Noise, nonlinear interactions, positive and negative feedbacks within signaling pathways, time delays, protein oligomerization, and crosstalk between different pathways are main characters in the regulatory of gene expression. However, only a single noise source or only delay time in the deterministic model is considered in the gene transcriptional regulatory system in previous researches. The combined effects of correlated noise and time delays on the gene regulatory model still remain not to be fully understood. The roles of time delay on gene switch and stochastic resonance are systematically explored based on a famous gene transcriptional regulatory model subject to correlated noise. Two cases, including linear time delay appearing in the degradation process (case I) and nonlinear time delay appearing in the synthesis process (case II) are considered, respectively. For case I: Our theoretical results show that time delay can induce gene switch, i.e., the TF-A monomer concentration shifts from the high concentration state to the low concentration state ("on"→"off"). With increasing the time delay, the transition from "on" to "off" state can be further accelerated. Moreover, it is found that the stochastic resonance can be enhanced by both the time delay and correlated noise intensity. However, the additive noise original from the synthesis rate restrains the stochastic resonance. It is also very interesting that a resonance bi-peaks structure appears under large additive noise intensity. The theoretical results by using small-delay time-approximation approach are consistent well with our numerical simulation. For case II: Our numerical simulation results show that time delay can also induce the gene switch, however different with case I, the TF-A monomer concentration shifts from the low concentration state to the high concentration state ("off"→"on"). With increasing time delay, the transition from "on" to "off" state can be further enhanced. Moreover, it is found that the stochastic resonance can be weaken by the time delay. The stochastic delay dynamic approach can identify key physiological control parameters to which the behavior of special genetic regulatory systems is particularly sensitive. Such parameters might provide targets for pharmacological intervention. Thus, it would be highly interesting to investigate if similar experimental techniques could be used to bring out the delay-induced switch and stochastic resonance in the stochastic gene transcriptional regulatory process.

The smart mechanical sensing technology based on mechanoluminescence (ML) has potential applications in the fields of wearable mechanical sensors and remote detection of human health due to its characteristics of non-contact, visualization, and remote signal transmission. Herein, a new strategy for multi-mode ML in a rigid and flexible medium by embedding fluoride nanocrystals (CaF₂: Tb³⁺) in amorphous media was proposed and the intrinsic physical mechanism of energy conversion was clarified. For the rigid transparent CaF₂: Tb³⁺ glass ceramics (GCs), without being fabricated with any special medium, recoverable trap-controlled ML can be generated under friction after X-ray pre-irradiation. Furthermore, the ML composite device fabricated using CaF₂: Tb³⁺ GC powder and flexible stretchable polydimethylsiloxane (PDMS) can achieve self-recovery ML under multimode mechanical stimulation due to the induction of inorganic-organic interface triboelectrification. Finally, rigid accurate stress detection at non-stressed point positions is designed based on the remote transmission of a ML signal owing to the unique optical waveguide effect of GCs, and a flexible mechanical-sensing optical skin for real-time monitoring of human health status is realized by using the CaF₂: Tb³⁺ GC powder/PDMS composite device. This work opens up a new avenue for the realization of multi-scene stress detection based on a rigid/flexible ML material.

First-principles calculations were employed to study the mechanical properties for the recently proposed tetragonal B₄CO₄ (t-B₄CO₄). The calculated structural parameters and elastic constants of t-B₄CO₄ are in excellent agreement with the previous results, indicating the reliability of the present calculations. The directional dependences of the Young’s modulus and shear modulus for t-B₄CO₄ are deduced in detail, and the corresponding results suggest that the t-B₄CO₄ possesses a high degree of anisotropy. Based on the strain-stress method, the ideal tensile and shear strengths along the principal crystal directions are calculated, and the obtained results indicate that the shear mode along (001)[100] slip system dominates the plastic deformation of t-B₄CO₄, which can be ascribed to the breaking of the ionic B-O bonds. The weakest ideal shear strength of 27.5 GPa demonstrates that the t-B₄CO₄ compound is not a superhard material, but is indeed a hard material. Based on the atomic explanation that the ternary B-C-O compounds cannot acquire high ideal strength, we propose two possible routes to design superhard B-C-O compounds.