22,316 research outputs found
The force of gravity in Schwarzschild and Gullstrand-Painlev\'e coordinates
We derive the exact equations of motion (in Newtonian, F=ma, form) for test
masses in Schwarzschild and Gullstrand-Painlev\'e coordinates. These equations
of motion are simpler than the usual geodesic equations obtained from
Christoffel tensors in that the affine parameter is eliminated. The various
terms can be compared against tests of gravity. In force form, gravity can be
interpreted as resulting from a flux of superluminal particles (gravitons). We
show that the first order relativistic correction to Newton's gravity results
from a two graviton interaction.Comment: 6 pages, Honorable mention in 2009 Gravity Essay Competition,
submitted IJMPD, added reference
Some non-linear s.p.d.e.'s that are second order in time
We extend Walsh's theory of martingale measures in order to deal with
hyperbolic stochastic partial differential equations that are second order in
time, such as the wave equation and the beam equation, and driven by spatially
homogeneous Gaussian noise. For such equations, the fundamental solution can be
a distribution in the sense of Schwartz, which appears as an integrand in the
reformulation of the s.p.d.e. as a stochastic integral equation. Our approach
provides an alternative to the Hilbert space integrals of Hilbert-Schmidt
operators. We give several examples, including the beam equation and the wave
equation, with nonlinear multiplicative noise terms
Multiple points of the Brownian sheet in critical dimensions
It is well known that an -parameter -dimensional Brownian sheet has no
-multiple points when , and does have such points when
. We complete the study of the existence of -multiple points by
showing that in the critical cases where , there are a.s. no
-multiple points.Comment: Published at http://dx.doi.org/10.1214/14-AOP912 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Digital second-order phase-locked loop
A digital second-order phase-locked loop is disclosed in which a counter driven by a stable clock pulse source is used to generate a reference waveform of the same frequency as an incoming waveform, and to sample the incoming waveform at zero-crossover points. The samples are converted to digital form and accumulated over M cycles, reversing the sign of every second sample. After every M cycles, the accumulated value of samples is hard limited to a value SGN = + or - 1 and multiplied by a value delta sub 1 equal to a number of n sub 1 of fractions of a cycle. An error signal is used to advance or retard the counter according to the sign of the sum by an amount equal to the sum
Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian
The differential-equation eigenvalue problem associated with a
recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of
the Riemann zeta function, is analyzed using Fourier and WKB analysis. The
Fourier analysis leads to a challenging open problem concerning the formulation
of the eigenvalue problem in the momentum space. The WKB analysis gives the
exact asymptotic behavior of the eigenfunction
Resonance Region Structure Functions and Parity Violating Deep Inelastic Scattering
The primary motive of parity violating deep inelastic scattering experiments
has been to test the standard model, particularly the axial couplings to the
quarks, in the scaling region. The measurements can also test for the validity
of models for the off-diagonal structure functions in the resonance region. The off-diagonal structure functions are
important for the accurate calculation of the -box correction to the
weak charge of the proton. Currently, with no data to determine
directly, models are constructed by modifying
existing fits to electromagnetic data. We present the asymmetry value for
deuteron and proton target predicted by several different models, and demonstrate that there are notable disagreements.Comment: 6 pages, 3 figures. New version contains additional descriptions of
competing structure function model
New Physics and the Proton Radius Problem
Background: The recent disagreement between the proton charge radius
extracted from Lamb shift measurements of muonic and electronic hydrogen
invites speculation that new physics may be to blame. Several proposals have
been made for new particles that account for both the Lamb shift and the muon
anomalous moment discrepancies. Purpose: We explore the possibility that new
particles' couplings to the muon can be fine-tuned to account for all
experimental constraints. Method: We consider two fine-tuned models, the first
involving new particles with scalar and pseudoscalar couplings, and the second
involving new particles with vector and axial couplings. The couplings are
constrained by the Lamb shift and muon magnetic moments measurements while mass
constraints are obtained by kaon decay rate data. Results: For the
scalar-pseudoscalar model, masses between 100 to 200 MeV are not allowed. For
the vector model, masses below about 200 MeV are not allowed. The strength of
the couplings for both models approach that of electrodynamics for particle
masses of about 2 GeV. Conclusions: New physics with fine tuned couplings may
be entertained as a possible explanation for the Lamb shift discrepancy.Comment: 6 pages, 6 figures, v2 contains revised comment on competing model of
Lamb Shift discrepanc
Operator-valued zeta functions and Fourier analysis
The Riemann zeta function is defined as the infinite sum
, which converges when . The Riemann
hypothesis asserts that the nontrivial zeros of lie on the line
. Thus, to find these zeros it is necessary to
perform an analytic continuation to a region of complex for which the
defining sum does not converge. This analytic continuation is ordinarily
performed by using a functional equation. In this paper it is argued that one
can investigate some properties of the Riemann zeta function in the region
by allowing operator-valued zeta functions to act on test
functions. As an illustration, it is shown that the locations of the trivial
zeros can be determined purely from a Fourier series, without relying on an
explicit analytic continuation of the functional equation satisfied by
.Comment: 8 pages, version to appear in J. Pays.
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