As you may have discovered, Pore-Cor v1.32 is quite difficult to use. Two of the difficulties are:

(i) it is sometimes very difficult to find a fit to an experimental mercury intrusion or water retention curve, even with the help of the Wizard or the optimisation routines, and

(ii) sometimes Pore-Cor v1.32 complains that it cannot find a structure, for example because it cannot model the experimental porosity.

The Simplex brain of Pore-Cor gets round these two difficulties. Take a two-dimensional optimization case - you want to optimise the values of two fitting parameters, throat skew and connectivity say, to get the best fit between simulation and experiment. In version 1.32, you obtain an optimisation surface like the one shown on the right.

The two parameters are plotted on the horizontal blue and red axes, and the quality parameter - the distance between simulation and experiment - is plotted on the vertical green axis. Then the task is to find the minimum point of the surface, excluding fragmented networks which are plotted as zero values. The current grid method works through a combination of a range of throat skew and connectivity values - as you can see, the surface shown on the right is based on discrete equally spaced values of each parameter. The optimum values are then simply the combination which give rise to the minimum value of the quality parameter, as marked by the yellow line. The precision of the estimate of minimum value is clearly limited by the spacing of the parameters. By contrast, the two-dimensional Simplex is a triangle, for example as shown purple in the diagram. The Simplex expands, contracts, shrinks and reflects itself to find the minimum value of the surface, with no limit to precision. In the 3-dimensional case, with 3 parameters rather than 2, the Simplex becomes tetragonal. In the four dimensions in which it is currently working, we are not sure how to describe the shape - please tell us if you know!

The Simplex in the diagram above is just diagrammatic - the Simplex graphics pages show a real two-dimensional Simplex moving (for obvious reasons we cannot plot the behaviour of the 3 or 4 dimensional Simplex).

So, problem solved, you may think. Not so - the hyper-surface within multidimensional parameter space is often bumpy and ill-behaved - especially for occluded samples such as clay-included sandstones and soils. Therefore a straightforward Simplex would never find the answer -it would dive off into cul-de-sacs and false minima - for example in the diagram above , it might get trapped near the gully to its right. The problem is substantially reduced by the use of Boltzmann annealing, which kicks the Simplex out of these blind alleys.

The Simplex graphics also show the control panel which runs the Simplex - amazingly , every control on the form is necessary to model soil. Don't worry, though - in Pore-Cor Research Suite, the advanced controls and sample starting grids will be supplied for you, so if you push the 'Check starting grid' and 'Run Simplex' buttons, the Simplex will, we hope, find the right answer fairly quickly.

You may notice that to get the Simplex to operate correctly, we have had to carry out various parameter transformations (analogous to those required for variance stabilization in chemometrics). These transformed or 'linearised' variables are shown on the Simplex control form.

Once a definite optimum has been achieved with the Simplex, a sensitivity analysis can be carried out with confidence.

The Annealed Simplex will be available in Pore-Cor Research Suite, which has a targeted release date as shown in its specifications. Until then, we are very happy to run a few individual samples free of charge, on condition that you tell us the material you are testing. You do not have to tell us anything confidential, but we wish to build up a directory of generic starting grids for different materials. (For larger tasks, please see our Consultancy terms).