Plane waves in thermoelasticity with one relaxation time

We apply the thermoelastic equations with one relaxation time developed by Lord and Shulman (1967) to solve some elastic half-space problems. Laplace transform is used to find the general solution. Problems concerning the ramp-type increase in boundary temperature and stress are studied in detail. Explicit expressions for temperature and stress are obtained for small values of time, where second sound phenomena are of relevance. Numerical values of stress and temperature are calculated and displayed graphically

Triangular bounded consistency of fuzzy preference relations

There are typically two types of consistency of fuzzy preference relations (FPR), namely additive and multiplicative consistency. They are defined based on the assumption that decision makers are rational and can provide strictly consistent FPRs. To take into consideration the bounded rationality of decision makers, the current study relaxes this assumption and proposes a new measure called triangular bounded consistency for judging the consistency of FPRs. To define triangular bounded consistency, a directed triangle is used to represent three FPRs among any three alternatives, with each directed edge representing an FPR. The condition of restricted max–max transitivity (RMMT) in the directed triangle is quantitatively examined. Under the assumption that the bounded rationality of a decision maker is characterized by their historical FPRs, which are represented by directed triangles that satisfy RMMT, triangular bounded consistency is determined using the historical FPRs. We then illustrate how triangular bounded consistency can be used to verify the consistency of FPRs that are newly provided by decision makers and how to estimate some missing FPRs that are not provided by decision makers. Finally, to demonstrate the application of triangular bounded consistency of FPRs in multi-attribute decision analysis, we investigate a problem that involves selecting areas to market products for a company

Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration

Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect without longitudinal spherical aberration, when the size of zero-index lens is large enough. Here, we designed and fabricated a prototype of zero-refractive-index lens by comprising large-area silicon nanopillar array with plane-concave profile. Near-zero refractive index was quantitatively measured near 1.55 um through anomalous focusing effect, predictable by effective medium theory. The zero-index lens was also demonstrated to perform ultralow longitudinal spherical aberration. Such IC compatible device provides a new route to integrate all-silicon zero-index materials into optical communication, sensing, and modulation, and to study fundamental physics on the emergent fields of topological photonics and valley photonics.Comment: 14 pages, 4 figure

Reanalysis of the Gross-Llewellyn Smith sum rule up to O(αs4){\cal O}(\alpha_s^4)-order QCD corrections

In the paper, we reanalyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the $\mathcal{O}(\alpha_s^4)$-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent pQCD contribution for GLS sum rule, e.g. $S^{\rm GLS}(Q_0^2=3{\rm GeV}^2)|_{\rm PMC}=2.559^{+0.023}_{-0.024}$, where the error is squared average of those from $\Delta\alpha_s(M_Z)$, the predicted $\mathcal{O}(\alpha_s^5)$-order terms predicted by using the Pad\'{e} approximation approach. After applying the PMC, a more convergent pQCD series has been obtained, and the contributions from the unknown higher-order terms are highly suppressed. In combination with the nonperturbative high-twist contribution, our final prediction of GLS sum rule agrees well with the experimental data given by the CCFR collaboration.Comment: 6 pages, 5 figure