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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]

In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]

This study presents the effect of the flow velocity, which varies exponentially with time, on solute transport in a finite porous medium with radial geometry. The two-dimensional advection-dispersion equation in the cylindrical coordinate system is solved by using finite difference method. The concentration profiles are established for a duration of four hours of infiltration. It appears that the concentrations are lower in the case of the decreasing exponential velocity. The analysis of the effect of the injection radius showed that the retention of pollutants decreases when the injection radius increases. These findings can be used to design the size of a filter system for drinking water provision, and the environment protection. [ABSTRACT FROM AUTHOR]

Numerical simulation of fatigue crack growth (FCG) is presented, based on the application of the extended finite element method (XFEM). Couple of case studies are presented, as a review of recent experience of the Belgrade school of XFEM simulations, established at the Faculty of Mechanical Engineering. Case studies comprised Charpy specimen with initial crack at the notch tip, oil rig pipe with an axial surface crack, pressure vessels with a crack at the welded joint with connecting pipe, turbine shaft with a crack at the transition radius, optimization of a wing spar in respect to FCG, the effect of mesh size on fatigue life estimation of a stringer panel, fatigue life estimation of wing‐to‐fuselage connecting lug, geometry effect on fatigue life of orthopedic plates and fatigue life of hip implant. Based on these case studies, XFEM is discussed in respect to its accuracy and efficiency. It is concluded that XFEM is a versatile tool for simulation of FCG, providing an excellent option for precise and reliable fatigue life of a cracked component. [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]

We present the observational mass–radius (M–R) relation for a sample of 47 magnetized white dwarfs (WDs) with the magnetic field strength (B) ranging from 1 to 773 MG, identified from the SDSS data release 7 (DR7). We derive their effective temperature, surface gravity (log g), luminosity, radius, and mass. While atmospheric parameters are derived using a Virtual Observatory Spectral Energy Distribution Analyzer (VOSA), the mass is derived using their location in the HR diagram in comparison with the evolutionary tracks of different masses. We implement this mass measurement instead of a more traditional method of deriving masses from log g , which is unreliable as is based on SED and generates errors from other physical parameters involved. The main disadvantage of this method is that we need to assume a core composition of WDs. As it is complicated to identify the exact composition of these WDs from low-resolution spectra, we use tracks for the masses 0.2 to 0.4 M⊙ assuming a He-core, 0.5 to 1.0 M⊙ assuming CO core, and above M⊙ assuming O–Ne–Mg core. We compare the observed M–R relation with those predicted by the finite temperature model by considering different B , which are well in agreement considering their relatively low-surface fields, ≲109 G. Currently, there is no direct observational detection of magnetized WDs with B > 109 G. We propose that our model can be further extrapolated to higher B , which may indicate the existence of super-Chandrasekhar mass (M > 1.4 M⊙) WDs at higher B. [ABSTRACT FROM AUTHOR]

Establish a new classification system of distal radius fracture based on computed tomographic (CT), and evaluate its reliability and reproducibility preliminarily, and provide a new theoretical reference for clinicians to use the clinical classification system. The imaging data and clinical data of 204 inpatients with distal radius fracture during 6 years from January 1, 2014 to January 1, 2019 in orthopaedic department were analyzed retrospectively and classified based on CT. Three observers evaluated the image data of 48 randomly selected cases based on CT at different time nodes of T1 and T2. Cohen's kappa was used to calculate the consistency. At the last follow-up, patients' Disabilities of the Arm, Shoulder and Hand (DASH), Patient Rated Wrist Evaluation (PRWE), and VAS scores were collected. Among 204 cases, there were 12 cases of type 1, including 6 cases of type 1-D, 4 cases of type 1-V and 2 cases of type 1-R. There were 6 cases of type 2, including 2 cases of type 2-DV, 2 cases of type 2-DR and 2 cases of type 2-VR. There were 186 cases of type 3, including 32 cases of type 3–0, 127 cases of type 3–1 and 27 cases of type 3–2. There was no significant difference in DASH, PRWE and VAS scores among all types (P > 0.05). The results of interobserver reproducibility were kappa = 0.985, ICC = 0.984 in the first evaluation, kappa = 0.986, ICC = 0.986 in the second evaluation. The results of intraobserver reproducibility were O1 = 0.991, O2 = 0.991, O3 = 0.989 respectively. The new classification system of distal radius fracture based on CT has theoretical and practical significance for incision selection, fracture reduction and internal fixation. 123 classification system is clear, comprehensive, easy to understand and remember. Moreover, it has higher interobserver reliability and intraobserver reproducibility than other systems reported at present. [ABSTRACT FROM AUTHOR]

Establish a new classification system of distal radius fracture based on computed tomographic (CT), and evaluate its reliability and reproducibility preliminarily, and provide a new theoretical reference for clinicians to use the clinical classification system. The imaging data and clinical data of 204 inpatients with distal radius fracture during 6 years from January 1, 2014 to January 1, 2019 in orthopaedic department were analyzed retrospectively and classified based on CT. Three observers evaluated the image data of 48 randomly selected cases based on CT at different time nodes of T1 and T2. Cohen's kappa was used to calculate the consistency. At the last follow-up, patients' Disabilities of the Arm, Shoulder and Hand (DASH), Patient Rated Wrist Evaluation (PRWE), and VAS scores were collected. Among 204 cases, there were 12 cases of type 1, including 6 cases of type 1-D, 4 cases of type 1-V and 2 cases of type 1-R. There were 6 cases of type 2, including 2 cases of type 2-DV, 2 cases of type 2-DR and 2 cases of type 2-VR. There were 186 cases of type 3, including 32 cases of type 3–0, 127 cases of type 3–1 and 27 cases of type 3–2. There was no significant difference in DASH, PRWE and VAS scores among all types (P > 0.05). The results of interobserver reproducibility were kappa = 0.985, ICC = 0.984 in the first evaluation, kappa = 0.986, ICC = 0.986 in the second evaluation. The results of intraobserver reproducibility were O1 = 0.991, O2 = 0.991, O3 = 0.989 respectively. The new classification system of distal radius fracture based on CT has theoretical and practical significance for incision selection, fracture reduction and internal fixation. 123 classification system is clear, comprehensive, easy to understand and remember. Moreover, it has higher interobserver reliability and intraobserver reproducibility than other systems reported at present. [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]

Ignition electrodes have an immense impact on the accurate measurement of the flame propagation spherical radius. In this study, a flame-radius calculation method is designed. The method is able to eliminate effects due to the ignition electrodes. The adaptability and optimization effects of the proposed method are analyzed. The results show that the ratio of the angle is affected by the ignition electrodes under the Han II method. There are three obvious divisions include a high-value area, a sharp-variation area, and a mild-variation area. The ratio of the angle affected by the ignition electrodes is only applicable to the mild-variation region when the flame presents respective convex and concave distributions. For these distributions, the increment rate of the mean radius is 0.4–0.85% and 0.42–3.19%. The reduced rate of the standard deviation of the radius extraction value is 11.91–22.1% and 5.13–17.99%, and the reduced rate of the radius extraction value range is 20.32–39.51% and 0.32–8.09%. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the q-numerical radius $ \omega _{q}(.) $ ω q (.) of bounded linear operators on Hilbert spaces. More precisely, first, we show that $ \omega _{q}(.) $ ω q (.) defines a norm which is equivalent to the operator norm. Next, the following compatible generalization of Kittaneh's inequality $$\begin{align*} \frac{1}{4}\left(\frac{q}{2-q^{2}}\right)^{2}\parallel T^{*}T +TT^{*}\parallel & \leq \omega_{q}^{2}(T) \leq \frac{(q+2\sqrt{1-q^2})^2}{2}\\ & \quad\times \Vert T^{*}T+TT^{*}\Vert. \end{align*}$$ 1 4 (q 2 − q 2 ) 2 ∥ T ∗ T + T T ∗ ∥ ≤ ω q 2 (T) ≤ (q + 2 1 − q 2 ) 2 2 × ‖ T ∗ T + T T ∗ ‖. is obtained. Finally, some generalizations of q-numerical radius inequalities for composition of operators are established. [ABSTRACT FROM AUTHOR]

The interface tends to behave as a circular shape under the effect of surface tension in the two-dimensional two-phase fluid flow. In this study, based on the coupled volume-of-fluid and level set (VOSET) method, an accurate circle-based interface reconstruction (CIR) algorithm for structured meshes is proposed, which features a straightforward implementation procedure. A portion of the standard circle is employed to approximate the curve interface, without the need for complex classification, coordinate transformation, and equation transformation. The radius of this circle is computed simply by the curvature and signed distance at the mixed cell center, and the center of this circle is determined using a straightforward dichotomy method under the mass conservation constraints. Results indicate that the coupled VOSET and CIR (VOSET-CIR) method maintains superior computational accuracy in the signed distance, interface curvature, and dynamic interface reconstruction compared to the coupled VOSET and piecewise linear interface calculation (VOSET-PLIC) method, with accuracy improvements ranging from 34% to 1490% across different test cases. Furthermore, the VOSET-CIR method outperforms the efficient least squares volume-of-fluid interface reconstruction (ELVIRA) and PLIC algorithms in reconstructing random circles and surpasses the quadratic spline based interface reconstruction (QUASI) algorithm in reconstructing random squares. In terms of computational efficiency, except for the initial PLIC algorithm, the time costs of the VOSET-CIR method are substantially lower than those of the ELVIRA and QUASI algorithms, as well as the VOSET-PLIC method. [ABSTRACT FROM AUTHOR]

We present several upper bounds for the numerical radii of 2 × 2 operator matrices. We employ these bounds to improve on some known numerical radius inequalities for powers of Hilbert space operators. In particular, we show that if T is a bounded linear operator on a complex Hilbert space, then for every r ≥ 1 and α ∈ [0, 1]. This substantially improves on the existing inequality. Here w(.) and ||.|| denote the numerical radius and the usual operator norm, respectively. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical technique based on Taylor's series method namely DTM has been used to solve the differential equation which governs the motion of three types of annular FGM plates. The differential equation has been obtained using Hamilton principle and classical plate theory. The mechanical properties of the plate (Young's modulus and density) are considered to be graded in thickness direction and vary following the power-law. The behaviour of volume fraction index and radii ratio has been investigated onto first three modes of frequency parameter for all three plates. Moreover, the novelty of this paper is the application of the versatile technique DTM to study the effect of radii ratio and volume fraction index on three different types of annular FGM plates. A comparison has been made between the obtained numerical results and the results are available in the literature. A good agreement of the results verifies the accuracy of the present technique. Three-dimensional mode shapes for all three plates are also presented. [ABSTRACT FROM AUTHOR]

Building a 15-minute radius livelihood service circle from the needs of residents is a topdown process of optimizing urban layout and promoting high-quality development implemented by the government. In September 2022, Xicheng District of Beijing served as a national pilot of the 15-minute radius livelihood service circle. Based on the data of POI, urban walking network and building outline, this paper studies the coverage of commercial service facilities in the 15-minute radius livelihood service circle of Chunshu Street by using kernel density analysis and urban network analysis tools. The research shows that the commercial facilities are concentrated in Zhuangsheng Square and Dazhalan commercial district. There are large gaps in housekeeping and couriers logistics facilities, which need to be further improved. [ABSTRACT FROM AUTHOR]

In Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function's radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones. [ABSTRACT FROM AUTHOR]

The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius r on networks. Furthermore, the radius r is flexible and the objective function is the conic combination of the traditional 1-median function and the value r. We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network G = (V,E) in O(|E||V|³) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree. [ABSTRACT FROM AUTHOR]

For a system of nonlinear integral equations on the semiaxis, we study a boundary value problem whose matrix kernel has unit spectral radius. This boundary value problem has applications in various areas of physics and biology. In particular, such problems arise in the dynamical theory of -adic strings for the scalar field of tachyons, in the mathematical theory of spread of epidemic diseases, in the kinetic theory of gases, and in the theory of radiative transfer. The questions of the existence, absence, and uniqueness of a nontrivial solution of this boundary value problem are discussed. In particular, it is proved that a boundary value problem with a zero boundary conditions at infinity has only a trivial solution in the class of nonnegative and bounded functions. It is also proved that if at least one of the values at infinity is positive, then this problem has a convex nontrivial nonnegative bounded and continuous solution. At the end of this paper, examples of the matrix kernel and nonlinearity are provided that satisfy all the conditions of the proved theorems. [ABSTRACT FROM AUTHOR]

Traffic noise mapping frequently employs Kriging, Inverse Distance Weighted (IDW), and Triangular Irregular Networks (TIN) spatial interpolations. This study uses the Henk de Kluijver noise model to evaluate the performance of spatial interpolations. Effective traffic noise mapping requires that noise observation points (Nops) be designed as 2 m grids. The upper and lower slopes function as noise barriers to reduce sound levels. Therefore, assessment of accuracy is essential for visualising noise levels in undulating and level terrain. In addition, this work gives an accurate comparison of traffic noise interpolation in undulating areas. The elements of spatial interpolations, such as the weighting factor, variogram, radius, and number of points influence the interpolation accuracy. The Kriging with a Gaussian variogram, where the radius is 5 m and the number of points is 12 demonstrates the highest level of precision. However, there is no direct relationship between accuracy validation and cross-validation. In cross-validation, however, the accuracy of the Gaussian variogram with a 7 m radius and 18 points is more accurate. In addition, this study demonstrates that Kriging is superior for extrapolating noise levels in undulating regions. Accurate visualising traffic noise levels requires a prior understanding of spatial interpolations. [ABSTRACT FROM AUTHOR]

Simple Summary: Traumatic brain injuries, a primary global health concern, can lead to severe disabilities. Acute subdural haematoma is one type of traumatic brain injury resulting from the rupture of bridging veins in the brain. Existing numerical models often oversimplify these structures. This study's main goals were to understand how the cerebral vein's cross-sectional shape affects its response, more akin to real-life testing, and to introduce a hyperelastic model for these veins that captures their non-linear behaviour. The results reveal that the vein's shape significantly influences its response to stretching, highlighting the need for more realistic geometries in modelling. Additionally, hyperelastic models, like the Marlow and polynomial models, were successfully implemented. This research provides valuable insights into the mechanical properties of bridging veins and their response to tensile loading, potentially improving our understanding of traumatic brain injuries. Traumatic brain injury (TBI) is a serious global health issue, leading to serious disabilities. One type of TBI is acute subdural haematoma (ASDH), which occurs when a bridging vein ruptures. Many numerical models of these structures, mainly based on the finite element method, have been developed. However, most rely on linear elasticity (without validation) and others on simplifications at the geometrical level. An example of the latter is the assumption of a regular cylinder with a constant radius, or the geometry of the vein acquired from medical images. Unfortunately, these do not replicate the real conditions of a mechanical tensile test. In this work, the main goal is to evaluate the influence of the vein's geometry in its mechanical behaviour under tensile loading, simulating the real conditions of experimental tests. The second goal is to implement a hyperelastic model of the bridging veins where it would be possible to observe its non-linear elastic behaviour. The results of the developed finite element models were compared to experimental data available in the literature and other models. It was possible to conclude that the geometry of the vein structure influences the tensile stress–strain curve, which means that flattened specimens should be modelled when validating constitutive models for bridging veins. Additionally, the implementation of hyperelastic material models has been verified, highlighting the potential application of the Marlow and reduced polynomial (of fourth and sixth orders) constitutive models. [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]

A classically studied geometric property associated to a complex polynomial p is the inradius (the radius of the largest inscribed disk) of its (filled) lemniscate Λ ≔ { z ∈ ℂ : | p (z) | < 1 }. In this paper, we study the lemniscate inradius when the defining polynomial p is random, namely, with the zeros of p sampled independently from a compactly supported probability measure μ. If the negative set of the logarithmic potential U μ generated by μ is non-empty, then the inradius is bounded from below by a positive constant with overwhelming probability (as the degree n of p tends to infinity). Moreover, the inradius has a deterministic limit if the negative set of U μ additionally contains the support of μ. We also provide conditions on μ guaranteeing that the lemniscate is contained in a union of n exponentially small disks with overwhelming probability. This leads to a partial solution to a (deterministic) problem concerning the area of lemniscates posed by Erdös, Herzog, and Piranian. On the other hand, when the zeros are sampled independently and uniformly from the unit circle, then we show that the inradius converges in distribution to a random variable taking values in (0 , 1 / 2). We also consider the characteristic polynomial of a Ginibre random matrix whose lemniscate we show is close to the unit disk with overwhelming probability. [ABSTRACT FROM AUTHOR]

• A three-dimensional helical metamaterial tapered rod with power-law radius is proposed. • Complex band analyses and experimental results demonstrate a broad omnidirectional bandgap with strong wave attenuation capacity. • Wave mode coupling and conversion open up different bandgap types in helical structure. • Complete bandgap can be tuned via adjusting geometric parameters of tapered helical rod lattice. Tapered metamaterials have drawn much attention due to the inherent advantage of vibration reduction. However, the bandgap performance in most traditionally periodic structures is only restricted to a single direction. In this paper, aiming at opening up the complete bandgap both in flexural and longitudinal directions, we propose a novel type of three-dimensional helical metamaterial tapered rod with a power-law radius. Complex band analyses and vibration transmission results demonstrate that this metamaterial possesses a broad complete bandgap and several single-directional flexural bandgaps. The formation mechanisms of two bandgap types are also revealed. The complete bandgap is created by the combination effect between the local resonance and Bragg scattering effect. The mode transformation phenomenon immediately takes place before and after this complete bandgap. On the other hand, below the complete bandgap, single-directional bandgaps are generated by the separation effect between the neighboring modes which belong to different dominant directions. It can also be found that the wave attenuation capacity in the complete bandgap is far more significant than that of the single-directional one. Meanwhile, by increasing the initial radius or reducing the residual radius, a stronger local resonance effect can enlarge the complete bandgap and improve the attenuation capacity for evanescent waves. To validate the dynamic characteristics, different tapered rod metamaterials are fabricated and tested. A good agreement can be observed between the numerical predictions and experimental results. Based on these analyses, the three-dimensional helical metamaterial tapered rod paves a promising way for realizing excellent omnidirectional wave attenuation. [ABSTRACT FROM AUTHOR]

The problem of numerical differentiation for periodic functions with finite smoothness is investigated. For multivariate functions, different variants of the truncation method are constructed and their approximation properties are obtained. Based on these results, sharp bounds (in the power scale) of the minimal radius of Galerkin information for the problem under study are found. [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]

Some exoplanets are slightly larger than Earth, and some are slightly smaller than Neptune. But there is a distinct lack of anything in between. Why? Cynthia Ho dives into the radius valley. [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]