Search for: All records

In this paper, we establish an analytic framework for studying setvalued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of the Hukuhara difference between sets, in order to compensate the lack of “inverse” operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. While proving the well-posedness of a class of set-valued BSDEs, we shall also address some fundamental issues regarding generalized Aumann–Itô integrals, especially when it is connected to the martingale representation theorem. In particular, we propose some necessary extensions of the integral that can be used to represent set-valued martingales with nonsingleton initial values. This extension turns out to be essential for the study of set-valued BSDEs. 

Ni-SiOC nanocomposites maintain crystal-amorphous dual-phase nanostructures after high-temperature annealing at different temperatures (600 °C, 800 °C and 1000 °C), while the feature sizes of crystal Ni and amorphous SiOC increase with the annealing temperature. Corresponding to the dual-phase nanostructures, Ni-SiOC nanocomposites exhibit a high strength and good plastic flow stability. In this study, we conducted a He implantation in Ni-SiOC nanocomposites at 300 °C by in-situ transmission electron microscope (TEM) irradiation test. In-situ TEM irradiation revealed that both crystal Ni and amorphous SiOC maintain stability under He irradiation. The 600 °C annealed sample presents a better He irradiation resistance, as manifested by a smaller He-bubble size and lower density. Both the grain boundary and crystal-amorphous phase boundary act as a sink to absorb He and irradiation-induced defects in the Ni matrix. More importantly, amorphous SiOC ceramic is immune to He irradiation damage, contributing to the He irradiation resistance of Ni alloy. 

Twin–twin interactions (TTIs) take place when multiple twinning modes and/or twin variants are activated and interact with each other. Twin–twin junctions (TTJs) form and affect subsequent twinning/detwinning and dislocation slip, which is particularly important in determining mechanical behavior of hexagonal metals because twinning is one major deformation mode. Atomic-level study, including crystallographic analysis, transmission electronic microscopy (TEM), and molecular dynamics (MD) simulations, can provide insights into understanding the process of TTIs and structural characters associated with TTJs. Crystallographic analysis enables the classification of TTIs and the prediction of possible interfaces of twin–twin boundaries (TTBs), characters of boundary dislocations, and possible reactions of twinning dislocations and lattice dislocations at TTBs. MD simulations can explore the process of TTIs, microstructures of TTJs, atomic structures of TTBs, and stress fields associated with TTJs. The predictions based on crystallographic analysis and the findings from MD can be partially verified by TEM. More importantly, these results provide explanation for microstructural characters of TTJs and guidance for further TEM characterizations. 

Abstract Enhancing electron correlation in a weakly interacting topological system has great potential to promote correlated topological states of matter with extraordinary quantum properties. Here, the enhancement of electron correlation in a prototypical topological metal, namely iridium dioxide (IrO₂), via doping with 3d transition metal vanadium is demonstrated. Single‐crystalline vanadium‐doped IrO₂nanowires are synthesized through chemical vapor deposition where the nanowire yield and morphology are improved by creating rough surfaces on substrates. Vanadium doping leads to a dramatic decrease in Raman intensity without notable peak broadening, signifying the enhancement of electron correlation. The enhanced electron correlation is further evidenced by transport studies where the electrical resistivity is greatly increased and follows an unusual dependence on the temperature (T). The lattice thermal conductivity is suppressed by an order of magnitude via doping even at room temperature where phonon‐impurity scattering becomes less important. Density functional theory calculations suggest that the remarkable reduction of thermal conductivity arises from the complex phonon dispersion and reduced energy gap between phonon branches, which greatly enhances phase space for phonon–phonon Umklapp scattering. This work demonstrates a unique system combining 3d and 5d transition metals in isostructural materials to enrich the system with various types of interactions.