Eqab. M. Rabei, Mohamed Ghaleb Al-Masaeed, Dumitru Baleanu
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
本研究探讨了共形电磁场理论。研究引入了保角三角函数的概念。随后，导出了共形麦克斯韦方程。
{"title":"The treatment of conformable electromagnetic theory of Maxwell as a singular system","authors":"Eqab. M. Rabei, Mohamed Ghaleb Al-Masaeed, Dumitru Baleanu","doi":"arxiv-2408.01881","DOIUrl":"https://doi.org/arxiv-2408.01881","url":null,"abstract":"The study explores the conformable electromagnetic field theory. The concept\u0000of the conformable delta function is introduced. Subsequently, the conformable\u0000Maxwell's equations are derived.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938541","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}
Mozhdeh Erfanian, Edward James Brambley, Francis Flanagan, Doireann O'Kiely, Alison O'Connor
A new semi-analytic model of the metal rolling processes is presented and validated against finite element simulations. The model generalizes the classical Slab Method of cold rolling, and for the first time is able to predict the through-thickness stress and strain oscillations present in long-aspect-ratio roll gaps. The model is based on the asymptotic Method of Multiple-Scales, with the systematic assumptions of a long thin roll gap and a comparably small Coulomb friction coefficient. The leading-order solution varies only on the long length scale of the roll gap length $hat{ell}$, and matches with Slab Theory. The next-order correction varies on both the long length scale and the short length scale of the workpiece thickness $2hat{h}_0$, and reveals rapid stress and strain oscillation both in the rolling direction and through-thickness. For this initial derivation, the model assumes a rigid perfectly-plastic material behaviour. Despite these strong assumptions, the model is shown to compare well with finite element simulations using realistic elasticity and hardening material models. These assumptions facilitate the simplest possible model to provide a foundational understanding of the complex through-thickness behaviour observed in the finite element simulations, while requiring an order of only seconds to compute. Matlab code for evaluating the model is provided in the supplementary material.
{"title":"Through-Thickness Modelling of Metal Rolling using Multiple-Scale Asymptotics","authors":"Mozhdeh Erfanian, Edward James Brambley, Francis Flanagan, Doireann O'Kiely, Alison O'Connor","doi":"arxiv-2408.01347","DOIUrl":"https://doi.org/arxiv-2408.01347","url":null,"abstract":"A new semi-analytic model of the metal rolling processes is presented and\u0000validated against finite element simulations. The model generalizes the\u0000classical Slab Method of cold rolling, and for the first time is able to\u0000predict the through-thickness stress and strain oscillations present in\u0000long-aspect-ratio roll gaps. The model is based on the asymptotic Method of\u0000Multiple-Scales, with the systematic assumptions of a long thin roll gap and a\u0000comparably small Coulomb friction coefficient. The leading-order solution\u0000varies only on the long length scale of the roll gap length $hat{ell}$, and\u0000matches with Slab Theory. The next-order correction varies on both the long\u0000length scale and the short length scale of the workpiece thickness\u0000$2hat{h}_0$, and reveals rapid stress and strain oscillation both in the\u0000rolling direction and through-thickness. For this initial derivation, the model\u0000assumes a rigid perfectly-plastic material behaviour. Despite these strong\u0000assumptions, the model is shown to compare well with finite element simulations\u0000using realistic elasticity and hardening material models. These assumptions\u0000facilitate the simplest possible model to provide a foundational understanding\u0000of the complex through-thickness behaviour observed in the finite element\u0000simulations, while requiring an order of only seconds to compute. Matlab code\u0000for evaluating the model is provided in the supplementary material.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938543","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}
Thinh Q. Bui, Samuel D. Oberdick, Frank M. Abel, Michael J. Donahue, Klaus N. Quelhas, Cindi L. Dennis, Thomas Cleveland, Yanxin Liu, Solomon I. Woods
In recent years, there has been increasing interest in the understanding and application of nanoparticle assemblies driven by external fields. Although these systems can exhibit marked transitions in behavior compared to non-interacting counterparts, it has often proven challenging to connect their dynamics with underlying physical mechanisms or even to verifiably establish their structure under realistic experimental conditions. We have studied colloidal iron oxide nanoparticles that assemble into ordered, few-particle linear chains under the influence of oscillating and pulsed magnetic fields. Cryo-EM has been used to flash freeze and image the structures formed by oscillatory drive fields, and magnetic relaxometry has been used to extract the multiple time constants associated with magnetic switching of the short chains. Armed with the physical structure from cryo-EM and the field-dependent switching times from magnetic measurements, we have conducted extensive micromagnetic simulations, revealing probable mechanisms for each time constant regime spanning $10^{9}$ in time and how switching develops from individual particles to entire chains. These types of magnetic nanomaterials have great potential for biomedical technologies, particularly magnetic particle imaging and hyperthermia, and rigorous elucidation of their physics will hasten their optimization.
{"title":"Magnetodynamics of few-nanoparticle chains","authors":"Thinh Q. Bui, Samuel D. Oberdick, Frank M. Abel, Michael J. Donahue, Klaus N. Quelhas, Cindi L. Dennis, Thomas Cleveland, Yanxin Liu, Solomon I. Woods","doi":"arxiv-2408.01561","DOIUrl":"https://doi.org/arxiv-2408.01561","url":null,"abstract":"In recent years, there has been increasing interest in the understanding and\u0000application of nanoparticle assemblies driven by external fields. Although\u0000these systems can exhibit marked transitions in behavior compared to\u0000non-interacting counterparts, it has often proven challenging to connect their\u0000dynamics with underlying physical mechanisms or even to verifiably establish\u0000their structure under realistic experimental conditions. We have studied\u0000colloidal iron oxide nanoparticles that assemble into ordered, few-particle\u0000linear chains under the influence of oscillating and pulsed magnetic fields.\u0000Cryo-EM has been used to flash freeze and image the structures formed by\u0000oscillatory drive fields, and magnetic relaxometry has been used to extract the\u0000multiple time constants associated with magnetic switching of the short chains.\u0000Armed with the physical structure from cryo-EM and the field-dependent\u0000switching times from magnetic measurements, we have conducted extensive\u0000micromagnetic simulations, revealing probable mechanisms for each time constant\u0000regime spanning $10^{9}$ in time and how switching develops from individual\u0000particles to entire chains. These types of magnetic nanomaterials have great\u0000potential for biomedical technologies, particularly magnetic particle imaging\u0000and hyperthermia, and rigorous elucidation of their physics will hasten their\u0000optimization.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938441","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}
W. BartelDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, C. W. ElversDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, L. JönssonLund University, Sweden, G. KempfDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, H. KrauseUniversität Hamburg, B. LoehrDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, E. LohrmannUniversität Hamburg, H. MeyerBergische Universität, Wuppertal, P. SteffenDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, E. WuenschDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany
Gravitational interactions were studied by measuring the influence of small external field masses on a microwave resonator. It consisted of two spherical mirrors, which acted as independent pendulumsindividually suspended by strings. Two identical field masses weremoved along the axis of the resonator symmetrically and periodically betweena near and a far position. Their gravitational interaction altered the distance between the mirrors, changing the resonance frequency, which was measured and found consistent with Newton's law of gravity. The acceleration of a single mirror caused by the two field masses at the closest position varied from $5.4 10^{-12} m/s^2$ to $259 10^{-12} m/s^2$.
{"title":"Measurements of Gravitational Attractions at small Accelerations","authors":"W. BartelDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, C. W. ElversDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, L. JönssonLund University, Sweden, G. KempfDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, H. KrauseUniversität Hamburg, B. LoehrDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, E. LohrmannUniversität Hamburg, H. MeyerBergische Universität, Wuppertal, P. SteffenDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany, E. WuenschDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany","doi":"arxiv-2407.21482","DOIUrl":"https://doi.org/arxiv-2407.21482","url":null,"abstract":"Gravitational interactions were studied by measuring the influence of small\u0000external field masses on a microwave resonator. It consisted of two spherical\u0000mirrors, which acted as independent pendulumsindividually suspended by strings.\u0000Two identical field masses weremoved along the axis of the resonator\u0000symmetrically and periodically betweena near and a far position. Their\u0000gravitational interaction altered the distance between the mirrors, changing\u0000the resonance frequency, which was measured and found consistent with Newton's\u0000law of gravity. The acceleration of a single mirror caused by the two field masses at the\u0000closest position varied from $5.4 10^{-12} m/s^2$ to $259 10^{-12} m/s^2$.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141865366","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}
Shengyang YuanNAVIER UMR 8205, Xianfeng LiuNAVIER UMR 8205, Yongxin WangNAVIER UMR 8205, Pierre DelageNAVIER UMR 8205, Patrick Aimedieu, Olivier Buzzi
Soil properties, such as wetting collapse behavior and permeability, are strongly correlated to the soil microstructure. To date, several techniques including mercury intrusion porosimetry (MIP), can be used to characterize the microstructure of soil, but all techniques have their own limitations. In this study, the features of mercury that penetrated and has been entrapped in the pore network of the specimens through MIP testing were investigated by X-Ray microtomography (X-$mu$CT), in order to give an insight into the geometry of macropores and possible ink-bottle geometry. Two conditions of water content and density were selected for the compacted Maryland clay. The distribution and geometry features of mercury entrapped in the microstructure after MIP were characterized and pore size distributions were also reconstructed. The results suggest that, for the two conditions studied in this paper, macropores were evenly distributed within the specimens, and most of them with a non-spherical shape, and with aspect ratio (ratio between the maximum and minimum thickness along a given segment) smaller than three. Different dominant entrance pore size of macropore was obtained from MIP and X-$mu$CT, due to the specific experimental protocol used in tests and the effect of ink-bottle geometry. Only the large pore bodies with high aspect ratio were imaged in X-$mu$CT, due to the extrusion of mercury during the process of depressurization and subsequent sample preparation for X- $mu$CT. But entire pore space was accessible in MIP. The difference in dominant entrance pore size was more significant for specimens with lower void ratio due to a more pronounced aspect ratio.
{"title":"X-Ray microtomography of mercury intruded compacted clay: An insight into the geometry of macropores","authors":"Shengyang YuanNAVIER UMR 8205, Xianfeng LiuNAVIER UMR 8205, Yongxin WangNAVIER UMR 8205, Pierre DelageNAVIER UMR 8205, Patrick Aimedieu, Olivier Buzzi","doi":"arxiv-2407.21083","DOIUrl":"https://doi.org/arxiv-2407.21083","url":null,"abstract":"Soil properties, such as wetting collapse behavior and permeability, are\u0000strongly correlated to the soil microstructure. To date, several techniques\u0000including mercury intrusion porosimetry (MIP), can be used to characterize the\u0000microstructure of soil, but all techniques have their own limitations. In this\u0000study, the features of mercury that penetrated and has been entrapped in the\u0000pore network of the specimens through MIP testing were investigated by X-Ray\u0000microtomography (X-$mu$CT), in order to give an insight into the geometry of\u0000macropores and possible ink-bottle geometry. Two conditions of water content\u0000and density were selected for the compacted Maryland clay. The distribution and\u0000geometry features of mercury entrapped in the microstructure after MIP were\u0000characterized and pore size distributions were also reconstructed. The results\u0000suggest that, for the two conditions studied in this paper, macropores were\u0000evenly distributed within the specimens, and most of them with a non-spherical\u0000shape, and with aspect ratio (ratio between the maximum and minimum thickness\u0000along a given segment) smaller than three. Different dominant entrance pore\u0000size of macropore was obtained from MIP and X-$mu$CT, due to the specific\u0000experimental protocol used in tests and the effect of ink-bottle geometry. Only\u0000the large pore bodies with high aspect ratio were imaged in X-$mu$CT, due to\u0000the extrusion of mercury during the process of depressurization and subsequent\u0000sample preparation for X- $mu$CT. But entire pore space was accessible in MIP.\u0000The difference in dominant entrance pore size was more significant for\u0000specimens with lower void ratio due to a more pronounced aspect ratio.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141865364","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}
When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order parameter, we show that phase transitions arise as a function of the dimension of the state space and inertia. We calculate the scaling exponents and the macroscopic lag time associated with the presence of first and second order transitions, and describe the regimes of co-existence of stable states and the accompanying hysteresis. Experiments with rolling cylinders corroborate our theoretical results on the scaling of the lag time. Experiments with spheres reveal closed orbits and their period-doubling in the overdamped and inertial limits respectively, providing visible manifestations of the hairy ball theorem and the doubly-connected nature of SO(3), the space of 3-dimensional rotations. Going beyond simple curiosity, our study might be relevant in a number of natural and artificial systems that involve the rolling of irregular objects, in systems ranging from nanoscale cellular transport to robotics.
{"title":"Phase transitions in rolling of irregular cylinders and spheres","authors":"Daoyuan Qian, Yeonsu Jung, L. Mahadevan","doi":"arxiv-2407.19861","DOIUrl":"https://doi.org/arxiv-2407.19861","url":null,"abstract":"When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls\u0000down in a straight line under gravity. But how is the rolling affected if these\u0000shapes are irregular or random? Treating the terminal rolling speed as an order\u0000parameter, we show that phase transitions arise as a function of the dimension\u0000of the state space and inertia. We calculate the scaling exponents and the\u0000macroscopic lag time associated with the presence of first and second order\u0000transitions, and describe the regimes of co-existence of stable states and the\u0000accompanying hysteresis. Experiments with rolling cylinders corroborate our\u0000theoretical results on the scaling of the lag time. Experiments with spheres\u0000reveal closed orbits and their period-doubling in the overdamped and inertial\u0000limits respectively, providing visible manifestations of the hairy ball theorem\u0000and the doubly-connected nature of SO(3), the space of 3-dimensional rotations.\u0000Going beyond simple curiosity, our study might be relevant in a number of\u0000natural and artificial systems that involve the rolling of irregular objects,\u0000in systems ranging from nanoscale cellular transport to robotics.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873044","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}
Self-propulsion is a quintessential aspect of biological systems, which can induce nonequilibrium phenomena that have no counterparts in passive systems. Motivated by biophysical interest together with recent advances in experimental techniques, active matter has been a rapidly developing field in physics. Meanwhile, over the past few decades, topology has played a crucial role to understand certain robust properties appearing in condensed matter systems. For instance, the nontrivial topology of band structures leads to the notion of topological insulators, where one can find robust gapless edge modes protected by the bulk band topology. We here review recent progress in an interdisciplinary area of research at the intersection of these two fields. Specifically, we give brief introductions to active matter and band topology in Hermitian systems, and then explain how the notion of band topology can be extended to nonequilibrium (and thus non-Hermitian) systems including active matter. We review recent studies that have demonstrated the intimate connections between active matter and topological materials, where exotic topological phenomena that are unfeasible in passive systems have been found. A possible extension of the band topology to nonlinear systems is also briefly discussed. Active matter can thus provide an ideal playground to explore topological phenomena in qualitatively new realms beyond conservative linear systems.
{"title":"Hermitian and non-Hermitian topology in active matter","authors":"Kazuki Sone, Kazuki Yokomizo, Kyogo Kawaguchi, Yuto Ashida","doi":"arxiv-2407.16143","DOIUrl":"https://doi.org/arxiv-2407.16143","url":null,"abstract":"Self-propulsion is a quintessential aspect of biological systems, which can\u0000induce nonequilibrium phenomena that have no counterparts in passive systems.\u0000Motivated by biophysical interest together with recent advances in experimental\u0000techniques, active matter has been a rapidly developing field in physics.\u0000Meanwhile, over the past few decades, topology has played a crucial role to\u0000understand certain robust properties appearing in condensed matter systems. For\u0000instance, the nontrivial topology of band structures leads to the notion of\u0000topological insulators, where one can find robust gapless edge modes protected\u0000by the bulk band topology. We here review recent progress in an\u0000interdisciplinary area of research at the intersection of these two fields.\u0000Specifically, we give brief introductions to active matter and band topology in\u0000Hermitian systems, and then explain how the notion of band topology can be\u0000extended to nonequilibrium (and thus non-Hermitian) systems including active\u0000matter. We review recent studies that have demonstrated the intimate\u0000connections between active matter and topological materials, where exotic\u0000topological phenomena that are unfeasible in passive systems have been found. A\u0000possible extension of the band topology to nonlinear systems is also briefly\u0000discussed. Active matter can thus provide an ideal playground to explore\u0000topological phenomena in qualitatively new realms beyond conservative linear\u0000systems.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775421","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}
Chenbo Shi, Jin Pan, Xin Gu, Shichen Liang, Le Zuo
Existing methods for calculating substructure characteristic modes require treating interconnected metal structures as a single entity to ensure current continuity between different metal bodies. However, when these structures are treated as separate entities, existing methods exhibit inaccuracies, affecting the assessment of structural performance. To address this challenge, we propose an enhanced electromagnetic model that enables accurate characteristic mode analysis for regional structures within interconnected metal bodies. Numerical results validate the accuracy of the proposed method, and an antenna design example demonstrates its practical utility.
{"title":"Computation of Characteristic Mode for Regional Structure of Interconnected Metal Bodies","authors":"Chenbo Shi, Jin Pan, Xin Gu, Shichen Liang, Le Zuo","doi":"arxiv-2407.14752","DOIUrl":"https://doi.org/arxiv-2407.14752","url":null,"abstract":"Existing methods for calculating substructure characteristic modes require\u0000treating interconnected metal structures as a single entity to ensure current\u0000continuity between different metal bodies. However, when these structures are\u0000treated as separate entities, existing methods exhibit inaccuracies, affecting\u0000the assessment of structural performance. To address this challenge, we propose\u0000an enhanced electromagnetic model that enables accurate characteristic mode\u0000analysis for regional structures within interconnected metal bodies. Numerical\u0000results validate the accuracy of the proposed method, and an antenna design\u0000example demonstrates its practical utility.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775423","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}
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum equations are derived in many excellent references available in the literature, they are not readily usable for solving physical problems due to the covariant, contravariant or mixed nature of the stress and strain tensors in the equations. We present the continuum equations in terms of physical components in a general differentiable manifold. This general formulation of the continuum equations can be used readily for modelling physical problems on arbitrary curved surfaces. We demonstrate this with the help of some examples.
{"title":"Representation of continuum equations in physical components for arbitrary curved surfaces","authors":"Sujit Kumar Nath","doi":"arxiv-2407.13800","DOIUrl":"https://doi.org/arxiv-2407.13800","url":null,"abstract":"Continuum equations are ubiquitous in physical modelling of elastic, viscous,\u0000and viscoelastic systems. The equations of continuum mechanics take nontrivial\u0000forms on curved surfaces. Although the curved surface formulation of the\u0000continuum equations are derived in many excellent references available in the\u0000literature, they are not readily usable for solving physical problems due to\u0000the covariant, contravariant or mixed nature of the stress and strain tensors\u0000in the equations. We present the continuum equations in terms of physical\u0000components in a general differentiable manifold. This general formulation of\u0000the continuum equations can be used readily for modelling physical problems on\u0000arbitrary curved surfaces. We demonstrate this with the help of some examples.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738557","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}
A ring may be regarded as a torus with r << R, where R is the major radius and r is the minor radius. When such a ring is placed on a rough rod and released with some angular velocity, it may continue to vertically spin around the rod for some time instead of falling down immediately. It was observed that two different kinds of motion for the rod exist, which are referred to as single point and double point contact motion, based on the number of contact points of the ring that are in contact with the rod. Single point contact motion was observed for rings and double point contact motion was observed in the case of a washer. We investigated the characteristics of the single point contact motion. An explanation is provided for the single point contact motion of the ring and an analysis of the forces on the ring is made. We observe a hyperbolic decay in the angular velocity of the ring. An explicit solution is determined for the single point contact motion of the ring and the obtained solutions match the observed motion of the ring.
环可以看作是一个 r << R 的环，其中 R 是大半径，r 是小半径。当把这样一个圆环放在一根粗糙的杆子上并以一定的角速度释放时，它可能会继续围绕杆子垂直旋转一段时间，而不是立即掉下来。根据圆环与圆棒接触点的数量，可以观察到圆棒存在两种不同的运动，即单点接触运动和双点接触运动。单点接触运动适用于圆环，双点接触运动适用于垫圈。我们研究了单点接触运动的特征。我们对圆环的单点接触运动进行了解释，并对圆环上的力进行了分析。我们观察到环的角速度呈双曲线衰减。确定了圆环单点接触运动的显式解，得到的解与观测到的圆环运动相吻合。
{"title":"An explicit solution to the spinning ring problem","authors":"Aradhya Jain","doi":"arxiv-2407.13794","DOIUrl":"https://doi.org/arxiv-2407.13794","url":null,"abstract":"A ring may be regarded as a torus with r << R, where R is the major radius\u0000and r is the minor radius. When such a ring is placed on a rough rod and\u0000released with some angular velocity, it may continue to vertically spin around\u0000the rod for some time instead of falling down immediately. It was observed that\u0000two different kinds of motion for the rod exist, which are referred to as\u0000single point and double point contact motion, based on the number of contact\u0000points of the ring that are in contact with the rod. Single point contact\u0000motion was observed for rings and double point contact motion was observed in\u0000the case of a washer. We investigated the characteristics of the single point\u0000contact motion. An explanation is provided for the single point contact motion\u0000of the ring and an analysis of the forces on the ring is made. We observe a\u0000hyperbolic decay in the angular velocity of the ring. An explicit solution is\u0000determined for the single point contact motion of the ring and the obtained\u0000solutions match the observed motion of the ring.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738556","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}
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