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A numerical model for the prediction of vibration behaviors of a laminated submarine structure consisting of spherical, cylindrical, and cone shells with multiple built-in annular plates is reported in this article. With the aid of the first-order shear deformation theory (FSDT) concerning plates and shells, the energy expressions of each substructure are derived. The displacement functions in the energy functionals are expanded by the employment of Legendre orthogonal polynomials and circumferential Fourier series. Then, the Rayleigh–Ritz procedure is performed to obtain the eigenfrequency and the corresponding eigenmode of the submarine model. The correctness of the structural model is examined by comparing the results with existing papers and the finite element method, and the maximum deviation is not more than 2.07%. Additionally, the influence of the plate's thickness, position, inner diameter, as well as the laying angle on the intrinsic vibration characteristics of laminated submarine-like structure is determined. The results reveal that rational geometry design and assemblage benefit the vibration performance of the combination. Increasing the thickness of all the annular plates, decreasing the inner radius, and regulating the laminated scheme, make remarkable influence on structural free vibration, with the maximum relative changing rate of frequency exceeding 97%, 16%, and 23%, respectively. [ABSTRACT FROM AUTHOR]

Compared with straight tunnels, over-excavation occurs on the inner side of the curved section during shield construction of small radius curved tunnels, and the disturbance to the ground surface and mechanical properties of surrounding rock and segment are more severe. This paper establishes the numerical models of small radius curve tunnels and straight tunnels to study the characteristics of surface deformation caused by the shield excavation of small radius curved tunnels and the influence of shield construction parameters on ground settlement, surrounding rock deformation, and segment force. The maximum error between the numerical simulation results and the measured surface settlement curve is 7.3%, which is in good agreement. The results show that: (1) The maximum value of the surface settlement of the small radius curve tunnel appears inside the curve section, and with the decrease in the curve radius, the surface settlement increases, and the distance between the peak settlement point and the tunnel center is larger. (2) When the curve radius of the tunnel is smaller, the lateral displacement of the ground surface moves farther to the inner side, and the range of soil mass with lateral displacement in the inner side is also wider. (3) Increasing the heading face pressure and grouting pressure can reduce surface settlement, but the heading face pressure should not exceed 350 kPa, and the grouting pressure should not exceed 250 kPa. (4) When the curve radius is smaller, the deformation of surrounding rock and the segment stress is larger. [ABSTRACT FROM AUTHOR]

In this study, the modelling of arithmetical mean roughness after turning of C45 steel was performed. Four parameters of cutting tool geometry were varied, i.e.: corner radius r, approach angle κ, rake angle γ and inclination angle λ. After turning, the arithmetical mean roughness Ra was measured. The obtained values of Ra ranged from 0.13 μm to 4.39 μm. The results of the experiments showed that surface roughness improves with increasing corner radius, increasing approach angle, increasing rake angle, and decreasing inclination angle. Based on the experimental results, models were developed to predict the distribution of the arithmetical mean roughness using the response surface method (RSM), Gaussian process regression with two kernel functions, the sequential exponential function (GPR-SE) and Mattern (GPR-Mat), and decision tree regression (DTR). The maximum percentage errors of the developed models were 3.898 %, 1.192 %, 1.364 %, and 0.960 % for DTR, GPR-SE, GPR-Mat, and RSM, respectively. In the worst case, the maximum absolute errors were 0.106 μm, 0.017 μm, 0.019 μm, and 0.011 μm for DTR, GPR-SE, GPR-Mat, and RSM, respectively. The results and the obtained errors show that the developed models can be successfully used for surface roughness prediction. [ABSTRACT FROM AUTHOR]

It was shown several years ago that dark matter halo outskirts are characterized by very steep density profiles in a very small radial range. This feature has been interpreted as a pile-up of different particle orbits at a similar location, namely, splashback material at half an orbit after collapse. Adhikari et al. (2014) obtained the location of the splashback radius through a very simple model by calculating a dark matter shell trajectory in the secondary infall model while it crosses a growing NFW profile-shaped dark matter halo. Because they imposed a halo profile instead of calculating it from the trajectories of the shells of dark matter, they were not able to find the dark matter profile around the splashback radius. In the present paper, we use an improved spherical infall model taking into account shell crossing as well as several physical effects such as ordered and random angular momentum, dynamical friction, adiabatic contraction, etc. This allows us to determine the density profile from the inner to the outer region and to study the behavior of the outer density profile. We compare the density profiles and their logarithmic slope of with the simulation results of Diemer and Kravtsov (2014), finding a good agreement between the prediction of the model and the simulations. [ABSTRACT FROM AUTHOR]

The problem of calculating the moisture content of pore space of sediment after its mechanical drying in a centrifuge with a peripheral filtering surface is studied. An analytical equation was derived along the radius of moisture filling of the sediment by filtrate of the capillary fringe, taking account of lognormal distribution of pore sizes. The proportion of moisture imported into the pores by the bound filtrate is determined. The presence of a basal layer of the capillary fringe is illustrated. The possibility of limiting determination of the smallest pore diameter toward larger size for constructing histograms and calculating the moisture content of the sediment is confirmed. The agreement of the results with the known experimental data received for suspensions of chemical and oil refining industries in filtering centrifuges is confirmed by an example of calculation. The main variable design and technological parameters for calculations based on effective mechanical drying of sediment in the filtering centrifuge rotor are the radius of the circumference of its filtering surface, the angular velocity, and the maximum size of pores in the sediment. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Polytechnic is the property of Journal of Polytechnic and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present new upper bounds for the numerical radius of n × n operator matrices defined on a complex Hilbert space, i.e., operator matrices of the form [Tij], and illustrate with numerical examples that these bounds are better than the existing bounds. [ABSTRACT FROM AUTHOR]

In this study we investigate the sharp radius of starlikeness of subclasses of Ma and Minda class for the ratio of analytic functions which are related to limaçon functions. This survey is connected also to the first-order differential subordinations. In this context, we get the condition on β for which certain differential subordinations associated with limaçon functions imply Ma and Minda starlike functions. Simple corollaries are provided for certain examples of our results. Finally, we present several geometries related to our study. [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]

In classical elasticity, when V-notches under tension are modeled with stress-free notch-face conditions and symmetry conditions ahead of notches, stress singularities occur when notch-tip radii are zero. This raises the question of when do notch-tip stresses first start to depart from physical reality as radii go to zero. To address this question here, cohesive stress action is taken into account as radii go to zero. To obtain sufficient resolution of the key notch-tip fields, finite element analysis with highly focused locally structured meshes is employed. Meshes are systematically refined until convergence checks indicate sufficient accuracy is obtained. This finite element analysis is further verified by comparison with a corresponding set of V-notch test problems. Results then show that only for very small notch-tip radii do peak stresses with cohesive stresses active differ significantly from peak stresses with classical boundary conditions. [ABSTRACT FROM AUTHOR]

The scattering of a linearly polarized electromagnetic plane-wave from a sphere composed of an orthorhombic dielectric–magnetic medium having concentric layer of the chiral material is considered. The incident, the internal, and the scattered field phasors are expanded in terms of suitable sets of vector waves. By ensuring the continuity of the tangential components of electromagnetic fields across the chiral/ free-space and the chiral/ orthorhombic dielectric-magnetic interfaces, a relation between the incident and the scattered fields expansion coefficients by a transition matrix is obtained. Thereafter, the total scattering, absorption, forward-scattering, and backscattering efficiencies of the scattered field were calculated. The influences of the chirality parameter on various cross sections for different core–shell radii ratio are discussed numerically. [ABSTRACT FROM AUTHOR]

This paper deals with stability analysis of anisotropic-charged cylindrical geometry coupled with f (R , T) modified gravity theory (ℳ ). In this ℳ , the Lagrangian is a varying function of traces of Ricci and stress tensors. In order to examine the stable behavior of the anisotropic cylindrical cosmic object under the electromagnetic effects, we calculated the modified equations of motion and equations of continuity. in the background of f (R , T) theory. By utilizing the perturbation technique, we constitute a modified collapse equation (ℳ ℰ), which contains geometrical and physical variables in the charged scenario. Our investigation continues under the nonminimally coupled function of ℳ . Furthermore, we investigate the dynamically stable phases of charged geometry at Newtonian () and post-Newtonian (p ) epochs with the help of the rigidity parameter of fluid (Γ) by imposing some constraints on physical parameters. [ABSTRACT FROM AUTHOR]

In this work, we establish precise local in time dispersive estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains \Omega \subset \mathbb {R}^3 with smooth boundary \partial \Omega \neq \emptyset. This result is the improved estimates established by Len Meas [C. R. Math. Acad. Sci. Paris 355 (2017), pp. 161–165]. Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Strichartz estimates for waves inside an arbitrary domain \Omega have been proved by Blair, Smith, Sogge [Proc. Amer. Math. Soc. 136 (2008), pp. 247–256; Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), pp.1817–1829]. Optimal estimates in strictly convex domains have been obtained by Ivanovici, Lebeau, and Planchon [Ann. of Math. 180 (2014), pp. 323–380]. Our case of cylindrical domains is an extension of the result of Ivanovici, Lebeau, and Planchon [Ann. of Math. 180 (2014), pp. 323–380] in the case when the nonnegative curvature radius depends on the incident angle and vanishes in some directions. [ABSTRACT FROM AUTHOR]

Since the structure of thin-walled shell component is sensitive to the thinning of shell thickness, it is essential to prevent material in critical deformation region, such as sharp corners, from exceeding the forming range. As a result, a shape calibration process (SCP) using flexible die was developed in this work, aiming at reducing the excessively accumulative strain in the corners with small radius in the multi-pass stamping. Elastomers with specific geometry were employed as the pressure-carrying medium in the SCP of annular and rectangular corners of a target shell component. Optimal process parameters in the proposed SCP were determined numerically, on the basis of which, forming experiments were conducted. The results showed that the forming accuracy and resultant uniformity of shell thickness were improved by selecting flexible die with appropriate Shore hardness, thickness, and geometry. Compared with SCP using rigid dies, thinning ratio of the shell thickness showed a sharp decrease of 72.9% in the SCP of rectangular corner and springback exhibited a dramatic decrease of 57.4% in the SCP of annular corner using flexible dies. Distribution of in-plane pressure, vector of metal flow, and load paths of deformed sheet were employed to clarify the forming mechanism of the SCP using flexible dies. More industrial applications of the proposed method will be expectable. [ABSTRACT FROM AUTHOR]

Let G be a digraph and A (G) be the adjacency matrix of G. Let D (G) be the diagonal matrix with outdegrees of vertices of G. For any real α ∈ [ 0 , 1 ] , define the matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G). The largest modulus of the eigenvalues of A α (G) is called the A α spectral radius of G. In this paper, we determine the digraphs which attain the maximum (or minimum) A α spectral radius among all strongly connected digraphs with given parameters such as girth, clique number, vertex connectivity or arc connectivity. We also propose an open problem. [ABSTRACT FROM AUTHOR]

The breakup process of the inviscid liquid bridge sandwiched between two coaxial and equal-sized rods is investigated by tracking its profile. Here, the focus is on the quasi-static profile of the liquid bridge close to rupture and its influence on the subsequent dynamic breakup behaviors. With the increasing distance between the two rods, the profile of the liquid bridge close to rupture undergoes a transition from symmetry to asymmetry. We found there exists a critical slenderness above which the liquid bridge will be asymmetric and present a profile that can be well fitted by one cycle of the sine wave. It is demonstrated both experimentally and theoretically that the ratio of the length of the bridge to its equivalent radius, defined as geometric mean of the radii at the peak and trough of the bridge, is always 2 π for the asymmetric bridge close to rupture. Different with the symmetric evolution of the short bridge, the long asymmetric bridge pinches off first from the side near the bigger sessile drop and then from the other side, which endows the satellite droplet with a lateral momentum, resulting in the satellite re-collected by the sessile drop. The influence of the slenderness on the time interval among the asymmetric pinch-off, velocity, destination, and size of the satellite was investigated. A scaling law was proposed to describe the relationship between the lateral momentum of the satellite and the time interval between two pinch-off. This work is expected to benefit the utilizing or suppressing the satellite in practice. [ABSTRACT FROM AUTHOR]

This paper presents results of a first-ever experimental study on the axial compressive behavior of large-scale square reinforced concrete (RC) columns confined with polyethylene naphthalate (PEN)/terephthalate (PET) fiber–reinforced polymer (FRP) composites, which is a new type of FRP with a large rupture strain (LRS) of over 5%. In total, 10 large-scale square RC columns were tested under axial compression, including 8 LRS FRP–wrapped RC columns and 2 RC columns, which served as control specimens. The key experimental parameters were the sectional corner radius and the thickness and type of LRS FRP. The test results show that the effective confinement stiffness ratio of an FRP jacket, as determined by the corner radius and FRP thickness, has a significant effect on the axial compressive behavior of LRS FRP–jacketed large-scale square RC columns. Based on the experimental results, this paper presents an evaluation of two existing LRS FRP–confined concrete models for noncircular columns. Finally, based on the test findings, a refined model for LRS FRP–confined large-scale square columns is presented to provide more accurate predictions of the compressive behavior of these columns. [ABSTRACT FROM AUTHOR]

We study the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed for the lattice translates of the correspondingly dilated polytope to cover the whole space. As our main result, we describe a new algorithm for this problem, which is simpler, more efficient and easier to implement than the only prior algorithm of Kannan (1992). Motivated by a variant of the famous Lonely Runner Conjecture, we use its geometric interpretation in terms of covering radii of zonotopes, and apply our algorithm to prove the first open case of three runners with individual starting points. [ABSTRACT FROM AUTHOR]

The behavior of energetic particles in the Earth's dipole and stretched magnetic‐field models is explored with a focus on the shift of the atmospheric loss cone away from the magnetic‐field direction and on non‐adiabatic behavior occurring when the particle gyroradius becomes comparable with the gradient scale length of the local magnetic field. It is shown that the equatorial loss cone is aberrated away from the magnetic‐field direction (pitch angle of 0°) by the perpendicular drift of a charged particle (which is referred to as the "Mozer transform" described in Mozer (1966, https://doi.org/10.1029/JZ071i011p02701). It is found that the Mozer coordinate transformation in pitch‐angle/gyrophase‐angle space better organizes the behavior of bounce times, mirror altitudes, drift speeds, and first adiabatic invariant. It also describes the loss‐cone shift accurately for a certain range of values of the adiabaticity parameter ϵ, defined by the ratio of the particle gyroradius to the local radius of curvature of the magnetic field. For particles with larger ϵ, the Mozer transform (evaluated with the standard gradient‐curvature drift) breaks down and the "central trajectory" theory can be used to calculate the angular shift of the loss cone, which now includes an Earthward shift. When ϵ becomes relatively large, stochastic field line curvature (FLC) scattering occurs: we show the intimate connection between the strength of FLC scattering and the loss‐cone shift. By comparing ion orbits in the dipole and Tsyganenko (Ts89 and Ts04) magnetic fields, we conclude that the loss cone of ring‐current ions is significantly modified during geomagnetically active times. Key Points: Numerical orbit integration is used to explore the aberration of the loss cone from the direction of the magnetic fieldThe loss cone of ring‐current ions is substantially modified during disturbed timesThe "Mozer transformed" angular coordinate system organizes the behavior of bounce motion [ABSTRACT FROM AUTHOR]

Rotation causes an increase in a neutron star’s mass and equatorial radius. The mass and radius depend sensitively on the unknown equation of state (EOS) of cold, dense matter. However, the increases in mass and radius due to rotation are almost independent of the EOS. The EOS independence leads to the idea of neutron star universality. In this paper, we compute sequences of rotating neutron stars with constant central density. We use a collection of randomly generated EOSs to construct simple correction factors to the mass and radius computed from the equations of hydrostatic equilibrium for nonrotating neutron stars. The correction factors depend only on the nonrotating star’s mass and radius and are almost independent of the EOS. This makes it computationally inexpensive to include observations of rotating neutron stars in EOS inference codes. We also construct a mapping from the measured mass and radius of a rotating neutron star to a corresponding nonrotating star. The mapping makes it possible to construct a zero-spin massâ€"radius curve if the masses and radii of many neutron stars with different spins are measured. We show that the changes in polar and equatorial radii are symmetric, in that the polar radius shrinks at the same rate in which the equatorial radius grows. This symmetry is related to the observation that the equatorial compactness (the ratio of mass to radius) is almost constant on one of the constant-density sequences. [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]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

One of the most crucial aspects of biaxial testing is the geometry of the cruciform specimen. The optimised cruciform geometry leads to obtain adequate stress-strain data. Different geometries of the cruciform specimen were investigated in the last few years, but none of them could be considered as a standard cruciform geometry. It is desirable to have more homogeneous stress and maximum plastic strain in the central area of the specimen. The parameters such as slit width, corner radius, and thickness of the specimen were varied during the FE simulation. The FE tool Abaqus Explicit with von Mises yield criterion was used. Nine alternatives were framed by using Taguchi L9 orthogonal array approach for parametric randomisation. The Technique of Order Preference by Similarity to Ideal Solution (TOPSIS) and Simple Additive Weighting (SAW) methods were employed to evaluate the overall performance of each alternative. The optimised geometry was further analysed with different stress ratios and slit width by keeping other parameters constant. It was noticed that the average plastic strain was decreased from 1.43% to 1.35% and 3.66% to 3.33% with the change in slit width from 0.2 mm to 0.6 mm at loading ratio 1:1 and 2:1, respectively. [ABSTRACT FROM AUTHOR]

In this paper we identify a new family of black holes and solitons that lead to the exact integration of scalar probes, even in the presence of a non-minimal coupling with the Ricci scalar which has a non-trivial profile. The backgrounds are planar and spherical black holes as well as solitons of SU (2) × SU (2) N = 4 gauged supergravity in four dimensions. On these geometries, we compute the spectrum of (quasi-)normal modes for the non-minimally coupled scalar field. We find that the equation for the radial dependence can be integrated in terms of hypergeometric functions leading to an exact expression for the frequencies. The solutions do not asymptote to a constant curvature spacetime, nevertheless the asymptotic region acquires an extra conformal Killing vector. For the black hole, the scalar probe is purely ingoing at the horizon, and requiring that the solutions lead to an extremum of the action principle we impose a Dirichlet boundary condition at infinity. Surprisingly, the quasinormal modes do not depend on the radius of the black hole, therefore this family of geometries can be interpreted as isospectral in what regards to the wave operator non-minimally coupled to the Ricci scalar. We find both purely damped modes, as well as exponentially growing unstable modes depending on the values of the non-minimal coupling parameter. For the solitons we show that the same integrability property is achieved separately in a non-supersymmetric solutions as well as for the supersymmetric one. Imposing regularity at the origin and a well defined extremum for the action principle we obtain the spectra that can also lead to purely oscillatory modes as well as to unstable scalar probes, depending on the values of the non-minimal coupling. [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]

The objective of the present paper is to study the maximum radius r of a connected graph of order n, minimum degree δ≥2 and girth at least g≥4. Erdős, Pach, Pollack and Tuza proved that if g=4, that is, the graph is triangle‐free, then r≤n−2δ+12, and noted that up to the value of the additive constant, this upper bound is tight. In this paper we shall determine the exact maximum. For larger values of g little is known. We settle the order of the maximum r for g=6,8 and 12, and prove an upper bound for every even g, which we conjecture to be tight up to a constant factor. Finally, we show that our conjecture implies the so‐called Erdős girth conjecture. [ABSTRACT FROM AUTHOR]

We study generalized covering radii, a fundamental property of linear codes that characterizes the trade-off between storage, latency, and access in linear data-query protocols such as PIR. We prove lower and upper bounds on the generalized covering radii of Reed-Muller codes, as well as finding their exact value in certain extreme cases. With the application to linear data-query protocols in mind, we also construct a covering algorithm that gets as input a set of points in space, and find a corresponding set of codewords from the Reed-Muller code that are jointly not farther away from the input than the upper bound on the generalized covering radius of the code. We prove that the algorithm runs in time that is polynomial in the code parameters. [ABSTRACT FROM AUTHOR]

The objective of this paper is to reveal the influence of different surface geometric conditions on the dynamic behavior characteristics of a laser-induced bubble collapse. A high-speed camera system was used to record the oscillation process of the laser-induced bubble on plane solid walls with different roughness and a wall containing reentrant cavities full of water or gas. The focus is on the quantitative analysis of the morphological characteristics of the cavitation bubble near the solid wall under different surface forms during the first two oscillation periods. The results show that the dimensionless ratio γ, defined as the distance from the center of the bubble to the wall divided by the maximum radius of the bubble, has a great influence on the change of the cavitation shape in the direction of the vertical wall. Different surface geometries without gas in our cases have no significant effect on the collapse time of cavitation bubbles. While for the surface containing gas, the direction of movement of the bubble accompanying the microjet will greatly change during the collapse of the cavitation bubble, and the collapse time seems to be independent of the dimensionless ratio γ. These achievements shed the light for engineering to avoid the damage of the microjet caused by designing suitable surface geometry. [ABSTRACT FROM AUTHOR]

A single-cell sequencing data set has always been a challenge for clustering because of its high dimension and multi-noise points. The traditional K-means algorithm is not suitable for this type of data. Therefore, this study proposes a Dissimilarity-Density-Dynamic Radius- K-means clustering algorithm. The algorithm adds the dynamic radius parameter to the calculation. It flexibly adjusts the active radius according to the data characteristics, which can eliminate the influence of noise points and optimize the clustering results. At the same time, the algorithm calculates the weight through the dissimilarity density of the data set, the average contrast of candidate clusters, and the dissimilarity of candidate clusters. It obtains a set of high-quality initial center points, which solves the randomness of the K-means algorithm in selecting the center points. Finally, compared with similar algorithms, this algorithm shows a better clustering effect on single-cell data. Each clustering index is higher than other single-cell clustering algorithms, which overcomes the shortcomings of the traditional K-means algorithm. [ABSTRACT FROM AUTHOR]

The work described in this paper is concerned with providing a rational asymptotic analysis for the partial wrinkling bifurcation of a thin elastic hemispherical segment in which the upper rim experiences in-plane circular shearing relative to the other circular edge. The mathematical structure of the associated complex-valued boundary eigenvalue problem is revealed by using the method of matched asymptotic expansions. Our key result is a three-term asymptotic formula for the critical load in terms of a suitable small parameter proportional to the ratio between the thickness and the radius of the shell. Comparisons of this formula with direct numerical simulations provide further insight into the range of validity of the results derived herein. [ABSTRACT FROM AUTHOR]

Starting from the skill characteristics of ski tourism, this paper discusses the impact of consumer skill on travel decisions, and the moderating effect of the ski resort's comprehensive leisure environment (including the ski resort sports environment and the regional cultural tourism environment), in order to both understand their impacts on the travel distance characteristics of skiers and attempt to provide necessary research support for the development of China's ski industry and the construction of destinations. Based on the data from multi-period visitor surveys, this paper constructs the consumption skill-travel radius decision-making influence model under the moderating effect of the ski resort comprehensive leisure environment. The results show three main characteristics. (1) The travel radius obviously differs among skiers with different skill levels. The skill level of skiers has a significant positive effect on the larger travel radius, and a significant negative effect on the smaller travel radius. That is, skiers with a higher skill level are more inclined to undertake long-distance skiing travel, while skiers with a lower skill level are more inclined to undertake short-distance skiing travel. (2) The comprehensive leisure environment has a significant moderating effect on the skiers' travel radius, with a significant positive impact on enlarging the travel radius, while the influences on high-skill and low-skill skiers are significantly higher than on middle-skill skiers. (3) In the comprehensive leisure environment, there are differences in the moderating effect of the ski resort sports environment and the regional cultural tourism environment on the skiers travel radius, and the positive moderating effect of the ski resort sports environment on the high-skill skiers' travel radius is more obvious. While the regional cultural tourism environment has a more obvious positive moderating effect on the travel radius of non-skiers and junior skiers, it is more conducive to promoting domestic travel. In general, the skier skill level in China was generally lower, and the ski resort comprehensive leisure environment optimization is conducive to overcoming the limitation of the travel radius caused by the disadvantageous skill level of consumers. However, to promote the development of China's ski industry in the long run, it is necessary to focus on improving the consumer's ski skill level, but prevent the risk of losing high-skill consumers overseas. In the course of improving the level of domestic ski sports facilities, we should also focus on the domestic leisure cultural tourism environment to better enhance the attractiveness of domestic ski destinations. [ABSTRACT FROM AUTHOR]

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

For an integer k ≥ 1, a k-distance enclaveless number (or k-distance B-differential) of a connected graph G = (V, E) is Ψ k (G) = max{|(V − X) ∩ Nk,G(X)| : X ⊆ V }. In this paper, we establish upper bounds on the k-distance enclaveless number of a graph in terms of its diameter, radius and girth. Also, we prove that for connected graphs G and H with orders n and m respectively, Ψk (G × H) ≤ mn − n − m + Ψk (G) + Ψk (H) + 1, where G × H denotes the direct product of G and H. In the end of this paper, we show that the k-distance enclaveless number Ψk (T) of a tree T on n ≥ k + 1 vertices and with n1 leaves satisfies inequality Ψ k (T) ≤ k(2n−2+n1) 2k+1 and we characterize the extremal trees. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to predict the performances of the turning process using an equivalent oblique cutting model. Based on the real tool, an equivalent cut geometry is performed considering the effects of nose and edge radii. Edge direction and normal cutting angles, uncut chip thickness, and depth of cut were redefined by their equivalent values and then used as new inputs. Turning performances, such as cutting force components, cutting temperatures, and tribology parameters at the tool/chip interface, were predicted over a wide range of cutting conditions. The position of the maximum temperature at the tool/chip interface and its value are determined by solving the heat equation in the chip using the Finite Difference Method. Different assumptions were concluded, and the thermal problem is simply resolved using Laplace transform. It was determined that the maximum tool/chip interface temperature is situated far from the cutting edge about 0.317 l c . It was also found that the partition coefficient is strongly related to sliding speed and it decreases about 20% when chip velocity increases from 1 to 5 m/s. Acceptable agreement was concluded between experimental cutting force components and those predicted from the equivalent oblique cutting model. It can thus be concluded that the equivalent model of cut is highly recommended to predict turning performances. [ABSTRACT FROM AUTHOR]

We investigate theoretically the effect of the coupling radius on the transfer function in 1D parallel and 2D SQUID arrays with different number of Josephson junctions in parallel and series at 77 K. Our results show a plateauing of the array maximum transfer function with the number of junctions in parallel. The plateauing defines the array coupling radius which we show increases with decreasing the normalised inductive reactance of the SQUID loop. The coupling radius is found to be independent of the number of junctions in series. Finally, we investigate the voltage versus magnetic field response and maximum transfer function of one 1D and two 2D SQIF arrays with different SQUID loop area distributions. [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]

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for H -matrices. The computational model can be thought of as a two-stage alternating iterative method, which well suits to the well-known Hermitian and skew-Hermitian splitting (HSS) approach, with the particularity here of considering only one inner iteration. Experimental parallel performance comparison is conducted between the generalized minimal residual (GMRES) algorithm, the standard HSS and our asynchronous variant, on both real and complex non-Hermitian linear systems, respectively, arising from convection–diffusion and structural dynamics problems. A significant gain on execution time is observed in both cases. [ABSTRACT FROM AUTHOR]

Instrumented indentation is gaining ground as a tool for generating mechanical phase maps in composite structures such as dual phase (DP) steels. The plastic zone evolution dictates the indentation parameters in such measurements and needs to be estimated accurately. This study uses finite element modeling to simulate nanoindentation responses on a ferrite–martensite DP steel to directly quantify the plastic zone in the heterogeneous microstructure. The polycrystalline tensile deformation response of individual phases of the composite structure are fed as input to a micro-mechanical finite element model to determine the indentation response. The effect of extrinsic parameters, such as tip radius and geometry, and intrinsic microstructural parameters, like the martensite volume fraction and hardness on the plastic zone evolution and the hardness derived thereof, is established. The model correctly predicts the trend in hardness of individual phases as well as the two-phase composite structure. More importantly, it allows for direct visualization of the plastic zone and the stress triaxiality underneath the complex stress state, enabling prediction of failure modes in these microstructures. This offers a complementary tool to the expensive process of locating and cross-sectioning the indents through site-specific micromachining tools to assess the damage zone under them. [ABSTRACT FROM AUTHOR]

The FEA(Finite Element Analysis) is used to study the optimization of the teardrop shape and stack‐up DOE. We use the viscoelastic model to optimize the teardrop shape parameter: the angle a and the arc‐radius r,. We studied Stack‐up optimization by changing the OCA modulus to reduce the risk of cohesion failure. An 8.0inch teardrop shape foldable AMOLED display prototype was fabricated with a bending radius R=1.5mm. [ABSTRACT FROM AUTHOR]

We parameterize the core of compact spherical star configurations by a mass ( m x ) and a radius ( r x ) and study the resulting admissible areas in the total-mass–total-radius plane. The employed fiducial equation-of-state models of the corona at radii r > r x and pressures p ≤ p x with p (r = r x) = p x are that of constant sound velocity and a proxy of DY Δ DD-ME2 provided by Buchdahl's exactly solvable ansatz. The core ( r < r x ) may contain any type of material, e.g., Standard-Model matter with unspecified equation of state or/and an unspecified Dark-Matter admixture. Employing a toy model for the cool equation of state with first-order phase transition, we also discuss the mass-radius relation of compact stars with an admixture of Dark Matter in a Mirror-World scenario. [ABSTRACT FROM AUTHOR]

Inverse Distance Weighted (IDW) based interpolation method is also widely used in earth science studies. In the classical IDW method, the directional distribution of the reference points around the point to be estimated within the critical circle and the slope differences are not taken into consideration. On the other hand, in the IDW-based method developed by Shepard, the ratio of the distances of the reference points within the critical circle to the critical circle radius (r), the anisotropy and the slope differences are taken into consideration. In this study, the results of the classical IDW method and Shepard method were compared to increase the accuracy of interpolation produced from UAV data. A software has been developed to make these comparisons in more detail. The classical IDW and Shepard based interpolation methods used in this software takes into consideration the anisotropy, the slope differences and the ratio of the distances to the critical circle radius. In this study, UAV flights were performed in three different study areas with different topographic features and 3D point cloud data were obtained in order to make detailed analyzes. Using developed software, data from three different study areas have been tested and the results from different Shepard interpolation models have been discussed. The major contribution of this paper is in evaluation of various IDW options when applied to UAV point data. As a result, especially in geodetic studies form UAV data, it was observed that the results improved with 11% to 37% by using the Shepard method with the suitable power parameter value considering the directional distribution of the reference points in the critical circle and the slope differences. [ABSTRACT FROM AUTHOR]

We introduce a notion of Ricci curvature for Cayley graphs that can be thought of as "medium-scale" because it is neither infinitesimal nor asymptotic, but based on a chosen finite radius parameter. We argue that it gives the foundation for a definition of Ricci curvature well adapted to geometric group theory, beginning by observing that the sign can easily be characterized in terms of conjugation in the group. With this conjugation curvature  κ , abelian groups are identically flat, and in the other direction we show that κ ≡ 0 implies the group is virtually abelian. Beyond that, κ captures known curvature phenomena in right-angled Artin groups (including free groups) and nilpotent groups, and has a strong relationship to other group-theoretic notions like growth rate and dead ends. We study dependence on generators and behavior under embeddings, and close with directions for further development and study. [ABSTRACT FROM AUTHOR]

This study has shown for the analysis of the standard spatial autocorrelation (SPAC) method that the upper limit wavelength (ULW) normalized by the array radius (normalized ULW, NULW) strongly depends on the array size if we include small (radius r less than a few tens of meters) and very small (r about 1 m or less) microtremor arrays in addition to conventional larger arrays. First, field data of microtremor arrays were analyzed to demonstrate the possible use of small/very small arrays. Specifically, it was shown that, (i) even in the case of a very small array, random errors in the analysis results for very long wavelengths relative to the array radius are kept in an acceptable range for practical use; (ii) the signal-to-noise ratio (SNR) is a crucial factor determining the NULW; and (iii) an equation determining the NULW applies, namely the relation (NULW) ∝ (SNR) holds through very small to large arrays. The field data used are those distributed for blind prediction (BP) experiments for an international symposium (BP data), which consist of high-quality microtremor array data with various radii from very small (r = 0.58 m) to large (r = 555 m). It was then shown that SNRs of the BP data, and consequently the NULWs, increase with a decrease of array radius. Statistical data obtained from a few hundred arrays in our previous research also exhibit a similar tendency. The BP data lie around the maximum values of these distributions, showing the high quality of the BP data as well as supporting the array-size dependency of the NULW. Finally, the BP data were processed to identify the characteristics of the soil attenuation. It was found that the array-size dependency of NULW, as well as the large variations in NULW, can generally be explained by soil attenuation. It is plausible that the SNR of small/very small arrays are generally determined by the soil attenuation if the self-noise of the recording system is excluded. A logical conclusion drawn from these results, and also empirically supported, is that the practicality of very small arrays increases as the soil gets softer. [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]

To address the problem that piezoelectric energy harvesters are difficult to apply in certain environments, this paper establishes the theoretical study of the intermediate fixed disc piezoelectric energy harvester (IFDPEH) based on the unimorph under concentrated force. The reliability of the model was indirectly verified by numerical simulation and Computer-Aided Engineering (CAE) simulation. The effects of load, radius ratio (piezoelectric layer/intermediate support), thickness ratio (piezoelectric layer/total thickness), and elastic modulus ratio (substrate/piezoelectric layer) on electrical energy were studied. The results indicate that the radius/thickness ratios of the IFDPEH based on aluminum and beryllium bronze are 0.05/0.31 and 0.05/0.48, respectively. In addition, through parameter comparison, it is found that the most important parameters affecting IFDPEH power are radius ratio and large load. The results are demonstrated to be meaningful for broadening the application of piezoelectric energy harvesters by the derived closed-form equations for the electrical energy along the diameters of the piezoelectric discs in the z-direction. [ABSTRACT FROM AUTHOR]

Mathematical model for designing the surface geometry of the Roots pump rotor based on the Cassini oval principle was derived. The polar coordinate system was used, and the radius vector, the direction of which was set by the φ angle, characterizes the location of the point on the surface of the rotor. The distance of this point from the axis of rotor rotation was set by the calculated value of the ρR polar radius vector. The γ angle of rotors rotation characterizes their mutual orientation in the plane of rotation. Peculiarities of the choice of the a and b parameters that satisfy the shape of the rotor surface geometry are considered. An example of rotor geometry is given for rotor radius R = 50 mm, rotor rounding radius r = 20 mm, parameters a = 33.166 and b = 28. Rotor geometry depends on normalized parameters of a and b, which are constant for a given shape of the surface and constructive dimensions. A mathematical model of the usable cross-sectional area of the pump has been developed. The usable cross-sectional area of the pump was simulated by the geometry of the rotors. The area of the rotor was determined by the geometry of the surface, which was described by an elliptic integral of the 2nd kind. The usable cross-sectional area for the given parameters is modelled. The results of simulation in the form of graphical dependences are given. Parameters a and b must meet the condition of √2/2 < b/a < 1. Under such conditions, the geometry of the rotor surface will be a Cassini oval. The rotation of the two rotors against each other will be by rolling one surface over another. [ABSTRACT FROM AUTHOR]

Let Jv(z) denote the Bessel function of the first kind of order v. In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function Nv(z) = az²Jv"(z) + bzvJ' (z) + cJv(z) in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag--Leffler expansion for function Nv(z) and properties of real and complex zeros of it. [ABSTRACT FROM AUTHOR]

The fracture toughness reflects the rock resistance to crack propagation, and therefore represents an important parameter for rock fracture assessments. From a strict point of view, the real fracture toughness ( K IC ) corresponds to a cracked situation in which the notch radius is theoretically equal to zero. However, most of the defects in rocks have a finite radius and, therefore, should be studied as notch-type defects. Here, the notch effect is numerically studied together with the influence of the grain size and the sorting coefficient (grain size uniformity) on the apparent fracture toughness ( K IN ). To this end, several four-point bending tests with different U-shaped notch radii, mean grain sizes and degrees of uniformity in grain size and shape have been simulated using the Discrete Element Method. In order to represent the grains of the rocks, the Voronoi tessellation is used to create randomly sized and distributed polygonal blocks. These Voronoi polygons have been defined, on the one hand, by an average edge length of 1, 2 and 3 mm, and, on the other hand, by a different number of iterations (n ) in the relaxation process during the generation of the polygons, which defines the grain size uniformity. The numerical analyses performed and the interpretation of the results show a clear notch effect in all the studied cases, as the apparent fracture toughness ( K IN ) increases with notch radius. Finally, the obtained stress fields at the notch tip have been compared to those obtained from the traditional finite element method. Highlights: Four-point bending tests with U-shaped notches simulated using the Discrete Element Method. Different notch radii, mean grain sizes and degrees of uniformity are studied. Results show a clear notch effect, increase of apparent fracture toughness with notch radius. Interpretation of the results using the Theory of Critical Distances. A linear relation between the critical distance of the rock and the grain size is observed. The critical distance slightly increases when less uniform grains are studied. [ABSTRACT FROM AUTHOR]

A general theoretical analysis of a 3D generic TENG structure is presented. Using a dimensionless formulation, it is demonstrated that the optimal TENG geometry does not depend on the frequency of the moving dielectric but the external ohmic impedance for maximum power output is inversely proportional to the frequency. It is also found that the energy is proportional to the cube of the size of the TENG, the square of the triboelectric charge density σT, and the angular frequency ω of the moving dielectric. In the case of a spherical TENG where the moving dielectric is a sphere and the electrodes are spherical caps on a larger sphere three dimensionless parameters that determine the harvested energy are identified: the ratio between the radii of the two spheres r^ = r/R, the polar angle θ of the two spherical caps formed by the electrodes, and Z^ = ZεRω, where Z is the external impedance, R is the radius of the large sphere, ε is the permittivity of the system, and ω is the angular frequency of the moving sphere. Under the crude assumption of constant charge density on the electrodes, the optimal parameters can be easily calculated. It is found that θ = 1.1 rad, r^= 0.67, and Z^= 0.18. [ABSTRACT FROM AUTHOR]