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Hyperbolic Systems of Conservation Laws [chapter]

C. M. Dafermos
1983 Systems of Nonlinear Partial Differential Equations  
This construction may yield highly oscillatory solutions, a manifestation of instability.  ...  In the Riemann problem for (4.1), a jump discontinuity between two nearby constant states L7_ and U+ is resolved into a wave fan, which is a superposition of n z-wave fans, one from each characteristic  ... 
doi:10.1007/978-94-009-7189-9_2 fatcat:zj3cocevzrd3zcjs5oht55cudm

Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory

Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, Antoine B. Jacquey
2021 Solid Earth  
We propose a multiscale approach for coupling multi-physics processes across the scales.  ...  A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead  ...  We thank Emily and Anders Crofoot of Castlepoint Station (NZ) for their hospitality and access to the beautiful rocks on their property.  ... 
doi:10.5194/se-12-869-2021 fatcat:sc5jydcpffazvihoy5zfcbpmim

An exponential transformation based splitting method for fast computations of highly oscillatory solutions

Qin Sheng, Shekhar Guha, Leonel P. Gonzalez
2011 Journal of Computational and Applied Mathematics  
This paper studies an alternative way for solving highly oscillatory paraxial wave problems via a modified splitting strategy.  ...  MSC: 65M06 65M50 65Z05 78A15 78M20 Keywords: Splitting method Transformations Linear and nonlinear equations Highly oscillatory wave problems Asymptotic stability Algorithmic efficiency a b s t r a c t  ...  Acknowledgments The authors would like to thank their colleagues for many discussions which helped to improve the study of fast numerical methods for highly oscillatory wave problems.  ... 
doi:10.1016/j.cam.2011.04.013 fatcat:kvegerx5dzhxdgnoazbddelc44

Decomposing non-stationary signals with time-varying wave-shape functions [article]

Marcelo A. Colominas, Hau-Tieng Wu
2021 arXiv   pre-print
We propose a novel nonlinear regression scheme to robustly decompose a signal into its constituting multiple oscillatory components with time-varying frequency, amplitude and wave-shape function.  ...  The signal processing mission is further challenged if each component has an oscillatory pattern, or the wave-shape function, far from a sinusoidal function, and the oscillatory pattern is even changing  ...  We applied the four methods to decompose an IP signal of 60 s long. We used a Gaussian window with σ = 0.05, a maximum jump of 2 Hz and ∆ = 2Hz, for the estimation of amplitudes and phases.  ... 
arXiv:2010.07394v2 fatcat:bcept6dlbbduzb5nft4hpi3bwa

Color Image Compression Based On Wavelet Packet Best Tree [article]

G. K. Kharate, V. H. Patil
2010 arXiv   pre-print
This method reduces the time complexity of wavelet packets decomposition as complete tree is not decomposed.  ...  Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression.  ...  This problem appears to be worse in JPEG than in JPEG-2000 [9] . Both JPEG-2000 and JPEG operate in spectral domain, trying to represent the image as a sum of smooth oscillating waves.  ... 
arXiv:1004.3276v1 fatcat:4aar7kw3vzblrcozt6lseyduxi

A domain decomposition method for conservation laws with discontinuous flux function

Michael Herty, Mohammed Seaïd, Anita K. Singh
2007 Applied Numerical Mathematics  
The associated conservation law for each subdomain having then a continuous flux function is solved using a nonoscillatory relaxation scheme.  ...  A domain decomposition method for scalar conservation laws with discontinuous flux function is presented.  ...  For instance, a third-order reconstruction for numerical fluxes in (3.6) based on essentially non-oscillatory method has been studied in [2, 3, 21] .  ... 
doi:10.1016/j.apnum.2006.04.003 fatcat:5ixepazd2jdsbc5uuxxltkfyde

Numerically efficient spectral representations for guided ocean acoustics

L.B. Felsen
1985 Computers and Mathematics with Applications  
Such representations, usually employed for range-independent oceans, can take the form of spectral integrals, of normal mode expansions with or (approximately) without continuous spectra, and of generalized  ...  decay and are only weakly oscillatory.  ...  However, since a single universal algorithm for all problems is presently far beyond reach, it is necessary to continue exploring new options which can complement existing ones. to modify them for greater  ... 
doi:10.1016/0898-1221(85)90165-8 fatcat:fvyjkmqjcbgoxfrwfiqu5dlt3q

Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes

Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, Antoine B. Jacquey, Piotr Szymczak (+1 others)
2021 Solid Earth  
Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale.  ...  In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike.  ...  We would especially like to acknowledge the thought-provoking experimental work of Francois Guillard and Itai Einav, as well as Barraclough et al., which may provide a new method for identification of  ... 
doi:10.5194/se-12-1829-2021 fatcat:zi4y3vq65ngkfjzrxxsi3lkyfq

Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis

Antonio Cicone, Jingfang Liu, Haomin Zhou
2016 Applied and Computational Harmonic Analysis  
These methods decompose a signal into a finite number of components on which the time-frequency analysis can be applied more effectively.  ...  Furthermore we design smooth filters with compact support from solutions of Fokker-Planck equations (FP filters) that can be used within both IF and ALIF methods.  ...  What is more important, denoising is automatically achieved by getting rid of the first few highly oscillatory IMFs.  ... 
doi:10.1016/j.acha.2016.03.001 fatcat:7l4eesvthzav3m2f6zgvvovyne

Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency analysis [article]

Antonio Cicone, Jingfang Liu, Haomin Zhou
2015 arXiv   pre-print
These methods decompose a signal into a finite number of components on which the time-frequency analysis can be applied more effectively.  ...  Furthermore we design smooth filters with compact support from solutions of Fokker-Planck equations (FP filters) that can be used within both IFs and ALIF methods.  ...  What is more important, denoising is automatically achieved by getting rid of the first few highly oscillatory IMFs.  ... 
arXiv:1411.6051v3 fatcat:din3aj3ixva2ve73eofnjve2ui

Empirical Mode Decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting

S. Sinclair, G. G. S. Pegram
2005 Hydrology and Earth System Sciences Discussions  
A data-driven method for extracting information, at temporally predictable scales, from spatial rainfall data (as measured by radar/satellite) is described, which extends the Empirical Mode Decomposition  ...  The EMD technique is used here to separate spatial rainfall data into a sequence of high through to 5 15 20 here to prepare the data for nowcasts based on the evolution of the lower frequency components  ...  The authors would like to thank the Water Research Commission of South Africa for supporting the work presented herein through contracts K5/1249 and K5/1425.  ... 
doi:10.5194/hessd-2-289-2005 fatcat:oplivmfw4fbdddz7r6x65igzyu

Empirical Mode Decomposition in 2-D space and time: a tool for space-time rainfall analysis and nowcasting

S. Sinclair, G. G. S. Pegram
2005 Hydrology and Earth System Sciences  
The EMD technique is used here to decompose spatial rainfall data into a sequence of high through to low frequency components.  ...  A data-driven method for extracting temporally persistent information, at different spatial scales, from rainfall data (as measured by radar/satellite) is described, which extends the Empirical Mode Decomposition  ...  The authors would like to thank the Water Research Commission of South Africa for supporting the work presented herein through contracts K5/1249 and K5/1425.  ... 
doi:10.5194/hess-9-127-2005 fatcat:wzapcvkn5fdwzoflc7uszlh6je

Stencil Selection Algorithms for WENO Schemes on Unstructured Meshes

Panagiotis Tsoutsanis
2019 Journal of Computational Physics  
In this paper, a family of stencil selection algorithms is presented for WENO schemes on unstructured meshes.  ...  The associated freedom of stencil selection for unstructured meshes, in the context of WENO schemes present a plethora of various stencil selection algorithms.  ...  grant EP/L000261/1 and the computing time on the University of Cambridge Tier-2 national high-performance computing service Peta4 provided through the EPSRC grant EP/P020259/1.  ... 
doi:10.1016/j.jcp.2019.07.039 fatcat:fml3t37p4nbidjqcl7pwhlzl34

Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems

M.J. Peake, J. Trevelyan, G. Coates
2013 Computer Methods in Applied Mechanics and Engineering  
When applied to wave problems, it has been shown that enriching BEM approximations with a partition-of-unity basis, in what has become known as the PU-BEM, allows highly accurate solutions to be obtained  ...  2013) 'Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems.', Computer methods in applied mechanics and engineering., 259 . pp. 93-102.  ...  The evaluation of the highly oscillatory plane waves in the XIBEM enrichment is also more expensive than evaluating a basis with only nodal values of potential and shape functions; however, this computational  ... 
doi:10.1016/j.cma.2013.03.016 fatcat:s4chjl7b6ve4rjg6qfsenrsx2e

Oscillation Preserving Galerkin Methods for Fredholm Integral Equations of the Second Kind with Oscillatory Kernels [article]

Yinkun Wang, Yuesheng Xu
2015 arXiv   pre-print
We then further propose oscillation preserving Galerkin methods for solving the equations by incorporating the standard approximation subspace of spline functions with a finite number of oscillatory functions  ...  For this purpose, we introduce a notion to describe the degree of oscillation of an oscillatory function based on the dependence of its norm in a certain function space on the wavenumber.  ...  We assume here that the forcing function is highly oscillatory with its oscillation being a combination of harmonic waves.  ... 
arXiv:1507.01156v2 fatcat:6cdqxfbx7bamhea5azvaffd4ei
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