Hydrodynamic Vortices and their Gravity Duals

In this talk we review analytical and numerical studies of hydrodynamic vortices in conformal fluids and their gravity duals. We present two conclusions. First, (3+1)-dimensional turbulence is within the range of validity of the AdS/hydrodynamics correspondence. Second, the local equilibrium of the fluid is equivalent to the ultralocality of the holographic correspondence, in the sense that the bulk data at a given point is determined, to any given precision, by the boundary data at a single point together with a fixed number of derivatives. With this criterion we see that the cores of hot and slow (3+1)-dimensional conformal generalizations of Burgers vortices are everywhere in local equilibrium and their gravity duals are thus easily found. On the other hand local equilibrium breaks down in the core of singular (2+1)-dimensional vortices, but the holographic correspondence with Einstein gravity may be used to define the boundary field theory in the region in which the hydrodynamic description fails.Comment: 6 pages, Padova Strings proceedings to appear in Fortschritte der Physi

Dynamic critical properties of a one-dimensional probabilistic cellular automaton

Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state. Values obtained for the dynamic critical exponents indicate that the transition belongs to the universality class of directed percolation. Finally the model is compared with a previously studied one to show that a difference in the nature of the absorbing states places them in different universality classes.Comment: 12 pages (LaTeX), 4 Figures (PostScript

Z0Z^0--Z0′{Z^0}^\prime and ordinary-exotic fermion mixings revisited using some special observables

We investigate the mixing of an extra ${Z^0}^\prime$ with the standard $Z^0$ and mixings of exotic fermions with their standard counterparts through some precisely measured electroweak observables. These observables are geared to search for physics beyond the Standard Model. We observe that although most of such mixings are severely constrained by the recent LEP data, some of the mixing angles could still be rather large, awaiting future tests.Comment: 11 pages, CERN-TH. 7196/94, Late

Entropy current and equilibrium partition function in fluid dynamics

Existence of an entropy current with non-negative divergence puts a lot of constraints on the transport coefficients of a fluid, so does the existence of equilibrium. In all the cases we have studied so far we have seen an overlap between these two sets of constraints. In this note we shall try to explore the reason for such an overlap. We shall also see how a part of the entropy current could be determined from the equilibrium partition function.Comment: 39 pages, Version-2: Added a new section and some more arguments in the old sections, added new references and corrected typos. 45 pages Version 3: 50 pages, introduction has been modified, added a new section, added reference