Small Triangles Research Articles

SLAM-guided catheter ablation of AVNRT: single-center experience

Abstract Aims Three-dimensional mapping systems have been utilized to reduce fluoroscopy and minimize complications in patients with AVNRT. Recently, voltage-gradient mapping has been introduced to visualize low-voltage bridges. However, there are some limitations of voltage assessment due to catheter contract. Therefore, new Slow pathway Late Activation Mapping (SLAM) has been recently used to reveal slow conduction zone in AVNRT patients. Method and materials Seven adult patients with diagnosis of typical AVNRT were included. Electro anatomical mapping systems was used in all patients. Voltage and late activation mapping were performed with high-definition multipolar catheter. His cloud was also tagged in all patients. Voltage of 0.20-0.50 mV was used to delineate voltage-bridges. Latest activation in the SP area along with voltage-guided bridges were targeted with either radiofrequency ablation (RFA) or focal cryoablation (Figure 1 and 2). Results Limited fluoroscopy was used in 4 patients. Acute success was achieved in all patients. Patients had no structural heart disease. Detailed clinical and procedural data was depicted in Table. Cryoablation was used in 2 patients due to very small Koch triangle. Each cryolesion applied for 240 secs and overall, 3-4 lesions were delivered. Ablation at late activation areas successfully eliminated slow pathway. In most of cases, one ablation lesion was adequate to see junctional beats and elimination of dual AV nodal physiology. Conclusion SLAM is effective in guiding catheter ablation of AVNRT, with a complete acute success rate and no recurrences at short-term follow-up.

Characterization of arbuscular mycorrhizal fungal species associating with Zea mays.

Taxonomic identification of arbuscular mycorrhizal (AM) fungal spores extracted directly from the field is sometimes difficult because spores are often degraded or parasitized by other organisms. Single-spore inoculation of a suitable host plant allows for establishing monosporic cultures of AM fungi. This study aimed to propagate AM fungal spores isolated from maize soil using single spores for morphological characterization. First, trap cultures were established to trigger the sporulation of AM fungal species. Second, trap cultures were established with individual morphotypes by picking up only one spore under a dissecting microscope and transferring it to a small triangle of sterilized filter paper, which was then carefully inoculated below a root from germinated sorghum seeds in each pot and covered with a sterile substrate. All pots were placed in sunbags and maintained in a plant growth room for 120 days. Spores obtained from single spore trap cultures from each treatment, maize after oats (MO), maize after maize (MM), maize after peas (MP), and maize after soybean (MS), were extracted using the sieving method. Healthy spores were selected for morphological analysis. Direct PCR was conducted by crushing spores in RNAlater and applying three sets of primer pairs: ITS1 × ITS4, NS31 × AML2, and SSUmcf and LSUmBr. Nucleotide sequences obtained from Sanger sequencing were aligned on MEGA X. The phylogenetic tree showed that the closest neighbors of the propagated AM fungal species belonged to the genera Claroideoglomus, Funneliformis, Gigaspora, Paraglomus, and Rhizophagus. The morphological characteristics were compared to the descriptive features of described species posted on the INVAM website, and they included Acaulospora cavernata, Diversispora spurca, Funneliformis geosporus, Funneliformis mosseae, Gigaspora clarus, Gigaspora margarita, Glomus macrosporum, Paraglomus occultum, and Rhizophagus intraradices. These findings can provide a great contribution to crop productivity and sustainable management of the agricultural ecosystem. Also, the isolate analyzed could be grouped into efficient promoters of growth and mycorrhization of maize independent of their geographical location.

Spontaneous perspective-taking in real-time language comprehension: evidence from eye-movements and grain of coordination

Linguistic communication requires interlocutors to consider differences in each other’s knowledge (perspective-taking). However, perspective-taking might either be spontaneous or strategic. We monitored listeners’ eye movements in a referential communication task. A virtual speaker gave temporally ambiguous instructions with scalar adjectives (“big” in “big cubic block”). Scalar adjectives assume a contrasting object (a small cubic block). We manipulated whether the contrasting object (a small triangle) for a competitor object (a big triangle) was in common ground (visible to both speaker and listener) or was occluded so it was in the listener’s privileged ground, in which case perspective-taking would allow earlier reference-resolution. We used a complex visual context with multiple objects, making strategic perspective-taking unlikely when all objects are in the listener’s referential domain. A turn-taking, puzzle-solving task manipulated whether participants could anticipate a more restricted referential domain. Pieces were either confined to a small area (requiring fine-grained coordination) or distributed across spatially distinct regions (requiring only coarse-grained coordination). Results strongly supported spontaneous perspective-taking: Although comprehension was less time-locked in the coarse-grained condition, participants in both conditions used perspective information to identify the target referent earlier when the competitor contrast was in privileged ground, even when participants believed instructions were computer-generated.

CD-type discretization for sea ice dynamics in FESOM version 2

Abstract. Two recently proposed variants of CD-type discretizations of sea ice dynamics on triangular meshes are implemented in the Finite-VolumE Sea ice–Ocean Model (FESOM version 2). The implementations use the finite element method in spherical geometry with longitude–latitude coordinates. Both are based on the edge-based sea ice velocity vectors but differ in the basis functions used to represent the velocities. The first one uses nonconforming linear (Crouzeix–Raviart) basis functions, and the second one uses continuous linear basis functions on sub-triangles obtained by splitting parent triangles into four smaller triangles. Test simulations are run to show how the performance of the new discretizations compares with the A-grid discretization using linear basis functions. Both CD discretizations are found to simulate a finer structure of linear kinematic features (LKFs). Both show some sensitivity to the representation of scalar fields (sea ice concentration and thickness). Cell-based scalars lead to a finer LKF structure for the first CD discretization, but the vertex-based scalars may be advantageous in the second case.

Bidirectional PWM Converter to Interface AC Part to DC Microgrid with Neutral Potential Balancing

This research presents a description of a bidirectional pulse width modulated converter that functions as a rectifier by using the direct power control strategy and space vector modulation technology. In contrast to the voltage-oriented control strategy, this method minimises the number of internal current loops and requires more tuning. While functioning as an inverter, it applies the space vector modulation technique as well. The approach, on the other hand, is not the same as rectifiers since it calculates the duty ratio of the neighbouring voltage vectors in each small triangle that is generated in each sector that has a period of 60 degrees. In both situations, the neutral point potential has been brought back into equilibrium.

Blefaroplastia reconstrutiva após remoção de carcinoma de células escamosas palpebral em equino - relato de caso

ABSTRACT Blepharoplasty in equines is rarely performed because periocular tissues present low mobility, especially in the lower eyelid, which frequently subjects this species to enucleation. Squamous cell carcinoma (SCC) is among the most common malignant neoplasms of the eyes and annexes, which increases local recurrences due to the lack of available safety margin. A 12-year-old Creole equine with a white coat presenting an ulcerative lesion on the lower right eyelid was treated. The treatment strategy considering the SCC suspicion was the surgical excision of the lesion and maintenance of the eye, followed by blepharoplasty for eyelid reconstruction. The hemi H-plasty technique was performed to reconstruct the right lower eyelid after a skin incision circumscribing the lesion and respecting a safety margin. Two parallel skin incisions were made from the base of the surgical wound, twice the length of the defect height, and small triangles of skin (Burow’s triangles) were excised, and then the flap was advanced into the wound and fixed. No postoperative complications or tumor recurrence were observed during the following 24 months of follow-up, and the technique ensured the functional and aesthetic reconstruction of the region.

16 Development of a Systematic Scoring System to Measure Adherence to a Temporal-Spatial Heuristic when Completing the Rey Complex Figure Task

Objective:It has been established that capturing how an individual draws the Rey Complex Figure Task (RCF) is as important as assessing what is drawn (Rey, 1941, Osterrieth, 1944). Despite the development of multiple systems that have been designed to measure these qualitative characteristics there are still no systematic means to measure adherence to the temporal-spatial heuristic that represents a typical drawing practice in healthy, neurotypical adults (Visser, 1973; Hamby et al, 1993).This study sought to develop a system for scoring temporal-spatial adherence when drawing the figure to provide objective, continuous data.Participants and Methods:Fifty-three English-speaking adults (mean age 44.61 yrs, SD 12.48; 44 female) were recruited. Exclusion criteria included vision and hearing impairment not corrected by aids; neurodivergent, neurological or psychiatric diagnosis, cancer or brain injury history. Participants completed the RCF copy phase as part of an extended neuropsychological battery. The RCF drawing process was recorded via video and a ball-point pen that digitally recorded drawing. Order data for the 18 RCF elements (Osterrieth, 1944,Taylor, 1959) was recorded by two scorers and analysed via Principal Component Analysis (PCA) with an equimax rotation to identify elements typically drawn together by a healthy, neurotypical adult. Using scoring methodology adapted from Geary et al (2011), the extent to which participants drew consecutively the member elements of each factor or 'strategy cluster’ was calculated and recorded. Strategy Cluster Scores across the population sample were examined to understand normative performance.Results:Order data was examined for interrater reliability via Pearson’s correlation coefficient and was considered good (r2 = 0.78, p < 0.001). PCA identified four factors or 'strategy clusters’ that were statistically robust and accounted for 67.34% of total variation. The strategy clusters were Core Structure (rectangle, diagonal, horizontal, vertical); Triangular Structure (triangle, horizontal in triangle, vertical in triangle, diamond); Internal Left-Hand Side (four horizontal lines, smaller rectangle, horizontal in top-left quad); and Internal Right-Hand Side (five lines, circle, vertical top-right quad, small triangle). The mean RCF Strategy Cluster Score was 6.23 (SD 1.94; possible range: 2.75 to 10). Population data spread indicated that healthy neurotypical adults only partially observed a temporal-spatial heuristic, rather than strict, absolute adherence.Conclusions:Four strategy clusters were identified where cluster members were typically drawn consecutively. RCF Cluster Strategy scoring was shown to measure the temporal-spatial heuristic objectively, providing continuous data that lends itself to clinical standardisation. Further, the study demonstrated that whilst healthy, neurotypical adults copy the RCF using a temporal-spatial heuristic, it is only partially adhered to. Traditionally deviation from strict adherence to the four strategy clusters during drawing was deemed to be indicative of cognitive dysregulation, however our findings demonstrate a normal distribution of typical population performance. These findings have important implications for interpreting how RCF drawing strategy informs clinical assessment and diagnosis as both very strict and very weak adherence to a temporal-spatial heuristic can be indicative of atypical function. The study supports this novel scoring system as a fast and reliable means to systematically measure RCF Cluster Strategy that with further validation could be adopted within clinical practice.

A rare variation of omohyoid and its embryological correlations- A case report

The omohyoid muscle is important in radical neck dissection, as it is a landmark for this operation. Because it divides the anterior and posterior cervical triangles into smaller triangles and its particular relationship to the large cervical vessels, the presence of an anatomical variation of the omohyoid muscle is important. Either belly may be absent or double; and the inferior belly may be attached directly to the clavicle and the superior is sometimes fused with sternohyoid. Variations in the omohyoid muscle might be linked to differences in embryological development, which could influence the muscle’s final form and function. Anderson (Anderson, 1881) theorized that the superior belly of the omohyoid muscle is a true infrahyoid muscle, whereas the inferior belly most likely shares a common embryology with the subclavius muscle. As omohyoid mucle is used to achieve the reconstruction of the laryngeal muscles and bowed vocal folds, the knowledge of the possible anomalies of the omohyoid muscle is important.In the present study, we have found a case with two inferior bellies & aberrant course of superior belly of omohyoid on right side of 40 years female cadaver embalmed with formalin during routine dissection at Department of Anatomy AIIMS Gorakhpur.Omohyoid muscle is closely related to large vessels of neck & brachial plexus, so variations in this muscle are clinically important.

Shaking table test on irregular and complex connected structure

Affected by the external environment, it is easy to cause complex and irregular problems in the building structure, bringing new safety hazards to the seismic resistance of the structure. Based on the background of the east building of the railway station with cross ground crack, the seismic performance of irregular and complex connected structures under different seismic intensities was analysed.The research results indicate that under the action of a 7-degree seismic fortification, the structure is basically in an elastic state, with a stiffness degradation of 12.9%, meeting the performance requirements of being undamaged during small earthquakes; Under seismic fortification, the structure is mainly characterized by cracking at the bottom beam end, with a small crack width and a stiffness degradation of 41.7%, meeting the requirements for moderate earthquake repairability; Under the rare earthquake of 8degree , plastic hinges begin to form at the beam and column ends of the structure and gradually develop, with stiffness degradation reaching 81.9%. All seismic responses of the structure comply with the limit requirements of the code (GB 50011-2010); Under the rare earthquake of 8 degree , there is a serious torsion phenomenon in the small triangle area, which leads to the disharmony of forces on the inner and outer beams and columns. In earthquakes, it is easy to cause structural collapse due to the first failure of the outer columns. Suggesting to increasethe stiffness of the small triangular column to solve the above problem. Under extremely rare earthquakes, the plastic hinge mechanism of the structure has developed completely, with stiffness degradation approaching 90% and no collapse phenomenon, indicating that complex connected structures have excellent seismic performance.

Comparison of algorithms for contrast enhancement based on triangle orientation discrimination assessments by convolutional neural networks

Within the last decades, a large number of techniques for contrast enhancement has been proposed. There are some comparisons of such algorithms for few images and figures of merit. However, many of these figures of merit cannot assess usability of altered image content for specific tasks, such as object recognition. In this work, the effect of contrast enhancement algorithms is evaluated by means of the triangle orientation discrimination (TOD), which is a current method for imager performance assessment. The conventional TOD approach requires observers to recognize equilateral triangles pointing in four different directions, whereas here convolutional neural network models are used for the classification task. These models are trained by artificial images with single triangles. Many methods for contrast enhancement highly depend on the content of the entire image. Therefore, the images are superimposed over natural backgrounds with varying standard deviations to provide different signal-to-background ratios. Then, these images are degraded by Gaussian blur and noise representing degradational camera effects and sensor noise. Different algorithms, such as the contrast-limited adaptive histogram equalization or local range modification, are applied. Then accuracies of the trained models on these images are compared for different contrast enhancement algorithms. Accuracy gains for low signal-to-background ratios and sufficiently large triangles are found, whereas impairments are found for high signal-to-background ratios and small triangles. A high generalization ability of our TOD model is found from the similar accuracies for several image databases used for backgrounds. Finally, implications of replacing triangles with real target signatures when using such advanced digital signal processing algorithms are discussed. The results are a step toward the assessment of those algorithms for generic target recognition.

OBNOXIOUS FACILITY LOCATION: THE CASE OF WEIGHTED DEMAND POINTS

The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three new optimal solution approaches are proposed. Two variants of the Big Small Triangle global optimization method, and a procedure based on intersection points between Apollonius circles. We also compared the results with a multi-start approach using the non-linear multi-purpose software SNOPT. Problems with 1,000 demand points are optimally solved in a fraction of a second of computer time.

Electronic and magnetic properties of polar magnets M2Mo3O8 (M = Mn, Fe, Co and Ni) from first principles studies

Through the first-principles density functional theory calculations, we systematically studied the electronic and magnetic properties of a series of polar magnets M2Mo3O8 (M ​= ​Mn, Fe, Co and Ni), which consists of alternative M2 and Mo3 two-dimensional honeycomb layers along the c axis. The electronic structural analysis indicate that the Mo ion exhibits 4+ oxidation state with 4d2 electronic configuration. Owning to the formation of Mo3 cluster, each small triangle with six electrons creates entirely filled molecular bonding states and completely empty antibonding states, giving rise to diamagnetic nature of Mo4+ ion. In nice agreement with the experimental observations, the ferrimagnetic ordering, in which the interactions among the tetrahedal and octahedral M2+ sites (both intralayer and interlayer ones) are exclusively antiferromagnetic, is established for Mn2Mo3O8, while the C-type antiferromagnetic configuration, where the antiferromagentic M2 honeycomb layers are ferromagnetic coupling along the c axis, is formed in M ​= ​Fe and Co case, nevertheless, the magnetic phase diagram of Ni2Mo3O8 is uncertain and complex, since all the magnetic orderings considered are almost degenerate within the limits of the calculated error. Furthermore, the variation of the electronic structures and magnetic properties were analyzed as occupation of 3d orbitals increasing from 3d5 (Mn2+) to 3d8 (Ni2+) in terms of the crystal field splitting and electronic correlation.

Polygon-Based Hierarchical Planar Networks Based on Generalized Apollonian Construction

Experimentally observed complex networks are often scale-free, small-world and have an unexpectedly large number of small cycles. An Apollonian network is one notable example of a model network simultaneously having all three of these properties. This network is constructed by a deterministic procedure of consequentially splitting a triangle into smaller and smaller triangles. In this paper, a similar construction based on the consequential splitting of tetragons and other polygons with an even number of edges is presented. The suggested procedure is stochastic and results in the ensemble of planar scale-free graphs. In the limit of a large number of splittings, the degree distribution of the graph converges to a true power law with an exponent, which is smaller than three in the case of tetragons and larger than three for polygons with a larger number of edges. It is shown that it is possible to stochastically mix tetragon-based and hexagon-based constructions to obtain an ensemble of graphs with a tunable exponent of degree distribution. Other possible planar generalizations of the Apollonian procedure are also briefly discussed.

High gain, wideband and low mutual coupling AMC-based millimeter wave MIMO antenna for 5G NR networks

A high gain and wideband multiple-input multiple-output (MIMO) for 5G new radio (NR) networks is introduced in this paper. The single unit is a monopole antenna with partial ground plane and two small triangles are cut out from the patch to produce the proposed frequency band. The two elements are located orthogonal to each other in order to reduce the mutual coupling without using isolation structure at the desired frequency 28 GHz. An artificial magnetic conductor (AMC) is located underneath the MIMO antenna to improve the gain by about 55% over the entire achieved frequency band (26-31.5 GHz). The Suggested antenna model with the AMC structure is fabricated to verify the simulation results in terms of S-parameters, radiation patterns, gain, and diversity parameters. It is worth noting that the experimental results have the same trend of the simulation ones which makes the suggested AMC-based MIMO antenna applicable for 5G NR networks.

Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

The structural-magnetic models of 25 antiferromagnetic kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2)—a perspective spin liquid—have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii–Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in length J3 magnetic couplings (strong J3(J12) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFM J3(J d) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality of J3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dual J3 couplings with anisotropic Dzyaloshinskii–Moriya interactions are capable to suppress frustration of kagome antiferromagnetics. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighbor J1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in length J3 magnetic couplings.

Experimental and numerical studies for flow over a sierpinski tetrahedron for potential windbreak application

Investigations have been conducted to study the flow characteristics behind the Sierpinsksi Tetrahedron to assess its potential as windbreaks. Sierpinski Tetrahedrons are fractal sets with an equilateral triangle as its based shape. The upper levels consist of subdivided small equilateral triangles until the apex is reached. Flow over the Sierpinski Tetrahedron at Re = 39,400 and 65,700 were analyzed in an open circuit wind tunnel and the measured velocities were used to validate the numerical simulation results. The validated numerical simulation results showed good agreement in general with the experimental data. 5 models are subsequently chosen to be investigated further numerically, at different orders of fractal sets, from order 0 to order 4. RANS numerical model was used with wind speeds ranging from Reynolds number 2.79 × 105 to 4.48 × 106. The results reveals that higher orders are more effective in reducing wind speed. The percentage in wind speed reduction measured at a distance of 12H (H being the height of the Sierpinski Tetrahedron) away from the Sierpinski Tetrahedron is 32% for orders 2, 3 and 4. Order 4 which has highest porosity has the lowest peak turbulence intensity and highest speed reduction. The present study also shows that staggered formation of laying the Sierpinski Tetrahedrons as windbreaks could help in providing a greater coverage area.

Gauging performance of biosynthesized silver nanoparticles loaded polypropylene nonwoven based textile electrodes for 3-lead health monitoring electro cardiogram on analogous system

This work reports the engineering of textile electrodes, considered safe for humans even if worn next to skin for a longer time. Obliging this phenomenon conductive Silver nanoparticles (AgNPs) were biosynthesized from Silver Sulphate (Ag2SO4) and medicinal values enriched Ocimum Sanctum (Tulsi)leaves extract. These conductive Silver nanoparticles were loaded by spray technique on polypropylene nonwoven fabric having inbuilt antifungal characteristics, to reduce its resistivity (10Ω) for the fabrication of textile electrodes. The adequate skin-electrode impedance values were observed for the fabricated textile electrodes, viz; 1.44 MΩ–1.83 MΩ and 1.01 MΩ–1.18 MΩ, in the dry and wet state respectively. The 3-lead health monitoring electrocardiograms (ECG) were obtained on the Analogous system with the textile electrodes; dry and wet state as well as gel electrodes. The cardiograms were also taken at a smaller triangle than usual, only for the high resistance textile electrodes. The wet electrodes have executed considerably better clarity of PQR wavelets than reference gel electrodes ECG plots, and their performance was found consistent when tested after six months’ time leap. However, higher motion artifacts caused in the case of dry electrodes have resulted in distorted PQR wavelets and the tracing became worsen with increased testing time leap. This was mainly due to the encapsulation of conductive AgNPs in the air voids of the fabric, increased resistivity. The cardiogram quality has not shown peculiar benefit for a higher heart pumping pressure at the smaller triangle in either of the cases.

Molecular phylogeny of the Austrolebias/ adloffi/ group (Cyprinodontiformes, Rivulidae), with description of two new endangered and highly endemic species of annual killifishes from the Laguna dos Patos system, southern Brazil.

The Austrolebias adloffi species group encompasses a diverse lineage of annual killifishes that occurs along the Laguna dos Patos/Lagoa Mirim system, in both Brazilian and Uruguayan territories. We herein employ an integrative taxonomy approach to describe two new species of the group, inferring their phylogenetic relationships and evaluating their conservation status. Austrolebias cheffei sp. nov. and Austrolebias lourenciano sp. nov. are herein described from the western portion of the Laguna dos Patos system. Austrolebias cheffei is distinguished from the remaining species of the A. adloffi species group by presenting a yellowish green or yellowish blue dorsal fin, with wide black to dark brown bars extending from the base to the middle portion of the dorsal and anal fins in the males. Austrolebias lourenciano is distinguished from the remaining species of the A. adloffi species group by presenting a yellowish green dorsal fin, with light yellow or light bluish bars forming small triangles, interspersed with small dark brown rows of blotches in the dorsal fin base, and greenish blue anal fin, sometimes with lighter elongated yellowish iridescent blotches, limited to the basal region. According to mitochondrial cytb sequences, both species are reciprocally monophyletic relative to other species of the A. adloffi species group, and present positive barcoding gap values. Interestingly, both new species form a grade that is closely related to Austrolebias aff. minuano 1, an undescribed species that occurs at the opposite margin of the Laguna dos Patos. Among the other evaluated species, A. bagual, A. aff. minuano 1, A. nigrofasciatus, A. pelotapes, A. pongondo, A. arachan, and A. viarius also revealed to be reciprocally monophyletic, whereas A. minuano and A. adloffi revealed to be paraphyletic in regard to A. charrua and A. aff. minuano 2, respectively, and A. nachtigalli is subdivided in two clades, one of which including A. reicherti, which points to the need of a taxonomic review of the group. In addition, we discussed the conservation status of the new species, corrected the type locality of A. pongondo, and provided a dichotomous identification key of the A. adloffi species group.

An improved approximation for hydraulic conductivity for pipes of triangular cross-section by asymptotic means

In this paper, we explore single-phase flow in pores with triangular cross-sections at the pore-scale level. We use analytic and asymptotic methods to calculate the hydraulic conductivity in triangular pores, a typical geometry used in network models of porous media flow. We present an analytical formula for hydraulic conductivity based on Poiseuille flow that can be used in network models contrasting the typical geometric approach leading to many different estimations of the hydraulic conductivity. We consider perturbations to an equilateral triangle by changing the length of one of the triangle sides. We look at both small and large triangles in order to capture triangles that are near and far from equilateral. In each case, the calculations are compared with numerical solutions and the corresponding network approximations. We show that the analytical solution reduces to a quantitatively justifiable formula and agrees well with the numerical solutions in both the near and far from equilateral cases.

The Nature of the Lithosphere‐Asthenosphere Boundary

AbstractPlate tectonic theory was developed 50 years ago and underpins most of our understanding of Earth's evolution. The theory explains observations of magnetic lineations on the seafloor, linear volcanic island chains, large transform fault systems, and deep earthquakes near deep sea trenches. These features occur through a system of moving plates at the surface of the Earth, which are the surface expression of mantle convection. The plate consists of the chemically distinct crust and some amount of rigid mantle, which move over a weaker mantle beneath. However, exactly where the transition between stronger and weaker mantle occurs and what determines and defines the plate are still debated. In the classic definition the plate is defined thermally, by the geotherm‐adiabat intersection, where the plate is the conductively cooling part of the mantle convection system. Many observations such as heat flow, seafloor bathymetry, seismic imaging, and magnetotelluric (MT) imaging are consistent with general lithospheric thickening with age, which suggests that temperature is an important factor in determining lithospheric thickness. However, while age averages give a good indication of overall properties, the range of lithospheric thicknesses reported is large for any given tectonic age interval, suggesting greater complexity. A number of observations including sharp discontinuities from teleseismic scattered waves and active source reflections and also strong anomalies from surface and body wave tomography and MT imaging cannot be explained by a purely thermal model. Another property or process is required to explain the anomalies and sharpen the boundary. Many subsolidus models have been proposed, although none can universally explain the variety of independent global observations. Alternatively, a small amount of partial melt can easily satisfy a range of observations. The presence of melt could also weaken the mantle over geologic timescales, and it would therefore define the lithosphere‐asthenosphere boundary (LAB). The location of melt is important to mantle dynamics and the LAB, although exactly where and exactly how much melt exists in the mantle are debated. Asthenospheric melt interpretations include a variety of forms: in small or large melt triangles beneath spreading ridges, in channels, in layers, along a permeability boundary leading to the ridge, at a depth of neutral buoyancy, punctuated, or pervasively over broad areas and either sharply or gradually falling off with depth. This variability in melt character or geometry may explain the previously described variability in LAB depths. The LAB is likely highly variable laterally as are the locations, forms, and amounts of melt, and the LAB is likely dynamic, dictated by small‐scale convection and the dynamics of melt generation and migration. A melt‐defined, dynamic LAB and a weak asthenosphere have broad implications for our understanding of Earth systems and planetary habitability. A weak asthenosphere caused by volatiles or melt could enable plate tectonic style convection, allow multiple scales of convection, and dictate the driving forces of the system. A better understanding of plate tectonics has broad implications for life on Earth. These include mitigating natural disasters caused by plate motions including volcanoes, earthquakes, and tsunamis. In addition, uplift and subsidence of the tectonic plates affects the sea level, impacting the level of the paleo‐oceans and potentially affecting climate change estimates through geologic time. Finally, plate tectonic processes shape the surface morphology of the planet, making continents that enable our existence on land and the ocean basins that hold our free‐surface water. Remarkably, despite large amounts of material transfer into and out of the mantle, and multiple scales of convection, plate tectonics has maintained a hydrosphere over billions of years that is favorable for life.