Coupled Nonlinear Dynamics in the Three-Mode Integrable System on a Regular Chain

The article suggests the nonlinear lattice system of three dynamical subsystems coupled both in their potential and kinetic parts. Due to its essentially multicomponent structure the system is capable to model nonlinear dynamical excitations on regular quasi-one-dimensional lattices of various physical origins. The system admits a clear Hamiltonian formulation with the standard Poisson structure. The alternative Lagrangian formulation of system’s dynamics is also presented. The set of dynamical equations is integrable in the Lax sense, inasmuch as it possesses a zero-curvature representation. Though the relevant auxiliary linear problem involves a spectral third-order operator, we have managed to develop an appropriate two-fold Darboux–Backlund dressing technique allowing one to generate the nontrivial crop solution embracing all three coupled subsystems in a rather unusual way.

О происхождении цепочек каверн во вращающемся потоке между цилиндрами

Cavitation between rotating and immobile cylinders appears in the form of a regular chain of bubbles. The bubble sizes are practically equal, as well as the distances between the bubbles and their azimuthal locations. Though such a form of cavitation has been observed in numerous experiments (in particular, in the experiments with bearings), its nature was not clarified. The presented analysis shows that breakdown of the flow axial symmetry due to displacement of the axis of one of cylinders leads to the regular wave-similar three-dimensional flow perturbations. Their “wavelength” is predetermined by the minimal gap between cylinders. Though the flow between cylinders is not curl-free, these perturbations can be determined with the use of a velocity potential.

AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES

In this paper, the theory of regular chains and a triangular decomposition method relying on modular computations are presented in order to symbolically solve multivariate polynomial systems. Based on the focus values for dynamic systems obtained by using normal form theory, this method is applied to compute the limit cycles bifurcating from Hopf critical points. In particular, a quadratic planar polynomial system is used to demonstrate the solving process and to show how to obtain center conditions. The modular computations based on regular chains are applied to a cubic planar polynomial system to show the computation efficiency of this method, and to obtain all real solutions of nine limit cycles around a singular point. To the authors' best knowledge, this is the first article to simultaneously provide a complete, rigorous proof for the existence of nine limit cycles in a cubic system and all real solutions for these limit cycles.

Modeling and Optimization of Inventory-Distribution Routing Problem for Agriculture Products Supply Chain

Mathematical models of inventory-distribution routing problem for two-echelon agriculture products distribution network are established, which are based on two management modes, franchise chain and regular chain, one-to-many, interval periodic order, demand depending on inventory, deteriorating treatment cost of agriculture products, start-up costs of vehicles and so forth. Then, a heuristic adaptive genetic algorithm is presented for the model of franchise chain. For the regular chain model, a two-layer genetic algorithm based on oddment modification is proposed, in which the upper layer is to determine the distribution period and quantity and the lower layer is to seek the optimal order cycle, quantity, distribution routes, and the rational oddment modification number for the distributor. By simulation experiments, the validity of the algorithms is demonstrated, and the two management modes are compared.

Theoretical Study on the Interaction between Shuffle 60° Dislocation and Hexavacancy in Silicon

The interaction of the shuffle 60° dislocation with a regular chain of hexavacancies was investigated via the molecular dynamics simulation with Stillinger-Weber potential. The results show that an attraction exists between the shuffle 60° dislocation and hexavacany. The attraction energy is dependent obviously upon the hexavacancy concentration. The dislocation can overcome the pinning of vacancies under a critical resolved shear stress, and a linear relationship is found between the critical stress and hexavacancy concentration.