Research focus
I develop numerical methods for acoustic and elastic wave propagation in complex media. These methods consider nonlinear effects, frequency-dependent attenuation, dispersion and heterogeneous material properties, including applications in biomedical ultrasound.
Many wave phenomena can be predicted by means of numerical methods. Here, I summarize the implemented computational methods for simulation of small amplitude acoustic waves, nonlinear acoustic waves, elastic waves and lattice dynamics.
Most of the codes presented here are developed on a variety of coordinate systems as cartesian 1D, 2D and 3D; and curvilinear coordinate systems as polar, cylindrical axisymmetric, cylindrical and spherical coordinate systems. The implementation of the codes is mainly based on finite differences in time domain (FDTD), but also pseudo-spectral time domain methods (PSTD) are employed in order to accurately solve the partial differential operators.
Acoustic numerical computations
Linear acoustics: fluids
Linear acoustics FDTD methods are useful for characterize the radiation of sound sources and also to study the scattering of sound waves by medium sized structures. Thus, arbitrary source conditions can be implemented on an arbitrary boundary conditions, and the acoustic fields can be explored and measured over the entire domain, leading to huge possibilities in the analysis and design of the acoustics systems.
Related publications
- 2022 · Journal article
Modelling the acoustic field generated by vibrating surfaces
Modelling in Science Education and Learning, 15 (2), 5-23, 2022
Linear acoustics: biological media
When considering ultrasound waves travelling through complex heterogeneous biological media, tissue attenuation response must be taken into account. Typical attenuation for the frequency range typical in medical ultrasound applications follows a frequency power law \(\alpha (f)=\alpha _0 f^{\gamma}\), where the exponent is in the range \(\gamma(1, 2)\). Including this behavior in time domain models could be a cumbersome task, however, if a multiple relaxation media is modeled a frequency power law can be achieved by a FDTD algorithm without including convolution operators.
Nonlinear acoustics: fluids
Accurate predictions of acoustic fields are fundamental in the developing of new ultrasound techniques for medical applications. Estimations of focused ultrasound fields for therapy and imaging requires to take into account a wide range of linear acoustics phenomena, but also in many practical applications the nonlinear processes cannot be neglected. Thus, the numerical solution of many ultrasound techniques are required in order to characterize nonlinear effects and obtain accurate predictions of acoustic fields.
Nonlinear acoustics in relaxing media
Many complex media exhibit acoustic dispersion and attenuation associated to relaxation processes. The relaxation of the molecules of oxygen and nitrogen in air, or the relaxation behavior observed in sea water are the most common examples. If a monochromatic wave is considered, this attenuation / dispersion can be included time domain models by adding losses over a slightly sound speed shifted media. However, when high amplitude waves travel, the nonlinear effects generates a cascade of harmonics, and each attenuates with different magnitude.
Nonlinear acoustics including frequency power law for soft-tissue simulation
Typical attenuation in the frequency range for medical ultrasound applications follows a frequency power law \(\alpha (f)=\alpha _0 f^{\gamma}\), where the exponent is in the range \(\gamma(1, 2)\). When high amplitude waves travel through tissue, the nonlinear effects generates a cascade of harmonics, and each attenuates according the above power law. Including this behavior directly in time domain is a complex task. The code developed accounts for this effect by means of a sum of relaxation processes, avoiding computational-expensive convolutional operators.
Elastodynamics numerical computations
Linear elastodynamics: solid media
If shear elasticity is included, transversal waves can propagate through the media. Thus, elasticity of solid media, leads to a variety of wave phenomena that can be modeled by numerical methods: shear wave propagation, surface wave predictions for SAW devices or geosciences, modes in elastic plates, or design new metamaterials are only few examples of the potential of numerical methods for elastodynamics.
Related publications
- 2019 · Journal article
Modelización de cerámicas y transductores piezoeléctricos vibrando en espesor mediante matrices de transferencia
Modelling in Science Education and Learning, 12 (1), 87-109, 2019
- 2013 · Journal article
Simulación numérica de una cerámica piezoeléctrica
Modelling in Science Education and Learning, 6 (12), 131--143, 2013
Linear elastodynamics: vegetal tissue propagation
The complex propagation of vegetable tissue for ultrasound quality evaluation can be modeled by means of elastodynamics numerical methods. Experimental observations of superficial waves travelling through the shell of the fruit serves as the basis for the numerical simulation data. Thus, superficial wave devices for orange fruit acoustic characterization has been constructed and provides indirect measurements of fruit dehydration state.
Related publications
- 2012 · Journal article
Ultrasonic evaluation of the hydration degree of the orange peel
Postharvest Biology and Technology, 67, 130-137, 2012
- 2009 · Degree dissertation
Simulación de tejidos vegetales mediante FDTD
Universidad Politécnica de Valencia, 2009
Related conference contributions (5)
- 2015 · Conference contribution
Ultrasonic evaluation of the hydration degree of the orange peel
Fruit Structure 2015. Angers, France. 30 November - 01 December, Oral, 2015
- 2015 · Conference contribution
Surface acoustic waves for the characterization of fruit
Fruit Structure 2015. Angers, France. 30 November - 01 December, Poster, 2015
- 2010 · Conference contribution
Simulación acústica de tejidos vegetales en coordenadas esféricas mediante FDTD
Tecniacústica 2010: 41º Congreso Español de Acústica y Encuentro Ibérico de Acústica. León, Spain. 13 - 15 October, Oral, 2010
- 2010 · Conference contribution
FDTD techniques applied to acoustic propagation in vegetable tissue: the elastodynamic behavior of the orange fruit
ICA 2010: 20th International Congress on Acoustics. Sydney, Australia. 23-27 August, Oral, 2010
- 2009 · Conference contribution
Estudio experimental y numérico de la propagación de ultrasonidos en medios heterogéneos
Tecniacústica 2009: 40º Congreso Español de Acústica y Encuentro Ibérico de Acústica. Cádiz, Spain. 23-25 September, Oral, 2009
Linear elastodynamics: anisotropic attenuation/dispersion models for bone
Bones are complex media: a porous solid structure filled by soft-tissue like and viscous fluids. Ultrasound waves travelling through bone presents high attenuations (~50 Np/m @ 0.5 MHz) with non-squared frequency dependence. Wave dispersion is significant factor in bone propagation too. But the most difficult goal to achieve on bone modelling and numerical methods is the anisotropy: elasticity, attenuation and dispersion presents different values depending on the propagation direction. The model developed includes all the above effects in a time-domain formulation without including computational operators.
Coulomb lattices computations
Coulomb linear chain
One of the most simple repulsive lattice is the one dimensional Coulomb chain. However, despite its simplicity, its dynamics is very rich: phonon propagation to nonlinear travelling localized structures, etc.. In this line I'm investigate travelling lattice kinks, with the application in characterization and modelling one dimensional nonlinear travelling excitations (or quodons after M. Russell works) in layered media as mica muscovite.
Related publications
- 2017 · Journal article
Nonlinear dispersive waves in repulsive lattices
Physical Review E, 96 (1), 012208, 2017
- 2015 · Journal article
Macroscopic acousto-mechanical analogy of a microbubble
The Journal of the Acoustical Society of America, 138 (6), 3600-3606, 2015
2015 · Edited bookQuodons in Mica: Nonlinear Localized Travelling Excitations in Crystals
Springer International Publishing, 2015
- 2015 · Journal article
Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials
Physical Review E, 91 (2), 022912, 2015
Chain of magnets
In order to demonstrate the ability of layered media to propagate nonlinear travelling one-dimensional excitation (quodons), experimental macroscopic modelling of the Coulomb chain by a chain of coupled magnet. These experiments are reproduced in numerical simulations o a chain of magnetically coupled pendulums, where kinks and nonlinear harmonic waves have been observed and measured.
Mechanical computations
Coupled pendulum chain
Pendulum is the most simple nonlinear oscillator. However, despite its simplicity, a wide range of nonlinear phenomena can be studied and modeled. Furthermore, if a chain of coupled pendula is considered, phonons can propagate through the lattice, and due to the existence of nonlinearities and dispersion, exotic wave phenomena can be observed. Here I study breathers, kink, intrinsic localized modes and chaotic behavior of the chain.
Ring of coupled pendula
By simply changing the boundary conditions of the chain, linking the last and the first pendulum, a ring can be formed. Moreover, under parametric excitation, the rich dynamics observed presents many analogies with the behavior of bubbles under the action of an external pressure field. Thus, the computational developed codes allows us to explore complex dynamics of discrete lattices, and extrapolate results to design new microbubble applications.
Related publications
- 2015 · Journal article
Macroscopic acousto-mechanical analogy of a microbubble
The Journal of the Acoustical Society of America, 138 (6), 3600-3606, 2015
- 2013 · Journal article
Modeling acoustically driven microbubbles by macroscopic discrete-mechanical analogues
Modelling in Science Education and Learning, 6 (7), 75-87, 2013
Related conference contributions (8)
- 2016 · Conference contribution
Localized nonlinear modes in microbubbles under the action of ultrasound
IUS 2016: IEEE International Ultrasonics Symposium. Tours, France. 18-21 September, Oral, 2016
- 2014 · Conference contribution
Lattice of nonlinear coupled oscillators: An acousto-mechanical analogy of gas microbubble
IUS 2014: IEEE International Ultrasonics Symposium. Chicago, USA. 3 - 6 September, Oral, 2014
- 2014 · Conference contribution
Analogie macroscopique et acousto-mécanique d’une microbulle d’agent de contraste
CFA 2014: 12ème Congrès Français d'Acoustique. Potiers, France. 22 - 25 April, Oral, 2014
- 2013 · Conference contribution
Vibration modes in a pendulums ring: analogy with gas microbubbles surface modes
IUS 2013: IEEE International Ultrasonics Symposium. Prague, Czech Republic. 21-25 July, Oral, 2013
- 2012 · Conference contribution
Spatio-temporal dynamics in a ring of coupled pendula: analogy with bubbles
LENCOS'12: Localized Excitations in Nonlinear Complex Systems, Seville, Spain. 9 - 12 July, Oral, 2012
- 2012 · Conference contribution
Modeling acoustically driven microbubbles by macroscopic discrete-mechanical analogues
III Jornadas de Modelización Matemática. Gandia, Spain. 7 - 8 June, Oral, 2012
- 2011 · Conference contribution
Modulational instability and localized modes for ultrasound contrast microbubbles surface oscillations
IUS 2011: IEEE International Ultrasonics Symposium. Orlando, Florida, USA. 18-21 October, Oral, 2011
- 2011 · Conference contribution
Modulational instability of microbubbles surface modes
ICU 2011: International Congress on Ultrasonics. Gdansk, Poland. 5 - 8 September, Oral, 2011
2-Dimensional coupled oscillators
If a surface of coupled oscillators is taken into account, vibration patterns can be observed both, in flat surfaces or in warped surfaces (i.e. spherical shape modes). This numerical codes allows to investigate the behavior of complicated systems like Ultrasound Contrast Agents or drops under the action of an ultrasonic field.
More publications in this research area
- 2021 · Book chapter
The Transfer Matrix Method in Acoustics
In: Acoustic Waves in Periodic Structures, Metamaterials, and Porous Media: From Fundamentals to Industrial Applications, Springer, pp. 103 - 164, 2021
- 2021 · Book chapter
Acoustic Metamaterial Absorbers
In: Acoustic Waves in Periodic Structures, Metamaterials, and Porous Media: From Fundamentals to Industrial Applications, Springer, pp. 167 - 204, 2021
- 2019 · Journal article
Efecto del método de definición de las propiedades acústicas de cráneo humano en la propagación focalizada de ultrasonidos
Revista de Acústica, 50 (1-2), 22-25, 2019
- 2018 · Book chapter
Kinks in a Lattice of Repelling Particles
In: Nonlinear Systems, Vol. 2: Nonlinear Phenomena in Biology, Optics and Condensed Matter, Springer International Publishing, pp. 261-282, 2018
- 2017 · Journal article
Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic Beams
Ultrasonics, 75, 106-114, 2017
- 2016 · Journal article
Time-Domain Simulation of Ultrasound Propagation in a Tissue-Like Medium Based on the Resolution of the Nonlinear Acoustic Constitutive Relations
Acta Acustica united with Acustica, 102 (5), 876--892, 2016
- 2015 · Book chapter
A supersonic crowdion in mica
In: Quodons in Mica: Nonlinear Localized Travelling Excitations in Crystals, Springer International Publishing, pp. 69-96, 2015
- 2014 · Book chapter
Supersonic Kinks in Coulomb Lattices
In: Localized Excitations in Nonlinear Complex Systems, Springer International Publishing, pp. 317-331, 2014
- 2014 · Book chapter
Spatio-Temporal Dynamics in a Ring of Coupled Pendula: Analogy with Bubbles
In: Localized Excitations in Nonlinear Complex Systems, Springer International Publishing, pp. 251--262, 2014
- 2013 · Journal article
Moving excitations In cation lattices
Ukranian Journal of Physics, 58 (7), 646-656, 2013
Related conference contributions (28)
- 2016 · Conference contribution
Second harmonic generation in a chain of magnetic pendulums
No Lineal 2016: International conference on nonlinear mathematics and physics. Seville, Spain. 7 - 10 June, Oral, 2016
- 2016 · Conference contribution
Acoustic gap solitons in layered media
No Lineal 2016: International conference on nonlinear mathematics and physics. Seville, Spain. 7 - 10 June, Oral, 2016
- 2016 · Conference contribution
Toy models for Nonlinear Acoustics
Invited speech at INSA Centre Val de Loire, Blois, France. February 25th, Invited, 2016
- 2015 · Conference contribution
Time-domain simulation of constitutive relations for nonlinear acoustics including relaxation for frequency power law attenuation media modelling
20th ISNA: 20th International Symposium on Nonlinear Acoustics. Lyon, France. June 19 - July 3rd,, Oral, 2015
- 2015 · Conference contribution
Efficient Second Harmonic Generation of Narrow Beams in 2D Sonic Crystals
Phononics 2015: 3rd International Conference on Phononic Crystals/Metamaterials, Phonon Transport and Phonon Coupling. Paris, France. May 31-June 5, Oral, 2015
- 2014 · Conference contribution
Nonlinear Acoustic Waves in Periodic Media
7th Forum Acusticum 2014. Krakow, Poland. 7 September, Oral, 2014
- 2013 · Conference contribution
Ondas acústicas de amplitud finita en medios con relajación: aplicación a la modelización de tejidos biológicos
Tecniacústica 2013: 44º Congreso Español de Acústica y Encuentro Ibérico de Acústica. Valladolid, Spain. 2 - 4 October, Oral, 2013
- 2013 · Conference contribution
Estudio paramétrico de la propagación transcranial de un haz ultrasónico para la apertura de la barrera hematoencefálica
Tecniacústica 2013: 44º Congreso Español de Acústica y Encuentro Ibérico de Acústica. Valladolid, Spain. 2 - 4 October, Oral, 2013
- 2013 · Conference contribution
A crowdion in mica. Between K40 recoil and transmission sputtering
Quodons in Mica: Nonlinear Localized Travelling Excitations in Crystals (QiM 2013). Altea, Spain. 18-22 September, Invited, 2013
- 2013 · Conference contribution
Simulación numérica con FDTD de una cerámica piezoeléctrica
23º Encuentro Ibérico de Enseñanza de la Física. Valenca, Spain. 16 July, Poster, 2013
- 2013 · Conference contribution
Parametric study of transcranial focused ultrasound propagation for blood–brain barrier opening
RSEF 2013: XXXIV Reunión Bienal de la Real Sociedad Española de Física. Valencia, Spain. 15 - 19 July, Poster, 2013
- 2013 · Conference contribution
Kinks supersónicos en redes repulsivas
RSEF 2013: XXXIV Reunión Bienal de la Real Sociedad Española de Física. Valencia, Spain. 15 - 19 July, Oral, 2013
- 2013 · Conference contribution
Interacción Coulombiana, estorninos y Angry Birds
23º Encuentro Ibérico de Enseñanza de la Física. Valenca, Spain. 16 July, Poster, 2013
- 2013 · Conference contribution
Focalización de ondas acústicas mediante una lente formada por dispersores toroidales rígidos
RSEF 2013: XXXIV Reunión Bienal de la Real Sociedad Española de Física. Valencia, Spain. 15 - 19 July, Poster, 2013
- 2013 · Conference contribution
Parametric study of transcranial focused ultrasound propagation for blood–brain barrier opening
ESUCB 2013: 5th European Symposium on Ultrasonic Characterization of Bone. Granada, Spain. 7-10 May, Oral, 2013
- 2013 · Conference contribution
Effect of ZBL potential on kinks in repusive lattices
IV International Symposium on Strong Nonlinear Vibronic and Electronic Interactions in Solids. Tartu, Estonia. 1 - 3 May, Oral, 2013
- 2012 · Conference contribution
Supersonic solitons and kinks in repulsive lattices
Lattice Solitons and Irradiation-Induced Nonlinear Phenomena in Solids. Tartu, Estonia. October 31th - November 2nd, Oral, 2012
- 2012 · Conference contribution
Moving excitations in cation lattices
Problems of theoretical physics (dedicated to the 100th anniversary of Alexander Davydov). Kiev, Ucraine. 8 - 11 October, Invited, 2012
- 2012 · Conference contribution
Simulación numérica de una cerámica piezoeléctrica
III Jornadas de Modelización Matemática. Gandia, Spain. 7 - 8 June, Oral, 2012
- 2011 · Conference contribution
Predicción numérica de ondas acústicas de amplitud finita bajo condiciones de contorno arbitrarias
Tecniacústica 2011: 42º Congreso Español de Acústica y Encuentro Ibérico de Acústica. Cáceres, Spain. 26 - 28 October, Oral, 2011
- 2011 · Conference contribution
Estudio de la propagación no lineal de haces de ultrasonidos focalizados a través del cráneo para la apertura de la barrera hematoencefálica
Tecniacústica 2011: 42º Congreso Español de Acústica y Encuentro Ibérico de Acústica. Cáceres, Spain. 26 - 28 October, Oral, 2011
- 2011 · Conference contribution
Efectos no lineales en la fuerza de radiación generada por haces focalizados de amplitud modulada
Tecniacústica 2011: 42º Congreso Español de Acústica y Encuentro Ibérico de Acústica. Cáceres, Spain. 26 - 28 October, Oral, 2011
- 2011 · Conference contribution
Numerical study of nonlinear, transcranial focused ultrasound wave propagation for blood-brain barrier (BBB) opening
ISTU 2011: 11th International Society for Therapeutic Ultrasound Symposium. New York, USA. 11-13 April, Oral, 2011
- 2011 · Conference contribution
Nonlinear effects in the radiation force generated by amplitude-modulated focused beams
ISTU 2011: 11th International Society for Therapeutic Ultrasound Symposium. New York, USA. 11-13 April, Poster, 2011
- 2010 · Conference contribution
Nonlinear focal shift in medium Fresnel-number focused acoustic beams
IUS 2010: IEEE International Ultrasonics Symposium. San Diego, USA. 11-14 October, Oral, 2010
- 2010 · Conference contribution
Más allá del foco geométrico en haces focalizados de ultrasonidos
Tecniacústica 2010: 41º Congreso Español de Acústica y Encuentro Ibérico de Acústica. León, Spain. 13 - 15 October, Oral, 2010
- 2010 · Conference contribution
Cálculo de campos acústicos no lineales mediante diferencias finitas en dominio temporal
Tecniacústica 2010: 41º Congreso Español de Acústica y Encuentro Ibérico de Acústica. León, Spain. 13 - 15 October, Oral, 2010
- 2010 · Conference contribution
Beyond the geometrical focus in focused acoustic beams
ICA 2010: 20th International Congress on Acoustics. Sydney, Australia. 23-27 August, Oral, 2010