All Figures

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f1.eps}} \end{figure}$ Figure 1: Sketch representing the relative contribution of the different length scales to ${\kappa }_{\rm mac}$ and ${\kappa }_{\rm int}$ . The scales $\lambda$ , R and $r_{\rm nl}$ are intrinsic to the system, the movable length L is the observation resolution.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f2a.e... ...r\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f2c.eps}} \end{figure}$ Figure 2: Abscissa: $\log(L/r_{\rm nl})$ . Ordinate: $\log \sigma^2 (L)$ at the three probed times. Solid line: expected functional dependence in the linear regime, $\sigma ^2 \propto L^{-n-3}$ .
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In the text

$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f3a.e... ... \resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f3c.eps}} \end{figure}$ Figure 3: Abscissa: $\log(L/r_{\rm nl})$ . Ordinate: $\log[\langle K \rangle / \varrho_b (\dot{a} r_{\rm nl})^2]$ at the three probed times: the lower points in each plot correspond to $\langle K_{\rm int} \rangle$ ; the upper points represent $10^3 \langle K_{\rm mac} \rangle$ . The solid line is proportional to $L^2 \sigma ^2 (L)$ , Eqs. (7), (10), (11).
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In the text

$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f4a.e... ...\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f4b.eps}} \end{figure}$ Figure 4: Abscissa: $\log(1+\delta)$ . Ordinate: $\log[{\kappa}_{\rm int}/\varrho_b (\dot{a} r_{\rm nl})^2]$ . The plots are arbitrarily shifted in horizontal direction for clarity. From left to right, $L/r_{\rm nl} \approx 2.67, 0.40, 0.08$ . When self-similarity holds, Eq. (3), curves corresponding to the same ratio $L/r_{\rm nl}$ fall on top of each other.
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In the text

$\begin{figure} \par\resizebox{8.4cm}{!}{\includegraphics[clip]{figures/0566f5.eps}} \end{figure}$ Figure 5: Abscissa: $\log(1+\delta)$ . Ordinate: $\log[{\kappa}_{\rm mac}/ \varrho_b (\dot{a} r_{\rm nl})^2]$ . Solid line: theoretical functional dependence, Eq. (4). All the probed coarsening lengths, at the three probed times (increasing from top to bottom) are plotted. The scatter bars are barely dependent on time, coarsening length and density; for clarity, they are shown only at the earliest time.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{figures/0566f6a.e... ...\resizebox{8.5cm}{!}{\includegraphics[clip]{figures/0566f6b.eps}} \end{figure}$ Figure 6: Abscissa: $1+\delta$ . Ordinate: ${\kappa}_{\rm mac}/ \varrho_b [\dot{a} L \sigma(L)]^2$ . Only plotted are the coarsening lengths such that $\sigma (L)<0.05$ if n=0 and $\sigma (L)<0.03$ if n=+1. The theoretical functional dependence, Eq. (11), is a constant. The scatter bars extend beyond the plotted area.
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In the text

$\begin{figure} \par\resizebox{8.4cm}{!}{\includegraphics[clip]{figures/0566f7.eps}} \end{figure}$ Figure 7: Abscissa: $\log(1+\delta)$ . Ordinate: $\log[{\kappa}_{\rm mac}/ \varrho_b (\dot{a} r_{\rm nl})^2]$ . ( ${\kappa }_{\rm mac}$ for the case n=0 is shifted by a factor 10³). Solid line: theoretical functional dependence, Eq. (13). Only plotted are the coarsening lengths such that $\sigma (L)>\sqrt {10}$ . The scatter bars are barely dependent on time, coarsening length and density; for clarity, they are shown only for n=0.
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In the text

$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f8.eps}} \end{figure}$ Figure 8: Abscissa: $\delta /\sigma (L)$ . Ordinate: ${\kappa}_{\rm int}/ \varrho_b [\dot{a} L \sigma(L)]^2$ . Solid line: theoretical prediction, Eq. (6). Only coarsening lengths are plotted such that $\sigma (L)<0.3$ .
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In the text

$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f9a.e... ...\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f9b.eps}} \end{figure}$ Figure 9: Abscissa: $1+\delta$ . Ordinate: ${\kappa}_{\rm int}/ \varrho_b (\dot{a} r_{\rm nl})^2$ . Theoretical prediction: a linear dependence. Only coarsening lengths such that $\sigma (L)<0.05$ if n=0 and $\sigma (L)<0.03$ if n=+1.
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In the text

$\begin{figure} \par\resizebox{8.34cm}{!}{\includegraphics[clip]{figures/0566f10a... ...esizebox{8.34cm}{!}{\includegraphics[clip]{figures/0566f10c.eps}} \end{figure}$ Figure 10: Abscissa: $\log(1+\delta)$ . Ordinate: $\log [{\kappa}_{\rm int}/ \varrho_b (\dot{a} L)^2]$ . Solid line: theoretical functional dependence, Eq. (8). Plotted only coarsening lengths at the latest time, $r_{\rm nl}=R/4$ , such that $\sigma (L)>3$ . For clarity, the scatter bars are omitted; see Fig. 11.
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In the text

$\begin{figure} \par\resizebox{8.34cm}{!}{\includegraphics[clip]{figures/0566f11a... ...esizebox{8.34cm}{!}{\includegraphics[clip]{figures/0566f11c.eps}} \end{figure}$ Figure 11: Same as Fig. 10, but now the ordinate is $\log[ {\kappa}_{\rm int}/ \varrho_b [\dot{a} L \sigma(L)]^2]$ . The solid lines ( ${\kappa }_{\rm int}\propto \delta ^{2-\eta }$ ) have $\eta =0$ and $\eta (n=-2) \approx 0.3$ , $\eta (n=0) \approx 0.5$ , $\eta (n=+1) \approx 0.6$ The case n=-2 shows also the same data furnished with scatter bars and shifted by a factor 10³ for clarity. The scatter bars of the other two cases are of the same size.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f12.eps}} \end{figure}$ Figure 12: For n=+1, $r_{\rm nl}=R/16$ , $\sigma (L)>3$ : the uppermost data are scaled like in Fig. 10, the lowermost data like in Fig. 11. For the other values of n, the behavior of the data is the same.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f13.eps}} \end{figure}$ Figure 13: Abscissa: $\log(1+\delta)$ . Ordinate: $\log {\kappa}_{\rm int}$ (arbitrary normalization) for the flat CDM model in a box of sidelength 128 Mpc. For clarity, only some coarsening lengths are plotted (decreasing top down). The solid lines ( ${\kappa }_{\rm int}\propto \delta ^{2-\eta }$ ) have $\eta =0$ and $\eta =0.5$ .
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f14.eps}} \end{figure}$ Figure 14: Abscissa: $\log(1+\delta)$ . Ordinate: $\log {\kappa}_{\rm int}$ (arbitrary normalization) for the flat CDM model in boxes of sidelength 128 Mpc and 512 Mpc, respectively. In the later case, ${\kappa }_{\rm int}$ was multiplied by a factor 10³. For clarity, only some coarsening lengths are plotted. The solid lines ( ${\kappa }_{\rm int}\propto \delta ^{2-\eta }$ ) have $\eta =0$ and $\eta =0.5$ .
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f1.eps}} \end{figure}$	Figure 1: Sketch representing the relative contribution of the different length scales to ${\kappa }_{\rm mac}$ and ${\kappa }_{\rm int}$ . The scales $\lambda$ , R and $r_{\rm nl}$ are intrinsic to the system, the movable length L is the observation resolution.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f2a.e... ...r\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f2c.eps}} \end{figure}$	Figure 2: Abscissa: $\log(L/r_{\rm nl})$ . Ordinate: $\log \sigma^2 (L)$ at the three probed times. Solid line: expected functional dependence in the linear regime, $\sigma ^2 \propto L^{-n-3}$ .
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$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f3a.e... ... \resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f3c.eps}} \end{figure}$	Figure 3: Abscissa: $\log(L/r_{\rm nl})$ . Ordinate: $\log[\langle K \rangle / \varrho_b (\dot{a} r_{\rm nl})^2]$ at the three probed times: the lower points in each plot correspond to $\langle K_{\rm int} \rangle$ ; the upper points represent $10^3 \langle K_{\rm mac} \rangle$ . The solid line is proportional to $L^2 \sigma ^2 (L)$ , Eqs. (7), (10), (11).
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$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f4a.e... ...\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f4b.eps}} \end{figure}$	Figure 4: Abscissa: $\log(1+\delta)$ . Ordinate: $\log[{\kappa}_{\rm int}/\varrho_b (\dot{a} r_{\rm nl})^2]$ . The plots are arbitrarily shifted in horizontal direction for clarity. From left to right, $L/r_{\rm nl} \approx 2.67, 0.40, 0.08$ . When self-similarity holds, Eq. (3), curves corresponding to the same ratio $L/r_{\rm nl}$ fall on top of each other.
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$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{figures/0566f6a.e... ...\resizebox{8.5cm}{!}{\includegraphics[clip]{figures/0566f6b.eps}} \end{figure}$	Figure 6: Abscissa: $1+\delta$ . Ordinate: ${\kappa}_{\rm mac}/ \varrho_b [\dot{a} L \sigma(L)]^2$ . Only plotted are the coarsening lengths such that $\sigma (L)<0.05$ if n=0 and $\sigma (L)<0.03$ if n=+1. The theoretical functional dependence, Eq. (11), is a constant. The scatter bars extend beyond the plotted area.
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$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f8.eps}} \end{figure}$	Figure 8: Abscissa: $\delta /\sigma (L)$ . Ordinate: ${\kappa}_{\rm int}/ \varrho_b [\dot{a} L \sigma(L)]^2$ . Solid line: theoretical prediction, Eq. (6). Only coarsening lengths are plotted such that $\sigma (L)<0.3$ .
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$\begin{figure} \par\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f9a.e... ...\resizebox{8.6cm}{!}{\includegraphics[clip]{figures/0566f9b.eps}} \end{figure}$	Figure 9: Abscissa: $1+\delta$ . Ordinate: ${\kappa}_{\rm int}/ \varrho_b (\dot{a} r_{\rm nl})^2$ . Theoretical prediction: a linear dependence. Only coarsening lengths such that $\sigma (L)<0.05$ if n=0 and $\sigma (L)<0.03$ if n=+1.
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$\begin{figure} \par\resizebox{8.34cm}{!}{\includegraphics[clip]{figures/0566f10a... ...esizebox{8.34cm}{!}{\includegraphics[clip]{figures/0566f10c.eps}} \end{figure}$	Figure 10: Abscissa: $\log(1+\delta)$ . Ordinate: $\log [{\kappa}_{\rm int}/ \varrho_b (\dot{a} L)^2]$ . Solid line: theoretical functional dependence, Eq. (8). Plotted only coarsening lengths at the latest time, $r_{\rm nl}=R/4$ , such that $\sigma (L)>3$ . For clarity, the scatter bars are omitted; see Fig. 11.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f12.eps}} \end{figure}$	Figure 12: For n=+1, $r_{\rm nl}=R/16$ , $\sigma (L)>3$ : the uppermost data are scaled like in Fig. 10, the lowermost data like in Fig. 11. For the other values of n, the behavior of the data is the same.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{figures/0566f13.eps}} \end{figure}$	Figure 13: Abscissa: $\log(1+\delta)$ . Ordinate: $\log {\kappa}_{\rm int}$ (arbitrary normalization) for the flat CDM model in a box of sidelength 128 Mpc. For clarity, only some coarsening lengths are plotted (decreasing top down). The solid lines ( ${\kappa }_{\rm int}\propto \delta ^{2-\eta }$ ) have $\eta =0$ and $\eta =0.5$ .
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