Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of classical mechanics taylor solution manual pdf free particles per finite fluid volume.

Check if you have access through your login credentials or your institution. Present address: Geotechnical Engineer, HNTB Federal Division, Baton Rouge, LA 70802, USA. Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful, in which case a drive will not be possible. Even if it is physically meaningful, its possibility would not necessarily mean that a drive can be constructed. So if exotic matter with the correct properties can not exist, then the drive could not be constructed. Another possible issue is that, although the Alcubierre metric is consistent with Einstein’s equations, general relativity does not incorporate quantum mechanics.

The Alcubierre drive, however, remains a hypothetical concept with seemingly difficult problems, though the amount of energy required is no longer thought to be unobtainably large. Low has argued that within the context of general relativity, it is impossible to construct a warp drive in the absence of exotic matter. Alcubierre metric has some apparently peculiar aspects. Alcubierre did in building his metric. The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space.

Krasnikov also notes that when the spacetime is not flat from the outset, a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments and to operate in a preassigned manner. Krasnikov’s finding “does not mean that Alcubierre bubbles, if it were possible to create them, could not be used as a means of superluminal travel. 2,600 years in the future according to external clocks, it would be required that someone had already begun work on warping the space from Earth to Deneb at least 2,600 years ago, in which case “A spaceship appropriately located with respect to the bubble trajectory could then choose to enter the bubble, rather like a passenger catching a passing trolley car, and thus make the superluminal journey. Earth to a distant star and back in an arbitrarily short time, as measured by clocks on Earth, by altering the metric along the path of their outbound trip. Counterarguments to these apparent problems have also been offered.

Belgium, in 1999, tried to address the potential issues. Van den Broeck detailed this by saying that the total energy can be reduced dramatically by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble. Furthermore, if the intensity of the space warp can be oscillated over time, the energy required is reduced even more. But in this case, the Alcubierre drive vessel can only travel routes that, like a railroad, have first been equipped with the necessary infrastructure. The pilot inside the bubble is causally disconnected with its walls and cannot carry out any action outside the bubble: the bubble cannot be used for the first trip to a distant star because the pilot cannot place infrastructure ahead of the bubble while “in transit”.