28,818 research outputs found
Information of Interest
A pricing formula for discount bonds, based on the consideration of the
market perception of future liquidity risk, is established. An
information-based model for liquidity is then introduced, which is used to
obtain an expression for the bond price. Analysis of the bond price dynamics
shows that the bond volatility is determined by prices of certain weighted
perpetual annuities. Pricing formulae for interest rate derivatives are
derived.Comment: 12 pages, 3 figure
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
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
Quantum Lattice Fluctuations and Luminescence in C_60
We consider luminescence in photo-excited neutral C_60 using the
Su-Schrieffer-Heeger model applied to a single C_60 molecule. To calculate the
luminescence we use a collective coordinate method where our collective
coordinate resembles the displacement of the carbon atoms of the Hg(8) phonon
mode and extrapolates between the ground state "dimerisation" and the exciton
polaron. There is good agreement for the existing luminescence peak spacing and
fair agreement for the relative intensity. We predict the existence of further
peaks not yet resolved in experiment. PACS Numbers : 78.65.Hc, 74.70.Kn,
36.90+
The rotational modes of relativistic stars: Numerical results
We study the inertial modes of slowly rotating, fully relativistic compact
stars. The equations that govern perturbations of both barotropic and
non-barotropic models are discussed, but we present numerical results only for
the barotropic case. For barotropic stars all inertial modes are a hybrid
mixture of axial and polar perturbations. We use a spectral method to solve for
such modes of various polytropic models. Our main attention is on modes that
can be driven unstable by the emission of gravitational waves. Hence, we
calculate the gravitational-wave growth timescale for these unstable modes and
compare the results to previous estimates obtained in Newtonian gravity (i.e.
using post-Newtonian radiation formulas). We find that the inertial modes are
slightly stabilized by relativistic effects, but that previous conclusions
concerning eg. the unstable r-modes remain essentially unaltered when the
problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure
Models of helically symmetric binary systems
Results from helically symmetric scalar field models and first results from a
convergent helically symmetric binary neutron star code are reported here;
these are models stationary in the rotating frame of a source with constant
angular velocity omega. In the scalar field models and the neutron star code,
helical symmetry leads to a system of mixed elliptic-hyperbolic character. The
scalar field models involve nonlinear terms that mimic nonlinear terms of the
Einstein equation. Convergence is strikingly different for different signs of
each nonlinear term; it is typically insensitive to the iterative method used;
and it improves with an outer boundary in the near zone. In the neutron star
code, one has no control on the sign of the source, and convergence has been
achieved only for an outer boundary less than approximately 1 wavelength from
the source or for a code that imposes helical symmetry only inside a near zone
of that size. The inaccuracy of helically symmetric solutions with appropriate
boundary conditions should be comparable to the inaccuracy of a waveless
formalism that neglects gravitational waves; and the (near zone) solutions we
obtain for waveless and helically symmetric BNS codes with the same boundary
conditions nearly coincide.Comment: 19 pages, 7 figures. Expanded version of article to be published in
Class. Quantum Grav. special issue on Numerical Relativit
Ferromagnetism of He Films in the Low Field Limit
We provide evidence for a finite temperature ferromagnetic transition in
2-dimensions as in thin films of He on graphite, a model system
for the study of two-dimensional magnetism. We perform pulsed and CW NMR
experiments at fields of 0.03 - 0.48 mT on He at areal densities of 20.5 -
24.2 atoms/nm. At these densities, the second layer of He has a
strongly ferromagnetic tendency. With decreasing temperature, we find a rapid
onset of magnetization that becomes independent of the applied field at
temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR
linewidth grow rapidly as well, which is consistent with a large (order unity)
polarization of the He spins.Comment: 4 figure
TreeGrad: Transferring Tree Ensembles to Neural Networks
Gradient Boosting Decision Tree (GBDT) are popular machine learning
algorithms with implementations such as LightGBM and in popular machine
learning toolkits like Scikit-Learn. Many implementations can only produce
trees in an offline manner and in a greedy manner. We explore ways to convert
existing GBDT implementations to known neural network architectures with
minimal performance loss in order to allow decision splits to be updated in an
online manner and provide extensions to allow splits points to be altered as a
neural architecture search problem. We provide learning bounds for our neural
network.Comment: Technical Report on Implementation of Deep Neural Decision Forests
Algorithm. To accompany implementation here:
https://github.com/chappers/TreeGrad. Update: Please cite as: Siu, C. (2019).
"Transferring Tree Ensembles to Neural Networks". International Conference on
Neural Information Processing. Springer, 2019. arXiv admin note: text overlap
with arXiv:1909.1179
Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell
Recent studies have raised doubts about the occurrence of r modes in
Newtonian stars with a large degree of differential rotation. To assess the
validity of this conjecture we have solved the eigenvalue problem for
Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the
presence of differential rotation. The results obtained indicate that the
eigenvalue problem is never singular and that, at least for the case of a
thin-shell, the analogues of r modes can be found for arbitrarily large degrees
of differential rotation. This work clarifies the puzzling results obtained in
calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ
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