Effect Of Curvature Research Articles

Lagrangian, game theoretic, and PDE methods for averaging G-equations in turbulent combustion: existence and beyond

G-equations are popular level set Hamilton–Jacobi nonlinear partial differential equations (PDEs) of first or second order arising in turbulent combustion. Characterizing the effective burning velocity (also known as the turbulent burning velocity) is a fundamental problem there. We review relevant studies of the G-equation models with a focus on both the existence of effective burning velocity (homogenization), and its dependence on physical and geometric parameters (flow intensity and curvature effect) through representative examples. The corresponding physical background is also presented to provide motivations for mathematical problems of interest. The lack of coercivity of Hamiltonian is a hallmark of G-equations. When either the curvature of the level set or the strain effect of fluid flows is accounted for, the Hamiltonian becomes highly nonconvex and nonlinear. In the absence of coercivity and convexity, the PDE (Eulerian) approach suffers from insufficient compactness to establish averaging (homogenization). We review and illustrate a suite of Lagrangian tools, most notably min-max (max-min) game representations of curvature and strain G-equations, working in tandem with analysis of streamline structures of fluid flows and PDEs. We discuss open problems for future development in this emerging area of dynamic game analysis for averaging noncoercive, nonconvex, and nonlinear PDEs such as geometric (curvature-dependent) PDEs with advection.

Contact acoustic nonlinearity and damping properties of completely free vibrating curved and delaminated CFRP plates

This study reports an experimental investigation on the effect of plate curvature and circular inter-ply delamination on the completely free vibration properties of carbon fiber reinforced polymer (CFRP) plates. Impact tests on wire suspended plates were performed and variations in measured natural frequencies and modal damping are reported. Delamination clapping type contact acoustic nonlinearity (CAN) was observed in the presence of a series of higher harmonics in the vibration spectrum. These higher harmonics consisted of five to seven equally distanced peaks grouped in a frequency range of around the double of odd mode M (5,0). Modal damping was highly sensitive to delamination which caused a 33% average increase in damping loss factors. Odd mode M (3,0) was the most affected with an average increase of 51% in damping loss factor, explained by the delamination location relative to the wavelength of that mode shape. Natural frequencies were less sensitive to delamination, on average decreasing 1.0% in flat plates and increasing 3.1% in curved plates. The modal frequencies calculated from embedded fiber optic sensor (FOS) or electrical resistance strain gauge signals agreed with finite element modeling (FEM) to within a 3.1% difference for all modes considered. The damping loss factors deducted from suspended plate tests were consistent with complementary results from dynamic mechanical analysis (DMA). The measured delamination clapping CAN and its related influence on damping can serve to enhance structural health monitoring (SHM) methods.

Thermodiffusively unstable laminar hydrogen flame in a sufficiently large 3D computational domain – Part II: NOx formation mechanism and flamelet modeling

In this work, the NOx formation mechanism in three-dimensional (3D) thermodiffusively unstable premixed hydrogen flames is investigated through direct numerical simulations (DNS) and a reaction path analysis based on the DNS dataset. In part I of this study (Wen et al., 2024), the characteristic patterns of the instabilities were studied using the same dataset. Here, first, the effects of the computational setup (2D vs. 3D) and curvature on the flux ratio of nitrogen atom are quantified. In addition, the composition space model (CSM) proposed in previous works is extended to account for the NOx chemical reaction mechanism to predict NOx formation in thermodiffusively unstable premixed hydrogen flames. The flamelet solutions are obtained from the premixed flamelet equations in composition space so that the wide range of curvatures associated with the strongly corrugated flame front can be considered. The performance of the CSM in predicting the NOx species and the important radicals involved in the NOx formation pathways is evaluated through an a priori analysis. To investigate the effects of curvature on the NOx formation pathways and the performance of the composition space model, the positively- and negatively-curved regions in the DNS are studied separately. The results show that different from the 2D simulation, the NNH reaction pathway becomes dominant in the 3D simulation due to the increased range of curvature, which promotes the accumulation of the highly diffusive H radical in the positively-curved regions. The NNH reaction pathway is dominant in the positively-curved regions, while the N2O reaction pathway is more important in the negatively-curved regions. The flamelet model based on the composition space solutions that consider the effects of curvature yields accurate predictions for the radicals that are sensitive to the effects of curvature.Novelty and significance statementThe novelty of the present work includes the following aspects,(i) Analysis of NOx formation mechanism based on the large-scale 3D DNS dataset of a laminar fuel-lean premixed hydrogen flame on a sufficiently large domain;(ii) Quantification of the effects of computational setup (2D and 3D) and curvature on the NOx formation pathways;(iii) Extension of the previous composition space model (CSM) by incorporating the NOx chemical reaction mechanism to consider the effects of curvature on the NOx formation.

An accurate trajectory tracking method for low-speed unmanned vehicles based on model predictive control

Trajectory tracking on a low-speed vehicle using the model predictive control (MPC) algorithm usually assumes a simple road terrain. This assumption does not correspond to the actual road situation, leading to low tracking accuracy. Therefore, a trajectory tracking method considering road curvature based on MPC is proposed in this paper. In this method, the controller can automatically switch between MPC types. Linear model predictive control (LMPC) is selected for small road curvatures, while nonlinear model predictive control (NMPC) is employed for large road curvatures. In addition, the NMPC algorithm in this work considers the effect of road curvature on tracking accuracy, making it suitable for tracking time-varying curvature roads. To verify the feasibility of the algorithm, simulation comparisons with the basic MPC model were carried out at different testing roads and vehicle longitudinal speeds. The results indicate that the method significantly improves trajectory tracking accuracy, all while ensuring real-time calculations. The intelligent switching capability of control models based on road curvature allows its application to track trajectories on arbitrarily complex roads.

Effect of evaporator curvature on the local non-equilibrium heat regulation in two-phase closed thermosyphon embankment in permafrost regions

The evaporator curvature can affect the heat transfer performance of two-phase closed thermosyphons (TPCTs) in permafrost regions. To explore the working features and control performance of TPCTs with different evaporator curvatures, two types of TPCTs with horizontal and inclined evaporator were designed. Then, a series of scale embankment models were conducted to test the thermal and deformation performance of the two TPCTs, including a TPCT embankment with inclined evaporator, a TPCT embankment with horizontal evaporator, and a contrast embankment without TPCTs. The results show that the thermal regulation performance of the TPCT with horizontal evaporator is much better than that with inclined evaporator. The thermal regime difference caused by the vapour-liquid interface interaction occurs in the whole pipe domain above the liquid pool for the TPCT with inclined evaporator while it mainly exists in the condenser domain for the TPCT with horizontal evaporator. Meanwhile, the TPCT with horizontal evaporator can decrease the temperature gradient, and thus weaken the frost heave of the embankment. Consequently, the TPCT with horizontal evaporator is more appropriate to adjust the local non-equilibrium heat process in embankment. The findings of this study supply a scientific reference for the design of TPCTs embankment in permafrost regions.

Effects of surface curvature and electric field on electronic and optical properties of an off-center hydrogenic donor impurity in 2D nanostructures

Effects of surface curvature and electric field on electronic and optical properties of an off-center hydrogenic donor impurity in 2D nanostructures

CFD for the optimization of spiral wound film assembly

In this paper, a conventional mesh shim for a spiral wound membrane assembly is structurally optimized by adding jet holes to achieve the jet function, and the effect of curvature on fluid flow is investigated. The three different gaskets are compared with each other and the performance of the optimized gaskets is investigated by using computational fluid dynamics (CFD) techniques and analyzed parametrically. This knowledge can be supplemented by the use of CFD techniques for spacers, whereby the geometry of the spacer can be optimized and the corresponding performance of the spiral wound film assembly can be improved.

Droplet migration through deformable stenosed microchannel: Dynamics and blockage

Understanding droplet migration in stenosed microchannels is crucial for various applications. This study explores how droplet properties (viscosity, surface tension, density, and diameter) and channel characteristics (stenosis degree and wall elasticity) affect droplet movement and blockage in deformable stenosed microchannels. Higher viscosities lead to lubrication film formation between droplet and wall, reducing viscous resistance, while increased surface tension enhances wall adherence, amplifying Laplace pressure. Droplet entry is primarily influenced by viscosity, while passage is governed by surface tension and curvature effects at the droplet–wall interface. Surface tension dominates pressure generation in the channel and within the droplet, influencing wall deformation and hydrodynamic resistance. The study examines the relationship among droplet viscosity, density, surface tension, channel wall elasticity, and the maximum capillary number (Camax) on the lubrication film thickness between the droplet and the channel wall. A lubrication film exists for Camax≥0.095, reducing blockage chances. A critical range of the modified Ohnesorge number Oh*×1000≤132 and the capillary number (Camax<0.095) indicates higher chances of droplet blockage. The blockage prediction method based on the modified Ohnesorge exhibits a sensitivity of 100%, specificity of 92.6%, and accuracy of 95.9%. Additionally, the study explores the impact of channel wall elasticity on droplet entry, transit, and hydrodynamic resistance. Higher wall elasticity facilitates faster entry but introduces curvature during passage, increasing frictional resistance and blockage likelihood as the wall softens.

Highly Curved Defect Sites: How Curvature Effect Influences Metal-Free Defective Carbon Electrocatalysts.

Topological defects are widely recognized as effective active sites toward a variety of electrochemical reactions. However, the role of defect curvature is still not fully understood. Herein, carbon nanomaterials with rich topological defect sites of tunable curvature is reported. The curved defective surface is realized by controlling the high-temperature pyrolytic shrinkage process of precursors. Theoretical calculations demonstrate bending the defect sites can change the local electronic structure, promote the charge transfer to key intermediates, and lower the energy barrier for oxygen reduction reaction (ORR). Experimental results convince structural superiority of highly-curved defective sites, with a high kinetic current density of 22.5mAcm-2 at 0.8V versus RHE for high-curvature defective carbon (HCDC), ≈18 times that of low-curvature defective carbon (LCDC). Further raising the defect densities in HCDC leads to the dual-regulated products (HCHDC), which exhibit exceptionally outstanding ORR activity in both alkaline and acidic media (half-wave potentials: 0.88 and 0.74V), outperforming most of the reported metal-free carbon catalysts. This work uncovers the curvature-activity relationship in carbon defect for ORR and provides new guidance to design advanced catalysts via curvature-engineering.

A numerical analysis of multi-dimensional iron flame propagation using boundary-layer resolved simulations

Iron combustion is emerging as a topic of immediate interest, given the need for the decarbonization of heat and power generation. Opposite to other solid fuels, iron particles burn predominantly in a non-volatile, heterogeneous combustion mode. For iron dust flames, two modes of flame propagation have been observed i.e. the discrete mode, when the heat transfer time scale is larger than the particle burn-time, and the continuous mode, when the heat transfer timescale is smaller than the burn-time of a single particle. The flame speed of such a flame primarily depends on the heat and mass transfer which is characterized by the distance between the particles for a dispersed mixture. Depending on the variation in particle distance and local distribution, planar or curved flames can form and propagate. The characteristics of flame propagation motivate this study and for the first time, three-dimensional particle boundary layer resolved simulations are used to analyse the effect of curvature and variable particle distances on iron–air flame propagation. Simulations are carried out for (1) planar flame propagation with constant particle spacing in the direction of propagation, and (2) curved flame propagation with varying particle spacing in the direction of propagation. The analysis of the flame speed for the planar flame propagation later guides the analysis of curved flames propagating through 900 boundary-layer resolved particles distributed in a 30 by 30 grid. The curved flame propagates with a uniform but decreased flame speed compared to the planar flame propagation with equivalent particle spacing. It is shown that positive curvature decreases the heat transfer from the burnt to the unburnt side while a variable spatial arrangement of particles allows for a local re-distribution of oxygen which causes some regions to burn richer or leaner than the corresponding planar flames with similar particle spacing.

3D electromagnetic analytical model for radial-flux eddy-current couplers

PurposeThis paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.Design/methodology/approachThe analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.FindingsThe obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.Practical implicationsThe proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.Originality/valueA new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

Global dynamics of two models for Quintom Friedman–Lemaître–Robertson–Walker universes

We comprehensively analyse the dynamics for the gravitational field equations for the Chiral-Quintom theory in a Friedman–Lemaître–Robertson–Walker cosmology with an additional matter source. We consider a new set of dimensionless variables and write the field equations in the equivalent form of an algebraic-differential system. Specifically, we consider two families of quintom models where the two scalar fields interact in the kinetic sector. We mathematically focus on the dynamical effect of spatial curvature. Physically, we find two periods of inflation related to the Universe’s early and late-time acceleration phases.

Improving the rheological behavior of magnetiz couple stress Buongiorno's nanofluid through resilient wavy channel with curvature effect: Nonlinear analysis

In biological systems, fluids with complex rheological behavior often encounter complex microenvironments. Couple stress fluids can be applied to model the flow of biological fluids in micro-vessels, capillaries, and other intricate structures. Couple stress fluids can be employed to model drug transport in microfluidic devices and capillaries, providing insights into the behavior of pharmaceuticals at small scales. Studying the couple stress fluids is crucial, particularly when considering the impact of particle viscosity in the existence of induced magnetic fields and nanoparticles that might enhance the characteristic motion. So, we studied the moderate and magnetic Reynold numbers and curvature effects of magnetized couple stress Buongiorno's nanofluid model through resilient wavy channel. The governing equations of this model are formed in non-dimensional form without any approximation, i.e., in the companionship of moderate Reynolds number and curvature effect, which aren't studied in this form. Using the Adomian decomposition approach, it is possible to obtain a solution of nonlinear system of partial differential equations analytically. The semi-analytical results are obtained and represented graphically for characteristic motion and bio-thermal properties for temperature and concentration, as well as magnetic features. Physically, by rising the magnetic Reynolds number, the magnetic permeability raises, so the ability of the couple stress fluid to form an internal magnetic field within itself with the impact of an applied magnetic field increases, which increases the magnetic force.

Unraveling the influence of channel size and shape in 3D printed ceramic scaffolds on osteogenesis

Bone has the capacity to regenerate itself for relatively small defects; however, this regenerative capacity is diminished in critical-size bone defects. The development of synthetic materials has risen as a distinct strategy to address this challenge. Effective synthetic materials to have emerged in recent years are bioceramic implants, which are biocompatible and highly bioactive. Yet nothing suitable for the repair of large bone defects has made the transition from laboratory to clinic. The clinical success of bioceramics has been shown to depend not only on the scaffold's intrinsic material properties but also on its internal porous geometry. This study aimed to systematically explore the implications of varying channel size, shape, and curvature in tissue scaffolds on in vivo bone regeneration outcomes. 3D printed bioceramic scaffolds with varying channel sizes (0.3 mm to 1.5 mm), shapes (circular vs rectangular), and curvatures (concave vs convex) were implanted in rabbit femoral defects for 8 weeks, followed by histological evaluation. We demonstrated that circular channel sizes of around 0.9 mm diameter significantly enhanced bone formation, compared to channel with diameters of 0.3 mm and 1.5 mm. Interestingly, varying channel shapes (rectangular vs circular) had no significant effect on the volume of newly formed bone. Furthermore, the present study systematically demonstrated the beneficial effect of concave surfaces on bone tissue growth in vivo, reinforcing previous in silico and in vitro findings. This study demonstrates that optimizing architectural configurations within ceramic scaffolds is crucial in enhancing bone regeneration outcomes. Statement of significanceDespite the explosion of work on developing synthetic scaffolds to repair bone defects, the amount of new bone formed by scaffolds in vivo remains suboptimal. Recent studies have illuminated the pivotal role of scaffolds’ internal architecture in osteogenesis. However, these investigations have mostly remained confined to in silico and in vitro experiments. Among the in vivo studies conducted, there has been a lack of systematic analysis of individual architectural features. Herein, we utilized bioceramic 3D printing to conduct a systematic exploration of the effects of channel size, shape, and curvature on bone formation in vivo. Our results demonstrate the significant influence of channel size and curvature on in vivo outcomes. These findings provide invaluable insights into the design of more effective bone scaffolds.

Patterns of Nanoporous Spherical Packing Emerging under Influence of Curvature and Confinement

Nanoporous membranes are popular in nanotechnology due to biomedical and industrial applications. During the past decade, experimental, theoretical and computational research into porous membranes and soft materials has opened up new mathematical dimensions. In bulk, diblock copolymers exhibit ordered morphologies such as parallel matrices of lamellae, bicontinuous matrices of gyroids, hexagonal matrices of cylinders and body-centred cubic matrices of spheres. In melt, confinement plays an essential role in tuning the frustration of the diblock copolymer system to predict more nanostructures. These nanostructures depend on the composition of the copolymers, their confining geometries and the degree of structural frustration. An isotropic 9-point stencil for Laplacian is constructed. The discrete finite-difference technique is used in polar grids to discretize the macromolecule of the diblock copolymer system to study spherical patterns to study the effect of curvature and confinement with a well-known and efficient cell dynamic simulation model. Intel FORTRAN (IFORT) codes are generated to run the CDS model and visualisation of simulation results is observed with the help of OPENDX. A comparison of the proposed study with existing experimental and computational studies is also presented.

End Effect Reduction by Modification Design of End Teeth for Linear Induction Motor

Using linear induction motors for magnetic trains has challenges in maintaining stability and safety, namely the emergence of holding forces. The force arises due to the magnetic flux interaction between the permanent magnet and the iron core. One source of resisting force is due to the dotted lines, which creates a finishing effect and generates vibration and noise from the system. Previous research has carried out several works, one of which is designing the shape of a gear at the end of a tooth with a convex curved shape in a linear synchronous motor which has succeeded in reducing the effect of the tip of the tooth. This study aims to determine the results of the effectiveness of calculations using MATLAB, which can produce much less resistance. This research uses descriptive research with a qualitative approach. In this study the calculations to redesign the shape of the dental arch at the end of the track were carried out by making a model with a parabolic approach. Plane dimensions X, Y, Z 660mm x 360mmx 360 mm. Magnetic density data were collected using Ansys software and 10 mm meshing, while the magnitude of the resistive force based on mathematical equations was carried out using MATLAB software. Investigation of the effect of curvature for the final effect value has been carried out using 6 models with different arcs. From the simulation, it is concluded that the sharpener for bow curvature gives the smallest resistance force value. The smallest result from the calculation A=A_x+y^' A_y gives the smallest detention force value. The smallest computation of A=A_x+y^' A_y with the sharpest curvature is a challenge to build and use for real activities.

Wetting geometry and deposition patterns manipulation with bi-dispersed particle-laden droplets

Polygonal deposition through evaporation of the suspension droplets holds promise for printing applications. The distinctive edges present in polygonal droplets offer the potential to enhance printing resolution and enable the fabrication of diverse thin depositions. Prior investigations revolve one dimensional control with the types of wetting geometries and deposition patterns initiate from different driving factors. The current study delves into the synergistic interplay between a bi-dispersed suspension mixing ratio and particle concentration, as they collectively influence the deposition pattern of octagonal droplets formed using a micropyramid cavity patterned substrate. The investigation culminates in the development of a comprehensive phase diagram categorizing four distinct types of deposition: octagonal outer-ring deposition, octagonal ring with irregular features, octagonal uniform deposition, and central deposition. Specifically, octagonal outer-ring deposition is observed when droplets consist predominantly of 3μm particles at lower concentrations. In cases where a suspension contains 10μm particles, an intermediate concentration exceeding 50% gives a rise to the octagonal outer-ring deposition intermingled with irregular features. The octagonal uniform deposition emerges when 3μm particles, co-aggregated with 10μm particles, are compelled to settle at the deposition center within the mixture at the 3:1 ratio at 1.0 wt% and 2.6 wt%. Notably, the “curvature effect”, exhibited by the aggregates adhering to the liquid–air interface, counter-intuitively suppresses octagonal deposition despite the presence of octagonal wetting geometry and forms the central deposition. In summary, the study introduces a robust method to achieve the uniform deposition and proposes a scalable and flexible strategy for generating diverse deposition types through the judicious mixing of two suspension solutions at distinct weight ratios.

Mechanochemical modeling of morphogenesis in cell polarization for budding yeast

Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.

The effect of canal curvature on cyclic fatigue resistance of rotary instruments using different irrigation materials ( in vitro study).

The mechanical qualities of Ni-Ti is crucial because they give the files their flexibility and enable us to prepare curved and double-curved canals with more ease. It happens frequently for instruments to separate during canal preparation, and cyclic fatigue (metal fatigue) is a frequent cause.This study aimed to assess how irrigation affected the two rotary endodontic instruments' cyclic fatigue resistance. The Edge File and Fanta File rotary endodontic instrument groups were chosen. Each group (n = 42) was split into 3 subgroups (n = 14 each), one receiving NaOH, one Glycine, and one EDTA treatment. The number of cycles to failure (NCF) was determined after each subgroup underwent testing for cyclic fatigue resistance. The result appeared different significant between the two group and sub-group with the different materials that used with it with the length of fractures and time that recorded in each group. NaOCl, glycine, and EDTA as chemical materials appeared to have considerably varied cycle fatigue resistance for various lengths of fractures and durations, according to the comparison between the two evaluated instruments.

Induced magnetic force and curvature effect of ternary hybrid nanofluid (jeffrey model) in ciliary peristaltic channels

ABSTRACT Ternary hybrid nanoparticles require infected blood cell base fluid flow. Blood vessels feature ciliated walls and peristaltic waves. Anemia comes from cancer treatment-induced red blood cell destruction. This study reproduces Jeffrey model blood flow through a ciliary peristaltic artery using ternary hybrid nanoparticles of gold, iron oxide, and copper. This work examines ternary hybrid nanofluid MHD ciliary peristaltic motion using Jeffrey curves. A nonlinear PDE system has heat and induced magnetic force equations. The Adomian Decomposition Method solved this system without long-wavelength approximation. Visualize how essential biological and physical elements affect velocity, temperature, trapping, magnetic force contours, induced magnetic field components, axial pressure, and normal pressure. Flow, temperature, magnetic features, and other important properties are plotted and discussed against biological and biomedical parameters. We discovered full consistency with modest scenario efforts. The increase in nanoparticles gives ternary hybrid nanofluid a larger friction force than hybrid, so its axial pressure gradient at the wall is stronger, decays at hybrid, decays further from nanofluid to base fluid, and reverses at the intermediate area. Peristaltic ciliary activity alters magnetic force contours, shrinks loops, and forms four contour groups with different implications.