[ABE-L] COLMEA - Colóquio Interinstitucional - 16 de fevereiro - quarta-feira

[Maria Eulalia Vares]

Prezados colegas,

Continuamos realizando de forma virtual as atividades do COLMEA, colóquio
interinstitucional que congrega vários grupos do Rio de Janeiro.

Nosso próximo encontro será no dia 16 de fevereiro (quarta-feira), com
início às 13 horas, utilizando a plataforma Zoom.  Na ocasião teremos a
seguinte programação:



*Marcelo R. Hilário (UFMG)*

*Percolation on the cubic lattice with lower dimensional disorder*

*Nuno A. M. Araújo (Universidade de Lisboa)*

*Kinetics of self-folding at the microscale*



Todos são muito bem-vindos.

Plataforma Zoom
https://impa-br.zoom.us/j/95805813232?pwd=Rnd4TU9pUTRhQm5xa0Mvb0gxa0xDUT09

Haverá transmissão pelo canal do YouTube COLMEA_UFRJ
<https://www.youtube.com/channel/UC331W0wSzooQiQr4XESnADA>

Mais informações sobre o COLMEA podem ser encontradas através da homepage
http://www.im.ufrj.br/~coloquiomea/

Os resumos das palestras estão no final da mensagem.

Agradecemos a divulgação.

Atenciosamente,

O comitê organizador:

Americo Cunha (UERJ)

Augusto Q. Teixeira (IMPA)

Evaldo M. F. Curado (CBPF)

João Batista M. Pereira (UFRJ)

Leandro P. R. Pimentel (UFRJ)

Maria Eulalia Vares (UFRJ)

Nuno Crokidakis (UFF)

Simon Griffiths (PUC-Rio)



========



*Percolation on the cubic lattice with lower dimensional disorder*
Marcelo R. Hilário (UFMG)

Percolation on the Euclidean d-dimensional lattice has been studied for
over sixty years and is still a fascinating source of interesting
mathematical problems. The fact that this model undergoes a non-trivial
phase transition is well-understood since the early studies in the
Bernoulli setting, where the lattice is regular and there are no
inhomogeneities on the parameters. One way to introduce random disorder is,
for example, either passing to a dilute lattice where lower dimensional
affine hyperplanes are removed or, alternately, introducing inhomogeneities
on the parameter along such hyperplanes. In these situations, even to
establish that non-trivial phase transition takes place may be a hard task.
In this talk we review some recent results on this topic and discuss some
open problems.




*Kinetics of self-folding at the microscale*
Nuno A. M. Araújo (Universidade de Lisboa)

Three-dimensional shells can be synthesized from the spontaneous
self-folding of two-dimensional templates of interconnected panels, called
nets. To design self-folding, one first needs to identify what are the nets
that fold into the desired structure. In principle, different nets can fold
into the same three-dimensional structure. However, recent experiments and
numerical simulations show that the stochastic nature of folding might lead
to misfolding and so, the probability for a given net to fold into the
desired structure (yield) depends strongly on the topology of the net and
experimental conditions. Thus, the focus has been on identifying what are
the optimal nets that maximize the yield. But, what about the folding time?
For practical applications, it is not only critical to reduce misfolding
but also to guarantee that folding occurs in due time. Here, we consider as
a prototype the spontaneous folding of a pyramid. We find that the total
folding time is a non-monotonic function of the number of faces, with a
minimum for five faces. The motion of each face is consistent with a
Brownian process and folding occurs through a sequence of irreversible
binding events that close edges between pairs of faces. The first edge
closing is well-described by a first-passage process in 2D, with a
characteristic time that decays with the number of faces. By contrast, the
subsequent edge closings are all first-passage processes in 1D and so the
time of the last one grows logarithmically with the number of faces. It is
the interplay between these two different sets of events that explains the
non-monotonic behavior. Implications in the self-folding of more complex
structures are discussed.
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