Contour Profiles Research Articles

Optimal design of a novel three-stage displacement amplifying mechanism with curved-axis flexure hinges

A novel three-stage displacement amplifying mechanism is proposed by integrating the lever-type, Scott-Russell and double-arm elliptical mechanisms with red blood cell inspired flexure hinges that well balances the displacement amplification ratio and main resonance frequency. Flexure hinges are loaded in tension and bending instead of compression and bending, which can be free from potential buckling problems due to the stress stiffening effects. The combination of the dynamic stiffness matrix method and the discrete-beam transfer matrix method is utilized to rapidly forecast the kinetostatic and dynamic performances of the proposed compliant amplifier, including the curved-axis flexure hinges with complex contour profiles. Then, the Pareto multi-objective optimization strategy, taking those key geometric parameters obtained by the sensitivity analysis into account, is represented based on NSGA-II and a linear frequency solution strategy to accelerate the calculation efficiency and parameter optimization iteration. Based on the application requirement, a point on the Pareto curve is chosen as the optimal configuration for operating conditions. At last, experiments of the piezoelectric compliant amplifier under two types of external mass loads are exhibited. A displacement amplification ratio of 12.2 and main resonance frequency of 1380.5 Hz are achieved for the piezoelectric compliant amplifier under no external mass load.

Study of Fifth-Order Nonlinear Caudrey–Dodd–Gibbon Model for Multiwave, M-Shaped Solitons, Lumps, Generalized Breathers, Manifold Periodic, Rogue Wave and Kink Wave Interactions

Numerous novel wave structures, such as lump, lump with one-kink, lump with two-kink soliton, generalized breather, Ma breather, Kuznetsov-Ma breather, Akhmediev breather, manifold periodic, and rogue wave solutions to [Formula: see text]-dimensional fifth-order nonlinear Caudrey–Dodd–Gibbon (FNCDG) model via symbolic computation are studied based on the ansatz function scheme. Studying the lump-type solution involves selecting the function as the generic quadratic polynomial function. The lump with one- and two-kink solutions is created by mixing a quadratic function with one or two exponential functions. By adding hyperbolic function with a quadratic function, the rogue wave solutions are manipulated. In addition, the multiwave, [Formula: see text]-shaped rational solitons and their interactions with kink waves are analytically evaluated. Furthermore, different 3D, 2D, and contour profiles are created in different dimensions by changing the parameter values.

M-shaped rational, homoclinic breather, kink-cross rational, multi-wave and interactional soliton solutions to the fifth-order Sawada-Kotera equation

In this work, we develop multi-wave, homoclinic breathers, M-shaped rational, 1-kink interactions with M-shaped, periodic-cross rational and kink-cross rational solutions for the fifth-order Sawada-Kotera equation, which represents the motion of long waves under gravity in shallow water, using several ansatz transformations. A three-wave approach is used to identify multi-wave solitons. Additionally, novel forms of exact solutions are constructed using the homoclinic breathers technique. The kink-cross rational and periodic-cross rational solitons are investigated using appropriate transformations. We develop M-shaped solitons and demonstrate their behavior by selecting suitable parameter values. Furthermore, the interactions between kink waves and M-shaped solitons are also studied. The obtained solutions are determined in 3D, 2D, and contour profiles, where the free parameters involved in the solutions are assigned specific values. Their physical relevance is explored to highlight the inner context of tangible incidents in the natural domain. Since these recently discovered solutions contain a few arbitrary constants, they can be used to explain the variation in qualitative characteristics of wave phenomena.

Fourier Features and Machine Learning for Contour Profile Inspection in CNC Milling Parts: A Novel Intelligent Inspection Method (NIIM)

Form deviation generated during the milling profile process challenges the precision and functionality of industrial fixtures and product manufacturing across various sectors. Inspecting contour profile quality relies on commonly employed contact methods for measuring form deviation. However, the methods employed frequently face limitations that can impact the reliability and overall accuracy of the inspection process. This paper introduces a novel approach, the novel intelligent inspection method (NIIM), developed to accurately inspect and categorize contour profiles in machined parts manufactured through the milling process by computer numerical control (CNC) machines. The NIIM integrates a calibration piece, a vision system (RAM-StarliteTM), and machine learning techniques to analyze the line profile and classify the quality of contour profile deformation generated during CNC milling. The calibration piece is specifically designed to identify form deviations in the contour profile during the milling process. The RAM-StarliteTM vision system captures contour profile images corresponding to curves, lines, and slopes. An algorithm generates a profile signature, extracting Fourier descriptor features from the contour profile to analyze form deviations compared to an image reference. A feed-forward neural network is employed to classify contour profiles based on quality properties. Experimental evaluations involving 60 machined calibration pieces, resulting in 356 images for training and testing, demonstrate the accuracy and computational efficiency of the proposed NIIM for profile line tolerance inspection. The results demonstrate that the NIIM offers 96.99% accuracy, low computational requirements, 100% inspection capability, and valuable information to improve machining parameters, as well as quality classification.

Lax integrability and nonlinear dispersive wave phenomenon for the (3 + 1) dimensional Kudryashov–Sinelshchikov equation

A (3 + 1) dimensional Kudryashov–Sinelshchikov equation is investigated in this paper, which describes bubbles in the liquid fluctuations. By virtue of the binary Bell polynomials, the bilinear representation, bilinear Bäcklund transformation with associated Lax pair are obtained, respectively. Moreover, utilizing Hirota’s bilinear representation, four new lump solutions are constructed and the interaction phenomenon between lump and periodic solution is thoroughly examined. The work also illustrates the intriguing dynamical behavior with the aid of Maple software, which plots the three-dimensional surface, two-dimensional density, and contour profiles of the solutions constructed in this work in various planes.

Influence of solvent viscosity ratio on the creeping flow of viscoelastic fluid over a channel confined circular cylinder

In this study, the role of solvent viscosity ratio (β) on the creeping flow characteristics of Oldroyd-B fluid over a channel-confined circular cylinder has been explored numerically. The flow governing equations have been solved by RheoTool, an open-source toolbox based on OpenFOAM, employing the finite volume method for extensive ranges of Deborah number (De=0.025–1.5) and solvent viscosity ratio (β=0.1–0.9) at a fixed wall blockage (B = 0.5). The present investigation has undergone extensive validation, with available literature under specific limited conditions, before obtaining detailed results for the relevant flow phenomena, such as stream function, pressure and stress contour profiles, pressure coefficient (Cp), wall shear stress (τw), normal stress (τxx), first normal stress difference (N1), and drag coefficient (CD). The flow profiles have exhibited a distinctive behavior characterized by a loss of symmetry in the presence of pronounced viscoelastic effects. The results for low De notably align closely with those for Newtonian fluids, and the drag coefficient (CD) remains relatively constant regardless of β, as the viscoelastic influence is somewhat subdued. These observations indicate that at high De and low β, viscoelasticity causes asymmetry in creeping flow around a circular cylinder. With an increase in De, the maximum velocity in gap between cylinder and channel walls increases; however, the cylinder experiences significantly less drag force. Within this parameter range, the prevailing force governing the flow is the pressure drag force.

Lump, Breather, Ma-Breather, Kuznetsov–Ma-Breather, Periodic Cross-Kink and Multi-Waves Soliton Solutions for Benney–Luke Equation

The goal of this research is to utilize some ansatz forms of solutions to obtain novel forms of soliton solutions for the Benney–Luke equation. It is a mathematically valid approximation that describes the propagation of two-way water waves in the presence of surface tension. By using ansatz forms of solutions, with an appropriate set of parameters, the lump soliton, periodic cross-kink waves, multi-waves, breather waves, Ma-breather, Kuznetsov–Ma-breather, periodic waves and rogue waves solutions can be obtained. Breather waves are confined, periodic, nonlinear wave solutions that preserve their amplitude and shape despite alternating between compression and expansion. For some integrable nonlinear partial differential equations, a lump soliton is a confined, stable solitary wave solution. Rogue waves are unusually powerful and sharp ocean surface waves that deviate significantly from the surrounding wave pattern. They pose a threat to maritime safety. They typically show up in solitary, seemingly random circumstances. Periodic cross-kink waves are a particular type of wave pattern that has frequent bends or oscillations that cross at right angles. These waves provide insights into complicated wave dynamics and arise spontaneously in a variety of settings. In order to predict the wave dynamics, certain 2D, 3D and contour profiles are also analyzed. Since these recently discovered solutions contain certain arbitrary constants, they can be used to describe the variation in the qualitative characteristics of wave phenomena.

Influence of grain concentrations gradients on the profiling behaviour of bronze bonded diamond grinding wheels

In this work, diamond grinding wheels are first manufactured with two different metallic bonds. These are a ductile and a brittle bronze. Two differently graded (varied grain concentration) grinding wheels and two non-graded reference grinding wheels are manufactured in each case. The mechanical properties of these are then determined. Subsequently, a method is presented that enables the profiling of graded grinding wheels. For this purpose, the grinding wheels are profiled with SiC rolls using different profiling parameters. The profile accuracy after profiling is analysed using contour profiles in polyurethane. In addition, the dressing ratio and the process duration of profiling are measured. These parameters are used to determine the economic efficiency of the profiling process. Finally, this provides a bond-dependent profiling process that can economically and reproducibly generate a target contour on a grinding tool.

Reg-Tune: A Regression-Focused Fine-Tuning Approach for Profiling Low Energy Consumption and Latency

Fine-tuning deep neural networks is pivotal for creating inference modules that can be suitably imported to edge or field-programmable gate array (FPGA) platforms. Traditionally, exploration of different parameters throughout the layers of deep neural networks has been done using grid search and other brute force techniques. Although these methods lead to the optimal choice of network parameters, the search process can be very time consuming and may not consider deployment constraints across different target platforms. This work addresses this problem by proposing Reg-Tune, a regression-based profiling approach to quickly determine the trend of different metrics in relation to hardware deployment of neural networks on tinyML platforms like FPGAs and edge devices. We start by training a handful of configurations belonging to different combinations of \(\mathcal {NN}\scriptstyle \langle q (quantization),\,s (scaling)\rangle \displaystyle\) or \(\mathcal {NN}\scriptstyle \langle r (resolution),\,s\rangle \displaystyle\) workloads to generate the accuracy values respectively for their corresponding application. Next, we deploy these configurations on the target device to generate energy/latency values. According to our hypothesis, the most energy-efficient configuration suitable for deployment on the target device is a function of the variables q , r , and s . Finally, these trained and deployed configurations and their related results are used as data points for polynomial regression with the variables q , r , and s to realize the trend for accuracy/energy/latency on the target device. Our setup allows us to choose the near-optimal energy-consuming or latency-driven configuration for the desired accuracy from the contour profiles of energy/latency across different tinyML device platforms. To this extent, we demonstrate the profiling process for three different case studies and across two platforms for energy and latency fine-tuning. Our approach results in at least 5.7 \(\times\) better energy efficiency when compared to recent implementations for human activity recognition on FPGA and 74.6% reduction in latency for semantic segmentation of aerial imagery on edge devices compared to baseline deployments.

Optical solitons for the Hirota–Ramani equation via improved G′G-expansion method

In this work, first it is shown that the Hirota–Ramani equation, which governs the nonlinear propagation of coupled Langmuir and dust-acoustec wave in a multicomponent dusty plasma, possesses kinds of wave profile such as singular periodic profile, periodic profile, singular soliton profile, M-shape rational profile, bright soliton profile, kink profile in the form of the trigonometric, hyperbolic, and rational solutions. With the aid of symbolic computation, we select the Hirota–Ramani equation with a source to investigate the validity and advantage of the improved [Formula: see text]-expansion method and construct some frames of the 3D profiles and the contour profiles to the equation along with the 2D profiles of some solutions to understand the traveling wave dynamics. Following the selection of appropriate values for the associated parameters, more generalized solutions are provided, along with certain patterns in the solutions that are examined. This improved method is effective, concise, reliable, and can be applied for further futuristic applications.

Multiwaves, breathers, lump and other solutions for the Heimburg model in biomembranes and nerves

In this manuscript, a mathematical model known as the Heimburg model is investigated analytically to get the soliton solutions. Both biomembranes and nerves can be studied using this model. The cell membrane’s lipid bilayer is regarded by the model as a substance that experiences phase transitions. It implies that the membrane responds to electrical disruptions in a nonlinear way. The importance of ionic conductance in nerve impulse propagation is shown by Heimburg’s model. The dynamics of the electromechanical pulse in a nerve are analytically investigated using the Hirota Bilinear method. The various types of solitons are investigates, such as homoclinic breather waves, interaction via double exponents, lump waves, multi-wave, mixed type solutions, and periodic cross kink solutions. The electromechanical pulse’s ensuing three-dimensional and contour shapes offer crucial insight into how nerves function and may one day be used in medicine and the biological sciences. Our grasp of soliton dynamics is improved by this research, which also opens up new directions for biomedical investigation and medical developments. A few 3D and contour profiles have also been created for new solutions, and interaction behaviors have also been shown.

Analysis of the properties and geometric characteristics of machined parts using computer vision

In milling contour profiles, tools create minute surface variations known as roughness. An algorithm is proposed to analyze the profile dimensional variation in milled parts by an artificial vision and Fourier descriptors as a measurement technique. The proposed method is based on the Fourier spectrum to analyze three profile signatures extracted from an image of a milled part with the aim of measuring the variation in three materials. It is found that when performing the profile machining process, the combination of the parameters: spindle speed, feed rate, cutting depth, and coolant fluid influence the dimensional variation of the part. The proposed approach concludes that this inspection method is faster and more efficient to guarantee the quality of parts manufactured by machining.

Dynamics of generalized time-fractional viscous-capillarity compressible fluid model

This analysis examines the time-fractional mixed hyperbolic-elliptic p-system of conservation laws by applying the new extended direct algebraic method. The p-system with generalized cubic van der Waals flux, and potential applications in the field of compressible isothermal viscosity-capillarity fluids, is investigated. In particular, this issue describes the longitudinal isothermal motion in elastic bars or fluids. A diverse periodic, kink, and singular soliton structures are extracted. The 3D dynamical behaviors and corresponding contour profiles of some obtained solitons are displayed. The fractional effects in the sense of Beta, M-truncated, and modified Riemann–Liouville, are discussed and illustrated. The method shows the straightforward, reliability, and efficiency for solving complex physical phenomena that is modeled by nonlinear partial differential equations.

A new flux coordinates-based solver for fixed-boundary tokamak equilibrium with toroidal flow

The plasma equilibrium plays a crucial role in nuclear fusion studies, serving as the foundation for various aspects of fusion research, including plasma stability, transport, and current drive. In this paper, a new Grad–Shafranov equation solver is developed for the fixed-boundary plasma equilibria with toroidal flow. This solver utilizes the pressure profile, safety factor profile (not current profile), and any two profiles of the toroidal angular velocity, plasma temperature, and square of the Mach number as inputs. The numerical results obtained by this solver exhibit good agreement with known analytic solution under identical parameters, and the potential applications of the solver are demonstrated through several numerical equilibria with toroidal flow. It is very convenient to apply this code to simulate the tokamak equilibrium with a smooth plasma shape. In addition, the effect of toroidal flow on the plasma equilibria is investigated as a simple application. The results reveal a notable outward shift in the contour profiles of magnetic flux surface, density, pressure, and temperature induced by toroidal flow.

Optical soliton for (2+1)-dimensional coupled integrable NLSE using Sardar-subequation method

The [Formula: see text]-dimensional coupled nonlinear Schrödinger equation has versatile applications for modeling nonlinear waves in different areas such as optics, atmospheric science, fluid dynamics, and plasma physics. This study focuses on the propagation of optical solitons and their interaction within various mediums such as multi-mode fiber and fiber arrays. The Sardar-subequation method is applied to achieve the bright, dark, combined bright–dark, periodic, combined dark-singular and singular optical solitons solutions. The 3D, contour and 2D profiles for some of the assimilation solutions are also plotted to show the physical behavior of the solutions. The obtained results demonstrate the effectiveness of the adopted methodology in obtaining traveling wave solutions and have many applications in applied mathematics and engineering. The novelty of our work lies in the successful application of Sardar-subequation method in obtaining diverse soliton solutions and exploring their physical behavior. This study goes beyond previous efforts in the literature by presenting a comprehensive analysis of soliton dynamics. This ability to describe and predict the behavior of optical solitons in diverse mediums opens up new opportunities for investigating the existing systems.

Planting Density Does Not Affect Root Shape Traits Associated with Market Class in Carrot

Carrot (Daucus carota var. sativus) cultivars with common root shape, appearance, and end-use are grouped and commercialized in market classes. The shape of the carrot storage root is the result of growth and development, which is highly influenced by genotype; however, the extent to which planting density affects root shape traits and its interaction with genotype remains unexplored. To observe the effects of market class and density on carrot root shape characteristics, five cultivars classified in five different market classes, including Imperator, Nantes, Danvers, Chantenay, and Ball, were each grown at five planting densities ranging from 0.5 million to 4.5 million plants/ha. A generalized complete block design with a two-way factorial treatment arrangement of the two factors, density and genotype, was used in three environments. Roots were phenotyped using a digital imaging pipeline and scored for root size (length, maximum width) and compound root shape traits including traits derived from the principal component analysis of root contour profiles like root fill and tip and shoulder curvature. The results suggest that planting density had minimal impact on the shape of carrot roots, and the expected shape for each market class was maintained regardless of planting density; however, the analysis was constrained by the presence of interactions among genotype, density, and environment, which influence the contribution of main effects to shape. For the Nantes, Danvers, Chantenay, and Imperator market classes, planting density influenced the size of the carrot root, with size decreasing by up to 50% in length and width at high planting densities. We found high estimates of broad-sense heritability for traits that determine the shape of the carrot root, such as root fill and length-to-width ratio, which capture size-independent variation of the storage root. Although environmental signals play a role, our results suggested that the shape of the carrot root is primarily determined by genotype, and that planting density generally does not have a significant effect on its shape.

Wave amplitudes and contour profiles of surface Rayleigh waves in a layered half-space with transversely isotropic materials

Wave amplitudes and contour profiles of surface Rayleigh waves in a layered half-space with transversely isotropic materials

Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo’s sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers.

On the exploration of soliton solutions of the nonlinear Manakov system and its sensitivity analysis

In this study, we investigate the fractional coupled nonlinear Schrödinger equation (FCNLSE) of Manakov type, which has numerous applications in different fields of physics, such as optics and plasma physics. In this study, we employ two different analytical methods, namely the auxiliary equation method (AEM) and the improved F-expansion method, to construct novel analytic exact solitary wave solutions, encompassing trigonometric, hyperbolic, and exponential functions. These solutions include solitary wave solutions dark, bright, combo, singular, rational form solutions, and periodic wave solutions. Additionally, using the characterizations of the Hamiltonian system, the stability property of the discovered soliton wave solutions is examined. We have also illustrated the sensitivity analysis for the modified dynamic structural system using different initial conditions. In order to illustrate various physical properties of wave structures, the well-furnished results are finally demonstrated in various 3D, 2D, contour, and density profiles. This work’s findings highlight the significance of researching diverse nonlinear wave phenomena in physics and nonlinear optics by demonstrating how crucial it is to comprehend the physical meaning and behavior of the examined equation. The procedures used are capable, effective, and succinct enough to make it possible for further research.

Three-Dimensional High-Precision Numerical Simulations of Free-Product DNAPL Extraction in Potential Emergency Scenarios: A Test Study in a PCE-Contaminated Alluvial Aquifer (Parma, Northern Italy)

Chlorinated organic compounds are widespread aquifer contaminants. They are known to be dense non-aqueous phase liquids (DNAPLs). Therefore, they are denser than water and immiscible with other fluids. Their migration into the environment in variably saturated zones can cause severe damage. For this reason, optimizing those actions that minimize the negative impact of these compounds in the subsurface is essential. This paper presented a numerical model simulating the free-product DNAPL migration and extraction through a purpose-designed pumping well in a potential emergency scenario. The numerical simulations were performed using CactusHydro, a numerical code that uses a high-resolution shock-capturing flux conservative method to resolve the non-linear coupled partial differential equations of a three-phase immiscible fluid flow recently proposed in the literature, including the contaminant extraction at the base of the aquifer. We investigated the temporal (and spatial) evolution of its migration in the Parma (Northern Italy) porous alluvial aquifer following the saturation contour profiles of the three-phase fluid flow in variably saturated zones. The results indicated that this numerical approach can simulate the contaminant migration in the subsurface and the pumping of the free-product from a well screened at the base of the aquifer system. Moreover, the simulation showed the possibility of recovering about two-thirds of the free-product, in agreement with the scientific literature.