Local Radius Of Curvature Research Articles

In Situ Multiphysical Metrology for Photonic Wire Bonding by Two-Photon Polymerization

Femtosecond laser two-photon polymerization (TPP) technology, known for its high precision and its ability to fabricate arbitrary 3D structures, has been widely applied in the production of various micro/nano optical devices, achieving significant advancements, particularly in the field of photonic wire bonding (PWB) for optical interconnects. Currently, research on optimizing both the optical loss and production reliability of polymeric photonic wires is still in its early stages. One of the key challenges is that inadequate metrology methods cannot meet the demand for multiphysical measurements in practical scenarios. This study utilizes novel in situ scanning electron microscopy (SEM) to monitor the working PWBs fabricated by TPP technology at the microscale. Optical and mechanical measurements are made simultaneously to evaluate the production qualities and to study the multiphysical coupling effects of PWBs. The results reveal that photonic wires with larger local curvature radii are more prone to plastic failure, while those with smaller local curvature radii recover elastically. Furthermore, larger cross-sectional dimensions contribute dominantly to the improved mechanical robustness. The optical-loss deterioration of the elastically deformed photonic wire is only temporary, and can be fully recovered when the load is removed. After further optimization based on the results of multiphysical metrology, the PWBs fabricated in this work achieve a minimum insertion loss of 0.6 dB. In this study, the multiphysical analysis of PWBs carried out by in situ SEM metrology offers a novel perspective for optimizing the design and performance of microscale polymeric waveguides, which could potentially promote the mass production reliability of TPP technology in the field of chip-level optical interconnection.

Substrate topography regulating membrane adhesion mediated by receptor–ligand bonds

Cell adhesion can be significantly influenced by the topography of the substrate surface. However, how the adhesion molecules essentially respond to this topographical stimulus is not fully understood yet. Here, we employ an effective Monte Carlo simulation to systematically investigate a fluctuating membrane interacting with a curved substrate via adhesive proteins. Interestingly, results show that, compared with the flat substrate, curved substrates regulate the membrane adhesion in a bond length dependent manner. The effects of the substrate surface amplitude and wavelength on the number of molecular bonds and adhesion pattern are also extracted from the scaling relationship between the characteristic lateral length of the membrane and the local substrate curvature radius. Furthermore, the local substrate curvature is found to select the bond distribution in terms of the bond length and stiffness. The results suggest that the bond stiffness enhances the clustering of molecular bonds, mainly due to synergistic interactions among these molecular bonds.

Dynamics of small solid particles on substrates of arbitrary topography

We study the dynamics of a small solid particle arising from the dewetting of a thin film on a curved substrate driven by capillarity, where mass transport is controlled by surface diffusion. We consider the case when the size of the deposited particle is much smaller than the local radius of curvature of the substrate surface. The application of the Onsager variational principle leads to a reduced-order model for the dynamic behavior of particles on arbitrarily curved substrates. We demonstrate that particles move towards region of the substrate surface with lower mean curvature with a determined velocity. In particular, the velocity is proportional to the substrate curvature gradient and inversely proportional to the size of the particle, with a coefficient that depends on material properties that include the surface energy, surface diffusivity, density, and Young’s (wetting) angle. The reduced model is validated by comparing with numerical results for the full, sharp-interface model in both two and three dimensions.

Three-dimensional assessment of subchondral arc and hip joint coverage angles in the asymptomatic young adult hip.

The primary objective of this study was to develop a custom algorithm to assess three-dimensional (3D) acetabular coverage of the femoral head based on surface models generated from computed tomography (CT) imaging. The secondary objective was to apply this algorithm to asymptomatic young adult hip joints to assess the regional 3D acetabular coverage variability and understand how these novel 3D metrics relate to traditional two-dimensional (2D) radiographic measurements of coverage. The algorithm developed automatically identifies the lateral- and medial-most edges of the acetabular lunate at one-degree intervals around the acetabular rim based on local radius of curvature. The acetabular edges and the center of a best-fit sphere to the femoral head are then used to compute the mean 3D subchondral arc angles and hip joint coverage angles in five acetabular octants. This algorithm was applied to hip models generated from pelvis/hip CT imaging or abdomen/pelvis CT angiograms of 50 patients between 17 and 25 years of age who had no history of congenital or developmental hip pathology, neuromuscular conditions, or bilateral pelvic and/or femoral fractures. Corresponding 2D acetabular coverage measures of lateral center edge angle (LCEA) and acetabular arc angle (AAA) were assessed on the patients' clinical or digitally reconstructed radiographs. The 3D subchondral arc angle in the superior region (58.0 [54.6-64.8] degrees) was significantly higher (p < 0.001) than all other acetabular subregions. The 3D hip joint coverage angle in the superior region (26.2 [20.7-28.5] degrees) was also significantly higher (p < 0.001) than all other acetabular subregions. 3D superior hip joint coverage angle demonstrated the strongest correlation with 2D LCEA (r = 0.649, p < 0.001), while 3D superior-anterior subchondral arc angle demonstrated the strongest correlation with 2D AAA (r = 0.718, p < 0.001). The 3D coverage metrics in the remaining acetabular regions did not strongly correlate with typical 2D radiographic measures. The discrepancy between standard 2D measures of radiographic acetabular coverage and actual 3D coverage identified on advanced imaging indicates potential discord between anatomic coverage and the standard clinical measures of coverage on 2D imaging. As 2D measurement of acetabular coverage is increasingly used to guide surgical decision-making to address acetabular deformities, this work would suggest that 3D measures of acetabular coverage may be important to help discriminate local coverage deficiencies, avoid inconsistencies resulting from differences in radiographic measurement techniques, and provide a better understanding of acetabular coverage in the hip joint, potentially altering surgical planning and guiding surgical technique.

Mechanism of temporal interface evolution and internal circulations during the droplet formation in a planar slit T-microchannel

The present study has numerically explored the mechanism of interface evolution and internal flow circulations during the droplet formation in two-phase flow through a planar T-microchannel. The two-dimensional unsteady form of the conservative level set equation coupled with Navier–Stokes equations has been solved using the finite element method. The range of parameters include the contact angle (θ) from 120° to 180°, and the flow rate ratio (Qr) from 0.1 to 10 for the low capillary number (Cac≤10−2). The present study indicates that surface wettability plays a crucial role in influencing the temporal evolution of the interface. The internal flow circulation in the droplet is controlled by the axial and radial velocities primarily influenced by shear stress. The newly introduced novel “interface-to-neck ratio” parameter has provided another platform to investigate the pinch-off dynamics of droplets. Moreover, the phenomenon of droplet pinch-off is primarily initiated and driven by the Laplace pressure, defined by three distinct approaches: the pressure difference method, the determination of the minimum local radius of curvature on the rear side, and a calculation of the neck width. The predictive correlations have been established to estimate the droplet characteristics as a function of the flow rate ratio and contact angle. The findings reported have significant implications for the design of droplet dispensing systems that depend on surface wettability as a critical regulating parameter.

Verification and validation of detonation-shock-dynamics relations for explosives described by general equation of state and chemical reaction models

Detonation shock dynamics is a powerful method to model the behaviour of High Explosives (HE). However in order to use this method, the underlying relationship between the local radius of curvature and the detonation speed must be known. Previous work has developed methods to calculate this effect using simple, single-step Arrhenius and polytropic gas, models for the chemical reaction and the equation of state, respectively. In recent years, more complex models for both reaction rates and equations of state have been developed which show better agreement with experimental data than these simple models, especially when considering condensed phase explosives.. This work presents the governing equations for solving these problems in a way that is generalised to use arbitrary equations of state as well as reaction models which may have more than a single step and multiple product species. This implementation is verified against exact solutions, demonstrating that the equations were implemented properly. The verified algorithm is then validated against experimental data and high fidelity simulations, showing that it is able to make accurate predictions in a regime where the underlying assumptions of the governing equations are valid. This approach has many applications: from creating equivalent detonation shock dynamics models for existing reactive burn calibrations for HE; to developing new functional forms and calibrations of reactive burn models for condensed phase high explosives.

The influences of the mechanical equilibrium among interfacial tensions at triple junction on the morphological evolution of eutectic lamella

In this work, the influence of the mechanical equilibrium among interfacial tensions at three-phase triple junctions on the morphological evolution of growing eutectic lamella was quantitatively investigated through the phase-field simulations. We found that, when eutectic lamella grows at the steady-state, the orientations of the three interfacial tensions under mechanical equilibrium state are highly coincident with the tangent lines of the contour of the corresponding interfacial morphologies at the three phases’ triple junction. It is argued that the eutectic lamellar growth is unable to reach the steady state when the interfacial tensions fail to achieve mechanical equilibrium at the triple junctions. Moreover, a strong dependence of interfacial morphology on the state of the mechanical equilibrium between interfacial tensions is determined, and quantified through the change of lamella spacing and local curvature radius of lamella with the interfacial tensions. Furthermore, the underlying mechanism about the effects of mechanical equilibrium state on eutectic morphological evolution is also explained. We conclude that the final steady-state of eutectic growth is determined by the complex interplay among solute diffusion, eutectic morphology and the mechanical equilibrium of interfacial tensions.

Modeling fatigue behavior of additively manufactured alloys with an emphasis on pore defect morphology

Additively manufactured (AM) materials are prone to porosity, which limits their widespread adoption in fatigue-limited applications. Experimental campaigns are vital in understanding the effects of porosity on fatigue resistance but are costly and time consuming. This work presents a modeling framework to predict fatigue life debits in AM materials due to representative pore defects including keyhole, lack of fusion, and linearly aligned/planar pores. Materials characterization data is leveraged from specimens of alloy 718 (also known as IN718) that have been intentionally seeded with pore defect structures via a systematic modification of the process parameters. Statistically equivalent microstructure (SEM) models are generated as analogues to the experimental specimens and undergo crystal plasticity simulations. A Bayesian inference framework is used to calibrate a critical value of a damage parameter, which is used to predict the fatigue lives of SEMs seeded with pores. A strategy based on the macro-scale treatment of notches is proposed to regularize micromechanical field variables in large stress gradients in the presence of pores, or more generally, geometric discontinuities, of various sizes and morphology. The regularization volume is inversely proportional to the local pore radius of curvature and adequately smooths micromechanical fields. The framework presented here can be used to augment experimental data and rapidly evaluate the detrimental effects of porosity on fatigue resistance in AM components.

On the failure behavior of a GFRP composite cylinder under Brazier crushing force – An experimental and computational study

The induced ovalization or out-of-plane deformation in the circular and transition airfoils of modern MegaWatt (MW) size wind turbine rotor blades is caused by the combined effect of the applied far-field bending loads and the local structural curvature. In general, the phenomenon of the ovalization or out-of-plane deformation of the circular elastic cross sections under the applied bending load or the internal/external pressure is termed the Brazier effect [1 2]. Considering the poor mechanical performance in the out-of-plane direction of the typically used laminated glass composites for wind turbine rotor blade construction, the current research work aims to develop a thoroughly validated computational methodology to understand the ovalization (out-of-plane deformation) induced failure behavior in circular cross-sections located between the root and transition region of a rotor blade, using a substructure level testing and modeling under representative load conditions. To this end, detailed manufacturing, testing, and a computational modeling campaign is devised and executed at different length scales starting from coupon to cylinder (substructure) level. The required elastic, strength, and fracture properties for the cylinder progressive damage analysis are evaluated using coupon-level experiments following various ASTM standards.The developed numerical methodology is thoroughly validated using the substructure level experimental load–displacement curves, strain, and damage profiles. Detailed experimental and numerical studies reveal that the induced ovalization leads to a non-linear relation between the applied crushing force and the local radius of curvature until the unstable collapse of the cylinder. Based on the thorough local stress and damage analysis, it is evident that along with the dominant interlaminar shear stress (ILSS), the presence of the interlaminar tensile (ILT) stress component is the key to the delamination induced collapse of the cylinder.

The effect of stent graft curvature on the hemodynamic displacement force after abdominal aortic aneurysm endovascular repair

Endovascular aortic aneurysm repair is a minimally invasive procedure with low mortality and morbidity. Clinical studies have revealed that a displacement force (DF) can cause stent graft (SG) migration in some circumstances requiring repeated intervention. This study aims to determine the relationship between the SG curvature and the calculated DF from four patient-specific computational fluid dynamics models. The SG's curvature was defined according to the centrelines of the implanted SG's branches. The centrelines were defined as either intersecting or separated lines. The centreline curvature (CLC) metrics were calculated based on the local curvature radii and the distances from the centrelines of idealized straight branches. The average CLC value and average variation were calculated to represent the entire graft's curvature. These CLC calculations were compared, and the method that gave the best correlation to the calculated DF was found. The optimal correlation is obtained from calculating the CLC average variation using separated centrelines and distance from straight lines, with an R 2 = 0.89. Understanding the relationship between vascular morphology and DF can help identify at-risk patients before the procedure. In these cases, we can provide appropriate treatment and follow up with the patient to prevent future failure.

A finite element procedure for time-dependent radio-frequency sheaths based on a two-dimensional microscale fluid model

In this paper, we present a finite element scheme for the analysis of time-dependent radio-frequency (RF) sheath behavior in a plasma-filled domain bounded by periodically curved plates. This numerical scheme is based on a two-dimensional (2D) microscale model in which the time-dependent cold-ion fluid equations, the Maxwell–Boltzmann relation for electrons, and Poisson's equation are solved subject to periodic boundary conditions (BCs) and conducting-wall BCs. The continuity of the total current is employed in localized regions to provide a constraint on the reference sheath potential. The primary purpose of this work is to understand 2D dynamic sheath behavior in order to improve predictive capabilities for RF wave interactions in magnetic fusion experiments. In particular, this work treats cases where the local radius of curvature of the wall surface is comparable to the non-neutral sheath width. Using the developed numerical code, the dependences of the ion, electron, and displacement admittances on the wall bump height, ion magnetization, ion mobility, and the magnetic field angle are investigated. It is shown that the ion and electron admittances are nearly unchanged over wide ranges of the bump height and ion magnetization. In addition, the 2D sheath effects are assessed through the spatial distributions of various quantities such as the electron density, electrostatic potential, ion velocity, and surface wall current.

Temporal instability of the liquid film formed by a liquid jet impinging on a curved cylindrical wall

The linear temporal instability of the confined curved liquid film formed by a liquid jet impinging on a curved wall has been investigated. The corresponding dispersion relation between the non-dimensional wave growth rate and wave number was derived. The dispersion relation further involves the influences of the local radius of curvature and the azimuthal angle of the liquid film. The dispersion relation could be verified with previous researches, and the optimal wavelength has been verified with experiments. Temporal stability analysis shows that the effects of gas-to-liquid velocity ratio, gas-to-liquid density ratio, the relative thickness of the liquid phase to the gas phase, and azimuthal wave number are similar to previous researches, but the unstable ranges are smaller than that in previous researches. This paper further studied the effects of the local radius of curvature and azimuthal angle of the liquid film. As the local radius of curvature decreases, the instability of confined curved films increases for the given conditions. And both the growth rate and instability range increase with the increase of the azimuthal angle. The solutions would be helpful to understand the atomization process of the liquid film formed by a liquid jet impinging on a curved wall.

Crack‐tip blunting and its implications on fracture of soft materials

AbstractFracture of compliant materials is preceded by large deformations that reshape initially sharp cracks into rounded defects. This phenomenon, known as elastic crack blunting, is peculiar of rubber‐like polymers and soft biological tissues, such as skin, vessel walls, and tendons. With this work, we aim to provide a discussion on crack‐tip blunting and its implications in terms of tearing resistance and flaw tolerance of soft elastic materials. The characteristic features of the crack‐tip zone in the framework of nonlinear elasticity are reviewed analytically and with the help of finite element analyses on pure shear cracked geometries. Specifically, the strain‐hardening behavior typical of soft biological tissues is addressed, and we illustrate its effect on crack‐tip blunting, in terms of a local radius of curvature at the crack tip. A simplified geometrically nonlinear model, proposed to describe the progressive blunting at the crack tip and its effect on flaw tolerance, is validated through finite element analyses and experimental tests on silicone samples. We show how this can lead to a simplified criterion to define the fracture condition in nonlinear soft materials.

Critical effects and scaling at meniscus osculation transitions.

We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature R_{w} in a confining parabolic geometry. We argue that the exponent β_{osc} characterizing the scale of the interfacial height ℓ_{0}∝R_{w}^{β_{osc}} at osculation, for large R_{w}, falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent ζ by β_{osc}=3ζ/(4-ζ). In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent β_{osc} takes the same value as the exponent β_{s}^{co} for complete wetting, which is determined directly by the intermolecular forces. The prediction β_{osc}=3/7 in d=2 for systems with short-range forces (corresponding to ζ=1/2) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in d=3, based on a microscopic model density-functional theory, determines that β_{osc}≈β_{s}^{co}≈0.326 close to the predicted value of 1/3 appropriate to the mean-field regime for dispersion forces.

Polyamide powder coating of copper substrates: Impact of process parameters on the surface properties, the adhesion strength and the interface microstructure

The aim of this work was to assess the impact of coating process parameters on the quality of biopolyamide coating on copper substrates obtained by conventional hot dipping fluidized bed coating process (CHDFB). The experiments carried out in this study allowed to understand the decohesion mechanism of virgin biopolyamide 11 before having assessed coating properties by chemical, mechanical and microstructural characterizations. The investigations showed that a higher thickness and better surface finishing were obtained for high preheating temperatures and intermediate immersion times mainly thanks to a higher heat energy stored by the metal support whereas long immersion times compromised the aspect. A laboratory-developed mechanical test was also carried out to determine the adhesion strength. This allowed to overcome the variability linked to the analyzed surface preparation or the local radius of curvature of pull-off and peel conventional adhesion tests respectively that could influence the adhesion strength data. It was concluded that, even if more severe metal preheating conditions improved the coating physical properties, they led to a worse adherence. Surface morphology and spectrometry analyses of the coating side facing the interface correlated to the mechanical test results allowed to highlight the growing formation of copper oxide and copper hydroxide compromising the coating adhesion. From all the results, the optimal process parameters were determined.

Properties of surface electronic states in layered organic conductors in out-of-plane magnetic field

In this paper, we have considered the properties of surface electronic states in quasi-two-dimensional organic conductors for an out-of-plane orientation of the magnetic field. The energies of these states have be calculated which allow the resonance magnetic fields and resonance angles corresponding to the positions of the peaks in oscillation spectra of surface resistance to be determined. We find that the energies of the magnetic-field induced surface states are decreasing significantly with increasing tilt angle from the surface. This is related to the fact that the surface states are realized due to electron transitions between different in size elliptical closed orbits obtained as cross-section of the Fermi surface with the plane [Formula: see text], [Formula: see text] const. In comparison to the case of in-plane magnetic field, where only the small closed orbits on the sides of the Fermi surface are involved in formation of the surface states, for out-of-plane magnetic field there are additionally present other, larger orbits that are spanning across the Fermi surface. We also find that the coordinate of the center of electron revolution is increasing significantly with increasing tilt angle but the maximum distance from the surface for the electrons involved in the surface states shows a steady increase indicating that the skipping trajectories are well confined within skin layer of the conductor. This indicates that the surface states can be observed for almost each field direction from the surface including those with higher quantum number. These studies allow to determine more accurately certain Fermi surface parameters such as the local radius of curvature in the plane perpendicular to the magnetic field as well as the Fermi velocity at each point on the elliptical cross-sections. We are highly convinced that our results will motivate new experimental investigations of surface phenomena in order to exploit the properties of surface electronic states for various scientific applications.

Modification of the Loss Cone for Energetic Particles in the Earth's Inner Magnetosphere

AbstractThe 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.

Analytic investigation on error of heat flux measurement and data processing for large curvature models in hypersonic shock tunnels

Due to short test time, heat conduction was considered as transient in hypersonic shock tunnels. The heat flux measurement and data processing were operated basing on one-dimensional semi-infinite heat conduction theory. However, for models with local large curvature or small radius, it resulted in significant compression or expansion of space for heat transfer, or lateral heat conduction, which made the hypothesis of one-dimensional unsatisfied and errors. In this paper, approximate solutions for the unsteady heat conduction in cylindrically convex and concave shells were established, and were used for further analysis of the errors, with forms of heating load, location and curvature radius of heated surface taken into consideration.

Long-wavelength equations of motion for thin double vorticity layers

We consider the time evolution in two spatial dimensions of a double vorticity layer consisting of two contiguous, infinite material fluid strips, each with uniform but generally differing vorticity, embedded in an otherwise infinite, irrotational, inviscid incompressible fluid. The potential application is to the wake dynamics formed by two boundary layers separating from a splitter plate. A thin-layer approximation is constructed where each layer thickness, measured normal to the common centre curve, is small in comparison with the local radius of curvature of the centre curve. The three-curve equations of contour dynamics that fully describe the double-layer dynamics are expanded in the small thickness parameter. At leading order, closed nonlinear initial-value evolution equations are obtained that describe the motion of the centre curve together with the time and spatial variation of each layer thickness. In the special case where the layer vorticities are equal, these equations reduce to the single-layer equation of Moore (Stud. Appl. Math., vol. 58, 1978, pp. 119–140). Analysis of the linear stability of the first-order equations to small-amplitude perturbations shows Kelvin–Helmholtz instability when the far-field fluid velocities on either side of the double layer are unequal. Equal velocities define a circulation-free double vorticity layer, for which solution of the initial-value problem using the Laplace transform reveals a double pole in transform space leading to linear algebraic growth in general, but there is a class of interesting initial conditions with no linear growth. This is shown to agree with the long-wavelength limit of the full linearized, three-curve stability equations.

Study of turbulent flame characteristics of water vapor diluted hydrogen-air micro-mixing combustion

Hydrogen has been regarded as an important alternative fuel, especially in gas turbine applications. However, the premixed combustion of pure hydrogen has problems such as easily flashback and high NOx emissions. A more reasonable method of combustion is to use micro-mixing technology combined with water vapor dilution. This work experimentally investigated the influences of dilution rate (D) and equivalence ratio (φ) on the flame characteristics of hydrogen-air micro-mixing combustion diluted with water vapor. Results show that increasing D reduces the flame area by reducing the downstream OH radical signal, which is contrary to the effect of CO2 dilution. The flame local curvature radius shows that the micro-mixing combustion is a high turbulence intensity combustion, and the convex structure is more frequent. Moreover, increasing φ or decreasing D leads to a decrease in the instantaneous average curvature radius (Rave), indicating more small-scale wrinkle structures are generated. D and φ have a similar influence on the fluctuations of Rave and flame area in the time domain, while the fluctuation of the flame area is more evident near the lean-burn limit. When D = 25%, the frequency characteristics of the flame structure and chemical reactions are synchronized.