637 research outputs found
The concentration-compactness principle for variable exponent spaces and applications
In this paper we extend the well-known concentration -- compactness principle
of P.L. Lions to the variable exponent case. We also give some applications to
the existence problem for the Laplacian with critical growth
convergence result for nonlocal elliptic-type problems via Tartar's method
In this work we obtain a compactness result for the convergence of a
family of nonlocal and nonlinear monotone elliptic-type problems by means of
Tartar's method of oscillating test functions.Comment: In this revision we added a new section that shows the
Gamma-convergence of the associated energy functional
Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond
Energy conservation has the status of a fundamental physical principle.
However, measurements in quantum mechanics do not comply with energy
conservation. Therefore, it is expected that a more fundamental theory of
gravity -- one that is less incompatible with quantum mechanics -- should admit
energy nonconservations. This paper begins by identifying the conditions for a
theory to have an energy-momentum tensor that is not conserved. Then, the
trajectory equation for pointlike particles that lose energy is derived,
showing that energy nonconservation produces a particular acceleration. As an
example, the unimodular theory of gravity is studied. Interestingly, in
spherical symmetry, given that there is a generalized Birkhoff theorem and that
the energy-momentum tensor divergence is a closed form, the trajectories of
test particles that lose energy can be found using well known methods. Finally,
limits on the energy nonconservation parameters are set using Solar system
observations.Comment: 13 pages. Accepted in Phys. Rev.
Phenomenology of Quantum Gravity and its Possible Role in Neutrino Anomalies
New phenomenological models of Quantum Gravity have suggested that a
Lorentz-Invariant discrete spacetime structure may become manifest through a
nonstandard coupling of matter fields and spacetime curvature. On the other
hand, there is strong experimental evidence suggesting that neutrino
oscillations cannot be described by simply considering neutrinos as massive
particles. In this manuscript we motivate and construct one particular
phenomenological model of Quantum Gravity that could account for the so-called
neutrino anomalies.Comment: For the proceedings of "Relativity and Gravitation: 100 Years after
Einstein in Prague" (June 2012, Prague
Review article: the diagnostic approach and current management of chylous ascites
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138889/1/apt14284.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138889/2/apt14284_am.pd
Space-time variation of the electron-to-proton mass ratio in a Weyl model
Seeking a possible explanation for recent data indicating a space-time
variation of the electron-to-proton mass ratio within the Milky Way, we
consider a phenomenological model where the effective fermion masses depend on
the local value of the Weyl tensor. We contrast the required values of the
model's free parameters with bounds obtained from modern tests on the violation
of the Weak Equivalence Principle and we find that these quantities are
incompatible. This result indicates that the variation of nucleon and electron
masses through a coupling with the Weyl tensor is not a viable model.Comment: 24 page
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