2D in-plane elastic waves in curved-tapered square lattice frame structure

This work proposes a unique configuration of two-dimensional metamaterial lattice grid comprising of curved and tapered beams. The propagation of elastic waves in the structure is analyzed using the dynamic stiffness matrix (DSM) approach and the Floquet-Bloch theorem. The DSM for the unit cell is formulated under the extensional theory of curved beam considering the effects of shear and rotary inertia. The study considers two types of variable rectangular cross-sections, viz. single taper and double taper along the length of the beam. Further, the effect of curvature and taper on the wave propagation is analysed through the band diagram along the irreducible Brillouin zone. It is shown that a complete band gap, i.e. attenuation band in all the directions of wave propagation, in a homogeneous structure can be tailored with a suitable combination of curvature and taper. Generation of the complete bandgap is hinged upon the coupling of axial and transverse component of the lattice grid. This coupling emerges due to the presence of the curvature and further enhanced due to tapering. The double taper cross-section is shown to have wider attenuation characteristics than single taper cross-sections. Specifically, 83.36% and 63% normalized complete bandwidth is achieved for the double and single taper cross-section for a homogeneous metamaterial, respectively. Additional characteristics of the proposed metamaterial in time and frequency domain of the finite structure, vibration attenuation, wave localization in the equivalent finite structure are also studied.

Broadband noise mitigation using coupled Helmholtz resonators: a numerical study

In this work we investigate a periodic structure in the frequency range from 20 Hz to 5500 Hz designed for broadband noise insulation. The considered unit cell consists of a simple structure: a pair of polymer pipes with slits carved along the axes, representing two coupled Helmholtz resonators. In order to develop a design with a broad band gap, we analyze the eigenmodes of the infinite two-dimensional structure considering their symmetry and interaction. This analysis is supported by parametric optimization of the resonator geometry. The obtained band diagram is compared with numerically determined transmission coefficient of a finite structure based on the same unit cell. The number of unit cells of the finite structure is chosen to be sufficient for demonstration of insulating properties and stop band formation. Furthermore, we analyze how the transmission coefficient is linked to the pressure field distribution inside the resonators. Owing to the simplicity of the geometry, the obtained results may become a basis for development of budget-friendly passive systems for broadband noise insulation within the audible range of frequencies.

Brazil's Comparative Advantages and Specialization Dynamics in Agri-food Trade

In the last decades Brazil has become a global agri-food powerhouse. The article interrogates the shape and its stability of revealed comparative advantages in 46 of its agri-food products for the period 1995-2017. The results support the argument that the Brazil's agri-food trade was formed by comparative advantages of specific agri-food sectors. The results show that the external shape of agri-food specialization has strengthened, first since early 2000s and second when the trade shifted more towards China. The pattern was stable according revealed comparative (dis)advantage of particular products, more changes occurred in each product's score and in ranking of products. Products without initial comparative advantage seem to remain uncompetitive whilst the products with strong initial comparative advantage continue to be competitive. The persistence in distribution has increased. This suggests, the shape of Brazil's revealed comparative advantage in agri-food trade has evolved towards its finite structure (ceteris paribus).

Chinese does have independent tense elements

Previous research on Chinese tense indicates that Chinese has either null tense or no tense. However, the present study suggests that the conclusions of previous studies regarding Chinese tense are either against the syntactic truth or illogical. The present study provides new evidence to support that Chinese has two independent tense elements, zai and guo, which clearly indicate present and past tense, contrary to the traditional assumption that they are aspectual markers. From the perspective of grammaticalization, both zai and guo witnessed grammaticalization from the spatial concept to the temporal concept. The semantic evidence shows that zai and guo are semantically different from the aspectual markers zhe and le and convey the meaning of time location. The fact that both zai and guo are allowed in negation but not permitted in non-finite structure provides syntactic evidence that they are tense markers. However, the present study also suggests there can be two different zai and guo; zai and guo used separately and independently and zai and guo used with zhe and le. In the latter case, zai is a time adverbial and guo is an aspectual marker. The existence of independent tense markers in Chinese also shows that Chinese may have at least four different mechanisms to anchor tense.

The complexity of definability by open first-order formulas

In this article, we formally define and investigate the computational complexity of the definability problem for open first-order formulas (i.e. quantifier free first-order formulas) with equality. Given a logic $\boldsymbol{\mathcal{L}}$, the $\boldsymbol{\mathcal{L}}$-definability problem for finite structures takes as an input a finite structure $\boldsymbol{A}$ and a target relation $T$ over the domain of $\boldsymbol{A}$ and determines whether there is a formula of $\boldsymbol{\mathcal{L}}$ whose interpretation in $\boldsymbol{A}$ coincides with $T$. We show that the complexity of this problem for open first-order formulas (open definability, for short) is coNP-complete. We also investigate the parametric complexity of the problem and prove that if the size and the arity of the target relation $T$ are taken as parameters, then open definability is $\textrm{coW}[1]$-complete for every vocabulary $\tau $ with at least one, at least binary, relation.

Taking it up a level: Copy-raising and cascaded tiers of morphosyntactic change

This paper uncovers evidence for two linked levels of morphosyntactic change occurring in Canadian English. The more ordinary is a lexical replacement: with finite subordination after seem, the complementizer like has been overtaking all the alternatives (as if, as though, that, and Ø). On top of this, there is a broader syntactic change whereby the entire finite structure (now represented primarily by like) is beginning to catch on at the expense of infinitival subordination after seem. Drawing on complementary evidence from British English and several partial precedents in the historical linguistics literature, I take this correlation to mean that like has reached sufficient rates among the finite strategy to have instigated the second level of change, to the point that it has ramifications for epistemic and evidential marking with the verb seem. I propose that the best model of these trajectories is a set of increasingly large envelopes of variation, one inside the next, and argue that the envelope might itself be an entity susceptible to change over time.

A complete logic for Database Abstract State Machines1

In database theory, the term database transformation was used to refer to a unifying treatment for computable queries and updates. Recently, it was shown that non-deterministic database transformations can be captured exactly by a variant of ASMs, the so-called Database Abstract State Machines (DB-ASMs). In this article we present a logic for DB-ASMs, extending the logic of Nanchen and Stärk for ASMs. In particular, we develop a rigorous proof system for the logic for DB-ASMs, which is proven to be sound and complete. The most difficult challenge to be handled by the extension is a proper formalization capturing non-determinism of database transformations and all its related features such as consistency, update sets or multisets associated with DB-ASM rules. As the database part of a state of database transformations is a finite structure and DB-ASMs are restricted by allowing quantifiers only over the database part of a state, we resolve this problem by taking update sets explicitly into the logic, i.e. by using an additional modal operator $[X]$, where $X$ is interpreted as an update set $\Delta$ generated by a DB-ASM rule. The DB-ASM logic provides a powerful verification tool to study properties of database transformations.