All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2657fig1.ps} % \end{figure}$ Figure 1: Linear swing amplification of a density wave in the shearing sheet. The wave is initialized as a delta like impulse in wave number space with an initial wave vector $(k_{x}^{\rm in}, k_{y}^{\rm in})= (-2,0.5)~k_{\rm crit}$ , which corresponds to initially leading arms, and an initial amplitude of 0.04. The impulse travels at constant wave number $k_{y}^{\rm in}$ with an effective radial wave number $k_{x}^{\rm eff}= k_{x}^{\rm in} +2 A k_{y}^{\rm in} t$ . The wave numbers are given in units of $k_{\rm crit}$ defined below, and the time unit is $\Omega _0^{-1}$ , the inverse of the mean angular velocity of the shearing sheet. Negative amplitudes at $t > 9.5 \Omega _0^{-1}$ are not shown. The parameters of the disk model are $A/\Omega _0$ = 0.5 and Q = 1.4.
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In the text

$\begin{figure} \par\includegraphics[width=5.1cm,clip]{2657fig2.ps} % \end{figure}$ Figure 2: Initial set up of the 32 768 particles in the simulation of the shearing sheet. The y-axis points into the direction of the shear flow. The size is $2 x_0 \times 2 y_0 = 20 \times 28 \lambda _{\rm crit}$ .
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{2657fig3.ps} % \end{figure}$ Figure 3: Dynamical evolution of the shearing sheet. Snapshots of particle positions are shown for t = 0.5, 1, ... 3.5, and 4, respectively. The y-axis is oriented in the direction of the shear flow. The size of each frame is the same as in Fig. 2.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{2657fig4.ps} % \end{figure}$ Figure 4: The rise of $Q'^2=\langle u^2 \rangle /\Sigma_0^2$ as function of time illustrating the disk heating. The time unit is the epicyclic period.
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In the text

$\begin{figure} \par\includegraphics[width=16.2cm,clip]{2657fig5.ps} % \end{figure}$ Figure 5: Same as Fig. 3, but the shearing sheet is dynamically cooled by accretion of particles during the simulation.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2657fig6.ps} % \end{figure}$ Figure 6: Same as Fig. 4, but the shearing sheet is dynamically cooled by accretion of particles during the simulation.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics {2657fig7.ps}} % \end{figure}$ Figure 7: Peaks of positive $A({\vec k})$ Fourier coefficients in the simulation presented in Fig. 5 at times t = 0.5, 1, ... 3.5, and 4, respectively. For clarity only contour levels of at least 40% of the maxima of the spikes are shown. The wave numbers are given in units of $k_{\rm crit}$ .
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics {2657fig8.ps}} % \end{figure}$ Figure 8: Power spectrum $\sqrt {A^2(k_{x},0.5)+B^2(k_{x},0.5)}$ of the density wave amplitudes in the simulation shown in Fig. 5. The dashed and solid lines correspond to times t=0 and t=2, respectively. The wave numbers are given in units of $k_{\rm crit}$ .
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In the text

$\begin{figure} \par\includegraphics[width=16.1cm,clip]{2657fig9.ps} % \end{figure}$ Figure 9: Response of the shearing sheet to an external impulsive potential perturbation with an initial wave vector $(k_{x}, k_{y}) = (-2, 0.5)~k_{\rm crit}$ traced in wave number space. Frames are shown for time t = 0, 0.25,..., 1.5, and 1.75, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=16.1cm,clip]{2657fi10.ps} % \end{figure}$ Figure 10: Response of the shearing sheet to two external impulsive potential perturbations with initial wave vectors $(k_{x}, k_{y}) = (-2, 0.5)~k_{\rm crit}$ and $(k_{x}, k_{y})= (-3, 1)~k_{\rm crit}$ , respectively traced in wave number space. Frames are shown for time t = 0, 0.25, 0.5, 0.88, 1.0, 1.13, 1.25, and 1.38, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=16.3cm,clip]{2657fi11.ps} % \end{figure}$ Figure 11: Same as Fig. 10, but with two external impulsive potential perturbations with initial wave vectors (k_x, k_y) = (-2, 0.5) $k_{\rm crit}$ and $(k_{x}, k_{y}) = (-3, 1.5)~k_{\rm crit}$ , respectively. Frames are shown for time t = 0, 0.25, 0.5, 0.75, 1.0, 1.13, 1.25, and 1.38, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=5.1cm,clip]{2657fig2.ps} % \end{figure}$	Figure 2: Initial set up of the 32 768 particles in the simulation of the shearing sheet. The y-axis points into the direction of the shear flow. The size is $2 x_0 \times 2 y_0 = 20 \times 28 \lambda _{\rm crit}$ .
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$\begin{figure} \par\includegraphics[width=16cm,clip]{2657fig3.ps} % \end{figure}$	Figure 3: Dynamical evolution of the shearing sheet. Snapshots of particle positions are shown for t = 0.5, 1, ... 3.5, and 4, respectively. The y-axis is oriented in the direction of the shear flow. The size of each frame is the same as in Fig. 2.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{2657fig4.ps} % \end{figure}$	Figure 4: The rise of $Q'^2=\langle u^2 \rangle /\Sigma_0^2$ as function of time illustrating the disk heating. The time unit is the epicyclic period.
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$\begin{figure} \par\includegraphics[width=16.2cm,clip]{2657fig5.ps} % \end{figure}$	Figure 5: Same as Fig. 3, but the shearing sheet is dynamically cooled by accretion of particles during the simulation.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2657fig6.ps} % \end{figure}$	Figure 6: Same as Fig. 4, but the shearing sheet is dynamically cooled by accretion of particles during the simulation.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics {2657fig7.ps}} % \end{figure}$	Figure 7: Peaks of positive $A({\vec k})$ Fourier coefficients in the simulation presented in Fig. 5 at times t = 0.5, 1, ... 3.5, and 4, respectively. For clarity only contour levels of at least 40% of the maxima of the spikes are shown. The wave numbers are given in units of $k_{\rm crit}$ .
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics {2657fig8.ps}} % \end{figure}$	Figure 8: Power spectrum $\sqrt {A^2(k_{x},0.5)+B^2(k_{x},0.5)}$ of the density wave amplitudes in the simulation shown in Fig. 5. The dashed and solid lines correspond to times t=0 and t=2, respectively. The wave numbers are given in units of $k_{\rm crit}$ .
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$\begin{figure} \par\includegraphics[width=16.1cm,clip]{2657fig9.ps} % \end{figure}$	Figure 9: Response of the shearing sheet to an external impulsive potential perturbation with an initial wave vector $(k_{x}, k_{y}) = (-2, 0.5)~k_{\rm crit}$ traced in wave number space. Frames are shown for time t = 0, 0.25,..., 1.5, and 1.75, respectively.
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$\begin{figure} \par\includegraphics[width=16.1cm,clip]{2657fi10.ps} % \end{figure}$	Figure 10: Response of the shearing sheet to two external impulsive potential perturbations with initial wave vectors $(k_{x}, k_{y}) = (-2, 0.5)~k_{\rm crit}$ and $(k_{x}, k_{y})= (-3, 1)~k_{\rm crit}$ , respectively traced in wave number space. Frames are shown for time t = 0, 0.25, 0.5, 0.88, 1.0, 1.13, 1.25, and 1.38, respectively.
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$\begin{figure} \par\includegraphics[width=16.3cm,clip]{2657fi11.ps} % \end{figure}$	Figure 11: Same as Fig. 10, but with two external impulsive potential perturbations with initial wave vectors (k_x, k_y) = (-2, 0.5) $k_{\rm crit}$ and $(k_{x}, k_{y}) = (-3, 1.5)~k_{\rm crit}$ , respectively. Frames are shown for time t = 0, 0.25, 0.5, 0.75, 1.0, 1.13, 1.25, and 1.38, respectively.
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