......some thoughts about the  MICRESS icon



This symbol, called Um-Yang or Taegeuk, represents the basic philosophy of duality where two things complement each other to form a unity:

blue - red
heaven - earth
     male - female
good  - evil
     all - nothing

Thoughts about duality are not only documented in such symbols but also in literature:


to be or not to be

In phase field modelling these words may be interpreted e.g.  as


"to be solid or not to be solid"

Note that in early phase field models describing solidification "not to be solid" was equated to "to be liquid" as no third phase was treated in these models ("tertium non datur"). The probability of a specific part of a sample being in the solid state is called 
Fs, and the probability of being in the liquid state is accordingly Fl. At any time and at any place within the sample it is obvious that

Fs + Fl  = 1 



In addition to the Um-Yang symbol above, the Yin and Yang symbol - the Tai Chi - comprises dots of Yang embedded in Yin and dots of Yin embedded in Yang.

This might be viewed as nucleation of solid from the liquid or initial melting in a solid environment. It is interesting to note that this "nucleation" occurs in regions of high curvature, indicating effects of "curvature undercooling".






The symbol on the left is called "Sam-taegeuk" and is very frequently seen in Korea. Although its history and full interpretation cannot easily be discovered (not even in the Internet :-), unlike the symbols above it obviously comprises the very important aspect of describing "three interrelated objects". In the "Sam-taegeuk" these three basic elements represent earth (red), heaven (blue) and mankind (yellow).

In terms of phase-field modelling this might be regarded as "three phase equilibria" or "triple junctions". It is interesting to note the colours forming 120 angles in the middle of the symbol as well as some kind of "torque" being present in the figure. These things may recall "Young's law" describing wetting phenomena at triple junctions, as well as "Herring torque terms" influencing these equilibrium angles in the case of highly viscous fluids.



..now let's have a look at the MICRESS icon:

We thought a "triple junction" to be an adequate basic structure for an icon,  as the multiphase-field concept underlying MICRESS was one of the early models adressing multiphase equilibria.

The "red - green - blue" colours complement each other to form white, and the outer square shape of the icon indicates the symmetry of the FDM grid being used to run MICRESS.

The white interfaces reveal a finite thickness typical of phase-field models. They form a variety of angles typically observed in equilibria of different phases. In total, they roughly form the Greek letter
gamma used in general to denote interfacial energies playing an important role in microstructure formation.

Other mathematical symbols represent  the major contributions to the evolution of a structure:

energy scale  - time scale - length scale






(energy scale)

(time scale)



(length scale)