From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Reentrant and whirling hexagons in non-Boussinesq convection

We review recent computational results for hexagon patterns in non- Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a vertical axis the transition from hexagons to rolls is replaced by a Hopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D) complex Ginzburg-andau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the cou- pling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.

Hexagons and spiral defect chaos in non-Boussinesq convection at low Prandtl numbers

We study the stability and dynamics of non-Boussinesq convection in pure gases ?CO2 and SF6? with Prandtl numbers near Pr? 1 and in a H2-Xe mixture with Pr= 0.17. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For Pr ? 1 and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the usual, transverse side-band instability is superseded by a longitudinal side-band instability. Moreover, the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF6 we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H2-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of targetlike components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.

Reentrant hexagons in non-Boussinesq convection.

While non-Boussinesq hexagonal convection patterns are known to be stable close to threshold (i.e. for Rayleigh numbers R ? Rc ), it has often been assumed that they are always unstable to rolls for slightly higher Rayleigh numbers. Using the incompressible Navier?Stokes equations for parameters corresponding to water as the working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime ( ? (R ? Rc )/Rc = O(1)). We find ?re-entrant? behaviour of the hexagons, i.e. as is increased they can lose and regain stability. This can occur for values of as low as = 0.2. We identify two factors contributing to the re-entrance: (i) far above threshold there exists a hexagon attractor even in Boussinesq convection as has been shown recently and (ii) the non-Boussinesq effects increase with . Using direct simulations for circular containers we show that the re-entrant hexagons can prevail even for sidewall conditions that favour convection in the form of competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons even become stable over the whole -range considered, 0 6 6 1.5.

Mechanism of interaction of hydrocalumites (Ca/Al-LDH) with methyl orange and acidic scarlet GR

The development of new materials for water purification is of universal importance. Among these types of materials are layered double hydroxides (LDHs). Non-ionic materials pose a significant problem as pollutants. The interaction of methyl orange (MO) and acidic scarlet GR (GR) adsorption on hydrocalumite (Ca/Al-LDH-Cl) were studied by X-ray diffraction (XRD), infrared spectroscopy (MIR), scanning electron microscope (SEM) and near-infrared spectroscopy (NIR). The XRD results revealed that the basal spacing of Ca/Al-LDH-MO was expanded to 2.45 nm, and the MO molecules were intercalated with a inter-penetrating bilayer model in the gallery of LDH, with 49o tilting angle. Yet Ca/Al-LDH-GR was kept the same d-value as Ca/Al-LDH-Cl. The NIR spectrum for Ca/Al-LDH-MO showed a prominent band around 5994 cm-1, assigned to the combination result of the N-H stretching vibrations, which was considered as a mark to assess MO- ion intercalation into Ca/Al-LDH-Cl interlayers. From SEM images, the particle morphology of Ca/Al-LDH-MO mainly changed to irregular platelets, with a “honey-comb” like structure. Yet the Ca/Al-LDH-GR maintained regular hexagons platelets, which was similar to that of Ca/Al-LDH-Cl. All results indicated that MO- ion was intercalated into Ca/Al-LDH-Cl interlayers, and acidic scarlet GR was only adsorped upon Ca/Al-LDH-Cl surfaces.

Hemi-field and full-field form-deprivation induce timing changes in multifocal ERG responses in chick

Purpose: In animal models hemi-field deprivation results in localised, graded vitreous chamber elongation and presumably deprivation induced localised changes in retinal processing. The aim of this research was to determine if there are variations in ERG responses across the retina in normal chick eyes and to examine the effect of hemi-field and full-field deprivation on ERG responses across the retina and at earlier times than have previously been examined electrophysiologically. Methods: Chicks were either untreated, wore monocular full-diffusers or half-diffusers (depriving nasal retina) (n = 6-8 each group) from day 8. mfERG responses were measured using the VERIS mfERG system across the central 18.2º× 16.7º (H × V) field. The stimulus consisted of 61 unscaled hexagons with each hexagon modulated between black and white according to a pseudorandom binary m-sequence. The mfERG was measured on day 12 in untreated chicks, following 4 days of hemi-field diffuser wear, and 2, 48 and 96 h after application of full-field diffusers. Results: The ERG response of untreated chick eyes did not vary across the measured field; there was no effect of retinal location on the N1-P1 amplitude (p = 0.108) or on P1 implicit time (p > 0.05). This finding is consistent with retinal ganglion cell density of the chick varying by only a factor of two across the entire retina. Half-diffusers produced a ramped retina and a graded effect of negative lens correction (p < 0.0001); changes in retinal processing were localized. The untreated retina showed increasing complexity of the ERG waveform with development; form-deprivation prevented the increasing complexity of the response at the 2, 48 and 96 h measurement times and produced alterations in response timing. Conclusions: Form-deprivation and its concomitant loss of image contrast and high spatial frequency images prevented development of the ERG responses, consistent with a disruption of development of retinal feedback systems. The characterisation of ERG responses in normal and deprived chick eyes across the retina allows the assessment of concurrent visual and retinal manipulations in this model. (Ophthalmic & Physiological Optics © 2013 The College of Optometrists.)

A particle based model to simulate microscale morphological changes of plant tissues during drying

Fundamental understanding on microscopic physical changes of plant materials is vital to optimize product quality and processing techniques, particularly in food engineering. Although grid-based numerical modelling can assist in this regard, it becomes quite challenging to overcome the inherited complexities of these biological materials especially when such materials undergo critical processing conditions such as drying, where the cellular structure undergoes extreme deformations. In this context, a meshfree particle based model was developed which is fundamentally capable of handling extreme deformations of plant tissues during drying. The model is built by coupling a particle based meshfree technique: Smoothed Particle Hydrodynamics (SPH) and a Discrete Element Method (DEM). Plant cells were initiated as hexagons and aggregated to form a tissue which also accounts for the characteristics of the middle lamella. In each cell, SPH was used to model cell protoplasm and DEM was used to model the cell wall. Drying was incorporated by varying the moisture content, the turgor pressure, and cell wall contraction effects. Compared to the state of the art grid-based microscale plant tissue drying models, the proposed model can be used to simulate tissues under excessive moisture content reductions incorporating cell wall wrinkling. Also, compared to the state of the art SPH-DEM tissue models, the proposed model better replicates real tissues and the cell-cell interactions used ensure efficient computations. Model predictions showed good agreement both qualitatively and quantitatively with experimental findings on dried plant tissues. The proposed modelling approach is fundamentally flexible to study different cellular structures for their microscale morphological changes at dehydration.

A novel approach for numerical simulation of plant tissue shrinkage during drying

Drying is a key processing techniques used in food engineering which demands continual developments on advanced analysis techniques in order to optimize the product and the process. In this regard, plant based materials are a frequent subject of interest where microstructural studies can provide a clearer understanding on the fundamental physical mechanisms involved. In this context, considering numerous challenges of using conventional numerical grid-based modelling techniques, a meshfree particle based model was developed to simulate extreme deformations of plant microstructure during drying. The proposed technique is based on a particle based meshfree method: Smoothed Particle Hydrodynamics (SPH) and a Discrete Element Method (DEM). A tissue model was developed by aggrading individual cells modelled with SPH-DEM coupled approach by initializing the cells as hexagons and aggregating them to form a tissue. The model also involves a middle lamella resembling real tissues. Using the model, different dried tissue states were simulated with different moisture content, the turgor pressure, and cell wall contraction effects. Compared to the state of the art grid-based microscale plant tissue drying models, the proposed model is capable of simulating plant tissues at lower moisture contents which results in excessive shrinkage and cell wall wrinkling. Model predictions were compared with experimental findings and a fairly good agreement was observed both qualitatively and quantitatively.

Structure-mediated thermal transport of monolayer graphene allotropes nanoribbons

We report the study of the thermal transport management of monolayer graphene allotrope nanoribbons (size ∼20 × 4 nm2) by the modulation of their structures via molecular dynamics simulations. The thermal conductivity of graphyne (GY)-like geometries is observed to decrease monotonously with increasing number of acetylenic linkages between adjacent hexagons. Strikingly, by incorporating those GY or GY-like structures, the thermal performance of graphene can be effectively engineered. The resulting hetero-junctions possess a sharp local temperature jump at the interface, and show a much lower effective thermal conductivity due to the enhanced phonon–phonon scattering. More importantly, by controlling the percentage, type and distribution pattern of the GY or GY-like structures, the hetero-junctions are found to exhibit tunable thermal transport properties (including the effective thermal conductivity, interfacial thermal resistance and rectification). This study provides a heuristic guideline to manipulate the thermal properties of 2D carbon networks, ideal for application in thermoelectric devices with strongly suppressed thermal conductivity.

Correlated electronic states of C-60 fragments

We have studied electronic states of various fragments of C-60 within the Pariser-Parr-Pople (PPP) model and have obtained structural, magnetic and spectral properties of these molecules. The fragments studied include corannulene, fluoranthene and pyracylene. Pyracylene is studied using the exact valence bond (VB) approach while fluoranthene and corannulene are studied using a novel restricted CI technique which employs molecular orbitals for constructing the VB functions. The electronic excitations, bond order and ring currents are calculated for these systems. From these studies, the wide range of absorptions in C-60 can be viewed as those localized on pyracylene units or on the corannulene/fluoranthene units. The bond orders and ring currents show the hexagons to be similar to benzene rings. The pentagon-hexagon bonds are also found to be longer than the hexagon-hexagon bonds.

Simple Structural And Bonding Representations Of Fullerenes

Bonding in buckminsterfullerene, C60, can be described in terms of a unique canonical representation in which all six membered rings have a benzenoid Kekule structure while the pentagons are all made of exclusively single bonds. The corresponding valence bond structure reflects the full symmetry of the molecule and is consistent with the observed bond length variations. Computational support for the bonding description is provided using localized MO's obtained at the MNDO level. The requirement of benzenoid structures for all the hexagons can be used as a criterion of stability of fullerenes which complements the pentagon isolation rule. A convenient two-dimensional representation of the fullerene structures incorporating the above bonding description is suggested, especially for use in mechanistic discussions.

On piercing (pseudo)lines and boxes

We say a family of geometric objects C has (l;k)-property if every subfamily C0C of cardinality at most lisk- piercable. In this paper we investigate the existence of g(k;d)such that if any family of objects C in Rd has the (g(k;d);k)-property, then C is k-piercable. Danzer and Gr̈ unbaum showed that g(k;d)is infinite for fami-lies of boxes and translates of centrally symmetric convex hexagons. In this paper we show that any family of pseudo-lines(lines) with (k2+k+ 1;k)-property is k-piercable and extend this result to certain families of objects with discrete intersections. This is the first positive result for arbitrary k for a general family of objects. We also pose a relaxed ver-sion of the above question and show that any family of boxes in Rd with (k2d;k)-property is 2dk- piercable.

The effect of structural dimensionality on the electrocatalytic properties of the nickel selenide phase

Nickel selenide (NiSe) nanostructures possessing different morphologies of wires, spheres and hexagons are synthesized by varying the selenium precursors, selenourea, selenium dioxide (SeO2) and potassium selenocyanate (KSeCN), respectively, and are characterized using X-ray diffraction, X-ray photoelectron spectroscopy, Raman spectroscopy, transmission electron microscopy and scanning electron microscopy techniques. Electrical measurements of a single nanowire and a hexagon carried out on devices fabricated by the focused ion beam (FIB) technique depict the semiconducting nature of NiSe and its ability to act as a visible light photodetector. The three different morphologies are used as catalysts for hydrogen evolution (HER), oxygen reduction (ORR) and glucose oxidation reactions. The wire morphology is found to be better than that of spheres and hexagons for all the reactions. Among the reactions studied, NiSe is found to be good for HER and glucose oxidation while ORR seems to terminate at the peroxide stage.

First principles DFT investigation Of Yttrium-decorated Boron-Nitride Nanotube: Electronic Structure and Hydrogen Storage

The electronic structure and hydrogen storage capability of Yttrium-doped BNNTs has been theoretically investigated using first principles density functional theory (DFT). Yttrium atom prefers the hollow site in the center of the hexagonal ring with a binding energy of 0.8048eV. Decorating by Y makes the system half-metallic and magnetic with a magnetic moment of 1.0 mu(B). Y decorated Boron-Nitride (8,0) nanotube can adsorb up to five hydrogen molecules whose average binding energy is computed as 0.5044eV. All the hydrogen molecules are adsorbed with an average desorption temperature of 644.708 K. Taking that the Y atoms can be placed only in alternate hexagons, the implied wt% comes out to be 5.31%, a relatively acceptable value for hydrogen storage materials. Thus, this system can serve as potential hydrogen storage medium.

Estradas e conectividade na Mata Atlântica: identificando áreas prioritárias para aplicação de medidas de mitigação

As rodovias podem representar um importante fator na fragmentação de habitat para espécies silvestres adaptadas a habitats de alta complexidade estrutural, como as florestas tropicais. As estradas reduzem a conectividade da paisagem e a capacidade da população regional em habitar todas as áreas adequadas e estes efeitos são mais significativos nas espécies que evitam a estrada, que são, muitas vezes, espécies de interior de florestas. A magnitude dos efeitos de barreira dependerá do comportamento e mobilidade destas espécies. Quando as estradas representam ralos (sink) ou barreiras para as populações, devido, respectivamente, aos atropelamentos ou à repulsa, medidas mitigadoras são indicadas para aumentar a conectividade entre as manchas de habitat separadas por essas estradas. A qualidade do habitat é um fator que deve ser considerado, mesmo com baixas frequências de atropelamentos nesses locais. O objetivo desse estudo foi propor dois métodos de seleção de áreas prioritárias para implantação de medidas mitigadoras dos efeitos das estradas sobre espécies de vertebrados florestais: Seleção Hierárquica Multivariada e Seleção Bivariada. A área de estudo foi o bioma Mata Atlântica, sendo recortado em paisagens hexagonais em três escalas diferentes (10.000, 1.000 e 100 km), usando a extensão Repeating Shapes no programa ArcGIS 9.3. Em cada hexágono foram calculados: área de floresta e de Unidade de Conservação, densidade de estradas e de hidrografia. Apenas os hexágonos cobertos por no mínimo 45% pela Mata Atlântica, com mais de 50% de cobertura florestal e mais de 1% de Unidades de Conservação foram incluídos nas análises. Após esta seleção, no método Seleção Hierárquica Multivariada, foi feita uma análise de componentes principais (PCA) com as quatro variáveis medidas, para cada escala separadamente. Os hexágonos foram então ordenados segundo o posicionamento deles no 1 Eixo da PCA de forma hierárquica e da maior para menor escala de hexágonos. Para área de estudo o método de Seleção Bivariada foi construído um gráfico de pontos, para cada escala de hexágono, com as variáveis cobertura florestal e rios. Foram selecionados os hexágonos que estavam localizados no quadrante do gráfico que representasse maior densidade de rios e maior porcentagem de cobertura florestal. Posteriormente foi feita uma simulação para avaliar se os métodos eram capazes de recuperar escores tão alto quanto a ordenação seguindo apenas o posicionamento dos hexágonos no Eixo 1 da PCA, sem uma análise hierárquica. O método de Seleção Hierárquica Multivariada foi mais eficiente para escolha de áreas prioritárias do que a Seleção Bivariada tanto para a escala intermediária (1.000 km) quanto para a menor escala (100 km). Os cinco hexágonos de 100 km mais prioritários estão localizados em São Paulo e Paraná, abrangendo quatro UCs (PARES de Jacupiranga, APA de Guaraqueçaba, APA Cananéia- Jacuípe e PARES da Ilha do Cardoso). Devido à simplicidade e fácil aplicabilidade do método, acredita-se que este pode ser uma opção interessante para escolha de áreas prioritárias para implantação de medidas mitigadoras dos efeitos de estradas