Mechanical extremal materials, a class of metamaterials that exist at the bounds of elastic theory, possess the extraordinary capability to engineer any desired elastic behavior by harnessing mechanical zero modes -- deformation modes that demand minimal or no elastic energy. However, the potential for arbitrary construction and reprogramming of metamaterials remains largely unrealized, primarily due to significant challenges in qualitatively transforming zero modes within the confines of existing metamaterial design frameworks. In this work, we show a method for explicitly defining and in situ reprogramming zero modes of two-dimensional extremal materials by employing straight-line mechanisms (SLMs) and planar symmetry, which prescribe and coordinate the zero modes, respectively. We design, test, and reprogram centimeter-scale isotropic, orthotropic, and chiral extremal materials by reorienting the SLMs in place, enabling these materials to smoothly and reversibly interpolate between extremal modalities (e.g., unimode to bimode) and material properties (e.g., negative to positive Poisson's ratios) without changing the metamaterial's global structure. Our methodology provides a straightforward and explicit strategy for the design and tuning of all varieties of two-dimensional extremal materials, enabling arbitrary and dynamic mechanical metamaterial construction to completely cover the gamut of elastic properties.
{"title":"Design and Reprogrammability of Zero Modes in 2D Materials from a Single Element","authors":"Daniel Revier, Molly Carton, Jeffrey I. Lipton","doi":"arxiv-2407.04934","DOIUrl":"https://doi.org/arxiv-2407.04934","url":null,"abstract":"Mechanical extremal materials, a class of metamaterials that exist at the\u0000bounds of elastic theory, possess the extraordinary capability to engineer any\u0000desired elastic behavior by harnessing mechanical zero modes -- deformation\u0000modes that demand minimal or no elastic energy. However, the potential for\u0000arbitrary construction and reprogramming of metamaterials remains largely\u0000unrealized, primarily due to significant challenges in qualitatively\u0000transforming zero modes within the confines of existing metamaterial design\u0000frameworks. In this work, we show a method for explicitly defining and in situ\u0000reprogramming zero modes of two-dimensional extremal materials by employing\u0000straight-line mechanisms (SLMs) and planar symmetry, which prescribe and\u0000coordinate the zero modes, respectively. We design, test, and reprogram\u0000centimeter-scale isotropic, orthotropic, and chiral extremal materials by\u0000reorienting the SLMs in place, enabling these materials to smoothly and\u0000reversibly interpolate between extremal modalities (e.g., unimode to bimode)\u0000and material properties (e.g., negative to positive Poisson's ratios) without\u0000changing the metamaterial's global structure. Our methodology provides a\u0000straightforward and explicit strategy for the design and tuning of all\u0000varieties of two-dimensional extremal materials, enabling arbitrary and dynamic\u0000mechanical metamaterial construction to completely cover the gamut of elastic\u0000properties.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abhishek Ghosh, Andrew McBride, Zhaowei Liu, Luca Heltai, Paul Steinmann, Prashant Saxena
Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour necessitates an understanding of the complex interactions between the structural deformation and the fields in the surrounding medium. For thin shell structures, this challenge is addressed by developing a shell model that effectively incorporates the three-dimensional field it is embedded in by appropriately accounting for the relevant boundary conditions. This study presents a model for the nonlinear deformation of thin hyperelastic shells, incorporating Kirchhoff-Love assumptions and a rigorous variational approach. The shell theory is derived from 3D nonlinear elasticity by dimension reduction while preserving the boundary conditions at the top and bottom surfaces of the shell. Consequently, unlike classical shell theories, this approach can distinguish between pressure loads applied at the top and bottom surfaces, and delivers a platform to include multi-physics coupling. Numerical examples are presented to illustrate the theory and provide a physical interpretation of the novel mechanical variables of the model.
{"title":"An embedding-aware continuum thin shell formulation","authors":"Abhishek Ghosh, Andrew McBride, Zhaowei Liu, Luca Heltai, Paul Steinmann, Prashant Saxena","doi":"arxiv-2407.04894","DOIUrl":"https://doi.org/arxiv-2407.04894","url":null,"abstract":"Cutting-edge smart materials are transforming the domains of soft robotics,\u0000actuators, and sensors by harnessing diverse non-mechanical stimuli, such as\u0000electric and magnetic fields. Accurately modelling their physical behaviour\u0000necessitates an understanding of the complex interactions between the\u0000structural deformation and the fields in the surrounding medium. For thin shell\u0000structures, this challenge is addressed by developing a shell model that\u0000effectively incorporates the three-dimensional field it is embedded in by\u0000appropriately accounting for the relevant boundary conditions. This study\u0000presents a model for the nonlinear deformation of thin hyperelastic shells,\u0000incorporating Kirchhoff-Love assumptions and a rigorous variational approach.\u0000The shell theory is derived from 3D nonlinear elasticity by dimension reduction\u0000while preserving the boundary conditions at the top and bottom surfaces of the\u0000shell. Consequently, unlike classical shell theories, this approach can\u0000distinguish between pressure loads applied at the top and bottom surfaces, and\u0000delivers a platform to include multi-physics coupling. Numerical examples are\u0000presented to illustrate the theory and provide a physical interpretation of the\u0000novel mechanical variables of the model.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bharti BhartiUiO, LOMA, Quentin FerreiraLOMA, Aditya JhaLOMA, Andreas CarlsonUiO, David S. DeanLOMA, Yacine AmaroucheneLOMA, Tak Shing ChanUiO, Thomas SalezLOMA
Soft lubrication has been shown to drastically affect the mobility of an object immersed in a viscous fluid in the vicinity of a purely elastic wall. In this theoretical study, we develop a minimal model incorporating viscoelasticity, carrying out a perturbation analysis in both the elastic deformation of the wall and its viscous damping. Our approach reveals the singular-perturbation nature of viscoelasticity to soft lubrication. Numerical resolution of the resulting non-linear, singular and coupled equations of motion reveals peculiar effects of viscoelasticity on confined colloidal mobility, opening the way towards the description of complex migration scenarios near realistic polymeric substrates and biological membranes.
{"title":"Singular viscoelastic perturbation to soft lubrication","authors":"Bharti BhartiUiO, LOMA, Quentin FerreiraLOMA, Aditya JhaLOMA, Andreas CarlsonUiO, David S. DeanLOMA, Yacine AmaroucheneLOMA, Tak Shing ChanUiO, Thomas SalezLOMA","doi":"arxiv-2407.04319","DOIUrl":"https://doi.org/arxiv-2407.04319","url":null,"abstract":"Soft lubrication has been shown to drastically affect the mobility of an\u0000object immersed in a viscous fluid in the vicinity of a purely elastic wall. In\u0000this theoretical study, we develop a minimal model incorporating\u0000viscoelasticity, carrying out a perturbation analysis in both the elastic\u0000deformation of the wall and its viscous damping. Our approach reveals the\u0000singular-perturbation nature of viscoelasticity to soft lubrication. Numerical\u0000resolution of the resulting non-linear, singular and coupled equations of\u0000motion reveals peculiar effects of viscoelasticity on confined colloidal\u0000mobility, opening the way towards the description of complex migration\u0000scenarios near realistic polymeric substrates and biological membranes.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lato-lato, a pendulum-based toy gaining popularity in Indonesian playgrounds, has sparked interest with competitions centered around maintaining its oscillatory motion. While some find it easy to play, the challenge lies in sustaining the oscillation, particularly in maintaining both "up and down collisions." Through a Newtonian dynamics numerical analysis using Python (code by ChatGPT), this study identifies two equilibrium phases - phase 1, characterized by normal pendulum motion, and phase 2, the double collision mode - by using the driven oscillation model. In addition, further analysis and discussion are done using the obtained numeric data. The difficulty in remaining in phase 2 highlights the intricate hand-eye coordination required, shedding light on the toy's appeal and the skill it demands.
{"title":"Playing Lato-lato is Difficult and This is Why","authors":"Fansen Candra, Zainul Abidin","doi":"arxiv-2407.02951","DOIUrl":"https://doi.org/arxiv-2407.02951","url":null,"abstract":"Lato-lato, a pendulum-based toy gaining popularity in Indonesian playgrounds,\u0000has sparked interest with competitions centered around maintaining its\u0000oscillatory motion. While some find it easy to play, the challenge lies in\u0000sustaining the oscillation, particularly in maintaining both \"up and down\u0000collisions.\" Through a Newtonian dynamics numerical analysis using Python (code\u0000by ChatGPT), this study identifies two equilibrium phases - phase 1,\u0000characterized by normal pendulum motion, and phase 2, the double collision mode\u0000- by using the driven oscillation model. In addition, further analysis and\u0000discussion are done using the obtained numeric data. The difficulty in\u0000remaining in phase 2 highlights the intricate hand-eye coordination required,\u0000shedding light on the toy's appeal and the skill it demands.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Matteo Gaibotti, Davide Bigoni, Arsenio Cutolo, Massimiliano Fraldi, Andrea Piccolroaz
The bifurcation problem of a circular Euler-Bernoulli rod subject to a uniform radial force distribution is investigated under three distinct loading conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.) dead load. Previous studies on this apparently 'familiar' structural problem have yielded controversial results, necessitating a comprehensive clarification. This study shows that results previously labelled as 'correct' or 'wrong' simply refer to different external constraints, whose presence becomes necessary only for the two latter loads, (ii.) and (iii.). Moreover, the paper presents the first experimental realization of a circular rod subjected to centrally-directed loads. The experimental findings align with the theoretical predictions and show the exploitation of a new type of load acting on a continuous structural element. The feasibility of this load is demonstrated through the use of inextensible cables and opens the way to applications in flexible robotics when cables are used for actuation.
{"title":"Effects of different loading on the bifurcation of annular elastic rods: theory vs. experiments","authors":"Matteo Gaibotti, Davide Bigoni, Arsenio Cutolo, Massimiliano Fraldi, Andrea Piccolroaz","doi":"arxiv-2407.02897","DOIUrl":"https://doi.org/arxiv-2407.02897","url":null,"abstract":"The bifurcation problem of a circular Euler-Bernoulli rod subject to a\u0000uniform radial force distribution is investigated under three distinct loading\u0000conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.)\u0000dead load. Previous studies on this apparently 'familiar' structural problem\u0000have yielded controversial results, necessitating a comprehensive\u0000clarification. This study shows that results previously labelled as 'correct'\u0000or 'wrong' simply refer to different external constraints, whose presence\u0000becomes necessary only for the two latter loads, (ii.) and (iii.). Moreover,\u0000the paper presents the first experimental realization of a circular rod\u0000subjected to centrally-directed loads. The experimental findings align with the\u0000theoretical predictions and show the exploitation of a new type of load acting\u0000on a continuous structural element. The feasibility of this load is\u0000demonstrated through the use of inextensible cables and opens the way to\u0000applications in flexible robotics when cables are used for actuation.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a pair-wise force law in a system of N particles that produces analytic solutions for arbitrary number of particles, masses, and initial conditions. Each pair of particles interacts via a force that is proportional to the product of their masses and their separation distance, with the force directed radially. We show that, despite the N-body interaction, each particle behaves as if it interacts only with the center of mass of the system. This effective two-body interaction behaves as Hooke's Law with a common frequency for all particles, with the familiar analytic solutions for the trajectories. With these analytic solutions, it is possible to efficiently simulate a collection of these particles and incorporate other external forces. As an example, we simulate the particles within an adiabatically expanding container and calculate pressure and temperature in both the attractive and repulsive cases.
我们提出了一个由 N 个粒子组成的系统中的成对受力定律，它能对任意粒子数、质量和初始条件产生解析解。每对粒子通过与它们的质量和分离距离的乘积成正比的力相互作用，受力方向为径向。我们的研究表明，尽管存在 N 体相互作用，但每个粒子的表现就好像它只与系统的质心相互作用。这种有效的两体相互作用表现为所有粒子具有共同频率的胡克定律，其轨迹具有我们熟悉的解析解。利用这些解析解，我们可以有效地模拟这些粒子的集合，并将其他外力纳入其中。例如，我们模拟了绝热膨胀容器中的粒子，并计算了吸引力和排斥力情况下的压力和温度。
{"title":"N-body linear force law allowing analytic solutions","authors":"Joseph West, Sean P. Bartz","doi":"arxiv-2407.02358","DOIUrl":"https://doi.org/arxiv-2407.02358","url":null,"abstract":"We present a pair-wise force law in a system of N particles that produces\u0000analytic solutions for arbitrary number of particles, masses, and initial\u0000conditions. Each pair of particles interacts via a force that is proportional\u0000to the product of their masses and their separation distance, with the force\u0000directed radially. We show that, despite the N-body interaction, each particle\u0000behaves as if it interacts only with the center of mass of the system. This\u0000effective two-body interaction behaves as Hooke's Law with a common frequency\u0000for all particles, with the familiar analytic solutions for the trajectories.\u0000With these analytic solutions, it is possible to efficiently simulate a\u0000collection of these particles and incorporate other external forces. As an\u0000example, we simulate the particles within an adiabatically expanding container\u0000and calculate pressure and temperature in both the attractive and repulsive\u0000cases.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"237 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
During the years 1948-2019 the ampere was defined via the magnetic force between two long thin parallel wires carrying stationary current. However, if a stationary current flows through a resistive wire, static electric charges appear on the surface of the wire, and this will lead to an additional electric force between the wires. This article discusses the ratio of electric over magnetic forces in the asymptotic limit of infinitely thin wires, which is not accessible by numerical methods. The electric force between the two wires depends also on the choice of the common ground node. For extremely thin or extremely long resistive wires the electric force dominates over the magnetic one.
{"title":"The Electric Force Between Two Straight Parallel Resistive Wires Carrying DC-Currents in the Asymptotic Limit of Infinitely Thin Wires","authors":"Udo Ausserlechner","doi":"arxiv-2407.02541","DOIUrl":"https://doi.org/arxiv-2407.02541","url":null,"abstract":"During the years 1948-2019 the ampere was defined via the magnetic force\u0000between two long thin parallel wires carrying stationary current. However, if a\u0000stationary current flows through a resistive wire, static electric charges\u0000appear on the surface of the wire, and this will lead to an additional electric\u0000force between the wires. This article discusses the ratio of electric over\u0000magnetic forces in the asymptotic limit of infinitely thin wires, which is not\u0000accessible by numerical methods. The electric force between the two wires\u0000depends also on the choice of the common ground node. For extremely thin or\u0000extremely long resistive wires the electric force dominates over the magnetic\u0000one.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ali El ArabiLEMTA, Denis MailletLEMTA, Nicolas BletLEMTA, Benjamin Remy
The junction temperature is a very important parameter for monitoring power electronics converters based on MOSFET transistors. They offer the possibility of switching at relatively higher frequencies than other transistors like IGTBTs. However, the electrical parameters of MOSFETs are highly thermally dependent. The thermo-dependence of MOSFET electrical parameters is rarely taken into consideration when implementing control strategies, for many technological reasons, such as the difficulty of measuring the junction temperature. In practice, the junction temperature of transistors is inaccessible for direct measurement. The presence of a gel covering the chips, that provides electrical and thermal insulation, makes measurement by infrared thermography impossible. Furthermore, direct thermocouple measurement cannot be implemented due to the electromagnetic disturbances in the environment. Several researchers have attempted to correlate chip temperature with thermosensitive electrical parameters. In the present work, a thermal convolutive model has been developed to estimate the junction temperatures of two MOSFET transistors belonging to the same electronic circuit from external temperature measurements in two well-chosen locations (far away enough from the junction to avoid electromagnetic interference), using also the measured power dissipated on each chip. The thermal coupling between the two transistors has been considered in the form of mutual transmittances. The model was first calibrated using three-dimensional numerical simulations in COMSOL Multiphysics, followed by an experimental study. The results are very promising, illustrating the robustness of the convolutional model.
{"title":"A convolutional model for estimating the junction temperatures of SiC MOSFET transistors","authors":"Ali El ArabiLEMTA, Denis MailletLEMTA, Nicolas BletLEMTA, Benjamin Remy","doi":"arxiv-2407.01078","DOIUrl":"https://doi.org/arxiv-2407.01078","url":null,"abstract":"The junction temperature is a very important parameter for monitoring power\u0000electronics converters based on MOSFET transistors. They offer the possibility\u0000of switching at relatively higher frequencies than other transistors like\u0000IGTBTs. However, the electrical parameters of MOSFETs are highly thermally\u0000dependent. The thermo-dependence of MOSFET electrical parameters is rarely\u0000taken into consideration when implementing control strategies, for many\u0000technological reasons, such as the difficulty of measuring the junction\u0000temperature. In practice, the junction temperature of transistors is\u0000inaccessible for direct measurement. The presence of a gel covering the chips,\u0000that provides electrical and thermal insulation, makes measurement by infrared\u0000thermography impossible. Furthermore, direct thermocouple measurement cannot be\u0000implemented due to the electromagnetic disturbances in the environment. Several\u0000researchers have attempted to correlate chip temperature with thermosensitive\u0000electrical parameters. In the present work, a thermal convolutive model has\u0000been developed to estimate the junction temperatures of two MOSFET transistors\u0000belonging to the same electronic circuit from external temperature measurements\u0000in two well-chosen locations (far away enough from the junction to avoid\u0000electromagnetic interference), using also the measured power dissipated on each\u0000chip. The thermal coupling between the two transistors has been considered in\u0000the form of mutual transmittances. The model was first calibrated using\u0000three-dimensional numerical simulations in COMSOL Multiphysics, followed by an\u0000experimental study. The results are very promising, illustrating the robustness\u0000of the convolutional model.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ronaldo S. S. Vieira, Luiz H. R. Daniel, Marcus A. M. de Aguiar
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject can be included in the schedule of an introductory classical mechanics course without the need to develop a robust theory of chaotic dynamics. To do this, we take as examples conservative non-linear oscillators subject to time-dependent periodic forces. By introducing the concept of stroboscopic maps we show that it is possible to visualize the appearance of chaos in these systems. We also address the example of the forced simple pendulum applying the same treatment. Finally, we briefly comment on the more general theory of chaos in conservative Hamiltonian systems.
{"title":"Chaos in undamped, forced oscillators via stroboscopic maps","authors":"Ronaldo S. S. Vieira, Luiz H. R. Daniel, Marcus A. M. de Aguiar","doi":"arxiv-2407.02526","DOIUrl":"https://doi.org/arxiv-2407.02526","url":null,"abstract":"Non-linear dynamics is not a usually covered topic in undergraduate physics\u0000courses. However, its importance within classical mechanics and the general\u0000theory of dynamical systems is unquestionable. In this work we show that this\u0000subject can be included in the schedule of an introductory classical mechanics\u0000course without the need to develop a robust theory of chaotic dynamics. To do\u0000this, we take as examples conservative non-linear oscillators subject to\u0000time-dependent periodic forces. By introducing the concept of stroboscopic maps\u0000we show that it is possible to visualize the appearance of chaos in these\u0000systems. We also address the example of the forced simple pendulum applying the\u0000same treatment. Finally, we briefly comment on the more general theory of chaos\u0000in conservative Hamiltonian systems.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
All existing derivations of the electrostatic potential of a uniformly charged disk are technically rather involved. In an old and now almost forgotten publication, Duffin and McWhirter proposed a method for calculating the electrostatic potentials of planar bodies by a skillful application of Green's theorem. It is shown that this method significantly simplifies the problem of calculating the electrostatic potential of a uniformly charged disk and makes it an almost trivial task.
{"title":"Electrostatic potential of a uniformly charged disk through Green's theorem","authors":"Alina E. Sagaydak, Zurab K. Silagadze","doi":"arxiv-2407.00392","DOIUrl":"https://doi.org/arxiv-2407.00392","url":null,"abstract":"All existing derivations of the electrostatic potential of a uniformly\u0000charged disk are technically rather involved. In an old and now almost\u0000forgotten publication, Duffin and McWhirter proposed a method for calculating\u0000the electrostatic potentials of planar bodies by a skillful application of\u0000Green's theorem. It is shown that this method significantly simplifies the\u0000problem of calculating the electrostatic potential of a uniformly charged disk\u0000and makes it an almost trivial task.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：