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Test of the Shoving Model by Flow Event Investigations - development and application of an algorithm for finding first order saddle points
Speciale, 3. modul, 2004, id:208
Vejleder:Johnny Ottesen (matematik) Jeppe Dyre (fysik)
Findes på RUb:Ja
English abstract
The purpose of the work reported in this thesis is to test the central assumption of the Shoving Model for the temperature dependence of the viscosity of supercooled liquids, developed at the Institute for Mathematics and Physics at Roskilde University, by performing numerical calculation on a model liquid. The central assumption of the Shoving Model is that the activation energy necessary to make a flow event in supercooled liquids is due to a compression of the surroundings of the rearranging molecules. Therefore the activation energy is only associated with the molecules in the surroundings defined as those which moves less than a certain threshold value during a flow event. The major part of the work done has been the development of an algorithm capable of finding the molecular configurations responsible for the activation energy. These configurations are equivalent to first order saddle points of the energy function of the entire system. Similar a flow event can be described as a transition from one minimum of this function to another. The system used in this work is a bulk binary Lennard-Jones model liquid consisting of 500 molecules in which the energy is given purely by pair interactions. The basic idea behind the algorithm, called Meta Line Drag (Meta LiD), is that a saddle point between the minima in a flow event can be found by making consecutive plane minimisations along the vector connecting the minima on hyperplanes which are perpendicular to this vector. The Meta LiD algorithm is able to find saddle points in 50% of the investigated flow events. The failure of the remaining is mainly due to a disability to handle directions of negative curvature within the minimisation hyperplanes or areas where the eigenvector of the smallest eigenvalue and the vector connecting the two minima in the flow event diverges. By performing energy calculations on the molecular configurations of the saddle points it is found that the majority (75%) of the activation energy is in the surroundings. This supports the central assumption of the Shoving Model, although only partly because the Shoving Model assumes that all of the activation energy is in the surroundings.

Database opslag den: 22-09-2017