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R. dell’Erba
We are relaxing the hypothesis that the neighbors always are the same to describe
liquid and gas; this needs an intermediate calculation step because you have to
compute who the neighbors are, defined in this case as the particles inside a specified
volume, at each time step.
We are introducing constrained on the particle’s motion to describe structured
object like pantograph (Giorgio et al. 2016; Boutin et al. 2017; Giorgio et al. 2018;
Spagnuolo et al. 2017; De Angelo 2019; Andreaus et al. 2018; Turco et al. 2016;
Turco and Rizzi 2016). It can be described as a set of beams with constrained point in
the pivot or, in the Hencky vision, can be conceived as a set of points interconnected
by springs.
Further developments are concerning different fracture mechanism, different
frame to avoid edge effects, other interactions rules and adaptive lattice.
A generalization of the interaction algorithm, to encompass the richness of
behavior of different materials like metal or plastic is auspicable, including potentially
complex biological tissues (Andreaus et al. 2013; Andreaus et al. 2012; Andreaus
et al. 2008; Lekszycki and Dell’Isola 2012; Giorgio et al. 2016). An appropriate
potential interaction could take into account different deformation regimes, such as
elastic and plastic ones together with fracture. To this aim, pseudoenergetic considerations are introduced also to achieve a better understanding of the process. This is
preliminary to introducing potential descriptive interactions depending on the relative
distance between the particles, which are able to reproduce the well-known physical
behavior.
Cellular automata seems to be a good candidate to enhance our work; a cellular
automata is a simple computational mechanism that, for example, changes the color
of each cell on a lattice based on the color of neighbors’ cells according to a transformation rule. Some attempts, to use them in mechanics, have been done (Dong
et al. 2013; Psakhie 2010). Principal limit of cellular automata is regarding as it does
not evolve sufficiently, so they quickly reach a limited asymptote in their order of
complexity and this will be the object of a future paper. An evolutionary process
involving conflict and competition is needed, like in biology systems to overcome
this difficult. 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 behavior. The question
posed here is concerning if we can work on patterns of information, rather than
matter and energy; this question is important and still open. We would like to make
a connection with our tool.
Moreover, how stable and robust is the model? What is possible to describe with
this model and what are the physical reasons of its success? Is there a hidden dynamic
inside? Does a connection exist between pseudoenergy and a real potential? Finally,
the mathematical study of the homogenization of lattice systems like the one here
considered seems to pose interesting problems, and will probably require non-trivial
ideas in the field of functional convergence (Alibert and Della Corte 2015; Dos Reis
and Ganghoffer 2011; Dos Reis and Ganghoffer 2012; Rahali et al. 2015; Goda et al.
2013; Alibert et al. 2017). These, and many others, are the object of a next job.
R. dell’Erba
We are relaxing the hypothesis that the neighbors always are the same to describe
liquid and gas; this needs an intermediate calculation step because you have to
compute who the neighbors are, defined in this case as the particles inside a specified
volume, at each time step.
We are introducing constrained on the particle’s motion to describe structured
object like pantograph (Giorgio et al. 2016; Boutin et al. 2017; Giorgio et al. 2018;
Spagnuolo et al. 2017; De Angelo 2019; Andreaus et al. 2018; Turco et al. 2016;
Turco and Rizzi 2016). It can be described as a set of beams with constrained point in
the pivot or, in the Hencky vision, can be conceived as a set of points interconnected
by springs.
Further developments are concerning different fracture mechanism, different
frame to avoid edge effects, other interactions rules and adaptive lattice.
A generalization of the interaction algorithm, to encompass the richness of
behavior of different materials like metal or plastic is auspicable, including potentially
complex biological tissues (Andreaus et al. 2013; Andreaus et al. 2012; Andreaus
et al. 2008; Lekszycki and Dell’Isola 2012; Giorgio et al. 2016). An appropriate
potential interaction could take into account different deformation regimes, such as
elastic and plastic ones together with fracture. To this aim, pseudoenergetic considerations are introduced also to achieve a better understanding of the process. This is
preliminary to introducing potential descriptive interactions depending on the relative
distance between the particles, which are able to reproduce the well-known physical
behavior.
Cellular automata seems to be a good candidate to enhance our work; a cellular
automata is a simple computational mechanism that, for example, changes the color
of each cell on a lattice based on the color of neighbors’ cells according to a transformation rule. Some attempts, to use them in mechanics, have been done (Dong
et al. 2013; Psakhie 2010). Principal limit of cellular automata is regarding as it does
not evolve sufficiently, so they quickly reach a limited asymptote in their order of
complexity and this will be the object of a future paper. An evolutionary process
involving conflict and competition is needed, like in biology systems to overcome
this difficult. 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 behavior. The question
posed here is concerning if we can work on patterns of information, rather than
matter and energy; this question is important and still open. We would like to make
a connection with our tool.
Moreover, how stable and robust is the model? What is possible to describe with
this model and what are the physical reasons of its success? Is there a hidden dynamic
inside? Does a connection exist between pseudoenergy and a real potential? Finally,
the mathematical study of the homogenization of lattice systems like the one here
considered seems to pose interesting problems, and will probably require non-trivial
ideas in the field of functional convergence (Alibert and Della Corte 2015; Dos Reis
and Ganghoffer 2011; Dos Reis and Ganghoffer 2012; Rahali et al. 2015; Goda et al.
2013; Alibert et al. 2017). These, and many others, are the object of a next job.