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Figure 1:
Schematic solution of a Riemann problem in special relativistic hydrodynamics. The initial state at ![]() ![]() ![]() ![]() ![]() |
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Figure 2:
Graphical solution in the ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 3:
Analytical pressure, density and flow velocity profiles at ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 4:
Relative velocity between the two initial states 1 and 2 as a function of the pressure at the contact discontinuity. Note that the curve shown is given by the continuous joining of three different curves describing the relative velocity corresponding to two shocks (dashed line), one shock and one rarefaction wave (dotted line), and two rarefaction waves (continuous line), respectively. The joining of the curves is indicated by filled circles. The small inset on the right shows a magnification for a smaller range of ![]() ![]() ![]() ![]() |
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Figure 5:
Schematic solution of the shock heating problem in spherical geometry. The initial state consists of a spherically symmetric flow of cold ( ![]() ![]() ![]() ![]() |
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Figure 6: (Movie)
MPEG movie showing the evolution of the density distribution for the shock heating problem with an inflow velocity ![]() ![]() ![]() |
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Figure 7:
Generation and propagation of a relativistic blast wave (schematic). The large pressure jump at a discontinuity initially located at ![]() |
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Figure 8:
Density distribution for the relativistic blast wave Problem 1 defined in Table 7 at t=0.314 obtained with the code SPH-RS-gr (see Table 5) of Muir [204] using 5500 SPH particles and a 1D version of the code. The solid lines give the exact solutions. |
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Figure 9:
Velocity distribution for the relativistic blast wave Problem 1 defined in Table 7 at t=0.314 obtained with the code SPH-RS-gr (see Table 5) of Muir [204] using 5500 SPH particles and a 1D version of the code. The solid lines give the exact solutions. |
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Figure 10: (Movie)
MPEG movie showing the evolution of the density distribution for the relativistic blast wave Problem 1 defined in Table 7. The final frame of the movie also shows the analytical solution (blue lines). The simulation has been performed with relativistic PPM on an equidistant grid of 400 zones. |
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Figure 11: (Movie)
MPEG movie showing the evolution of the density distribution for the relativistic blast wave Problem 2 defined in Table 7. The final frame of the movie also shows the analytical solution (blue lines). The simulation has been performed with relativistic PPM on an equidistant grid of 2000 zones. |
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Figure 12:
Results from [295] for the relativistic blast wave Problems 1 (left column) and Problem 2 (right column), respectively. Relativistic Glimm’s method is only used in regions with steep gradients. Standard finite difference schemes are applied in the smooth remaining part of the computational domain. In the above plots, Lax and LW stand for Lax and Lax-Wendroff methods, respectively; G refers to pure Glimm’s method. |
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Figure 13:
The top panel shows a sequence of snapshots of the density profile for the colliding relativistic blast wave problem up to the moment when the waves begin to interact. The density profile of the new states produced by the interaction of the two waves is shown in the bottom panel (note the change in scale on both axes with respect to the top panel). |
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Figure 14: (Movie)
MPEG movie showing the evolution of the density distribution for the colliding relativistic blast wave problem up to the interaction of the waves. The final frame of the movie also shows the analytical solution (blue lines). The computation has been performed with relativistic PPM on an equidistant grid of 4000 zones. |
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Figure 15: (Movie)
MPEG movie showing the evolution of the density distribution for the colliding relativistic blast wave problem around the time of interaction of the waves at an enlarged spatial scale. The final frame of the movie also shows the analytical solution (blue lines). The computation has been performed with relativistic PPM on an equidistant grid of 4000 zones. |
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Figure 16:
Time evolution of a light, relativistic (beam flow velocity equal to 0.99) jet with large internal energy. The logarithm of the proper rest mass density is plotted in grey scale, the maximum value corresponding to white and the minimum to black. |
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Figure 17:
Logarithm of the proper rest mass density and energy density (from top to bottom) of an evolved, powerful jet propagating through the intergalactic medium. The white contour encompasses the jet material responsible for the synchrotron emission. |
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Figure 18:
Snapshots of the logarithm of the density (normalized to the density of the ambient medium) for a cold baryonic (top panel), a cold leptonic (central panel) and a hot leptonic (bottom panel) relativistic jet at ![]() ![]() ![]() |
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Figure 19: (Movie)
MPEG movie showing the logarithm of the density (normalized to the density of the ambient medium) for a hot leptonic relativistic jet at ![]() |
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Figure 20:
Computed radio maps of a compact relativistic jet showing the evolution of a superluminal component (from left to right). Two resolutions are shown: present VLBI resolution (white contours) and resolution provided by the simulation (black/white images). |
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Figure 21: (Movie)
MPEG movie illustrating the propagation of a relativistic jet from a collapsar, whose progenitor is a rotating He star with a radius of ![]() ![]() ![]() |
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