Action functionals for relativistic perfect fluids

Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered here depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.Comment: 40 pages, plain Te

Janus and Multifaced Supersymmetric Theories

We investigate the various properties Janus supersymmetric Yang-Mills theories. A novel vacuum structure is found and BPS monopoles and dyons are studied. Less supersymmetric Janus theories found before are derived by a simpler method. In addition, we find the supersymmetric theories when the coupling constant depends on two and three spatial coordinates.Comment: 20 pages, no figures, typos, equations corrected. Additional comment

Intermittency of velocity time increments in turbulence

We analyze the statistics of turbulent velocity fluctuations in the time domain. Three cases are computed numerically and compared: (i) the time traces of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the "dynamic" case); (ii) the time evolution of tracers advected by a frozen turbulent field (the "static" case), and (iii) the evolution in time of the velocity recorded at a fixed location in an evolving Eulerian velocity field, as it would be measured by a local probe (referred to as the "virtual probe" case). We observe that the static case and the virtual probe cases share many properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is clearly different; it bears the signature of the global dynamics of the flow.Comment: 5 pages, 3 figures, to appear in PR

Lagrangian Structure Functions in Turbulence: A Quantitative Comparison between Experiment and Direct Numerical Simulation

A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers is achieved. The local scaling properties of the Lagrangian velocity increments for the experimental and numerical data are in good quantitative agreement for all time lags. The degree of intermittency changes when measured close to the Kolmogorov time scales or at larger time lags. This study resolves apparent disagreements between experiment and numerics.Comment: 13 RevTeX pages (2 columns) + 8 figures include