Article
Physics, Applied
Jensen Li, Xinhua Wen, Ping Sheng
Summary: This tutorial is divided into two parts, one focusing on resonance-based acoustic metamaterials and the other on topological acoustics. The first part introduces decorated membrane resonators and broadband optimal acoustic absorption structures, while the second part discusses constructing Dirac cones and topological bandgaps.
JOURNAL OF APPLIED PHYSICS
(2021)
Article
Mathematics, Applied
Yavar Kian, Masahiro Yamamoto
Summary: This study focuses on the well-posedness of initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. The existence of weak and strong solutions is proven, with sharp conditions ensuring solutions have more regularity in time and space. An optimal compatibility condition is introduced for strong solutions.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Interdisciplinary Applications
Rania Saadeh, Mohamed A. Abdoon, Ahmad Qazza, Mohammed Berir
Summary: In this article, the numerical adaptive predictor corrector (Apc-ABM) method is introduced for solving generalized Caputo fractional initial value problems. The Apc-ABM method is used to establish approximate series solutions. This approach is an extension to the original Adams-Bashforth-Moulton approach. Numerical simulations and figures are presented to demonstrate the efficiency of the proposed method. In the future, this method can be utilized to create and simulate various generalized Caputo-type fractional models using the provided generalized Caputo fractional derivative.
FRACTAL AND FRACTIONAL
(2023)
Article
Acoustics
Xueliang Liu, Haijun Wu, Weikang Jiang
Summary: The study aims to develop a boundary element method for 3D acoustic problems in a subsonic uniform flow, using a hybrid convected boundary integral formula based on the Burton-Miller method to avoid the fictitious eigenfrequency problem. By utilizing a method based on polar coordinate transformation, the difficulties related to hypersingular integrals in the convected normal derivative boundary integral equation are effectively resolved, eliminating various kinds of singularities in CBIE and NDBIE.
Article
Mathematics
Roja Mahmoudi Matankolae, Bahram Agheli, Sirous Ghobadi, Rahmat Darzi, Mohammad Adabitabar Firozja
Summary: In this paper, the theory of q-fractional hybrid differential equations involving Riemann-Liouville q-differential operators is extended. An existence theorem for FHDEs under Lipschitz and Caratheodory conditions is also proven. Additionally, some fundamental fractional differential inequalities are presented to indicate the existence of external solutions for such problems. The required tools and a comparison principle are provided for further research on the qualitative behavior of solutions.
JOURNAL OF MATHEMATICS
(2022)
Article
Engineering, Mechanical
Lifeng Ma, Zhiyi Tang, Zitong Bian, Junbei Zhu, Marian Wiercigroch
Summary: This paper presents an analytical solution for circular inhomogeneous inclusions in plane elasticity problems, using complex variable potential and Green's function method. By overcoming the main challenge in solving inhomogeneous inclusion problems, a general explicit analytical solution is derived. The introduced formulation has potential applications in mechanics of fiber composites, thermoelasticity, and nano-mechanics of defects in solids.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Sudi Mungkasi
Summary: This paper focuses on obtaining explicit solutions through order verification method for truncated asymptotic formal expansion solutions, which simplifies the process and enhances accuracy without involving least-squares fit of error data.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Rodrigo M. Pereira, Natacha Nguyen Van Yen, Kai Schneider, Marie Farge
Summary: This study investigates the use of adaptive Galerkin methods for time-dependent partial differential equations and demonstrates their dissipative nature. The selection of basis functions, such as filtering out weak wavelet coefficients from the solution, introduces energy dissipation in numerical examples. Furthermore, adaptive wavelet regularization allows the truncated Galerkin solution to converge to physically relevant entropy solutions.
MULTISCALE MODELING & SIMULATION
(2022)
Article
Mathematics, Applied
Gung-Min Gie, Chang-Yeol Jung, Hoyeon Lee
Summary: In this study, new semi-analytic time differencing methods were implemented for singularly perturbed non-linear initial value problems. By introducing correctors to improve the classical integrating factor and exponential time differencing methods, better approximations for stiff problems were achieved. Numerical simulations confirmed the effectiveness of the new enriched schemes compared to classical methods without correctors.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
M. A. Abdelkawy
Summary: This paper presents spectral collocation techniques to deal with the distributed-order fractional initial value problem, using shifted fractional order Jacobi orthogonal functions and algebraic equation systems for approximation. Numerical examples demonstrate the accuracy and applicability of the technique. By employing fractional order Jacobi functions instead of classical Jacobi functions, the deterioration in accuracy for nonsmooth solutions is prevented.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2021)
Article
Mathematics, Applied
Xian-Min Zhang
Summary: This paper focuses on the initial value problem for two types of impulsive fractional differential equations with the Hilfer-generalized fractional derivative. By constructing an approximate solution and calculating the error, it is revealed that there are multiple solutions for these equations. Numerical examples are provided to illustrate the obtained results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Environmental Sciences
Zhang-Long Chen, Yiyi Huang, Hongwei Fang, Tian-Chyi Jim Yeh, Yuanyuan Zha
Summary: Srivastava and Yeh derived an exact solution to the linearized Richards equation for two-layer medium infiltration using the Laplace transform method with a specific initial condition. However, this method is not suitable for deriving an exact solution that considers arbitrary initial conditions or arbitrary number of layers. We propose a new solution strategy by combining the variable separation method and the transfer matrix method, which overcomes these difficulties and provides a valuable benchmark for related numerical models.
WATER RESOURCES RESEARCH
(2023)
Article
Engineering, Multidisciplinary
Xueliang Liu, Haijun Wu, Ruihua Sun, Weikang Jiang
Summary: This paper presents a fast multipole boundary element method (FMBEM) for solving half-space acoustic problems in a subsonic uniform flow. The method overcomes the non-uniqueness difficulty and uses the fast multipole method to improve calculation efficiency. The impact of the infinite plane on the results is computed using a mirror-image model.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics
Peijun Li, Xu Wang
Summary: This paper examines the well-posedness and regularity of distributional solutions for stochastic acoustic and elastic scattering problems, and concludes that the regularity of solutions is influenced by the regularity of both the random medium and the random source.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Hu Chen, Martin Stynes
Summary: Time-fractional initial-boundary value problems are studied, showing that the solution converges to the solution of the classical parabolic initial-boundary value problem as alpha approaches 1(-). Rigorous analyses of numerical methods for this problem typically have error bounds that blow up as alpha -> 1(-), but in some cases, these analyses can be modified to obtain robust error bounds.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2021)
Article
Acoustics
Elliott S. Wise, Jiri Jaros, Ben T. Cox, Bradley E. Treeby
Summary: Pseudospectral time domain methods are commonly used in acoustics for solving wave equations, with Fourier collocation spectral method offering computational advantages. This study introduces spectral collocation methods based on sine or cosine basis, allowing for different boundary conditions to be imposed. The technique utilizes discrete sine and cosine transforms for numerical computation, showcasing its potential for solving wave equations with various boundary conditions.
JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS
(2021)
Article
Engineering, Multidisciplinary
Santeri Kaupinmaki, Ben Cox, Simon Arridge, Christian Baker, David Sinden, Bajram Zeqiri
Summary: The article introduces a numerical model of a phase-insensitive pyroelectric ultrasound sensor, which consists of three components: acoustic, thermal, and electrical. The model simulates the propagation, absorption, and temperature change of ultrasound waves, and outputs the sensor response for comparison with empirical data.
MEASUREMENT SCIENCE AND TECHNOLOGY
(2021)
Article
Acoustics
Khoa Pham, Sacha Noimark, Nam Huynh, Edward Zhang, Filip Kuklis, Jiri Jaros, Adrien Desjardins, Ben Cox, Paul Beard
Summary: The system utilizes a carbon nanotube-polydimethylsiloxane film as an ultrasound transmitting layer to generate high-resolution 3-D imaging of biological tissues. By measuring the instrument line-spread function, the system demonstrates superior spatial resolution for imaging.
IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL
(2021)
Article
Acoustics
Marina Bakaric, Paul Fromme, Andrew Hurrell, Srinath Rajagopal, Piero Miloro, Bajram Zeqiri, Benjamin T. Cox, Bradley E. Treeby
Summary: The research highlights the significant impact of temperature on the output of PZT transducers, showing an increase in efficiency with temperature. Results were consistent when using the same signal chain for measurement, but transducers exhibited different behavior when driven using a pulser.
Article
Mathematics, Applied
Felix Lucka, Mailyn Perez-Liva, Bradley E. Treeby, Ben T. Cox
Summary: This study focuses on the challenges faced by high resolution 3D ultrasound tomography (UST) scanners and proposes a comprehensive computational strategy to overcome them, including reducing memory footprint, utilizing source encoding for stochastic gradient estimates, and implementing a stochastic LBFGS method for optimization. Extensive numerical proof-of-concept studies demonstrate the effectiveness of these methods in achieving accurate UST images within a reasonable time frame.
Article
Acoustics
Marina Bakaric, Piero Miloro, Ashkan Javaherian, Ben T. Cox, Bradley E. Treeby, Michael D. Brown
Summary: The study characterized the acoustic properties of eight 3D-printed photopolymer materials and measured their density, sound speed, and attenuation values. The materials were fabricated using PolyJet and SLA techniques, with density values ranging from 1120-1180 kg/m^3, sound speed values between 2020 to 2630 m/s, and attenuation values typically in the range of 3-9 dB/MHz·cm.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2021)
Article
Acoustics
Petr Kleparnik, Pavel Zemcik, Bradley E. Treeby, Jiri Jaros
Summary: This article presents a new method for calculating the average acoustic intensity during ultrasound simulation. By resolving the time staggering on-the-fly, this method saves significant disk space and does not affect the simulation speed or the accuracy of thermal dose prediction. The new approach is more economical from the standpoint of supercomputers and increases the chances of practical use of acoustic simulations.
IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL
(2022)
Article
Acoustics
Maria Miscouridou, Jose A. Pineda-Pardo, Charlotte J. Stagg, Bradley E. Treeby, Antonio Stanziola
Summary: This study compared three methods for generating pseudo-CT (pCT) images from magnetic resonance (MR) images as an alternative to CT for transcranial ultrasound therapy. Through comparison with ground-truth CT images and ultrasound simulations, it was found that acoustic simulations based on MR images can achieve comparable accuracy to those based on CT.
IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL
(2022)
Article
Acoustics
Rui Xu, Bradley E. Treeby, Eleanor Martin
Summary: The use of ultrasound has been shown to increase rewarming rates compared to thermal conduction alone, which can contribute to the cryopreservation of large biological samples. An experiment was conducted using a custom-designed tubular piezoelectric transducer and frozen ground beef samples to test the rewarming rates. The results demonstrated a ten-fold increase in rewarming rate when ultrasound was applied, with a maximum recorded rewarming rate of 57 degrees C/min. Coupled acoustic and thermal simulations also showed good agreement with the experimental results, suggesting the potential for ultrasonic cryovial rewarming in large volume applications.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2023)
Article
Acoustics
Srinath Rajagopal, Thomas Allen, Martin Berendt, Di Lin, Shaif-ul Alam, David J. J. Richardson, Ben T. T. Cox
Summary: This article demonstrates experimentally that a planar laser-generated ultrasound source with a hard reflective backing produces higher acoustic pressures compared to a source with an acoustically matched backing when the stress confinement condition is not met. Additionally, when the laser pulse is short enough to ensure stress confinement, the source with an acoustically matched backing has a broader bandwidth, while the bandwidths of both source types converge as the laser pulse duration increases beyond stress confinement. Numerical simulations support the explanation of the results.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2023)
Article
Acoustics
Antonio Stanziola, Simon Arridge, Ben T. Cox, Bradley E. Treeby
Summary: A new method called the learned Born series (LBS) is introduced for solving the wave equation, where the components of the LBS are determined through training. The LBS is found to be more accurate than the convergent Born series for the same number of iterations, especially in the presence of high contrast scatterers, while maintaining a similar computational complexity. It is capable of generating a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.
JASA EXPRESS LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jiaqi Zhu, Nam Huynh, Olumide Ogunlade, Rehman Ansari, Felix Lucka, Ben Cox, Paul Beard
Summary: The use of finite aperture planar detection geometries in photoacoustic tomography leads to limited-view problem, affecting image quality. In order to address this issue, model-based iterative reconstruction methods were compared with one-step reconstruction methods, and the iterative methods were found to provide better image quality. For the total variation approaches, the impact of the regularization parameter on image features and amplitude was evaluated, and the compensating ability of Bregman iterations for amplitude bias introduced by total variation was studied.
IEEE TRANSACTIONS ON MEDICAL IMAGING
(2023)
Article
Acoustics
Morgan Roberts, Eleanor Martin, Michael D. Brown, Ben T. Cox, Bradley E. Treeby
Summary: In this study, an open-source 256-element transducer ring array was developed for ultrasound tomography (UST) imaging. The system showed similar acoustic performance to existing systems and was compatible with state-of-the-art image reconstruction methods. The results demonstrated the accessibility and suitability of the open-UST system for UST imaging research.
IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL
(2023)
Article
Acoustics
Eleanor Martin, Morgan Roberts, Bradley Treeby
Summary: Modeling pressure fields generated by a 555kHz 32-element ultrasonic array can be affected by errors stemming from differences in transducer parameters and variations in relative outputs of array elements. By predicting crosstalk and determining positions experimentally, errors in pressure amplitude and focal position can be significantly reduced.
JASA EXPRESS LETTERS
(2021)