A critical analysis of the effect of crosslinking on the linear viscoelastic behavior of styrene–butadiene rubber and other elastomers

The linear viscoelastic behavior in dynamic shear and tensile creep at temperatures from −30 to 70 °C is measured for an styrene–butadiene rubber (SBR) elastomer cured with dicumyl peroxide to crosslinking densities between 0 and 23.5 × 10⁻⁵ mol/cm³. The G′, G″, and tan δ isotherms are analyzed by time–temperature superposition (TTS), where the tan δ master curves are consistent with those of Mancke and Ferry. However, to achieve the TTS in the lightly crosslinked SBR systems, an anomalous vertical shift is required in the narrow temperature region from 10 to 30 °C. The vertical shift factor in this temperature region is not the standard from rubber elasticity. No anomalous behavior is detected in the equilibrium modulus, which is a linear function of temperature in accordance with the classical theory of rubber elasticity. In contrast to SBR, standard vertical shifts are required to effect TTS for uncrosslinked polybutadiene and an ethylene propylene diene monomer elastomer. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Prediction of polyurethane behaviour via time-temperature superposition: Meanings and limitations

Two main issues are essential nowadays for practitioners in the field of polymeric materials: how a polymer will behave under dynamic loading conditions and for how long a polymer is reliable. In this sense, the time-temperature superposition principle was applied to the main viscoelastic properties (E′, E″ and tan δ) of a series of polyurethane coatings (PU-DEG-TMP) tested for mechatronic devices. Polyurethanes are derived from an ester glycol (poly(ethylene adipate) glycol), an aromatic diisocyanate (4,4′-dibenzyldiisocyanate) and di/trifunctional chain extenders - diethylene glycol (DEG) and trimethylol propane (TMP). Despite polyurethane intrinsic rheologic complexity, the moduli/loss factor curves superimpose well over several decades of reduced frequency at the glass transition temperature (T_g), 0 °C and 15 °C, the last temperature being considered the midpoint of the practical testing range. Three criteria were for checking the applicability of the time-temperature superposition: the Cole-Cole plot, the similarity between the a_T calculated from both moduli (E′, E″) and the visual appearance of the final master curve. The presence of both hydrogen bonding and chemical joint points, along with some dangling chains put in a broader context the discussion of the microstructural features resulted from the application of the William-Landell-Ferry (WLF) equation.     

Disentangling stochastic signals superposed on short localized oscillations

We introduce a procedure for separating periodic oscillations superposed on a stochastic signal. The procedure combines empirical mode decomposition (EMD) of a signal with tools of data analysis based on stochastic differential equations, namely nonlinear Langevin equations. Taking the set of modes retrieved from the EMD of the signal, our procedure is able to separate them into two groups, one composing the periodic signal and another composing the stochastic signal. The framework is robust for a broad family of localized oscillations, in the range of large frequencies. In particular, we show that, in this context, the EMD method outperforms a low-pass filter and is robust for a wide interval of different frequency ranges and amplitudes of the periodic oscillation, as well as for a broad family of different non-linear Langevin processes.     

HTPB复合底排药压缩屈服应力模型研究

目前广泛应用于底排增程技术的 HTPB 复合底排药 (composite base bleed grain,CBBG) 是一种颗粒填充含能材料,战场环境中将承受冲击、温度等载荷作用. 为研究 HTPB CBBG 冲击压缩力学性能,进行了不同温度 (233$\sim$323 K) 和应变率 (1100$\sim$7900 s$^{-1}$) 下的分离式霍普金森压杆实验. 实验结果表明,各工况下,应力应变曲线均呈现屈服-$\!$-应变硬化特征,HTPB CBBG 保持高韧性. 提高应变率和降低温度均导致相同应变下的应力幅值上升,但温度较应变率对HTPB CBBG 冲击压缩力学性能的影响更为显著. 基于所研究温度范围高于 HTPB CBBG 玻璃化转变温度,通过将水平、垂直移位因子与温度的关系表示为 WLF 方程的形式,将时温等效原理引入协同模型,并计及内应力的应变率增强效应,提出了一种新的屈服应力模型.选取参考温度,利用水平、垂直移位因子-$\!$-温度曲线和屈服应力主曲线拟合模型参数.模型预测值与实验数据对比结果表明:该模型可准确表征 233$\sim$323 K 时 HTPB CBBG 屈服应力的双线性应变率相关性,明确了较低和较高应变率时,应变率效应分别主要由内应力和驱动力贡献.      

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.     

原子与单模场相互作用中克尔效应与斯塔克效应的统一处理

处理了包含克尔效应和斯塔克效应的原子与场相互作用模型。由于在其有效哈密顿中作了旋转波近似，两种效应的影响可以归结为对原子与场失谐的改变，这种失谐变化依赖于一个系统的守恒量。研究表明，克尔效应和斯塔克效应在一定条件下是等价的。研究了当场的初态为宏观可区分量子迭加态时，光子的反聚束效应。探讨了在广义的克尔介质中原子与场相互作用模型的求解。     

激光陀螺中背向散射的研究

为了研究谐振腔形状变化对激光陀螺中背向散射的影响,基于矢量叠加理论,分析了激光陀螺背向散射源及其对总的背向散射的影响.根据背向散射对顺逆时针光的耦合作用,推导出了总的背向散射系数与顺逆时针旋转光光强的关系式.基于这一关系,设计实验,通过施加电压使谐振腔反射镜到不同位置来改变光腔形状变化,同时测量光强交流量的振幅,得到了总的背向散射系数的变化曲线.通过与仿真结果对比,验证了背向散射的矢量叠加理论.     

Superposition rules, lie theorem, and partial differential equations

A rigorous geometric proof of the Lie theorem on nonlinear superposition rules for solutions of nonautonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the superposition function is solved, the key point being the codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as a more convincing argument supporting the use of this alternative definition of superposition rule, it is shown that this definition allows an immediate generalization of the Lie theorem for the case of systems of partial differential equations.