Modelling of Mechanical Systems: Discrete Systems: 1

Non-local interactions can be considered both for mechanical and socio-economical systems and can be modeled as parallel links connecting nodes, in addition to serial links connecting only neighboring nodes. Therefore, given the elementary constitutive equations describing the link behavior that can be mechanically modeled as non-linear springs and the state variables characterizing the nodes, the basic dynamics of any discrete system can be in principle simulated according to the numerical techniques proper of non-linear mechanics.

A non-locality index can also be used to classify and distinguish between different networks, as shown in Infuso and Paggi to interpret the response of a discrete system upon removal of nodes in different locations. From numerical simulations in Infuso and Paggi , we observed that the higher the value of the non-locality index, the higher the total force supported by the network, for the same type of node removal.

Significant differences are also present among discrete systems in different disciplines.

Links between atoms or molecules are always constructed on a deterministic basis, i. The situation in socio-economic systems is in reality much more complex, since the existence of links between nodes may depend on the reputation or the economic state of the nodes themselves, to cite two possible influencing state variables. Therefore, links are created dynamically and are probably the result of an optimization problem that should be modeled and solved at the local level. Although these differences may suggest that a unified theory for the simulation of complex networks is still to come and should be the result of a joint cross-disciplinary effort involving mathematicians, engineers, physicists, and economists, they also open interesting perspectives for mechanics.

For instance, the fact that local optimization problems should take place at the local level, in mechanics they could be the result of the mechanical response of a constituent of a metamaterial, whose configuration is such that it can minimize or maximize certain properties depending on the intensity of diffusive external fields temperature, humidity, electro-chemical potentials, etc. Within a bottom-up approach to model this cyber-physical system, given the links formed at the lower scale and their constitutive behavior that may depend on time, the global mechanical response of the network can then be simulated by minimizing the total energy of the system, using numerical methods proper of mechanics.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Lattice discretization in quantum scattering. Coupling methods for continuum model with molecular model. A self-organized model for network evolution. Complex Systems and Interdisciplinary Science , Vol.

Unified approach for molecular dynamics and density-functional theory. Statistical mechanics of competitive resource allocation using agent-based models.

Decay of correlations in linear systems. Flaw-tolerance of nonlocal discrete systems and interpretation according to network theory. An analysis of the quasicontinuum method. Discrete symmetry analysis of lattice systems. On kinematic waves II — a theory of traffic on long crowded roads. Generalized Born solvation model SM Micropolar beams model for lattice grids with rigid joints. A generalized-Born solvation model for macromolecular hybrid-potential calculations.

Shockwaves on the highway. Fracture simulations of concrete using lattice models: An adaptive finite element approach to atomic-scale mechanics — the quasicontinuum method. Quasicontinuum analysis of defects in solids. Linear and Nonlinear Waves. A bridging domain method for coupling continua with molecular dynamics. Crowd modeling and simulation technologies.

Infuso A and Paggi M Computational modeling of discrete mechanical systems and complex networks: The use, distribution or reproduction in other forums is permitted, provided the original author s or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Login Register Login using. The situation in socio-economic systems is in reality much more complex, since the existence of links between nodes may depend on the reputation or the economic state of the nodes themselves, to cite two possible influencing state variables.

Therefore, links are created dynamically and are probably the result of an optimization problem that should be modeled and solved at the local level. Although these differences may suggest that a unified theory for the simulation of complex networks is still to come and should be the result of a joint cross-disciplinary effort involving mathematicians, engineers, physicists, and economists, they also open interesting perspectives for mechanics.

For instance, the fact that local optimization problems should take place at the local level, in mechanics they could be the result of the mechanical response of a constituent of a metamaterial, whose configuration is such that it can minimize or maximize certain properties depending on the intensity of diffusive external fields temperature, humidity, electro-chemical potentials, etc. Within a bottom-up approach to model this cyber-physical system, given the links formed at the lower scale and their constitutive behavior that may depend on time, the global mechanical response of the network can then be simulated by minimizing the total energy of the system, using numerical methods proper of mechanics.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Lattice discretization in quantum scattering. Coupling methods for continuum model with molecular model. A self-organized model for network evolution. Complex Systems and Interdisciplinary Science , Vol. Unified approach for molecular dynamics and density-functional theory.

Account Options

Statistical mechanics of competitive resource allocation using agent-based models. Decay of correlations in linear systems.

Flaw-tolerance of nonlocal discrete systems and interpretation according to network theory. An analysis of the quasicontinuum method. Discrete symmetry analysis of lattice systems. On kinematic waves II — a theory of traffic on long crowded roads. Generalized Born solvation model SM Micropolar beams model for lattice grids with rigid joints.

A generalized-Born solvation model for macromolecular hybrid-potential calculations. Shockwaves on the highway. Fracture simulations of concrete using lattice models: An adaptive finite element approach to atomic-scale mechanics — the quasicontinuum method. Quasicontinuum analysis of defects in solids. Linear and Nonlinear Waves. A bridging domain method for coupling continua with molecular dynamics.

Crowd modeling and simulation technologies. Infuso A and Paggi M Computational modeling of discrete mechanical systems and complex networks: The use, distribution or reproduction in other forums is permitted, provided the original author s or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Login Register Login using. You can login by using one of your existing accounts. We will be provided with an authorization token please note: This means that you will not need to remember your user name and password in the future and you will be able to login with the account you choose to sync, with the click of a button.

Suggest a Research Topic. Computational modeling of discrete mechanical systems and complex networks: Stefano Mariani , Politecnico di Milano, Italy.