Possible explanations of phase transitions in highway traffic

It is shown that all the phase transitions in and out of freely flowing traffic reported earlier for a German site could be caused by bottlenecks, as are all the transitions observed at two other sites examined here. The evidence suggests that bottlenecks cause these transitions in a predictable way, and does not suggest that stoppages (jams) appear spontaneously in free flow traffic for no apparent reason. It is also shown that many of the complicated instability phenomena observed at all locations can be explained qualitatively in terms of a simple Markovian theory specific to traffic that does not necessarily include spontaneous transitions into the queued state as a feature

The application of Buckingham π theorem to Lattice-Boltzmann modelling of sewage sludge digestion

YesFor the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupling occur through a smoothed-kernel averaging procedure). Laboratory-scale tests display grid-independence problems due to bubble diameter being larger than voxel size, thereby breaking the pointwise Euler-Lagrange assumption of negligible particle size. To tackle this problem and thereby have grid-independent results, a novel data-scaling approach to pointwise Euler-Lagrange grid independence evaluation, based on an application of the Buckingham π theorem, is proposed. Evaluation of laboratory-scale flow patterns and comparison to experimental data show only marginal differences in between the models, and between numerical modelling and experimental data. Pilot-scale simulations show that all the models produce grid-independent, coherent data if the Euler-Lagrange assumption of negligible (or at least, small) particle size is recovered. In both cases, a second-order convergence was achieved. A discussion follows on the opportunity of applying the proposed data-scaling approach rather than the smoothing-kernel model

Nonorientable spacetime tunneling

Misner space is generalized to have the nonorientable topology of a Klein bottle, and it is shown that in a classical spacetime with multiply connected space slices having such a topology, closed timelike curves are formed. Different regions on the Klein bottle surface can be distinguished which are separated by apparent horizons fixed at particular values of the two angular variables that eneter the metric. Around the throat of this tunnel (which we denote a Klein bottlehole), the position of these horizons dictates an ordinary and exotic matter distribution such that, in addition to the known diverging lensing action of wormholes, a converging lensing action is also present at the mouths. Associated with this matter distribution, the accelerating version of this Klein bottlehole shows four distinct chronology horizons, each with its own nonchronal region. A calculation of the quantum vacuum fluctuations performed by using the regularized two-point Hadamard function shows that each chronology horizon nests a set of polarized hypersurfaces where the renormalized momentum-energy tensor diverges. This quantum instability can be prevented if we take the accelerating Klein bottlehole to be a generalization of a modified Misner space in which the period of the closed spatial direction is time-dependent. In this case, the nonchronal regions and closed timelike curves cannot exceed a minimum size of the order the Planck scale.Comment: 11 pages, RevTex, Accepted in Phys. Rev.

On the warp drive space-time

In this paper the problem of the quantum stability of the two-dimensional warp drive spacetime moving with an apparent faster than light velocity is considered. We regard as a maximum extension beyond the event horizon of that spacetime its embedding in a three-dimensional Minkowskian space with the topology of the corresponding Misner space. It is obtained that the interior of the spaceship bubble becomes then a multiply connected nonchronal region with closed timelike curves and that the most natural vacuum allows quantum fluctuations which do not induce any divergent behaviour of the re-normalized stress-energy tensor, even on the event (Cauchy) chronology horizon. In such a case, the horizon encloses closed timelike curves only at scales close to the Planck length, so that the warp drive satisfies the Ford's negative energy-time inequality. Also found is a connection between the superluminal two-dimensional warp drive space and two-dimensional gravitational kinks. This connection allows us to generalize the considered Alcubierre metric to a standard, nonstatic metric which is only describable on two different coordinate patchesComment: 7 pages, minor comment on chronology protection added, RevTex, to appear in Phys. Rev.

From black strings to black holes: nuttier and squashed AdS5_5 solutions

We construct new solutions of the Einstein equations with negative cosmological constant in five spacetime dimensions. They smoothly emerge as deformations of the known AdS$_5$ black strings. The first type of configurations can be viewed as the $d=4$ Taub-NUT-AdS solutions uplifted to five dimensions, in the presence of a negative cosmological constant. We argue that these solutions provide the gravity dual for a ${\cal N}=4$ super-Yang-Mills theory formulated in a $d=4$ homogeneous G\"odel-type spacetime background. A different deformation of the AdS$_5$ black strings leads to squashed AdS black holes and their topological generalizations. In this case, the conformal infinity is the product of time and a circle-fibration over a base space that is a two-dimensional Einstein space.Comment: 19 pages, 7 figure

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Scale Vs. Conformal Invariance in the AdS/CFT Correspondence

We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a specific type. We define this using the AdS/CFT correspondence, which relates the physics of gravity in asymptotically Anti-de Sitter (AdS) spacetimes to that of a conformal field theory (CFT) in one dimension fewer. The AdS rotating (Kerr) black holes in five and seven dimensions provide us with the examples, since by the correspondence we are able to define and compute the action and stress tensor of four and six dimensional field theories residing on rotating Einstein universes, using the ``boundary counterterm'' method. The rotation breaks conformal but not scale invariance. The AdS/CFT framework is therefore a natural arena for generating such examples of non-trivial scale invariant theories which are not conformally invariant.Comment: 4 pages, RevTeX (v3: references added