Analytical Calculation of 2D- and 3D-Structures That Have Maximum Entropy And That Are Based on New Material Modifications

Up to now the modelling and the simulation of selforganizing processes are based on numerical and iterative calculation methods. The advantages of these methods are the predictability of intermediate states and transient processes. But their disadvantages are the facts, that the computing time is incredible high and that the calculated final states are approximated solutions. An exact prediction or analytical solutions of final topologies are available for only very few exceptions. But the development of general analytical solutions is absolutely possible: the key is the phenomenon that selforganized structures are systems states with maximum entropy. The combination of differential geometry and physics supplies definite solutions. This mathematical knowledge should support the analytical calculation of new material modifications such as k-noids, helicoids, graphene and graphane to name just a few. Furthermore the availability of an analytical formalism for complex structural topologies will support their additive manufacture.