Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

Comprehensive performance of a ball-milled La0.5Pr0.5Fe11.4Si1.6B0.2Hy/Al magnetocaloric composite

Due to the hydrogen embrittlement effect, La(Fe,Si)₁₃-based hydrides can only exist in powder form, which limits their practical application. In this work, ductile and thermally conductive Al metal was homogeneously mixed with La_0.5Pr_0.5Fe_11.4Si_1.6B_0.2 using the ball milling method. Then hydrogenation and compactness shaping of the magnetocaloric composites were performed in one step via a sintering process under high hydrogen pressure. As the Al content reached 9 wt.%, the La_0.5Pr_0.5Fe_11.4Si_1.6B_0.2H_y/Al composite showed the mechanical behavior of a ductile material with a yield strength of ~44 MPa and an ultimate strength of 269 MPa accompanied by a pronounced improvement in thermal conductivity. Due to the ease of formation of Fe-Al-Si phases and the several micron and submicron sizes of the composite particles caused by ball milling process, the magnetic entropy change of the composites was substantially reduced to ~1.2 J/kg· K-1.5 J/kg· K at 0 T-1.5 T.     

On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Facile Preparation and Properties of Crosslinked Copolyether Elastomers with 1,2,3-Triazole and Urethane Subunit via Click Polymerization

An azide terminated ethylene oxide-tetrahydrofuran copolymer with urethane segments (ATUPET) as a novel binder pre-polymer, has been prepared through ethylene oxide-tetrahydrofuran random copolymer (PET) end-capping modification via one-pot method. The structure characterization of the modifier has been analyzed by FTIR, ¹H NMR, ¹³C NMR and GPC. In comparison with PET, ATUPET has a slightly higher viscosity because it has additional hydrogen bonding interaction generated by the urethane in ATUPET. Triazole cross-linked elastomers based on ATUPET with various functional molar ratios were prepared using tripropargylamine as a curing agent and cross-linker. Mechanical properties indicate that the modulus E and tensile strength σ_b exhibit a parabolic dependence with the increase in R. At around the stoichiometric ratio, the modulus E and tensile strength σ_b reach a maximum and the elongation at break exhibit an acceptable value at the same time. Swelling tests demonstrate that the apparent cross-linking densities (N₀) have a maximum value at the stoichiometric ratio. Thermal analysis shows that the ATUPET prepolymer and its polytriazoles elastomers exhibit a satisfactory stability. The results demonstrated that ATUPET might be a promising polymeric binder for future propellant formulations especially in the field of isocyanate-free curing technology.     

Reentrant phase behavior of nanoparticle solutions probed by small-angle scattering

The nanoparticles in solution represent a model system, where the well-established colloidal theories such as the Debye–Hückel theory and/or Derjaguin–Landau–Verwey–Overbeek theory can be implemented to predict the nanoparticle phase behavior. Recently, reentrant phase transitions in a wide range of colloids (e.g., inorganic and organic nanoparticles, polymers, and biomolecules) have been observed, which are not consistent with these theories. The colloids in the reentrant phase behavior undergo a phase change and return back to the original phase with respect to a specific physiochemical parameter (e.g., ionic strength, concentration of different additives, temperature, and so on). The nanoparticle–polymer/multivalent ion systems, demonstrating such phase transition and the corresponding phase behavior in terms of interparticle interactions, have been probed by small-angle scattering. It has been shown how the tuning in interparticle interactions using external parameters can lead to reentrant phase behavior and use the nanoparticle aggregation for building nanohybrids. The deviations of the present observations from those of the standard colloidal theories and the anticipated challenges are also discussed.     

The global existence and asymptotic stability of solutions for a reaction–diffusion system

This paper studies the solutions of a reaction–diffusion system with nonlinearities that generalize the Lengyel–Epstein and FitzHugh–Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the solutions. Furthermore, we present some numerical examples.     

阻尼Navier-Stokes系统的渐近吸引子

本文通过构造一个有限维解序列,研究了二维阻尼驱动Navier-Stokes方程的渐近吸引子,并证明了该解序列在长时间内无限逼近全局吸引子,最后给出了渐近吸引子的维数估计.