Spontaneous recovery in random hypergraphs.

In many real-world phenomena, such as the reconstruction of disaster areas after an earthquake or the stock market's recovery after an economic crisis, damaged networks are spontaneously active after receiving assistance. To reveal how the recovery process, the research of dynamic network recovery has become a hot topic in the field of network science. Previous studies on network recovery have been limited to simple networks with pairwise interactions. However, real-world systems are usually networks with higher-order interactions that are composed of multiple units. To better understand the recovery phenomenon on complex networks in the real world, we propose a novel spontaneous recovery model applied to hypergraphs. The model considers two types of recovery, internal recovery and fast recovery, where inactive nodes in the network can either recover internally with independent probabilities or receive sufficient resources from the hyperedge for fast recovery. We find that the number of active nodes in the system shows a phase change from continuous to discontinuous as the fast recovery condition is relaxed. Moreover, under the influence of higher-order interactions, increasing both average hyperedge cardinality and network heterogeneity contribute to increasing the network resilience. These findings help us understand the recovery mechanisms of complex networks and provide essential insights into designing highly resilient systems.

Thermal Deformation Behavior and Dynamic Softening Mechanisms of Zn-2.0Cu-0.15Ti Alloy: An Investigation of Hot Processing Conditions and Flow Stress Behavior.

Through isothermal hot compression experiments at various strain rates and temperatures, the thermal deformation behavior of Zn-2.0Cu-0.15Ti alloy is investigated. The Arrhenius-type model is utilized to forecast flow stress behavior. Results show that the Arrhenius-type model accurately reflects the flow behavior in the entire processing region. The dynamic material model (DMM) reveals that the optimal processing region for the hot processing of Zn-2.0Cu-0.15Ti alloy has a maximum efficiency of about 35%, in the temperatures range (493-543 K) and a strain rate range (0.01-0.1 s-1). Microstructure analysis demonstrates that the primary dynamic softening mechanism of Zn-2.0Cu-0.15Ti alloy after hot compression is significantly influenced by temperature and strain rate. At low temperature (423 K) and low strain rate (0.1 s-1), the interaction of dislocations is the primary mechanism for the softening Zn-2.0Cu-0.15Ti alloys. At a strain rate of 1 s-1, the primary mechanism changes to continuous dynamic recrystallization (CDRX). Discontinuous dynamic recrystallization (DDRX) occurs when Zn-2.0Cu-0.15Ti alloy is deformed under the conditions of 523 K/0.1 s-1, while twinning dynamic recrystallization (TDRX) and CDRX are observed when the strain rate is 10 s-1.