Geometric Boundary Research Articles

An experimental study of the effect of individual upper airway anatomical features on the deposition of dry powder inhaler formulations

This study aims to investigate the effects of different pharynx anatomical features on the delivery of inhaled aerosols. Six in-vitro upper airway models reconstructed using anatomical images acquired by Magnetic Resonance Imaging (MRI) were used for the experiments. A geometrically accurate airway model was produced, and five other different airway models, each missing one or more specific anatomical features: the uvula, epiglottis, and/or soft palate, were derived from the original model. Hence, the geometrical boundaries of the six models were the same except at regions where specific anatomical structures were removed, and this was done to allow meaningful comparisons between the different geometries to be made using specific measurements. Spray-dried mannitol powder (volume median particle size and span were 3.22 μm and 1.90 μm, respectively) was loaded into a capsule-based dry powder inhaler with different resistance, an Osmohaler™ (low resistance), or Handihaler® (high resistance), attached to the inlet of the airway model, which its outlet was connected to a Next-Generation Impactor (NGI). The studies were performed using flow rates of 30 and 60 LPM. High-performance liquid chromatography (HPLC) was used to quantify the mass deposition of particles in different stages of the NGI and airway replicas. Results from this study show that widening the space between the oral cavity and oropharynx, exemplified by one of the six replicas developed, significantly decreases upper airway deposition as well as increases the fine particle fraction. The case with the highest deposition (63.5%) occurred in the pharynx replica with the soft palate present (at 60 LPM with the Hanihaler), while the lowest deposition (26.0%) occurred in the replica without the soft palate and epiglottis (at 30 LPM with the Osmohaler). This study highlights that in addition to the resistance of the inhalers, their interactions with the human airway anatomical features are likely to play important roles in the subsequent lung dose. Results from this study are novel because while the effects of different inhaler resistance in a given airway replica is known, the effects contributed by specific pharynx anatomical features on particle transport behaviour have not been studied experimentally or reported on in the literature. This study shows that space adjacent to the soft palate affects particle deposition dramatically but the effect appears to be more significant when using the Handihaler and for the high flow rate cases.

Warped-Area Reparameterization of Differential Path Integrals

Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing. We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method.

Theoretical analysis for free vibration of submerged conical motor stator

The conical rim-driven motor stator is a structure with variable thickness and non-standard boundaries, which can be treated as an orthotropic conical shell. To prevent resonance and reduce electromagnetic noise, a modal analysis of the stator is necessary. This paper presents an analytical model for the free vibration of the conical stator in both onshore and underwater environments. Due to the relatively large thickness of the motor stator, the first-order shear deformation theory (FSDT) is employed. The fluid loading is calculated by discretizing the conical shell into a series of narrow cylindrical shells featuring diverse radii and thickness. The resulting equations are solved employing the transfer matrix method (TMM), which is capable of different types of boundary conditions (BCs). The convergence and accuracy of the proposed method are validated through a comparative analysis involving numerical simulations and outcomes derived from the thin shell theory. The importance of considering shear deformation and rotatory inertia in determining the natural frequency of motor stators is demonstrated. Finally, the impact of fluid loading on the vibration behavior of stators with various geometric parameters and boundary conditions are investigated and discussed. The proposed model presents a precise and convenient approach for analyzing the free vibration of submerged conical motor stators, and can be extended to conventional cylindrical motor stators through appropriate degradation procedures.

Predicting monotonic lateral load-displacement behavior of offshore flexible piles in saturated MCC soils: An application of the cavity expansion theory

This paper proposes an application of the cavity expansion theory to predict the load-displacement response of monotonically laterally loaded piles and the effective stress distribution of saturated modified Cam-clay (MCC) soil surrounding the pile. This approach incorporates geometric relationship, equilibrium equation, and boundary conditions to derive governing equations. These equations are subsequently solved to obtain monotonic p-y curves, which encompass the elastic, elastoplastic, and critical processes. To determine the load-displacement behavior and effective stress distribution of the soil, the proposed approach combines the deflection equilibrium differential equation with the finite-difference method. The accuracy and effectiveness of the approach are validated through a comparison with a Finite Element Method (FEM) simulation. Parametric studies are also presented to investigate the effects of overconsolidation ratio, in-situ coefficient, and mean effective stress. The validity and capacity of the proposed model are further demonstrated using model pile tests. The results affirm that this approach can well predict the monotonic load-displacement response of the pile and effectively captures important phenomena observed in pile tests.

Minimum-time and minimum-energy trajectory planning under dynamic constraints for a quadrotor

This article proposes an approach for optimizing the trajectory planning of quadrotors in structured environments, taking into consideration the trade-off between task execution time and energy consumption. The constraints taken into account are geometrical (boundary conditions in position and orientation, obstacle avoidance), kinematic (boundary conditions in velocity, linear velocity, and acceleration limits of the system), and dynamic (limit capacities in torque of the actuators, constraints related to the under-actuation of the system). The approach extends the Random Trajectory Profile Approach (RPA) to the case of quadrotors. The results of this approach are validated through experimental tests and compared with those in the literature, demonstrating its effectiveness in offline and online scenarios. The proposed approach offers a promising solution for achieving optimal trajectory planning of quadrotors in structured environments.

Static bending and buckling of FG sandwich nanobeams with auxetic honeycomb core

This study is the first of its kind to apply an analytical technique to offer an accurate solution for the static buckling and static bending of functionally graded (FG) sandwich nanobeams, in which the core layer is an auxetic honeycomb. One notable aspect of this work is the use of third-order shear deformation theory for the computations. It is worth noting that the displacement field of the nanobeam is contingent upon a single parameter. This approach enables the resolution of stability and static bending issues encountered in nanobeams including auxetic honeycomb cores, while also providing a realistic depiction of the beam's mechanical behavior. The two surface layers are composed of different materials, each of which has mechanical characteristics that change in accordance with the exponential function law. The precise solution described in this work is very adaptable and may be used to investigate the mechanical behavior of beams with different boundary constraints, taking into consideration the effect of the nonlocal parameter. When the angle α of the cell varies, the honeycomb core's mechanical characteristics, such as Poisson's coefficient and elastic modulus E, vary continually. This results in static bending and buckling responses that are distinct from those of other auxetics. This study also found it intriguing that the wall angle α has a value of around 90° and that sandwich nanobeams have the highest load capacity. In addition, numerical calculations have been performed to demonstrate the influence of certain geometrical parameters, materials, and boundary constraints on the critical buckling load and maximum deflection of the nanobeam.

A compatible boundary condition-based topology optimization paradigm for static mechanical cloak design

We propose a novel compatible boundary condition-based topology optimization formulation for realizing static mechanical cloaking of linear elastic structures. The key idea is to make the actual boundary conditions along the exterior of the cloaking region consistent with the reference boundary conditions, including the displacement and the nodal force, by designing the cloak structure solely. This compatible boundary condition-based optimization paradigm is not only applicable to various shaped voids (e.g., circle, ellipse, star, Mickey, square, “DUT” logo) and diverse loading conditions (e.g., pressure-sliding, biaxial-stretching, linear-stretching, random-stretching, stretching-sliding) but also demonstrates insensitivity to element quantities and slight variations of external load, ensuring consistent and robust elastostatic cloaking performance. Additionally, adopting the Moving Morphable Voids (MMV) method guarantees the optimized structures have the merits of explicit geometric boundaries and easy fabrication. Numerical examples and experimental validation demonstrate the effectiveness of the proposed approach. The present approach can be easily extended for cloak design in three dimensions and multiphysics.

A rapid performance prediction method for Two-Phase liquid metal MHD generators based on Quasi-One-Dimensional model

Liquid metal magnetohydrodynamic (LMMHD) power generation is a novel and highly efficient technology with broad application prospects. In our previous study, a novel LMMHD enhanced Closed-Brayton-Cycle power generation system for hypersonic vehicles was proposed, and its excellent power generation performance was demonstrated by thermodynamic analysis. The most important component of LMMHD system is the power generation channel, and the rapid and accurate performance prediction and optimization design methods of which are the prerequisites for further research. In this study, a quasi-one-dimensional modeling method for LMMHD power generation channels based on a two-fluid model is developed. The performance variation laws with the geometric structure, magnetic field and boundary conditions, as well as the potential loss mechanisms are investigated. Results indicate that the most optimal or appropriate design can be achieved by optimizing the channel geometry and magnetic field, such as the optimal aspect ratio of 1 and the optimal Hartmann number of 2000. But it is difficult to balance the power output and efficiency through the boundary condition optimization. The gas–liquid slip can lead to approximately 20–40% of energy losses, making the elimination and suppression of slip effects a significant research focus in the relevant field.

Geometrical scalar back-reaction effects in inflation

Starting with the Lagrangian formulation of General Relativity, we will conduct an investigation into the production of spacetime waves, due to a geometric boundary term of a closed extended manifold, within the tensor and scalar sectors. This scheme will be studied in an inflationary universe. We explore two distinct scenarios: Cold Inflation and Warm Inflation. The scalar modes ZkR and ZkI oscillate within the horizon, and become constant at (or right after) horizon crossing k≃aH and they remain so when radiation starts to dominate. The larger k/k0 the Zk’s amplitudes increase too. In general, we can notice that radiation reduces the size of the Zk’s amplitudes, hence yielding smaller signals of such modes. The tensor sector shows an irregular journey due to their abrupt growth just as they cross the horizon. This in turn hinders any probable observational hint or signal. However, we expect that this novel mechanism of spacetime waves production brings new cosmological sources, for which no astrophysical source has been identified.

A study of the natural frequencies of the functionally graded curved beams including porosities: Deterministic and stochastic modeling

In this research article, an investigation into the natural frequencies of functionally graded porous curved beams is presented, covering both deterministic and stochastic domains. The stochastic finite element analysis is based on a three-node, C0 continuous element, and higher-order shear deformation theory, utilizing the first-order perturbation technique (FOPT). The study includes a comparative analysis of three porosity distribution models, including a recently proposed sinusoidal model. Additionally, the study examines the influence of various factors, such as porosity distributions, boundary conditions, volume fraction indices, and geometric configurations, on the natural frequencies. The analysis encompasses uncertain natural frequencies in functionally graded curved beams, accounting for material stochasticity through FOPT. Monte Carlo simulation (MCS) is used to validate the accuracy of the FOPT model, increasing the approach’s reliability. Potential future research in this area could investigate the effects of stochastic variations in geometric parameters, including dimensions and boundary conditions.

Grid cells in rats deprived of geometric experience during development

The medial entorhinal cortex (MEC) is part of the brain's network for dynamic representation of location. The most abundant class of neurons in this circuit is the grid cell, characterized by its periodic, hexagonally patterned firing fields. While in developing animals some MEC cell types express adult-like firing patterns already on the first exposure to an open spatial environment, only days after eye opening, grid cells mature more slowly, over a 1-to-2-wk period after the animals leave their nest. Whether the later emergence of a periodic grid pattern reflects a need for experience with spatial environments has not been determined. We here show that grid-like firing patterns continue to appear during exploration of open square environments in rats that are raised for the first months of their life in opaque spherical environments, in the absence of stable reference boundaries to guide spatial orientation. While strictly periodic firing fields were initially absent in these animals, clear grid patterns developed after only a few trials of training. In rats that were tested in the same open environment but raised for the first months of life in opaque cubes, with sharp vertical boundaries, grid-like firing was from the beginning indistinguishable from that of nondeprived control animals growing up in large enriched cages. Thus, although a minimum of experience with peripheral geometric boundaries is required for expression of regular grid patterns in a new environment, the effect of restricted spatial experience is overcome with short training, consistent with a preconfigured experience-independent basis for the grid pattern.

Vibration mode shifting due to scale-dependency for cylindrical, conical, and spherical microshells

Microshells structures are broadly utilized in micro-electro-mechanical systems (MEMS) such as microresonator, microgyroscope, microsensor, microactuator, microantenna, and microgripper. Taking into consideration the scale-dependency in such a scale and the importance of vibration characteristics in design of such microstructures, the current study aims to analyze the role of scale-decency in mode shifting of common types of thin microshells in MEMS. A scale-dependent quadrilateral finite shell element based on the modified couple stress theory is developed to compute the frequencies and mode shapes of the system. Verification studies are presented to display the accuracy of the established numerical model for the prediction of the vibrational response of microshells with and without scale-dependency. A comprehensive examination is then carried out to disclose the impact of material length scale parameters together with geometrical parameters and boundary conditions on the mode shifting of microscale cylindrical, conical, and spherical shells. It is believed that the results of the present study are handy in the design of the microshells when the scale-decency is of great importance.

Physical Phenomena Governing Mineral Morphogenesis in Molluscan Nacre.

Mollusks, as well as many other living organisms, have the ability to shape mineral crystals into unconventional morphologies and to assemble them into complex functional mineral-organic structures, an observation that inspired tremendous research efforts in scientific and technological domains. Despite these, a biochemical toolkit that accounts for the formation of the vast variety of the observed mineral morphologies cannot be identified yet. Herein, phase-field modeling of molluscan nacre formation, an intensively studied biomineralization process, is used to identify key physical parameters that govern mineral morphogenesis. Manipulating such parameters, various nacre properties ranging from the morphology of a single mineral building block to that of the entire nacreous assembly are reproduced. The results support the hypothesis that the control over mineral morphogenesis in mineralized tissues happens via regulating the physico-chemical environment, in which biomineralization occurs: the organic content manipulates the geometric and thermodynamic boundary conditions, which in turn, determine the process of growth and the form of the biomineral phase. The approach developed here has the potential of providing explicit guidelines for the morphogenetic control of synthetically formed composite materials.

Extended concrete capacity design method for anchors close to non‐rectangular edges

AbstractFastenings in concrete are widely applicable in construction. A significant benefit of fastening technology lies in the fact that it can adapt to various geometries and construction sequences. As a result, the need to design and realize a fastening in structural elements with unconventional geometric configurations can be encountered. Existing design standards rely on the concrete capacity design (CCD) method for concrete‐related failures, which typically covers detailing situations with rectangular configurations of the fastenings and the concrete members. However, the lack of guidelines for a wider range of applications may lead to over‐conservative dimensioning or design constraints. This study investigates the influence of beveled concrete edges on the load‐bearing behavior of anchors. As part of the research, a series of experiments and numerical simulations were conducted. The results derived from the investigations are used to develop an analytical concept that extends the area of applicability of the CCD method and can be used for reliable dimensioning of fastenings close to non‐rectangular concrete edges and geometrical boundaries.

Heat transfer and pressure drop analysis of a microchannel heat sink using nanofluids for energy applications

Abstract The present research aims to enhance heat transfer in straight and wavy profile heat sinks using the same length and hydraulic diameter with different microchannel geometries (triangular, rectangular, trapezoidal, semi-circular, and circular) for uses in electronics, inkjet printing, high heat flux cooling of lasers, and other domains. The nanofluid employed is water/aluminum oxide (water/Al2O3), and the flow regime is laminar. The range of Reynolds number (Re) in this study was 220 ≤ Re ≤ 550, and the concentrations of nanoparticle Al2O3 with Heavy Water (2H2O) were 1.2 % volume. This investigation uses 3-dimensional Computational Fluid Dynamics (CFD) simulation software to investigate the heat transfer characteristics of several cross-sectioned microchannels. The numerical investigation utilizes the finite volume approach, and the CFD analysis is validated with accessible literature with different wavy profiles. According to the CFD simulation results, the microchannel with a circular cross-section has the highest heat transfer performance (up to 18 %) among the other cross-sections. The circular cross-section microchannel seemed to have the most significant increase in coolant temperature (by 9–22 %). The analysis outcomes prove that the microchannel with a circular cross-section has the highest performance for heat transfer; the triangular channel has the lowest performance under the same geometric parameters and boundary conditions. So, it is suggested that a circular microchannel can be used for a heat-carrying capacity of 150 W/cm2, a hydraulic diameter of 500 µm, and a Reynolds number equal to 500.

Straightforward Free Vibration Solutions of Open Cylindrical Shells by the Finite Integral Transform Method

Straightforward analytical free vibration solutions of non-Lévy-type open cylindrical shells are obtained in this study by the finite integral transform method, which was not achieved by conventional semi-inverse methods. Three double finite integral transforms are imposed on the high-order partial differential equations (PDEs) for the problems, with some boundary conditions input, by which the relations between the transformed quantities and specific unknowns are given. Substituting the corresponding inverse transforms into the other boundary conditions provides systems of linear algebraic equations for determining the final analytical solutions. Comprehensive benchmark results for representative open cylindrical shells under different boundary conditions are shown. The results are well verified by other solution methods. With the present solutions, the effects of geometric parameters and boundary conditions on the vibration behaviors are quantitatively revealed by a parametric study. Due to its rigorous and straightforward solution procedure, this study presents a solid easy-to-implement way to explore new analytical solutions of similar problems.

Aircraft engine nozzle guide vane surface temperature optimization

An optimization method based on the sensitivity of global and local geometric parameters is proposed to improve the cooling efficiency of E3 engine nozzle guide vane. For 29 geometric parameters that affect the vane maximum temperature in the cooling design, the sensitivity ranking of them is firstly obtained by the DOE method. Then the most influential parameters including the diameter or location of the film cooling hole are selected as the optimization variables to decrease the maximum surface temperature of the nozzle guide vane. On this basis, to further reduce the local temperature downstream the pressure side, a new duck-paw type film cooling hole is applied. The duck-paw type film cooling hole was produced with the adjoint method through identifying the sensitivity of the geometric boundary parameters of the film cooling holes. Compared to the cylindrical holes, the duck-paw shaped film cooling hole can greatly improve the cooling efficiency under the same conditions. The duck-paw type film cooling holes are applied to the last two rows of film cooling holes located on the pressure side of nozzle guide vane. Three-dimensional conjugate flow and heat transfer analysis results show that the maximum temperature of the optimized cooling structure vane is reduced by 39K, and the average temperature decreases by nearly 20K.

Experimental investigation on stress state and deformation in bolts through tightening of perfect flange connections

AbstractThe fatigue loads of bolts in ring flange connections are significantly influenced by the pressure body between the compressed flanges, which in turn depends on two main scattering parameters ‐ geometric flange imperfections and the preload level. Depending on the tightening method and geometric boundary conditions, shear and bending stresses occur in addition to the axial stress in the bolt during prestressing of the connection. This multiaxial stress condition leads to different plastic deformations in the threads and thereby influence the performance respective the maximum achievable preload of tightening methods. In accordance with the objective, the authors identify the stress state in HV‐bolts during installation for different tightening procedures through experimental testing. Based on a comparison of the strain measurements with the 3D scan of the bolt geometry, this study evaluate to what extent the initial imperfections corresponds to bolt bending. Derived from the scope of a joint national research project, this contribution point out that the yield controlled tightening ensure prestresses close to the individual yield strength of the bolt within a narrow scatter.

Partition-of-unity generalized node method based on isolated blocks for simulating multiple cracks

A partition-of-unity generalized node method (PUGNM) based on isolated blocks was developed to model multiple cracks. This study accommodates the extended finite element method (XFEM) and the numerical manifold method (NMM) within the same framework using the “path-connectivity” concept. In the PUGNM, (1) a cracked body is discretized by a structured square mesh; (2) the pre-assumed isolated blocks (or square elements) are partitioned into isolated sub-blocks by cracks and geometric boundaries; (3) the generalized nodes associated with each square node are defined on the isolated blocks; (4) the generalized nodes with actual independent deformations are obtained by merging all initial generalized nodes on the continuous blocks; (5) the displacement approximation based on the partition-of-unity (PU) method is constructed by a product of the standard quadrilateral finite element (FE) shape functions with the local functions associated with independently deformed generalized nodes. It was demonstrated that almost identical formulations can be derived for the classic XFEM, NMM, and PUGNM from the perspective of generalized nodes. Thus, construction of generalized nodes based on isolated blocks in the PUGNM is actually another implementation of the NMM based on the “path-connectivity” concept. The excellent numerical results show that the PUGNM can model multiple cracks.

A CP-FDTD Preprocessor in Cartesian and Rectangular Coordinates

In. this paper we present a versatile mesh generator in Cartesian and Rectangular co-ordinates for the Contour path Finite Difference Time Domain method wherein the grid is adjusted locally, to follow the contour of the geometric boundaries. The information about geometry, curved interfaces (dielectric/dielectric, PEC/air etc) material parameters, angles are obtained from the geometry of the intersecting interfaces at the mesh stage itself and does not need any particular area calculation for implementation at the FDTD solver stage. When run on a stair stepped or o contour path FDTD solver, the conformal approximation permits modeling of sloped and curved boundaries, while the stepped approximation permits modeling of linear material media. Additionally, to model thin layers smaller than the spatiaL step size a local sub girding approach that aLlows fine geometries to be modeled is used at the mesh stage itseLf. This means structures that are less than the grid discretization such as thin plates and small bumps are incorporated into the mesh at negligibLe costs.