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The normalized distance Laplacian of a graph G is defined as D L (G) = T (G) − 1 / 2 (T (G) − D (G)) T (G) − 1 / 2 where D (G) is the matrix with pairwise distances between vertices and T (G) is the diagonal transmission matrix. In this project, we study the minimum and maximum spectral radii associated with this matrix, and the structures of the graphs that achieve these values. In particular, we prove a conjecture of Reinhart that the complete graph is the unique graph with minimum spectral radius, and we give several partial results towards a second conjecture of Reinhart regarding which graph has the maximum spectral radius. [ABSTRACT FROM AUTHOR]

The standard configuration of a sonic black hole (SBH) is a discrete set of rings with back cavities at a duct termination, whose inner radii decrease according to a power-law. Although several practical realizations of this type of slow-sound waveguide have been investigated, the continuous problem in which the number of ring/cavity sets goes to infinity has not been analyzed in depth. Understanding its performance is interesting in itself and could provide clues for new designs. For this purpose, we transform the generalized Webster equation for the acoustic pressure inside the ideal SBH into a spatially varying wavenumber Helmholtz equation for a new locally scaled pressure. We eliminate the singularity of the original problem at the SBH termination by considering a rigid residual surface that will be shown to play a role analogous to that of the acoustic black hole (ABH) residual thickness in beams and plates. The variational formulation of the Helmholtz equation is presented and solved by expanding the unknown scaled pressure in terms of a basis of Gaussian functions. The same framework is used to set up an eigenvalue problem that provides the SBH modes and thereby a modal decomposition for the pressure within the SBH. Once the theoretical foundations are established, the variation of the speed of sound and wavenumber in the SBH is presented. The dependence of the shape and distribution of the modes on the residual surface and damping helps to clarify the occurrence and disappearance of oscillations in the input admittance and reflection coefficient of the SBH at different frequencies. For the latter, a detailed parametric study is carried out. Alternative profiles to the power law are also investigated, some showing reflection coefficient values similar to those of the classical SBH. • Sonic black holes at the end of ducts provide minimal wave reflection. • A theoretical approach is proposed to solve the SBH governing equation. • The modal distribution in the SBH is strongly affected by the residual radius. • The modal distribution explains the oscillations in the reflection coefficient. • Alternative SBH profiles to the power law are studied. [ABSTRACT FROM AUTHOR]

Let 0 < ρ ≤ 2 and w ρ (X) be the operator radius of a bounded linear Hilbert space operator X. In this paper we present characterizations of operators satisfying w ρ (X) ≤ 1. We also give an expression for the ρ -radii based on the numerical radius of a certain 2 × 2 block matrix. This enables us to investigate the properties of the operator radii w ρ (⋅). In particular, we obtain lower and upper bounds for the operator radii. In addition, we define a norm on Hilbert space operators, which generalizes the operator radii and prove some basic properties of this norm. Our results extend or improve some theorems due to Ando [4] , Bhatia–Jain [9] and Kittaneh [19]. [ABSTRACT FROM AUTHOR]

A fractional matching of a graph G is a function f : E (G) → [ 0 , 1 ] such that for any v ∈ V (G) , ∑ e ∈ E G (v) f (e) ≤ 1 , where E G (v) = { e ∈ E (G) : e is incident with v in G }. The fractional matching number of G is μ f (G) = max { ∑ e ∈ E (G) f (e) : f is a fractional matching of G }. Let k ∈ (0 , n) is an integer. In this paper, we prove a tight lower bound of the spectral radius to guarantee μ f (G) > n − k 2 in a graph with minimum degree δ , which implies the result on the fractional perfect matching due to Fan et al. (2022) [6]. For a set { A , B , C , ... } of graphs, an { A , B , C , ... } -factor of a graph G is defined to be a spanning subgraph of G each component of which is isomorphic to one of { A , B , C , ... }. We present a tight sufficient condition in terms of the spectral radius for the existence of a { K 2 , { C k } } -factor in a graph with minimum degree δ , where k ≥ 3 is an integer. Moreover, we also provide a tight spectral radius condition for the existence of a { K 1 , 1 , K 1 , 2 , ... , K 1 , k } -factor with k ≥ 2 in a graph with minimum degree δ , which generalizes the result of Miao et al. (2023) [10]. [ABSTRACT FROM AUTHOR]

Let B (H) be the algebra of all bounded linear operators on a Hilbert space H and let N (⋅) be a norm on B (H). For every 0 ≤ ν ≤ 1 , we introduce the w (N , ν) (A) as an extension of the classical numerical radius by w (N , ν) (A) : = sup θ ∈ R ⁡ N (ν e i θ A + (1 − ν) e − i θ A ⁎) and investigate basic properties of this notion and prove inequalities involving it. In particular, when N (⋅) is the Hilbert–Schmidt norm ‖ ⋅ ‖ 2 , we present several the weighted Hilbert–Schmidt numerical radius inequalities for operator matrices. Furthermore, we give a refinement of the triangle inequality for the Hilbert–Schmidt norm as follows: ‖ A + B ‖ 2 ≤ 2 w (‖ ⋅ ‖ 2 , ν) 2 ([ 0 A B ⁎ 0 ]) − (1 − 2 ν) 2 ‖ A − B ‖ 2 2 ≤ ‖ A ‖ 2 + ‖ B ‖ 2. Our results extend some theorems due to F. Kittaneh et al. (2019). [ABSTRACT FROM AUTHOR]

The eccentricity matrix ɛ (G) of a graph G is obtained from the distance matrix D (G) by retaining only for each row and each column the largest distance, and setting the remaining elements as 0. In this paper, we firstly show that the eccentricity matrix of clique trees is irreducible. We identify the t -clique trees with given diameter odd d having the maximum ɛ -spectral radius, and the corresponding extremal graphs are also determined. We determine the upper bounds for the ɛ -spectral radius of t -clique trees which d and n satisfy that one is odd and the other is even. Finally, we propose some potential topics for further study. [ABSTRACT FROM AUTHOR]

By developing an analytical model considering the J 2 perturbation and small eccentricity, the effects of an in-track maneuver on the umbra and penumbra arcs of near-circular orbits are analyzed. The effectiveness of the analytical model is validated by comparing it with the numerical difference and a published model for the cylindrical eclipse. Three major conclusions are draw. First, the proposed analytical model agrees well with the numerical difference method in common situations, and the effect of an in-track maneuver on the eclipse arc center is much smaller than that on the eclipse arc length. Second, although the precision of the proposed analytical model decreases as the eccentricity increases, the effects of a small in-track maneuver on the orbital eclipse could be considered as small values in common situations. Those effects could be notable as the maneuver magnitude increases. Third, when the orbital sun angle approaches the critical angle defined by the ratio of the Earth radius to the satellite's semimajor axis, the effects of an in-track maneuver on the penumbra arc length could not be a small value any more, the precision of the analytical model would be considerably degraded. In the neighborhood of the critical angle, the differences between the effects of an in-track maneuver on the umbra, penumbra and cylindrical eclipse reach the maximum. Moreover, the reasons for the properties presented above are successfully explained by the analytical partial derivatives in the developed model. [ABSTRACT FROM AUTHOR]

A graph G is called fractional [ a , b ] -covered if for every edge e of G there is a fractional [ a , b ] -factor with the indicator function h such that h (e) = 1. In this paper, we provide a tight spectral radius condition for graphs being fractional [ a , b ] -covered. [ABSTRACT FROM AUTHOR]

• Dynamic theory of lattice conical shell with nonconstant stiffness and density was proposed. • Fourier decomposition and power series methods were employed to get recurrence relations. • Analytical solution reflects circumferential wave number and geometric parameter effects. Composite anisogrid lattice conical shells have been applied in rocket adapters and the fundamental frequency is the basic design parameter. Free vibrations of three types composite anisogrid lattice conical shells under arbitrary boundary conditions are considered in the paper to theoretically evaluate the fundamental frequency. The lattice conical shell is modelled as continuous conical shell with nonconstant stiffness and density by equivalent continuum method. Employing Fourier decomposition and power series method, the governing equations of motion based on Donnell-type thin shell theory are converted into the recurrence relations through identity transformation. Displacement and stress resultants expressions containing the unknown frequency and initial terms are obtained through the recurrence relations, respectively. Compared with the previous and numerical results, the analytical solution is remarkably accurate and efficient in dealing with lattice conical shells with variable cross-sectional radius, nonconstant stiffness and density for different number of circumferential waves and geometric parameters. The effect of radius ratio, height of cone and thickness of ribs on the value of frequencies is studied using a parametric analysis. It is shown that the fundamental frequency increase with the thickness of rib and decrease with increasing height of cone. [ABSTRACT FROM AUTHOR]

Let G be a graph and let k ⩾ 2 be an integer. A { K 1 , j : 1 ⩽ j ⩽ k } -factor of G is a spanning subgraph of G , in which each component is isomorphic to a member in { K 1 , j : 1 ⩽ j ⩽ k }. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a { K 1 , j : 1 ⩽ j ⩽ k } -factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a { K 1 , j : 1 ⩽ j ⩽ k } -factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible. [ABSTRACT FROM AUTHOR]

We classify maximal digraphs whose Hermitian spectral radius is at most 2. [ABSTRACT FROM AUTHOR]

For a general radially symmetric, non-increasing, non-negative kernel h ∈ L l o c 1 (R d) , we study the rigidity of measurable sets in R d with constant nonlocal h -mean curvature. Under a suitable "improved integrability" assumption on h , we prove that these sets are finite unions of equal balls, as soon as they satisfy a natural nondegeneracy condition. Both the radius of the balls and their mutual distance can be controlled from below in terms of suitable parameters depending explicitly on the measure of the level sets of h. In the simplest, common case, in which h is positive, bounded and decreasing, our result implies that any bounded open set or any bounded measurable set with finite perimeter which has constant nonlocal h -mean curvature has to be a ball. [ABSTRACT FROM AUTHOR]

In this article we present new numerical radius inequalities for sectorial matrices, and their analogues. For example, we show that if A is a sectorial matrix with sectorial index γ ∈ [ 0 , π 2) , then ‖ A A ⁎ + A ⁎ A ‖ 2 (1 + sin 2 ⁡ γ) ≤ w (A) 2 , where w (A) is the numerical radius of A. The significance of this result is the geometric meaning of the obtained inequality. In particular, we will show how this interpolates some well known inequalities in the literature, in a way that depends on the angle of the sector that contains the numerical range of the sectorial matrix A. Many other interpolating inequalities will be presented to show how the ratio ‖ A ‖ w (A) depends mainly on the angle of the sector that contains the numerical range of the matrix A. Our discussion will lead to a new vision about those matrices which contain the origin in the interior of their numerical ranges. [ABSTRACT FROM AUTHOR]

We present a novel approach to control the blending of line and polygon skeleton-based convolution surfaces using locally varying Ratio of Support radius and Thickness (RST). With our method, solutions for local convolution surface approximation with prescribed surface thickness and support radii can be derived analytically. In addition, iso-surface shrinkage can be avoided by offsetting the endpoints of line skeletons and the edges of polygon skeletons. Our RST-based blending for convolution surfaces is local and can generate desired blending effects while approximating shapes with a specified thickness. Moreover, our method is intuitive and users can control the blending by adjusting the skeletal radius or the support radius of the finite support kernel independently. As our blending utilizes convolution integration only without requiring any extra composition operators, it allows for successive convolution blending operations to create complex shapes. [Display omitted] • Blending control for convolution surfaces using locally varying RSTs. • Analytical solutions for surface thickness approximation with prescribed RSTs. • Numerical solutions for approximating the skeleton boundaries with given RSTs. [ABSTRACT FROM AUTHOR]

For any real number α ∈ [ 0 , 1 ] and a graph G , Nikiforov [20] defined matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G). The A α - spectral radius of G is the largest eigenvalue of A α (G). In this paper, we determine the first three largest extremal graphs in Halin graphs by their A α - spectral radii when 1 2 ≤ α < 1. For 0 ≤ α ≤ 1 , the 3-regular Halin graph alone minimizes the A α - spectral radius for Halin graphs. [ABSTRACT FROM AUTHOR]

As the PEMFC is a complex multi-physics device whose reliability and durability depend on the thermal-mechanical-electrical and chemical parameters. In this paper, theoretical and numerical studies is proposed to optimize the fuel cell performance using multiphysics model and design of experiments. 3D finite element analysis including a fully coupling of thermal-electrical-mechanical model is proposed to predict the electrical resistance of fuel cell. As the mechanical parameters (bending radius of the bipolar plate, thickness of the GDL and clamping pressure) remain uncertain, the design of experiments procedure is used to optimize the fuel cell behavior under several conditions. [Display omitted] • Development of a 3D Multiphysics model to optimize the fuel cell performance. • Relationship between the mechanical parameters and the contact pressure. • Choice of optimal parameters resulting from the design of experiments. • Stochastic finite element method to study the mechanical uncertainties parameters. [ABSTRACT FROM AUTHOR]

A comprehensive approach to lightning protection is comprised of four key steps, namely protection against direct lightning strikes, dealing with surges and transients, dissipation of lightning currents via earthing and bonding, and protecting people. This paper deals with new research findings associated with direct-strike protection with lightning rods or "air terminals", namely the effect of accumulated corona space charge around the tips of these components. There is now a great deal of consensus amongst lightning researchers and practitioners that space charge accumulation reduces the efficiency of an air terminal by inhibiting the initiation and development of an upward leader, a critical stage in the lightning attachment process. The paper describes measurements carried out in a high-voltage laboratory to quantify the amount of corona discharge that would be emitted under thunderstorm conditions from a variety of air terminals of different geometries. A unique, previously unreported aspect of these experiments was the corona testing of air terminals under dry and wet conditions. The results of these experiments showed that corona discharge (and hence space charge accumulation) from a standard Franklin rod is substantially higher than from the range of significantly blunter "corona minimising" air terminals that were tested. The previously reported polarity difference in corona characteristics was also observed, i.e., the magnitude of negative corona was larger than positive corona for the same ambient electric field. Differences in corona discharge were also observed under wet and dry conditions, where wet air terminals were found to produce modestly more corona. The paper then addresses the optimisation of air terminals, i.e., minimising corona discharge, for practical lightning protection applications, where the air terminal radius of curvature is tailored to its height and position of installation. Various researchers have made these calculations, the outcomes of which are summarised in this paper. In general, radii of curvature in the range 1–100 mm are required, depending on the installation height and location of the air terminal. • Space charge effects around the tips of air terminals reduce the efficiency of lightning capture by inhibiting upward leader development. • Corona characteristics of air terminals have been quantified by simulating the electric field of a thundercloud in a HV laboratory. • Air terminals can be optimised for corona performance via their geometry or radius of curvature. • Typical optimum radii of curvature are in the range 1–100 mm, depending on installation height and location. [ABSTRACT FROM AUTHOR]

The deep borehole heat exchanger systems (DBHE) are offering potential low carbon heating for buildings. However, the study of DBHE is hindered by both modeling and system complexity. Although some analytical models of DBHE are presented in literature, the involved expression of complex integral calculation on the contrary slows down the computation speed and many calculations are redundant in algorithm. In this study, a Response Factor Matrix method (RFM) is proposed based on simple analytical expression and well-designed data structure for DBHE. The RFM can be prefabricated and then used in each time step updates of temperature field. A superposition algorithm is designed for fast computation of DBHE array. The proposed model and algorithms are verified by measurements from two independent engineering projects. Based on the new tool, both thermal radius and heating capacity of DBHE array are investigated in details. The step-ascending pattern of thermal radius is recognized. The correlation of borehole spacing and system heating capacity is identified. In the end, the computational efficiency of the new tool is justified and some outlooks are proposed for a further development and applications. • A fast computational model is proposed for single and multiple deep borehole system. • The proposed new model is verified through comparison with experimental data. • The thermal impact radius of deep borehole system is investigated. • The spacing of deep borehole array is critical for system heat capacity. [ABSTRACT FROM AUTHOR]

In this investigation, Direct Simulation Monte Carlo Method is used to compute the surface properties of inflatable aerodynamic decelerators (IAD) applied for the reentry, recovery, and reuse of cubeSats. Surface properties calculation is of fundamental importance for flexible thermal protection system materials selection that withstand the harsh reentry environment. Furthermore, simulations are extremely important to detect possible hot spots at the IAD before design and flight. In this work, three IAD configurations are exposed to a rarefied hypersonic flow with freestream conditions that correspond to those found at reentry conditions at 105 km altitude. All geometries are assumed to be axisymmetric and have a maximum radius of 0.3 m from the center line to the shoulder edge. The main differences between the geometries are the angle between the IAD and cubeSat body and the IAD curvature for geometry 3. According to the results, all IAD geometries are effective in protecting the cubeSat during the reentry phase. It is shown that the IAD geometry has a significant influence on the heat transfer, pressure, and skin friction coefficient distribution over the flexible heat shield. The maximum heat transfer coefficient computed for geometry 1, 2, and 3 is 0.90, 0.97, and 0.84, respectively. [ABSTRACT FROM AUTHOR]

The radius evolution for the synchronous collapse motion of a circular vapor bubble cluster in an ideal and infinite fluid is studied. With the assumption that all bubbles are evenly distributed around the circumference and have the same initial conditions, we establish the associated governing equation for this case from a modified Rayleigh–Plesset equation. The inverted analytical solution in the form of t = t (r) and analytical approximations in the form of r = r (t) for the radius evolution to the initial value problem of the dimensionless governing equation are derived. These novel analytical approximations extend the previous ones for a single bubble by adding the effects of surface tension and multiple bubbles. In addition, we point out that the analytical results and dynamic behaviors for multiple bubbles will degenerate into the corresponding ones for single bubbles when the radius of the bubble cluster approaches to infinity. • The governing equation for the synchronous collapse motion of a circular vapor bubble cluster is established. • The inverted analytical solution and analytical approximations are derived. • The effects of surface tension and multiple bubbles are included in the obtained solutions. • The limiting behaviors of the circular vapor bubble cluster are discussed. [ABSTRACT FROM AUTHOR]

This study focuses on the blade design and optimization of Dual Darrieus Wind turbines (DDWTs). Based on Genetic Expression Programming (GEP) model, a power prediction formula C P = f (Δ , β , θ) , containing radius difference Δ , chord ratio β , and offset angle θ , is proposed in this study. Hence, the power coefficient of various blade layouts can be directly calculated, corresponding to their optimum TSR. Meanwhile, orthogonal array L 9 (34) and Modified Additive Model (MAM) are combined to ensure the representative sample and consider the interaction effects. Additionally, each configuration in dataset requires to execute Computational Fluid Dynamics (CFD) analyses under various Tip Speed Ratios (TSRs) to figure out the highest power coefficient. The optimum layout of double-layer blades, derived from Taguchi Method and C P = f (Δ , β , θ) , features the parameter combination as radius difference Δ of 0.25 m and chord ratio β of 3, which can improve the power output by 7.5%. The power prediction formula established by GEP is competent to approximate C P value of double-layer blades precisely which is verified by the correlation index R2 = 0.993 and supplementary CFD cases. The proposed methodology indicates that DDWTs deserve to be further researched and developed. [ABSTRACT FROM AUTHOR]

The present research introduces a novel two-objective optimization computational framework, named H ∞ optimization criterion-constrained Two-Objective Optimization Genetic Algorithm (H ∞ − cTOOGA). Within this optimization framework, the objectives considered are: (i) the sprung mass isolation, and (ii) the wave energy extraction of a heaving buoy coupled with a sprung (overlying) mass. In such a two-body heaving wave energy converter (WEC), the satisfaction of both objectives is pursued by proper selection of the buoy geometry (i.e., radius r and draft Dr) and the characteristics of the power take-off (PTO). The interrelation among potential buoy geometries and PTO characteristics is performed on the basis of a critical condition. The critical condition refers to the formation of equal double peaks in the sprung mass acceleration response curve and is imposed as the sprung mass acceleration limit that is not allowed to be exceeded throughout the entire frequency range of interest. The two-objective optimization is realized with r , Dr and the tuning ratio δ OPT being the decision variables. The value of δ OPT is constrained by the value of the critical tuning ratio δ crit , that is, δ OPT < δ crit. This ensures the minimization of the maximum sprung mass acceleration response. Then, the Pareto-optimal solutions result to optimal wave energy extraction. • A two-objective optimization computational framework is developed for a two-body WEC. • The two objectives are the sprung mass isolation and the wave energy extraction. • The optimized parameters concern the buoy geometry and the PTO characteristics. • The optimum parameters are interrelated through a critical condition-constrained framework. • A Genetic algorithm is adopted to derive Pareto-optimal solutions. [ABSTRACT FROM AUTHOR]

A tree T with exactly one node u of degree larger than two is called a starlike tree and u is called the root node of T. Let S T n be a family of graphs consists of all starlike trees and the path with n + 1 nodes. For a fixed connected graph H with at least one edge, we construct a family of graphs F H (v) , n = { H (v) • T | T ∈ S T n } , where H (v) • T denotes the graph obtained by identifying some node, say v , of H with the root node of T. In this paper, we give an ordering of graphs in F H (v) , n by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. • The spectral radius of the graph powerfully characterizes dynamic processes on networks, such as virus spread and synchronization. • In this paper, we give an ordering of graphs in F H (v) , n by spectral radii coincides with the shortlex ordering of nondecreasing sequences of their branch lengths. • The result generalizes the main result of Oliveira et al. in [10]. [ABSTRACT FROM AUTHOR]

[Display omitted] • The choice of nozzle height is almost independent of nozzle height for R ≥ 80 mm. • H significantly affects cartridge cleaning performance with smaller R. • Peak static pressure distribution along filter cartridge height. • The main vortex reduces the static pressure inside the cartridge. The inner cone double-layer filter cartridges have the capability to guide the flow, which can optimize the airflow distribution inside the cartridge and reduce the cartridge's incomplete cleaning. However, the selection of different cone radius and nozzle heights can affect the cartridge's cleaning performance. More thorough investigations of the static pressure distribution properties within double-layer cartridges are required to improve their design and optimization. The results show that double-layer cartridges' peak static pressure at different nozzle heights has a similar distribution law. Peak static pressure increases progressively with cartridge height in the middle and lower sections (OM3-OM5, IM2-IM5), with the lower section having a larger peak static pressure. The cleaning performance of cartridges with a cone radius of R ≥ 80 mm is little impacted by the nozzle height. The stability of the cartridge's cleaning performance improves and then deteriorates as the cone radius increases, with the best cleaning effect and stability reached at R = 80 mm. In practical applications, double-layer filter cartridges with larger cone radius should be considered. [ABSTRACT FROM AUTHOR]

Metal additive manufacturing (AM) technology has been utilized in many industries including automotive, aerospace, and medical. AM Ti6Al4V (Ti64) alloy is highly noticed for production of medical instruments such as dental implants and the machining process is mostly needed during the production or post-processing of these components. Numerical model, as a powerful tool, can be efficiently used for analyzing the machining process. A customized model was employed using a user-written subroutine in this work to evaluate machinability and microstructural changes in cryogenic machining of AM Ti64 alloy. For this purpose, the microstructural changes were simulated as the new numerical outputs. The numerical results of cutting forces, temperature, nano-hardness, and alpha lamellae thickness (grain size) were successfully verified by corresponding experiments from literature. Then, the impact of tool geometry (including rake and clearance angles, cutting edge radius, and nose radius) on the machinability performance was examined. It was found that, the variation of clearance and rake angles were more effective on depth of the hardened layer compared to the other parameters. Thickness of alpha lamellae phase near the machined surface and depth of the affected layer by nano-hardness changes were changed from 0.9 to 1.58 µm, and from 18 to 40 µm, respectively. Overall, it was concluded that the variation of insert positioning made by tool holder (change in rake and clearance angles) was an effective parameter on the process outputs when machining AM Ti64 alloy. [ABSTRACT FROM AUTHOR]

• Most accurate geometry of attached mortar geometry for recycled aggregate concrete (RAC) modelling; • Comparative analysis with several attached mortar geometries; • Comparison of the mechanical behaviour of RAC with natural aggregate concrete (NAC). The geometry of the attached mortar present in recycled concrete aggregates influences the behaviour of recycled aggregate concrete, since this mortar is porous, rough and tends to increase the elongation of aggregate particles. These factors influence shape, volume, and complexity of the mesoscopic phases of concrete (including the interfacial transition zone), but studies on this topic so far have not realistically represented the geometry and mesoscopic phases of recycled aggregate concrete. This hinders a proper analysis of the effect of the attached mortar's geometry. This paper develops a mesoscopic model for recycled aggregate concrete, considering four types of attached mortar's geometry based on experimental observation. Concrete mixes numerically modelled with either: i) the four attached mortar's geometries combined on a mixed model (representative of real cases); or ii) a single type of attached mortar's geometry was analysed regarding the effect of the attached mortar's geometry on the compressive and tensile behaviour and on fracture development. The main findings of the paper are: (1) the geometry of the attached mortar is relevant to the behaviour of recycled aggregate concrete; (2) modelling the attached mortar as present in both ends of the larger radius of the recycled aggregate leads to more realistic results; (3) modelling the attached mortar as fully enclosing the recycled aggregate overestimates the mechanical properties. [ABSTRACT FROM AUTHOR]

The Maxwell-Smoluchowski (MS) theory of gas diffusion is revisited here in the context of gas transport in straight channels in the Knudsen regime of large mean free path. This classical theory is based on a phenomenological model of gas-surface interaction that posits that a fraction ϑ of molecular collisions with the channel surface consists of diffuse collisions, i.e., the direction of post-collision velocities is distributed according to the Knudsen Cosine Law, and a fraction 1 − ϑ undergoes specular reflection. From this assumption one obtains the value D = 2 − ϑ ϑ D K for the self-diffusivity constant, where D K is a reference value corresponding to ϑ = 1. In this paper we show that ϑ can be expressed in terms of micro- and macro-geometric parameters for a model consisting of hard spheres colliding elastically against a rigid surface with prescribed microgeometry. Our refinement of the MS theory is based on the observation that the classical surface scattering operator associated to the microgeometry has a canonical velocity space diffusion approximation by a generalized Legendre differential operator whose spectral theory is known explicitly. More specifically, starting from an explicit description of the effective channel surface microgeometry—a concept which incorporates both the actual surface microgeometry and the molecular radius—and using this operator approximation, we show that ϑ can be resolved into easily obtained geometric parameters, ϑ = λ h / C , having the following interpretation: C is a macroscopic parameter determined by the shape of the channel cross-section; h is a parameter that precisely captures the degree of roughness of the effective microgeometry, and λ is a parameter that characterizes the overall curvature of the surface microgeometry independent of h. Thus ϑ is resolved as the quotient of microscopic (λh) over macroscopic (C) signature parameters of the channel geometry. The identity ϑ = λ h / C holds up to higher order terms in the roughness parameter h , so our main result better applies to well polished, or low roughness, surfaces. • The Maxwell-Smoluchowski theory of gas diffusion is revisited in the context of gas transport in straight channels in the Knudsen regime of large mean free path, in the special case of channel surface having low roughness. • A factorization of the phenomenological tangential momentum accommodation coefficient introduced in the Maxwell-Smoluchowski model is derived in terms of micro- and macro-geometric parameters based on a detailed analysis of the surface scattering of gas molecules under the assumption of low roughness. • A new concept of roughness is proposed which enters into the description of self-diffusivity in a more direct way than standard definitions, and these different notions of roughness are compared. • Utilizing a very simple model of micro-geometry, the new analysis obtains estimates for self-diffusivity of gas transport in carbon nanotubes in line with the very high values observed experimentally. [ABSTRACT FROM AUTHOR]

• Combined impact of conduction, dispersion and buoyancy-driven flow on thermal losses of ATES is assessed. • Conduction always occurs and dominates dispersion effects, buoyancy-driven flow effects depend on conditions. • Storage geometry (A/V and L/R th) influences the recovery efficiency for all storage temperatures. • For conduction dominated conditions, the geometry is improved by decreasing A/V (smallest at L/R th =2). • For conditions with high potential for buoyancy-driven flow, increasingly smaller L/R th (<1) decreases thermal losses. The technical and economic success of an Aquifer Thermal Energy Storage (ATES) system depends strongly on its thermal recovery efficiency, i.e. the ratio of the amount of energy that is recovered to the energy that was injected. Typically, conduction most strongly determines the thermal recovery efficiency of ATES systems at low storage temperatures (<25 °C), while the impact of buoyancy-driven flow can lead to high additional heat losses at high storage temperatures (>50 °C). To date, however, it is unclear how the relative contribution of these processes and mechanical dispersion to heat losses across a broad temperature range is affected by their interaction for the wide range of storage conditions that can be encountered in practice. Since such process-based insights are important to predict ATES performance and support the design phase, numerical thermo-hydraulic ATES simulations were conducted for a wide range of realistic operational storage conditions ([15–90 °C], [50,000–1,000,000 m3/year]) and hydrogeological conditions (aquifer thickness, horizontal hydraulic conductivity, anisotropy). The simulated heat loss fractions of all scenarios were evaluated with respect to analytical solutions to assess the contribution of the individual heat loss processes. Results show that the wide range of heat losses (10–80 % in the 5th year) is the result of varying contributions of conduction, dispersion and buoyancy-driven flow, which are largely determined by the geometry of the storage volume (ratio of screen length / thermal radius, L/R th) and the potential for buoyancy-driven flow (q 0) as affected by the storage temperature and hydraulic conductivity of the aquifer. For ATES systems where conduction dominates the heat losses, a L/R th ratio of 2 minimizes the thermal area over volume ratio (A/V) and resulting heat losses for a given storage volume. In contrast however, the impact of dispersion decreases with L/R th and particularly for ATES systems with a high potential for buoyancy-driven flow (q 0 > 0.05 m/d), increasingly smaller L/R th ratios (<1) strongly reduce the heat losses due to tilting. Overall, the results of this study support the assessment of thermal recovery efficiencies for particular aquifer and storage conditions, thereby aiding the optimization of initial ATES designs. [Display omitted] [ABSTRACT FROM AUTHOR]

The Born equation is a seminal model to study the solvation process of ions in solution, devised originally for ions at infinite dilution. Diverse modifications have been proposed in literature since the publication of the original work by Max Born in 1920, with varying degrees of success. In this work, we analyze and discuss various modifications to the Born equation. We verify their performance for Gibbs Free Energy, Enthalpy, and Entropy of solvation using data from a comprehensive database of 143 ions with charges from −4 to ＋4 in 26 different solvents. We show how the Born radius is a natural consequence of introducing the dielectric saturation effect in an approximate form, and therefore most of the proposed models are special cases of considering a continuous radial dependence for the dielectric constant. Finally, we propose a new analytical modification to the Born equation, which encloses the previous theoretical modifications and has a better performance than previous modifications. [Display omitted] • The Born radius is a consequence of dielectric saturation in the Born equation. • The S-Born model is an alternative to the proposed versions of the Born equation. • A temperature-dependent correction improves results for solvation properties. [ABSTRACT FROM AUTHOR]

Let A be a bounded linear operator on a complex Hilbert space and ℜ (A) (ℑ (A)) denote the real part (imaginary part) of A. Among other refinements of the lower bounds for the numerical radius of A , we prove that w (A) ≥ 1 2 ‖ A ‖ + 1 2 | ‖ ℜ (A) ‖ − ‖ ℑ (A) ‖ | and w 2 (A) ≥ 1 4 ‖ A ⁎ A + A A ⁎ ‖ + 1 2 | ‖ ℜ (A) ‖ 2 − ‖ ℑ (A) ‖ 2 | , where w (A) and ‖ A ‖ are the numerical radius and operator norm of A , respectively. We study the equality conditions for w (A) = 1 2 ‖ A ⁎ A + A A ⁎ ‖ and prove that w (A) = 1 2 ‖ A ⁎ A + A A ⁎ ‖ if and only if the numerical range of A is a circular disk with center at the origin and radius 1 2 ‖ A ⁎ A + A A ⁎ ‖. We also obtain upper bounds for the numerical radius of commutators of operators which improve on the existing ones. [ABSTRACT FROM AUTHOR]

In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues. [ABSTRACT FROM AUTHOR]

With the growing popularity of flexible micro-electronics and health-monitoring sensors, wearable flexible thermoelectric generators (TEGs) are receiving attention due to their ability to convert body heat into electricity. In this study, a three-dimensional model of wearable TEGs encapsulated in the PDMS material is established based on the nonlinearly coupled thermoelectric transport constitutive law, large deformation of materials, and the 3-parameter Mooney-Rivlin nonlinear hyperelastic constitutive law of polydimethylsiloxane (PDMS) material. The thermoelectric performance and mechanical reliability of the wearable TEG are investigated under the bending load by employing finite element method. A comparison between numerical results and experimental data is conducted for validation of the model. Effects of the leg shape, filling factor and height of the legs are examined on the thermoelectric performance and mechanical reliability of the wearable TEGs. The optimized dimensions of wearable thermoelectric generators are obtained and analyzed. The results show that, thermoelectric performance and flexibility of the wearable TEG can be enhanced by increasing the number of thermocouples in the TEG. The results of this paper provide useful suggestions for the structural design and practical application of wearable TEGs encapsulated in PDMS materials. • Thermoelectric performance and mechanical strength of wearable TEG are investigated. • Effects of the geometry and bending radius on the performance are studied by a 3D numerical model. • Increasing the number of thermocouples can enhance the output performance and flexibility. • The bending radius shall not be less than 24.92mm when the fill factor is 0.25. [ABSTRACT FROM AUTHOR]

The ABC spectral radius of a graph G is the largest eigenvalue of the ABC matrix of G , whose (u , v) -entry is d u + d v − 2 d u d v if u v ∈ E (G) and 0 otherwise for u , v ∈ V (G) , where d u denotes the degree of u in G , and V (G) (E (G) , respectively) denotes the vertex (edge, respectively) set of G. The unicyclic graphs with the first four largest ABC spectral radii are determined. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of fast constructions of source-wise round-trip spanners in weighted directed graphs. For a source vertex set S ⊆ V in a graph G (V , E) , an S -sourcewise round-trip spanner of G of stretch k is a subgraph H of G such that for every pair of vertices u , v ∈ S × V , their round-trip distance in H is at most k times of their round-trip distance in G. We show that for a graph G (V , E) with n vertices and m edges, an s -sized source vertex set S ⊆ V and an integer k > 1 , there exists an algorithm that in time O (m s 1 / k log 5 ⁡ n) constructs an S -sourcewise round-trip spanner of stretch O (k log ⁡ n) and O (n s 1 / k log 2 ⁡ n) edges with high probability. Compared to the fast algorithms for constructing all-pairs round-trip spanners [26,12] , our algorithm improves the running time and the number of edges in the spanner when k is super-constant. Compared with the existing algorithm for constructing source-wise round-trip spanners [36] , our algorithm significantly improves their construction time Ω (min ⁡ { m s , n ω }) (where ω ∈ [ 2 , 2.373) and 2.373 is the matrix multiplication exponent) to nearly linear O (m s 1 / k log 5 ⁡ n) , at the expense of paying an extra O (log ⁡ n) in the stretch. As an important building block of the algorithm, we develop a graph partitioning algorithm to partition G into clusters of bounded radius and prove that for every u , v ∈ S × V at small round-trip distance, the probability of separating them in different clusters is small. The algorithm takes the size of S as input and does not need the knowledge of S. With the algorithm and a reachability vertex size estimation algorithm, we show that the recursive algorithm for constructing standard round-trip spanners [26] can be adapted to the source-wise setting. We rigorously prove the correctness and computational complexity of the adapted algorithms. Finally, we show how to remove the dependence on the edge weight in the source-wise case. [ABSTRACT FROM AUTHOR]

During the last decade several research groups have published results on sufficient conditions for the hamiltonicity of graphs in terms of their spectral radius and their signless Laplacian spectral radius. Here we extend some of these results. All of our results involve the characterization of the exceptional graphs, i.e., all the nonhamiltonian graphs that satisfy the condition. The proofs of our main results are based on the Bondy–Chvátal closure, a degree sequence condition due to Chvátal, and an operation on the edges that is known as Kelmans' transformation. [ABSTRACT FROM AUTHOR]

We show that the kite graph K 4 (n) uniquely maximizes the distance spectral radius among all connected 4-chromatic planar graphs on n vertices. [ABSTRACT FROM AUTHOR]

Let G n , k D be the set of all k -connected graphs of order n with diameter D. In this paper, we determine the graphs with maximal signless Laplacian spectral radius among all graphs in G n , k D. [ABSTRACT FROM AUTHOR]

• Solution for in-service shallow-buried twin tunnels subjected to surcharge loads is presented. • The Flamant solution and the complex variable method are iteratively combined. • Twin tunnels of arbitrary geometry and surcharge loads of different form are considered. This paper presents an analytical solution for the stress and displacement for shallow twin tunnels subjected to surcharge loads. Multi-interactions, including the interaction between liners and geomaterial, the interaction between twin tunnels, and the interaction between surcharge loads and twin tunnels, are considered in the proposed solution. The solution is elaborated using an iterative three-step procedure based on the Schwarz alternating method. The complex variable method and the Flamant solution and its modification are employed in the derivation. Verification of the analytical solution is obtained through comparisons to a corresponding numerical solution and an existing case study. The close correspondence indicates the accuracy and generality of the proposed solution. A parametric investigation is performed to investigate the influence of surcharge load (including load position, range and distribution), elastic parameters of geomaterial, and liner geometry (including tunnel radius and liner thickness). Based on the parametric investigation, several advices for surcharge loads and liners are provided to help tunnel designers to avoid possible damages for shallow twin tunnels. [ABSTRACT FROM AUTHOR]

As the GDL (Gas diffusion layer) is the most sensitive component in the fuel cell, any change in its structure causes a change in its porosity, which strongly influences the contact between the components of the fuel cell. Note that the state of contact depends on the applied clamping pressure, the thickness and the porosity of the GDL, and the geometry of the rib (bending radius) of the BPP (Bipolar plates). These components can be subject to variations coming from very high compression, so it is necessary to consider the reliability of their dimension via modeling/simulation by the integration of uncertainties. In this article, we will study the influence on the contact pressure of the uncertainties of the mechanical design parameters. A probabilistic approach (Gauss's law) is applied to evaluate the effect of the mechanical uncertainties parameter on the contact pressure between GDL/MEA and GDL/BPP. [Display omitted] • Probabilistic approach is applied to study the mechanical parameter uncertainties. • Stochastic study performed via a numerical design of experiment. • Effect of GDL porosity uncertainty on the contact pressure. • Relationship between the random input parameters and the random contact pressure. [ABSTRACT FROM AUTHOR]

The ABC matrix of a graph G , proposed by Estrada in 2017, can be regarded as a weighed version of adjacency matrices of graphs, in which the (u , v) -entry is equal to d u + d v − 2 d u d v if uv is an edge of a graph G , and 0 otherwise, where d u represents the degree of u in G. The research about ABC spectral radius (largest eigenvalue of ABC matrix) of graphs is rather active in recent years. In this paper, we characterize the bicyclic graphs with the first two maximum ABC spectral radii, which are just the unique two bicyclic graphs of order n with maximum degree n − 1 if n ≥ 7. [ABSTRACT FROM AUTHOR]

The spectral radius ρ (G) of a graph G is the largest eigenvalue of its adjacency matrix A (G). In this paper, we first give a sharp lower bound of the spectral radius of a graph G in terms of the degree and the average 2-degree which generalizes a result of Das and Kumar (2003), and then as an application, a sharp upper bound of the energy of G is given which generalizes a result of Liu et al. (2007). [ABSTRACT FROM AUTHOR]

A perfect matching in a graph G is a set of disjoint edges covering all vertices of G. Let ρ (G) be the spectral radius of a graph G , and let θ (n) be the largest root of x 3 − (n − 4) x 2 − (n − 1) x + 2 (n − 4) = 0. In this paper, we prove that for a positive even integer n ≥ 8 or n = 4 , if G is an n -vertex graph with ρ (G) > θ (n) , then G has a perfect matching; for n = 6 , if ρ (G) > 1 + 33 2 , then G has a perfect matching. It is sharp for every positive even integer n ≥ 4 in the sense that there are graphs H with ρ (H) = θ ′ (n) and no perfect matching, where θ ′ (n) = θ (n) if n = 4 or n ≥ 8 and θ ′ (6) = 1 + 33 2. [ABSTRACT FROM AUTHOR]

Given a discrete-time linear switched system Σ (A) associated with a finite set A of matrices, we consider the measures of its asymptotic behavior given by, on the one hand, its deterministic joint spectral radius ρ d (A) and, on the other hand, its probabilistic joint spectral radii ρ p (ν , P , A) for Markov random switching signals with transition matrix P and a corresponding invariant probability ν. Note that ρ d (A) is larger than or equal to ρ p (ν , P , A) for every pair (ν , P). In this paper, we investigate the cases of equality of ρ d (A) with either a single ρ p (ν , P , A) or with the supremum of ρ p (ν , P , A) over (ν , P) and we aim at characterizing the sets A for which such equalities may occur. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how the adjacency spectral radius and signless Laplacian spectral radius behave when a connected uniform hypergraph is perturbed by grafting edges. We extend the classical theorem of Li and Feng (1979) [10] about spectral radius from connected graphs to connected uniform hypergraphs by using a constructive method. This result also generalizes the results of Cvetković and Simić (2009) [2] , and Su et al. (2018) [22]. As applications, we determine the k -uniform supertrees of order n with the first two smallest adjacency spectral radii (signless Laplacian spectral radii, respectively). Also, we determine the k -uniform supertrees of order n with the first two smallest Laplacian spectral radii, in the case when k is even. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected connected graph. The Harary matrix of graph G , which is also called as the Reciprocal Distance matrix, was introduced by Plavsić et al. in 1993. Bapat and Panda, in 2018, defined the Reciprocal Distance Laplacian matrix, and Alhevaz et al., in 2019, defined the Reciprocal Distance signless Laplacian matrix. In this article, we find upper bounds and lower bounds for the spectral radius of the Reciprocal Distance matrix, Reciprocal Distance Laplacian matrix and Reciprocal Distance signless Laplacian matrix. [ABSTRACT FROM AUTHOR]

The rank and the spectral radius of a graph is the rank and the spectral radius of its adjacency matrix, respectively. In this paper we find the graphs with extremal spectral radius over the set of all connected graphs with n vertices and rank 4. [ABSTRACT FROM AUTHOR]

The ultimate strength of medium-thick composite pressure shells under hydrostatic pressure was studied by experimental test and finite element method in this paper. The ultimate strength, damage form and strain response of cylindrical shells were obtained by hydrostatic destruction test, which carried out for two T700 carbon fiber/epoxy composite cylindrical pressure shells with different length. Meanwhile, finite element models were built to predict the strength failure pressure based on the progressive damage mechanism of composite materials and its initial defects. The finite element results were in close agreement with the experimental results. A parametric study was carried out to discuss the effect of radius-length ratio and radius-thickness ratio on ultimate strength. Based on the numerical results, an empirical formula was proposed as a function of radius-length ratio and radius-thickness ratio to predict the ultimate strength of medium-thick composite pressure shells. • The hydrostatic test of composite cylindrical shells was carried out to obtain the ultimate damage load and strain response of the shells. • A numerical calculation model for the ultimate strength of composites was established based on the progressive damage mechanism. • The effects of different structural geometry parameters on the ultimate strength of cylindrical shells were revealed. • An empirical formula for predicting the ultimate strength of composite cylindrical shells was proposed. [ABSTRACT FROM AUTHOR]

The recombination radii between various point defects and defect clusters are essential input parameters for mathematical and computational models of radiation-induced damage evolution. In this work, such recombination radii is calculated by the kinetic Activation Relaxation Technique (k-ART)—an off-lattice, self-learning kinetic Monte Carlo algorithm—in conjunction with molecular dynamics simulations. We found vacancy clusters exhibit larger average recombination radii with interstitials than single vacancies, reaching as large as 2.2 a 0 (a 0 is the lattice parameter of nickel). Such recombination enhancement can be attributed to the intensified distortion near cluster surfaces. Unlike vacancy clusters, free surfaces feature smaller recombination radii than single vacancies. Their recombination radii are correlated with the angle between surface normal and <110> directions. Finally, the recombination radii of interstitial clusters are larger than vacancy clusters and strongly depends on the cluster configurations. Overall, the recombination radii of most internal defect clusters range from ∼ 2 a 0 to ∼ 2.4 a 0. Because previous research has found that recombination radii affect the density-size distribution of point defect clusters but not the fraction of a particular defect, our analysis suggests that given an accurate initial estimate of cluster density-size distributions, choosing a uniform recombination radius for different clusters in object kinetic Monte Carlo simulations should be sufficient to predict subsequent microstructural evolution. [ABSTRACT FROM AUTHOR]