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The dislocation densities are the internal variables.
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Then, it is easy to see that if ||R[ z]w|| p is bounded, then the input ξ to the static quantizer, which is the internal variable of the Δ Σ modulator, is bounded.
For in situ analysis the best controls are the internal ones, demonstrating variable pattern of staining that correlates with particular ultrastructures as expected based on the experimental design.
A numerical implementation of the framework is proposed in which the kinematic and internal variables are simultaneously solved, because the internal variables are directly coupled in the framework.
Thus, we expect there to be relationships between the internal variables as well.
where in F ( X, Y, Z ), X is the internal state variable of the given node, Y is the node connected to X with inhibitory coupling, and Z is the node connected to X with excitatory learned pattern coupling.
The two surfaces of damage and plasticity and the rate equations for the internal variables are postulated and thermodynamic consistency is subsequently investigated.
Also the commonly used elastic predictor-plastic corrector method is employed to update the internal variables.
Here, the internal variables are chosen as the distances that separate neighboring cells.
The constitutive relations for the stress tensor and the internal variables are deduced using the Clausius Duhem inequality.
The corresponding yield surface and evolution equations of the internal variables are derived from thermodynamic considerations enabling satisfaction of the second law.
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