Exact Solution of the Start-Up Electroosmotic Flow of Generalized Maxwell Fluids in Triangular Microducts

Unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo-Fabrizio time-fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson-Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique we use is new, leads to exact solutions, is completely different from those available in the literature and is applicable to other similar problems. The new expression for the velocity field displays experimentally observed 'velocity overshoot' as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo-Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.

Influence of Assembly Gap Size on the Structure and Properties of SUS301L Stainless Steel Laser Welded Lap Joint

The microstructure and properties of laser welding lap joints with different assembly gap sizes are experimentally investigated. The laser weld joint is composed of γ-austenite and δ-ferrite, and the strip ferrite phase is mainly distributed at the austenite grain boundary. The weld metal presents the austenitic-ferritic (AF) solidification mode. When there is a gap between the two plates, a triangular region composed of similar equiaxed crystals can be found, and the size of the cellular crystals in this region decreases significantly. When the assembly gap size increases from 0.1 mm to 0.4 mm, the weld penetration state of the joint changes from full penetration to semi-penetration, and the surface collapse increases. The excessive size of the gap leads to a decrease in the tensile-shear force and fatigue strength of laser welded joints. In order to ensure that the surface morphology and properties of the welded joint meet the quality standard and requirement, the assembly gap should be less than 0.1mm.

Water collection and transport in bioinspired nested triangular patterns

To address water shortages worldwide, proactive measures are needed to supplement the water supply. In arid regions, many plants and animals use fog or the moisture in air as a source of water. An important consideration for efficient water collection is to transport collected water droplets as rapidly as possible to storage/use before they are evaporated. Triangular geometry has been used for faster transport of water droplets. In the case of a triangular geometry, if a droplet is placed at its apex, the droplet is driven across the triangular region by the Laplace pressure gradient. However, the magnitude of the gradient decreases along the triangle. In this study, nested triangles were designed to provide a higher pressure gradient. Water condensation and transport studies were carried out on the nested pattern at a temperature below the dew point in ambient air. It was found that the nested pattern increases the droplet travel speed. This article is part of the theme issue ‘Bioinspired materials and surfaces for green science and technology (part 3)’.

Expanding Universe Illusion

We present a new induced movement illusion from global expansion or contraction in a triangular region filled with rising or falling textures. Objective global expansion or contraction induces lateral movement in the oblique edges of the triangle. The effects may be due to common and relative movements operating within a single texture.

Estimation of Causal Functional Linear Regression Models

We present a methodology for estimating causal functional linear models using orthonormal tensor product expansions. More precisely, we estimate the functional parameters $\alpha$ and $\beta$ that appear in the causal functional linear regression model:$$\mathcal{Y}(s)=\alpha(s)+\int_a^b\beta(s,t)\mathcal{X}(t)\mathrm{d}t+\mathcal{E}(s),$$ where $\mbox{supp } \beta \subset \mathfrak{T},$ and $\mathfrak{T}$ is the closed triangular region whose vertexes are $(a,a) , (b,a)$ and $(b,b).$ We assume we have an independent sample $\{ (\mathcal{Y}_k,\mathcal{X}_k) : 1\le k \le N, k\in \mathbb{N}\}$ of observations where the $\mathcal{X}_k $'s are functional covariates, the $\mathcal{Y}_k$'s are time order preserving functional responses and $\mathcal{E}_k,$ $1\le k \le N,$ is i.i.d. zero mean functional noise.

Rocking in Presence of Cracking of Masonry Wall Piers

The wall pier represents the vertical element of multi-storey walls with openings, the main resistant structural components of a masonry building. Structural systems of wall piers and spandrels are required to sustain the in-plane seismic actions acting on the wall, opposing with their weights to the action of horizontal forces. The behavior of masonry constructions results to be very far from the one characterizing ductile structures, because of the lack of energy dissipation during the deformation. A strength resource of masonry structures, properly reinforced in order to avoid early local failures, consists in exhibiting rocking behavior, until a failure condition is attained. An investigation on the dynamic behavior of masonry wall piers is carried out by following Housner’s studies and properly introducing the effect of diagonal cracks, shown by typical post-earthquake cracking patterns. As a consequence, the system is characterized by the detachment of a lower triangular region that becomes ineffective during the development of the mechanism and does not oppose with its weight to the overturning. Finally, it is shown that the occurrence of diagonal cracks can be prevented by the execution of suitable retrofit interventions.

Signed Lozenge Tilings

It is well-known that plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in bijection. In this work we consider regions that are more general than hexagons. They are obtained by further removing upward-pointing triangles. We call the resulting shapes triangular regions. We establish signed versions of the latter three bijections for triangular regions. We first investigate the tileability of triangular regions by lozenges. Then we use perfect matchings and families of non-intersecting lattice paths to define two signs of a lozenge tiling. Using a new method that we call resolution of a puncture, we show that the two signs are in fact equivalent. As a consequence, we obtain the equality of determinants, up to sign, that enumerate signed perfect matchings and signed families of lattice paths of a triangular region, respectively. We also describe triangular regions, for which the signed enumerations agree with the unsigned enumerations.

Signed polyomino tilings by n-in-line polyominoes and Gröbner bases

Conway and Lagarias observed that a triangular region T(m) in a hexagonal lattice admits a signed tiling by three-in-line polyominoes (tribones) if and only if m 2 {9d?1, 9d}d2N. We apply the theory of Gr?bner bases over integers to show that T(m) admits a signed tiling by n-in-line polyominoes (n-bones) if and only if m 2 {dn2 ? 1, dn2}d2N. Explicit description of the Gr?bner basis allows us to calculate the ?Gr?bner discrete volume? of a lattice region by applying the division algorithm to its ?Newton polynomial?. Among immediate consequences is a description of the tile homology group for the n-in-line polyomino.