Planar Networks Research Articles

A planar network proof for Hankel total positivity of type B Narayana polynomials

The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar network proof of this result. In this paper, we present such a proof by constructing a planar network allowing negative weights, applying the Lindström-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths.

The Evolution of Geometric Structures, Electronic Properties, and Chemical Bonding of Small Phosphorus-Boron Clusters

We report a comprehensive theoretical investigation on phosphorus–boron mixed neutral, anionic, and cationic clusters P2Bn/P2Bn−/P2Bn+ (n = 3–7) with two phosphorus atoms and three to seven boron atoms. We reveal the common character of all the structures (i.e., the phosphorus atoms choose to occupy the peripheral position), whereas the boron atoms tend to be in the central and inside position of the ground state phosphorus—boron mixed clusters at each stoichiometry. Any three atoms preferentially form a stable triangle and grow with zigzag shape in a planar network. Interestingly, a series of planar motifs (including tetra-, penta-, and hexa-coordination) have been discovered in the phosphorus–boron clusters. The large binding energies (3.6 to 4.6 eV/atom) and quite large HOMO–LUMO gaps (5 to 10 eV) indicate the high stability of the clusters. The energy differences Δ1E, Δ2E, and energy gaps display oscillating behavior with increasing numbers of boron atoms. The electron affinity (EA) and ionization potential (IP) generally have small variations, with the EA values ranging from 2 to 3 eV, and the IP values ranging from 7 to 9 eV. Chemical bond analysis shows that the existence of multi-center delocalized bonds stabilize the clusters.

Spinning the Matrix – Mechanisms of Basement Membrane Secretion and Assembly

Basement membranes (BMs) are sheet‐like extracellular matrices that line the basal surfaces of epithelial tissues and surround muscles, adipose tissue, and nerves. My lab studies how regulated changes to BM architecture contribute to tissue morphogenesis. In Drosophila, elongation of the initially spherical egg chamber coincides with the generation of a polarized network of fibrils in its surrounding BM. We found that BM fibrils are assembled from newly synthesized proteins in the pericellular spaces between the egg chamber’s epithelial cells and undergo oriented insertion into the planar BM network by directed epithelial migration. We further found that a Rab10‐dependent secretion pathway ensures that a subset of new BM proteins exit the cell through a basal region of the lateral membrane for fibril formation. Rab10 recruits kinesin motors to BM secretory vesicles and transports them to this location on a polarized microtubule array. Finally, by manipulating Rab10 function, we showed for the first time that BM fibrils play an instructive role in egg chamber elongation. This work identifies a novel intracellular trafficking pathway for BM proteins and highlights how regulated protein secretion can synergize with tissue movement to build a polarized BM architecture that controls tissue shape.

Three Keggin POMs-based coordination polymers constructed by linear N-heterocyclic ligand for proton conduction, photocatalytic activity and magnetic property

POMs-based coordination polymers are promising materials for their potential application in the fields of proton conduction, catalysis and magnetism. Three new coordination polymers namely, {[Co2(bib)3(H2O)2(H4W12O40)]·7H2O}n (1), {[Zn3(bib)8(H3ZnW12O40)2]·12H2O}n (2) and {[Ag5(bib)5(H3W12O40)]·5H2O}n (3) were synthesized under hydrothermal conditions based on linear nitrogen heterocyclic ligand 1,4-bis(1-imidazolyl)benzene (bib). In compound 1, CoII ions are linked with [H4W12O40]4– anions to form a planar network and can be simplified as kgd topology, which are further linked with bib ligands to form a 3D framework. Zn2 ions of compound 2 alternately connect with bib ligands and [H3ZnW12O40]3– anions to form 1D chain structure, while Zn1 ion forms isolated unit with three bib ligands and one [H3ZnW12O40]3– anion, and a 3D framework is finally constructed through π … π stacking interactions. In compound 3, the 3D structure is constructed from a number of 1D chains formed by AgI ions and bib ligands in different directions through π … π stacking interaction and Ag⋯O weak connection. The proton conductivity of 1–3 are 2.03 ​× ​10−5, 1.04 ​× ​10−6 and 1.87 ​× ​10−4 ​S ​cm−1 at 98% RH and 358 ​K, respectively. In addition, compounds 1–3 exhibit photocatalytic degradation capacity towards RhB and compound 1 displays antiferromagnetic behavior.

The quantitative characterization of hydraulic fracture connectivity from a postmortem investigation

AbstractTwo bio-siliceous Onnagawa (ONG I and ONG II) shale samples have been hydraulically fractured under two constant differential stresses (60 and 85 MPa, respectively) to investigate the fracture network's connectivity evolution by a postmortem analysis. The pressure inside the drilled borehole in a cylindrical core sample is increased above the confining pressure (10 MPa) until failure by hydraulic fracture. The two samples failed at two different borehole pressures (ONG I: 42 MPa, ONG II: 16 MPa). Fractured samples were scanned in an industrial X-ray CT machine and the tomographic images of the fracture network were extracted for a postmortem investigation. From the fracture volume segments, obtained by thresholding the frequency distribution of the fracture network's voxel values, a quantitative estimation of fracture connectivity was carried out. The connectivity was quantified based on the relative entropy of size distribution of fractures (${H_r}$), a method adapted from information theory. Fracture connectivity estimation shows that ${H_r}$ is at a maximum value when the fractures show a significant distribution with very limited connectivity. The value of ${H_r}$ is at a minimum and close to 0 when a well-linked fracture network is formed. In both samples, this minimum was attained at the threshold of 43k indicating the highest connectivity and the best representation of the fracture network. The extracted fracture network of ONG I showed a multi-winged hydraulic fracture network while a planar conventional two-winged hydraulic fracture network had been generated in ONG II with a lower fracture volume.

Effective acetylene length dependence of the elastic properties of different kinds of graphynes

• A serial combination of springs is capable to describe the elasticity of graphynes; • Values of elastic moduli of 10 graphynes of each one of 7 families are shown; • Linear compressibility of graphynes depend linearly on acetylene length; • Two families of graphyne present negative linear compressibility; Graphyne is a planar network of connected carbon chains, each formed by n acetylene linkages. Uncountable ways to make these connections lead to uncountable structural graphyne families (GFs). As the synthesis of graphynes with n > 1 has been reported in literature, it is of interest to find out how their physical properties depend on n for each possible GF. Although literature already present specific models to describe the dependence on n of the elastic properties of specific GFs, there is not yet enough amount of data for the physical properties of different graphynes with different values of n . Based on fully atomistic molecular dynamics simulations, the Young's modulus, shear modulus, linear compressibility and Poisson's ratio of 10 graphyne members of 7 different GFs are calculated. A simple elastic model consisting of a serial combination of n springs is proposed to describe the dependence on n of the elastic properties of these 7 GFs. We show that except for the Poisson's ratio, this simple unique elastic model is able to numerically describe, with good precision, the Young's modulus, shear modulus and linear compressibility of all different graphynes, including anisotropy and negative values of linear compressibility of some GFs.

Solution-Processable Semiconducting Conjugated Planar Network.

After the emergence of graphene in the material science field, top-down and bottom-up studies to develop semiconducting organic materials with layered structures became highly active. However, most of them have suffered from poor processability, which hampers device fabrication and frustrates practical applications. Here, we suggest an unconventional approach to fabricating semiconducting devices, which avoids the processability issue. We designed a soluble amorphous network using a solution process to form a thin film on a substrate. We then employed heat treatment to develop a flattened organic structure in the thin film, as an active layer for organic thin-film transistors (TFTs). The fabricated TFTs showed good performance in both horizontal and vertical charge transport, suggesting a versatile and useful approach for the development of organic semiconductors.

Combinatorial topology and geometry of fracture networks.

A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to regular polygons, and the isoperimetric ratio. The map serves as a low-dimensional signature of the fracture network and is visually presented as a pair of three-dimensional graphs. A systematic study is made of a wide collection of real crack networks for various materials, collected from different sources. To identify the characteristics of the real materials, several well-known mathematical models of convex polygonal networks are presented and worked out. These geometric models may correspond to different physical fracturing processes. The proposed map is shown to be discriminative, and the points corresponding to materials of similar properties are found to form closely spaced groups in the parameter space. Results for the real and simulated systems are compared in an attempt to identify crack networks of unknown materials.

On Computation of Degree-Based Entropy of Planar Octahedron Networks

Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies. The degree-based entropy is inspired by Shannon’s entropy. The connectivity pattern such as planar octahedron network is used to predict physiochemical activity. In this article, we present some degree-based entropies of planar octahedron network.

Minimum Flows in Directed 1−n Planar Static and Dynamic Networks with Arcs and Nodes Capacities

Planar networks are an important special class of networks that arise in several application contexts. Because of the special structure of planar networks, network flow algorithms often run faster on these networks than they do on more general networks. In first part (Secs. 2–5), we present an algorithm for finding maximum cut and an algorithm for finding minimum flow in directed [Formula: see text] planar static networks with arcs and nodes capacities. This part is presented in Ciurea et al. [Proc. 5th Int. Conf. Control Decision and Information Technologies (CoDIT2018), Thessaloniki, Greece (2018), pp. 110–115]. In the second part (Secs. 6–8), we present this problem in directed [Formula: see text] planar dynamic networks with arcs and nodes capacities.

A Lab-in-a-Fiber optofluidic device using droplet microfluidics and laser-induced fluorescence for virus detection

Microfluidics has emerged rapidly over the past 20 years and has been investigated for a variety of applications from life sciences to environmental monitoring. Although continuous-flow microfluidics is ubiquitous, segmented-flow or droplet microfluidics offers several attractive features. Droplets can be independently manipulated and analyzed with very high throughput. Typically, microfluidics is carried out within planar networks of microchannels, namely, microfluidic chips. We propose that fibers offer an interesting alternative format with key advantages for enhanced optical coupling. Herein, we demonstrate the generation of monodisperse droplets within a uniaxial optofluidic Lab-in-a-Fiber scheme. We combine droplet microfluidics with laser-induced fluorescence (LIF) detection achieved through the development of an optical side-coupling fiber, which we term a periscope fiber. This arrangement provides stable and compact alignment. Laser-induced fluorescence offers high sensitivity and low detection limits with a rapid response time making it an attractive detection method for in situ real-time measurements. We use the well-established fluorophore, fluorescein, to characterize the Lab-in-a-Fiber device and determine the generation of sim 0.9 nL droplets. We present characterization data of a range of fluorescein concentrations, establishing a limit of detection (LOD) of 10 nM fluorescein. Finally, we show that the device operates within a realistic and relevant fluorescence regime by detecting reverse-transcription loop-mediated isothermal amplification (RT-LAMP) products in the context of COVID-19 diagnostics. The device represents a step towards the development of a point-of-care droplet digital RT-LAMP platform.

Recent advances in single-crystalline two-dimensional polymers: Synthesis, characterization and challenges

Two-dimensional polymers (2DPs) are emerging crystalline 2D organic material comprising free-standing, single-atom/monomer-thick, planar, and covalent networks with long-ranging structural order. Benefiting from their intrinsic porosity, crystallinity, and electrical properties, 2DPs have displayed great potential for separation, energy conversion and electronic fields. In this mini review, we aim to provide the recent progress in crystalline 2DPs films form synthesis strategies to characterization methods, as well as the future trends. We first present the synthesis strategy of single-crystalline 2DPs films including crystal engineering approaches and surface science. Also, we summarize the characterization methods of 2DPs films and highlight the advantages and limitations of different methods focusing on chemical bonding, morphology, and crystal structure. Finally, we will present the current challenges and trends regarding the future developments of crystallinity, monomer design, synthesis strategy and characterization.

Two-Dimensional Dirac Nodal Line Carbon Nitride to Anchor Single-Atom Catalyst for Oxygen Reduction Reaction.

Two-dimensional carbon nitride (2DCN) materials have emerged as an important class of 2D materials beyond graphene. However, 2DCN materials with nodal-line semimetal characteristic are rarely reported. In this work, a new nodal-line semimetal 2DCN with the stoichiometry C4 N4 is designed by using density functional theory (DFT) calculations and its application to anchor single-atom catalysts (SACs) for the oxygen reduction reaction (ORR) is investigated. C4 N4 is a planar covalent network (sp2 hybridization) with regular holes formed by the four N atoms, which is dynamically, thermodynamically, and mechanically stable. The nodal line is contributed by the pz orbitals of C and px/y orbitals of N atoms. C4 N4 shows an anisotropic Fermi velocity and high electron mobility. Because of its porous structure, C4 N4 can anchor heteroatoms as SACs for electrocatalysis. C4 N4 anchored with Fe or Co is shown to be highly active for the ORR with a rather high half-wave potential of around 0.90 V, which is higher than those of SACs on other carbon nitrides. These findings may provide a new strategy to design novel substrates for SACs.

Planar Networks of Boron Triangles: Analogies to Benzene and Other Planar Aromatic Hydrocarbons.

The lowest energy structures for Bn species (n = 6 to 23 except for 20) observed experimentally in the gas phase with a mass spectrometer are planar networks of boron triangles. Such networks are considered to consist of trigonal planar sp2-hybridized boron atoms having perpendicular p orbitals similar to the carbon atoms in benzene and other planar aromatic hydrocarbons. Electron bookkeeping for reasonable chemical bonding topologies of wheel-like structures such as B@Bn-1 (n = 6-9) leads to two π-electrons for B6 and B7+ similar to the cyclopropenyl cation and six π-electrons for B82- and B9- similar to benzene. Related chemical bonding topology analyses for low-energy oval B10 and B11- structures as well as for larger planar boron triangle networks with 12, 13, and 14 boron atoms suggest six π-electrons in such structures. Planar networks of boron triangles having 16-19 boron atoms are shown to be systems with 10 π-electrons similar to naphthalene. Similarly, low-energy planar B22 and B23- structures are shown to be 4 π-electron systems 1analogous to linear anthracene and angular phenanthrene, respectively. Intermediate B15- and B21- systems are shown to be systems with 4k rather than 4k + 2 π-electrons with 8 and 12 π-electrons, respectively. Structures based on planar networks of boron triangles are strongly energetically disfavored for B20 relative to a nonplanar decagonal antiprism structure with ideal D10d symmetry.

A numerical model of grain growth

Abstract A numerical model for grain growth has been developed. The governing equations for the model are derived from a variational principle that enforces the balance between energy dissipation and changes of internal energy. This approach significantly simplifies previous modelling of grain growth by replacing a curved grain boundary with several straight lines and relaxing constraints on triple point angles. Such simplifications provide a basis for a finite element method by reducing the analysis of a complex network of interconnected curved lines to the motion of interacting points. In the finite element formulation two approaches are used, namely an element based formulation and a node based formulation. In the latter case, the properties of the elements are lumped together at their common nodes. Such an approach allows the nodal velocity to be determined independently of the forces on other nodes in a lumped mobility methodology, leading to a further reduction of computer time. Several planar grain networks of Voronoi polygons have been studied. The evolution of the grain structures determined from these two approaches is found to exhibit the same trends as those obtained using other models published in the literature. Owing to its simplicity, the node based formulation is recommended.

Tunable Spin Wave Propagation in YIG/Fe-Rh Stripe

Here, we present the results of an experimental and numerical study of controllable spin-wave propagation in the yttrium iron garnet stripe with an Fe-Rh slab. The transformation of spin-wave dispersion and transmission are observed by the focusing laser light on top of the Fe-Rh slab. It was shown that the geometry variation and design of the Fe-Rh slab significantly affect spin-wave propagation. The static internal magnetic field profile in the yttrium iron garnet is subject to position and the geometric parameters of the Fe-Rh slab. Additionally, the possibility of width mode filtering was shown for a surface magnetostatic spin wave by the means of micromagnetic simulation. The qualitative correspondence between the behavior of spin waves in the numerical simulation and microwave spectroscopy data was observed. The proposed structure can be used as a functional unit with the simultaneous frequency selective and spin-wave mode filtration regime in planar magnonic networks.

Time-Varying Formation Control for Heterogeneous Planar Underactuated Multivehicle Systems

Abstract This paper presents a distributed control approach for time-varying formation of heterogeneous planar underactuated vehicle networks without global position measurements. All vehicles in the network are modeled as generic three degree-of-freedom planar rigid bodies with two control inputs, and are allowed to have nonidentical dynamics. Feasible trajectories are generated for each vehicle using the nonholonomic constraints of the vehicle dynamics. By exploiting the cascaded structure of the planar vehicle model, a transformation is introduced to define the reduced order error dynamics, and then, a sliding-mode control law is proposed. Low-level controller for each vehicle is derived such that it only requires relative position and local motion information of its neighbors in a given directed communication network. The proposed formation control law guarantees the uniform global asymptotic stability (UGAS) of the closed-loop system subject to bounded uncertainties and disturbances. The proposed approach can be applied to underactuated vehicle networks consisting of mobile robots, surface vessels, and planar aircraft. Simulations are presented to demonstrate the effectiveness of the proposed control scheme.

Noncoordinating-substituents-induced various Co and Ni coordination polymers with multiple pathways detection of Fe3+ and Cr(Ⅵ)

Six coordination polymers (CPs) based on a bis-pyridyl-bis-amide ligand containing thiophene, [Co(4-bmptd)(IPA)(H2O)] (1), [Co(4-bmptd)(5-HIP)(H2O)2]·2H2O (2), [Co(4-bmptd)(5-NIP)] (3), [Ni2(4-bmptd)2(IPA)2(H2O)2]·2H2O (4), [Ni(4-bmptd)(5-HIP)(H2O)2]·2H2O (5) and [Ni(4-bmptd)(5-NIP)] (6) [4-bmptd = N,N'-bis(4-methylenepyridyl)-2,5-thiophene dicarbonamide, H2IPA = isophthalic acid, 5-H2HIP = 5-hydroxyisophthalic acid, 5-H2NIP = 5-nitroisophthalic acid] were synthesized under hydrothermal conditions. CPs 1–6 were characterized by elemental analysis, IR and X-ray diffraction. CP 1 is a wavy 2D structure, CPs 2 and 5 are isostructural, showing the 2D interpenetrating structure. CPs 3 and 6 are isostructural, both of which are bilayer planar structures, while CP 4 is a planar 2D network. Taking CP 2 as an example, its fluorescence sensing properties for Fe3+ and Cr(VI) were studied. The carbon paste electrodes bulk-modified by CPs 1–4 were used as electrochemical sensors for the detection of Fe3+ and Cr(VI).

Signal-to-noise-ratio and maximum-signal-to-noise-ratio detection statistics in template-bank searches for exotic physics transients with networks of quantum sensors

Quantum sensor networks such as the existing networks of atomic clocks and magnetometers offer intriguing capabilities in searches for transient signals such as dark matter or fields sourced by powerful astrophysical events. The common matched-filter technique relies on the signal-to-noise-ratio (SNR) detection statistic to probe such transients. For macroscopic dark matter objects, the network would register a sweeping signal as the object propagates through at galactic velocities. A potential event is registered when the SNR from a specific template exceeds a threshold set by a desired false positive rate. Generically, to span the continuous parameter space for the network-exotic-physics encounter, one has to deal with multiple templates. In such template-bank searches, the natural generalization of the SNR statistic is the maximum-signal-to-noise-ratio (SNR-max) statistic, defined as the maximum of the absolute values of SNRs determined from individual template matching. While individual SNR realizations are Gaussian distributed, SNR-max probability distribution is non-Gaussian. Moreover, as the individual template-bank SNRs are computed using the same network data streams, SNRs become correlated between the templates. Cross-template correlations have a sizable effect on the SNR-max probability and cumulative distributions, and on the threshold SNR-max values. Computing threshold SNR-max values for large template banks is computationally prohibitive and we develop analytic approaches to computing properties of the SNR-max statistic. This is done for cases when the template bank is nearly orthogonal (small cross-template correlations) and for banks with cross-template correlation coefficient distribution ``squeezed'' about the most probable cross-template correlation value. Since the cross-template correlation coefficients quantify the similarity of templates, increasing correlations tend to decrease SNR-max thresholds for specific values of false positive rates. Increasing the number of templates in the bank increases the SNR-max thresholds. Our derivations are carried out for networks that may exhibit colored noise and cross-node correlations. Specific applications are illustrated with a dark matter search with atomic clocks onboard satellites of a Global Positioning System and with a ``toy'' planar network with cyclic rotational symmetry.

Nanoscale dynamics of actin filaments in the red blood cell membrane skeleton.

Red blood cell (RBC) shape and deformability are supported by a planar network of short actin filament (F-actin) nodes (∼37 nm length, 15–18 subunits) interconnected by long spectrin strands at the inner surface of the plasma membrane. Spectrin-F-actin network structure underlies quantitative modeling of forces controlling RBC shape, membrane curvature, and deformation, yet the nanoscale organization and dynamics of the F-actin nodes in situ are not well understood. We examined F-actin distribution and dynamics in RBCs using fluorescent-phalloidin labeling of F-actin imaged by multiple microscopy modalities. Total internal reflection fluorescence and Zeiss Airyscan confocal microscopy demonstrate that F-actin is concentrated in multiple brightly stained F-actin foci ∼200–300 nm apart interspersed with dimmer F-actin staining regions. Single molecule stochastic optical reconstruction microscopy imaging of Alexa 647-phalloidin-labeled F-actin and computational analysis also indicates an irregular, nonrandom distribution of F-actin nodes. Treatment of RBCs with latrunculin A and cytochalasin D indicates that F-actin foci distribution depends on actin polymerization, while live cell imaging reveals dynamic local motions of F-actin foci, with lateral movements, appearance and disappearance. Regulation of F-actin node distribution and dynamics via actin assembly/disassembly pathways and/or via local extension and retraction of spectrin strands may provide a new mechanism to control spectrin-F-actin network connectivity, RBC shape, and membrane deformability.