Array of obstacles

Khokhlov A R and Nechaev S K 1985 Polymer chain in an array of obstacles Phys. Lett. A 112 156... 

Some versions of the so-called model chain in an array of obstacles , which geometrically can be considered in a certain sense as a generalization of Edwards-Frisch model this will be considered in Sect. 2.2.3 ... 

The model polymer chain in an array of obstacles (PCAO) (see Fig. 4) combines the geometrical clarity of its image with the possibility to investigate the influence of entanglements on equilibrium and dynamic properties of polymers quite precisely. 

It is noteworthy that for investigation of properties of real polymer systems with topological constraints it is not enough to be able to calculate the statistical characteristics of chains in the lattice of obstacles. It is also necessary to be able to compare any concrete physical system with the unique lattice of obstacles, which is a much more complicated problem than the first task. In this way, the model polymer chain in an array of obstacles is an intermediate between the microscopical and phenomenological approaches. The direct investigation of the PCAO-model was fulfilled in Refs. [16-25]. 

The experiments were carried out in a wind tunnel at University of Surrey, UK. A model canopy was installed on the ground plane of a wind tunnel which has a working section with dimensions of 1.37 m in width and of 1.68 m in height. The canopy was formed from an extended array of obstacles. Earlier, cylindrical wooden pegs [411] and metal rods [213] were used as individual obstacles. In this experiment, it was aimed to vary the vertical distribution of the projected area of obstructions. 

Macdonald, R., Griffiths, R.F., and Hall, DJ. (1998) A comparison of results from scaled field and wind tunnel modelling of dispersion in arrays of obstacles, Atmospheric Environment 32, 3845-3862. 

For extensive arrays of obstacles, Belcher et al. (2003) propose that there are three stages in the adjustment of a turbulent boundary layer how upon encountering the canopy ... 

Yee, E. and Biltoft, C.A., 2004. Concentration fluctuations measurements in a plume dispersing through a regular array of obstacles. Bound. Layer Meteorol., Ill, pp. 363-415. 

Fig. 11.22. Dislocation in a random array of obstacles (adapted from Foreman and Makin (1967)).

As noted above, one interesting application of these ideas is to the motion of a dislocation through an array of obstacles. An alternative treatment of the field due to the disorder is to construct a particular realization of the random field by writing random forces at a series of nodes and using the finite element method to interpolate between these nodes. An example of this strategy is illustrated in fig. 12.27. With this random field in place we can then proceed to exploit the type of line tension dislocation dynamics described above in order to examine the response of a dislocation in this random field in the presence of an increasing stress. A series of snapshots in the presence of such a loading history is assembled in fig. 12.28. 

Foreman A. J. E. and Makin M. J., Dislocation Movement Through Random Arrays of Obstacles, Canadian J. Phys. 45, 511 (1967). 

In all equations below, we shall assume biD = b and a = ax for simplicity. Ph)rsically, the tension force is believed to arise from entropic effects. If the chain end moves in random directions, there are more possibilities for it to increase the tube length than to decrease it. This can be easily illustrated using the picture of a chain moving in an array of obstacles. However, it is difficult to derive any quantitative result from such a picture, and any such result will depend on the geometry of constraints. Thus, the indirect result (eqn [64]) is used. 

Rice, J.R., 1988, Cracks fronts trapped by arrays of obstacles solution based on linear perturbation theory, In Analytical, Numerical and Experimental Aspects of Three Dimensional Fracture Process, A. Rosakis, K. Ravi Chandar and Y. Rajapakse, eds., 91, ASME, p. 175. 

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