The unknown interfacial stresses are expanded in series of Jacobi orthogonal polynomials displaying complex singularity.
The underlying quantum model for graphene is a massless Dirac equation, whose eigenvalues display a conical singularity responsible for non-adiabatic transitions between the two modes.
Moreover, the symmetric stress field turns out to be finite at the crack tip, whereas the skew-symmetric stress field displays a strong singularity.
The shear-induced nonlinearity in the particle-filled system appears to display features of a singularity near the phase transition point.
Both mechanical patterns exhibit the same rotational sense and a core region displayed by a phase singularity (red circles).
Crusta represents the globe as a 30-sided polyhedron to avoid distortion of the display, in particular the singularities at the poles characteristic of other projections.
The damage of the systems displayed catastrophic characteristics when the load tended to reach the failure point, i.e., the damage increased rapidly, and the damage rate displayed a power-law singularity at the failure point.
Co-localizing vortex core regions displayed by phase singularities (PS, voltage: green circles, calcium: orange circles, strain-rate: red circles).
It is important to note that the locations displayed here may be caused by singularity issues in the model, and that they should be taken as assumptions of failure points until further experiments validate or invalidate them.
As Fig. 2 shows, the geomagnetic time series display an heterogeneous scaling behaviour exhibiting sharp singularities and is, therefore, suitable for a multi-scale analysis based on a power-law exponent estimation.
This raises the issue whether individual rhombomeric components of such complex anatomic units have shared connectivity and functional properties, or display segmental differences due to local molecular singularities.
