Polygonal Base Research Articles

Harnessing unconventional buckling of tube origami metamaterials based on Kresling pattern

Kresling tube metamaterials are well known to exhibit a chirality-dependent exotic mechanical feature: a shortening or lengthening in the direction of the tube’s axis produces a relative rotation of the two polygonal bases of the tube. This property can be easily grasped by fabricating a single-storey Kresling tube using cardboard. What has not been stressed much, if not even recognized, in the literature is the fact that such a mechanical feature is not depending only on the (chiral) geometrical pattern and unaffected by the in-plane/bending stiffness of facets and the creases’ resistance to folding. Assuming to neglect the bending stiffness of facets, in the present contribution we prove, through some numerical simulations based on a discrete model taking into account inertial terms, that only when the in-plane-to-folding stiffness ratio is large the Kresling tube exhibits the aforementioned exotic feature as described in the literature. We also prove that a low in-plane-to-folding stiffness ratio reveals: (i) an unconventional buckling mode, both for axial shortening and lengthening, which resembles the mechanism of a camera diaphragm; (ii) a kind of auxetic behavior, i.e. a stenosis in a shortening test.

Light scattering by particles of a polygonal-based in the WKB approximation

Using the Wentzel-Kramers-Brillouin (WKB) approximation, we obtain a general analytical expression of the form factor for a particle with polygonal bases in the case where the wave vector of the incident light is parallel to this base. This expression allows a rapid calculation of the form factor for any shape regular particle. After a brief description of the WKB approximation, we present the new calculation of form factor which is based on the geometric decomposition of the particle has simple regions. Finally, for the validation of this expression, we applied it to some special cases.

Structure, Morphology, Transport, and Mechanism of Oxygen Loss in YBa-=SUB=-2-=/SUB=-Cu-=SUB=-3-=/SUB=-O-=SUB=-7-delta-=/SUB=- Thin Films Obtained by Pulsed Laser Deposition with Velocity Filtration in Erosion Plume

We report the study of YBa2Cu3O7-delta films, synthesized on SrTiO3(100) substrates by pulsed laser deposition with velocity filtration, using X-ray diffractometry, transport measurements, and scanning electron microscopy. We have revealed the dependence of the structure of 100-200 nm thick YBa2Cu3O7-delta films on deposition time and velocity of particles in erosion plume, set by velocity filter. After deposition, the films, or their part, close to the substrate, consisted of 3-10-nm crystals with oxygen index delta=0.08, the same as in the target. For deposition time from 10 to 60 min, we observed the growth of regular pyramids with triangular and quadrangular bases from 20 to 500 nm in size at the base and spiral pyramids with polygonal bases on the film surface. The maximum oxygen loss up to delta=0.35 and T(R=0) up to 77.4 K coincided with the appearance of spiral pyramids up to 100 nm-high. These findings evidence in favor of oxygen depletion of the top layers of YBa2Cu3O7-delta thin films through the formation and growth of oxygen-deficient pyramids on their surface. The oxygen index in the range of delta=0.08-0.15 in both nanocrystals and regular pyramids of 20-300 nm in size provided T(R=0)=84-87 K and the width of superconducting transition Delta T=2.5-3.5 K. Keywords: pulsed laser deposition, surface morphology, film transport properties, film evolution, SrTiO3.

Структура, морфология, транспорт и механизм потери кислорода в тонких пленках YBa-=SUB=-2-=/SUB=-Cu-=SUB=-3-=/SUB=-O-=SUB=-7-delta-=/SUB=-, полученных импульсным лазерным напылением со скоростной фильтрацией эрозионного факела

We report the study of YBa2Cu3O7‒delta films, synthesized on SrTiO3(100) substrates by pulsed laser deposition with velocity filtration, using X-ray diffractometry, transport measurements, and scanning electron microscopy. We have revealed the dependence of the structure of 100-200 nm thick YBa2Cu3O7‒delta films on deposition time and velocity of particles in erosion plume, set by velocity filter. After deposition, the films, or their part, close to the substrate, consisted of 3‒10-nm crystals with oxygen index delta = 0.08, the same as in the target. For deposition time from 10 to 60 min, we observed the growth of regular pyramids with triangular and quadrangular bases from 20 to 500 nm in size at the base and spiral pyramids with polygonal bases on the film surface. The maximum oxygen loss up to delta = 0.35 and T (R = 0) up to 77.4 K coincided with the appearance of spiral pyramids up to 100 nm-high. These findings evidence in favor of oxygen depletion of the top layers of YBa2Cu3O7‒delta thin films through the formation and growth of oxygen-deficient pyramids on their surface. The oxygen index in the range of delta = 0.08‒0.15 in both nanocrystals and regular pyramids of 20‒300 nm in size provided T(R = 0) =84‒87 K and the width of superconducting transition DeltaT = 2.5‒3.5 K.

Equal-Order Polygonal Analysis for Fluid Computation in Curved Domain

Our research introduces a novel advanced method for fluid computation in complicated domain. It makes use of an advanced polygonal finite element applying equal-order scheme; within each element. Both velocity and pressure fields are represented by a polygonal basis shape function system. This technique is based on a combination of the equal-order mixed scheme method, the polygon finite element method (PFEM) and the adapted local projection method that is used to stabilize the pressure. In order to simulate the fluid flow, MATLAB is utilized for coding and programming. A numerical example of an incompressible fluid flow governed by Stokes system in curved domain is performed to demonstrate the applicability of our developed polygon element. Besides, through the numerical analysis, we show the high flexibility of PFEM for curved domains.

An equal-order mixed polygonal finite element for two-dimensional incompressible Stokes flows

Abstract In this study, a novel equal-order mixed polygonal finite element is developed to solve the incompressible fluid problems. Our developed element, so-called Pe1Pe1, is established by the system of polygonal basis functions for both fluid pressure and velocity fields. The superiority of the present formulation over the existent low-order polygonal element is its full applicability in all arbitrary polygonal mesh families. Furthermore, our element provides a better approximation solution for pressure field in fluid analysis. To avoid the well-known instability in equal-order mixed discretizations, we develop an adequate stabilization method, which is extremely effective, yet simple, to improve the numerical performance of our polygonal finite element. In this research, the quality of the present approach with respect to the convergence rate and its stability is presented by a variety of numerical samples of the incompressible Stokes flow problems.

A high-order mixed polygonal finite element for incompressible Stokes flow analysis

This paper presents a new high-order mixed scheme of polygonal finite element method (PFEM) for incompressible flow computation. The system of polygonal basis functions with bubble-enriched functions is applied to represent the fluid velocity field, while the pressure field is approximated by the set of polygonal basis functions. The new element is named as MINIPe. From a practical point of view, the present element naturally satisfies the well-known inf–sup condition. The numerical tests of the incompressible fluid flow problems governed by Stokes equation systems are presented to verify the performance quality of proposed method with respect to the stability and convergence rate.

Stenomaps: Shorthand for shapes.

We address some of the challenges in representing spatial data with a novel form of geometric abstraction-the stenomap. The stenomap comprises a series of smoothly curving linear glyphs that each represent both the boundary and the area of a polygon. We present an efficient algorithm to automatically generate these open, C1-continuous splines from a set of input polygons. Feature points of the input polygons are detected using the medial axis to maintain important shape properties. We use dynamic programming to compute a planar non-intersecting spline representing each polygon's base shape. The results are stylised glyphs whose appearance may be parameterised and that offer new possibilities in the 'cartographic design space'. We compare our glyphs with existing forms of geometric schematisation and discuss their relative merits and shortcomings. We describe several use cases including the depiction of uncertain model data in the form of hurricane track forecasting; minimal ink thematic mapping; and the depiction of continuous statistical data.

An Optimal Bivariate Polynomial Interpolation Basis for the Application of the Evaluation-Interpolation Technique

A new basis of interpolation points for the special case of the Newton two variable polynomial interpolation problem is proposed. This basis is implemented when the upper bound of the total degree and the degree in each variable is known. It is shown that this new basis under certain conditions (that depends on the degrees of the interpolation polynomial), coincides either with the known triangular/rectangular basis or it is a polygonal basis. In all cases it use s the least interpolation points with further consequences to the complexity of the algorithms that we use.

On Fertilization in Chaetopleura apiculata and Selected Chitonida

Early events of fertilization are described in Chaetopleura apiculata and other selected Chitonida. C. apiculata egg hulls are elaborated into multi-branched spines with interlocking polygonal bases. Around the perimeter of each base are a series of open pores, ranging in size from 0.1-0.5 microm, which permit sperm direct access to the vitelline layer. In Callochitonidae (Chitonida) even larger pores occur in egg jelly coats, but this is considered to be the plesiomorphic condition, found also in Lepidopleurida such as Deshayesiella curvata. Other Chitonina, such as Rhyssoplax tulipa and Acanthopleura granulata, have a continuous outer dense layer that lacks pores and must be digested by penetrating sperm. Fertilization in Chitonida is unique and involves injection of chromatin into the egg via a narrow tubular nuclear extension that appears to exclude other sperm organelles, including mitochondria, centrioles, and flagellum. New evidence from studies of fertilization in Mopalia muscosa (Chitonida: Acanthochitonina) supports this hypothesis. This type of fertilization implies maternal inheritance of both mitochondria and centrioles, which is highly unusual, because in most animals one sperm centriole assists movements of pronuclei and regulates organization of the mitotic spindle. This mechanism of fertilization is defined by a series of apomorphic characters that unify the order Chitonida.

Perforation of sheets by pyramidal weapons such as arrowheads

Perforation experiments were performed through metal sheets employing pyramidal indenters having both regular polygonal bases and also non-regular lozenge-shaped bases. The tools also have a range of ‘point angles’. The evolution of petal radii as perforation proceeded was recorded. In the case of lozenge-based pyramids, fracture occurred only at the sharper edges located at the ends of the longer diagonal, with uncracked stretch zones at the ends of the shorter diagonal. Regular pyramids with a small number of edges produced cracking at every corner but perforations with six-sided indenters resulted in only a limited number of petals and cracks, fewer cracks being produced the ‘flatter’ the point. Experiments with cones also resulted in only limited number of petals and cracks. The results for forces, energy and petal radii of curvature were interpreted using modifications of the Wierzbicki and Thomas [Closed form solution for wedge cutting force through thin sheets. Int J Mech Sci 1993;35:209–29] analysis for the cutting of thin plates by wedges, together with independent determinations of yield strength and fracture toughness of the metal sheets. Experimental results make overall sense in relation to the theory but there is a consistent mismatch that is probably attributable to initial dishing of the sheets before initial perforation is complete. The relevance of the analysis to the performance of arrowheads perforating armour is discussed. What constitutes the best design of weapon against particular armour is investigated.

Adaptive computations using material forces and residual-based error estimators on quadtree meshes

Quadtree is a hierarchical data structure that is well-suited for h-adaptive mesh refinement. Due to the presence of hanging nodes, classical shape functions are non-conforming on quadtree meshes. In this paper, we use natural neighbor basis functions to construct conforming interpolants on quadtree meshes. To this end, the recently proposed construction of polygonal basis functions is adapted to quadtree elements. A fast technique for calculating stiffness matrix on quadtree meshes is introduced. Residual-based error estimators and material force technique are used to estimate the error on quadtree meshes. The performance of the adaptive technique is demonstrated through the solution of linear and nonlinear boundary-value problems.

Buffon type problem in the euclidean spaceR 3

Consider a sphere of radiusr whose centre is uniformly distributed inR 3 in the sense that the kinematic measure associated with the centre is that given in Santalo (1976). Consider a lattice of planes whose elementary cell consists of a prism of heighth and with the base an arbitrary triangle of sidesa, b, c. Bosetto (1997) considered the case when the base of the prism is a right-angled triangle, computed the probability that the random sphere cuts at least one of the planes of the lattice and established some independence properties of certin events. Here the same probability is computed for prisms of arbitrary triangular bases and expressed in terms of symmetric expressions. Independence properties and generalization to prisms with arbitrary polygonal bases are also considered.

Nonlinear forced vibrations of shallow shells on regular polygonal bases

The nonlinear, large amplitude vibrations of elastic, shallow shells when subjected to transient pressure loading are analyzed in a relatively simple manner. The isoamplitude contour lines approach is used to derive the basic equations for shallow shell vibrations. The coupled system of governing equations thus obtained is solved for shells of regular polygonal planform with various types of dynamic loading. Also, an equivalent analysis in which Berger’s approximation is used is presented and a comparison is made of the results obtained by both methods. Some comparison is also made with previously obtained results, as available in the literature. All details are explained by graphs.

Moments of Inertia about Selected Axes of Regular Polygons, Right Pyramids on Regular Polygonal Bases, and of the Platonic and Some Archimedian Polyhedra

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