Relative Radius Research Articles

A Theoretical Solution for Interaction Between Lined Twin Tunnels at Great Depths by a New Alternating Procedure

In designing tunnels, rock-lining interactions are an important issue that needs to be accurately predicted and analyzed. For the closely located twin tunnels, the rock-lining interaction is more complex because of the interaction between tunnels. Based on the classical Schwarz alternating method, a new alternating procedure with fast convergence is presented, which can be used to solve the elastic problems of lined multiple holes. In consideration of the real interaction between tunnels and the interaction between rock and linings, an analytical model for the elastic mechanical responses of lined twin circular tunnels at great depths is proposed using the new analytical procedure. The solutions in all the alternating steps can be superposed to obtain the final solutions that satisfy all the boundary and continuity conditions and the solutions are efficiently calculated because of the analytical expressions. A good agreement between the analytical and numerical results indicates the correctness of the solutions. Based on the analytical model, the influences of the pillar width, relative tunnel radius, the lining stiffnesses and lateral pressure coefficient on the stress and displacement around the tunnels are obtained. The proposed method can be further applied to multiple-lined tunnel problems to quickly predict the supporting force.

Study on the mechanical behavior of microcapsules during the mixing process of asphalt mixture

To enhance the survival rate of microcapsules during the mixing process of asphalt mixture, the mechanical behavior of microcapsules during this process was investigated through simulation. Initially, the asphalt mixture containing microcapsules was divided into mesoscopic and microscopic scales. Utilizing composite material models, the stepwise inclusion method and high-temperature tensile tests, the equivalent mechanical parameters for the microcapsules, asphalt mastic and asphalt mortar at mixing temperature were estimated. Following this, the mixing process of the asphalt mixture incorporating microcapsules was simulated employing the discrete element method (DEM) coupled with multi-body dynamics (MBD). This simulation was instrumental in identifying optimal mixing parameters and enabled the analysis of force chain transmission across the multi-scale model. Furthermore, the finite element method (FEM) was employed to develop a monomer model of the microcapsules, facilitating the assessment of their mechanical behavior under optimal mixing conditions. Finally, a detailed sensitivity analysis was performed to investigate the influence of various parameters on the mechanical behavior of microcapsules. The results indicated that, at the mixing temperature, the equivalent Young’s modulus and Poisson's ratio for urea-formaldehyde (UF) resin microcapsules, asphalt mastic, and asphalt mortar were determined to be 0.22 GPa and 0.478, 19.87 GPa and 0.4986, and 88.77 GPa and 0.468, respectively. The optimal mixing parameters for AC-16 asphalt mixture including mixing speed, filling rate and mixing duration were identified as 49 rpm, 50 % and 53 s, under which the most adverse load on the microcapsule is 80 mN. Under the most adverse load, microcapsules might rupture from the inside out, and their survival rate was not less than 68.9 %. Increasing the particle size of microcapsules and reducing the relative radius of the microcapsule core could potentially enhance the crack resistance of microcapsules during mixing.

Prediction of cavity inception speed and underwater radiated noise of a full-scale marine propeller based on a cavitation tunnel model test

Propeller cavitation is a dominant source of underwater radiated noise (URN) from shipping, and the appropriate evaluation of propeller noise mitigation measures is important for ecological ship design. In this study, a model test procedure and scaling method to predict the full-scale URN level from hydrodynamic noise sources were introduced. The cavity size based on the empirical vortex model was considered in the proposed scaling method for a quiet cruise condition with isolated tip vortex cavitation. This relation provides information on the equivalent cavitation number for the model test to have the same relative radius as that of the full-scale tip vortex cavitation. The alternative test cavitation number can also be chosen as close as possible to the point that gives the equivalent tip vortex cavity size if sheet cavitation exists in the condition for the equivalent cavity size. In this case, additional noise scaling should be performed using the ratio of the tip vortex cavity radii. The new scaling exponent introduced in this study varies according to the distance from the cavitation inception condition and shows a decreasing trend from the value at the inception condition as the equivalent cavitation number for the model test decreases. The scaled URN levels based on the proposed method showed reasonable agreement with the measurement results of a full-scale ship. Finally, the noise reduction effect of the specially designed wake control fin and propeller was investigated through a comparative model test following the proposed scaling strategy, and significant noise reductions were observed with changes in the design configuration.

Given a wingspan, which windplane design maximizes power?

Windplanes (i.e. Fly-Gen airborne wind energy systems) harvest wind power via the turbines placed on the tethered wing, which flies crosswind trajectories. In this paper, the optimal design of windplanes is investigated with simplified models, enabling an intuitive understanding of their physical characteristics. The windplane is then idealized as a point mass flying circular fully crosswind trajectories. If the gravity is neglected, the dynamic problem is axial symmetric and the solution is steady. The generated power can be expressed in non-dimensional form by normalizing it with the wind power passing by a disk with radius the wingspan. Since the reference area is taken to be a function of just the wingspan, looking for the design which maximizes this power coefficient addresses the question ”Given a wingspan, which design maximizes power?”. This is different from the literature, where the design problem is formulated per wing area and not per wingspan. The optimal designs have a finite aspect ratio and operate at the maximum lift-to-drag ratio of the airfoil. Airfoils maximizing the lift-to-drag ratio are then optimal for windplanes. If gravity is included in the model, gravitational potential energy is being exchanged over one revolution. Since this exchange comes with an associated efficiency, the plane mass and the related trajectory radius are designed to reduce the potential energy fluctuating over the loop. However, for decreasing turning radii, the available wind power decreases because the windplane sweeps a lower area. For these two conflicting reasons, the optimal mass is finite.

Study on crack resistance of self-healing microcapsules in asphalt pavement by multi-scale method.

Self-healing microcapsules in the asphalt pavement must be kept intact under vehicle load to ensure there is enough rejuvenator in capsules when cracks appear in asphalt pavement. In this paper, the crack resistance of self-healing microcapsules in asphalt pavement was evaluated. Firstly, an expanding multi-scale analysis was conducted based on proposed mesoscopic mechanical models with the aim to determine the mechanical parameters for the following contracting multi-scale analysis. Secondly, the periodic boundary condition was introduced for the contracting multi-scale analysis and the stress field of the capsule wall was obtained. Finally, the effects of the design parameters of the microcapsule on its crack resistance in asphalt pavement were investigated. The results showed that the incorporation of microcapsules has almost no effect on the elastic constants of the asphalt mixture. The core could be simplified as an approximately incompressible solid with the elastic constants determined by the proposed mesoscopic mechanical model. With the increase of the modulus of the capsule wall, the mean maximum tensile stress of the capsule wall increased from 0.372 MPa to 0.465 MPa, while with the decrease of the relative radius of the capsule core, the mean maximum tensile stress of the capsule wall increased from 0.349 MPa to 0.461 MPa. The change in the mean maximum tensile stress of the capsule wall caused by the change of capsule diameter was within 5%. The relative radius of the capsule core and the elastic modulus of capsule wall were two key parameters in capsule design. Besides, the microcapsules with the wall made of resin would not crack under the vehicle load before microcracks occurred in asphalt pavement.

PUNCHING THIN DISCS. PART 4. INVESTIGATION OF THE DEFORMATION OF THE PROTRUSION WITH AN ANNULAR PUNCH

A mathematical description of the deformation by a peripheral annular punch of a protrusion formed as a result of the introduction of the central punch in the course of obtaining large disks or disks from hard-to-deform materials by plastic deformation is obtained. The maximum force of deformation by an annular punch at the moment of completion of the deformation process is found. The relative radius of the annular punch is determined, which ensures the equality of the forging forces of the central and annular punches.

On the Possibility of an Upper Limit on Magnetically Induced Radius Inflation in Low-mass Stars

The radii of low-mass stars are observed to be inflated above standard model predictions, especially in magnetically active stars. Typically, the empirical relative radius inflations ΔR/R are ≤10% but in (rare) cases may be ≥20%. Our magneto-convective stellar models have already replicated many empirical ΔR/R values. Here, we ask: is there any theoretical upper limit on the amount of such inflation? We use our magneto-convective model to compute ΔR/R using empirically plausible values of the surface field strength parameter δ. Inside each model, the maximum internal field is set to a particular value: B ceil = 10, or 100 kG, or 1 MG. When B ceil = 10 kG, peak inflation with ΔR/R ≈ 90% occurs in stars with masses of 0.7 M ⊙. With B ceil = 100 kG, peak inflation with ΔR/R ≈ 140% occurs in stars with M ≈ 0.5 M ⊙. But with B ceil = 1 MG, we find no peak in ΔR/R as a function of δ; instead, the larger δ is, the larger ΔR/R becomes, reaching 300%–350% in the case of the largest δ considered. Thus, magneto-convective modeling can accommodate ΔR/R values which are considerably larger than any reported empirical inflations. We find that a maximum occurs in ΔR/R as a function of δ only in model stars where the field reaches its maximum strength B ceil inside the convective envelope. Moreover, our models of completely convective stars undergo smaller amounts of relative radius inflation than models with radiative cores, a result consistent with some previous reports.

Preliminary study of dual annular multiple-beam cathode for V-band coaxial transit-time oscillator

Since the research toward high-power millimeter-wave generator becomes a tendency in high-power microwave, overmoded structure with the high-order mode has been a considerable interest because of its potential to increase power handling capacity (PHC). To expand the PHC of V-band transit-time oscillator and excite higher mode TM03, a dual annular multiple-beam cathode has been proposed. In the geometric structure of the dual annular multiple-beam diode, cathode rods around two concentric circles are uniformly placed on cathode base, and each circle has several graphite rods. Because of space charge shielding effect and fluctuation of electron beam, explosive emission current of inner and outer cathode circles is difficult to be balanced, and the electron beam transmission rate is not very high. To solve those two problems, the relative length (ΔL) and the relative radius (Δr) between the inner and outer cathode circles are optimized to obtain balanced currents of inner and outer beams and a good transmission rate. In this paper, the preliminary study of a dual annular multiple-beam cathode is carried out by optimizing the cathode structure. When ΔL and Δr are equal to 2.5 and 4 mm, respectively, the dual annular multiple-beams cathode can provide 2.71 kA uniform intense relativistic electron beams under 421 kV, and the magnetic field is 1.2T. As a simulation result, explosively emitted and the 95.2% of total beam current transmission rate can be reached.

The Distribution of Semidetached Binaries. I. An Efficient Pipeline

Semidetached binaries are in the stage of mass transfer and play a crucial role in studying the physics of mass transfer between interacting binaries. Large-scale time-domain surveys provide many light curves of binary systems, while Gaia offers high-precision astrometric data. In this paper, we develop, validate, and apply a pipeline that combines the Markov Chain Monte Carlo method with a forward model and DBSCAN clustering to search for semidetached binaries and estimate the inclination, relative radius, mass ratio, and temperature ratio of each using light curves. We train our model on the mock light curves from Physics of Eclipsing Binaries (PHOEBE), which provides broad coverage of light-curve simulations for semidetached binaries. Applying our pipeline to Transiting Exoplanet Survey Satellite sectors 1–26, we have identified 77 semidetached binary candidates. Utilizing the distance from Gaia, we determine their masses and radii with median fractional uncertainties of ∼26% and ∼7%, respectively. With the added 77 candidates, the catalog of semidetached binaries with orbital parameters has been expanded by approximately 20%. The comparison and statistical results show that our semidetached binary candidates align well with the compiled samples and the PARSEC model in T eff–L and M–R relations. Combined with the literature samples, comparative analysis with stability criteria for conserved mass transfer indicates that ∼97.4% of samples are undergoing nuclear-timescale mass transfer, and two samples (GO Cyg and TIC 454222105) are located within the limits of stability criteria for dynamical- and thermal-timescale mass transfer, and are currently undergoing thermal-timescale mass transfer. Additionally, one system (IR Lyn) is very close to the upper limit of delayed dynamical-timescale mass transfer.

Gaussian clustering and quantification of the sperm chromatin dispersion test using convolutional neural networks.

Sperm DNA fragmentation is a sign of sperm nuclear damage. The sperm chromatin dispersion (SCD) test is a reliable and economical method for the evaluation of DNA fragmentation. However, the cut-off value for differentiation of DNA fragmented sperms is fixed at 1/3 with limited statistical justification, making the SCD test a semi-quantitative method that gives user-dependent results. We construct a collection of deep neural networks to automate the evaluation of bright-field images for SCD tests. The model can detect valid sperm nuclei and their locations from the input images captured with a 20× objective and predict the geometric parameters of the halo ring. We construct an annotated dataset consisting of N = 3120 images. The ResNet 18 based network reaches an average precision (AP50) of 91.3%, a true positive rate of 96.67%, and a true negative rate of 96.72%. The distribution of relative halo radii is fit to the multi-peak Gaussian function (p > 0.99). DNA fragmentation is regarded as those with a relative halo radius 1.6 standard deviations smaller than the mean of a normal cluster. In conclusion, we have established a deep neural network based model for the automation and quantification of the SCD test that is ready for clinical application. The DNA fragmentation index is determined using Gaussian clustering, reflecting the natural distribution of halo geometry and is more tolerable to disturbances and sample conditions, which we believe will greatly improve the clinical significance of the SCD test.

Effective Strains Determination in Continuous Constrained Double Bending with Active Friction Forces

In this work, a new process for severe plastic deformation (SPD) with active friction forces - CCDB Conform R3D2, a variation of the so-called "active bending", which is a continuous two-stage bending in calibers with small relative bending radius, is analyzed. A mechanical scheme of a device for realization of the process with a bending roller is proposed, based on a developed 3D virtual tool for its realization. Using CAD/CAE software 3D simulation, two virtual solutions of the process were compared, differing in terms of the location of the bending roller relative to the axes of the feeding and output rolls. The distribution and magnitude of the effective strains in the volume of the deformed long workpiece in the two bending stages at small relative bending radiuses were analyzed. An analytical expression is developed to determine the effective strains achieved in the SPD operation by constrained continuous bending in calibers with grooved rolls. The strain calculation methodology is based on the results obtained by simulation modelling of the CCB Conform R3D2 process in trapezoidal calibers with a bending roller located above and below the rolls line.

Integrating geometries of ReLU feedforward neural networks.

This paper investigates the integration of multiple geometries present within a ReLU-based neural network. A ReLU neural network determines a piecewise affine linear continuous map, M, from an input space ℝm to an output space ℝn. The piecewise behavior corresponds to a polyhedral decomposition of ℝm. Each polyhedron in the decomposition can be labeled with a binary vector (whose length equals the number of ReLU nodes in the network) and with an affine linear function (which agrees with M when restricted to points in the polyhedron). We develop a toolbox that calculates the binary vector for a polyhedra containing a given data point with respect to a given ReLU FFNN. We utilize this binary vector to derive bounding facets for the corresponding polyhedron, extraction of "active" bits within the binary vector, enumeration of neighboring binary vectors, and visualization of the polyhedral decomposition (Python code is available at https://github.com/cglrtrgy/GoL_Toolbox). Polyhedra in the polyhedral decomposition of ℝm are neighbors if they share a facet. Binary vectors for neighboring polyhedra differ in exactly 1 bit. Using the toolbox, we analyze the Hamming distance between the binary vectors for polyhedra containing points from adversarial/nonadversarial datasets revealing distinct geometric properties. A bisection method is employed to identify sample points with a Hamming distance of 1 along the shortest Euclidean distance path, facilitating the analysis of local geometric interplay between Euclidean geometry and the polyhedral decomposition along the path. Additionally, we study the distribution of Chebyshev centers and related radii across different polyhedra, shedding light on the polyhedral shape, size, clustering, and aiding in the understanding of decision boundaries.

Effects of pellet ratio on the burden movement and distribution characteristics in the BF throat

In order to solve the urgent problem of energy conservation and emission reduction in the iron and steel industry, the use of high proportion pellets in blast furnace smelting will be the trend of ironmaking development in recent years. In the present work, a geometric model of a serial-hopper bell-less type charging system based on the discrete element method was built, which was used to investigate the distribution behavior of burden under the condition of multi-ring charging and different pellet ratios. The results show: (1) the overall velocity and particle flow width of the burden at the chute outlet become larger which results the average radius of falling point increases. (2) The pellet ratio has a significant effect on the distribution characteristics and the burden profiles at the furnace throat. When the pellet ratio increases from 0% to 100%, the relative radius of peak position of the burden layer increases from 0.491 R to 0.639 R, while the peak height decreases from 0.860 m to 0.543 m. (3) The burden segregation occurs at both the radial and longitudinal positions of the layer. In the radial position, the distribution of pellets near the center is relatively concentrated compared with sinter and there is no burden segregation occurs near the relative radius of 0.590 R. In the longitudinal position, the pellets are mainly distributed at the bottom of the burden layer, while the upper part is relatively less distributed. The research content and results may give a reference for the charging operation of BF under the condition of large pellet ratio, and consequently reduce CO2 emission in ironmaking process.

Understanding the negative effects of alkalis on long-term strength of Portland cement

It has long been known that alkalis favor an increase in the early strength of cementitious materials but have a negative impact on long-term strengths. The reasons for the negative effect on later strengths are not clear. In this paper we investigated the influence of alkali addition on the properties of a white cement and for the first time propose a plausible mechanism for the late strength reduction. Quantitative XRD analysis and strength results showed that the addition of alkali generally limits the total degree of hydration (DoH) after 1 day. The evolution of internal relative humidity (RH) and saturated pore radius indicate that the more alkali added, the faster the decrease of internal RH and desaturation of the larger pores. The remaining solution in higher alkali system is concentrated in the smaller pores, where the needed supersaturation is higher. As a consequence, the hydration rate of cement is depressed by added alkali.

A mathematical model for the motion of a micro-robot consisting of three spheres linked with axially aligned retractable arms in Stokes flow that gives expressions for mean distance moved, mean drift velocity and energy efficiency of the non-reciprocal cyclic swimming motion

The problem studied was the non-reciprocal cyclic swimming motion of three spheres linked with axially aligned retractable arms in Stokes flow. The arms are assumed to be able to retract at a steady speed to half their length, and then at a later time in the motion extend at the same steady speed back to their original length. It is important in the field of medical biology, because this motion could enable a micro-robotic device to swim within the arterial and cellular fluid to perform medical biological procedures such as surgery or drug delivery. The method used was the development of a theoretical mathematical model in low Reynolds number Stokes flow, that takes the mathematical expression for steady motion of a sphere, and from this obtains the motion for three spheres by assuming leading order interactions between the spheres. This gives an interaction matrix from which the important results of the study are obtained which are exact mathematical expressions for the mean distance travelled, mean drift velocity and energy efficiency of the motion. These are that the mean distance travelled is 3a0ln(9/8), the mean drift velocity is (3a0/2A)ln(9/8), and the energy efficiency of the motion is 9a02/(4A2)[ln(9/8)]2, where a0 is the sphere radius and A is the arm length. The conclusions to be drawn from the results are that the most efficient design has the largest ratio for sphere radius in relation to arm length. The novelty of the work is that it gives exact mathematical expressions for distance travelled, velocity and energy efficiency not given previously in the literature.

Effects of relative curvature radius on erosion and sedimentation patterns in a 90o bend with and without bendway weirs

Bendway weirs are low-level transverse structures constructed on the outer bank of a channel bend to improve navigation, create aquatic habitat and control bend migration. This experimental study was aimed at investigating the erosion and sedimentation patterns in a 90° bend by varying the relative curvature radius (i.e. normalized to the channel width), in the absence and in the presence of bendway weirs, under different flow conditions. A series of flat weirs with relative heights of 30% and 70% were considered. The results indicate that as the relative curvature increases, the erosion near the weirs decreases while the point-bar at the inner bend wall extends. Regardless of the weir height, the increase in the relative curvature leads to a deeper scour depth at the tip of the weirs. Bendway weirs with submergence ratio of 70% are found to be the most efficient in protecting the outer bank from erosion.

Single and two-cells shape analysis from energy functionals for three-dimensional vertex models.

Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the definition of an energy functional, which fully determines the cellular response and conclusions. While two-dimensional vertex models have been widely employed, three-dimensional models are far more scarce, mainly due to the large amount of configurations that they may adopt and the complex geometrical transitions they undergo. We here investigate the shape of single and two-cells configurations as a function of the energy terms, and we study the dependence of the final shape on the model parameters: namely the exponent of the term penalising cell-cell adhesion and surface contractility. In single cell analysis, we deduce analytically the radius and limit values of the contractility for linear and quadratic surface energy terms, in 2D and 3D. In two-cells systems, symmetrical and asymmetrical, we deduce the evolution of the aspect ratio and the relative radius. While in functionals with linear surface terms yield the same aspect ratio in 2D and 3D, the configurations when using quadratic surface terms are distinct. We relate our results with well-known solutions from capillarity theory, and verify our analytical findings with a three-dimensional vertex model.

Extremely Large Polymer Light‐Emitting Electrochemical Cells with Concentric Circular Electrodes

AbstractPlanar polymer light‐emitting electrochemical cells (LECs) with concentric circle electrodes are demonstrated. With a fixed outer electrode radius of 6.8 mm, the inner electrode radius is varied from 1 to 3 mm. All cells can be activated with a 40 V bias at 360 K. The extremely large electrode gap size allows for time‐lapsed imaging of the in situ electrochemical p‐ and n‐doping processes. When the advancing p‐ and n‐doping fronts meet, a light‐emitting junction in the shape of a jagged ring is formed near the center of the electrode gap. Reversing bias polarity pushes the light‐emitting junction outward to near the negative electrode. It is possible to achieve a perfectly centered emitting junction by fine tuning the inner electrode radius. The sensitivity of junction position to relative electrode radius indicates the p‐ and n‐doping reactions are strongly coupled. The concentric circular electrode configuration offers a cross sectional view of an LEC‐based light‐emitting fiber. In any fiber shaped light‐emitting device, the inner and outer electrodes always differ in size. This electrode asymmetry should be considered and exploited to achieve optimal cell performance.

Modeling of discharge in compound open channels with convergent and divergent floodplains using soft computing methods

Abstract In this research, the estimation of discharge in compound open channels with convergent and divergent floodplains using soft computing methods, including the neural fuzzy group method of data handling (NF-GMDH), support vector regression (SVR), and M5 tree algorithm were performed. For this purpose, the geometric and hydraulic characteristics of the flow, including relative roughness (ff), relative area (Ar), relative hydraulic radius (Rr), relative dimension of the flow aspects (δ*), relative width (β), relative flow depth (Dr), relative longitudinal distance (Xr), convergent or divergent angle (θ) of the floodplain and longitudinal slope (So) of the bed were used as input variables and discharge was considered as the target (output) variable. The results showed that the statistical indices of the NF-GMDH in the testing stage are RMSENF-GMDH = 0.004, R2NF-GMDH = 0.923 and in the same stage for SVR are RMSESVR= 0.002 and R2SVR = 0.941 and finally for M5 tree algorithm are RMSEM5 = 0.002, R2M5= 0.931. The evaluation of the structure of the M5 tree algorithm showed that the most effective parameters are ff, Dr, Rr, δ*, and θ which confirm the important parameters specified by MARS, GMDH, and GEP algorithms used by previous researchers.

The relationship between plate prominence and need for removal after volar plate osteosynthesis of distal radius fractures.

This study aimed to assess the incidence of plate-related complications and the need for plate removal after volar plate osteosynthesis of the distal radius in relation to Soong classification. All consecutive patients (age > 16years) in our level II trauma center treated with plate osteosynthesis for distal radius fractures from January 2017 until June 2019 were retrospectively evaluated. The main outcome measures were volar plate positioning according to Soong classification and incidence of plate removal. In addition, the incidence of tendon ruptures, reasons for volar plate removal, and improvement of complaints after removal were evaluated. The overall incidence of plate removal in the 336 included patients was 16.9% (n = 57). Removal incidence in Soong 2 plates (28.2%) was significantly higher compared to Soong 0 and 1 plates (8.0% and 14.4%, respectively), P = 0.003. Multivariable binary logistic regression analysis showed Soong grade 2 as an independent predictor for plate removal, OR 4.3 (95% CI 1.4-13.7, P = 0.013). Four cases of flexor and four cases of extensor tendon rupture were reported, all in Soong 2 grade plating. The main reasons for volar plate removal were pain (42%) and reduced functionality (12%). In cases where pain was the main reason for removal, 81% of patients reported a decrease in pain during follow-up after surgery. This study suggests an association between plate prominence graded by Soong and plate removal using a single plating system. Plate prominence should be reduced in volar plating whenever technically feasible.