288 research outputs found
A high-order nonconservative approach for hyperbolic equations in fluid dynamics
It is well known, thanks to Lax-Wendroff theorem, that the local conservation
of a numerical scheme for a conservative hyperbolic system is a simple and
systematic way to guarantee that, if stable, a scheme will provide a sequence
of solutions that will converge to a weak solution of the continuous problem.
In [1], it is shown that a nonconservative scheme will not provide a good
solution. The question of using, nevertheless, a nonconservative formulation of
the system and getting the correct solution has been a long-standing debate. In
this paper, we show how get a relevant weak solution from a pressure-based
formulation of the Euler equations of fluid mechanics. This is useful when
dealing with nonlinear equations of state because it is easier to compute the
internal energy from the pressure than the opposite. This makes it possible to
get oscillation free solutions, contrarily to classical conservative methods.
An extension to multiphase flows is also discussed, as well as a
multidimensional extension
Unitarity of Minkowski non-local theories made explicit
In this work we explicitly show that the perturbative unitarity of analytic
infinite derivative (AID) scalar field theories can be achieved using a
modified prescription for computing scattering amplitudes. The crux of the new
prescription is the analytic continuation of a result obtained in the Euclidean
signature to the Minkowski external momenta. We explicitly elaborate an example
of a non-local model for various infinite derivative operators.
General UV properties of amplitudes in non-local theories are discussed.Comment: 16 pages, 7 figure
Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography
The mathematical problems and their solutions of the Third International
Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider
mathematical problems related to the construction of algebraic immune vectorial
Boolean functions and big Fermat numbers, problems about secrete sharing
schemes and pseudorandom binary sequences, biometric cryptosystems and the
blockchain technology, etc. Two open problems in mathematical cryptography are
also discussed and a solution for one of them proposed by a participant during
the Olympiad is described. It was the first time in the Olympiad history
UV graviton scattering and positivity bounds from IR dispersion relations
Scattering amplitudes mediated by graviton exchange display IR singularities
in the forward limit. This obstructs standard application of positivity bounds
based on twice subtracted dispersion relations. Such divergences can be
cancelled only if the UV limit of the scattering amplitude behaves in a
specific way, which implies a very non-trivial connection between the UV and IR
behaviors of the amplitude. We show that this relation can be expressed in
terms of an integral transform, obtaining analytic results when . Carefully applying this limit to dispersion relations,
we find that infinite arc integrals, which are usually taken to vanish, can
give a non-trivial contribution in the presence of gravity, unlike in the case
of finite negative . This implies that gravitational positivity bounds
cannot be trusted unless the size of this contribution is estimated in some
way, which implies assumptions on the UV completion of gravitational
interactions. We discuss the relevance of these findings in the particular case
of QED coupled to gravity.Comment: 20 pages, 2 figure
Post-inflationary GW production in generic higher (infinite) derivative gravity
Gravity can be embedded into a renormalizable theory by means of adding
quadratic in curvature terms. However, this at first leads to the presence of
the Weyl ghost. It is possible to get rid of this ghost if the locality
assumption is weakened and the propagator of the graviton is represented by an
entire function of the d'Alembertian operator without new poles and zeros.
Models of this type admit a cosmological solution describing the , or
Starobinsky, inflation. We study graviton production after inflation in this
model and show that it is negligible despite the presence of the higher
derivative operators which could potentially cause instabilities.Comment: We dedicate this paper to the memory of Valery Rubako
Positronium oscillations to Mirror World revisited
We present a calculation of the branching ratio of orthopositronium decay
into an invisible mode, which is done in the context of Mirror World models,
where ordinary positronium can disappear from our world due to oscillation into
its mirror twin. In this revision we clarify some formulas and approximations
used previously, correct them at some places, add new effects relevant for a
feasible experiment and finally perform a combined analysis. We include into
consideration various effects due to external magnetic and electric fields,
collisions with cavity walls and scattering off gas atoms in the cavity.
Oscillations of the Rydberg positroniums are also considered. To perform a
numerical estimates in a realistic case we wrote computer code, which can be
adopted in any experimental setup. Its work is illustrated with an example of a
planned positronium experiment within the AEgIS project.Comment: 23 pages, 4 figures, typos corrected, references added, published
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