3,407 research outputs found
Equation of Motion of an Electric Charge
The appearance of the time derivative of the acceleration in the equation of
motion (EOM) of an electric charge is studied. It is shown that when an
electric charge is accelerated, a stress force exists in the curved electric
field of the accelerated charge, and this force is proportional to the
acceleration. This stress force acts as a reaction force which is responsible
for the creation of the radiation (instead of the "radiation reaction force"
that actually does not exist at low velocities). Thus the initial acceleration
should be supplied as an initial condition for the solution of the EOM of an
electric charge. It is also shown that in certain cases, like periodic motions
of an electric charge, the term that includes the time derivative of the
acceleration, represents the stress reaction force.Comment: 12 pages, 2 figure
On the fibration method for zero-cycles and rational points
Conjectures on the existence of zero-cycles on arbitrary smooth projective
varieties over number fields were proposed by Colliot-Th\'el\`ene, Sansuc, Kato
and Saito in the 1980's. We prove that these conjectures are compatible with
fibrations, for fibrations into rationally connected varieties over a curve. In
particular, they hold for the total space of families of homogeneous spaces of
linear groups with connected geometric stabilisers. We prove the analogous
result for rational points, conditionally on a conjecture on locally split
values of polynomials which a recent work of Matthiesen establishes in the case
of linear polynomials over the rationals.Comment: 54 pages; v3: minor updates, added Remark 9.12(ii), v4: improved
exposition, final versio
The Grothendieck construction for model categories
The Grothendieck construction is a classical correspondence between diagrams
of categories and coCartesian fibrations over the indexing category. In this
paper we consider the analogous correspondence in the setting of model
categories. As a main result, we establish an equivalence between suitable
diagrams of model categories indexed by and a new notion of
\textbf{model fibrations} over . When is a model
category, our construction endows the Grothendieck construction with a model
structure which gives a presentation of Lurie's -categorical
Grothendieck construction and enjoys several good formal properties. We apply
our construction to various examples, yielding model structures on strict and
weak group actions and on modules over algebra objects in suitable monoidal
model categories.Comment: Includes revisions based on the comments of the refere
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