143,179 research outputs found
Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity
For a long time, it is generally believed that spin-spin interactions can
only exist in a theory where Lorentz symmetry is gauged, and a theory with
spin-spin interactions is not perturbatively renormalizable. But this is not
true. By studying the motion of a spinning particle in gravitational field, it
is found that there exist spin-spin interactions in gauge theory of gravity.
Its mechanism is that a spinning particle will generate gravitomagnetic field
in space-time, and this gravitomagnetic field will interact with the spin of
another particle, which will cause spin-spin interactions. So, spin-spin
interactions are transmitted by gravitational field. The form of spin-spin
interactions in post Newtonian approximations is deduced. This result can also
be deduced from the Papapetrou equation. This kind of interactions will not
affect the renormalizability of the theory. The spin-spin interactions will
violate the weak equivalence principle, and the violation effects are
detectable. An experiment is proposed to detect the effects of the violation of
the weak equivalence principle.Comment: 17 pages, no figur
Choosing a density functional for static molecular polarizabilities
Coupled-cluster calculations of static electronic dipole polarizabilities for
145 organic molecules are performed to create a reference data set. The
molecules are composed from carbon, hydrogen, nitrogen, oxygen, fluorine,
sulfur, chlorine, and bromine atoms. They range in size from triatomics to 14
atoms. The Hartree-Fock and 2nd-order M{\o}ller-Plesset methods and 34 density
functionals, including local functionals, global hybrid functionals, and
range-separated functionals of the long-range-corrected and screened-exchange
varieties, are tested against this data set. On the basis of the test results,
detailed recommendations are made for selecting density functionals for
polarizability computations on relatively small organic molecules
Direct and secondary nuclear excitation with x-ray free-electron lasers
The direct and secondary nuclear excitation produced by an x-ray free
electron laser when interacting with a solid-state nuclear target is
investigated theoretically. When driven at the resonance energy, the x-ray free
electron laser can produce direct photoexcitation. However, the dominant
process in that interaction is the photoelectric effect producing a cold and
very dense plasma in which also secondary processes such as nuclear excitation
by electron capture may occur. We develop a realistic theoretical model to
quantify the temporal dynamics of the plasma and the magnitude of the secondary
excitation therein. Numerical results show that depending on the nuclear
transition energy and the temperature and charge states reached in the plasma,
secondary nuclear excitation by electron capture may dominate the direct
photoexcitation by several orders of magnitude, as it is the case for the 4.8
keV transition from the isomeric state of Mo, or it can be negligible,
as it is the case for the 14.4 keV M\"ossbauer transition in
. These findings are most relevant for future nuclear quantum
optics experiments at x-ray free electron laser facilities.Comment: 17 pages, 7 figures; minor corrections made; accepted by Physics of
Plasma
Box Drawings for Learning with Imbalanced Data
The vast majority of real world classification problems are imbalanced,
meaning there are far fewer data from the class of interest (the positive
class) than from other classes. We propose two machine learning algorithms to
handle highly imbalanced classification problems. The classifiers constructed
by both methods are created as unions of parallel axis rectangles around the
positive examples, and thus have the benefit of being interpretable. The first
algorithm uses mixed integer programming to optimize a weighted balance between
positive and negative class accuracies. Regularization is introduced to improve
generalization performance. The second method uses an approximation in order to
assist with scalability. Specifically, it follows a \textit{characterize then
discriminate} approach, where the positive class is characterized first by
boxes, and then each box boundary becomes a separate discriminative classifier.
This method has the computational advantages that it can be easily
parallelized, and considers only the relevant regions of feature space
Decay of weak solutions to the 2D dissipative quasi-geostrophic equation
We address the decay of the norm of weak solutions to the 2D dissipative
quasi-geostrophic equation. When the initial data is in only, we prove
that the norm tends to zero but with no uniform rate, that is, there are
solutions with arbitrarily slow decay. For the initial data in ,
with , we are able to obtain a uniform decay rate in . We
also prove that when the norm of the initial data
is small enough, the norms, for have uniform
decay rates. This result allows us to prove decay for the norms, for , when the initial data is in .Comment: A paragraph describing work by Carrillo and Ferreira proving results
directly related to the ones in this paper is added in the Introduction. Rest
of the article remains unchange
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