5,254 research outputs found
Finding nonlocal Lie symmetries algorithmically
Here we present a new approach to compute symmetries of rational second order
ordinary differential equations (rational 2ODEs). This method can compute Lie
symmetries (point symmetries, dynamical symmetries and non-local symmetries)
algorithmically. The procedure is based on an idea arising from the formal
equivalence between the total derivative operator and the vector field
associated with the 2ODE over its solutions (Cartan vector field). Basically,
from the formal representation of a Lie symmetry it is possible to extract
information that allows to use this symmetry practically (in the 2ODE
integration process) even in cases where the formal operation cannot be
performed, i.e., in cases where the symmetry is nonlocal. Furthermore, when the
2ODE in question depends on parameters, the procedure allows an analysis that
determines the regions of the parameter space in which the integrable cases are
located
2D pattern evolution constrained by complex network dynamics
Complex networks have established themselves along the last years as being
particularly suitable and flexible for representing and modeling several
complex natural and human-made systems. At the same time in which the
structural intricacies of such networks are being revealed and understood,
efforts have also been directed at investigating how such connectivity
properties define and constrain the dynamics of systems unfolding on such
structures. However, lesser attention has been focused on hybrid systems,
\textit{i.e.} involving more than one type of network and/or dynamics. Because
several real systems present such an organization (\textit{e.g.} the dynamics
of a disease coexisting with the dynamics of the immune system), it becomes
important to address such hybrid systems. The current paper investigates a
specific system involving a diffusive (linear and non-linear) dynamics taking
place in a regular network while interacting with a complex network of
defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models,
whose nodes can be displaced spatially. More specifically, the complex network
is expected to control, and if possible to extinguish, the diffusion of some
given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination,
and virus or bacteria reproduction during an infection). Two types of pattern
evolution are considered: Fick and Gray-Scott. The nodes of the defensive
network then interact with the diffusing patterns and communicate between
themselves in order to control the spreading. The main findings include the
identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome
Efeitos da água residuária do café em plantas e no substrato de cultivo de aveia, milho e alface.
bitstream/item/33456/1/Efeitos-das-aguas.pd
NN Scattering: Chiral Predictions for Asymptotic Observables
We assume that the nuclear potential for distances larger than 2.5 fm is
given just by the exchanges of one and two pions and, for the latter, we adopt
a model based on chiral symmetry and subthreshold pion-nucleon amplitudes,
which contains no free parameters. The predictions produced by this model for
nucleon-nucleon observables are calculated and shown to agree well with both
experiment and those due to phenomenological potentials.Comment: 16 pages, 12 PS figures included, to appear in Physical Review
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