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This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or G -structures of second order. While their normal Cartan connections are well-known, we use the dressing field method to obtain their local, mostly gauge invariant, connections. Lastly, we recall how to obtain the tractor bundle from conformal structures, and then show that we can define a projective tractor bundle using the same kind of construction. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) exhibit a unique buckling behavior due to their slender tubular geometry and thin-walled circular cross section. This study aims to analyze effect of nonlinear cross-sectional deformation on buckling of CNTs. To accomplish this, CNTs are modeled as beam structures, and the analysis is conducted using the Variational Asymptotic Method (VAM) and a geometrically exact beam theory, as well as nonlinear finite element analysis (FEA). The study considers various loading cases, including pure axial compression and combined loading scenarios, such as bending-axial compression and torsion-axial compression. The results of the study indicate that inclusion of cross-sectional deformation-induced nonlinearity reduces the critical buckling load of CNTs. The reduction is 2–5% for pure axial compression and 10–40% for combined loading cases. The results are validated against existing literature and commercial finite element software, ABAQUS®. Additionally, parametric studies with different slenderness and radius-to-thickness ratios were carried out to further understand the impact of these parameters on buckling of CNTs. Finally, the study presents 3D deformed shapes of CNTs during buckling by combining the results of the 1D analysis and the 2D cross section analysis. The findings show that nonlinearity associated with radius-to-thickness ratio has a significant impact on the cross-sectional ovalisation of CNTs and is critical in evaluating their buckling behavior. This aspect of nonlinearity is often overlooked in continuum modeling methods of CNTs, making this study an important contribution to the field. [ABSTRACT FROM AUTHOR]

In this paper, we perform a comprehensive analysis of conformal symmetries in the generalized Vaidya spacetime and establish several new results. First, a proper conformal Killing vector is shown to exist in the radial direction and interestingly the generalized Vaidya spacetimes with this symmetry are shown to be the subclass of those, which are embeddable in five-dimensional Euclidean space. The general form of the mass function that enables the proper and planar conformal symmetry in the v–r plane is also determined. This treatment also includes earlier results. We also consider the gravitational collapse of these spacetimes with proper planar conformal symmetry in the context of cosmic censorship conjecture. We obtain an interesting and novel result that censorship is always obeyed for these spacetimes, and no locally naked central singularity forms as the end state of the continual collapse. [ABSTRACT FROM AUTHOR]

We study left invariant locally conformally product structures on simply connected Lie groups and give their complete description in the solvable unimodular case. Based on previous classification results, we then obtain the complete list of solvable unimodular Lie algebras up to dimension 5 which carry LCP structures, and study the existence of lattices in the corresponding simply connected Lie groups. [ABSTRACT FROM AUTHOR]

A new antenna array architecture is proposed here to overcome a current bottleneck in phased arrays concerning the enhancement of radiation efficiency and avoidance of scan blindness. In contrast to the conventional approach of using patches with circular or square geometries that exploit 90 ∘ or 180 ∘ rotational symmetry, this work proposes to use waveguide radiating elements based on 120 ∘ symmetry. To implement such symmetry, the tri-ridge aperture is proposed, and its capability to scan widely within a broad frequency bandwidth is demonstrated. A modal analysis is performed to explain the physical phenomena underlying such superior performance. A successful experimental validation is provided by means of a monolithic prototype built in metal additive manufacturing. The measured results show, for the first time, that it is possible to achieve high radiation efficiency and circular polarization when scanning widely in a broad bandwidth. Such an accomplishment constitutes a major achievement in the field of active electronically steered phased arrays, and impacts significantly the capabilities and potential of modern radar and communication systems. [ABSTRACT FROM AUTHOR]

In this manuscript, Conformal Mapping Technique (CMT) is applied to predict the resonant frequency of an Equilateral Triangular Microstrip Antenna (ETMA). The ETMA is mapped into a simple circular geometry with the aid of CMT. The wave equation is solved in the transformed domain using Galerkin technique to obtain the approximate solution of eigenfunction and eigenvalue. Twenty-three measured data are collected from the open literature to validate our theory. Our theoretical results are also compared with several CAD models to show the effectiveness of the present theory. It is found that our proposed theory can predict the resonant frequency of the ETMA with an error of less than 1.5%, whereas those CAD models can produce a large error (sometimes, 10-19% error). Internal field patterns, input impedance, far-field radiation patterns, quality factor, bandwidth gain, and directivity of the ETMA for the dominant mode are also investigated using CMT. [ABSTRACT FROM AUTHOR]

We compute all signatures of P S L 2 ( 7) and P S L 2 ( 1 1) which classify all orientation preserving actions of the groups P S L 2 ( 7) and P S L 2 ( 1 1) on compact, connected, orientable surfaces with orbifold genus ≥ 0. This classification is well-grounded in the other branches of Mathematics like topology, smooth and conformal geometry, algebraic categories, and it is also directly related to the inverse Galois problem. [ABSTRACT FROM AUTHOR]

Thermal metamaterials have garnered significant attention for their potential to manipulate heat flow, leading to the development of various thermal metadevices such as thermal cloaks, concentrators, and rotators. However, the theoretical study of thermal metadevices with nonconformal geometry remains limited due to design and fabrication challenges. This letter proposes a method for designing and manufacturing nonconformal thermal metamaterials using the conformal discrete theory to simplify the anisotropic thermal conductivity tensors. The method involves 3D printing three thermal metadevices (a thermal cloak, concentrator, and rotator) with complex nonconformal geometry. Simulation and experimental results demonstrate the successful implementation of cloaking, concentrating, and rotating functionalities. Moreover, the thermal metadevices still maintained thermal functionality well under the condition of omnidirectional heat flow. This work provides guidance for the design and manufacture of nonconformal thermal metamaterials, as well as their potential applications in other fields such as electrics/magnetics, electromagnetics/optics, and acoustics. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an invariant by image viewpoint changes by applying an important theorem in conformal geometry stating that every surface of the Minkowski space R 3 , 1 leads to an invariant by conformal transformations. For this, we identify the domain of an image to the disjoint union of horospheres ∐ α H α of R 3 , 1 by means of the powerful tools of the conformal Clifford algebras. We explain that every viewpoint change is given by a planar similarity and a perspective distortion encoded by the latitude angle of the camera. We model the perspective distortion by the point at infinity of the conformal model of the Euclidean plane described by D. Hestenesand we clarify the spinor representations of the similarities of the Euclidean plane. This leads us to represent the viewpoint changes by conformal transformations of ∐ α H α for the Minkowski metric of the ambient space. [ABSTRACT FROM AUTHOR]

The present study reports the thermal behavior of multiple jets on a hot concave surface with different nozzle geometries such as circular and elliptical and different orientation. Tests are performed with five different nozzles at different values of nondimensional nozzle to surface distance (z/d = 2–10) and Reynolds number (5000–28,000). Here, the parameter coefficient of variation (COV) is used to estimate the non-uniformity in the local Nu variation. For N-2, the value of $CO{V_{y,non - dim}}$COVy,non−dim is found to be 50–60% higher compared to N-3 at z/d = 2; while at z/d ≥ 8, for N-3, the value of $CO{V_{y,non - dim}}$COVy,non−dim is found to be 10–15% higher compared to N-2. The higher temperature uniformity ($CO{V_{x,non - dim}}$COVx,non−dim) is noted in the fountain region compared to impingement region for the circular and elliptical nozzles. The thermal performance of elliptical jets is found to be sensitive toward the jet orientation at lower z/d values. The magnitude of temperature non-uniformity decreases with the increase in the z/d values. Among the tested nozzles, Nozzle N-2 consistently demonstrates superior performance across all nozzle-to-plate distances and with an increase in the z/d value improvement with nozzle N-2 reduces. [ABSTRACT FROM AUTHOR]

Advancements in cancer treatment have underscored the importance of understanding the intricate interplay between tumour microenvironments and drug delivery mechanisms. This research delves into the dynamic relationship between blood-mediated drug transport and the density of the tumour matrix within solid tumours. The study seeks to unravel the effects of varying tumour matrix densities on drug transport characteristics and, subsequently, on the perfusion efficacy of therapeutic agents. Through computational fluid dynamics simulation, this research elucidates the intricate balance between transport dynamics and drug distribution within solid tumours. A simple two-dimensional circular geometry has been chosen to represent the tumour and the surrounding microcirculation. The drug molecules diffuse into the interstitial tumour matrix through the microcirculation and then from the matrix into the tumour cells. The matrix is considered to be a porous medium, and the porosity of the media has been varied to simulate the effect of the matrix density on drug perfusion. Simulation results have shown that the density significantly affects the transport flux of the drug through the tumour matrix. The outcomes of this research hold potential implications for optimising drug delivery strategies in cancer therapy possibly by designing drug molecules that can effectively diffuse through dense tumour matrices. [ABSTRACT FROM AUTHOR]

Experimental results from several tokamaks suggest a strong impact of divertor density regimes on turbulent transport in the edge plasma. Reciprocally, the change in transverse transport and SOL width affects the access to density regimes, making it a fundamental topic for heat exhaust issue. Such phenomenology is highly nonlinear and can only be approached quantitatively using numerical simulations treating turbulence and neutrals recycling physics self‐consistently. In this study, the SOLEDGE3X edge multi‐fluid code is used to investigate the mutual interaction between edge plasma turbulence and neutrals recycling. A fluid neutrals model based on the assumption of a charge‐exchange‐dominated plasma‐neutral interaction has been implemented. Two simulations in circular geometry are compared: one without neutrals, where the particle flux is driven by a constant in flux from the core region, and the other one with neutrals recycling included in which the particle input to the system is self‐consistently injected by a gas puff from the midplane. The presence of the neutrals triggers three types of perturbations on the plasma: a local and non‐axisymmetric one driven by the gas puff, a global perturbation affecting both profiles and turbulence properties in the whole domain, and a local one in the vicinity of the limiter where recycling occurs. The largest effect of the inclusion of self‐consistent neutrals recycling is a large‐scale reorganization of the plasma profiles and turbulence properties due to the dissociation of particle and energy fluxes. These effects are expected to be more important at higher densities regimes or in diverted configuration. [ABSTRACT FROM AUTHOR]

In this paper, we establish some improved weighted Sobolev trace inequalities H 1 (ρ 1 − 2 σ , n + 1) ↪ L q ( n) under the zero higher order moments constraint via the concentration compactness principle, where ρ is a defining function of n + 1 and σ ∈ (0 , 1). This relates to the fractional (conformal) Laplacians and related problems in conformal geometry. We construct some test functions and show that the inequality is almost optimal when σ ∈ (0 , 1 2 ]. [ABSTRACT FROM AUTHOR]

Despite the considerable research interest in InGaN‐based microdisk lasers, owing to their unique circular geometry distinct from vertical cavity surface‐emitting lasers (VCSEL) or edge‐emitting lasers, commercial products remain scant due to deficient performance under electrical injection. This study proposes an innovative method integrating a thin‐film configuration with a metallic undercut, significantly augmenting optical confinement, overlap factor, and thus lasing performance. This approach results in a diminished lasing threshold from 1500 to 670 Wcm−2 and a record high quality (Q) factor of 10100 under electrical injection. Strain relaxation in the metallic undercut, identified via scanning near‐field optical microscopy (SNOM), beneficially mitigates the Quantum Confined Stark Effect (QCSE), boosting the internal quantum efficiency of the laser. Furthermore, a beneficial blue‐shift in the emission spectrum aligns with the lasing peak, strengthening the Q factor. A tactfully implemented recessed top contact enables electrical injection lasing without optical performance compromise. The study provides invaluable insights for future microdisk laser technology advancements, potentially leading to specialized functionalities, including quantum optics, thereby opening new avenues for research and applications in this field. [ABSTRACT FROM AUTHOR]

The purpose of this work is to study the conformal geometry of complete quasi Yamabe gradient solitons, which correspond to an interesting generalization for gradient Yamabe solitons. In this sense, we present a rigidity result for complete quasi Yamabe gradient solitons with constant scalar curvature. Moreover, we prove that quasi Yamabe gradient solitons can be conformally changed to constant scalar curvature. [ABSTRACT FROM AUTHOR]

To improve our understanding of Bacillus subtilis growth and biofilm formation under different environmental conditions, two versions of a microfluidic reactor with two channels separated by a polydimethylsiloxane (PDMS) membrane were developed. The gas phase was introduced into the channel above the membrane, and oxygen transfer from the gas phase through the membrane was assessed by measuring the dissolved oxygen concentration in the liquid phase using a miniaturized optical sensor and oxygen-sensitive nanoparticles. B. subtilis biofilm formation was monitored in the growth channels of the microbioreactors, which were designed in two shapes: one with circular extensions and one without. The volumes of these microbioreactors were (17 ± 4) μL for the reactors without extensions and (28 ± 4) μL for those with extensions. The effect of microbioreactor geometry and aeration on B. subtilis biofilm growth was evaluated by digital image analysis. In both microbioreactor geometries, stable B. subtilis biofilm formation was achieved after 72 h of incubation at a growth medium flow rate of 1 μL/min. The amount of oxygen significantly influenced biofilm formation. When the culture was cultivated with a continuous air supply, biofilm surface coverage and biomass concentration were higher than in cultivations without aeration or with a 100% oxygen supply. The channel geometry with circular extensions did not lead to a higher total biomass in the microbioreactor compared to the geometry without extensions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of fully nonlinear equations on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and establish the existence results. Our results can be viewed as an extension of previous results given by Gursky–Viaclovsky and Li–Sheng. [ABSTRACT FROM AUTHOR]

This paper elucidates the design of an S-band conformal loop filter. A combination of loop filter loaded with split ring resonator loading is proposed for the Band Pass Filter (BPF) in the proposed design. The reduced insertion loss and improved fractional bandwidth are achieved using the symmetrical tuning stubs in the loop filter. The operating range of the proposed filter in the S-band is between 2.12 GHz to 2.24 GHz, with a fractional bandwidth of 5.5% and a reduced insertion loss of 1.1 dB. The conformal geometry has been simulated on an EM solver, and the simulation results are analyzed. The simulation results of conformal geometry show an excellent match with the planar structure. The proposed filter is further fabricated, and the S-parameters are measured. The Sparameter results of the realized filter from simulations match closely with those from measurements of prototypes but with a small shift in frequency. The measured filter operates at 2.21 GHz to 2.41 GHz with a Fractional Band-Width (FBW) of 8.6% and a minimum insertion loss of 1.4 dB. [ABSTRACT FROM AUTHOR]

This study presents a novel absorption cell with a circular geometry that can be integrated into microfluidic devices for optical spectroscopy applications. The absorption cell is made of PDMS/SU8 and offers an optical path length that is 8.5 times its diameter, resulting in a significant increase in the sensitivity of the measurements. Overall, this design provides a reliable and efficient solution for optical spectroscopy in microfluidic systems, enabling the precise detection and analysis of small quantities of analytes. [ABSTRACT FROM AUTHOR]

This paper proposed a model to estimate sensor spacing and a new deployment geometry and evaluates the performance of an ultrasonic sensor array according to the deployment geometry. The proposed spacing estimation model is based on the probability of false detection alarms, the aperture angle, and the sensor range. A design technique has been proposed for elliptical deployment geometry, giving expressions for its parameters to help designers of experimental prototypes to reduce errors related to sensor disposition. A practical method for calibrating ultrasonic sensors has been designed to reduce measurement errors. An experiment was conducted, and the data were analysed using a statistical significance test. An evaluation of the performance of an ultrasonic sensor array with linear and circular deployment geometry with and without our method was done and then compared to our proposed deployment geometry which was combined with the proposed method. The result of the statistical significance test shows that elliptical deployment geometry combined with the suggested strategy works better than circular and linear geometry. This applies to performance such as linear correlation, RMSE, MAPE, and standard deviation. These results show the importance of the choice of deployment geometry for application. [ABSTRACT FROM AUTHOR]

In this paper, a compact low-profile dual-band wearable textile antenna is proposed for on-body and off-body communications. The presented antenna works efficiently in the 5G n79 frequency band (4.4 − 5 GHz) and the ISM band (5.725 − 5.875 GHz). The designed antenna has an ultra-wide impedance bandwidth of 2.01 GHz and peak realized gains of 10.5 dBi and 12 dBi at 4.5 GHz and 5.8 GHz, respectively. The antenna has a small footprint (π × 0.3λ02), which is inspired by circular fractal geometry. The performance of the presented wearable antenna is evaluated at various body parts, including the arm, wrist, and chest. The link margin is evaluated in the on-body and off-body communication scenarios, i.e., communication with the implantable antenna and the outside-body antenna, which is 80 dB and 65 dB at 4.5 GHz and 5.8 GHz, respectively. The 1 gm/10 gm specific absorption rate values at 4.5 GHz and 5.8 GHz are 0.12/0.098 and 0.11/0.082, respectively, which are significantly lower than the standard values, making the proposed antenna suitable for modern wearable applications. [ABSTRACT FROM AUTHOR]

Data fusion plays a crucial part in performance evaluation processes in multisensor systems; thus, it is important to use an effective technique to cut down on errors. By improving the sensors' location and their capacity to adjust to the deployment geometry, the paper's technique for reducing data fusion errors is proposed. The preprocessing stage of data is also included in the suggested technique, which starts with the design of the data‐collecting device and ends with a hybrid model algorithm. Particle swarm optimization and artificial neural network methods are combined in the hybrid algorithm. Preprocessing is based on the compensation and adjustment factors to ensure data gathering synergy. A true experimental apparatus was designed under three different deployment geometries, comprising five ultrasonic sensors constituting a multisensor system and a hardwood target (Triplochiton scleroxylon and Milicia excelsa). The results obtained show that the suggested deployment geometry has mean absolute percentage errors of 3.97, mean square errors of 0.182, and mean absolute errors of 0.045 which are lower than those associated with the deployment configurations found in the literature. The results of the proposed method show an overall detection accuracy in linear deployment geometry of 97.308%. Then, the circular deployment geometry obtained a detection accuracy of 97.005%. Finally, elliptical deployment geometry obtained a detection accuracy of 98.745%. These results show that the proposed method better predicts the range of a target with a lower error rate than conventional methods. [ABSTRACT FROM AUTHOR]

We perform Rayleigh‐wave group‐velocity dispersion measurements from 14,706 regional‐waveforms at periods of 10–120 s, followed by ray‐based tomography and inversion to obtain 3D‐Vs structure of the crust and upper mantle. The group‐velocity maps have 3–5° lateral resolution, and Vs models have ∼3%–7% average‐Vs uncertainty. The Moho depth is assigned to the bottom of the steepest‐gradient layer with Vs between 4.1 and 4.5 km s−1, and the sedimentary‐layers have Vs ≤ 2.9 km s−1. Indian cratons have high average‐crustal‐Vs of 3.6–3.9 km s−1 and thickness of 40–50 km. The intervening rift‐basins are filled with low‐Vs sedimentary‐rocks. The Himalayan Foreland Basin has along‐arc variation in sedimentary thickness with the thickest layer (8–10 km) beneath the Eastern Ganga Basin. The Indian lithospheric mantle has high‐Vs (>4.4 km s−1), and along with high‐Vs crust attest to a cold, rigid lithosphere. This lithosphere underthrust entire Western Tibet and up to the Qiangtang Terrane in Central‐Eastern Tibet. The top of the underthrusting Indian‐crust is marked by lower‐Vs and thrust‐fault earthquakes. The shallow crust beneath Tibet (0–10 km) has high‐Vs and is mechanically strong; whereas, the mid‐crust (20–40 km) has ∼5%–10% low‐Vs anomalies due to radiogenic/shear heating within the thickened crust. This layer is weak and decouples the deformation of the shallow and deep layers. Low‐Vs upper‐mantle with deeper high‐Vs layer is present beneath the Deccan and Raj‐Mahal Traps, suggesting plume‐volcanism related thermal anomaly and refertilization of the upper mantle. The intra‐cratonic basins with circular geometry, high‐Vs lithosphere and no basement earthquakes, possibly formed by thermal subsidence of isostatically‐balanced cratonic lithosphere. Plain Language Summary: We perform 1D‐path‐average surface‐wave dispersion measurements for 14,706 regional ray‐paths (10 and 120 s period), and combine these into 2D variation maps, followed by modeling to obtain 3D shear‐wave velocity structure beneath India, Himalaya and Tibet. The 2D maps have 3–5° lateral resolution and the 3D structure has 5%–7% average‐velocity uncertainty. The Indian Cratons have high average crustal‐velocity and crustal thickness of 40–50 km, and are underlain by high‐velocity upper mantle. The intervening rift‐basins are filled with lower‐velocity sedimentary‐rocks. The sedimentary layer thickness in the Himalayan Foreland Basin varies along‐arc and is thickest (8–10 km) beneath the Eastern Ganga Basin. The high‐velocity (cold, rigid) Indian plate underthrust entire Western Tibet and up to the Qiangtang Terrane in Central‐Eastern Tibet. A mid‐crustal low‐velocity‐layer is present beneath Tibet, which is weak and decouples the deformation of the shallow and deep layers. The upper‐mantle beneath Deccan and Raj‐Mahal Traps has low‐velocity overlying a high‐velocity layer suggesting plume‐volcanism related thermal anomaly. From the velocity‐structure and geometry we speculate about the origin of the intra‐cratonic Tarim and Eastern Tajik Basins. Key Points: Indian Cratonic lithosphere (ICL) has high average‐crustal Vs 3.6–3.9 km s−1, upper mantle Vs > 4.4 km s−1 and crustal thickness of 40–50 kmLow Vs upper‐mantle with a deeper high Vs layer beneath Deccan Traps suggest plume‐volcanism related thermal anomaly/refertilizationICL underthrusts entire W Tibet and up to the Qiangtang Terrane beneath Central‐E Tibet with a mid‐crustal low‐velocity anomaly of 5%–10% [ABSTRACT FROM AUTHOR]

Over forty years ago, Paneitz, and independently Fradkin and Tseytlin, discovered a fourth-order conformally invariant differential operator, intrinsically defined on a conformal manifold, mapping scalars to scalars. This operator is a special case of the so-termed extrinsic Paneitz operator defined in the case when the conformal manifold is itself a conformally embedded hypersurface. In particular, this encodes the obstruction to smoothly solving the five-dimensional scalar Laplace equation, and suitable higher dimensional analogs, on conformally compact structures with constant scalar curvature. Moreover, the extrinsic Paneitz operator can act on tensors of general type by dint of being defined on tractor bundles. Motivated by a host of applications, we explicitly compute the extrinsic Paneitz operator. We apply this formula to obtain: an extrinsically-coupled  Q -curvature for embedded four-manifolds, the anomaly in renormalized volumes for conformally compact five-manifolds with negative constant scalar curvature, Willmore energies for embedded four-manifolds, the local obstruction to smoothly solving the five-dimensional singular Yamabe problem, and new extrinsically-coupled fourth- and sixth-order operators for embedded surfaces and four-manifolds, respectively. [ABSTRACT FROM AUTHOR]

This work aims to develop an effective method for evaluating the stress concentration at the tip of permeable interfacial cracks near a circular hole in functionally graded piezoelectric bi-materials. The structure is loaded by anti-plane incident SH-wave and all material parameters are assumed to obey exponential variations. Fracture analysis is performed by the Green function method, which is used to solve the boundary conditions problem. The mechanical model of the cracks is constructed by crack-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack tips can be derived. The validity of the present method is verified by comparison with references. Numerical cases reveal parametric dependence of DSIFs on the geometry of circular holes and cracks, the characteristics of the incident waves and the inhomogeneity of materials. The method proposed in this paper can circumvent the limitations of using dual integral equations to deal with asymmetric defects and opens up a new way for the research on fracture problems in functionally graded piezoelectric materials with more complex defects. [ABSTRACT FROM AUTHOR]

This work is devoted to the consideration of the behavior of conformal quasi-harmonics that characterize the behavior of vortex domains within the framework of the conformal mapping of the Vaitkevichius-Volk function. A conformal analysis of the automorphic function of this conformal mapping was carried out and the pattern of existence of the connectivity of the function with the core of the lemniscate strip was revealed. The mechanism of formation of isogonal potential and isothermal vortex fields of function (1) on a circle of a Riemannian two-sheet plane was studied. A new characteristic is given to the complex values of the divergence and shear of these fields. [ABSTRACT FROM AUTHOR]

We study self-similar viscous fingering for the case of divergent flow within a wedge-shaped Hele-Shaw cell. Previous authors have conjectured the existence of a countably infinite number of selected solutions, each distinguished by a different value of the relative finger angle. Interestingly, the associated solution branches have been posited to merge and disappear in pairs as the surface tension decreases. For the first time, we demonstrate how the selection mechanism can be derived based on exponential asymptotics. Asymptotic predictions of the finger-to-wedge angle are additionally given for different sized wedges and surface-tension values. The merging of solution branches is explained; this feature is qualitatively different to the case of classic Saffman-Taylor viscous fingering in a parallel channel configuration. Moreover, because the asymptotic framework does not highly depend on specifics of the wedge geometry, the proposed theory for branch merging in our self-similar problem likely relates much more widely to tip-splitting instabilities in time-dependent flows in circular and other geometries, where the viscous fingers destabilise and divide in two. [ABSTRACT FROM AUTHOR]

Understanding the stress distribution around shallow magma chambers is vital for forecasting eruption sites and magma propagation directions. To achieve accurate forecasts, comprehensive insight into the stress field surrounding magma chambers and near the surface is essential. Existing stress models for pressurized magma chambers often assume a homogenous elastic half‐space or a heterogeneous crust with varying mechanical properties in horizontal layers. However, as many volcanoes have complex, non‐horizontal, and heterogeneous layers, we enhance these assumptions by considering mechanically stratified layers with varying dips. We employed the Finite Element Method (FEM) to create numerical models simulating three chamber geometries: circular, sill‐like and prolate. The primary condition was a 10 MPa excess pressure within the magma chamber, generating the stress field. Layers dips by 20‐degree increments, with differing elastic moduli, represented by stiffness ratios of the successive layers (EU/EL) ranging from 0.01 to 100. Our findings validate prior research on heterogeneous crustal modeling, showing that high stiffness ratios disrupt stress within layers and induce local stress rotations at mismatched interfaces. Layer dip further influences stress fields, shifting the location of maximum stress concentration over varying distances. This study underscores the significance of accurately understanding mechanical properties, layer dip in volcanoes, and magma chamber geometry. Improving forecasting of future eruption vents in active volcanoes, particularly in the Andes with its deformed, folded, and non‐horizontal stratified crust, hinges on this knowledge. By expanding stress models to incorporate complex geological structures, we enhance our ability to forecast eruption sites and magma propagation paths. Plain Language Summary: Understanding crustal stress distribution within active volcanoes is crucial to forecast how magma will propagate inside a volcano and where and when a volcanic eruption may occur. Currently, the models used to understand the stress field within volcanoes assume that the Earth's crust is made of the same materials or with horizontally layered different materials. Both cases are seldom correct. Volcanoes often have layers that are both mechanically diverse and dipping at different angles and directions. To improve forecast models, we considered a crust with layers of different mechanical properties and with variable dips. We used numerical models to simulate 3 pressurized magma chamber geometries. We changed the dip of the layers and investigated how the rocks respond to the applied pressure. We found that when the layers are inclined they respond differently to the applied pressure and the possible location of a new eruption is displaced by up to 2 km, compared to the expected location using common modeling protocols. This research improves volcano understanding, especially in regions like the Andes, where the crust is often made by geologically diverse dipping layers. By making our models more realistic we can better forecast where eruptions may occur. Key Points: FEM models used to analyze the influence of layer dip on crustal stresses resulting from magma chamber pressurizationPeak surface tensile stresses can shift by more than 2 km, deviating from homogeneous elastic half‐space assumptionsThe effect is more pronounced with an idealized circular chamber when compared to a sill‐like chamber [ABSTRACT FROM AUTHOR]

We show that the Gauduchon metric g_0 of a compact locally conformally product manifold (M,c,D) of dimension greater than 2 is adapted, in the sense that the Lee form of D with respect to g_0 vanishes on the D-flat distribution of M. We also characterize adapted metrics as critical points of a natural functional defined on the conformal class. [ABSTRACT FROM AUTHOR]

In this paper, we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary. We prove the a priori estimates for solutions to these equations and establish an existence result. [ABSTRACT FROM AUTHOR]

The notion of discrete conformality proposed by Luo (2004) and Bobenko et al. (2015) on triangle meshes has rich mathematical theories and wide applications. Gu et al. (2019) and Wu and Zhu (2020) proved that the discrete uniformizations approximate the continuous uniformization for closed surfaces of genus ≥ 1 , given that the approximating triangle meshes are reasonably good. In this paper, we generalize this result to the remaining case of genus zero surfaces, by reducing it to planar cases via stereographic projections. [ABSTRACT FROM AUTHOR]

A locally conformally product (LCP) structure on compact manifold M is a conformal structure c together with a closed, non-exact and non-flat Weyl connection D with reducible holonomy. Equivalently, an LCP structure on M is defined by a reducible, non-flat, incomplete Riemannian metric h D on the universal cover M ̃ of M , with respect to which the fundamental group π 1 (M) acts by similarities. It was recently proved by Kourganoff that in this case (M ̃ , h D) is isometric to the Riemannian product of the flat space ℝ q and an incomplete irreducible Riemannian manifold (N , g N). In this paper, we show that for every LCP manifold (M , c , D) , there exists a metric g ∈ c such that the Lee form of D with respect to g vanishes on vectors tangent to the distribution on M defined by the flat factor ℝ q , and use this fact in order to construct new LCP structures from a given one by taking products. We also establish links between LCP manifolds and number field theory, and use them in order to construct large classes of examples, containing all previously known examples of LCP manifolds constructed by Matveev–Nikolayevsky, Kourganoff and Oeljeklaus–Toma (OT-manifolds). [ABSTRACT FROM AUTHOR]

In a recent work [On factorization and vector bundles of conformal blocks from vertex algebras, preprint (2019), arXiv:1909.04683], Damiolini et al. showed that for a C 2 -cofinite rational vertex operator algebra , sheaves of conformal blocks are locally free and satisfy the factorization property. In this paper, we prove that if is C 2 -cofinite, the sewing of conformal blocks is convergent. This proves a conjecture proposed by Zhu [Global vertex operators on Riemann surfaces, Commun. Math. Phys. 165(3) (1994) 485–531] and Huang [Some open problems in mathematical two-dimensional conformal field theory, preprint (2016), arXiv:1606.04493], generalizing previous results on the convergence of products, iterates, and traces (but not pseudo-traces) of vertex operators and intertwining operators in [Y. Zhu, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc. 9(1) (1996) 237–302; Y. Z. Huang, A theory of tensor products for module categories for a vertex operator algebra, IV, J. Pure Appl. Algebra 100(1–3) (1995) 173–216; Y. Z. Huang, Differential equations, duality and modular invariance, Commun. Contemp. Math. 7(05) (2005) 649–706; Y. Z. Huang, J. Lepowsky and L. Zhang, Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps, preprint (2011), arXiv:1110.1929] and on the convergence of projective factors related to the central charge of the Virasoro algebra in [Y. Z. Huang, Two-Dimensional Conformal Geometry and Vertex Operator Algebras, Vol. 148 (Springer Science & Business Media, 1997)]. [ABSTRACT FROM AUTHOR]

We investigate geometric aspects of complete spacelike mean curvature flow solitons of codimension one in a generalized Robertson–Walker (GRW) spacetime $-I\times _{f}M^n$ , with base $I\subset \mathbb R$ , Riemannian fiber $M^n$ and warping function $f\in C^\infty (I)$. For this, we apply suitable maximum principles to guarantee that such a mean curvature flow soliton is a slice of the ambient space and to obtain nonexistence results concerning these solitons. In particular, we deal with entire graphs constructed over the Riemannian fiber $M^n$ , which are spacelike mean curvature flow solitons, and we also explore the geometry of a conformal vector field to establish topological and further rigidity results for compact (without boundary) mean curvature flow solitons in a GRW spacetime. Moreover, we study the stability of spacelike mean curvature flow solitons with respect to an appropriate stability operator. Standard examples of spacelike mean curvature flow solitons in GRW spacetimes are exhibited, and applications related to these examples are given. [ABSTRACT FROM AUTHOR]

Additive friction extrusion deposition (AFED) is a recently developed additive manufacturing technique that promises high deposition rates at low forces. Due to the novelty of the process, the underlying phenomena and their interactions are not fully understood, and in particular, the processing strategy and tool design are still in their infancy. This work contributes to the state-of-the-art of AFED through a comprehensive analysis of its working principles and an experimental program, including a representative sample component. The working principle and process mechanics of AFED are broken down into their individual components. The forces and their origins and effects on the process are described, and measures of process efficiency and theoretical minimum energy consumption are derived. Three geometrical features of the extrusion die were identified as most relevant to the active material flow, process forces, and deposition quality: the topography of the inner and outer circular surfaces and the geometry of its extrusion channels. Based on this, the experimental program investigated seven different tool designs in terms of efficiency, force reduction, and throughput. The experiments using AA 6061-T6 as feedstock show that AFED is capable of both high material throughput (close to 550 mm3/s) and reduced substrate forces, for example, the forces for a run at 100 mm3/s remained continuously below 500 N and for a run at 400 mm3/s below 3500 N. The material flow and microstructure of AFED were assessed from macro-sections. Significant differences were found between the advancing and retracting sides for both process effects and material flow. Banded structures in the microstructure show strong similarities to other solid-state processes. The manufacturing of the sample components demonstrates that AFED is already capable of producing industrial-grade components. In mechanical tests, interlayer bonding defects resulted in more brittle failure behavior in the build direction of the structure, whereas in the horizontal direction, mechanical properties corresponding to a T4 temper were achieved. [ABSTRACT FROM AUTHOR]

Bioinspiration has widely been demonstrated to be a powerful approach for the design of innovative structures and devices. Recently, this concept has been extended to the field of elasticity, dynamics, and metamaterials. In this paper, we propose a seashell-inspired metasensor that can simultaneously perform spatial frequency mapping and act as a polarizer. The structure emerges from a universal parametric design that encompasses diverse spiral geometries with varying circular cross sections and curvature radii, all leading to tonotopic behavior. Adoption of an optimization process leads to a planar geometry that enables us to simultaneously achieve tonotopy for orthogonally polarized modes, leading to the possibility to control polarization as well as the spatial distribution of frequency maxima along the spiral axis. We demonstrate the versatility of the device and discuss the possible applications in the field of acoustics and sensing. [ABSTRACT FROM AUTHOR]

Scour around the bridge piers is the main cause of bridge failure below any bridge pier placed within the waterways. It is more than hundred years back a number of researchers described the vortex shedding phenomenon and the resulting Aeolian tones from a circular cylinder. Since then there have been a large number of investigations dealing with various aspects of this phenomenon. In many practical works and situations, flow takes place around more than one obstruction and objects in close proximity. Invariably in all these cases, interference effects occur and the forces on the obstructions are much influenced by these effects. These effects play a key role in the structures like flow-induced vibration of TV and transmission towers, and in many other practical situations. In this research paper the changes in the flow field that occur due to the interference effects are shown, analysed and the results as given in literature are compared with the present experimental work. The features have been brought out in this paper mainly make use of stand and geometry of circular cylinders in close proximity and the flow part of geometry in side by side arrangement. [ABSTRACT FROM AUTHOR]

We report the close form expressions of the photon number statistics for a generalized coherent state and a generalized photon-added coherent state, which are shown to be crucial for proposing a variety of quantum scissor operations. The analytically obtained distributions are also capable of predicting the precise laser intensity windows for realizing a variety of quantum scissors. Truncating a photon added state overcomes the selection rule of obtaining the lower order Fock states. Photon addition also enables us to obtain a higher order Fock state in a lower order superposition. The importance of circular geometry is also demonstrated for engineering such quantum scissors. [ABSTRACT FROM AUTHOR]

Internal heating/cooling using roughness elements such as ribs are a promising passive heat-transfer enhancement technique for many thermal applications. The curved ribs are roughness elements that boost the fluid residence time and enhance the thermal-hydraulic performance of the system. In the present study, curved ribs of different cross-sections were fitted at the inner wall of the circular tube to intensify convection heat transfer to the fluid flowing through it. Novel curved ribs of inline configurations of different shapes and geometrical parameters were numerically studied for convection heat transfer using a three-dimensional computational model. The finite volume method discretizes the tube fluid flow domain's mass, momentum, and energy equations. The local heat transfer enhancement over the tube surface is 2.75 times the smooth tube flow, with Reynolds numbers ranging from 10,000 to 50,000. The cost-effectiveness of this heat transfer enhancement method was quantified using a thermohydraulic performance evaluation factor. This factor accounts for the increased heat transfer at the same pumping power and the same available surface area for heat dissipation. The average heat transfer enhancement at the same Reynolds number and pumping power was found to be 120% to 450% and 98% to 260% of the smooth tube flow. [ABSTRACT FROM AUTHOR]

We consider the sphere S2n+1$\mathbb {S}^{2n+1}$ equipped with its standard contact form. In this paper, we construct explicit contact forms on S2n+1∖S2k+1$\mathbb {S}^{2n+1}\setminus \mathbb {S}^{2k+1}$, which are conformal to the standard one and whose related Webster metrics have constant Webster curvature; in particular, it is positive if 2k

This article discusses various concepts in differential geometry of space curves, including evolutes, involutes, osculating circles, and pseudo-evolutes. It explores the properties and interrelations of these concepts, providing mathematical formulas and propositions to support its claims. The article highlights the relevance of these concepts in modern mathematics, particularly in the study of completely integrable systems and curved origami. The authors acknowledge the support they received for their research. [Extracted from the article]

We define a conformally invariant action on gauge connections on a closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the gauge connection. The Euler–Lagrange equations of , with respect to variation of the gauge connection, provide a higher-order conformally invariant analogue of the (source-free) Yang–Mills equations. For any gauge connection A on M , we define (A) by first defining a Lagrangian density associated to A. This is not conformally invariant but has a conformal transformation analogous to a Q -curvature. Integrating this density provides the conformally invariant action. In the special case that we apply to the conformal Cartan-tractor connection, the functional gradient recovers the natural conformal curvature invariant called the Fefferman–Graham obstruction tensor. So in this case, the Euler–Lagrange equations are exactly the "obstruction-flat" condition for 6-manifolds. This extends known results for 4-dimensional pseudo-Riemannian manifolds where the Bach tensor is recovered in the Yang–Mills equations of the Cartan-tractor connection. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlinear elliptic equations in the Krylov type, which can be viewed as a generalization of the Hessian equation for Schouten tensor. After a conformal change, we considered the Dirichlet problem for a modified Schouten tensor in the smooth closed Riemannian manifold with smooth boundary. A unique k-admissible solution can be assured under some suitable settings. [ABSTRACT FROM AUTHOR]

In this note we introduce the Dirac-Einstein equations on a spin manifold and we review some recent results, in particular: the compactness of the variational solutions, the classification of the Palais-Smale sequences for the related conformal problem, and finally some existence results.

This study comprehensively analyzes five circular-shaped flow field configurations (one-path, two-path, two-channel, two-segment, and four-segment serpentine), using membrane electrode assembly (MEA) area of 38.5 cm2. Here, it aims to identify the optimal pattern in terms of velocity, pressure, liquid saturation, temperature, and current density distribution. Further, a comparison is conducted between the uniformity index, polarization curves, and average membrane temperature curves of various cases. Using a finite element method, a three-dimensional, non-isothermal, two-phase model is developed based on the conservation equations of mass, momentum, electric charge, energy, and species. To confirm modelling reliability, the numerical results have been validated and demonstrated a strong match with the experimental data. Findings indicate that the one-path, followed by the two-path serpentine pattern, yield the most favorable flow distribution and temperature uniformity within the PEMWE. Conversely, the four-segment serpentine flow pattern results in the least desirable outcomes. At a cell voltage of 2.1 V, the uniformity index of liquid saturation, temperature and current density and average membrane temperature for one-path and two-path serpentine patterns exhibit reductions of 70 and 29 %, 95.5 and 95.2 %, 33 and 31 %, and 9.1 and 6 K, respectively, compared to four-segment serpentine design. Moreover, the four-segment, two-segment, and two-path serpentine flow patterns exhibit optimal performance in terms of polarization curves. • A three-dimensional, non-isothermal, two-phase model is developed for PEMWE. • Five proposal circular-shaped flow patterns for PEMWE have been investigated. • A comprehensive comparison of diverse circular flow patterns is introduced. • Different parameter distributions are studied across the proposal flow patterns. • The uniformity index, polarization curves, and MEA temperature are studied. [ABSTRACT FROM AUTHOR]