14 Flocking Rules Governing Swarm Robot as Tool to Describe …
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as a set of point interconnected by springs. Further developments are concerning
different fracture mechanism, different frame to avoid edge effects, other interaction
rules and adaptive lattices. Cellular automata seems to be a good candidate to enhance
our work; cellular automata is a simple computational mechanism that, for example,
changes the colour of each cell on a lattice based on the colour of neighbours cells
according to a transformation rule. Some attempts to use them in mechanics have
been done, but one of their principal limits is that they do not evolve sufficiently, so
they quickly reach a limited asymptote in their order of complexity. An evolutionary
process involving conflict and competition is needed, like in biology systems. Moreover, there is no way to predict the outcome of a cellular process without actually
running the process. So even though our decisions are determined, there is no way
to predetermine what these decisions will be. But the system has succeeded, especially in fluid dynamics to describe complex behaviour. The question of whether
one can work on patterns of information, rather than matter and energy, as the more
fundamental building blocks of reality is still open, and we would like to make a
connection with our tool.
Funding The authors received no financial support for the research, authorship, and/or publication
of this article.
References
Abali, B. E., Müller, W. H., & Eremeyev, V. A. (2015). Strain gradient elasticity with geometric
nonlinearities and its computational evaluation. Mechanics of Advanced Materials and Modern
Processes, 1(1), 4.
Abali, B. E., Müller, W. H., & Dell’Isola, F. (2017). Theory and computation of higher gradient
elasticity theories based on action principles. Archive of Applied Mechanics, 87(9), 1495–1510.
Abdoul-Anziz, H., & Seppecher, P. (2018). Strain gradient and generalized continua obtained by
homogenizing frame lattices. Mathematics and Mechanics of Complex Systems, 6(3), 213–250.
Alibert, J. J., Seppecher, P., & Dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1), 51–73.
Altenbach, H., & Eremeyev, V. A. (2009). On the linear theory of micropolar plates. ZAMM-Journal
of Applied Mathematics and Mechanics/Zeitschrift Für Angewandte Mathematik Und Mechanik,
89(4), 242–256.
Altenbach, H., Bîrsan, M., & Eremeyev, V. A. (2013). Cosserat-type rods. In Generalized Continua
from the Theory to Engineering Applications (pp. 179–248). Springer, Vienna.
Andreaus, U., Spagnuolo, M., Lekszycki, T., & Eugster, S. R. (2018). A Ritz approach for the
static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams.
Continuum Mechanics and Thermodynamics, 30(5), 1103–1123.
Auffray, N., Dirrenberger, J., & Rosi, G. (2015). A complete description of bi-dimensional
anisotropic strain-gradient elasticity. International Journal of Solids and Structures, 69, 195–206.
Avella, M., dell’Erba, R., Martuscelli, E., & Ragosta, G. (1993). Influence of molecular mass,
thermal treatment and nucleating agent on structure and fracture toughness of isotactic
polypropylene. Polymer, 34(14), 2951–2960.
239
as a set of point interconnected by springs. Further developments are concerning
different fracture mechanism, different frame to avoid edge effects, other interaction
rules and adaptive lattices. Cellular automata seems to be a good candidate to enhance
our work; cellular automata is a simple computational mechanism that, for example,
changes the colour of each cell on a lattice based on the colour of neighbours cells
according to a transformation rule. Some attempts to use them in mechanics have
been done, but one of their principal limits is that they do not evolve sufficiently, so
they quickly reach a limited asymptote in their order of complexity. An evolutionary
process involving conflict and competition is needed, like in biology systems. Moreover, there is no way to predict the outcome of a cellular process without actually
running the process. So even though our decisions are determined, there is no way
to predetermine what these decisions will be. But the system has succeeded, especially in fluid dynamics to describe complex behaviour. The question of whether
one can work on patterns of information, rather than matter and energy, as the more
fundamental building blocks of reality is still open, and we would like to make a
connection with our tool.
Funding The authors received no financial support for the research, authorship, and/or publication
of this article.
References
Abali, B. E., Müller, W. H., & Eremeyev, V. A. (2015). Strain gradient elasticity with geometric
nonlinearities and its computational evaluation. Mechanics of Advanced Materials and Modern
Processes, 1(1), 4.
Abali, B. E., Müller, W. H., & Dell’Isola, F. (2017). Theory and computation of higher gradient
elasticity theories based on action principles. Archive of Applied Mechanics, 87(9), 1495–1510.
Abdoul-Anziz, H., & Seppecher, P. (2018). Strain gradient and generalized continua obtained by
homogenizing frame lattices. Mathematics and Mechanics of Complex Systems, 6(3), 213–250.
Alibert, J. J., Seppecher, P., & Dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1), 51–73.
Altenbach, H., & Eremeyev, V. A. (2009). On the linear theory of micropolar plates. ZAMM-Journal
of Applied Mathematics and Mechanics/Zeitschrift Für Angewandte Mathematik Und Mechanik,
89(4), 242–256.
Altenbach, H., Bîrsan, M., & Eremeyev, V. A. (2013). Cosserat-type rods. In Generalized Continua
from the Theory to Engineering Applications (pp. 179–248). Springer, Vienna.
Andreaus, U., Spagnuolo, M., Lekszycki, T., & Eugster, S. R. (2018). A Ritz approach for the
static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams.
Continuum Mechanics and Thermodynamics, 30(5), 1103–1123.
Auffray, N., Dirrenberger, J., & Rosi, G. (2015). A complete description of bi-dimensional
anisotropic strain-gradient elasticity. International Journal of Solids and Structures, 69, 195–206.
Avella, M., dell’Erba, R., Martuscelli, E., & Ragosta, G. (1993). Influence of molecular mass,
thermal treatment and nucleating agent on structure and fracture toughness of isotactic
polypropylene. Polymer, 34(14), 2951–2960.