Influence of wall surface on growth of frost layer is studied by using mesoscale lattice Boltzmann method. Nucleation probability model is coupled with improved enthalpy model. A lattice Boltzmann model of frost layer growth process based on nucleation probability theory is established. It simulates thickening of frost layer growth on macro scale, and dynamic change of frost layer structure caused by growth of ice branches in microscale as well. Average thickness, average density and frosting amount of frost layer are obtained. Formation and growth of frost layer on cold wall surface are studied. Temporal and spatial evolution of topological structure of frost layer are obtained. Average thickness, average density and average solid volume fraction of frost at different time were calculated and effects of cold wall surface temperature, relative humidity and cold surface infiltration on frost were discussed.

Dynamical behavior of a class of 4D memristive chaotic circuits was discussed, and attracting domain of multi-stability was studied. In order to guarantee efficiency and accuracy of calculation results, CPU+GPU large-scale computing power were introduced and more than 128 decimal places of precision GMP library and MPFR library were applied to calculate domain of corresponding attractor. Finally, existence of hyperchaos was proved by using method of topological horseshoe theory and constructing memristive analog circuit.

It is hard to apply topological horseshoe in 3D maps due to high dimension and complex structure since dimension of a chaotic attractor is often lower than its state space. We fit a surface with attractor near a selected unstable periodic orbit, and present a "dimension reduction" method to find topological horseshoes with one-directional expansion in 3D space. It is realized with a MATLAB toolbox. Compass walking model is shown to verify effectiveness, and illustrates detailed procedure for finding a topological horseshoe. It successfully verifys existence of chaotic gait and analyzes chaotic invariant set with horseshoe.