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The equilibrium radiation diffusion equation has been widely used in astrophysics, inertial confinement fusion and others. Since the simulation domain consists of many complicated domains and the material properties in each domain are different, the diffusion coefficient usually has a strong discontinuity at the interface. Because the equilibrium radiation diffusion equation is often built on complicated domains as well as interfaces and has a strong nonlinearity, it is challenging to solve by means of finite difference method and so on. By treating T 4 with different linearization methods, three meshfree methods are utilized to approximate the two-dimensional equilibrium radiation diffusion equation with jump coefficient. Firstly, the time term is discretized by the fully implicit scheme. Then, three different linearization methods (direct linearization, Picard-Newton linearization and Richtmyer linearization) are utilized to linearize T 4. Finally, the linearized algebraic equations are solved numerically by a non-symmetric collocation method with a compactly supported radial basis function. Numerical experiments are performed on the three algorithms for different regular and irregular domains with highly curved interfaces. The effectiveness of the proposed algorithms is verified by numerical results. [ABSTRACT FROM AUTHOR]

[Display omitted] • A mechanism of grain thinning and shearing induced recrystallization was proposed for the refinement of centimeter-grade coarse grains of Ti 2 AlNb alloy. • Reduction per compression in multi-directional isothermal forging is more vital than total strain for the refinement of this alloy. • Recrystallization relies on the shear bands and truncation of the thinned grains prepared by prior compressions. • Thinned grains were sheared and truncated due to the bending and bowing of the neighbor grains. Centimeter-grade coarse grains commonly exist in heavy ingots of Ti 2 AlNb-based alloy and severely deteriorate their workability. To investigate the refinement of coarse grains, multi-directional isothermal forging (MDIF) was carried out on samples cut from an ingot weighing about three tons. The results showed that the alloy can be refined by MDIF after 4 passes with 40% reduction per compression at 1200℃, while it cannot be refined even after 10 passes with 30% reduction per compression at 1200℃ or with 40% reduction per compression at 1050℃. The investigation showed that, as an intermetallics with low strain hardening rate, the material is very difficult to be refined by recrystallization if only increasing the total strain. The special refinement mechanism, i.e. , grain thinning and shearing (GTS) induced recrystallization, is proposed. The reduction per compression is crucial to refine the coarse grains of this alloy. Coarse grains should be firstly squashed and thinned by large reduction, and then bent and bowed to form shear bands in the following perpendicular compressions. Coarse grains are truncated by repeated shearing, and the truncation increases interfaces within the coarse grains and contributes to the local misorientation accumulation, which in turn promotes the completion of recrystallization. [ABSTRACT FROM AUTHOR]

• N treatment approach and sampling time affected fine root biomass and morphology. • Canopy N addition increased fine root biomass. • Fine root biomass and morphology were mainly affected in the growing season. • Fine root biomass was most affected by NH 4 -N and NO 3 -N in growing season. Global nitrogen (N) deposition patterns have profoundly affected the production and morphological structure of fine roots, which in turn changed the distribution of carbon in forests. However, traditional experiments of N addition in forests have ignored the ecological processes in the canopy, such as nitrogen retention, and the effects of these on N deposition and fine root functional traits remain unclear. In this study, we quantified the effects of the canopy (CAN) and understory N addition (UAN) on the biomass and morphology of fine roots in a temperate deciduous forest. Based on the three-way ANOVA, we found that the N treatment approach (CAN vs. UAN; p < 0.05) and sampling time (July, October, and January; p < 0.001) significantly affected the fine root biomass, specific root length, specific root surface area, and root tissue density and diameter. Through the summation of fine root biomass, it was found that CAN treatment increased fine root biomass, while UAN treatment decreased fine root biomass, and canopy N addition at 50 kg ha-1yr−1 (CAN50) significantly increased fine root biomass compared with understory N addition at 50 kg ha-1yr−1 (UAN50) in July and October (p < 0.05). Redundancy analysis (RDA) showed that fine root biomass was most affected by NH 4 -N and NO 3 -N in July. There was no consistent response of fine root morphology to the N application method and N addition rate; it was mainly affected by season (p < 0.001). Different results were obtained using different N treatment approaches. The effects of UAN on forest fine root biomass were likely overestimated compared to the effects of CAN. Our experimental results will provide a scientific basis for a more accurate prediction of the impacts of future global N deposition on fine roots in forest ecosystems. [ABSTRACT FROM AUTHOR]