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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 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]

• 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]