The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity

By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a 1D discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of kx = ky = kz = k and k = ±π/6α0 in the Brillouin zone, as well as has 3D vortices in the direction of kx = ky = kz = k and k = ±π/α0 in the Brillouin zone.

Equilibrium Energy and Entropy of Vortex Filaments in the Context of Tornadogenesis and Tornadic Flows

In this work, we study approximations of supercritical or suction vortices in tornadic flows and their contribution to tornadogenesis and tornado maintenance using self-avoiding walks on a cubic lattice. We extend the previous work on turbulence by A. Chorin and collaborators to approximate the statistical equilibrium quantities of vortex filaments on a cubic lattice when both an energy and a statistical temperature are involved. Our results confirm that supercritical (smooth, “straight”) vortices have the highest average energy and correspond to negative temperatures in this model. The lowest-energy configurations are folded up and “balled up” to a great extent. The results support A. Chorin’s findings that, in the context of supercritical vortices in a tornadic flow, when such high-energy vortices stretch, they need to fold and transfer energy to the surrounding flow, contributing to tornado maintenance or leading to its genesis. The computations are performed using a Markov Chain Monte Carlo approach with a simple sampling algorithm using local transformations that allow the results to be reliable over a wide range of statistical temperatures, unlike the originally used pivot algorithm that only performs well near infinite temperatures. Efficient ways to compute entropy are discussed and show that a system with supercritical vortices will increase entropy by having these vortices fold and transfer their energy to the surrounding flow.

Experimental and numerical simulation of bird-strike performance of lattice-material-infilled curved plate

The anti-bird-strike performance of a lattice-material-infilled curved plate is investigated herein.Since automatically filling the curved structure by classical lattice material filling methods will cause a large number of manufacturing defects,a space-dependent lattice material filling method for the curved plate is firstly proposed in this paper Next,using a face-centered cubic lattice,a lattice-material-infilled test piece with a hollow ratio of 40.8%is built.The test pieces are manufactured via additive manufacturing using titanium alloy.In bird-strike experimental tests,the test pieces are crashed against gelatin birds at an impact velocity of 200 m/s.Dynamic strain gauges are used to record the crash history and the results are discussed.Furthermore,a numerical analysis to simulate the bird-strike experiment is performed.The results from the experimental tests and numerical simulation agree well.This work shows that the lattice-material-infilled curved plate yields promising bird-strike resistance.Therefore,lattice-infilled materials are feasible for protecting aerospace components against bird-strike as well as for reducing the component weight.

The Study of the Three-Dimensional Spin-3/2 Ising Model on a Cellular Automaton

The spin-3/2 Ising model on the simple cubic lattice with nearest-neighbour ferromagnetic bilinear interaction(J>0)is simulated on a cellular automaton by using the cooling algorithm improved from the Creutz cellular automaton.The phase diagrams of the model are constructed in the(D/J,kT/J)and(K/J,kT/J)plane.Comparison of the results are made with those of other methods.The temperature dependence of the order parameters and associated fluctuations are calculated at various of the model parameters and the static critical exponents are estimated within the framework of the finite-size scaling.The results are compatible with the universal Ising critical behavior except for D/J=−3 and K/J=−2.3.