Based on the Voronoi diagram of some nodes, the natural element method (NEM) constructs the shape functions by the natural neighbor interpolation method, and its shape functions satisfy the Kronecker ...delta property, which makes it impose essential boundary conditions easily. Based on the geometrical nonlinear relations and material nonlinear constitutive relations, we extend the NEM to material and geometrical bi-nonlinear problems in this paper. Numerical examples show that the NEM is effective, rational and feasible in dealing with problems of both material and geometrical bi-nonlinear.
Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, ...constructing higher-order EPs still remains as a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in PT -symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also nonHermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform towards the investigation of the higher-order EPs, and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.
Firstly, this paper studies the credit mechanism of business incubation network under E-commerce, on the basis of credit mechanism. We put the method of building incubated enterprises virtual ...communities and customers virtual communities to increase the B to C e-commerce trust within the business incubation network. Then, on the basis of game theory analysis the trigger policy of incubated enterprises' dishonesty on the incubation network virtual communities, designing stimulating mechanism and restraint mechanism to ensure enterprise sincere sale on the incubation network virtual communities.
In this paper, we present a model of 'collective innovation' built upon the business incubation network formation formalism. In our model, incubator and incubatee localized on a circle benefit from ...knowledge flows from other agents with whom they are directly or indirectly connected They support costs for direct connections which are linearly increasing with geographic distance by incubator. The dynamic process of business incubation network formation exhibits preferential meeting for close agents (in the relational network and in the geographic metrics). We show how the set of business incubation networks selected in the long run is affected by the degree of knowledge transferability. We find critical values of this parameter for which Incubation networks are dynamically selected.
