44,098 research outputs found
Growing interfaces: A brief review on the tilt method
The tilt method applied to models of growing interfaces is a useful tool to
characterize the nonlinearities of their associated equation. Growing
interfaces with average slope , in models and equations belonging to
Kardar-Parisi-Zhang (KPZ) universality class, have average saturation velocity
when .
This property is sufficient to ensure that there is a nonlinearity type square
height-gradient. Usually, the constant is considered equal to the
nonlinear coefficient of the KPZ equation. In this paper, we show
that the mean square height-gradient ,
where for the continuous KPZ equation and otherwise, e.g.
ballistic deposition (BD) and restricted-solid-on-solid (RSOS) models. In order
to find the nonlinear coefficient associated to each system, we
establish the relationship and we test it through the
discrete integration of the KPZ equation. We conclude that height-gradient
fluctuations as function of are constant for continuous KPZ equation and
increasing or decreasing in other systems, such as BD or RSOS models,
respectively.Comment: 11 pages, 4 figure
Cluster algebras in scattering amplitudes with special 2D kinematics
We study the cluster algebra of the kinematic configuration space
of a n-particle scattering amplitude restricted to the
special 2D kinematics. We found that the n-points two loop MHV remainder
function found in special 2D kinematics depend on a selection of
\XX-coordinates that are part of a special structure of the cluster algebra
related to snake triangulations of polygons. This structure forms a necklace of
hypercubes beads in the corresponding Stasheff polytope. Furthermore in , the cluster algebra and the selection of \XX-coordinates in special 2D
kinematics replicates the cluster algebra and the selection of \XX-coordinates
of two loop MHV amplitude in 4D kinematics.Comment: 22 page
Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem
The concept of measurement in classical scattering is interpreted as an
overlap of a particle packet with some area in phase space that describes the
detector. Considering that usually we record the passage of particles at some
point in space, a common detector is described e.g. for one-dimensional systems
as a narrow strip in phase space. We generalize this concept allowing this
strip to be transformed by some, possibly non-linear, canonical transformation,
introducing thus a canonically transformed detector. We show such detectors to
be useful in the context of the inverse scattering problem in situations where
recently discovered scattering echoes could not be seen without their help.
More relevant applications in quantum systems are suggested.Comment: 8 pages, 15 figures. Better figures can be found in the original
article, wich can be found in
http://www.sm.luth.se/~norbert/home_journal/electronic/v12s1.html Related
movies can be found in www.cicc.unam.mx/~mau
A symmetric quantum calculus
We introduce the -symmetric difference derivative and the
-symmetric N\"orlund sum. The associated symmetric quantum
calculus is developed, which can be seen as a generalization of the forward and
backward -calculus.Comment: Submitted 26/Sept/2011; accepted in revised form 28/Dec/2011; to
Proceedings of International Conference on Differential & Difference
Equations and Applications, in honour of Professor Ravi P. Agarwal, to be
published by Springer in the series Proceedings in Mathematics (PROM
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