In this note, the equilibrium curve of a thermodynamic system is used to depict entropy production in the process of thermalization with a reservoir. For the given initial and final equilibrium states of the system, the entropy production is reduced when work is also extracted during thermalization. The case of maximum work extraction corresponds to a reversible process. For less than optimal work extraction, the lost available work is shown to be directly proportional to the entropy produced.
{"title":"A visual proof of entropy production during thermalization with a heat reservoir","authors":"Ramandeep S. Johal","doi":"arxiv-2409.03581","DOIUrl":"https://doi.org/arxiv-2409.03581","url":null,"abstract":"In this note, the equilibrium curve of a thermodynamic system is used to\u0000depict entropy production in the process of thermalization with a reservoir.\u0000For the given initial and final equilibrium states of the system, the entropy\u0000production is reduced when work is also extracted during thermalization. The\u0000case of maximum work extraction corresponds to a reversible process. For less\u0000than optimal work extraction, the lost available work is shown to be directly\u0000proportional to the entropy produced.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224579","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}
This paper develops a comprehensive physical model and numerical implementation schemes for a grand piano, building upon the prior works of Chabassier et al. The model encompasses various subsystems, including hammer felt, hammer shank, string, soundboard, air and room barriers, each modelled in three dimensions to approach their realistic dynamics. A general framework for 3D elastic solids accounting for prestress and prestrain is introduced, particularly addressing the complexities of prestressed piano strings. The study also examines coupling between subsystem through mechanisms of surface force transmission and displacement/velocity continuity. To facilitate numerical simulations, strong PDEs are translated into weak ODEs via a flexible space discretization approach. Modal transformation of system ODEs is then employed to decouple and reduce DOFs, and an explicit time discretization scheme is customized for generating digital audio in the time domain. The study concludes with a discussion of the piano models capabilities, limitations, and potential future enhancements.
{"title":"Physical Modelling of Piano Sound","authors":"Haifan Xie","doi":"arxiv-2409.03481","DOIUrl":"https://doi.org/arxiv-2409.03481","url":null,"abstract":"This paper develops a comprehensive physical model and numerical\u0000implementation schemes for a grand piano, building upon the prior works of\u0000Chabassier et al. The model encompasses various subsystems, including hammer\u0000felt, hammer shank, string, soundboard, air and room barriers, each modelled in\u0000three dimensions to approach their realistic dynamics. A general framework for\u00003D elastic solids accounting for prestress and prestrain is introduced,\u0000particularly addressing the complexities of prestressed piano strings. The\u0000study also examines coupling between subsystem through mechanisms of surface\u0000force transmission and displacement/velocity continuity. To facilitate\u0000numerical simulations, strong PDEs are translated into weak ODEs via a flexible\u0000space discretization approach. Modal transformation of system ODEs is then\u0000employed to decouple and reduce DOFs, and an explicit time discretization\u0000scheme is customized for generating digital audio in the time domain. The study\u0000concludes with a discussion of the piano models capabilities, limitations, and\u0000potential future enhancements.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186295","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 Maxwell stress tensor for the linear and uniform media in static electromagnetic field implies a new form of pressure caused by the mutual field energy density. When it is introduced into the fundamental thermodynamic equation for the media, we have a new pressure-volume work term. The combination of new term and proper electromagnetic work term naturally gives the well-known form that is currently obtained by a working hypothesis.
{"title":"Deriving a working hypothesis in thermodynamics on electromagnetic work from first principles","authors":"Q. H. Liu","doi":"arxiv-2409.01203","DOIUrl":"https://doi.org/arxiv-2409.01203","url":null,"abstract":"The Maxwell stress tensor for the linear and uniform media in static\u0000electromagnetic field implies a new form of pressure caused by the mutual field\u0000energy density. When it is introduced into the fundamental thermodynamic\u0000equation for the media, we have a new pressure-volume work term. The\u0000combination of new term and proper electromagnetic work term naturally gives\u0000the well-known form that is currently obtained by a working hypothesis.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186296","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}
Gabriel C. Grime, Ricardo L. Viana, Yves Elskens Iberê L. Caldas
Nontwist area-preserving maps violate the twist condition at specific orbits, resulting in shearless invariant curves that prevent chaotic transport. Plasmas and fluids with nonmonotonic equilibrium profiles may be described using nontwist systems, where even after these shearless curves breakdown, effective transport barriers persist, partially reducing transport coefficients. Some nontwist systems present multiple shearless curves in phase space, increasing the complexity of transport phenomena, which have not been thoroughly investigated until now. In this work, we examine the formation of effective transport barriers in a nontwist area-preserving mapping with multiple shearless transport barriers. By quantifying the effectiveness of each transport barrier in phase space, we identified two scenarios where particular barriers dominate over others. Our results also reveal configurations where the interplay of two transport barriers creates regions in phase space with significant orbit trapping, thereby influencing the overall transport dynamics.
{"title":"Effective transport barriers in the biquadratic nontwist map","authors":"Gabriel C. Grime, Ricardo L. Viana, Yves Elskens Iberê L. Caldas","doi":"arxiv-2409.00785","DOIUrl":"https://doi.org/arxiv-2409.00785","url":null,"abstract":"Nontwist area-preserving maps violate the twist condition at specific orbits,\u0000resulting in shearless invariant curves that prevent chaotic transport. Plasmas\u0000and fluids with nonmonotonic equilibrium profiles may be described using\u0000nontwist systems, where even after these shearless curves breakdown, effective\u0000transport barriers persist, partially reducing transport coefficients. Some\u0000nontwist systems present multiple shearless curves in phase space, increasing\u0000the complexity of transport phenomena, which have not been thoroughly\u0000investigated until now. In this work, we examine the formation of effective\u0000transport barriers in a nontwist area-preserving mapping with multiple\u0000shearless transport barriers. By quantifying the effectiveness of each\u0000transport barrier in phase space, we identified two scenarios where particular\u0000barriers dominate over others. Our results also reveal configurations where the\u0000interplay of two transport barriers creates regions in phase space with\u0000significant orbit trapping, thereby influencing the overall transport dynamics.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186298","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}
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy density in the case of a two-dimensional space. It is also shown that the general form of the energy density so determined may be further reduced. The three-dimensional case is also discussed.
{"title":"A Note on the Objectivity (Rotational Invariance) of the Stored Energy Density in Continuum Physics","authors":"Jiashi Yang","doi":"arxiv-2409.07478","DOIUrl":"https://doi.org/arxiv-2409.07478","url":null,"abstract":"This short note is concerned with the rotational invariance of the stored\u0000energy density in continuum physics as a scalar function of a few vectors. A\u0000simple derivation is presented for the determination of the general form of the\u0000energy density in the case of a two-dimensional space. It is also shown that\u0000the general form of the energy density so determined may be further reduced.\u0000The three-dimensional case is also discussed.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186297","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}
After Helmholtz, the mechanical foundation of thermodynamics included the First Law $d E = delta Q + delta W$, and the first part of the Clausius heat theorem $delta Q^text{rev}/T = dS$. The resulting invariance of the entropy $S$ for quasistatic changes in thermally isolated systems invites a connection with Noether's theorem (only established later). In this quest, we continue an idea, first brought up by Wald in black hole thermodynamics and by Sasa $textit{et al.}$ in various contexts. We follow both Lagrangian and Hamiltonian frameworks, and emphasize the role of Killing equations for deriving a First Law for thermodynamically consistent trajectories, to end up with an expression of ``heat over temperature'' as an exact differential of a Noether charge.
{"title":"First part of Clausius heat theorem in terms of Noether's theorem","authors":"Aaron Beyen, Christian Maes","doi":"arxiv-2408.15773","DOIUrl":"https://doi.org/arxiv-2408.15773","url":null,"abstract":"After Helmholtz, the mechanical foundation of thermodynamics included the\u0000First Law $d E = delta Q + delta W$, and the first part of the Clausius heat\u0000theorem $delta Q^text{rev}/T = dS$. The resulting invariance of the entropy\u0000$S$ for quasistatic changes in thermally isolated systems invites a connection\u0000with Noether's theorem (only established later). In this quest, we continue an\u0000idea, first brought up by Wald in black hole thermodynamics and by Sasa\u0000$textit{et al.}$ in various contexts. We follow both Lagrangian and\u0000Hamiltonian frameworks, and emphasize the role of Killing equations for\u0000deriving a First Law for thermodynamically consistent trajectories, to end up\u0000with an expression of ``heat over temperature'' as an exact differential of a\u0000Noether charge.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186375","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}
Manish Yadav, Swati Chauhan, Manish Dev Shrimali, Merten Stender
Mechanical systems are known to exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness, and also due to changes to external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, or even infeasible. This study uses a data-driven approach to investigate how bifurcations can be learned from a few system response measurements. Particularly, the concept of reservoir computing (RC) is employed. As proof of concept, a minimal training dataset under the resource constraint problem of a Duffing oscillator with harmonic external forcing is provided as training data. Our results indicate that the RC not only learns to represent the system dynamics for the trained external forcing, but it also manages to provide qualitatively accurate and robust system response predictions for completely unknown textit{multi-}parameter regimes outside the training data. Particularly, while being trained solely on regular period-2 cycle dynamics, the proposed framework can correctly predict higher-order periodic and even chaotic dynamics for out-of-distribution forcing signals.
{"title":"Predicting multi-parametric dynamics of externally forced oscillators using reservoir computing and minimal data","authors":"Manish Yadav, Swati Chauhan, Manish Dev Shrimali, Merten Stender","doi":"arxiv-2408.14987","DOIUrl":"https://doi.org/arxiv-2408.14987","url":null,"abstract":"Mechanical systems are known to exhibit complex dynamical behavior from\u0000harmonic oscillations to chaotic motion. The dynamics undergo qualitative\u0000changes due to changes to internal system parameters like stiffness, and also\u0000due to changes to external forcing. Mapping out complete bifurcation diagrams\u0000numerically or experimentally is resource-consuming, or even infeasible. This\u0000study uses a data-driven approach to investigate how bifurcations can be\u0000learned from a few system response measurements. Particularly, the concept of\u0000reservoir computing (RC) is employed. As proof of concept, a minimal training\u0000dataset under the resource constraint problem of a Duffing oscillator with\u0000harmonic external forcing is provided as training data. Our results indicate\u0000that the RC not only learns to represent the system dynamics for the trained\u0000external forcing, but it also manages to provide qualitatively accurate and\u0000robust system response predictions for completely unknown\u0000textit{multi-}parameter regimes outside the training data. Particularly, while\u0000being trained solely on regular period-2 cycle dynamics, the proposed framework\u0000can correctly predict higher-order periodic and even chaotic dynamics for\u0000out-of-distribution forcing signals.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"67 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186340","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}
Hamad M. Alkhoori, Akhlesh Lakhtakia, Nikolaos L. Tsitsas
The perturbation of a magnetostatic field by a toroid made of a homogeneous anisotropic magnetic material was formulated using the solutions of the Laplace equation in the toroidal coordinate system. That was straightforward in the region outside the toroid, but an affine coordinate transformation had to be employed inside the toroid. The coefficients of the series expansion of the perturbation potential in terms of appropriate toroidal basis functions were related to the coefficients of the series expansion of the source potential in terms of appropriate toroidal basis functions by a transition matrix. As a result of the solution of this novel problem, the consequences of material anisotropy on perturbing the magnetostatic field are clearly evident in the region near the toroid.
{"title":"Theory of perturbation of the magnetostatic field by an anisotropic magnetic toroid","authors":"Hamad M. Alkhoori, Akhlesh Lakhtakia, Nikolaos L. Tsitsas","doi":"arxiv-2408.13573","DOIUrl":"https://doi.org/arxiv-2408.13573","url":null,"abstract":"The perturbation of a magnetostatic field by a toroid made of a homogeneous\u0000anisotropic magnetic material was formulated using the solutions of the Laplace\u0000equation in the toroidal coordinate system. That was straightforward in the\u0000region outside the toroid, but an affine coordinate transformation had to be\u0000employed inside the toroid. The coefficients of the series expansion of the\u0000perturbation potential in terms of appropriate toroidal basis functions were\u0000related to the coefficients of the series expansion of the source potential in\u0000terms of appropriate toroidal basis functions by a transition matrix. As a\u0000result of the solution of this novel problem, the consequences of material\u0000anisotropy on perturbing the magnetostatic field are clearly evident in the\u0000region near the toroid.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186299","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 room acoustics was established based on Sabine's reverberation theory. However, in Sabine's theory, the reverberation time does not reach zero, even if the absolute absorption condition is satisfied. Eyring revised the reverberation theory to resolve this contradiction. However, Eyring's theory is inconsistent in its formulation of the steady state and decay processes. Therefore, the author has revised Sabine's theory (Hanyu, Acoustical Science & Technology 45, 3, 2024), taking a different approach from that of Eyring. This revised theory was constructed by introducing the concept of "reverberation of a direct sound". In this paper, a new mathematical model of reverberation using reflection orders is proposed. This means that the revised theory already proposed by the author is reconstructed to include the temporal energy distributions in each reflection order. The new mathematical model also uses the concept of "reverberation of a direct sound" but describes the reverberation of only reflected sounds without the direct sound. This means that the concept of "reverberation of a direct sound" is essential also to the entire reverberation process. Reverberation decay of the new model is consistent with that of the already proposed revised theory. The new model showed good correspondence with the simulation results.
{"title":"Reconstruction of reverberation theory in a diffuse sound field by using reflection orders","authors":"Toshiki Hanyu","doi":"arxiv-2408.11670","DOIUrl":"https://doi.org/arxiv-2408.11670","url":null,"abstract":"The room acoustics was established based on Sabine's reverberation theory.\u0000However, in Sabine's theory, the reverberation time does not reach zero, even\u0000if the absolute absorption condition is satisfied. Eyring revised the\u0000reverberation theory to resolve this contradiction. However, Eyring's theory is\u0000inconsistent in its formulation of the steady state and decay processes.\u0000Therefore, the author has revised Sabine's theory (Hanyu, Acoustical Science &\u0000Technology 45, 3, 2024), taking a different approach from that of Eyring. This\u0000revised theory was constructed by introducing the concept of \"reverberation of\u0000a direct sound\". In this paper, a new mathematical model of reverberation using\u0000reflection orders is proposed. This means that the revised theory already\u0000proposed by the author is reconstructed to include the temporal energy\u0000distributions in each reflection order. The new mathematical model also uses\u0000the concept of \"reverberation of a direct sound\" but describes the\u0000reverberation of only reflected sounds without the direct sound. This means\u0000that the concept of \"reverberation of a direct sound\" is essential also to the\u0000entire reverberation process. Reverberation decay of the new model is\u0000consistent with that of the already proposed revised theory. The new model\u0000showed good correspondence with the simulation results.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186300","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}
Majdi O. Gzal, Lawrence A. Bergman, Kathryn H. Matlack, Alexander F. Vakakis
This study investigates a vibroacoustic phononic metamaterial system composed of repeated monolayered membrane-air cavity unit-cells to assess its efficacy in controlling sound waves. Assuming low-frequency axisymmetric modes, the coupled membrane-cavity vibroacoustic system for a representative unit-cell is solved entirely analytically. Unlike previous research that relied on an infinite series of eigenfunctions, our analysis offers a single-term exact solution for the membrane's displacement field, fully accounting for coupling with the acoustic cavities. Utilizing the transfer matrix method and the Bloch-Floquet theorem, we offer a comprehensive analytical characterization of the band structure, including closed-form analytical expressions for determining the bounding frequencies of the bandgaps and the dispersion branches. Interaction between Bragg and local resonance bandgaps is examined by adjusting Bragg bandgap positions, with detailed mathematical descriptions provided for their overlapping and transition. Additionally, a "plasma bandgap" analogous to metallic plasma oscillations is identified, with a derived analytical expression for its frequency. First two passbands remain robust against cavity depth variations, limiting wave manipulation capabilities. Analysis of the finite phononic system involves constructing the global transfer matrix to study natural frequencies and scattering coefficients. Interaction between Bragg and local resonance bandgaps in finite systems results in ultra-narrow passbands, creating transparency windows analogous to electromagnetically induced transparency by quantum interference. This theoretical framework enables precise characterization and engineering of bandgaps in the monolayered vibroacoustic phononic metamaterial, highlighting its potential for controlling low-frequency sound wave propagation across multiple frequencies.
{"title":"Analytical Study of a Monolayered Vibroacoustic Metamaterial","authors":"Majdi O. Gzal, Lawrence A. Bergman, Kathryn H. Matlack, Alexander F. Vakakis","doi":"arxiv-2408.09660","DOIUrl":"https://doi.org/arxiv-2408.09660","url":null,"abstract":"This study investigates a vibroacoustic phononic metamaterial system composed\u0000of repeated monolayered membrane-air cavity unit-cells to assess its efficacy\u0000in controlling sound waves. Assuming low-frequency axisymmetric modes, the\u0000coupled membrane-cavity vibroacoustic system for a representative unit-cell is\u0000solved entirely analytically. Unlike previous research that relied on an\u0000infinite series of eigenfunctions, our analysis offers a single-term exact\u0000solution for the membrane's displacement field, fully accounting for coupling\u0000with the acoustic cavities. Utilizing the transfer matrix method and the\u0000Bloch-Floquet theorem, we offer a comprehensive analytical characterization of\u0000the band structure, including closed-form analytical expressions for\u0000determining the bounding frequencies of the bandgaps and the dispersion\u0000branches. Interaction between Bragg and local resonance bandgaps is examined by\u0000adjusting Bragg bandgap positions, with detailed mathematical descriptions\u0000provided for their overlapping and transition. Additionally, a \"plasma bandgap\"\u0000analogous to metallic plasma oscillations is identified, with a derived\u0000analytical expression for its frequency. First two passbands remain robust\u0000against cavity depth variations, limiting wave manipulation capabilities.\u0000Analysis of the finite phononic system involves constructing the global\u0000transfer matrix to study natural frequencies and scattering coefficients.\u0000Interaction between Bragg and local resonance bandgaps in finite systems\u0000results in ultra-narrow passbands, creating transparency windows analogous to\u0000electromagnetically induced transparency by quantum interference. This\u0000theoretical framework enables precise characterization and engineering of\u0000bandgaps in the monolayered vibroacoustic phononic metamaterial, highlighting\u0000its potential for controlling low-frequency sound wave propagation across\u0000multiple frequencies.","PeriodicalId":501482,"journal":{"name":"arXiv - PHYS - Classical Physics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186301","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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