المؤلفون: Hawkins, Stuart C., Bennetts, Luke G., Nethercote, Matthew A., Peter, Malte A., Peterseim, Daniel, Putley, Henry J., Verfürth, Barbara

مصطلحات موضوعية: metamaterials, wave propagation, Rayleigh–Bloch waves, T-matrix, multiple wave scattering

الوصف: Peer reviewed: True ; Publication status: Published ; Multiple scattering of waves is eminent in a wide range of applications and extensive research is being undertaken into multiple scattering by ever more complicated structures, with emphasis on the design of metamaterial structures that manipulate waves in a desired fashion. Ongoing research investigates the design of structures and new solution methods for the governing partial differential equations. There is a pressing need for easy-to-use software that empowers rapid prototyping of designs and for validating other solution methods. We develop a general formulation of the multiple scattering problem that facilitates efficient application of the multipole-based method. The shape and morphology of the scatterers is not restricted, provided their T-matrices are available. The multipole method is implemented in the Tmatsolver software package, which uses our general formulation and the T-matrix methodology to simulate accurately multiple scattering by complex configurations with a large number of identical or non-identical scatterers that can have complex shapes and/or morphologies. This article provides a mathematical description of the algorithm and demonstrates application of the software to four contemporary metamaterial problems. It concludes with a brief overview of the object-oriented structure of the Tmatsolver code.

وصف الملف: application/pdf; text/xml

العلاقة: https://www.repository.cam.ac.uk/handle/1810/369940Test

الإتاحة: https://www.repository.cam.ac.uk/handle/1810/369940Test

المؤلفون: Hawkins, Stuart C., Bennetts, Luke G., Nethercote, Matthew A., Peter, Malte A., Peterseim, Daniel, Putley, Henry J., Verfürth, Barbara

مصطلحات موضوعية: T-matrix, wave propagation, Rayleigh–Bloch waves, multiple wave scattering, metamaterials

الوصف: Peer reviewed: True ; Publication status: Published ; Multiple scattering of waves is eminent in a wide range of applications and extensive research is being undertaken into multiple scattering by ever more complicated structures, with emphasis on the design of metamaterial structures that manipulate waves in a desired fashion. Ongoing research investigates the design of structures and new solution methods for the governing partial differential equations. There is a pressing need for easy-to-use software that empowers rapid prototyping of designs and for validating other solution methods. We develop a general formulation of the multiple scattering problem that facilitates efficient application of the multipole-based method. The shape and morphology of the scatterers is not restricted, provided their T-matrices are available. The multipole method is implemented in the Tmatsolver software package, which uses our general formulation and the T-matrix methodology to simulate accurately multiple scattering by complex configurations with a large number of identical or non-identical scatterers that can have complex shapes and/or morphologies. This article provides a mathematical description of the algorithm and demonstrates application of the software to four contemporary metamaterial problems. It concludes with a brief overview of the object-oriented structure of the Tmatsolver code.

وصف الملف: application/pdf; text/xml

العلاقة: https://www.repository.cam.ac.uk/handle/1810/370094Test

الإتاحة: https://www.repository.cam.ac.uk/handle/1810/370094Test

المؤلفون: Hawkins, Stuart C, Bennetts, Luke G, Nethercote, Matthew A, Peter, Malte A, Peterseim, Daniel, Putley, Henry J, Verfürth, Barbara

مصطلحات موضوعية: metamaterials, wave propagation, Rayleigh–Bloch waves, T-matrix, multiple wave scattering

الوصف: Peer reviewed: True ; Publication status: Published ; Multiple scattering of waves is eminent in a wide range of applications and extensive research is being undertaken into multiple scattering by ever more complicated structures, with emphasis on the design of metamaterial structures that manipulate waves in a desired fashion. Ongoing research investigates the design of structures and new solution methods for the governing partial differential equations. There is a pressing need for easy-to-use software that empowers rapid prototyping of designs and for validating other solution methods. We develop a general formulation of the multiple scattering problem that facilitates efficient application of the multipole-based method. The shape and morphology of the scatterers is not restricted, provided their T-matrices are available. The multipole method is implemented in the T matsolver software package, which uses our general formulation and the T-matrix methodology to simulate accurately multiple scattering by complex configurations with a large number of identical or non-identical scatterers that can have complex shapes and/or morphologies. This article provides a mathematical description of the algorithm and demonstrates application of the software to four contemporary metamaterial problems. It concludes with a brief overview of the object-oriented structure of the T matsolver code.

وصف الملف: application/pdf; text/xml

العلاقة: https://www.repository.cam.ac.uk/handle/1810/369955Test

الإتاحة: https://www.repository.cam.ac.uk/handle/1810/369955Test

المؤلفون: Gower, AL, Parnell, WJ, Abrahams, ID

مصطلحات موضوعية: wave propagation, random media, inhomogeneous media, composite materials, backscattering, multiple scattering, ensemble averaging

الوصف: © 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved. For over 70 years it has been assumed that scalar wave propagation in (ensembleaveraged) random particulate materials can be characterized by a single effective wavenumber. Here, however, we show that there exist many effective wavenumbers, each contributing to the effective transmitted wave field. Most of these contributions rapidly attenuate away from boundaries, but they make a significant contribution to the reflected and total transmitted field beyond the low-frequency regime. In some cases at least two effective wavenumbers have the same order of attenuation. In these cases a single effective wavenumber does not accurately describe wave propagation even far away from boundaries. We develop an efficient method to calculate all of the contributions to the wave field for the scalar wave equation in two spatial dimensions, and then compare results with numerical finite-difference calculations. This new method is, to the best of the authors' knowledge, the first of its kind to give such accurate predictions across a broad frequency range and for general particle volume fractions.

وصف الملف: application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/301709Test

الإتاحة: https://doi.org/10.17863/CAM.48780Test
https://www.repository.cam.ac.uk/handle/1810/301709Test

المؤلفون: Magri, L

مصطلحات موضوعية: Adjoint equations, Acoustics, Wave propagation

الوصف: Adjoint methods enable the accurate calculation of the sensitivities of a quantity of interest. The sensitivity is obtained by solving the adjoint system, which can be derived by continuous or discrete adjoint strategies. In acoustic wave propagation, continuous and discrete adjoint methods have been developed to compute the eigenvalue sensitivity to design parameters and passive devices (Aguilar, J. G. et al, 2017, J. Computational Physics, vol. 341, 163-181). In this short communication, it is shown that the continuous and discrete adjoint characteristic decompositions, and Riemann invariants, are connected by a similarity transformation. The results are shown in the Laplace domain. The adjoint characteristic decomposition is applied to a one-dimensional acoustic resonator, which contains a monopole source of sound. The proposed framework provides the foundation to tackle larger acoustic networks with a discrete adjoint approach, opening up new possibilities for adjoint-based design of problems that can be solved by the method of characteristics.

وصف الملف: application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/291278Test

الإتاحة: https://doi.org/10.17863/CAM.38457Test
https://www.repository.cam.ac.uk/handle/1810/291278Test

المؤلفون: Gower, Artur L, Abrahams, I David, Parnell, William J

مصطلحات موضوعية: Wiener–Hopf, backscattering, ensemble averaging, multiple scattering, random media, wave propagation

الوصف: Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterize wave propagation through an inhomogeneous material, the most crucial parameter is the effective wavenumber. For this reason, there are many published studies on how to calculate a single effective wavenumber. Here, we present a proof that there does not exist a unique effective wavenumber; instead, there are an infinite number of such (complex) wavenumbers. We show that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field. However, to accurately calculate the reflection and transmission coefficients, a large number of the (highly attenuating) effective waves is required. For clarity, we present results for scalar (acoustic) waves for a two-dimensional material filled (over a half-space) with randomly distributed circular cylindrical inclusions. We calculate the effective medium by ensemble averaging over all possible inhomogeneities. The proof is based on the application of the Wiener-Hopf technique and makes no assumption on the wavelength, particle boundary conditions/size or volume fraction. This technique provides a simple formula for the reflection coefficient, which can be explicitly evaluated for monopole scatterers. We compare results with an alternative numerical matching method.

وصف الملف: Print-Electronic; application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/297015Test

الإتاحة: https://doi.org/10.17863/CAM.44056Test
https://www.repository.cam.ac.uk/handle/1810/297015Test

المؤلفون: Özgen, I, Zhao, JH, Liang, DF, Hinkelmann, R

مصطلحات موضوعية: Porosity, Macroscopic modeling of urban flooding, Wave propagation speed, Godunov flux, Single porosity shallow water model, Anisotropic porosity shallow water model

الوصف: In urban flood modeling, so-called porosity shallow water equations (PSWEs), which conceptually account for unresolved structures, e.g., buildings, are a promising approach to addressing high CPU times associated with state-of-the-art explicit numerical methods. The PSWE can be formulated with a single porosity term, referred to as the single porosity shallow water model (SP model), which accounts for both the reduced storage in the cell and the reduced conveyance, or with two porosity terms: one accounting for the reduced storage in the cell and another accounting for the reduced conveyance. The latter form is referred to as an integral or anisotropic porosity shallow water model (AP model). The aim of this study was to analyze the differences in wave propagation speeds of the SP model and the AP model and the implications of numerical model results. First, augmented Roe-type solutions were used to assess the influence of the source terms appearing in both models. It is shown that different source terms have different influences on the stability of the models. Second, four computational test cases were presented and the numerical models were compared. It is observed in the eigenvalue-based analysis as well as in the computational test cases that the models converge if the conveyance porosity in the AP model is close to the storage porosity. If the porosity values differ significantly, the AP model yields different wave propagation speeds and numerical fluxes from those of the BP model. In this study, the ratio between the conveyance and storage porosities was determined to be the most significant parameter.

وصف الملف: application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/275155Test

الإتاحة: https://doi.org/10.17863/CAM.22335Test
https://www.repository.cam.ac.uk/handle/1810/275155Test

المؤلفون: O'Kane, A, Copley, A

مصطلحات موضوعية: Earthquake ground motions, Earthquake hazards, Seismicity and tectonics, Wave propagation, Continental tectonics: compressional

الوصف: SUMMARYRapid urban growth has led to large population densities in foreland basin regions, and therefore a rapid increase in the number of people exposed to hazard from earthquakes in the adjacent mountain ranges. It is well known that earthquake-induced ground shaking is amplified in sedimentary basins. However, questions remain regarding the main controls on this effect. It is, therefore, crucial to identify the main controls on earthquake shaking in foreland basins as a step towards mitigating the earthquake risk posed to these regions. We model seismic-wave propagation from range-front thrust-faulting earthquakes in a foreland-basin setting. The basin geometry (depth and width) and source characteristics (fault dip and source-to-basin distance) were varied, and the resultant ground motion was calculated. We find that the source depth determines the amount of near-source ground shaking and the basin structure controls the propagation of this energy into the foreland basin. Of particular importance is the relative length scales of the basin depth and dominant seismic wavelength (controlled by the source characteristics), as this controls the amount of dispersion of surface-wave energy, and so the amplitude and duration of ground motion. The maximum ground motions occur when the basin depth matches the dominant wavelength set by the source. Basins that are shallow compared with the dominant wavelength result in low-amplitude and long-duration dispersed waveforms. However, the basin structure has a smaller effect on the ground shaking than the source depth and geometry, highlighting the need for understanding the depth distribution and dip angles of earthquakes when assessing earthquake hazard in foreland-basin settings. ; EPSRC iCASE PhD Studentship in collaboration with Ove Arup and Partners Ltd.

وصف الملف: application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/315188Test

الإتاحة: https://doi.org/10.17863/CAM.62296Test
https://www.repository.cam.ac.uk/handle/1810/315188Test

المؤلفون: Young, T. J., Schroeder, D. M., Jordan, T. M., Christoffersen, P., Tulaczyk, S. M., Culberg, R., Bienert, N. L.

مصطلحات موضوعية: BIOGEOSCIENCES, Biogeochemical kinetics and reaction modeling, Biogeochemical cycles, processes, and modeling, CRYOSPHERE, Glaciers, Ice streams, Glaciology, Biogeochemistry, Snow, Ice, GLOBAL CHANGE, Cryospheric change, HYDROLOGY, Snow and ice, OCEANOGRAPHY: BIOLOGICAL AND CHEMICAL, PALEOCEANOGRAPHY, RADIO SCIENCE, Radio wave propagation, Research Article, Antarctica, birefringence, fabric, ice penetrating radar, polarimetry

الوصف: In airborne radargrams, undulating periodic patterns in amplitude that overprint traditional radiostratigraphic layering are occasionally observed, however, they have yet to be analyzed from a geophysical or glaciological perspective. We present evidence supported by theory that these depth‐periodic patterns are consistent with a modulation of the received radar power due to the birefringence of polar ice, and therefore indicate the presence of bulk fabric anisotropy. Here, we investigate the periodic component of birefringence‐induced radar power recorded in airborne radar data at the eastern shear margin of Thwaites Glacier and quantify the lateral variation in azimuthal fabric strength across this margin. We find the depth variability of birefringence periodicity crossing the shear margin to be a visual expression of its shear state and its development, which appears consistent with present‐day ice deformation. The morphology of the birefringent patterns is centered at the location of maximum shear and observed in all cross‐margin profiles, consistent with predictions of ice fabric when subjected to simple shear. The englacial fabric appears stronger inside the ice stream than outward of the shear margin. The detection of birefringent periodicity from non‐polarimetric radargrams presents a novel use of subsurface radar to constrain lateral variations in fabric strength, locate present and past shear margins, and characterize the deformation history of polar ice sheets.

وصف الملف: text/xml; application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/323089Test

الإتاحة: https://doi.org/10.17863/CAM.70541Test
https://www.repository.cam.ac.uk/handle/1810/323089Test

المؤلفون: Leng, K, Nissen-Meyer, T, Van Driel, M, Hosseini, K, Al-Attar, D

مصطلحات موضوعية: Structure of the Earth, Numerical solutions, Computational seismology, Theoretical seismology, Wave propagation

الوصف: We present a novel numerical method to simulate global seismic wave propagation in realis- tic aspherical 3-D Earth models across the observable frequency band of global seismic data. Our method, named AxiSEM3D, is a hybrid of spectral element method and pseudo-spectral method. It describes the azimuthal dimension of global wavefields with a substantially reduced number of degrees of freedom via a global Fourier series parametrisation, of which the num- ber of terms can be locally adapted to the inherent azimuthal complexity of the wavefields. AxiSEM3D allows for material heterogeneities, such as velocity, density, anisotropy and at- tenuation, as well as for finite undulations on radial discontinuities, both solid-solid and solid- fluid, and thereby a variety of aspherical Earth features such as ellipticity, surface topography, variable crustal thickness, undulating transition zone and core-mantle boundary topography. Undulating discontinuities are honoured by means of the “particle relabelling transformation”, so that the spectral element mesh can be kept spherical. The implementation of the particle relabelling transformation is verified by benchmark solutions against a discretised 3-D spectral element method, considering ellipticity, topography and bathymetry (with the ocean approxi- mated as a hydrodynamic load) and a tomographic mantle model with an undulating transition zone. For the state-of-the-art global tomographic models with aspherical geometry but without a 3-D crust, efficiency comparisons suggest that AxiSEM3D can be 2 to 3 orders of magnitude faster than a discretised 3-D method for a seismic period at 5 s or below, with the speed-up in- creasing with frequency and decreasing with model complexity. We also verify AxiSEM3D for localised small-scale heterogeneities with strong perturbation strength. With reasonable com- puting resources, we have achieved a corner frequency up to 1 Hz for 3-D mantle models.

وصف الملف: application/pdf

العلاقة: https://www.repository.cam.ac.uk/handle/1810/296532Test

الإتاحة: https://doi.org/10.17863/CAM.43579Test
https://www.repository.cam.ac.uk/handle/1810/296532Test