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 , which corresponds to initially leading arms, and an initial amplitude of 0.04. The impulse travels at constant wave number with an effective radial wave number . The wave numbers are given in units of defined below, and the time unit is , the inverse of the mean angular velocity of the shearing sheet. Negative amplitudes at are not shown. The parameters of the disk model are = 0.5 and Q = 1.4. | |
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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 . | |
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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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Figure 4: The rise of as function of time illustrating the disk heating. The time unit is the epicyclic period. | |
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Figure 5: Same as Fig. 3, but the shearing sheet is dynamically cooled by accretion of particles during the simulation. | |
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Figure 6: Same as Fig. 4, but the shearing sheet is dynamically cooled by accretion of particles during the simulation. | |
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Figure 7: Peaks of positive 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 . | |
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Figure 8: Power spectrum 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 . | |
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Figure 9: Response of the shearing sheet to an external impulsive potential perturbation with an initial wave vector traced in wave number space. Frames are shown for time t = 0, 0.25,..., 1.5, and 1.75, respectively. | |
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Figure 10: Response of the shearing sheet to two external impulsive potential perturbations with initial wave vectors and , 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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Figure 11: Same as Fig. 10, but with two external impulsive potential perturbations with initial wave vectors (k_{x}, k_{y}) = (-2, 0.5) and , 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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