Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

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.     

Study on the mechanism of catalytic synthesis of dimethyldichlorosilane by AlCl3/MIL‐53(Al)@γ‐Al2O3

Dimethyldichlorosilane, one of the most consumed organosilicon monomers in the industry, can be prepared in a highly efficient and environmentally friendly synthesis method of disproportionating methylchlorosilanes. However, the internal mechanism of the reaction remains unclear. In this paper, the mechanism catalyzed by AlCl₃/MIL‐53(Al) and AlCl₃/MIL‐53(Al)@γ‐Al₂O₃ catalysts was calculated at B3LYP/6‐311++G(3df, 2pd) level by using the density functional theory (DFT). The results showed that although the two catalysts had similar active structures, the catalytic effects were significantly different. The Lewis acid center on the surface of γ‐Al₂O₃ in the core‐shell catalyst is complementary to the classic Lewis acid AlCl₃ through the spatial superposition effect, which greatly improves the Lewis acid catalytic activity of AlCl₃/MIL‐53(Al)@γ‐Al₂O₃.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

铟镓共掺杂对n-ZnO纳米棒/p-GaN异质结生长行为和光电性能的影响

利用低温水热法在p-GaN薄膜上生长了铟(In)和镓(Ga)共掺杂的ZnO纳米棒。X射线衍射(XRD)、X射线光电子能谱(XPS)和X射线能量色谱仪(EDS)结果表明,In和Ga已固溶到ZnO晶格中。扫描电子显微镜(SEM)结果表明, ZnO纳米棒具有良好的c轴取向性,随着In和Ga共掺杂浓度的增加,纳米棒的直径减小,密度增加。XRD结果表明,In和Ga共掺杂引起ZnO晶格常数增大,导致(002)衍射峰向低角度方向偏移。同时,ZnO的光学性质受到In和Ga共掺杂的影响。与纯ZnO相比, 共掺杂ZnO纳米棒的紫外发射峰都出现轻微红移,这是表面共振和带隙重整效应综合作用的结果。I-V特性曲线表明,随着In和Ga共掺杂浓度的增加,n-ZnO纳米棒/p-GaN异质结具有更好的导电性。     

Optical and static dielectric study of a terminally fluorinated liquid crystalline compound

Optical and static dielectric studies on a terminally fluorinated liquid crystalline compound have been carried out. Measurements of temperature variation of refractive indices of the compound are done by using thin prism method. A four-parameter model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the compound with the theoretical ones. Refractive index and density data are utilized for determination of orientational order parameter. The temperature variation of dielectric permittivities of the compound are measured by a LCR meter.     

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.