For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid.
The threshold difference for self-consistent field (SCF) convergence in the total free energy was set to 1 × 10 5 eV, and a Gaussian-type smearing of the Fermi level, equivalent to a temperature of 1.2 K, was applied.
Self-consistent energy convergence (EDIFF) was set to 1 × 10−4 eV and the structural energy convergence criterion (EDIFFG) was set to − 0.02 eV/Å.
This allows to investigate the asymptotic properties of the self-mapping, the convergence of the solution to fixed points, then the system stability, etc. in a unified way for different dynamic systems.
First principles density functional theory (DFT) calculations were performed based on the generalized gradient approximation of Perdew–Burke Ernzerhof and projector-augmented plane wave pseudopotentials implemented in the Vienna ab initio simulation package (VASP) [13 15] with an energy cutoff of 500 eV and a self-consistency field convergence of 10−5 eV.
First validity tests showed good convergence (Self-regulation), concurrence and discriminant validity between cancer patients and healthy control and confirmed a good responsiveness of the ICS during cancer treatment.
The current literature points to a convergence of self- related activity in the cortical midline regions, specifically the prefrontal dorsal and ventral medial cortex as well as the posterior medial and precuneus regions [10 for a review], which was observed using different operationalizations of the self [6], [9], [27], [28].
This scale has demonstrated appropriate psychometric properties, including yielding to the four-factor structure proposed, good correlations with existing measures of emotion-regulation strategies and convergence between self and peer reports (Niven et al., 2011).
In this paper we study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the Euler and the Navier Stokes equations, where the sense of convergence and self-similarity are considered in various generalized senses.
