335 research outputs found
A new integrable system related to the Toda lattice
A new integrable lattice system is introduced, and its integrable
discretizations are obtained. A B\"acklund transformation between this new
system and the Toda lattice, as well as between their discretizations, is
established.Comment: LaTeX, 14 p
Legendre transformations on the triangular lattice
The main purpose of the paper is to demonstrate that condition of invariance
with respect to the Legendre transformations allows effectively isolate the
class of integrable difference equations on the triangular lattice, which can
be considered as discrete analogues of relativistic Toda type lattices. Some of
obtained equations are new, up to the author knowledge. As an example, one of
them is studied in more details, in particular, its higher continuous
symmetries and zero curvature representation are found.Comment: 13 pages, late
Competitive localization of vortex lines and interacting bosons
We present a theory for the localization of three-dimensional vortex lines or
two-dimensional bosons with short-ranged repulsive interaction which are
competing for a single columnar defect or potential well. For two vortices we
use a necklace model approach to find a new kind of delocalization transition
between two different states with a single bound particle. This
exchange-delocalization transition is characterized by the onset of vortex
exchange on the defect for sufficiently weak vortex-vortex repulsion or
sufficiently weak binding energy corresponding to high temperature. We
calculate the transition point and order of the exchange-delocalization
transition. A generalization of this transition to arbitrary vortex number is
proposed.Comment: 5 pages, 2 figure
On the structure of the B\"acklund transformations for the relativistic lattices
The B\"acklund transformations for the relativistic lattices of the Toda type
and their discrete analogues can be obtained as the composition of two duality
transformations. The condition of invariance under this composition allows to
distinguish effectively the integrable cases. Iterations of the B\"acklund
transformations can be described in the terms of nonrelativistic lattices of
the Toda type. Several multifield generalizations are presented
A note on the integrable discretization of the nonlinear Schr\"odinger equation
We revisit integrable discretizations for the nonlinear Schr\"odinger
equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the
non-locality, can be overcome. Namely, we factorize the non-local difference
scheme into the product of local ones. This must improve the performance of the
scheme in the numerical computations dramatically. Using the equivalence of the
Ablowitz--Ladik and the relativistic Toda hierarchies, we find the
interpolating Hamiltonians for the local schemes and show how to solve them in
terms of matrix factorizations.Comment: 24 pages, LaTeX, revised and extended versio
Higher Order Variational Integrators: a polynomial approach
We reconsider the variational derivation of symplectic partitioned
Runge-Kutta schemes. Such type of variational integrators are of great
importance since they integrate mechanical systems with high order accuracy
while preserving the structural properties of these systems, like the
symplectic form, the evolution of the momentum maps or the energy behaviour.
Also they are easily applicable to optimal control problems based on mechanical
systems as proposed in Ober-Bl\"obaum et al. [2011].
Following the same approach, we develop a family of variational integrators
to which we refer as symplectic Galerkin schemes in contrast to symplectic
partitioned Runge-Kutta. These two families of integrators are, in principle
and by construction, different one from the other. Furthermore, the symplectic
Galerkin family can as easily be applied in optimal control problems, for which
Campos et al. [2012b] is a particular case.Comment: 12 pages, 1 table, 23rd Congress on Differential Equations and
Applications, CEDYA 201
Tobacco and cannabis use trajectories from adolescence to young adulthood
The main objective of this longitudinal research is to answer the following question: What is the relationship between tobacco and cannabis use trajectories from adolescence to young adulthood?
And more specifically we are interested in:
A. If the use of one of the substances (tobacco or cannabis) decreases overtime, does the use of the other one increase to compensate? Are other substances (such as alcohol, for example) also used to compensate in these cases?
B. Does the probability to become a tobacco smoker increase when cannabis use is heavier or has lasted longer?
C. What are the risk and protective factors that can predict that the use of tobacco and/or cannabis will increase or decrease overtime
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