20,829 research outputs found
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- nuclei and kaon condensation
We extend previous relativistic mean-field (RMF) calculations of multi- nuclei, using vector boson fields with SU(3) PPV coupling constants and
scalar boson fields constrained phenomenologically. For a given core nucleus,
the resulting separation energy , as well as the
associated nuclear and -meson densities, saturate with the number
of mesons for . 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 generally does not exceed 200 MeV, it is argued that
multi- 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
mesons, or protons and mesons, and study their properties.Comment: 21 pages, 8 figures, revised text and reference
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
Collisionless shocks in plasmas
Collisionless shocks in plasmas, dissipation and dispersion in determining shock structur
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 -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 , 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 is found to be a
strikingly non-monotonic function of . 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
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