Minimum Radius Research Articles

Extremal spectral radii of uniform supertrees

For a hypergraph $\mathcal{G}=(V, E)$ consisting of a nonempty vertex set $V=V(\mathcal{G})$ and an edge set $E=E(\mathcal{G})$, its adjacency matrix $\mathcal {A}_{\mathcal{G}}=[(\mathcal {A}_{\mathcal{G}})_{ij}]$ is defined as $(\mathcal {A}_{\mathcal{G}})_{ij}=\sum_{e\in E_{ij}}\frac{1}{|e| - 1}$, where $E_{ij} = \{e \in E : i, j \in e\}$. The spectral radius of a hypergraph $\mathcal{G}$, denoted by $\rho(\mathcal {G})$, is the maximum modulus among all eigenvalues of $\mathcal {A}_{\mathcal{G}}$. In this paper, we represent some results on the spectral radius changing under some graphic structural perturbations. With these results, among all $k$-uniform ($k\geq 3$) supertrees with fixed number of vertices, the supertrees with the maximum, the second maximum, and the minimum spectral radius are completely determined, respectively.

Modeling and Analysis of Inter-Panel Slipping for the Design of Rolled Gossamer Arrays

Abstract Many deployable satellite systems benefit from having low mass and high surface area, which has led to the proliferation of gossamer structures in space-based applications. Gossamer structures are characterized by lightweight, low-stiffness membranes, which can flex and roll to compactly stow. An effect of rolling a gossamer structure is that there is a tangential separation along adjacent panels as they roll, resulting in relative motion between panels. To aid designers in predicting and accommodating this motion, a method for modeling the slippage between adjacent panels that occurs while rolling is presented. This analytical slippage model and algorithm is a function of (1) the number of panels, (2) the thickness of each panel, (3) the length of each panel, and (4) the minimum bend radius of the material. It is shown that the thickness and length have a positive correlation with increased slippage, whereas the number of panels and minimum bend radius have a negative correlation with increased slippage. This model allows designers to predict both the magnitude of slippage that occurs where panels meet, as well as the relative range of slippage that occurs within the whole pattern. With these predictions, an appropriate strategy can be selected for accommodating this motion.

Thin-shell wormholes with non-collapsing dark energy throats connecting flat Minkowski spacetimes

This research revisits the thin-shell wormhole connecting two Minkowski spacetimes — originally introduced by Matt Visser. Upon setting a particular timelike hypersurface with a de-sitter-induced line element, the corresponding thin-shell wormhole (TSW) possesses a minimum radius and a uniform surface energy–momentum tensor in the form of dark energy. The bounded from below radius for the throat implies that it does not collapse. The r−τ profile curve of the hypersurface is a Catenary in r−τ plane where r and τ are the radial coordinate and the proper time on the throat, respectively. It is also shown that while the throat is dynamic, the surface energy–momentum tensor of the dark energy is in the form of an effective cosmological constant in the spherically symmetric TSW. The 4-dimensional cylindrically symmetric TSW with a similar throat profile shares the same features as its spherical counterpart, however, its uniform surface energy–momentum tensor does not mimic an effective cosmological constant. The higher-dimensional generalization of the spherically symmetric TSW admits the same properties as in the 4-dimensional one.

Analytical properties and solutions for the synchronous pulsating bubble clusters distributed on a spherical surface

The present work concerns with the nonlinear dynamics for the synchronous pulsating bubble clusters uniformly distributed on a spherical surface. First, the governing equation for such clusters with 4/6/8/12/20 coupled bubbles are established. Second, the maximum and minimum radii for the gas-filled bubble clusters are analyzed according to the first integral. Third, by introducing suitable nonlocal transformations, two novel equivalent parametric analytical solutions in the form of Weierstrass elliptic function are constructed for the gas-filled bubble clusters for a specific polytropic exponent κ=3/2 without considering the surface tension, and based on which we immediately derive the parametric analytical solution for the corresponding vapor bubble clusters. Further, to consider the case of arbitrary polytropic exponent and surface tension, we develop a direct approach to construct the parametric analytical solution using Jacobi elliptic function for gas-filled bubble clusters. It is shown that, the behaviors and results for the bubble clusters will degenerate to the corresponding ones for single bubbles as the radius of the bubble cluster approaches infinity. In addition, on the basis of the analytical results, dynamic properties and motion laws of the bubble clusters are also discussed.

СОГЛАСОВАНИЕ ГЕОМЕТРИЧЕСКИХ ХАРАКТЕРИСТИК ФАКТИЧЕСКОГО ПОВОРОТА КОЛЁСНОЙ МАШИНЫ

Based on the above calculation scheme of controlled curvilinear motion of a wheeled vehicle, it was revealed that the steering trapezoid causes some discrepancy between the kinematics of real and correct rotation. It is established that when adjusting the track width of the machine, the kinematic mismatch between the optimal rolling conditions of the wheels increases, and, consequently, the calculated dependences of the parameters of the ideal turn will not give a satisfactory result when analyzing the actual turn. The minimum theoretical turning radius is taken as an estimated indicator of the turnability of a wheeled vehicle. The conclusion of a multifunctional analytical dependence for determining the theoretical minimum turning radius of a wheeled vehicle, the wheels of which are controlled by a steering trapezoid, is presented. The resulting formula includes the longitudinal base of the machine, the pin track, the angles of rotation of the inner and outer steerable wheels. A comparison of the calculation results according to the developed and known formulas is given, which confirmed the complete convergence. It was found that, for example, an increase in the pivot track of the machine by 0.2 m leads to an increase in the theoretical minimum radius of the actual turn by 16.5%, and the distance from the continuation of the rear axle to the instantaneous center of rotation by 45.07...98.02% when the angle of rotation of the inner steering wheel changes from 20° to 40°.

Flame Front Model with the Clusters Condensation

The processes model in a flame during the n-alkanes air mixture combustion initiation is proposed, taking into account the supramolecular structures formation possibility in the peroxide clusters form. This approach is justified by the n-alkanes melting temperatures correlation with their autoignition temperatures and anti-knock indexes. The condensation possibility is provided for such high molecular structures. Boiling temperatures values at flame front pressures characteristic were evaluated. To predict the peroxide clusters melting temperatures, a formula developed earlier for the hydrocarbons condensed state was used, which takes into account the length and molecular weight of modeled clusters. Expected peroxide clusters melting temperatures were predicted for conditions of dimeric and tetrameric structures. A linear dependence was used to recalculation the obtained values in boiling temperatures. It is shown that the calculated clusters phase transitions characteristic temperatures can be realized in the flame front preparatory zone. Based on the condensation theory, the flame front thickness and the minimum non-extinguishing sphere radius during ignition were estimated: the obtained data closely coincide with these parameters known values.

Evaluation of the effect of forming strategy in newly introduced flexible roll forming process

In recent years, with the emergence of Industry 4.0 trends and the impact of the COVID-19 pandemic, the agile manufacturing paradigm has gained increasing significance. Substantial efforts have been directed towards introducing new methods, driven by the dual objectives of flexibility and agility. This paper presents an innovative machine that employs two rollers to apply localized deformation to sheet metal through repetitive movement along the length of the sheet. As with all incremental forming processes, the forming strategy is a critical parameter influencing both the forming force and the dimensional accuracy of the manufactured workpiece. In this research, two different forming strategies, internal and external, were implemented for manufacturing elongated 90 deg bends on 1 mm and 3 mm thick AISI 304 sheets. Both numerical and experimental analyses were performed to assess the effects of these different strategies. The results confirm that the forming force with the external strategy is 50 % and 47 % less for the 1 mm and 3 mm sheets, respectively. Moreover, the external forming strategy allows for better control of the obtained angle, but limits the minimum obtainable bending radius.

Small-angle X-ray scattering analysis of poly(amic acid) dispersed in a liquid matrix to understand the size control of polyimide nanoparticles.

Poly(amic ‍acid) ‍nanoparticles ‍prepared ‍by ‍‍precipitation ‍polymerization with a dispersant were evaluated by small-angle X-ray scattering (SAXS) and field-emission scanning electron microscopy (FE-SEM). The particle size evaluation of poly(amic acid) nanoparticles in the liquid phase by SAXS was performed to gain insight into the size control of poly(amic acid) nanoparticles, and showed good agreement with visual observation by FE-SEM, explaining the effect of the dispersant in obtaining polyimide nanoparticles with small particle size. This indicates that the particle size is maintained without change during the solvent evaporation process. The polyamide nanoparticles controlled by the dispersant effect maintained their size after imidization, and polyimide nanoparticles with a minimum radius of about 60 nm were prepared.

Thin-film evaporation in microchannels: A combined analytical and computational fluid dynamics approach to assessing meniscus curvature impact

Computational fluid dynamics (CFD) is employed to investigate the effects of variation in bulk meniscus curvature on evaporative heat and mass transfer in microchannels. Evaporation in microchannels presents a classic multiscale problem, encompassing both microscopic and macroscopic length scales in the thin-film and bulk meniscus regions, respectively. Therefore, the liquid-vapor interface or meniscus shape is first determined through thin-film evaporation analysis using numerical approaches found in the literature. However, a new approach for establishing boundary conditions is also proposed, allowing for the representation of varying curvatures within the bulk meniscus region. Then, the obtained meniscus thickness profiles are exported to a two-dimensional CFD framework. The primary advantage of this developed CFD framework lies in its capability to simultaneously analyze evaporative heat and mass transfer from both microscopic and macroscopic regions, a feature that enhances research endeavors concerning micro and miniature heat pipes. The developed model is applied to various rectangular microchannel sizes, ranging from 10 to 100 μm in width, with wall superheats varying from 0.1 to 3.0 K. The aim is to quantify the effects of variations in bulk meniscus curvature on the evaporative characteristics of the extended meniscus (comprising both thin-film and bulk meniscus regions), using the concept of thermal resistance. Consequently, based on the CFD simulation results, multiple regression analysis is employed to formulate the total thermal resistance in terms of independent parameters, namely the microchannel width, wall superheat, and the radius of curvature (Rc). It is observed that the radius of curvature has a marginal impact on the total thermal resistance, allowing its influence to be expressed by a power-law function of (Rc/Rm)0.102, where Rm represents the minimum radius of curvature.

Geometry of the atom

An analysis of the harmonic series reveals a geometric structure of atomic hydrogen that defines the minimum radius of the bound electron. Subsequently, hydrogen’s energy states, velocities, and angular momentum are determined. Based on these findings, a theoretical value is determined for Planck’s reduced constant and the electron rest mass. In addition, an examination of hydrogen’s quantum energy states suggests that they are the result of a combinatorial effect.

External Steering of Vine Robots via Magnetic Actuation.

This article explores the concept of external magnetic control for vine robots to enable their high curvature steering and navigation for use in endoluminal applications. Vine robots, inspired by natural growth and locomotion strategies, present unique shape adaptation capabilities that allow passive deformation around obstacles. However, without additional steering mechanisms, they lack the ability to actively select the desired direction of growth. The principles of magnetically steered growing robots are discussed, and experimental results showcase the effectiveness of the proposed magnetic actuation approach. We present a 25-mm-diameter vine robot with an integrated magnetic tip capsule, including 6 degrees of freedom (DOF) localization system and camera, and demonstrate a minimum bending radius of 3.85 cm with an internal pressure of 30 kPa. Furthermore, we evaluate the robot's ability to form tight curvature through complex navigation tasks, with magnetic actuation allowing for extended free-space navigation without buckling. The suspension of the magnetic tip was also validated using the 6 DOF localization system to ensure that the shear-free nature of vine robots was preserved. Additionally, by exploiting the magnetic wrench at the tip, we showcase preliminary results of vine retraction. The findings contribute to the development of controllable vine robots for endoluminal applications, providing high tip force and shear-free navigation.

Adaptive Curve Passing Control in Autonomous Vehicles with Integrated Dynamics and Camera-Based Radius Estimation

Autonomous vehicles frequently encounter performance degradation during high-speed cornering due to excessive speed and lateral acceleration, potentially leading to collisions or rollovers. This paper proposes a novel curve-passing control approach that first estimates the curve radius and then controls the steer and speed for smooth and comfortable handling. In particular, the curve radius is innovatively estimated using a combination of a camera-based lane detection model and a steering wheel dynamic model. The curve-passing control approach is validated on high-speed ramps and curves, demonstrating its robustness and intelligence to adapt to dynamic changes in curve curvature. The model effectively prevents vehicles from entering curves at dangerously high speeds from straight roads and mitigates sudden accelerations or decelerations when entering curves. Experimental results indicate that the vehicle speed is reduced to around 50 km/h and the corresponding acceleration is −0.6 m/s2 upon entering curves with a minimum radius of 150 m. This demonstrates that the proposed control model can ensure a comfortable and safe driving experience by autonomously decelerating the vehicle before entering various types of curves.

Bulk and fracture process zone contribution to the rate-dependent adhesion amplification in viscoelastic broad-band materials

The contact between a rigid Hertzian indenter and an adhesive broad-band viscoelastic substrate is considered. The material behavior is described by a modified power law model, which is characterized by only four parameters, the glassy and rubbery elastic moduli, a characteristic exponent n and a timescale τ0. The maximum adherence force that can be reached while unloading the rigid indenter from a relaxed viscoelastic half-space is studied by means of a numerical implementation based on the boundary element method, as a function of the unloading velocity, preload and by varying the broadness of the viscoelastic material spectrum. Through a comprehensive numerical analysis we have determined the minimum contact radius that is needed to achieve the maximum amplification of the pull-off force at a specified unloading rate and for different material exponents n. The numerical results are then compared with the prediction of Persson and Brener viscoelastic crack propagation theory, providing excellent agreement. However, comparison against experimental tests for a glass lens indenting a PDMS substrate shows data can be fitted with the linear theory only up to an unloading rate of about 100μm/s showing the fracture process zone rate-dependent contribution to the energy enhancement is of the same order of the bulk dissipation contribution. Hence, the limitations of the current numerical and theoretical models for viscoelastic adhesion are discussed in light of the most recent literature results.

A Study of the Comets with Large Perihelion Distances C/2019 L3 (ATLAS) and C/2019 O3 (Palomar)

This work analyzes the photometric data of the Oort spike comets C/2019 L3 (ATLAS) and C/2019 O3 (Palomar) obtained between 2016 and 2023 by the ATLAS network and the Belgian Olmen Observatory. The comets Palomar and ATLAS have a typical and unusually high activity level, respectively, based on the Afρ parameter corrected to phase angle zero at perihelion. The absolute magnitude of comets ATLAS and Palomar in the o-band is 4.71 ± 0.05 and 4.16 ± 0.02 respectively. The cometary activity of comets ATLAS and Palomar probably began at r > 13 au before perihelion and will end at r >14 au after perihelion, which means that they could remain active until the second half of 2026. The nucleus of comet ATLAS has a minimum radius of 7.9 km, and the nucleus of comet Palomar could be a little larger. The c − o colors of the comets ATLAS and Palomar are redder and bluer, respectively, at perihelion than the solar twin YBP 1194. These comets showed a bluish trend in the coma color with decreasing heliocentric distance. Comet Palomar probably had two outbursts after its perihelion, each releasing about 108 kg of dust. The slopes of the photometric profile of the comae of these comets were between 1 and 1.5, indicating a steady state during the observation campaign.

Solute transport in stochastic discrete fracture-matrix systems: Impact of network structure

Obtaining a comprehensive understanding of solute transport in fractured rocks is crucial for various geoengineering applications, including waste disposal and construction of geo-energy infrastructure. It was realized that solute transport in fractured rocks is controlled by stochastic discrete fracture-matrix systems. However, the impacts and specific uncertainty caused by fracture network structures on solute transport in discrete fracture-matrix systems have yet not been fully understood. In this article, we aim to investigate the influence of fracture network structure on solute transport in stochastic discrete fracture-matrix systems. The fluid flow and solute transport are simulated using a three-dimensional discrete fracture matrix model with considering various values of fracture density and size (i.e., radius). The obtained results reveal that as the fracture density or minimum fracture radius increases, the corresponding fluid flow and solute transport channels increase, and the solute concentration distribution range expands in the matrix. This phenomenon, attributed to the enhanced connectivity of the fracture network, leads to a rise in the effluent solute concentration mean value from 0.422 to 0.704, or from 0.496 to 0.689. Furthermore, when solute transport reached a steady state, the coefficient of variation of effluent concentration decreases with the increasing fracture density or minimum fracture radius in different scenarios, indicating an improvement in the homogeneity of solute transport results. The presented analysis results of solute transport in stochastic discrete fracture-matrix systems can be helpful for uncertainty management in the geological disposal of high-level radioactive waste.

On spectral extrema of graphs with given order and generalized 4-independence number

Characterizing the graph having the maximum or minimum spectral radius in a given class of graphs is a classical problem in spectral extremal graph theory, originally proposed by Brualdi and Solheid. Given a graph G, a vertex subset S is called a maximum generalized 4-independent set of G if the induced subgraph G[S] dose not contain a 4-tree as its subgraph, and the subset S has maximum cardinality. The cardinality of a maximum generalized 4-independent set is called the generalized 4-independence number of G. In this paper, we firstly determine the connected graph (resp. bipartite graph, tree) having the largest spectral radius over all connected graphs (resp. bipartite graphs, trees) with fixed order and generalized 4-independence number, in addition, we establish a lower bound on the generalized 4-independence number of a tree with fixed order. Secondly, we describe the structure of all the n-vertex graphs having the minimum spectral radius with generalized 4-independence number ψ, where ψ⩾⌈3n/4⌉. Finally, we identify all the connected n-vertex graphs with generalized 4-independence number ψ∈{3,⌈3n/4⌉,n−1,n−2} having the minimum spectral radius.

Orbifolded elliptic genera of non-compact models

We revisit the flavored elliptic genus of the N=2 superconformal cigar model and generalize the analysis of the path integral result to the case of real central charge. It gives rise to a non-holomorphic modular covariant function generalizing completed mock modular forms. We also compute the genus for angular orbifolds of the cigar and Liouville theory and decompose it in terms of discrete and continuous contributions. The orbifolded elliptic genus at fractional level is a completed mock modular form with a shadow related to U(1) modular invariants at rational radius squared. We take the limit of the orbifolded genera towards a weighted ground state index and carefully interpret the contributions. We stress that the orbifold cigar and Liouville theories have a maximal and a minimal radius, respectively.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Study on Pulsed Gas Tungsten Arc Lap Welding Techniques for 304L Austenitic Stainless Steel

The lap welding process for 304L stainless steel welded using the pulsed gas tungsten arc welding (P-GTAW) procedure was studied, and the effects of the pulse welding parameters (the peak current, background current, duty cycle, pulse frequency, and welding speed) on the macroscopic morphology, microstructure, and mechanical properties of the resultant lap joints were investigated. Tensile tests, hardness measurements, and SEM/EDS/XRD analyses were conducted to reveal the characterization of the joint. The relationships between the welding parameters; certain joint characteristic dimensions (the weld width, D; the weld width on the lower plate, La; the weld depth on the lower plate, P; and the minimum fusion radius, R); and the maximum tensile bearing capacity were studied. The weld zone was primarily composed of vermicular ferrite, skeletal ferrite, and austenite, and no obvious welding defects, precipitation, or phase transformations were evident in the weld. Microhardness tests demonstrated that the weld microhardness was highest in the base metal zone and lowest in the weld zone. As the heat input increased, the average microhardness decreased. The hardness difference reached 17.6 Hv10 due to the uneven grain size and the transformation of the structure to ferrite in the weld. The fracture location in welded joints varied as the heat input changed. In some parameter combinations, the weld tensile strength was significantly higher than that of the base material, with fractures occurring in the weld. Scanning electron microscopy results exhibited an obvious dimple morphology, which is a typical form of ductile fracture. XRD revealed no significant phase changes in the weld zone, with a higher intensity of the austenite diffraction peaks compared to the ferrite diffraction peaks.

The weighted Euclidean one-center problem in $${\mathbb {R}}^n$$

AbstractGiven a finite set of distinct points in $${\mathbb {R}}^n$$ R n and a positive weight for each point, primal and dual algorithms are developed for finding the Euclidean ball of minimum radius so that the weighted Euclidean distance between the center of the ball and each point is less than or equal to the radius of the ball. Each algorithm is based on a directional search method in which the search path at each iteration is either a ray or a two-dimensional circular arc in $${\mathbb {R}}^n$$ R n . At each iteration, a search path is constructed by intersecting bisectors of pairs of points, where the bisectors are either hyperplanes or n-dimensional spheres. Each search path preserves complementary slackness and primal (dual) feasibility for the primal (dual) algorithm. The step size along each search path is determined explicitly. Test problems up to 1000 dimensions and 10,000 points were solved to optimality by both primal and dual algorithms. Computational results also show that these algorithms outperform several open-source SOCP codes.