$ Figure 5: Statistical properties of a layer of 100 km thickness around optical depth unity. Upper left: probability density function (PDF) of the field strength, signed with the vertical orientation of the field vector. Upper right: joint PDF of field strength and the inclination angle of ${\vec B}$ with respect to the horizontal, theta( ${\vec B}$ ). Lower left: joint PDF of flow velocity, multiplied with the sign of its vertical component, and field strength. Lower right: joint PDF of the inclination angles of the flow, theta( ${\vec v}$ ), and of the magnetic field, theta( ${\vec B}$ ). The grey-scaling indicates the probability density, with intervals of 0.5 on the $\log_{10}$ scale between greyscale levels.
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In the text

$\begin{figure} \includegraphics[width=12.2cm,clip]{1507f12.eps}\hspace*{2mm}\includegraphics[width=5cm,clip]{1507f13.eps} \end{figure}$ Figure 6: Left: face-on view of a thin magnetic sheet. The spreading of the field lines in the upper photosphere is clearly visible. At a depth of approximately 300 km below the surface, the sheet is disrupted. The grey, horizontal plane in dicates the height z=0. Right: magnetic map of the sheet at z=0. The arrow shows the viewing direction of the field line plot on the left.
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In the text

$\begin{figure} \par\includegraphics[width=12.2cm,clip]{1507f14.eps} \end{figure}$ Figure 7: The same sheet as in Fig. 6, from a different angle. The isosurface $\tau _{\rm Ross}=1$ is shown as shaded surface.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{1507f15.eps}\hspace*{2mm}\includegraphics[width=5cm,clip]{1507f16.eps} \end{figure}$ Figure 8: Three-dimensional field line plot ( left) and corresponding magnetic map ( right) of a micropore. The translucent plane shows the field strength at z=0; strong fields appear white.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{1507f17.eps}\par\vspace*{3mm} \hspace*{1.5mm}\includegraphics[width=8.3cm,clip]{1507f18.eps} \end{figure}$ Figure 9: Upper panel: horizontally averaged gas pressure inside (solid) and outside (dashed) strong field regions, and total (gas + magnetic) pressure in strong field regions (dotted). (See the text for the definition of strong fields used here.) Lower panel: average (rms) field strength inside (solid) and outside (dotted) strong fields as a function of height. The dashed line shows the field strength which would balance the difference between the inside and outside gas pressures.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1507f19.eps} \end{figure}$ Figure 10: Average plasma- $\beta$ in strong-field regions as a function of height.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1507f20.eps} \end{figure}$ Figure 11: Horizontally averaged (rms) horizontal velocity in regions of strong and weak magnetic field as function of height.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{1507f21.eps}\par\vspace*{2mm} \includegraphics[width=8cm,clip]{1507f22.eps} \end{figure}$ Figure 12: Detailed view of the flow and magnetic structure of a flux concentration. Upper panel: vectors of horizontal velocity superimposed on a greyscale map of the vertical magnetic field at a height of 550 km above the visible surface. Lower panel: the same at a height of 100 km. The longest arrows correspond to a velocity of $7\;{\rm~km~s^{-1}}$ .
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In the text

$\begin{figure} \par {\includegraphics[width=7.5cm,clip]{1507f23.eps}\hspace*{6mm}} \par\vspace*{2mm} \includegraphics[width=8cm,clip]{1507f24.eps} \end{figure}$ Figure 13: Upper panel: joint probability distribution of magnetic field strength and frequency-integrated brightness. The grey-shading indicates the probability density, with level-intervals of 0.5 on the $\log_{10}$ -scale. Lower panel: probability distribution functions of the magnetic field strength inside the magnetic network ( $\vert B_z\vert > 500 \;{\rm G}$ ), for regions brighter and darker than average, respectively. The field strength distribution on the $\tau =1$ or $\tau = 0.1$ levels would, however, lead to a somewhat different picture since in dark structures the strong Wilson depression results in higher observed field strengths.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{1507f25.eps}\par\vspace*{2mm} \includegraphics[width=7cm,clip]{1507f26.eps} \end{figure}$ Figure 14: Vertical field strength at z=0 ( upper panel) and intensity map ( lower panel) for a sheet-like magnetic structure. The vertical lines indicate the position of the cuts shown in Fig. 15.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{1507f27.eps}\par\vspace*{2mm} \includegraphics[width=7.7cm,clip]{1507f28.eps} \end{figure}$ Figure 15: Vertical cut through the sheet-like magnetic structure shown in Fig. 14. Left panel: density (grey-scaled) and magnetic field vectors projected on the veertical plane. The longest vector correponds to a field strength of 2000 G. Right panel: temperature structure and radiative flux vectors. The solid lines indicate the level $\tau _{\rm Ross}=1$ (for the Rosseland opacity average).
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1507f29.eps} \end{figure}$ Figure 16: Radiative and joule heating across a flux sheet. The solid line shows the heating rate due to horizontal influx of radiation energy into the sheet along the cut indicated in Fig. 14, at a depth of 80 km below z=0. The dashed line shows the joule heating occuring at the sheet boundaries at the same depth.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{1507f30.eps} \end{figure}$ Figure 17: Time series of vertical magnetic field ( left; light shades indicate strong fields), intensity ( middle), and vertical velocity ( right; light and dark shades indicate up- and downflows, respectively) during the formation of a micropore. An initially bright, small granule shrinks, while the magnetic field surrounding it forms a small pore which appears dark in the intensity picture.
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In the text

$\begin{figure} \par\includegraphics[width=13.5cm,clip]{1507f31.eps} \end{figure}$ Figure D.1: The numerical stencil for the artificial diffusivities. Empty circles indicate the staggered grid on which the hyperdiffusive coefficients are defined. Left and middle panel: grid and stencil for the terms $\partial _x(\nu \partial _x u)$ and $\partial _y(\nu \partial _y u)$ , respectively. Right panel: stencil for the term $\partial _y(\nu \partial _x u)$ with mixed derivatives.

In the text

Intensity.mpg

MagneticField.mpg

Temperature.mpg

Velocity.mpg

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{1507f1.eps} \end{figure}$	Figure 1: The intensity at gridpoint F is obtained by solving the transfer equation along the short characteristic $\overline {\rm EF}$ . The intensity at the upwind point E is interpolated from the (already known) intensity values at the surrounding gridpoints, A to D.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=5cm,clip]{1507f2.eps} \end{figure}$	Figure 2: The walking order of the short-characteristics method in a 2D grid for a ray direction pointing into the upper right quadrant. Black circles represent gridpoints on the upwind boundaries, where the intensity values are assumed to be given.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1507f3.eps} \end{figure}$	Figure 3: Geometrical setup of the simulation run. The vector ${\vec B}_0$ indicates the vertical homogeneous magnetic field introduced into the hydrodynamic convection at the beginning of the magnetic phase.
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$\begin{figure} \includegraphics[width=12.2cm,clip]{1507f12.eps}\hspace*{2mm}\includegraphics[width=5cm,clip]{1507f13.eps} \end{figure}$	Figure 6: Left: face-on view of a thin magnetic sheet. The spreading of the field lines in the upper photosphere is clearly visible. At a depth of approximately 300 km below the surface, the sheet is disrupted. The grey, horizontal plane in dicates the height z=0. Right: magnetic map of the sheet at z=0. The arrow shows the viewing direction of the field line plot on the left.
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$\begin{figure} \par\includegraphics[width=12.2cm,clip]{1507f14.eps} \end{figure}$	Figure 7: The same sheet as in Fig. 6, from a different angle. The isosurface $\tau _{\rm Ross}=1$ is shown as shaded surface.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{1507f15.eps}\hspace*{2mm}\includegraphics[width=5cm,clip]{1507f16.eps} \end{figure}$	Figure 8: Three-dimensional field line plot ( left) and corresponding magnetic map ( right) of a micropore. The translucent plane shows the field strength at z=0; strong fields appear white.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1507f19.eps} \end{figure}$	Figure 10: Average plasma- $\beta$ in strong-field regions as a function of height.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1507f20.eps} \end{figure}$	Figure 11: Horizontally averaged (rms) horizontal velocity in regions of strong and weak magnetic field as function of height.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{1507f21.eps}\par\vspace*{2mm} \includegraphics[width=8cm,clip]{1507f22.eps} \end{figure}$	Figure 12: Detailed view of the flow and magnetic structure of a flux concentration. Upper panel: vectors of horizontal velocity superimposed on a greyscale map of the vertical magnetic field at a height of 550 km above the visible surface. Lower panel: the same at a height of 100 km. The longest arrows correspond to a velocity of $7\;{\rm~km~s^{-1}}$ .
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$\begin{figure} \par\includegraphics[width=7cm,clip]{1507f25.eps}\par\vspace*{2mm} \includegraphics[width=7cm,clip]{1507f26.eps} \end{figure}$	Figure 14: Vertical field strength at z=0 ( upper panel) and intensity map ( lower panel) for a sheet-like magnetic structure. The vertical lines indicate the position of the cuts shown in Fig. 15.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{1507f29.eps} \end{figure}$	Figure 16: Radiative and joule heating across a flux sheet. The solid line shows the heating rate due to horizontal influx of radiation energy into the sheet along the cut indicated in Fig. 14, at a depth of 80 km below z=0. The dashed line shows the joule heating occuring at the sheet boundaries at the same depth.
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