On a reaction-diffusion-advection system : fixed boundary or free boundary

This paper is devoted to the asymptotic behaviors of the solution to a reaction–diffusion–advection system in a homogeneous environment with fixed boundary or free boundary. For the fixed boundary problem, the global asymptotic stability of nonconstant semi-trivial states is obtained. It is also shown that there exists a stable nonconstant co-existence state under some appropriate conditions. Numerical simulations are given not only to illustrate the theoretical results, but also to exhibit the advection-induced difference between the left and right boundaries as time proceeds. For the free boundary problem, the spreading–vanishing dichotomy is proved, i.e., the solution either spreads or vanishes finally. Besides, the criteria for spreading and vanishing are further established

On a reaction–diffusion–advection system: fixed boundary or free boundary

This paper is devoted to the asymptotic behaviors of the solution to a reaction–diffusion–advection system in a homogeneous environment with fixed boundary or free boundary. For the fixed boundary problem, the global asymptotic stability of nonconstant semi-trivial states is obtained. It is also shown that there exists a stable nonconstant co-existence state under some appropriate conditions. Numerical simulations are given not only to illustrate the theoretical results, but also to exhibit the advection-induced difference between the left and right boundaries as time proceeds. For the free boundary problem, the spreading–vanishing dichotomy is proved, i.e., the solution either spreads or vanishes finally. Besides, the criteria for spreading and vanishing are further established

Involvement of NF-κB/IL-6 Pathway in the Processing of Colorectal Carcinogenesis in Colitis Mice

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Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk

Twinning-assisted static recrystallization and texture evolution in a Mg-Gd-Y-Zr alloy

The formability and mechanical properties of magnesium (Mg) alloys are strongly related to the crystallographic basal texture. Twins play critical roles in adjusting crystallographic orientation of grains during both deformation and annealing treatment via deformation twinning and twinning-assisted recrystallization. In this study, cold rolling and subsequent annealing were conducted on a Mg-5.9Gd-3.3Y-0.5Zr alloy to investigate the recrystallization behavior and texture evolution. Electron backscatter diffraction and transmission electron microscopy techniques were applied to characterize the nucleation of recrystallized grains, especially the twinning-assisted recrystallization, at multi-scales. The results indicated that a large number of {10-12}, {10-11} twins and {10-11} - {10-12} double twins were introduced after cold rolling. The {10-11} - {10-12} double twins, double twin - grain boundary intersections and dense twin-twin intersections acted as the preferential nucleation sites for recrystallization during annealing treatment, while the coarse and parallel {10-12} twins were unfavorable for the nucleation of recrystallized grains. Although {10-12} tension twins are the most common twins in Mg alloys, the interface of this type of twin has strong mobility and is easy to expand. Therefore, it is generally difficult for a single {10-12} twin to recrystallize. However, the {10-11} compression twins and {10-11} - {10-12} double twins are generally difficult to expand and can store high deformation energy, so they are conducive to becoming nucleation sites for recrystallization. During the recrystallization process, the texture type (basal texture) of the cold rolled sample remained unchanged, but the overall texture intensity was significantly reduced due to the dispersion of grain orientations brought by new grains generated by twinning recrystallization