Well-posedness of Hydrodynamics on the Moving Elastic Surface

The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the dynamic equations of the two-dimensional fluid, and the incompressible equation, all of which operate within a curved geometry. In this paper, we prove the local existence and uniqueness of the solution to the reduced elastic surface model by reformulating the model into a new system in the isothermal coordinates. One major difficulty is that of constructing an appropriate iterative scheme such that the limit system is consistent with the original system.Comment: The introduction is rewritte

Particle Acceleration at Relativistic Shocks

I review the current status of Fermi acceleration theory at relativistic shocks. I first discuss the relativistic shock jump conditions, then describe the non-relativistic Fermi mechanism and the differences introduced by relativistic flows. I present numerical calculations of the accelerated particle spectrum, and examine the maximum energy attainable by this process. I briefly consider the minimum energy for Fermi acceleration, and a possible electron pre-acceleration mechanism.Comment: 17 pages, 4 figures. To appear in "Relativistic Flows in Astrophysics", A.W. Guthmann, M. Georganopoulos, A. Marcowith and K. Manolokou, eds., Lecture Notes in Pysics, Springer Verla

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is therefore realized either along one trajectory or along two equivalent paths. Zero point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multi-stability and tunneling phenomena.Comment: 11 pages, 8 eps figures, Revtex-

A lower bound on the local extragalactic magnetic field

Assuming that the hard gamma-ray emission of Cen A is a result of synchrotron radiation of ultra-relativistic electrons, we derive a lower bound on the local extragalactic magnetic field, $B> 10^{-8}$ G. This result is consistent with (and close to) upper bounds on magnetic fields derived from consideration of cosmic microwave background distortions and Faraday rotation measurements.Comment: Includes extensive discussion of particle acceleration above 10^20 eV in the hot spot-like region of Cen

Multimessenger astronomy with the Einstein Telescope

Gravitational waves (GWs) are expected to play a crucial role in the development of multimessenger astrophysics. The combination of GW observations with other astrophysical triggers, such as from gamma-ray and X-ray satellites, optical/radio telescopes, and neutrino detectors allows us to decipher science that would otherwise be inaccessible. In this paper, we provide a broad review from the multimessenger perspective of the science reach offered by the third generation interferometric GW detectors and by the Einstein Telescope (ET) in particular. We focus on cosmic transients, and base our estimates on the results obtained by ET's predecessors GEO, LIGO, and Virgo.Comment: 26 pages. 3 figures. Special issue of GRG on the Einstein Telescope. Minor corrections include

Threshold Bound States

Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher dimensions can be easily understood

Corrections to flat-space particle dynamics arising from space granularity

The construction of effective Hamiltonians describing corrections to flat space particle dynamics arising from the granularity of space at very short distances is discussed in the framework of an heuristic approach to the semiclassical limit of loop quantum gravity. After some general motivation of the subject, a brief non-specialist introduction to the basic tools employed in the loop approach is presented. The heuristical semiclassical limit is subsequently defined and the application to the case of photons and spin 1/2 fermions is described. The resulting modified Maxwell and Dirac Hamiltonians, leading in particular to Planck scale corrections in the energy-momentum relations, are presented. Alternative interpretations of the results and their limitations, together with other approaches are briefly discussed along the text. Three topics related to the above methods are reviewed: (1) The determination of bounds to the Lorentz violating parameters in the fermionic sector, obtained from clock comparison experiments.(2) The calculation of radiative corrections in preferred frames associated to space granularity in the framework of a Yukawa model for the interactions and (3) The calculation of synchrotron radiation in the framework of the Myers-Pospelov effective theories describing Lorentz invariance violations, as well as a generalized approach to radiation in Planck scale modified electrodynamics. The above exploratory results show that quantum gravity phenomenology provides observational guidance in the construction of quantum gravity theories and opens up the possibility of probing Planck scale physics.Comment: 49 pages, 6 figures and 4 tables. Extended version of the talk given at the 339-th WE-Heraeus-Seminar: Special Relativity, will it survive the next 100 years?, Potsdam, february 200

UHECR as Decay Products of Heavy Relics? The Lifetime Problem

The essential features underlying the top-down scenarii for UHECR are discussed, namely, the stability (or lifetime) imposed to the heavy objects (particles) whatever they be: topological and non-topological solitons, X-particles, cosmic defects, microscopic black-holes, fundamental strings. We provide an unified formula for the quantum decay rate of all these objects as well as the particle decays in the standard model. The key point in the top-down scenarii is the necessity to adjust the lifetime of the heavy object to the age of the universe. This ad-hoc requirement needs a very high dimensional operator to govern its decay and/or an extremely small coupling constant. The natural lifetimes of such heavy objects are, however, microscopic times associated to the GUT energy scale (sim 10^{-28} sec. or shorter). It is at this energy scale (by the end of inflation) where they could have been abundantly formed in the early universe and it seems natural that they decayed shortly after being formed.Comment: 11 pages, LaTex, no figures, updated versio

Constraining Very Heavy Dark Matter Using Diffuse Backgrounds of Neutrinos and Cascaded Gamma Rays

We consider multi-messenger constraints on very heavy dark matter (VHDM) from recent Fermi gamma-ray and IceCube neutrino observations of isotropic background radiation. Fermi data on the diffuse gamma-ray background (DGB) shows a possible unexplained feature at very high energies (VHE), which we have called the "VHE Excess" relative to expectations for an attenuated power law extrapolated from lower energies. We show that VHDM could explain this excess, and that neutrino observations will be an important tool for testing this scenario. More conservatively, we derive new constraints on the properties of VHDM for masses of 10^3-10^10 GeV. These generic bounds follow from cosmic energy budget constraints for gamma rays and neutrinos that we developed elsewhere, based on detailed calculations of cosmic electromagnetic cascades and also neutrino detection rates. We show that combining both gamma-ray and neutrino data is essential for making the constraints on VHDM properties both strong and robust. In the lower mass range, our constraints on VHDM annihilation and decay are comparable to other results; however, our constraints continue to much higher masses, where they become relatively stronger.Comment: 33 pages, 21 figures, accepted for publication in JCA