Identifying frequency-domain operating deflection shapes and internal damage in structures using geometric vision method
Haoran Zhang, Jiaren Zuo, Zhangyu Yao
et al.
Operating deflection shape (ODS) analysis characterizes structural vibration in the frequency domain without requiring prior knowledge of excitation, offering an automatic means to assess dynamic behavior and detect damage in service. Building on this, we present a geometric vision–based sensing method for ODS identification under a depth-parameterization framework, enabling direct recovery of full-field vibration responses from spatiotemporal image motion captured by a stereo imaging system. To ensure accurate ODS reconstruction, a random sample consensus–based calibration algorithm is developed to rectify stereo geometry and establish a depth-parameterized projective system. Within this framework, we formulate a linear model that maps measured image motion of object points to their ODS responses in the frequency domain. In addition, a wavelet-based algorithm is proposed to extract damage parameters from defective structures using the reconstructed ODS fields. Experimental validations confirm that the proposed vision-based sensing method and damage identification approach are both effective and robust, providing a promising pathway for structural vibration monitoring and health assessment in complex operational environments.
Numerical Assessment of Pipeline Damage Due to an External Circumferential Semi-Elliptical Crack
Mohammed Amine Khater, Chaaban Aroussi, Elamine Abdelouahed
et al.
This paper presents a numerical evaluation of pipeline damage caused by an external circumferential semi-elliptical crack. The study utilizes the Abaqus software and the Extended Finite Element Method (XFEM) to model and analyze the crack behavior. Various parameters such as crack size, internal pressure, and loading conditions are investigated to assess their influence on pipeline integrity. The results reveal that as internal pressure increases from 300 to 600 bar, the pipe’s bearing capacity significantly decreases due to heightened stress concentrations around crack tips, leading to increased hoop stress and Stress Intensity Factors (SIFs), which accelerate crack propagation. Higher pressures also promote crack nucleation and growth, further reducing the effective cross-sectional area and weakening the pipe's load-carrying ability. Additionally, the analysis highlights the critical influence of defect size (a/t ratio) on stress distribution and residual strength: as the a/t ratio increases, the pipe becomes more vulnerable to failure at lower stress levels. The critical crack size is identified at the intersection of the resistance curve and the ultimate stress line, beyond which failure occurs before reaching the material’s full strength. Non-physical regions, where resistance exceeds ultimate stress, are disregarded to ensure realistic defect assessments. Under an internal pressure of 30 MPa, pipes with a/t ratios of 0.50 and 0.62 remain within the safety zone, while those with a/t ratios of 0.75 and 0.80 enter the failure zone, indicating a substantial loss of structural integrity and an increased risk of fracture.
Engineering machinery, tools, and implements, Mechanics of engineering. Applied mechanics
Numerical investigation on structure optimization and heat transfer of a phase change accumulator based on changing eccentricity and fin parameters
Shi Yiting, Zhang Liting, Yang Yongwen
et al.
In the contemporary era, the scarcity and strain of energy resources, combined with the pursuit of their efficient utilization, have posed critical challenges to the global community. Energy storage technology provides a solution to defer the utilization of heat or cold, thus tackling the root cause of energy shortages. Significantly, the integration of new energy sources has further enhanced the demand for energy storage. In contrast, the cost of heat storage is only one-tenth of that of electricity storage, which endows heat storage with more promising application prospects. Within the domain of heat storage, phase change heat storage has emerged as a prominent research focus due to its unique advantages such as high heat storage density, compact volume, and convenient control and matching capabilities. Consequently, we have made efforts to investigate the characteristics of phase change heat storage and improve heat transfer efficiency. Specifically, based on CFD simulation software and the enthalpy method mathematical model, a numerical model of the phase transformation process of tubular paraffin coupled with thermal conductivity and natural convection was established, and its heat absorption and heat release characteristics were simulated. The results indicate that the phase transition interface is symmetrical in general, but asymmetrical in the upper and lower parts, with the paraffin at the top having the fastest melting speed. To enhance the heat absorption and release process of phase change, the eccentric sleeve and fin were introduced. With the increase of eccentricity, the circulating flow range caused by natural convection expands. This is because the amount of paraffin in the lower part decreases and the thermal resistance reduces, which accelerates the melting speed. Moreover, increasing the eccentricity within a certain range is beneficial to accelerating the melting process. The addition of fins can significantly shorten the melting time of paraffin wax. Also, increasing the fin height and fin width can effectively reduce the melting time. However, as the fin height and fin width increase, the shortening gradient gradually decreases.
Mechanics of engineering. Applied mechanics, Fuel
Teaching Empirical Research Methods in Software Engineering: An Editorial Introduction
Daniel Mendez, Paris Avgeriou, Marcos Kalinowski
et al.
Empirical Software Engineering has received much attention in recent years and became a de-facto standard for scientific practice in Software Engineering. However, while extensive guidelines are nowadays available for designing, conducting, reporting, and reviewing empirical studies, similar attention has not yet been paid to teaching empirical software engineering. Closing this gap is the scope of this edited book. In the following editorial introduction, we, the editors, set the foundation by laying out the larger context of the discipline for a positioning of the remainder of this book.
Influence of Ali Al -Gharbi Earthquake on Braced Excavation in Silty Clay Soil (Numerical Study)
Hadeel Khaleel Abd Al-Ameer, Hassan Obaid Abbas
The design of the braced excavation system is one of the important and necessary matters for the implementation of various projects. The braced excavation system is used to support excavations in temporary projects, so there are shortcomings in the study of this aspect, although sometimes there are many projects that take long periods of time especially the projects of underground tunnels and high buildings. This was the main reason for the study. Therefore, the possibility of exposing the drilling system to earthquakes is great, especially in seismically active areas. If the drilling system is exposed to an earthquake, it can cause great human and material losses, so it must be designed against earthquakes so that ensure complete collapse and failure does not occur. This study aims to investigate the behavior of braced excavations under the influence of the Ali Al-Gharbi earthquake in both x- and y- directions. A numerical study is carried out on braced excavation system of (14×6) m and depth 9m using software Plaxis 3D. The braced excavation system consists of three type of bracing system with three levels of strut and wales connected with sheet pile wall to support sides of excavation and prevent them from collapsing. The results of study showed that the horizontal displacement of braced excavation system is (100-155) % more than vertical displacement (settlement) with seismic time when system is subjected to Ali Al-Gharbi earthquake in both directions with the other factors remaining constant. The stiffness of sheet pile wall also play an important role increases and decreases lateral displacement in both direction. Also, the results showed that the movement of of braced excavation system depends on several factors like as type of soil, time acceleration and the direction of earthquake. Settlement of Ali Al-Gharbi earthquake in Y- direction is 13% more than in X-direction.
Engineering machinery, tools, and implements, Mechanics of engineering. Applied mechanics
Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models
Borong Zhang, Martín Guerra, Qin Li
et al.
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate reconstructions, leveraging conditional diffusion models to draw samples, and also honors the symmetries of the underlying physics of wave-propagation. The procedure is factored into two steps: the first step, inspired by the filtered back-propagation formula, transforms data into a physics-based latent representation, while the second step learns a conditional score function conditioned on this latent representation. These two steps individually obey their associated symmetries and are amenable to compression by imposing the rank structure found in the filtered back-projection formula. Empirically, our framework has both low sample and computational complexity, with its number of parameters scaling only sub-linearly with the target resolution, and has stable training dynamics. It provides sharp reconstructions effortlessly and is capable of recovering even sub-Nyquist features in the multiple-scattering regime.
The Potential of Citizen Platforms for Requirements Engineering of Large Socio-Technical Software Systems
Jukka Ruohonen, Kalle Hjerppe
Participatory citizen platforms are innovative solutions to digitally better engage citizens in policy-making and deliberative democracy in general. Although these platforms have been used also in an engineering context, thus far, there is no existing work for connecting the platforms to requirements engineering. The present paper fills this notable gap. In addition to discussing the platforms in conjunction with requirements engineering, the paper elaborates potential advantages and disadvantages, thus paving the way for a future pilot study in a software engineering context. With these engineering tenets, the paper also contributes to the research of large socio-technical software systems in a public sector context, including their implementation and governance.
Curling morphology of knitted fabrics: Structure and Mechanics
Kotone Tajiri, Riki Murakami, Shunsuke Kobayashi
et al.
Knitted fabrics are two-dimensional-like structures formed by stitching one-dimensional yarn into three-dimensional curves. Plain stitch or stockinette stitch, one of the most fundamental knitting stitches, consists of periodic lattices of bent yarns, where three-dimensional (3D) curling behavior naturally emerges at the edges. The elasticity and geometry of knitted fabrics have been studied in previous studies, primarily based on 2D modeling. Still, the relation between 3D geometry and the mechanics of knitted fabrics has not been clarified so far. The curling behavior of knits is intricately related to the forces and moments acting on the yarns, geometry of the unit knitted loops, mechanical properties, and contacts, hence requiring a 3D analysis. Here, we show that the curling of plain knits emerges through the elasticity and geometry of the knitted loops, combining desktop-scale experiments and reduced elasticity-based simulations. We find that by changing the horizontal and vertical knitting numbers, three types of curl shapes emerge: side curl and top/bottom curl shapes, which are curled only horizontally and vertically, and double curl shape, in which both curl shapes appear together. The fundamental mechanism of intricate shape deformation is clarified through the force and moment balance along yarn whose centerline shape is discretized through the B-spline curves where elastic stretching, bending, and contact mechanics are taken into account. We reveal that the 3D structure of the single-knitted loop plays a critical role in the curling behavior. Our results imply that the change in shape per a single knitted loop has the potential to control the 3D natural overall shape of knitted fabrics, and could be applied in predicting or designing more complex 3D shapes made of knitted fabrics.
en
cond-mat.soft, cond-mat.stat-mech
Towards Understanding the Impact of Data Bugs on Deep Learning Models in Software Engineering
Mehil B Shah, Mohammad Masudur Rahman, Foutse Khomh
Deep learning (DL) techniques have achieved significant success in various software engineering tasks (e.g., code completion by Copilot). However, DL systems are prone to bugs from many sources, including training data. Existing literature suggests that bugs in training data are highly prevalent, but little research has focused on understanding their impacts on the models used in software engineering tasks. In this paper, we address this research gap through a comprehensive empirical investigation focused on three types of data prevalent in software engineering tasks: code-based, text-based, and metric-based. Using state-of-the-art baselines, we compare the models trained on clean datasets with those trained on datasets with quality issues and without proper preprocessing. By analysing the gradients, weights, and biases from neural networks under training, we identify the symptoms of data quality and preprocessing issues. Our analysis reveals that quality issues in code data cause biased learning and gradient instability, whereas problems in text data lead to overfitting and poor generalisation of models. On the other hand, quality issues in metric data result in exploding gradients and model overfitting, and inadequate preprocessing exacerbates these effects across all three data types. Finally, we demonstrate the validity and generalizability of our findings using six new datasets. Our research provides a better understanding of the impact and symptoms of data bugs in software engineering datasets. Practitioners and researchers can leverage these findings to develop better monitoring systems and data-cleaning methods to help detect and resolve data bugs in deep learning systems.
A comparative study on the response of the L-shaped base isolated multi-storey building to near and far field earthquake ground motion
Jitendra Gudainiyan, Praveen Kumar Gupta
This study aims to understand the behaviour of a base isolated l-shaped building under far field and near field earthquake ground motion. A ten-storey l-shaped building was considered for the study and modelled using SAP2000, which is finite-element-based software. At first, a non-isolated model was created, and the required data was generated in order to develop an isolated model. After that, a non-linear time history analysis was performed, and the results of storey displacement, torsional irregularity, and base shear have been discussed for the base isolated model and the non-isolated model. The fundamental time period of base isolated l-shaped building was found to be 2.56 s while the base model had fundamental time period of 0.88 s. It was found in this study that higher peak ground acceleration (PGA) and peak ground velocity (PGV) of the ground motion led to higher storey displacement, storey drift, and base shear but a lower torsional irregularity ratio under near field ground motion, while torsional irregularity ratio of base isolated building was found to be increased under far field ground motion.
Mechanics of engineering. Applied mechanics, Technology
Finite difference analysis on radiative flow on a perpendicular plate using the influence of thermal conductivity
D. Iranian, K. Sudarmozhi, S. Karthik
et al.
This study aims to investigate the influence of radiation, thermal conductivity and variable viscosity on natural convective flow on a semi-infinite perpendicular plate. Variable viscosity, thermal conductivity and thermal radiation are considered for the given study. The dimensional governing equations are framed with the use of the mentioned parameters and then these equations were converted into dimensionless equations by applying non dimensional quantities. The main aim of this study is to find the Nusselt number and skin friction for both air and water for considered parameters. Using the finite difference method through Fortran software, numerical solutions to the governing heat equations and dimensionless momentum equations were computed. The results for the parameters thermal conductivity, variable viscosity, radiation, and Prandtl number for both air and water are displayed via various graphs. The skin friction coefficients, Nusselt parameter, and local Nusselt numbers were discussed for both the air and water. The key conclusions of this study are that the succeeding velocity declines as the radiation's increases. By increasing the radiation value and the fluctuation time, the temperature distribution increases. Notably, the temperature profile increases significantly when the variable viscosity parameter decreases.
Mechanics of engineering. Applied mechanics, Technology
Free Vibration and Buckling Analyses of Nanobeam Embedded in Pasternak Foundation
Yajuvindra Kumar, Imran Ali
In this paper, free transverse vibration and buckling analyses of a nanobeam are presented by coupling the Euler-Bernoulli beam (EBT) theory and Eringen’s nonlocal elasticity theory. The nanobeam is embedded in the Pasternak foundation. Hamilton’s energy principle is used to derive governing differential equations. The Lagrange polynomial-based differential quadrature method (PDQM) and a harmonic differential quadrature method (HDQM) are used to convert the governing differential equation and boundary conditions into a set of linear algebraic equations. The first three frequencies and the lowest critical buckling loads for clamped-clamped, clamped-simply supported, and simply supported-simply supported boundary conditions are obtained by implementing the bisection method through a computer program written in C++. The impacts of nonlocal Eringen’s parameter (scaling effect parameter), boundary conditions, axial force, and elastic foundation moduli on frequencies are examined. The effects of nonlocal Eringen’s parameter, boundary conditions, and elastic foundation moduli on critical buckling load are also studied. A convergence study of both versions of DQM is conducted to validate the present analysis. A comparison of frequencies and critical buckling loads with those available in the literature is presented.
Mechanics of engineering. Applied mechanics
Evaluation of welding-induced residual stress and distortion in A-TIG welding of duplex stainless steel
Amir Siyavoshi, Saeed Shakhesi, Mohammad Reza Afshar
et al.
Applying non-uniform heat in welding causes residual stress and distortion, which affects the life of components. In the present study, the residual stress and distortion of Duplex 2205 stainless steel in A-TIG welding were investigated numerically and experimentally. The optimal welding parameters for highest penetration depth in welded samples were obtained experimentally. Uncoupled thermal-mechanical analysis using ABAQUS 2017 software has been done. Goldak's parameters were measured by empirical tests. The results include simulation diagrams of four samples consisting of the optimal sample without flux powder and three samples with the highest penetration depth. The simulation results show that the sample without flux has a higher maximum temperature and lower welding-induced distortions. The efficiency used in this research changes using and not using powder; it is concluded that, in similar conditions in A-TIG welding, fewer values of parameters are needed to achieve the appropriate result comparing conventional TIG. The efficiency of workpieces with flux should be considered about 20% lower to have similar results to the conventional TIG. The numerical modeling results showed a good agreement with experimental data both for temperature distribution and welding-induced residual stress and distortion. The distortion in the pieces with conventional TIG welding has increased to 11% at the farthest point from the welding line. The error obtained from comparing the results in residual stress is between 12 and 34%.
Mechanical engineering and machinery, Mechanics of engineering. Applied mechanics
ChatGPT & Mechanical Engineering: Examining performance on the FE Mechanical Engineering and Undergraduate Exams
Matthew Frenkel, Hebah Emara
The launch of ChatGPT at the end of 2022 generated large interest into possible applications of artificial intelligence in STEM education and among STEM professions. As a result many questions surrounding the capabilities of generative AI tools inside and outside of the classroom have been raised and are starting to be explored. This study examines the capabilities of ChatGPT within the discipline of mechanical engineering. It aims to examine use cases and pitfalls of such a technology in the classroom and professional settings. ChatGPT was presented with a set of questions from junior and senior level mechanical engineering exams provided at a large private university, as well as a set of practice questions for the Fundamentals of Engineering Exam (FE) in Mechanical Engineering. The responses of two ChatGPT models, one free to use and one paid subscription, were analyzed. The paper found that the subscription model (GPT-4) greatly outperformed the free version (GPT-3.5), achieving 76% correct vs 51% correct, but the limitation of text only input on both models makes neither likely to pass the FE exam. The results confirm findings in the literature with regards to types of errors and pitfalls made by ChatGPT. It was found that due to its inconsistency and a tendency to confidently produce incorrect answers the tool is best suited for users with expert knowledge.
Modeling the evolution of representative dislocation structures under high thermo-mechanical conditions during Additive Manufacturing of Alloys
Markus Sudmanns, Athanasios P. Iliopoulos, Andrew J. Birnbaum
et al.
Mesoscale simulations of discrete defects in metals provide an ideal framework to investigate the micro-scale mechanisms governing the plastic deformation under high thermal and mechanical loading conditions. To bridge size and time-scale while limiting computational effort, typically the concept of representative volume elements (RVEs) is employed. This approach considers the microstructure evolution in a volume that is representative of the overall material behavior. However, in settings with complex thermal and mechanical loading histories careful consideration of the impact of modeling constraints in terms of time scale and simulation domain on predicted results is required. We address the representation of heterogeneous dislocation structure formation in simulation volumes using the example of residual stress formation during cool-down of laser powder-bed fusion (LPBF) of AISI 316L stainless steel. This is achieved by a series of large-scale three-dimensional discrete dislocation dynamics (DDD) simulations assisted by thermo-mechanical finite element modeling of the LPBF process. Our results show that insufficient size of periodic simulation domains can result in dislocation patterns that reflect the boundaries of the primary cell. More pronounced dislocation interaction observed for larger domains highlight the significance of simulation domain constraints for predicting mechanical properties. We formulate criteria that characterize representative volume elements by capturing the conformity of the dislocation structure to the bulk material. This work provides a basis for future investigations of heterogeneous microstructure formation in mesoscale simulations of bulk material behavior.
en
cond-mat.mtrl-sci, math.NA
Multi-Point Detection of the Powerful Gamma Ray Burst GRB221009A Propagation through the Heliosphere on October 9, 2022
Andrii Voshchepynets, Oleksiy Agapitov, Lynn Wilson
et al.
We present the results of processing the effects of the powerful Gamma Ray Burst GRB221009A captured by the charged particle detectors (electrostatic analyzers and solid-state detectors) onboard spacecraft at different points in the heliosphere on October 9, 2022. To follow the GRB221009A propagation through the heliosphere we used the electron and proton flux measurements from solar missions Solar Orbiter and STEREO-A; Earth magnetosphere and the solar wind missions THEMIS and Wind; meteorological satellites POES15, POES19, MetOp3; and MAVEN - a NASA mission orbiting Mars. GRB221009A had a structure of four bursts: less intense Pulse 1 - the triggering impulse - was detected by gamma-ray observatories at 131659 UT (near the Earth); the most intense Pulses 2 and 3 were detected on board all the spacecraft from the list, and Pulse 4 detected in more than 500 s after Pulse 1. Due to their different scientific objectives, the spacecraft, which data was used in this study, were separated by more than 1 AU (Solar Orbiter and MAVEN). This enabled tracking GRB221009A as it was propagating across the heliosphere. STEREO-A was the first to register Pulse 2 and 3 of the GRB, almost 100 seconds before their detection by spacecraft in the vicinity of Earth. MAVEN detected GRB221009A Pulses 2, 3, and 4 at the orbit of Mars about 237 seconds after their detection near Earth. By processing the time delays observed we show that the source location of the GRB221009A was at RA 288.5 degrees, Dec 18.5 degrees (J2000) with an error cone of 2 degrees
en
astro-ph.HE, astro-ph.IM
Stop Words for Processing Software Engineering Documents: Do they Matter?
Yaohou Fan, Chetan Arora, Christoph Treude
Stop words, which are considered non-predictive, are often eliminated in natural language processing tasks. However, the definition of uninformative vocabulary is vague, so most algorithms use general knowledge-based stop lists to remove stop words. There is an ongoing debate among academics about the usefulness of stop word elimination, especially in domain-specific settings. In this work, we investigate the usefulness of stop word removal in a software engineering context. To do this, we replicate and experiment with three software engineering research tools from related work. Additionally, we construct a corpus of software engineering domain-related text from 10,000 Stack Overflow questions and identify 200 domain-specific stop words using traditional information-theoretic methods. Our results show that the use of domain-specific stop words significantly improved the performance of research tools compared to the use of a general stop list and that 17 out of 19 evaluation measures showed better performance. Online appendix: https://zenodo.org/record/7865748
The Impact of Urban Infill: A Study of Contemporary Malls in Baghdad
Ashwaq Fadhel Muhkaber Alomare, Tahrir Taki Ali AL-Musawi
The impact of urban infill has been an important topic within urban research. Despite the vast knowledge, however, there is a gap in reporting the effect of adding contemporary malls to Baghdad urban context; therefore, we studied two main contemporary malls built after 2003, Al-Mansour Mall in Al-Mansour district and Baghdad Mall in Harthiya district, selected for this study because of their large-scale and their contribution to the development growth of the city. The findings of this research showed they both have a strong impact on different aspects such as urban, social, economic, and the environment. The paper also highlights critical views concerning the spread of malls in Baghdad and discusses the importance of traditional suqs and the reasons of transition to the contemporary malls with suggestions for improvement. This paper contributes to the urban literature by developing a theoretical framework of urban infill indicators. Findings may have implications for future infill developments both for architecture and urban design strategies for city growth.
Engineering machinery, tools, and implements, Mechanics of engineering. Applied mechanics
Optical, Electrical Properties and Surface Morphology of Thermal Evaporated Zinc Telluride (ZnTe) Thin Films for Photovoltaic Applications
Rasaq Ayinla Babatunde, Rasaki Kola Odunaike
ZnTe bilayer thin films were deposited onto soda-lime glass by a thermal vacuum evaporation technique using the NANO 36 thermal evaporator under a vacuum pressure of 2.9 x 10-5 torr. The optical characteristics of the film were measured using an AVANTEX UV spectrophotometer in the wavelength range from 239.534 nm to 999.495 nm. Also, the electrical characteristics of the thin films were investigated using KEITHLEY four-point probe techniques. The investigation of the optical properties of the thin films as-deposited and annealed at different temperatures showed high transmission in the NIR region with good absorption in the visible and UV regions. The extrapolated band gap energies were 2.60 eV and 3.20 eV for annealed and as-deposited samples, respectively. electrical resistivity decreased as the annealing temperature increases. The images of the film as-deposited and on annealing have a uniform distribution on the glass slides.
Mechanics of engineering. Applied mechanics, Technology
Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics
Loc Vu-Quoc, Alexander Humer
Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional integration methods. Here, methods (1) and (2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3) relying on convolutional neural networks. Pure ML methods to solve (nonlinear) PDEs are represented by Physics-Informed Neural network (PINN) methods, which could be combined with attention mechanism to address discontinuous solutions. Both LSTM and attention architectures, together with modern and generalized classic optimizers to include stochasticity for DL networks, are extensively reviewed. Kernel machines, including Gaussian processes, are provided to sufficient depth for more advanced works such as shallow networks with infinite width. Not only addressing experts, readers are assumed familiar with computational mechanics, but not with DL, whose concepts and applications are built up from the basics, aiming at bringing first-time learners quickly to the forefront of research. History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics, even in well-known references. Positioning and pointing control of a large-deformable beam is given as an example.