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• Chandrasekaran, Sri Nivas; Holm, Sverre & Näsholm, Sven Peter (2023). Wave equations of the two common sediment acoustic theories. Proceedings of Meetings on Acoustics (POMA). 51. doi: 10.1121/2.0001795. Fulltekst i vitenarkiv Vis sammendrag

  Two popular theories for wave propagation in sediments, the Biot poroelastic theory and the Viscous Grain Shearing (VGS) theory, have been formulated in terms of dispersion relations. The lack of explicit wave equations for these models could be considered to be a weakness. Hence, providing wave equations that are fully consistent with these theories might confirm that they have a physical basis. In the Biot theory, it is the frequency-dependent viscodynamic operator that poses the problem as there is no equivalent time-domain operator. Previous work has shown that this factor can be approximated well with a simplified square root operator. Drawing on the parallel to the Cole-Davidson dielectric theory for complex media where the same factor appears, and using the equivalent time-domain operator, which is a fractional pseudo-differential operator, enables the formulation of wave equations for all three wave modes of the Biot theory. The same operator turns out to be central for transforming the dispersion relations of the VGS theory to time-space wave equations. In this case, the relation between the dispersion equations and the wave equations is exact. The wave equations of these two theories will enable a closer study of the properties of the medium models.

• Holm, Sverre; Chandrasekaran, Sri Nivas & Näsholm, Sven Peter (2023). Adding a low frequency limit to fractional wave propagation models. Frontiers in Physics. 11, s. 1–8. doi: 10.3389/fphy.2023.1250742. Fulltekst i vitenarkiv Vis sammendrag

  Power-law attenuation in elastic wave propagation of both compressional and shear waves can be described with multiple relaxation processes. It may be less physical to describe it with fractional calculus medium models, but this approach is useful for simulation and for parameterization where the underlying relaxation structure is very complex. It is easy to enforce a low-frequency limit on a relaxation distribution and this gives frequency squared characteristics for low frequencies which seems to fit some media in practice. Here the goal is to change the low-frequency behavior of fractional models also. This is done by tempering the relaxation moduli of the fractional Kelvin-Voigt and diffusion models with an exponential function and the effect is that the low-frequency attenuation will increase with frequency squared and the square root of frequency respectively. The time-space wave equations for the tempered models have also been found, and for this purpose the concept of the fractional pseudo-differential operator borrowed from the field of Cole-Davidson dielectrics is useful. The tempering does not remove the singularity in the relaxation moduli of the models, but this has only a minor effect on the solutions.

• Chandrasekaran, Sri Nivas; Näsholm, Sven Peter & Holm, Sverre (2022). Wave equations for porous media described by the Biot model. Journal of the Acoustical Society of America. ISSN 0001-4966. 151(4), s. 2576–2586. doi: 10.1121/10.0010164. Fulltekst i vitenarkiv Vis sammendrag

  Single-mode equivalent space-time representations of the acoustic wave propagating in a Biot poroelastic medium have previously been found only for asymptotic cases: In the low frequency regime, where the viscous skin depth is greater than the characteristic pore size, the time domain equivalent is represented with integer order temporal and spatial loss terms, whereas in the high frequency regime, it is represented with fractional order temporal and spatial loss terms. In the current work, a time domain representation in terms of a partial differential equation is proposed for all three wave solutions of the Biot model across all frequencies, and it is derived from the material response function of the Biot poroelastic medium with suitable approximations for the compressional modes and the dynamic permeability. The dynamic permeability in the time domain is represented by a fractional pseudo-differential operator. Optimal correction factors are introduced into the wave equation to compensate for the discrepancies in the compressional wave dispersion and attenuation. Additionally, the method for incorporating the squirt flow mechanism into the wave equation via the Extended Biot poroviscoelastic model is described. The proposed wave equation has a physical basis and satisfies the passivity criterion.

• Chandrasekaran, Sri Nivas & Holm, Sverre (2019). A multiple relaxation interpretation of the extended Biot model. Journal of the Acoustical Society of America. ISSN 0001-4966. 146(1), s. 330–339. doi: 10.1121/1.5116139. Fulltekst i vitenarkiv
• Chandrasekaran, Sri Nivas; Holm, Sverre & Prieur, Fabrice Jean Gabriel (2017). Focused ultrasound setup for the study of acoustic radiation force induced biological effects in cells. Proceedings - IEEE Ultrasonics Symposium. ISSN 1948-5719. doi: 10.1109/ULTSYM.2017.8091996. Fulltekst i vitenarkiv

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• Holm, Sverre; Chandrasekaran, Sri Nivas & Näsholm, Sven Peter (2023). Finding wave equations for sediment acoustics theories. Fulltekst i vitenarkiv Vis sammendrag

  The two main theories for wave propagation in sediments, the Extended Biot theory and the Viscous Grain Shearing (VGS) theory, have been formulated in terms of dispersion equations only. Some have considered the lack of a wave equation to be a weakness that may indicate lack of a physical basis for these theories. In the Biot theory, it is the frequency-dependent viscodynamic operator which models viscous boundary effects in pores that poses the problem. It can be formulated as a ratio of Bessel functions for circular pores and as a ratio of tanh-functions for a 2D parallel plane duct. There is no simple equivalent time domain operator for use in the wave equation. In both geometries, the factor may, however, be approximated well with (1 + icω)1/2, where c is a constant. This factor also appears in the Cole-Davidson dielectric theory for complex media. The equivalent time domain operator, the fractional pseudo-differential operator, enables the formulation of wave equations for all three wave modes. The same operator turns out to be central for transforming the dispersion relations of the VGS theory to time-space wave equations. These wave equations enable a closer study of properties of the medium models than that obtained from dispersion relations alone.

• Chandrasekaran, Sri Nivas & Holm, Sverre (2019). Erratum: A multiple relaxation interpretation of the extended Biot model (Journal of the Acoustical Society of America (2019) 146 (330-339) DOI: 10.1121/1.5116139). Journal of the Acoustical Society of America. ISSN 0001-4966. 146(6), s. 4322–4323. doi: 10.1121/1.5139414. Fulltekst i vitenarkiv
• Chandrasekaran, Sri Nivas; Evensen, Karen Brastad; Ramsdal, Elisabeth Grønn & Holm, Sverre (2018). Integrating the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) in the Biot viscosity extended framework. Journal of the Acoustical Society of America. ISSN 0001-4966. 143(3). doi: 10.1121/1.5036507. Fulltekst i vitenarkiv
• Chandrasekaran, Sri Nivas & Holm, Sverre (2018). Integrating the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) in the Biot viscosity extended framework. Fulltekst i vitenarkiv
• Chandrasekaran, Sri Nivas; Holm, Sverre & Prieur, Fabrice Jean Gabriel (2017). Focused ultrasound setup for the study of acoustic radiation force induced biological effects in cells. Fulltekst i vitenarkiv Vis sammendrag

  Low intensity pulsed ultrasound (LIPUS) is a therapy used clinically for bone fracture and soft tissue healing LIPUS induces functional alterations in cell behavior and has shown potential for cancer therapy. In order to understand the underlying biophysical mechanisms, the ability to control acoustic exposure parameters and elimination of unwanted effects such as the formation of standing wave patterns, heating, and cavitation, is vital. In this study, we designed an in-vitro focused ultrasound setup (FUS) with repeatable exposure conditions where the cells or spheroids are surrounded by an agar substrate with sufficient absorption to eliminate unwanted reflections and cell culture medium which acts as an effective coolant. The measured maximum temperature rise with the presence of coolant was 1°C and the estimated mechanical index was 1.28. The shear wave propagation induced by acoustic radiation force was monitored and no reflection was observed. We propose an in-vitro FUS cell stimulation setup which can induce non-thermal and non-cavitation biological response with no unwanted artifacts.

• Chandrasekaran, Sri Nivas (2026). A generalized mathematical framework to model geoacoustic properties of the seabed.Towards a unified sediment acoustics model. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Modeling How Sound Travels Through the Seabed The seabed is a complex, sponge-like medium where seawater permeates the spaces between solid grains. We rely on sound waves for underwater navigation, communication, and offshore energy exploration, but the seabed can strongly influence how these waves propagate. Accurate modeling of the seabed’s geoacoustic behavior is therefore important for reliable marine operations. However, a definitive understanding of how sound speed and attenuation vary with propagation frequency, even in simple sediments, has not yet been achieved. The problem becomes more challenging when sediments are layered or uneven. Existing models work under limited conditions, and their physical consistency and reliability across the full frequency range remain uncertain. We develop a physically consistent and unified mathematical framework to describe how sound waves travel through seabed sediments across a wide range of frequencies. The framework uses fractional calculus, a mathematical approach that captures the material’s “memory,” to derive corresponding wave equations. It also enables incorporation of different physical mechanisms within sediments that influence sound attenuation. The proposed approach improves the accuracy and reliability of seabed acoustic modeling, supporting enhanced sonar performance, precise seabed characterization, and improved tools for marine research and offshore engineering, while providing a foundation for studying wave propagation in complex materials.

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