Pub Date : 2025-06-22DOI: 10.1016/j.wavemoti.2025.103595
Philip G. Kaufinger , John M. Cormack , Kyle S. Spratt , Mark F. Hamilton
Plane nonlinear shear waves in isotropic media are subject only to cubic nonlinearity at leading order and therefore generate only odd harmonics during propagation. Wavefront curvature in shear wave beams breaks the symmetry in the material response and yields quadratic nonlinearity, such that a second harmonic may be generated at second order in a shear wave beam depending on the polarization of the wave field. The governing paraxial wave equation accounting for both quadratic and cubic nonlinearity in isotropic elastic media was derived originally by Zabolotskaya (1986), with its formulation employed in the present work developed subsequently by Wochner et al. (2008). Closed-form analytical solutions for the fields at the source frequency and the second harmonic are derived by perturbation for both the transverse and longitudinal particle displacement components in focused shear wave beams radiated by a source defined by affine polarization, Gaussian amplitude shading, and quadratic phase shading to account for focusing. Examples of field distributions are presented based on parameters reported by Cormack et al. (2024) for measurements of radially polarized focused shear wave beams generated in tissue-mimicking phantoms. Second-harmonic generation in shear wave beams with other polarizations is also discussed. Calculations are presented to estimate the vibration amplitude required for observable second-harmonic generation in tissue-mimicking phantoms. It is postulated that the second harmonic may be used to estimate the third-order elastic material property as an additional biomarker for diseased tissue.
{"title":"Perturbation solution for second-harmonic generation in focused shear wave beams in soft solids","authors":"Philip G. Kaufinger , John M. Cormack , Kyle S. Spratt , Mark F. Hamilton","doi":"10.1016/j.wavemoti.2025.103595","DOIUrl":"10.1016/j.wavemoti.2025.103595","url":null,"abstract":"<div><div>Plane nonlinear shear waves in isotropic media are subject only to cubic nonlinearity at leading order and therefore generate only odd harmonics during propagation. Wavefront curvature in shear wave beams breaks the symmetry in the material response and yields quadratic nonlinearity, such that a second harmonic may be generated at second order in a shear wave beam depending on the polarization of the wave field. The governing paraxial wave equation accounting for both quadratic and cubic nonlinearity in isotropic elastic media was derived originally by Zabolotskaya (1986), with its formulation employed in the present work developed subsequently by Wochner et al. (2008). Closed-form analytical solutions for the fields at the source frequency and the second harmonic are derived by perturbation for both the transverse and longitudinal particle displacement components in focused shear wave beams radiated by a source defined by affine polarization, Gaussian amplitude shading, and quadratic phase shading to account for focusing. Examples of field distributions are presented based on parameters reported by Cormack et al. (2024) for measurements of radially polarized focused shear wave beams generated in tissue-mimicking phantoms. Second-harmonic generation in shear wave beams with other polarizations is also discussed. Calculations are presented to estimate the vibration amplitude required for observable second-harmonic generation in tissue-mimicking phantoms. It is postulated that the second harmonic may be used to estimate the third-order elastic material property as an additional biomarker for diseased tissue.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103595"},"PeriodicalIF":2.1,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-21DOI: 10.1016/j.wavemoti.2025.103598
Maoxun Sun , Miaohong Tan , Cheng Shan , Yue Zhang , Hongye Liu
Underground or underwater pipe-like structures are usually subjected to corrosion or plastic deformation, during which the micro-cracks probably appear and gradually evolve into macro-cracks, resulting in the leakage of pipes. Therefore, to avoid catastrophic accidents, it is necessary to locate micro-cracks accurately and repair or replace pipes in time. Wave mixing has the advantages of micro-crack localization compared with second harmonics, and it can avoid the interference of nonlinearities in measurement systems. However, few reports are available on nonlinear mixing of counter-propagating guided waves caused by contact acoustic nonlinearity (CAN) in pipes. In this paper, the interaction of the guided wave mixing and micro-cracks in pipe-like structures is theoretically and numerically investigated via CAN and vector analyses, as well as pulse-inversion techniques and two-dimensional fast Fourier transforms (2D-FFT), respectively. It is theoretically demonstrated that the amplitudes of second-order harmonics increase monotonically with ε0/ε0, while the amplitudes of third-order harmonics first increase and then drop with ε0/ε0. In simulations, nonlinear mixing of counter-propagating guided waves occurs in the regions that contain micro-cracks, and the generated difference-frequency components or sum-frequency components propagate to both ends of pipes at the same time. The difference-frequency components mainly contain F(m,1) modes, and the sum-frequency components mainly contain F(m,2) modes and F(m,3) modes, which are predicted in advance by theoretical investigations. In addition, the normalized amplitudes of difference-frequency components and sum-frequency components exhibit “mountain-shape” trends between 0° and 90° as well as during 90° and 180°, with the peaks corresponding to micro-crack angles of 45° and 135° Note that they reach the minimums when angles of micro-cracks equal to 0°, 90° or 180°, which is in a good agreement with the theoretical investigations. Finally, the z-coordinates of micro-cracks can be determined by the relationship between the normalized amplitudes of difference-frequency components or sum-frequency components and positions of mixing zones. The φ-coordinates of micro-cracks can be obtained based on normalized amplitudes of difference-frequency components in Uz with respect to φ-coordinates.
{"title":"Analytical and numerical investigations of the interaction between nonlinear guided wave mixing and micro-cracks in pipe-like structures","authors":"Maoxun Sun , Miaohong Tan , Cheng Shan , Yue Zhang , Hongye Liu","doi":"10.1016/j.wavemoti.2025.103598","DOIUrl":"10.1016/j.wavemoti.2025.103598","url":null,"abstract":"<div><div>Underground or underwater pipe-like structures are usually subjected to corrosion or plastic deformation, during which the micro-cracks probably appear and gradually evolve into macro-cracks, resulting in the leakage of pipes. Therefore, to avoid catastrophic accidents, it is necessary to locate micro-cracks accurately and repair or replace pipes in time. Wave mixing has the advantages of micro-crack localization compared with second harmonics, and it can avoid the interference of nonlinearities in measurement systems. However, few reports are available on nonlinear mixing of counter-propagating guided waves caused by contact acoustic nonlinearity (CAN) in pipes. In this paper, the interaction of the guided wave mixing and micro-cracks in pipe-like structures is theoretically and numerically investigated via CAN and vector analyses, as well as pulse-inversion techniques and two-dimensional fast Fourier transforms (2D-FFT), respectively. It is theoretically demonstrated that the amplitudes of second-order harmonics increase monotonically with <em>ε</em><sub>0</sub>/<em>ε</em><sup>0</sup>, while the amplitudes of third-order harmonics first increase and then drop with <em>ε</em><sub>0</sub>/<em>ε</em><sup>0</sup>. In simulations, nonlinear mixing of counter-propagating guided waves occurs in the regions that contain micro-cracks, and the generated difference-frequency components or sum-frequency components propagate to both ends of pipes at the same time. The difference-frequency components mainly contain F(<em>m</em>,1) modes, and the sum-frequency components mainly contain F(<em>m</em>,2) modes and F(<em>m</em>,3) modes, which are predicted in advance by theoretical investigations. In addition, the normalized amplitudes of difference-frequency components and sum-frequency components exhibit “mountain-shape” trends between 0° and 90° as well as during 90° and 180°, with the peaks corresponding to micro-crack angles of 45° and 135° Note that they reach the minimums when angles of micro-cracks equal to 0°, 90° or 180°, which is in a good agreement with the theoretical investigations. Finally, the <em>z</em>-coordinates of micro-cracks can be determined by the relationship between the normalized amplitudes of difference-frequency components or sum-frequency components and positions of mixing zones. The <em>φ</em>-coordinates of micro-cracks can be obtained based on normalized amplitudes of difference-frequency components in U<em><sub>z</sub></em> with respect to <em>φ</em>-coordinates.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103598"},"PeriodicalIF":2.1,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-20DOI: 10.1016/j.wavemoti.2025.103599
Tianshu Liang, Ying Liu, Qingxiao Gu
Based on the light sensitivity of liquid crystal elastomers, a Grille-like phononic crystal plate is proposed in this paper with the aim to achieve multi-mode band opto-tuning. The indirect coupling strategy is used to determine the opto-band variation in phononic crystal plate. The spontaneous deformation of the phononic crystal plate is firstly investigated. Then the wave dispersion in the opto-deformed phononic crystal plate is explored. The band structure in undeformed phononic crystal plate is also given for comparison. The effects of geometrical sizes of unit cells and light intensity are clarified in detail. The result indicates that the band structures in phononic crystal plates can be tuned by adjusting the light intensity, which displays sensitive dependence on the unit cell geometrical sizes. The phononic crystal plate with opto-deformable slabs provides a choice in design of opto-controlling phononic crystal plate, and has prospective applications in optical controlling of devices and systems.
{"title":"Opto-band tuning in a liquid crystal elastomer phononic crystal plate","authors":"Tianshu Liang, Ying Liu, Qingxiao Gu","doi":"10.1016/j.wavemoti.2025.103599","DOIUrl":"10.1016/j.wavemoti.2025.103599","url":null,"abstract":"<div><div>Based on the light sensitivity of liquid crystal elastomers, a Grille-like phononic crystal plate is proposed in this paper with the aim to achieve multi-mode band opto-tuning. The indirect coupling strategy is used to determine the opto-band variation in phononic crystal plate. The spontaneous deformation of the phononic crystal plate is firstly investigated. Then the wave dispersion in the opto-deformed phononic crystal plate is explored. The band structure in undeformed phononic crystal plate is also given for comparison. The effects of geometrical sizes of unit cells and light intensity are clarified in detail. The result indicates that the band structures in phononic crystal plates can be tuned by adjusting the light intensity, which displays sensitive dependence on the unit cell geometrical sizes. The phononic crystal plate with opto-deformable slabs provides a choice in design of opto-controlling phononic crystal plate, and has prospective applications in optical controlling of devices and systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103599"},"PeriodicalIF":2.1,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-18DOI: 10.1016/j.wavemoti.2025.103561
R. Abouem A. Ribama , Z.I. Djoufack , J.P. Nguenang
We investigate the mass ratio influence on the formation of gap intrinsic localized structures and energy distribution in a 1D Frenkel–Kontorova quantum diatomic chain. We analyze the coupled nonlinear excitations and it is found that : On the one hand, a gap frequency is obtained through the linear spectrum as well as different families of gap breather solutions depending on the gap frequency values, On the other hand, the existence of intrinsic localized structures for some particular frequencies in the vicinity of the gap and the formation of the modulation instability (MI) zones, as well as the intensity of the growth rate in addition to the amplitude of energy density can be influenced by the mass ratio of particles. Furthermore, there is a large gap opened in the phonon spectrum for a very small mass ratio and the phenomenon of gap cannot exist if the above condition is not satisfied. The accuracy of the analytical studies is confirmed by an excellent agreement with the numerical simulations.
{"title":"Influence of the mass ratio on the formation of gap intrinsic localized structures and energy distribution in a 1D Frenkel–Kontorova quantum diatomic chain","authors":"R. Abouem A. Ribama , Z.I. Djoufack , J.P. Nguenang","doi":"10.1016/j.wavemoti.2025.103561","DOIUrl":"10.1016/j.wavemoti.2025.103561","url":null,"abstract":"<div><div>We investigate the mass ratio influence on the formation of gap intrinsic localized structures and energy distribution in a 1D Frenkel–Kontorova quantum diatomic chain. We analyze the coupled nonlinear excitations and it is found that : On the one hand, a gap frequency is obtained through the linear spectrum as well as different families of gap breather solutions depending on the gap frequency values, On the other hand, the existence of intrinsic localized structures for some particular frequencies in the vicinity of the gap and the formation of the modulation instability (MI) zones, as well as the intensity of the growth rate in addition to the amplitude of energy density can be influenced by the mass ratio of particles. Furthermore, there is a large gap opened in the phonon spectrum for a very small mass ratio and the phenomenon of gap cannot exist if the above condition is not satisfied. The accuracy of the analytical studies is confirmed by an excellent agreement with the numerical simulations.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103561"},"PeriodicalIF":2.1,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-11DOI: 10.1016/j.wavemoti.2025.103584
Majid Madadi , Mustafa Inc , Mustafa Bayram
Research in real-world applications has been driving the progress of nonlinear science, with fluid dynamics and plasma physics currently capturing significant attention. This paper explores a newly proposed (2+1)-dimensional nonlinear wave equation, combining the Kadomtsev–Petviashvili (KPE) and Boiti–Leon–Manna–Pempinelli equations (BLMPE). The equation, which includes nonlinear and dispersive terms, has potential applications in fluid dynamics, plasma physics, nonlinear optics, and geophysical flows. We analyze its integrability, showing that it does not satisfy the Painlevé property but admits multi-soliton solutions. Using the Hirota bilinear approach and extended homoclinic test approach, we derive analytic solutions such as lump waves, soliton interactions, and breather waves, with the latter leading to rogue wave formation.
在现实世界中的应用研究已经推动了非线性科学的进步，流体动力学和等离子体物理学目前引起了极大的关注。结合Kadomtsev-Petviashvili （KPE）和boi - leon - manna - pempinelli （BLMPE）方程，提出了一种新的（2+1）维非线性波动方程。该方程包含非线性和色散项，在流体动力学、等离子体物理、非线性光学和地球物理流中具有潜在的应用。我们分析了它的可积性，表明它不满足painlevel性质，但允许多孤子解。利用Hirota双线性方法和扩展同斜检验方法，我们导出了块波、孤子相互作用和呼吸波等解析解，后者导致异常波的形成。
{"title":"Nonlinear wave behaviors for a combined Kadomtsev–Petviashvili–Boiti–Leon–Manna–Pempinelli equation in fluid dynamics, plasma physics and nonlinear optics","authors":"Majid Madadi , Mustafa Inc , Mustafa Bayram","doi":"10.1016/j.wavemoti.2025.103584","DOIUrl":"10.1016/j.wavemoti.2025.103584","url":null,"abstract":"<div><div>Research in real-world applications has been driving the progress of nonlinear science, with fluid dynamics and plasma physics currently capturing significant attention. This paper explores a newly proposed (2+1)-dimensional nonlinear wave equation, combining the Kadomtsev–Petviashvili (KPE) and Boiti–Leon–Manna–Pempinelli equations (BLMPE). The equation, which includes nonlinear and dispersive terms, has potential applications in fluid dynamics, plasma physics, nonlinear optics, and geophysical flows. We analyze its integrability, showing that it does not satisfy the Painlevé property but admits multi-soliton solutions. Using the Hirota bilinear approach and extended homoclinic test approach, we derive analytic solutions such as lump waves, soliton interactions, and breather waves, with the latter leading to rogue wave formation.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103584"},"PeriodicalIF":2.1,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-06DOI: 10.1016/j.wavemoti.2025.103582
W. Rodríguez-Cruz , D.M. Uriza-Prias , M. Roque-Vargas , A. Díaz-de-Anda
We develop a theory that significantly improves the correspondence between theoretical and experimental results in beams with structures excited with bending waves. We use beam theory and Timoshenko-Ehrenfest continuity conditions with the transfer matrix method to solve the fourth-order differential equation. First, we analyze the continuity conditions to understand the deformation in the cross-section between the notch-body interface. Then, using analytical and numerical methods, we determine an effective cross-section between the notch-body interface that, when included in the continuity conditions of the Timoshenko–Ehrenfest beam theory, brings the theoretical results into a high agreement with the experimental results with a relative error of less than 12%.
{"title":"Correction in the continuity conditions for beams with structure governed by the Timoshenko–Ehrenfest equation","authors":"W. Rodríguez-Cruz , D.M. Uriza-Prias , M. Roque-Vargas , A. Díaz-de-Anda","doi":"10.1016/j.wavemoti.2025.103582","DOIUrl":"10.1016/j.wavemoti.2025.103582","url":null,"abstract":"<div><div>We develop a theory that significantly improves the correspondence between theoretical and experimental results in beams with structures excited with bending waves. We use beam theory and Timoshenko-Ehrenfest continuity conditions with the transfer matrix method to solve the fourth-order differential equation. First, we analyze the continuity conditions to understand the deformation in the cross-section between the notch-body interface. Then, using analytical and numerical methods, we determine an effective cross-section between the notch-body interface that, when included in the continuity conditions of the Timoshenko–Ehrenfest beam theory, brings the theoretical results into a high agreement with the experimental results with a relative error of less than 12%.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103582"},"PeriodicalIF":2.1,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144229919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-06DOI: 10.1016/j.wavemoti.2025.103583
Giuseppe Saccomandi
We analyze the recent paper Nonlinear incompressible shear wave models in hyperelasticity and viscoelasticity frameworks, with applications to Love waves, published in Wave Motion (132, #103434, 2025) by McAdam, Agyemang, and Cheviakov. This work contains a fundamental issue that has previously appeared in the literature and has already been addressed and corrected. In this paper, we revisit this issue in detail, providing a thorough analysis to clarify and definitively resolve the problem.
{"title":"A recurrent mistake in nonlinear elasticity: How a recent paper keeps the error alive","authors":"Giuseppe Saccomandi","doi":"10.1016/j.wavemoti.2025.103583","DOIUrl":"10.1016/j.wavemoti.2025.103583","url":null,"abstract":"<div><div>We analyze the recent paper <em>Nonlinear incompressible shear wave models in hyperelasticity and viscoelasticity frameworks, with applications to Love waves</em>, published in <em>Wave Motion</em> (132, #103434, 2025) by McAdam, Agyemang, and Cheviakov. This work contains a fundamental issue that has previously appeared in the literature and has already been addressed and corrected. In this paper, we revisit this issue in detail, providing a thorough analysis to clarify and definitively resolve the problem.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103583"},"PeriodicalIF":2.1,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-02DOI: 10.1016/j.wavemoti.2025.103580
Zeyuan Dong, Chang Su, Hao Chen, Weijun Lin, Yubing Li
Accurately solving high-fidelity acoustic fields is critical for advancing ultrasonic research. While conventional numerical solvers remain widely used, emerging approaches like Physics-Informed Neural Networks (PINNs) provide a promising alternative for modeling physical phenomena governed by partial differential equations. However, PINNs often struggle to resolve wavefields in large-scale, complex velocity models described by the Helmholtz equation, limiting their practical applications. To address these issues, we propose the Agent-Physics-Informed Neural Network (APINNs) architecture, which integrates the agent field concept and employs a multi-frequency band training strategy. Initially, APINNs are trained on single-frequency forward problems, with agent fields enhancing sensitivity to scattered waves. Subsequently, a step-by-step training methodology enables APINNs to directly predict scattered wavefields at arbitrary frequencies within a prescribed frequency band. By convolving the scattered fields with the source wavelet and applying an inverse Fourier transform, the time-evolving wave propagation in large-scale, heterogeneous models can also be reconstructed. Moreover, we extend APINNs to imaging-related inverse problems, such as velocity model reconstruction, within an ultrasound computed tomography framework. This extension only requires computational costs less than one order of magnitude higher than forward APINNs. Conversely, conventional FWI shows a higher cost ratio between inverse and forward problems. While this does not mean that inverse APINNs are currently more efficient than traditional FWI — since the ratio reflects only internal balance and forward APINN training remains expensive — training-driven APINNs are better positioned to benefit from advances in deep learning, potentially improving efficiency and scalability. Numerical experiments validate the effectiveness of APINNs in solving both forward and inverse problems based on the Helmholtz equation in complex scenarios.
{"title":"Agent-Physics-Informed Neural Network solving frequency-domain Helmholtz equation related forward and inverse problems","authors":"Zeyuan Dong, Chang Su, Hao Chen, Weijun Lin, Yubing Li","doi":"10.1016/j.wavemoti.2025.103580","DOIUrl":"10.1016/j.wavemoti.2025.103580","url":null,"abstract":"<div><div>Accurately solving high-fidelity acoustic fields is critical for advancing ultrasonic research. While conventional numerical solvers remain widely used, emerging approaches like Physics-Informed Neural Networks (PINNs) provide a promising alternative for modeling physical phenomena governed by partial differential equations. However, PINNs often struggle to resolve wavefields in large-scale, complex velocity models described by the Helmholtz equation, limiting their practical applications. To address these issues, we propose the Agent-Physics-Informed Neural Network (APINNs) architecture, which integrates the agent field concept and employs a multi-frequency band training strategy. Initially, APINNs are trained on single-frequency forward problems, with agent fields enhancing sensitivity to scattered waves. Subsequently, a step-by-step training methodology enables APINNs to directly predict scattered wavefields at arbitrary frequencies within a prescribed frequency band. By convolving the scattered fields with the source wavelet and applying an inverse Fourier transform, the time-evolving wave propagation in large-scale, heterogeneous models can also be reconstructed. Moreover, we extend APINNs to imaging-related inverse problems, such as velocity model reconstruction, within an ultrasound computed tomography framework. This extension only requires computational costs less than one order of magnitude higher than forward APINNs. Conversely, conventional FWI shows a higher cost ratio between inverse and forward problems. While this does not mean that inverse APINNs are currently more efficient than traditional FWI — since the ratio reflects only internal balance and forward APINN training remains expensive — training-driven APINNs are better positioned to benefit from advances in deep learning, potentially improving efficiency and scalability. Numerical experiments validate the effectiveness of APINNs in solving both forward and inverse problems based on the Helmholtz equation in complex scenarios.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103580"},"PeriodicalIF":2.1,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-05-25DOI: 10.1016/j.wavemoti.2025.103579
Mark J. Ablowitz , Justin T. Cole , Sean D. Nixon
Spiral wave patterns are investigated in continuous linear and nonlinear dispersive wave equations. These models can be derived from reductions of lattice Floquet topological insulators. Specifically, continuous nonlinear Dirac and Lieb systems are analyzed. In the linear limit, both of these systems reduce to the Klein–Gordon equation. A stationary phase approximation is used to reveal the structure of the spirals. The spiral solutions of the underlying Klein–Gordon equation explain the dynamics in the motivating Floquet lattice system. In the nonlinear Dirac equation, a family of localized modes in the spectral band gap are found to approach a single low energy pulse. Spiral waves are found in the nonlinear Klein–Gordon equation even with large nonlinear coefficients.
{"title":"Spiral waves and localized modes in dispersive wave equations","authors":"Mark J. Ablowitz , Justin T. Cole , Sean D. Nixon","doi":"10.1016/j.wavemoti.2025.103579","DOIUrl":"10.1016/j.wavemoti.2025.103579","url":null,"abstract":"<div><div>Spiral wave patterns are investigated in continuous linear and nonlinear dispersive wave equations. These models can be derived from reductions of lattice Floquet topological insulators. Specifically, continuous nonlinear Dirac and Lieb systems are analyzed. In the linear limit, both of these systems reduce to the Klein–Gordon equation. A stationary phase approximation is used to reveal the structure of the spirals. The spiral solutions of the underlying Klein–Gordon equation explain the dynamics in the motivating Floquet lattice system. In the nonlinear Dirac equation, a family of localized modes in the spectral band gap are found to approach a single low energy pulse. Spiral waves are found in the nonlinear Klein–Gordon equation even with large nonlinear coefficients.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103579"},"PeriodicalIF":2.1,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-05-20DOI: 10.1016/j.wavemoti.2025.103581
Weizhuo Zhang, Yan Wang
This study investigates the interaction between highly nonlinear solitary waves (HNSWs) in particle chain and hyperelastic materials (e.g., silicone and fluorine rubber) through simulations and theoretical modeling. A discrete element/finite element (DE/FE) coupled model was developed based on Hertz contact law and Newton’s second law, analyzing two contact methods: direct particle-material contact and the addition of a face sheet. Results demonstrate that hyperelastic material properties (Young’s modulus, compressive strength) and incident particle velocity significantly influence the amplitude and delay of reflected solitary waves. The inclusion of a face sheet enhances sensitivity, enabling precise differentiation between material types. This work advances HNSW-based health diagnosis theory for hyperelastic materials, offering practical applications in non-destructive testing and material characterization.
{"title":"Coupling mechanism of highly nonlinear solitary waves with hyperelastic materials","authors":"Weizhuo Zhang, Yan Wang","doi":"10.1016/j.wavemoti.2025.103581","DOIUrl":"10.1016/j.wavemoti.2025.103581","url":null,"abstract":"<div><div>This study investigates the interaction between highly nonlinear solitary waves (HNSWs) in particle chain and hyperelastic materials (e.g., silicone and fluorine rubber) through simulations and theoretical modeling. A discrete element/finite element (DE/FE) coupled model was developed based on Hertz contact law and Newton’s second law, analyzing two contact methods: direct particle-material contact and the addition of a face sheet. Results demonstrate that hyperelastic material properties (Young’s modulus, compressive strength) and incident particle velocity significantly influence the amplitude and delay of reflected solitary waves. The inclusion of a face sheet enhances sensitivity, enabling precise differentiation between material types. This work advances HNSW-based health diagnosis theory for hyperelastic materials, offering practical applications in non-destructive testing and material characterization.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103581"},"PeriodicalIF":2.1,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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