Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page

Multi-Kˉ\bar{K} nuclei and kaon condensation

We extend previous relativistic mean-field (RMF) calculations of multi-$\bar K$ nuclei, using vector boson fields with SU(3) PPV coupling constants and scalar boson fields constrained phenomenologically. For a given core nucleus, the resulting $\bar K$ separation energy $B_{\bar K}$, as well as the associated nuclear and $\bar K$-meson densities, saturate with the number $\kappa$ of $\bar K$ mesons for $\kappa > \kappa_{\rm sat} \sim 10$. Saturation appears robust against a wide range of variations, including the RMF nuclear model used and the type of boson fields mediating the strong interactions. Because $B_{\bar K}$ generally does not exceed 200 MeV, it is argued that multi-$\bar K$ nuclei do not compete with multihyperonic nuclei in providing the ground state of strange hadronic configurations and that kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter. Last, we explore possibly self-bound strange systems made of neutrons and ${\bar K}^0$ mesons, or protons and $K^-$ mesons, and study their properties.Comment: 21 pages, 8 figures, revised text and reference

Collisionless shocks in plasmas

Collisionless shocks in plasmas, dissipation and dispersion in determining shock structur

Stochastic methods for solving high-dimensional partial differential equations

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms

Experimental Upper Bound on Superradiance Emission from Mn12 Acetate

We used a Josephson junction as a radiation detector to look for evidence of the emission of electromagnetic radiation during magnetization avalanches in a crystal assembly of Mn_12-Acetate. The crystal assembly exhibits avalanches at several magnetic fields in the temperature range from 1.8 to 2.6 K with durations of the order of 1 ms. Although a recent study shows evidence of electromagnetic radiation bursts during these avalanches [J. Tejada, et al., Appl. Phys. Lett. {\bf 84}, 2373 (2004)], we were unable to detect any significant radiation at well-defined frequencies. A control experiment with external radiation pulses allows us to determine that the energy released as radiation during an avalanche is less than 1 part in 10^4 of the total energy released. In addition, our avalanche data indicates that the magnetization reversal process does not occur uniformly throughout the sample.Comment: 4 RevTeX pages, 3 eps figure

Isospin fractionation and isoscaling in dynamical nuclear collisions

Isoscaling is found to hold for fragment yields in the antisymmetrized molecular dynamics (AMD) simulations for collisions of calcium isotopes at 35 MeV/nucleon. This suggests the applicability of statistical considerations to the dynamical fragment emission. The observed linear relationship between the isoscaling parameters and the isospin asymmetry of fragments supports the above suggestion. The slope of this linear function yields information about the symmetry energy in low density region where multifragmentation occurs.Comment: 11 pages, 6 figure

Chiral Dynamics of Deeply Bound Pionic Atoms

We present and discuss a systematic calculation, based on two-loop chiral perturbation theory, of the pion-nuclear s-wave optical potential. A proper treatment of the explicit energy dependence of the off-shell pion self-energy together with (electromagnetic) gauge invariance of the Klein-Gordon equation turns out to be crucial. Accurate data for the binding energies and widths of the 1s and 2p levels in pionic ^{205}Pb and ^{207}Pb are well reproduced, and the notorious "missing repulsion" in the pion-nuclear s-wave optical potential is accounted for. The connection with the in-medium change of the pion decay constant is clarified.Comment: preprint ECT*-02-16, 4 pages, 3 figure

Testing Einstein's time dilation under acceleration using M\"ossbauer spectroscopy

The Einstein time dilation formula was tested in several experiments. Many trials have been made to measure the transverse second order Doppler shift by M\"{o}ssbauer spectroscopy using a rotating absorber, to test the validity of this formula. Such experiments are also able to test if the time dilation depends only on the velocity of the absorber, as assumed by Einstein's clock hypothesis, or the present centripetal acceleration contributes to the time dilation. We show here that the fact that the experiment requires $\gamma$-ray emission and detection slits of finite size, the absorption line is broadened; by geometric longitudinal first order Doppler shifts immensely. Moreover, the absorption line is non-Lorenzian. We obtain an explicit expression for the absorption line for any angular velocity of the absorber. The analysis of the experimental results, in all previous experiments which did not observe the full absorption line itself, were wrong and the conclusions doubtful. The only proper experiment was done by K\"{u}ndig (Phys. Rev. 129 (1963) 2371), who observed the broadening, but associated it to random vibrations of the absorber. We establish necessary conditions for the successful measurement of a transverse second order Doppler shift by M\"{o}ssbauer spectroscopy. We indicate how the results of such an experiment can be used to verify the existence of a Doppler shift due to acceleration and to test the validity of Einstein's clock hypothesis.Comment: 11 pages, 4 figure

Discrete charge patterns, Coulomb correlations and interactions in protein solutions

The effective Coulomb interaction between globular proteins is calculated as a function of monovalent salt concentration $c_s$, by explicit Molecular Dynamics simulations of pairs of model proteins in the presence of microscopic co and counterions. For discrete charge patterns of monovalent sites on the surface, the resulting osmotic virial coefficient $B_2$ is found to be a strikingly non-monotonic function of $c_s$. The non-monotonicity follows from a subtle Coulomb correlation effect which is completely missed by conventional non-linear Poisson-Boltzmann theory and explains various experimental findings.Comment: 4 twocolumn pages with 4 figure