1,343 research outputs found
Hamiltonian flows on null curves
The local motion of a null curve in Minkowski 3-space induces an evolution
equation for its Lorentz invariant curvature. Special motions are constructed
whose induced evolution equations are the members of the KdV hierarchy. The
null curves which move under the KdV flow without changing shape are proven to
be the trajectories of a certain particle model on null curves described by a
Lagrangian linear in the curvature. In addition, it is shown that the curvature
of a null curve which evolves by similarities can be computed in terms of the
solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio
Elementary Darboux transformations and factorization
A general theorem on factorization of matrices with polynomial entries is
proven and it is used to reduce polynomial Darboux matrices to linear ones.
Some new examples of linear Darboux matrices are discussed.Comment: 10 page
Bubble concentration on spheres for supercritical elliptic problems
We consider the supercritical Lane-Emden problem (P_\eps)\qquad
-\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\
\partial\mathcal{A}
where is an annulus in \rr^{2m}, and
p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0.
We prove the existence of positive and sign changing solutions of (P_\eps)
concentrating and blowing-up, as \eps\to0, on dimensional spheres.
Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and
Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a
nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be
solved by a Ljapunov-Schmidt finite dimensional reduction
Aptitud de dos sedimentitas rojas cretácicas del departamento Confluencia, Neuquén, para ser usadas como barreras aislantes en rellenos sanitarios
En este trabajo se presenta la caracterización de dos sedimentitas de grano fino del departamento Confluencia, Neuquén, que forman parte de las formaciones Huincul y Anacleto (Grupo Neuquén - Cretácico Superior) con el objetivo dedeterminar su aptitud para ser usadas como materiales para impermeabilizar la base de rellenos sanitarios. Las muestras fueron extraídas de dos canteras inactivas de arcillas rojas, explotadas como materia prima para la industria de la cerámica, y representan el material que se comercializaba para este fin. Los resultados fueron comparados con una bentonita sódica natural comercial la cual se utilizó como material de referencia. En función de la distribución del tamaño de partículas, las sedimentitas se clasifican como una fangolita (F. Huincul) y una arcilita (F. Anacleto). La mineralogía de la fracción arcilla de estas sedimentitas está representada principalmente por un interestratificado I/S tipo R0 (55-80% Sm). Las sedimentitas rojas ensayadas cumplieron con los requisitos de conductividad hidráulica estipulados por la legislación internacional para suuso como barrera impermeable (menor que 1 x 10-9 m/s). Su capacidad de intercambio catiónico, como también la plasticidad y compresibilidad de las mismas, demostraron un comportamiento satisfactorio para su uso en rellenos sanitarios. En mezclas con una arena mal seleccionada, el agregado de un 15% de la arcilita de la Formación Anacleto permitió superar el requisito legal de conductividad hidráulica, mientras que la fangolita de la Formación Huincul no cumplió con dicha condición. No obstante, a diferencia de una bentonita sódica natural, estas sedimentitas podrían ser utilizadas sin ser mezcladas con otros materiales naturales (suelos o arena) por su baja compresibilidad y menor potencial expansivo. El uso de los materiales ensayados en el diseño de sistemas de impermeabilización de rellenos sanitarios constituiría una alternativa efectiva no sólo porque cumplen con los requisitos técnicos estipulados para este fin, sino también por su abundancia y bajo costo de extracción en el área de estudio
Ruled Laguerre minimal surfaces
A Laguerre minimal surface is an immersed surface in the Euclidean space
being an extremal of the functional \int (H^2/K - 1) dA. In the present paper,
we prove that the only ruled Laguerre minimal surfaces are up to isometry the
surfaces R(u,v) = (Au, Bu, Cu + D cos 2u) + v (sin u, cos u, 0), where A, B, C,
D are fixed real numbers. To achieve invariance under Laguerre transformations,
we also derive all Laguerre minimal surfaces that are enveloped by a family of
cones. The methodology is based on the isotropic model of Laguerre geometry. In
this model a Laguerre minimal surface enveloped by a family of cones
corresponds to a graph of a biharmonic function carrying a family of isotropic
circles. We classify such functions by showing that the top view of the family
of circles is a pencil.Comment: 28 pages, 9 figures. Minor correction: missed assumption (*) added to
Propositions 1-2 and Theorem 2, missed case (nested circles having nonempty
envelope) added in the proof of Pencil Theorem 4, missed proof that the arcs
cut off by the envelope are disjoint added in the proof of Lemma
An integrable discretization of the rational su(2) Gaudin model and related systems
The first part of the present paper is devoted to a systematic construction
of continuous-time finite-dimensional integrable systems arising from the
rational su(2) Gaudin model through certain contraction procedures. In the
second part, we derive an explicit integrable Poisson map discretizing a
particular Hamiltonian flow of the rational su(2) Gaudin model. Then, the
contraction procedures enable us to construct explicit integrable
discretizations of the continuous systems derived in the first part of the
paper.Comment: 26 pages, 5 figure
Lagrangian Curves in a 4-dimensional affine symplectic space
Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic
Convergence of vector bundles with metrics of Sasaki-type
If a sequence of Riemannian manifolds, , converges in the pointed
Gromov-Hausdorff sense to a limit space, , and if are vector
bundles over endowed with metrics of Sasaki-type with a uniform upper
bound on rank, then a subsequence of the converges in the pointed
Gromov-Hausdorff sense to a metric space, . The projection maps
converge to a limit submetry and the fibers converge to
its fibers; the latter may no longer be vector spaces but are homeomorphic to
, where is a closed subgroup of ---called the {\em wane
group}--- that depends on the basepoint and that is defined using the holonomy
groups on the vector bundles. The norms converges to a map
compatible with the re-scaling in and the -action
on converges to an action on compatible with the
limiting norm.
In the special case when the sequence of vector bundles has a uniform lower
bound on holonomy radius (as in a sequence of collapsing flat tori to a
circle), the limit fibers are vector spaces. Under the opposite extreme, e.g.
when a single compact -dimensional manifold is re-scaled to a point, the
limit fiber is where is the closure of the holonomy group of the
compact manifold considered.
An appropriate notion of parallelism is given to the limiting spaces by
considering curves whose length is unchanged under the projection. The class of
such curves is invariant under the -action and each such curve preserves
norms. The existence of parallel translation along rectifiable curves with
arbitrary initial conditions is also exhibited. Uniqueness is not true in
general, but a necessary condition is given in terms of the aforementioned wane
groups .Comment: 44 pages, 1 figure, in V.2 added Theorem E and Section 4 on
parallelism in the limit space
Diagrammatic approach to non-Gaussianity from inflation
We present Feynman type diagrams for calculating the n-point function of the
primordial curvature perturbation in terms of scalar field perturbations during
inflation. The diagrams can be used to evaluate the corresponding terms in the
n-point function at tree level or any required loop level. Rules are presented
for drawing the diagrams and writing down the corresponding terms in real space
and Fourier space. We show that vertices can be renormalised to automatically
account for diagrams with dressed vertices. We apply these rules to calculate
the primordial power spectrum up to two loops, the bispectrum including loop
corrections, and the trispectrum.Comment: 17 pages, 13 figures. v2: Comments and references added, v3:
Introduction expanded, subsection on evaluating loop diagrams added, minor
errors corrected, references adde
Classical approximation to quantum cosmological correlations
We investigate up to which order quantum effects can be neglected in
calculating cosmological correlation functions after horizon exit. As a toy
model, we study theory on a de Sitter background for a massless
minimally coupled scalar field . We find that for tree level and one loop
contributions in the quantum theory, a good classical approximation can be
constructed, but for higher loop corrections this is in general not expected to
be possible. The reason is that loop corrections get non-negligible
contributions from loop momenta with magnitude up to the Hubble scale H, at
which scale classical physics is not expected to be a good approximation to the
quantum theory. An explicit calculation of the one loop correction to the two
point function, supports the argument that contributions from loop momenta of
scale are not negligible. Generalization of the arguments for the toy model
to derivative interactions and the curvature perturbation leads to the
conclusion that the leading orders of non-Gaussian effects generated after
horizon exit, can be approximated quite well by classical methods. Furthermore
we compare with a theorem by Weinberg. We find that growing loop corrections
after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references,
conclusions unchanged; v3: added section in which we compare with stochastic
approach; this version matches published versio
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