The aim of this project was to develop a new Reservoir Computer implementation, based on a chaotic Chua circuit. In addition to suitable classification and regression benchmarks, the Reservoir Computer was applied to Post-Quantum Cryptography, with its suitability for this application investigated and assessed. The cryptographic algorithm utilised was the Learning with Errors problem, for both encryption and decryption. To achieve this, the Chua circuit was characterised, in simulation, and by physical circuit testing. The Reservoir Computer was designed and implemented using the results of the characterisation. As part of this development, noise was considered and mitigated. The benchmarks demonstrate that the Reservoir Computer can achieve current literature benchmarks with low error. However, the results with Learning with Errors suggest that a Chua-based Reservoir Computer is not sufficiently complex to tackle the high non-linearity in Post-Quantum Cryptography. Future work would involve researching the use of different combinations of multiple Chua Reservoir Computers in larger neural network architectures. Such architectures may produce the required high-dimensional behaviour to achieve the Learning with Errors problem. This project is believed to be only the second instance of a Chua-based Reservoir Computer in academia, and it is the first to be applied to challenging real-world tasks such as Post-Quantum Cryptography. It is also original by its investigation of hitherto unexplored parameters, and their impact on performance. It demonstrates a proof-of-concept for a mass-producible, inexpensive, low-power consumption hardware neural network. It also enables the next stages in research to occur, paving the road for using Chua-based Reservoir Computers across various applications.
{"title":"New Reservoir Computing Kernel Based on Chaotic Chua Circuit and Investigating Application to Post-Quantum Cryptography","authors":"Matthew John Cossins, Sendy Phang","doi":"arxiv-2406.12948","DOIUrl":"https://doi.org/arxiv-2406.12948","url":null,"abstract":"The aim of this project was to develop a new Reservoir Computer\u0000implementation, based on a chaotic Chua circuit. In addition to suitable\u0000classification and regression benchmarks, the Reservoir Computer was applied to\u0000Post-Quantum Cryptography, with its suitability for this application\u0000investigated and assessed. The cryptographic algorithm utilised was the\u0000Learning with Errors problem, for both encryption and decryption. To achieve\u0000this, the Chua circuit was characterised, in simulation, and by physical\u0000circuit testing. The Reservoir Computer was designed and implemented using the\u0000results of the characterisation. As part of this development, noise was\u0000considered and mitigated. The benchmarks demonstrate that the Reservoir Computer can achieve current\u0000literature benchmarks with low error. However, the results with Learning with\u0000Errors suggest that a Chua-based Reservoir Computer is not sufficiently complex\u0000to tackle the high non-linearity in Post-Quantum Cryptography. Future work\u0000would involve researching the use of different combinations of multiple Chua\u0000Reservoir Computers in larger neural network architectures. Such architectures\u0000may produce the required high-dimensional behaviour to achieve the Learning\u0000with Errors problem. This project is believed to be only the second instance of a Chua-based\u0000Reservoir Computer in academia, and it is the first to be applied to\u0000challenging real-world tasks such as Post-Quantum Cryptography. It is also\u0000original by its investigation of hitherto unexplored parameters, and their\u0000impact on performance. It demonstrates a proof-of-concept for a\u0000mass-producible, inexpensive, low-power consumption hardware neural network. It\u0000also enables the next stages in research to occur, paving the road for using\u0000Chua-based Reservoir Computers across various applications.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520800","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}
In the context of the ultrasonic determination of mechanical properties, it is common to use oblique incident waves to characterize fluid-immersed anisotropic samples. The lateral displacement of the ultrasonic field owing to leaky guided wave phenomena poses a challenge for data inversion because beam spreading is rarely well represented by plane-wave models. In this study, a finite beam model based on the angular spectrum method was developed to estimate the influence of the transducer shape and position on the transmitted signals. Additionally, anisotropic solids were considered so that the beam skewing effect was contemplated. A small-emitter large-receiver configuration was chosen, and the ideal shape and position of the receiving transducer were obtained through a meta-heuristic optimization approach with the goal of achieving a measurement system that sufficiently resembles plane-wave propagation. A polyvinylidene fluoride receiver was fabricated and tested in three cases: a single-crystal silicon wafer, a lightly anisotropic stainless-steel plate, and a highly anisotropic composite plate. Good agreement was found between the measurements and the plane-wave model.
{"title":"PVDF transducer shape optimization for the characterization of anisotropic materials","authors":"Diego Cowes, Ignacio Mieza, Martín Gómez","doi":"arxiv-2406.12749","DOIUrl":"https://doi.org/arxiv-2406.12749","url":null,"abstract":"In the context of the ultrasonic determination of mechanical properties, it\u0000is common to use oblique incident waves to characterize fluid-immersed\u0000anisotropic samples. The lateral displacement of the ultrasonic field owing to\u0000leaky guided wave phenomena poses a challenge for data inversion because beam\u0000spreading is rarely well represented by plane-wave models. In this study, a\u0000finite beam model based on the angular spectrum method was developed to\u0000estimate the influence of the transducer shape and position on the transmitted\u0000signals. Additionally, anisotropic solids were considered so that the beam\u0000skewing effect was contemplated. A small-emitter large-receiver configuration\u0000was chosen, and the ideal shape and position of the receiving transducer were\u0000obtained through a meta-heuristic optimization approach with the goal of\u0000achieving a measurement system that sufficiently resembles plane-wave\u0000propagation. A polyvinylidene fluoride receiver was fabricated and tested in\u0000three cases: a single-crystal silicon wafer, a lightly anisotropic\u0000stainless-steel plate, and a highly anisotropic composite plate. Good agreement\u0000was found between the measurements and the plane-wave model.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"176 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520801","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 study experimentally the manifestation of non-Weyl graph behavior in open systems using microwave networks. For this a coupling variation to the network is necessary, which was out of reach till now. The coupling to the environment is changed by indirectly varying the boundary condition at the coupling vertex from Dirichlet to Neumann using a dangling bond with variable length attached the coupling vertex. A transformation of equal length spectra to equal reflection phase spectra of the dangling bond allows to create spectra with different fixed coupling strength. This allows to follow the resonances in the complex plane as a function of the coupling. While going from closed (Dirichlet) to fully open (Neumann) graph we see resonances escaping via a superradiant transition leading to non-Weyl behavior if the coupling to the outside is balanced. The open tetrahedral graph displays a rich parametric dynamic of the resonances in the complex plane presenting loops, regions of connected resonances and resonances approaching infinite imaginary parts.
{"title":"Non-Weyl Behavior Induced by Superradiance: A Microwave Graph Study","authors":"Junjie Lu, Tobias Hofmann, Hans-Jürgen Stöckmann, Ulrich Kuhl","doi":"arxiv-2406.11606","DOIUrl":"https://doi.org/arxiv-2406.11606","url":null,"abstract":"We study experimentally the manifestation of non-Weyl graph behavior in open\u0000systems using microwave networks. For this a coupling variation to the network\u0000is necessary, which was out of reach till now. The coupling to the environment\u0000is changed by indirectly varying the boundary condition at the coupling vertex\u0000from Dirichlet to Neumann using a dangling bond with variable length attached\u0000the coupling vertex. A transformation of equal length spectra to equal\u0000reflection phase spectra of the dangling bond allows to create spectra with\u0000different fixed coupling strength. This allows to follow the resonances in the\u0000complex plane as a function of the coupling. While going from closed\u0000(Dirichlet) to fully open (Neumann) graph we see resonances escaping via a\u0000superradiant transition leading to non-Weyl behavior if the coupling to the\u0000outside is balanced. The open tetrahedral graph displays a rich parametric\u0000dynamic of the resonances in the complex plane presenting loops, regions of\u0000connected resonances and resonances approaching infinite imaginary parts.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510237","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}
Antoine Demiquel, Vassos Achilleos, Georgios Theocharis, Vincent Tournat
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model the system, we formulate discrete equations that describe the longitudinal and rotational displacements of each individual rigid unit mass using a lump element approach. By applying the multiple-scales method in the context of a semi-discrete approximation, we derive an effective nonlinear Schr"odinger equation that characterizes the evolution of rotational and slowly varying envelope waves from the aforementioned discrete motion equations. We thus show that this flexible mechanical metamaterial chain supports envelope vector solitons where the rotational component has the form of either a bright or a dark soliton. In addition, due to nonlinear coupling, the longitudinal displacement displays kink-like profiles thus forming the 2-components vector soliton. These findings, which include specific vector envelope solutions, enrich our knowledge on the nonlinear wave solutions supported by flexible mechanical metamaterials and open new possibilities for the control of nonlinear waves and vibrations.
{"title":"Envelope vector solitons in nonlinear flexible mechanical metamaterials","authors":"Antoine Demiquel, Vassos Achilleos, Georgios Theocharis, Vincent Tournat","doi":"arxiv-2406.09871","DOIUrl":"https://doi.org/arxiv-2406.09871","url":null,"abstract":"In this paper, we employ a combination of analytical and numerical techniques\u0000to investigate the dynamics of lattice envelope vector soliton solutions\u0000propagating within a one-dimensional chain of flexible mechanical metamaterial.\u0000To model the system, we formulate discrete equations that describe the\u0000longitudinal and rotational displacements of each individual rigid unit mass\u0000using a lump element approach. By applying the multiple-scales method in the\u0000context of a semi-discrete approximation, we derive an effective nonlinear\u0000Schr\"odinger equation that characterizes the evolution of rotational and\u0000slowly varying envelope waves from the aforementioned discrete motion\u0000equations. We thus show that this flexible mechanical metamaterial chain\u0000supports envelope vector solitons where the rotational component has the form\u0000of either a bright or a dark soliton. In addition, due to nonlinear coupling,\u0000the longitudinal displacement displays kink-like profiles thus forming the\u00002-components vector soliton. These findings, which include specific vector\u0000envelope solutions, enrich our knowledge on the nonlinear wave solutions\u0000supported by flexible mechanical metamaterials and open new possibilities for\u0000the control of nonlinear waves and vibrations.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520725","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}
Yu Wei, Yi Chen, Wen Cheng, Xiaoning Liu, Gengkai Hu
Extremal elastic materials here refer to a specific class of elastic materials whose elastic matrices exhibit one or more zero eigenvalues, resulting in soft deformation modes that, in principle, cost no energy. They can be approximated through artificially designed solid microstructures. Extremal elastic materials have exotic bulk wave properties unavailable with conventional solids due to the soft modes, offering unprecedented opportunities for manipulating bulk waves, e.g., acting as phonon polarizers for elastic waves or invisibility cloaks for underwater acoustic waves. Despite their potential, Rayleigh surface waves, crucially linked to bulk wave behaviors of such extremal elastic materials, have largely remained unexplored so far. In this paper, we theoretically investigate the propagation of Rayleigh waves in extremal elastic materials based on continuum theory and verify our findings with designed microstructure metamaterials based on pantographic structures. Dispersion relations and polarizations of Rayleigh waves in extremal elastic materials are derived, and the impact of higher order gradient effects is also investigated by using strain gradient theory. This study provides a continuum model for exploring surface waves in extremal elastic materials and may stimulate applications of extremal elastic materials for controlling surface waves.
{"title":"Rayleigh surface waves of extremal elastic materials","authors":"Yu Wei, Yi Chen, Wen Cheng, Xiaoning Liu, Gengkai Hu","doi":"arxiv-2406.07462","DOIUrl":"https://doi.org/arxiv-2406.07462","url":null,"abstract":"Extremal elastic materials here refer to a specific class of elastic\u0000materials whose elastic matrices exhibit one or more zero eigenvalues,\u0000resulting in soft deformation modes that, in principle, cost no energy. They\u0000can be approximated through artificially designed solid microstructures.\u0000Extremal elastic materials have exotic bulk wave properties unavailable with\u0000conventional solids due to the soft modes, offering unprecedented opportunities\u0000for manipulating bulk waves, e.g., acting as phonon polarizers for elastic\u0000waves or invisibility cloaks for underwater acoustic waves. Despite their\u0000potential, Rayleigh surface waves, crucially linked to bulk wave behaviors of\u0000such extremal elastic materials, have largely remained unexplored so far. In\u0000this paper, we theoretically investigate the propagation of Rayleigh waves in\u0000extremal elastic materials based on continuum theory and verify our findings\u0000with designed microstructure metamaterials based on pantographic structures.\u0000Dispersion relations and polarizations of Rayleigh waves in extremal elastic\u0000materials are derived, and the impact of higher order gradient effects is also\u0000investigated by using strain gradient theory. This study provides a continuum\u0000model for exploring surface waves in extremal elastic materials and may\u0000stimulate applications of extremal elastic materials for controlling surface\u0000waves.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"140 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510137","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}
It is shown that using Noether's Theorem explicitly employing gauge invariance for variations of the electromagnetic four-potential $A^mu$ straightforwardly ensures that the resulting electromagnetic energy-momentum tensor is symmetric. The Belinfante symmetrization procedure is not necessary. The method is based on Bessel-Hagen's 1921 clarification of Noether's original procedure, suggesting that the symmetry problem arises from an incomplete implementation of Noether's Theorem.
{"title":"Using gauge invariance to symmetrize the energy-momentum tensor of electrodynamics","authors":"Helmut Haberzettl","doi":"arxiv-2406.06785","DOIUrl":"https://doi.org/arxiv-2406.06785","url":null,"abstract":"It is shown that using Noether's Theorem explicitly employing gauge\u0000invariance for variations of the electromagnetic four-potential $A^mu$\u0000straightforwardly ensures that the resulting electromagnetic energy-momentum\u0000tensor is symmetric. The Belinfante symmetrization procedure is not necessary.\u0000The method is based on Bessel-Hagen's 1921 clarification of Noether's original\u0000procedure, suggesting that the symmetry problem arises from an incomplete\u0000implementation of Noether's Theorem.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520722","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}
Ferromagnetic matter finds its microscopic origin in the intrinsic electron spin, which is considered to be a purely quantum mechanical property of the electron. To incorporate the influence of the electron spin in the microscopic and macroscopic Maxwell equations -- and thereby in classical physics -- two models have been utilized: the electric current and the magnetic charge model. This paper aims to highlight fundamental problems of the commonly used current loop model, widely employed in textbooks. This work demonstrates that the behavior of a constant electric current dipole is not described by the laws of classical electrodynamics. More precisely, the electric current model is dependent on external forces, not included in Maxwells field and force equations, in order to maintain the force balance on the electric charge density inside the electron. These external forces change dynamically and do work on the system as the electron interacts with external fields. Consequently, the energies derived from classical physics (gravitational potential energy, kinetic energy, electrodynamic field energy) are not conserved in a system including constant electric current dipoles. In contrast to the electric current model, the magnetic charge model employs separate magnetic charges to model the electron spin, requiring the Maxwell equations to be extended by magnetic sources. This paper intends to illustrate that the magnetic charge model has significant advantages over the electric current model as it needs no external forces and energies, is a closed electromechanical system and is fully modeled by the classical laws of physics. This work forms the basis for the derivation and consideration of equivalent problems in macroscopic systems involving ferromagnetic matter.
{"title":"Classical Models of the Electron Spin -- Comparison of the Electric Current Model and the Magnetic Charge Model","authors":"Bela Schulte Westhoff","doi":"arxiv-2406.05919","DOIUrl":"https://doi.org/arxiv-2406.05919","url":null,"abstract":"Ferromagnetic matter finds its microscopic origin in the intrinsic electron\u0000spin, which is considered to be a purely quantum mechanical property of the\u0000electron. To incorporate the influence of the electron spin in the microscopic\u0000and macroscopic Maxwell equations -- and thereby in classical physics -- two\u0000models have been utilized: the electric current and the magnetic charge model.\u0000This paper aims to highlight fundamental problems of the commonly used current\u0000loop model, widely employed in textbooks. This work demonstrates that the\u0000behavior of a constant electric current dipole is not described by the laws of\u0000classical electrodynamics. More precisely, the electric current model is\u0000dependent on external forces, not included in Maxwells field and force\u0000equations, in order to maintain the force balance on the electric charge\u0000density inside the electron. These external forces change dynamically and do\u0000work on the system as the electron interacts with external fields.\u0000Consequently, the energies derived from classical physics (gravitational\u0000potential energy, kinetic energy, electrodynamic field energy) are not\u0000conserved in a system including constant electric current dipoles. In contrast\u0000to the electric current model, the magnetic charge model employs separate\u0000magnetic charges to model the electron spin, requiring the Maxwell equations to\u0000be extended by magnetic sources. This paper intends to illustrate that the\u0000magnetic charge model has significant advantages over the electric current\u0000model as it needs no external forces and energies, is a closed\u0000electromechanical system and is fully modeled by the classical laws of physics.\u0000This work forms the basis for the derivation and consideration of equivalent\u0000problems in macroscopic systems involving ferromagnetic matter.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"111 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520721","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}
Victor MatrayLMPS, Faisal AmlaniLMPS, Frédéric FeyelLMPS, David NéronLMPS
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order modeling (ROM) framework and recently-introduced Graph Neural Networks (GNNs), where the latter is trained on highly heterogeneous databases of varying numerical discretization sizes. The proposed techniques are shown to be particularly suitable for non-parametric geometries, ultimately enabling the treatment of a diverse range of geometries and topologies. Performance studies are presented in an application context related to the design of aircraft seats and their corresponding mechanical responses to shocks, where the main motivation is to reduce the computational burden and enable the rapid design iteration for such problems that entail non-parametric geometries. The methods proposed here are straightforwardly applicable to other scientific or engineering problems requiring a large number of finite element-based numerical simulations, with the potential to significantly enhance efficiency while maintaining reasonable accuracy.
{"title":"A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems","authors":"Victor MatrayLMPS, Faisal AmlaniLMPS, Frédéric FeyelLMPS, David NéronLMPS","doi":"arxiv-2406.02615","DOIUrl":"https://doi.org/arxiv-2406.02615","url":null,"abstract":"This work introduces a new approach for accelerating the numerical analysis\u0000of time-domain partial differential equations (PDEs) governing complex physical\u0000systems. The methodology is based on a combination of a classical reduced-order\u0000modeling (ROM) framework and recently-introduced Graph Neural Networks (GNNs),\u0000where the latter is trained on highly heterogeneous databases of varying\u0000numerical discretization sizes. The proposed techniques are shown to be\u0000particularly suitable for non-parametric geometries, ultimately enabling the\u0000treatment of a diverse range of geometries and topologies. Performance studies\u0000are presented in an application context related to the design of aircraft seats\u0000and their corresponding mechanical responses to shocks, where the main\u0000motivation is to reduce the computational burden and enable the rapid design\u0000iteration for such problems that entail non-parametric geometries. The methods\u0000proposed here are straightforwardly applicable to other scientific or\u0000engineering problems requiring a large number of finite element-based numerical\u0000simulations, with the potential to significantly enhance efficiency while\u0000maintaining reasonable accuracy.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520724","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}
The covariance of the d'Alembert equation for acoustic phenomena, described by mechanical waves in one or three spatial dimensions, under Galilean transformations, is demonstrated without the need to abandon the hypothesis that time is absolute in Classical Mechanics. This is true only if and only if the phase velocity of sound depends on the velocity of the observer. On the other hand, it is also shown that the same d'Alembert equation is covariant under Lorentz transformations if and only if the phase velocity of light does not depend on the observer.
{"title":"On the covariance of the d'Alembert equation: the cases of sound and light","authors":"Francisco Caruso, Vitor Oguri","doi":"arxiv-2406.02627","DOIUrl":"https://doi.org/arxiv-2406.02627","url":null,"abstract":"The covariance of the d'Alembert equation for acoustic phenomena, described\u0000by mechanical waves in one or three spatial dimensions, under Galilean\u0000transformations, is demonstrated without the need to abandon the hypothesis\u0000that time is absolute in Classical Mechanics. This is true only if and only if\u0000the phase velocity of sound depends on the velocity of the observer. On the\u0000other hand, it is also shown that the same d'Alembert equation is covariant\u0000under Lorentz transformations if and only if the phase velocity of light does\u0000not depend on the observer.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548562","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}
Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in non-Hermitian physics. Although it is established that one-dimensional NHSE originates from the nontrivial spectral winding topology, the topological origin behind the higher-dimensional NHSE remains unclear so far. This poses a substantial challenge in constructing and manipulating high-dimensional NHSEs. Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is proposed, through assembling multiple independent one-dimensional NHSEs. Not only the elusive high-dimensional NHSEs can be effectively predicted from the well-defined one-dimensional spectral winding topologies, but also the high-dimensional generalized Brillouin zones can be directly synthesized from the one-dimensional counterparts. As examples, two two-dimensional nonreciprocal acoustic metamaterials are experimentally implemented to demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological effects, where the sound fields can be frequency-selectively localized at any desired corners and boundaries. These results offer a practicable strategy for engineering high-dimensional NHSEs, which could boost advanced applications such as selective filters and directional amplifiers.
{"title":"Construction and Observation of Flexibly Controllable High-Dimensional Non-Hermitian Skin Effects","authors":"Qicheng Zhang, Yufei Leng, Liwei Xiong, Yuzeng Li, Kun Zhang, Liangjun Qi, Chunyin Qiu","doi":"arxiv-2406.02593","DOIUrl":"https://doi.org/arxiv-2406.02593","url":null,"abstract":"Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in\u0000non-Hermitian physics. Although it is established that one-dimensional NHSE\u0000originates from the nontrivial spectral winding topology, the topological\u0000origin behind the higher-dimensional NHSE remains unclear so far. This poses a\u0000substantial challenge in constructing and manipulating high-dimensional NHSEs.\u0000Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is\u0000proposed, through assembling multiple independent one-dimensional NHSEs. Not\u0000only the elusive high-dimensional NHSEs can be effectively predicted from the\u0000well-defined one-dimensional spectral winding topologies, but also the\u0000high-dimensional generalized Brillouin zones can be directly synthesized from\u0000the one-dimensional counterparts. As examples, two two-dimensional\u0000nonreciprocal acoustic metamaterials are experimentally implemented to\u0000demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological\u0000effects, where the sound fields can be frequency-selectively localized at any\u0000desired corners and boundaries. These results offer a practicable strategy for\u0000engineering high-dimensional NHSEs, which could boost advanced applications\u0000such as selective filters and directional amplifiers.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141520723","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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