This is done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point.
Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled.
A new set of time invariant element matrices that describe the coupling between the reference motion and elastic deformations is developed.
The uncertain nonlinear system is represented using a fuzzy function having constant matrices and time varying uncertain matrices that describe the nominal model and the uncertainty in the nonlinear system respectively.
A brain connectome at the macroscale is typically mathematically represented with connectivity matrices that describe the interaction between the different brain regions.
We additionally assume that the connectivity is local, since we are interested in matrices that describe connectivity of biological networks.
Correlation matrices that describe interneuronal noise correlations for a simulated population of neurons were constructed by assigning correlated noise (rnoise) to each pair of neurons (either hypothetical or real) according to the measured relationship between rnoise and the signal correlation between the pair of tuning curves, that is r signal (Gu et al., 2011).
P and D are diagonal matrices that describe respectively the birefringence in the form of phase retardation η with complex phase factors as P = [ ei η/2, 0; 0, e -i η/2] and the diattenuation with polarization dependent attenuation factors ε1,2 as D = [ ε1, 0; 0, ε2].
At the same time, we associate the LN with a Markov matrix that describes the probabilities of passing from one state to other in the new 2D space.
A new relation is proposed, based only on the particle size, volume fraction, and relative moduli of filler and matrix, that describes the experimental results for reinforcement of both filled rubbers and a model system.
