The Nanometric and Micrometric Scales of the Structure and Mechanics of Materials Revisited : An Introduction to the Challenge of Fully Deterministic Numerical Descriptions
نویسندگان
چکیده
Nano-science and nano-technology as well as the fine modelling of the structure and mechanics of materials from the nanometric to the micrometric scales use descriptions ranging from the quantum to the statistical mechanics. This paper revisits the modelling at these scales and points out the main challenges related to the numerical solution of such models that some times are discrete but involves an extremely large number of particles (as it is the case of molecular dynamics simulations or coarse-grained molecular dynamics) and other times are continuous but they are defined in highly multidimensional spaces leading to the well known curse of dimensionality issues. The curse of dimensionality concerned by some of these deterministic models will be emphasized and their numerical implications will be addressed in the second part of this work.
منابع مشابه
The Nanometric and Micrometric Scales of the Structure and Mechanics of Materials Revisited: An Introduction to the Challenges of Fully Deterministic Numerical Descriptions
Nano-science and nano-technology as well as the fine modelling of the structure and mechanics of materials from the nanometric to the micrometric scales use descriptions ranging from the quantum to the statistical mechanics. This paper revisits the modelling at these scales and points out the main challenges related to the numerical solution of such models that some times are discrete but invol...
متن کاملConsolidation Around a Heat Source in an Isotropic Fully Saturated Rock with Porous Structure in Quasi-Static State
The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the ...
متن کاملAsymptotic Analysis of Binary Gas Mixture Separation by Nanometric Tubular Ceramic Membranes: Cocurrent and Countercurrent Flow Patterns
Analytical gas-permeation models for predicting the separation process across membranes (exit compositions and area requirement) constitutes an important and necessary step in understanding the overall performance of membrane modules. But, the exact (numerical) solution methods suffer from the complexity of the solution. Therefore, solutions of nonlinear ordinary differential equations th...
متن کاملMultiscale Analysis of Transverse Cracking in Cross-Ply Laminated Beams Using the Layerwise Theory
A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numeric...
متن کاملA finite elements study on the role of primary cilia in sensing mechanical stimuli to cells by calculating their response to the fluid flow
The primary cilium which is an organelle in nearly every cell in the vertebrate body extends out of the cell surface like an antenna and is known as cell sensor of mechanical and chemical stimuli. In previous numerical simulations, researchers modeled this organelle as a cantilevered beam attached to the cell surface. In the present study, however, we present a novel model that accommodates for...
متن کامل