Polymer elasticity discrete and continuum models

2005 ◽  
pp. 67-117 ◽  
Author(s):  
Robert G. C. Arridge ◽  
Peter J. Barham
Keyword(s):  
Continuum Models ◽  
Polymer Elasticity

Simulation of three Dimensional Defect Images in Transmission Electron Microscopy

1976 ◽  
Vol 34 ◽  
pp. 470-471
Author(s):  
W. D. Cooper ◽  
C. S. Hartley ◽  
J. J. Hren
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Three Dimensional ◽  
Crystalline Lattice ◽  
Continuum Models ◽  
Thin Foils ◽  
Transmission Electron ◽  
Microscope Images ◽  
General Computer Program ◽  
General Computer

Interpretation of electron microscope images of crystalline lattice defects can be greatly aided by computer simulation of theoretical contrast from continuum models of such defects in thin foils. Several computer programs exist at the present time, but none are sufficiently general to permit their use as an aid in the identification of the range of defect types encountered in electron microscopy. This paper presents progress in the development of a more general computer program for this purpose which eliminates a number of restrictions contained in other programs. In particular, the program permits a variety of foil geometries and defect types to be simulated.The conventional approximation of non-interacting columns is employed for evaluation of the two-beam dynamical scattering equations by a piecewise solution of the Howie-Whelan equations.

scholarly journals A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

2020 ◽  
pp. 1-35
Author(s):  
Benjamin D. Goddard ◽  
Tim D. Hurst ◽  
Mark Wilkinson
Keyword(s):  
Liouville Equation ◽  
Particle Dynamics ◽  
Fundamental Importance ◽  
Continuum Models ◽  
Hard Particle ◽  
Interacting Particles ◽  
Weak Formulation ◽  
Physical Systems ◽  
Physical Particle

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using two examples.

scholarly journals Flow of long chain hydrocarbons through carbon nanotubes (CNTs)

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pranay Asai ◽  
Palash Panja ◽  
Raul Velasco ◽  
Milind Deo
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamic ◽  
Continuum Models ◽  
Molecular Dynamic Simulations ◽  
Dynamic Simulations ◽  
Pharmaceutical Applications ◽  
Molecular Sizes ◽  
Hydrocarbon Molecules ◽  
Pressure Driven Flow ◽  
Long Chain

AbstractThe pressure-driven flow of long-chain hydrocarbons in nanosized pores is important in energy, environmental, biological, and pharmaceutical applications. This paper examines the flow of hexane, heptane, and decane in carbon nanotubes (CNTs) of pore diameters 1–8 nm using molecular dynamic simulations. Enhancement of water flow in CNTs in comparison to rates predicted by continuum models has been well established in the literature. Our work was intended to observe if molecular dynamic simulations of hydrocarbon flow in CNTs produced similar enhancements. We used the OPLS-AA force field to simulate the hydrocarbons and the CNTs. Our simulations predicted the bulk densities of the hydrocarbons to be within 3% of the literature values. Molecular sizes and shapes of the hydrocarbon molecules compared to the pore size create interesting density patterns for smaller sized CNTs. We observed moderate flow enhancements for all the hydrocarbons (1–100) flowing through small-sized CNTs. For very small CNTs the larger hydrocarbons were forced to flow in a cork-screw fashion. As a result of this flow orientation, the larger molecules flowed as effectively (similar enhancements) as the smaller hydrocarbons.

scholarly journals Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments

2020 ◽  
Vol 102 (4) ◽  
Author(s):  
Aleksandra Ardaševa ◽  
Alexander R. A. Anderson ◽  
Robert A. Gatenby ◽  
Helen M. Byrne ◽  
Philip K. Maini ◽  
...  
Keyword(s):  
Comparative Study ◽  
Continuum Models ◽  
Cell Populations

Continuum models according to Piola

2014 ◽  
Vol 21 (4) ◽  
pp. 506-522
Author(s):  
Giuseppe Ruta
Keyword(s):  
Continuum Models

Atomistic Aspects of Fracture Modelling in the Framework of Continuum Mechanics

1998 ◽  
Vol 538 ◽  
Author(s):  
F. Cleri
Keyword(s):  
Continuum Mechanics ◽  
Constitutive Relations ◽  
Point Of View ◽  
Atomic Scale ◽  
Continuum Models ◽  
Cohesive Law ◽  
Macroscopic Models ◽  
Scale Models ◽  
Level Information ◽  
Set Up

AbstractThe validity and predictive capability of continuum models of fracture rests on basic informations whose origin lies at the atomic scale. Examples of such crucial informations are, e.g., the explicit form of the cohesive law in the Barenblatt model and the shear-displacement relation in the Rice-Peierls-Nabarro model. Modem approaches to incorporate atomic-level information into fracture modelling require to increase the size of atomic-scale models up to millions of atoms and more; or to connect directly atomistic and macroscopic, e.g. finite-elements, models; or to pass information from atomistic to continuum models in the form of constitutive relations. A main drawback of the atomistic methods is the complexity of the simulation results, which can be rather difficult to rationalize in the framework of classical, continuum fracture mechanics. We critically discuss the main issues in the atomistic simulation of fracture problems (and dislocations, to some extent); our objective is to indicate how to set up atomistic simulations which represent well-posed problems also from the point of view of continuum mechanics, so as to ease the connection between atomistic information and macroscopic models of fracture.

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