WorldWideScience

Sample records for wave-equation reflection imaging

  1. Wave-equation reflection traveltime inversion

    KAUST Repository

    Zhang, Sanzong

    2011-01-01

    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

  2. Ultra Deep Wave Equation Imaging and Illumination

    Energy Technology Data Exchange (ETDEWEB)

    Alexander M. Popovici; Sergey Fomel; Paul Sava; Sean Crawley; Yining Li; Cristian Lupascu

    2006-09-30

    In this project we developed and tested a novel technology, designed to enhance seismic resolution and imaging of ultra-deep complex geologic structures by using state-of-the-art wave-equation depth migration and wave-equation velocity model building technology for deeper data penetration and recovery, steeper dip and ultra-deep structure imaging, accurate velocity estimation for imaging and pore pressure prediction and accurate illumination and amplitude processing for extending the AVO prediction window. Ultra-deep wave-equation imaging provides greater resolution and accuracy under complex geologic structures where energy multipathing occurs, than what can be accomplished today with standard imaging technology. The objective of the research effort was to examine the feasibility of imaging ultra-deep structures onshore and offshore, by using (1) wave-equation migration, (2) angle-gathers velocity model building, and (3) wave-equation illumination and amplitude compensation. The effort consisted of answering critical technical questions that determine the feasibility of the proposed methodology, testing the theory on synthetic data, and finally applying the technology for imaging ultra-deep real data. Some of the questions answered by this research addressed: (1) the handling of true amplitudes in the downward continuation and imaging algorithm and the preservation of the amplitude with offset or amplitude with angle information required for AVO studies, (2) the effect of several imaging conditions on amplitudes, (3) non-elastic attenuation and approaches for recovering the amplitude and frequency, (4) the effect of aperture and illumination on imaging steep dips and on discriminating the velocities in the ultra-deep structures. All these effects were incorporated in the final imaging step of a real data set acquired specifically to address ultra-deep imaging issues, with large offsets (12,500 m) and long recording time (20 s).

  3. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    KAUST Repository

    Zhang, Sanzong; Schuster, Gerard T.; Luo, Yi

    2012-01-01

    way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity

  4. Resolution limits for wave equation imaging

    KAUST Repository

    Huang, Yunsong

    2014-08-01

    Formulas are derived for the resolution limits of migration-data kernels associated with diving waves, primary reflections, diffractions, and multiple reflections. They are applicable to images formed by reverse time migration (RTM), least squares migration (LSM), and full waveform inversion (FWI), and suggest a multiscale approach to iterative FWI based on multiscale physics. That is, at the early stages of the inversion, events that only generate low-wavenumber resolution should be emphasized relative to the high-wavenumber resolution events. As the iterations proceed, the higher-resolution events should be emphasized. The formulas also suggest that inverting multiples can provide some low- and intermediate-wavenumber components of the velocity model not available in the primaries. Finally, diffractions can provide twice or better the resolution than specular reflections for comparable depths of the reflector and diffractor. The width of the diffraction-transmission wavepath is approximately λ at the diffractor location for the diffraction-transmission wavepath. © 2014 Elsevier B.V.

  5. Detecting breast microcalcifications using super-resolution and wave-equation ultrasound imaging: a numerical phantom study

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Lianjie [Los Alamos National Laboratory; Simonetti, Francesco [IMPERIAL COLLEGE LONDON; Huthwaite, Peter [IMPERIAL COLLEGE LONDON; Rosenberg, Robert [UNM; Williamson, Michael [UNM

    2010-01-01

    Ultrasound image resolution and quality need to be significantly improved for breast microcalcification detection. Super-resolution imaging with the factorization method has recently been developed as a promising tool to break through the resolution limit of conventional imaging. In addition, wave-equation reflection imaging has become an effective method to reduce image speckles by properly handling ultrasound scattering/diffraction from breast heterogeneities during image reconstruction. We explore the capabilities of a novel super-resolution ultrasound imaging method and a wave-equation reflection imaging scheme for detecting breast microcalcifications. Super-resolution imaging uses the singular value decomposition and a factorization scheme to achieve an image resolution that is not possible for conventional ultrasound imaging. Wave-equation reflection imaging employs a solution to the acoustic-wave equation in heterogeneous media to backpropagate ultrasound scattering/diffraction waves to scatters and form images of heterogeneities. We construct numerical breast phantoms using in vivo breast images, and use a finite-difference wave-equation scheme to generate ultrasound data scattered from inclusions that mimic microcalcifications. We demonstrate that microcalcifications can be detected at full spatial resolution using the super-resolution ultrasound imaging and wave-equation reflection imaging methods.

  6. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    KAUST Repository

    Zhang, Sanzong

    2012-11-04

    The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.

  7. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    KAUST Repository

    Zhang, Sanzong

    2015-05-26

    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  8. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    KAUST Repository

    Zhang, Sanzong; Luo, Yi; Schuster, Gerard T.

    2015-01-01

    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  9. Born reflection kernel analysis and wave-equation reflection traveltime inversion in elastic media

    KAUST Repository

    Wang, Tengfei

    2017-08-17

    Elastic reflection waveform inversion (ERWI) utilize the reflections to update the low and intermediate wavenumbers in the deeper part of model. However, ERWI suffers from the cycle-skipping problem due to the objective function of waveform residual. Since traveltime information relates to the background model more linearly, we use the traveltime residuals as objective function to update background velocity model using wave equation reflected traveltime inversion (WERTI). The reflection kernel analysis shows that mode decomposition can suppress the artifacts in gradient calculation. We design a two-step inversion strategy, in which PP reflections are firstly used to invert P wave velocity (Vp), followed by S wave velocity (Vs) inversion with PS reflections. P/S separation of multi-component seismograms and spatial wave mode decomposition can reduce the nonlinearity of inversion effectively by selecting suitable P or S wave subsets for hierarchical inversion. Numerical example of Sigsbee2A model validates the effectiveness of the algorithms and strategies for elastic WERTI (E-WERTI).

  10. Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

    KAUST Repository

    Wang, T.

    2017-05-26

    Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive and linearly related to the low-wavenumber model perturbation. Therefore, building initial P and S wave velocity models for EFWI by using elastic wave-equation reflections traveltime inversion (WERTI) would be effective and robust, especially for the deeper part. In order to distinguish the reflection travletimes of P or S-waves in elastic media, we decompose the surface multicomponent data into vector P- and S-wave seismogram. We utilize the dynamic image warping to extract the reflected P- or S-wave traveltimes. The P-wave velocity are first inverted using P-wave traveltime followed by the S-wave velocity inversion with S-wave traveltime, during which the wave mode decomposition is applied to the gradients calculation. Synthetic example on the Sigbee2A model proves the validity of our method for recovering the long wavelength components of the model.

  11. Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers

    KAUST Repository

    Guo, Bowen; Schuster, Gerard T.

    2017-01-01

    Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images

  12. Extended common-image-point gathers for anisotropic wave-equation migration

    KAUST Repository

    Sava, Paul C.; Alkhalifah, Tariq Ali

    2010-01-01

    In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes

  13. Multiple attenuation to reflection seismic data using Radon filter and Wave Equation Multiple Rejection (WEMR) method

    Energy Technology Data Exchange (ETDEWEB)

    Erlangga, Mokhammad Puput [Geophysical Engineering, Institut Teknologi Bandung, Ganesha Street no.10 Basic Science B Buliding fl.2-3 Bandung, 40132, West Java Indonesia puput.erlangga@gmail.com (Indonesia)

    2015-04-16

    Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, in case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.

  14. Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

    KAUST Repository

    Li, Jing; Schuster, Gerard T.; Zeng, Zhaofa

    2017-01-01

    A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method

  15. REFLECT: a program to integrate the wave equation through a plane stratified plasma

    International Nuclear Information System (INIS)

    Greene, J.W.

    1975-01-01

    A program was developed to integrate the wave equation through a plane stratified plasma with a general density distribution. The reflection and transmission of a plane wave are computed as a function of the angle of incidence. The polarization of the electric vector is assumed to be perpendicular to the plane of incidence. The model for absorption by classical inverse bremsstrahlung avoids the improper extrapolation of underdense formulae that are singular at the plasma critical surface. Surprisingly good agreement with the geometric-optics analysis of a linear layer was found. The system of ordinary differential equations is integrated by the variable-step, variable-order Adams method in the Lawrence Livermore Laboratory Gear package. Parametric studies of the absorption are summarized, and some possibilities for further development of the code are discussed. (auth)

  16. Born reflection kernel analysis and wave-equation reflection traveltime inversion in elastic media

    KAUST Repository

    Wang, Tengfei; Cheng, Jiubing

    2017-01-01

    Elastic reflection waveform inversion (ERWI) utilize the reflections to update the low and intermediate wavenumbers in the deeper part of model. However, ERWI suffers from the cycle-skipping problem due to the objective function of waveform residual

  17. Extended common-image-point gathers for anisotropic wave-equation migration

    KAUST Repository

    Sava, Paul C.

    2010-01-01

    In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes anisotropy parameters (Gray et al., 2001). In particular, it is important to construct subsurface velocity models using techniques that are consistent with the methods used for imaging. Generally speaking, there are two possible strategies for velocity estimation from surface seismic data in the context of wavefield-based imaging (Sava et al., 2010). One possibility is to formulate an objective function in the data space, prior to migration, by matching the recorded data with simulated data. Techniques in this category are known by the name of waveform inversion. Another possibility is to formulate an objective function in the image space, after migration, by measuring and correcting image features that indicate model inaccuracies. Techniques in this category are known as wave-equation migration velocity analysis (MVA).

  18. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Synthetic and field data examples

    KAUST Repository

    Zhang, Sanzong

    2015-05-26

    Full-waveform inversion requires the accurate simulation of the dynamics and kinematics of wave propagation. This is difficult in practice because the amplitudes cannot be precisely reproduced for seismic waves in the earth. Wave-equation reflection traveltime tomography (WT) is proposed to avoid this problem by directly inverting the reflection-traveltime residuals without the use of the high-frequency approximation. We inverted synthetic traces and recorded seismic data for the velocity model by WT. Our results demonstrated that the wave-equation solution overcame the high-frequency approximation of ray-based tomography, was largely insensitive to the accurate modeling of amplitudes, and mitigated problems with ambiguous event identification. The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime residual estimation for complex models.

  19. Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers

    KAUST Repository

    Guo, Bowen

    2017-06-01

    Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, a WEMVA method using plane-wave CIGs is presented. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic datasets and a field dataset validate the efficiency and effectiveness of this method.

  20. Angle gathers in wave-equation imaging for transversely isotropic media

    KAUST Repository

    Alkhalifah, Tariq Ali; Fomel, Sergey B.

    2010-01-01

    In recent years, wave-equation imaged data are often presented in common-image angle-domain gathers as a decomposition in the scattering angle at the reflector, which provide a natural access to analysing migration velocities and amplitudes. In the case of anisotropic media, the importance of angle gathers is enhanced by the need to properly estimate multiple anisotropic parameters for a proper representation of the medium. We extract angle gathers for each downward-continuation step from converting offset-frequency planes into angle-frequency planes simultaneously with applying the imaging condition in a transversely isotropic with a vertical symmetry axis (VTI) medium. The analytic equations, though cumbersome, are exact within the framework of the acoustic approximation. They are also easily programmable and show that angle gather mapping in the case of anisotropic media differs from its isotropic counterpart, with the difference depending mainly on the strength of anisotropy. Synthetic examples demonstrate the importance of including anisotropy in the angle gather generation as mapping of the energy is negatively altered otherwise. In the case of a titled axis of symmetry (TTI), the same VTI formulation is applicable but requires a rotation of the wavenumbers. © 2010 European Association of Geoscientists & Engineers.

  1. Angle gathers in wave-equation imaging for transversely isotropic media

    KAUST Repository

    Alkhalifah, Tariq Ali

    2010-11-12

    In recent years, wave-equation imaged data are often presented in common-image angle-domain gathers as a decomposition in the scattering angle at the reflector, which provide a natural access to analysing migration velocities and amplitudes. In the case of anisotropic media, the importance of angle gathers is enhanced by the need to properly estimate multiple anisotropic parameters for a proper representation of the medium. We extract angle gathers for each downward-continuation step from converting offset-frequency planes into angle-frequency planes simultaneously with applying the imaging condition in a transversely isotropic with a vertical symmetry axis (VTI) medium. The analytic equations, though cumbersome, are exact within the framework of the acoustic approximation. They are also easily programmable and show that angle gather mapping in the case of anisotropic media differs from its isotropic counterpart, with the difference depending mainly on the strength of anisotropy. Synthetic examples demonstrate the importance of including anisotropy in the angle gather generation as mapping of the energy is negatively altered otherwise. In the case of a titled axis of symmetry (TTI), the same VTI formulation is applicable but requires a rotation of the wavenumbers. © 2010 European Association of Geoscientists & Engineers.

  2. Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

    KAUST Repository

    Li, Jing

    2017-12-22

    A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method with synthetic seismograms and field data. The benefits of WD are that 1) there is no layered medium assumption, as there is in conventional inversion of dispersion curves, so that the 2D or 3D S-velocity model can be reliably obtained with seismic surveys over rugged topography, and 2) WD mostly avoids getting stuck in local minima. The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic media and the inversion of dispersion curves associated with Love wave. The liability is that is almost as expensive as FWI and only recovers the Vs distribution to a depth no deeper than about 1/2~1/3 wavelength.

  3. Seismic Imaging, One-Way Wave Equations, Pseudodifferential Operators, Path Integrals, and all that Jazz

    Science.gov (United States)

    Artoun, Ojenie; David-Rus, Diana; Emmett, Matthew; Fishman, Lou; Fital, Sandra; Hogan, Chad; Lim, Jisun; Lushi, Enkeleida; Marinov, Vesselin

    2006-05-01

    In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.

  4. True amplitude wave equation migration arising from true amplitude one-way wave equations

    Science.gov (United States)

    Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

    2003-10-01

    One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

  5. Azimuth and angle gathers from wave equation imaging in VTI media

    KAUST Repository

    Alkhalifah, Tariq Ali

    2009-01-01

    Angles in common-image angle domain gathers refer to the scattering angle at the reflector and provide a natural access to analyzing migration velocities and amplitudes. In the case of anisotropic media, the importance of angle gathers is enhanced by the need to properly estimate multiple anisotropic parameters for a proper representation of the medium. We extract angle gathers for each downward-continuation step from converting offset-space-frequency planes into angle-space planes simultaneously with applying the imaging condition in a transversely isotropic (VTI) medium. The analytic equations, though cumbersome, are exact within the framework of the acoustic approximation. They are also easily programmable and show that angle gather mapping in the case anisotropic media differs from its isotropic counterpart, difference depending mainly on the strength of anisotropy.

  6. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  7. Wave-equation Q tomography

    KAUST Repository

    Dutta, Gaurav

    2016-10-12

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

  8. Wave-equation Q tomography

    KAUST Repository

    Dutta, Gaurav; Schuster, Gerard T.

    2016-01-01

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

  9. Skeletonized Least Squares Wave Equation Migration

    KAUST Repository

    Zhan, Ge; Schuster, Gerard T.

    2010-01-01

    of the wave equation. Only the early‐arrivals of these Green's functions are saved and skeletonized to form the migration Green's function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF

  10. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing; Feng, Zongcai; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

  11. Skeletonized Least Squares Wave Equation Migration

    KAUST Repository

    Zhan, Ge

    2010-10-17

    The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

  12. Skeletonized wave-equation inversion for Q

    KAUST Repository

    Dutta, Gaurav

    2016-09-06

    A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

  13. Skeletonized wave-equation inversion for Q

    KAUST Repository

    Dutta, Gaurav; Schuster, Gerard T.

    2016-01-01

    A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

  14. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  15. Wave equation of hydrogen atom

    International Nuclear Information System (INIS)

    Suwito.

    1977-01-01

    The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)

  16. The relativistic electron wave equation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1977-08-01

    The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

  17. Wave equations in higher dimensions

    CERN Document Server

    Dong, Shi-Hai

    2011-01-01

    Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

  18. Linear superposition solutions to nonlinear wave equations

    International Nuclear Information System (INIS)

    Liu Yu

    2012-01-01

    The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

  19. Wave-equation reflection traveltime inversion

    KAUST Repository

    Zhang, Sanzong; Schuster, Gerard T.; Luo, Yi

    2011-01-01

    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear

  20. Wave-equation Q tomography and least-squares migration

    KAUST Repository

    Dutta, Gaurav

    2016-03-01

    This thesis designs new methods for Q tomography and Q-compensated prestack depth migration when the recorded seismic data suffer from strong attenuation. A motivation of this work is that the presence of gas clouds or mud channels in overburden structures leads to the distortion of amplitudes and phases in seismic waves propagating inside the earth. If the attenuation parameter Q is very strong, i.e., Q<30, ignoring the anelastic effects in imaging can lead to dimming of migration amplitudes and loss of resolution. This, in turn, adversely affects the ability to accurately predict reservoir properties below such layers. To mitigate this problem, I first develop an anelastic least-squares reverse time migration (Q-LSRTM) technique. I reformulate the conventional acoustic least-squares migration problem as a viscoacoustic linearized inversion problem. Using linearized viscoacoustic modeling and adjoint operators during the least-squares iterations, I show with numerical tests that Q-LSRTM can compensate for the amplitude loss and produce images with better balanced amplitudes than conventional migration. To estimate the background Q model that can be used for any Q-compensating migration algorithm, I then develop a wave-equation based optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through numerical tests on synthetic and field data, I show that noticeable improvements in the migration image quality can be obtained from Q models inverted using wave-equation Q tomography. A key feature of skeletonized inversion is that it is much less likely to get stuck in a local minimum than a standard waveform inversion method. Finally, I develop a preconditioning technique for least-squares migration using a directional Gabor-based preconditioning approach for isotropic

  1. Wave equations for pulse propagation

    International Nuclear Information System (INIS)

    Shore, B.W.

    1987-01-01

    Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

  2. Some isometrical identities in the wave equation

    Directory of Open Access Journals (Sweden)

    Saburou Saitoh

    1984-01-01

    Full Text Available We consider the usual wave equation utt(x,t=c2uxx(x,t on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.

  3. Subsurface offset behaviour in velocity analysis with extended reflectivity images

    NARCIS (Netherlands)

    Mulder, W.A.

    2013-01-01

    Migration velocity analysis with the constant-density acoustic wave equation can be accomplished by the focusing of extended migration images, obtained by introducing a subsurface shift in the imaging condition. A reflector in a wrong velocity model will show up as a curve in the extended image. In

  4. Diffusion phenomenon for linear dissipative wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

  5. The damped wave equation with unbounded damping

    Czech Academy of Sciences Publication Activity Database

    Freitas, P.; Siegl, Petr; Tretter, C.

    2018-01-01

    Roč. 264, č. 12 (2018), s. 7023-7054 ISSN 0022-0396 Institutional support: RVO:61389005 Keywords : damped wave equation * unbounded damping * essential spectrum * quadratic operator funciton with unbounded coefficients * Schrodinger operators with complex potentials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

  6. Resolution limits for wave equation imaging

    KAUST Repository

    Huang, Yunsong; Schuster, Gerard T.

    2014-01-01

    migration (LSM), and full waveform inversion (FWI), and suggest a multiscale approach to iterative FWI based on multiscale physics. That is, at the early stages of the inversion, events that only generate low-wavenumber resolution should be emphasized

  7. Subsurface offset behaviour in velocity analysis with extended reflectivity images

    NARCIS (Netherlands)

    Mulder, W.A.

    2012-01-01

    Migration velocity analysis with the wave equation can be accomplished by focusing of extended migration images, obtained by introducing a subsurface offset or shift. A reflector in the wrong velocity model will show up as a curve in the extended image. In the correct model, it should collapse to a

  8. Blowing-up Semilinear Wave Equation with Exponential ...

    Indian Academy of Sciences (India)

    Blowing-up Semilinear Wave Equation with Exponential Nonlinearity in Two Space ... We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. ... Current Issue

  9. Skeletonized wave equation of surface wave dispersion inversion

    KAUST Repository

    Li, Jing; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel

  10. Relativistic wave equations and compton scattering

    International Nuclear Information System (INIS)

    Sutanto, S.H.; Robson, B.A.

    1998-01-01

    Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

  11. Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

    KAUST Repository

    Dutta, Gaurav

    2013-08-20

    Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.

  12. Bifurcation of the spin-wave equations

    International Nuclear Information System (INIS)

    Cascon, A.; Koiller, J.; Rezende, S.M.

    1990-01-01

    We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)

  13. The damped wave equation with unbounded damping

    Science.gov (United States)

    Freitas, Pedro; Siegl, Petr; Tretter, Christiane

    2018-06-01

    We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential. These analytic results are illustrated by examples.

  14. Seismic reflection imaging, accounting for primary and multiple reflections

    Science.gov (United States)

    Wapenaar, Kees; van der Neut, Joost; Thorbecke, Jan; Broggini, Filippo; Slob, Evert; Snieder, Roel

    2015-04-01

    Imaging of seismic reflection data is usually based on the assumption that the seismic response consists of primary reflections only. Multiple reflections, i.e. waves that have reflected more than once, are treated as primaries and are imaged at wrong positions. There are two classes of multiple reflections, which we will call surface-related multiples and internal multiples. Surface-related multiples are those multiples that contain at least one reflection at the earth's surface, whereas internal multiples consist of waves that have reflected only at subsurface interfaces. Surface-related multiples are the strongest, but also relatively easy to deal with because the reflecting boundary (the earth's surface) is known. Internal multiples constitute a much more difficult problem for seismic imaging, because the positions and properties of the reflecting interfaces are not known. We are developing reflection imaging methodology which deals with internal multiples. Starting with the Marchenko equation for 1D inverse scattering problems, we derived 3D Marchenko-type equations, which relate reflection data at the surface to Green's functions between virtual sources anywhere in the subsurface and receivers at the surface. Based on these equations, we derived an iterative scheme by which these Green's functions can be retrieved from the reflection data at the surface. This iterative scheme requires an estimate of the direct wave of the Green's functions in a background medium. Note that this is precisely the same information that is also required by standard reflection imaging schemes. However, unlike in standard imaging, our iterative Marchenko scheme retrieves the multiple reflections of the Green's functions from the reflection data at the surface. For this, no knowledge of the positions and properties of the reflecting interfaces is required. Once the full Green's functions are retrieved, reflection imaging can be carried out by which the primaries and multiples are

  15. Wave equations on anti self dual (ASD) manifolds

    Science.gov (United States)

    Bashingwa, Jean-Juste; Kara, A. H.

    2017-11-01

    In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

  16. Wide-azimuth angle gathers for anisotropic wave-equation migration

    KAUST Repository

    Sava, Paul C.

    2012-10-15

    Extended common-image-point gathers (CIP) constructed by wide-azimuth TI wave-equation migration contain all the necessary information for angle decomposition as a function of the reflection and azimuth angles at selected locations in the subsurface. The aperture and azimuth angles are derived from the extended images using analytic relations between the space- and time-lag extensions using information which is already available at the time of migration, i.e. the anisotropic model parameters. CIPs are cheap to compute because they can be distributed in the image at the most relevant positions, as indicated by the geologic structure. If the reflector dip is known at the CIP locations, then the computational cost can be reduced by evaluating only two components of the space-lag vector. The transformation from extended images to angle gathers is a planar Radon transform which depends on the local medium parameters. This transformation allows us to separate all illumination directions for a given experiment, or between different experiments. We do not need to decompose the reconstructed wavefields or to choose the most energetic directions for decomposition. Applications of the method include illumination studies in complex areas where ray-based methods fail, and assuming that the subsurface illumination is sufficiently dense, the study of amplitude variation with aperture and azimuth angles. © 2012 European Association of Geoscientists & Engineers.

  17. Wide-azimuth angle gathers for anisotropic wave-equation migration

    KAUST Repository

    Sava, Paul C.; Alkhalifah, Tariq Ali

    2012-01-01

    Extended common-image-point gathers (CIP) constructed by wide-azimuth TI wave-equation migration contain all the necessary information for angle decomposition as a function of the reflection and azimuth angles at selected locations in the subsurface. The aperture and azimuth angles are derived from the extended images using analytic relations between the space- and time-lag extensions using information which is already available at the time of migration, i.e. the anisotropic model parameters. CIPs are cheap to compute because they can be distributed in the image at the most relevant positions, as indicated by the geologic structure. If the reflector dip is known at the CIP locations, then the computational cost can be reduced by evaluating only two components of the space-lag vector. The transformation from extended images to angle gathers is a planar Radon transform which depends on the local medium parameters. This transformation allows us to separate all illumination directions for a given experiment, or between different experiments. We do not need to decompose the reconstructed wavefields or to choose the most energetic directions for decomposition. Applications of the method include illumination studies in complex areas where ray-based methods fail, and assuming that the subsurface illumination is sufficiently dense, the study of amplitude variation with aperture and azimuth angles. © 2012 European Association of Geoscientists & Engineers.

  18. Skeletonized wave equation of surface wave dispersion inversion

    KAUST Repository

    Li, Jing

    2016-09-06

    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

  19. Anisotropic wave-equation traveltime and waveform inversion

    KAUST Repository

    Feng, Shihang; Schuster, Gerard T.

    2016-01-01

    The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially

  20. Wave Equation Inversion of Skeletonized SurfaceWaves

    KAUST Repository

    Zhang, Zhendong; Liu, Yike; Schuster, Gerard T.

    2015-01-01

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve

  1. Exponential decay for solutions to semilinear damped wave equation

    KAUST Repository

    Gerbi, Sté phane; Said-Houari, Belkacem

    2011-01-01

    This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data

  2. Local energy decay for linear wave equations with variable coefficients

    Science.gov (United States)

    Ikehata, Ryo

    2005-06-01

    A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

  3. Anisotropic wave-equation traveltime and waveform inversion

    KAUST Repository

    Feng, Shihang

    2016-09-06

    The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.

  4. Automatic specular reflections removal for endoscopic images

    Science.gov (United States)

    Tan, Ke; Wang, Bin; Gao, Yuan

    2017-07-01

    Endoscopy imaging is utilized to provide a realistic view about the surfaces of organs inside the human body. Owing to the damp internal environment, these surfaces usually have a glossy appearance showing specular reflections. For many computer vision algorithms, the highlights created by specular reflections may become a significant source of error. In this paper, we present a novel method for restoration of the specular reflection regions from a single image. Specular restoration process starts with generating a substitute specular-free image with RPCA method. Then the specular removed image was obtained by taking the binary weighting template of highlight regions as the weighting for merging the original specular image and the substitute image. The modified template was furthermore discussed for the concealment of artificial effects in the edge of specular regions. Experimental results on the removal of the endoscopic image with specular reflections demonstrate the efficiency of the proposed method comparing to the existing methods.

  5. Nonlinear vibrations and the wave equation

    CERN Document Server

    Haraux, Alain

    2018-01-01

    This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.

  6. Separate P‐ and SV‐wave equations for VTI media

    KAUST Repository

    Pestana, Reynam C.; Ursin, Bjø rn; Stoffa, Paul L.

    2011-01-01

    In isotropic media we use the scalar acoustic wave equation to perform reverse time migration RTM of the recorded pressure wavefleld data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic VTI media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SV-waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where ε - δ is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method REM to propagate the waveflelds in time. © 2011 Society of Exploration Geophysicists.

  7. Linear fractional diffusion-wave equation for scientists and engineers

    CERN Document Server

    Povstenko, Yuriy

    2015-01-01

    This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

  8. N-body bound state relativistic wave equations

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1988-06-01

    The manifestly covariant formalism with constraints is used for the construction of relativistic wave equations to describe the dynamics of N interacting spin 0 and/or spin 1/2 particles. The total and relative time evolutions of the system are completely determined by means of kinematic type wave equations. The internal dynamics of the system is 3 N-1 dimensional, besides the contribution of the spin degrees of freedom. It is governed by a single dynamical wave equation, that determines the eigenvalue of the total mass squared of the system. The interaction is introduced in a closed form by means of two-body potentials. The system satisfies an approximate form of separability

  9. Relativistic covariant wave equations and acausality in external fields

    International Nuclear Information System (INIS)

    Pijlgroms, R.B.J.

    1980-01-01

    The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)

  10. Wave Equation Inversion of Skeletonized SurfaceWaves

    KAUST Repository

    Zhang, Zhendong

    2015-08-19

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.

  11. Unified formulation of radiation conditions for the wave equation

    DEFF Research Database (Denmark)

    Krenk, Steen

    2002-01-01

    A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second......-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choice of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms...

  12. An Unconditionally Stable Method for Solving the Acoustic Wave Equation

    Directory of Open Access Journals (Sweden)

    Zhi-Kai Fu

    2015-01-01

    Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.

  13. Four-Mirror Freeform Reflective Imaging Systems

    Data.gov (United States)

    National Aeronautics and Space Administration — Central Objectives: The research involves a revelation of the solution space for revolutionary families of four-mirror freeform reflective imaging systems. A...

  14. Semilinear damped wave equation in locally uniform spaces

    Czech Academy of Sciences Publication Activity Database

    Michálek, Martin; Pražák, D.; Slavík, J.

    2017-01-01

    Roč. 16, č. 5 (2017), s. 1673-1695 ISSN 1534-0392 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : damped wave equations * nonlinear damping * unbounded domains Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.801, year: 2016 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14110

  15. Topological horseshoes in travelling waves of discretized nonlinear wave equations

    International Nuclear Information System (INIS)

    Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming

    2014-01-01

    Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes

  16. ''Localized'' tachyonic wavelet-solutions of the wave equation

    International Nuclear Information System (INIS)

    Barut, A.O.; Chandola, H.C.

    1993-05-01

    Localized-nonspreading, wavelet-solutions of the wave equation □φ=0 with group velocity v>c and phase velocity u=c 2 /v< c are constructed explicitly by two different methods. Some recent experiments seem to find evidence for superluminal group velocities. (author). 7 refs, 2 figs

  17. Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations

    Directory of Open Access Journals (Sweden)

    Waheed A. Ahmed

    2017-11-01

    Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.

  18. Quadratic algebras in the noncommutative integration method of wave equation

    International Nuclear Information System (INIS)

    Varaksin, O.L.

    1995-01-01

    The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras

  19. Analysis of wave equation in electromagnetic field by Proca equation

    International Nuclear Information System (INIS)

    Pamungkas, Oky Rio; Soeparmi; Cari

    2017-01-01

    This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

  20. The scalar wave equation in a Schwarzschild spacetime

    International Nuclear Information System (INIS)

    Stewart, J.M.; Schmidt, B.G.

    1978-09-01

    This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild spacetime in a neighbourhood of spatial infinity, which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which accurs in a flat spacetime. (orig.) [de

  1. Topological horseshoes in travelling waves of discretized nonlinear wave equations

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)

    2014-04-15

    Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

  2. The wave equation on a curved space-time

    International Nuclear Information System (INIS)

    Friedlander, F.G.

    1975-01-01

    It is stated that chapters on differential geometry, distribution theory, and characteristics and the propagation of discontinuities are preparatory. The main matter is in three chapters, entitled: fundamental solutions, representation theorems, and wave equations on n-dimensional space-times. These deal with general construction of fundamental solutions and their application to the Cauchy problem. (U.K.)

  3. Exponential decay for solutions to semilinear damped wave equation

    KAUST Repository

    Gerbi, Stéphane

    2011-10-01

    This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].

  4. An inhomogeneous wave equation and non-linear Diophantine approximation

    DEFF Research Database (Denmark)

    Beresnevich, V.; Dodson, M. M.; Kristensen, S.

    2008-01-01

    A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...

  5. Scattering for wave equations with dissipative terms in layered media

    Directory of Open Access Journals (Sweden)

    Mitsuteru Kadowaki

    2011-05-01

    Full Text Available In this article, we show the existence of scattering solutions to wave equations with dissipative terms in layered media. To analyze the wave propagation in layered media, it is necessary to handle singular points called thresholds in the spectrum. Our main tools are Kato's smooth perturbation theory and some approximate operators.

  6. Rarita-Schwinger field and multicomponent wave equation

    International Nuclear Information System (INIS)

    Kaloshin, A.E.; Lomov, V.P.

    2011-01-01

    We suggest a simple method to solve a wave equation for Rarita-Schwinger field without additional constraints. This method based on the use of off-shell projection operators allows one to diagonalize spin-1/2 sector of the field

  7. A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

    Science.gov (United States)

    Wapenaar, Kees

    2017-06-01

    A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.

  8. Skeletonized Wave Equation Inversion in VTI Media without too much Math

    KAUST Repository

    Feng, Shihang

    2017-05-17

    We present a tutorial for skeletonized inversion of pseudo-acoustic anisotropic VTI data. We first invert for the anisotropic models using wave equation traveltime inversion. Here, the skeletonized data are the traveltimes of transmitted and/or reflected arrivals that lead to simpler misfit functions and more robust convergence compared to full waveform inversion. This provides a good starting model for waveform inversion. The effectiveness of this procedure is illustrated with synthetic data examples and a marine data set recorded in the Gulf of Mexico.

  9. Skeletonized Wave Equation Inversion in VTI Media without too much Math

    KAUST Repository

    Feng, Shihang; Schuster, Gerard T.

    2017-01-01

    We present a tutorial for skeletonized inversion of pseudo-acoustic anisotropic VTI data. We first invert for the anisotropic models using wave equation traveltime inversion. Here, the skeletonized data are the traveltimes of transmitted and/or reflected arrivals that lead to simpler misfit functions and more robust convergence compared to full waveform inversion. This provides a good starting model for waveform inversion. The effectiveness of this procedure is illustrated with synthetic data examples and a marine data set recorded in the Gulf of Mexico.

  10. Paraxial WKB solution of a scalar wave equation

    International Nuclear Information System (INIS)

    Pereverzev, G.V.

    1993-04-01

    An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)

  11. Finite element and discontinuous Galerkin methods for transient wave equations

    CERN Document Server

    Cohen, Gary

    2017-01-01

    This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...

  12. Asymptotic solutions and spectral theory of linear wave equations

    International Nuclear Information System (INIS)

    Adam, J.A.

    1982-01-01

    This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

  13. Control Operator for the Two-Dimensional Energized Wave Equation

    Directory of Open Access Journals (Sweden)

    Sunday Augustus REJU

    2006-07-01

    Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

  14. Hidden regularity for a strongly nonlinear wave equation

    International Nuclear Information System (INIS)

    Rivera, J.E.M.

    1988-08-01

    The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt

  15. On the Stochastic Wave Equation with Nonlinear Damping

    International Nuclear Information System (INIS)

    Kim, Jong Uhn

    2008-01-01

    We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping

  16. Invariant measures for stochastic nonlinear beam and wave equations

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Ondreját, Martin; Seidler, Jan

    2016-01-01

    Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf

  17. A wave equation interpolating between classical and quantum mechanics

    Science.gov (United States)

    Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

    2015-10-01

    We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

  18. Wave-equation Qs Inversion of Skeletonized Surface Waves

    KAUST Repository

    Li, Jing

    2017-02-08

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  19. Periodic solutions for one dimensional wave equation with bounded nonlinearity

    Science.gov (United States)

    Ji, Shuguan

    2018-05-01

    This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

  20. Skeletonized wave-equation Qs tomography using surface waves

    KAUST Repository

    Li, Jing

    2017-08-17

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy.

  1. Wave-equation Qs Inversion of Skeletonized Surface Waves

    KAUST Repository

    Li, Jing; Dutta, Gaurav; Schuster, Gerard T.

    2017-01-01

    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  2. Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

    KAUST Repository

    Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

    2018-01-01

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes

  3. An acoustic wave equation for pure P wave in 2D TTI media

    KAUST Repository

    Zhan, Ge; Pestana, Reynam C.; Stoffa, Paul L.

    2011-01-01

    In this paper, a pure P wave equation for an acoustic 2D TTI media is derived. Compared with conventional TTI coupled equations, the resulting equation is unconditionally stable due to the complete isolation of the SV wave mode. To avoid numerical dispersion and produce high quality images, the rapid expansion method REM is employed for numerical implementation. Synthetic results validate the proposed equation and show that it is a stable algorithm for modeling and reverse time migration RTM in a TTI media for any anisotropic parameter values. © 2011 Society of Exploration Geophysicists.

  4. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN

    OpenAIRE

    Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development.

  5. Reflections on imaging diagnosis of sella masses

    International Nuclear Information System (INIS)

    Hernandez Yero, Jose Arturo; Jorge Gonzalez, Raquel

    2005-01-01

    Some reflections were made on imaging diagnosis of sella masses, specifying some characteristics of the main sella masses and their appearance in magnetic resonance imaging. The purpose was to call the attention on this important issue on the basis that modern imaging advances offer very useful distinctive elements in the diagnosis of a group of masses located in the sella turcica region. The paper underlined details of signal intensity in pituitary adenomas, craniopharyngiomas, Rathkes pouch cysts, hypophyseal hyperplasia and the so-called empty sella syndrome, among other causes of anatomical changes in sella region. It was concluded that magnetic resonance imaging would be the ideal method for a better diagnosis of sella masses, but if this technique was not available, then contrast-enhanced tomography would be useful in under 2 mm views. The importance of a multidisciplinary team of clinicians, endocrinologists, imaging specialists, neurosurgeons and anatomy pathologists to reach more accurate diagnosis and better therapeutic results was stressed

  6. Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

    KAUST Repository

    Djebbi, Ramzi

    2014-02-18

    Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.

  7. Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase

    KAUST Repository

    Djebbi, Ramzi; Alkhalifah, Tariq Ali

    2014-01-01

    Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.

  8. New solutions of the generalized ellipsoidal wave equation

    Directory of Open Access Journals (Sweden)

    Harold Exton

    1999-10-01

    Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.

  9. The scalar wave equation in a Schwarzschild space-time

    International Nuclear Information System (INIS)

    Schmidt, B.G.; Stewart, J.M.

    1979-01-01

    This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild space-time in a neighbourhood of spatial infinity which includes parts of future and pass null infinity. The behaviour of such fields is essentially different from that which occurs in a flat space-time. In particular fields which have a Bondi-type expansion in powers of 'r(-1)' near past null infinity do not have such an expansion near future null infinity. Further solutions which have physically reasonable Cauchy data probably fail to have Bondi-type expansions near null infinity. (author)

  10. A nonlinear wave equation in nonadiabatic flame propagation

    International Nuclear Information System (INIS)

    Booty, M.R.; Matalon, M.; Matkowsky, B.J.

    1988-01-01

    The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time

  11. Controllability for a Wave Equation with Moving Boundary

    Directory of Open Access Journals (Sweden)

    Lizhi Cui

    2014-01-01

    Full Text Available We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than 1-1/e, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.

  12. Gabor Wave Packet Method to Solve Plasma Wave Equations

    International Nuclear Information System (INIS)

    Pletzer, A.; Phillips, C.K.; Smithe, D.N.

    2003-01-01

    A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

  13. Quaternion wave equations in curved space-time

    Science.gov (United States)

    Edmonds, J. D., Jr.

    1974-01-01

    The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

  14. Relativistic wave equations without the Velo-Zwanziger pathology

    International Nuclear Information System (INIS)

    Khalil, M.A.K.

    1976-06-01

    For particles described by relativistic wave equations of the form: (-iGAMMA x delta + m) psi(x) = 0 interacting with an external field B(x) it is known that the ''noncausal'' propagation characteristics are not present when (1) GAMMA 0 is diagonalizable and (2) B(x) = -eGAMMA/sub mu/A/sup mu/(x) (Amar--Dozzio). The ''noncausality''difficulties arise for the Rarita--Schwinger spin 3 / 2 equation, with nondiagonalizable GAMMA 0 , in minimal coupling (i.e., B(x) = -eGAMMA x A(x)) and the PDK spin 1 equation, with diagonalizable GAMMA 0 , in a quadrupole coupling (Velo--Zwanziger) where either (1) or (2) of the Amar--Dozzio (sufficient) conditions are violated. Some sufficient conditions are derived and explored where the Velo--Zwanziger ''noncausality'' pathology can be avoided, even though one, or the other, or both of the conditions (1) and (2) are violated. Examples with both reducible and irreducible wave equations are included

  15. Electromagnetic interactions in relativistic infinite component wave equations

    International Nuclear Information System (INIS)

    Gerry, C.C.

    1979-01-01

    The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group

  16. The Appell transformation for the paraxial wave equation

    International Nuclear Information System (INIS)

    Torre, A

    2011-01-01

    Some issues related to the 1D heat equation are revisited and framed within the context of the free-space paraxial propagation, formally accounted for by the 2D paraxial wave equation. In particular, the Appell transformation, which is well known in the theory of the heat equation, is reformulated in optical terms, and accordingly interpreted in the light of the propagation of given source functions, which are in a definite relation with the source functions of the original wavefunctions. Basic to the discussion is the Lie-algebra-based approach, as developed in a series of seminal papers by Kalnins, Miller and Boyer, to evolutionary-type equations, ruled by Hamiltonian operators underlying a harmonic oscillator-like symmetry algebra. Indeed, both the heat equation and the paraxial wave equation are particular cases of this kind of equation. When interpreting such an approach in terms of the propagation of assigned 'source' functions, the transformations between wavefunctions may be traced back to definite relations between the respective source functions. Thus, the optical Appell transformation is seen to be a manifestation of the correspondence between wavefunctions generated by eigenstates of operators, which are linked through a Fourier-similarity transformation. As a mere consequence, one can introduce the fractional Appell transformation, thus displaying a family of symmetry transformations parameterized by a continuous parameter

  17. Terahertz wave reflective sensing and imaging

    Science.gov (United States)

    Zhong, Hua

    Sensing and imaging technologies using terahertz (THz) radiation have found diverse applications as they approach maturity. Since the burgeoning of this technique in the 1990's, many THz sensing and imaging investigations have been designed and conducted in transmission geometry, which provides sufficient phase and amplitude contrast for the study of the spectral properties of targets in the THz domain. Driven by rising expectations that THz technology will be a potential candidate in the next generation of security screening, remote sensing, biomedical imaging and non-destructive testing (NDT), most THz sensing and imaging modalities are being extended to reflection geometry, which offers unique and adaptive solutions, and multi-dimensional information in many real scenarios. This thesis takes an application-focused approach to the advancement of THz wave reflective sensing and imaging systems: The absorption signature of the explosive material hexahydro-1,3,5-trinitro-1,3,5triazine (RDX) is measured at 30 m---the longest standoff distance so far attained by THz time-domain spectroscopy (THz-TDS). The standoff distance sensing ability of THz-TDS is investigated along with discussions specifying the influences of a variety of factors such as propagation distance, water vapor absorption and collection efficiency. Highly directional THz radiation from four-wave mixing in laser-induced air plasmas is first observed and measured, which provides a potential solution for the atmospheric absorption effect in standoff THz sensing. The simulations of the beam profiles also illuminate the underlying physics behind the interaction of the optical beam with the plasma. THz wave reflective spectroscopic focal-plane imaging is realized the first time. Absorption features of some explosives and related compounds (ERCs) and biochemical materials are identified by using adaptive feature extraction method. Good classification results using multiple pattern recognition methods are

  18. Discriminating Yogurt Microstructure Using Diffuse Reflectance Images

    DEFF Research Database (Denmark)

    Skytte, Jacob Lercke; Møller, Flemming; Abildgaard, Otto Højager Attermann

    2015-01-01

    The protein microstructure of many dairy products is of great importance for the consumers’ experience when eating the product. However, studies concerning discrimination between protein microstructures are limited. This paper presents preliminary results for discriminating different yogurt...... microstructures using hyperspectral (500-900nm) diffuse reflectance images (DRIs) – a technique potentially well suited for inline process control. Comparisons are made to quantified measures of the yogurt microstructure observed through confocal scanning laser microscopy (CSLM). The output signal from both...... modalities is evaluated on a 24 factorial design covering four common production parameters, which significantly change the chemistry and the microstructure of the yogurt. It is found that the DRIs can be as discriminative as the CSLM images in certain cases, however the performance is highly governed...

  19. The wave equation: From eikonal to anti-eikonal approximation

    Directory of Open Access Journals (Sweden)

    Luis Vázquez

    2016-06-01

    Full Text Available When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti-eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.

  20. Explicit solution for a wave equation with nonlocal condition

    Science.gov (United States)

    Bazhlekova, Emilia; Dimovski, Ivan

    2012-11-01

    An initial-boundary value problem with a nonlocal boundary condition for one-dimensional wave equation is studied. Applying spectral projections, we find a series solution of the problem. The character of the solution found shows that the oscillation amplitude of the system described by this equation increases with time at any fixed x in absence of external forces. To find a representation of the solution more convenient for numerical calculation we develop a two-dimensional operational calculus for the problem. The solution is expressed as a sum of non-classical convolution products of particular solutions and the arbitrary initial functions. This result is an extension of the classical Duhamel principle for the space variable. The representation is used successfully for numerical computation and visualization of the solution. Numerical results obtained for specific test problems with known exact solutions indicate that the present technique provides accurate numerical solutions.

  1. Closed form solutions of two time fractional nonlinear wave equations

    Directory of Open Access Journals (Sweden)

    M. Ali Akbar

    2018-06-01

    Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation

  2. On a class of nonlocal wave equations from applications

    Science.gov (United States)

    Beyer, Horst Reinhard; Aksoylu, Burak; Celiker, Fatih

    2016-06-01

    We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form a system of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain ℝn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.

  3. Chiral symmetry breaking and confinement - solutions of relativistic wave equations

    International Nuclear Information System (INIS)

    Murugesan, P.

    1983-01-01

    In this thesis, an attempt is made to explore the question whether confinement automatically leads to chiral symmetry breaking. While it should be accepted that chiral symmetry breaking manifests in nature in the absence of scalar partners of pseudoscalar mesons, it does not necessarily follow that confinement should lead to chiral symmetry breaking. If chiral conserving forces give rise to observed spectrum of hadrons, then the conjuncture that confinement is responsible for chiral symmetry breaking is not valid. The method employed to answer the question whether confinement leads to chiral symmetry breaking or not is to solve relativistic wave equations by introducing chiral conserving as well as chiral breaking confining potentials and compare the results with experimental observations. It is concluded that even though chiral symmetry is broken in nature, confinement of quarks need not be the cause of it

  4. Time evolution of the wave equation using rapid expansion method

    KAUST Repository

    Pestana, Reynam C.; Stoffa, Paul L.

    2010-01-01

    Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.

  5. Closed form solutions of two time fractional nonlinear wave equations

    Science.gov (United States)

    Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

    2018-06-01

    In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

  6. Nonlinear wave equation with intrinsic wave particle dualism

    International Nuclear Information System (INIS)

    Klein, J.J.

    1976-01-01

    A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)

  7. Time evolution of the wave equation using rapid expansion method

    KAUST Repository

    Pestana, Reynam C.

    2010-07-01

    Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.

  8. Lipschitz Metrics for a Class of Nonlinear Wave Equations

    Science.gov (United States)

    Bressan, Alberto; Chen, Geng

    2017-12-01

    The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.

  9. Computational study on full-wave inversion based on the elastic wave-equation; Dansei hado hoteishiki full wave inversion no model keisan ni yoru kento

    Energy Technology Data Exchange (ETDEWEB)

    Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

    1997-05-27

    Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.

  10. ''Free-space'' boundary conditions for the time-dependent wave equation

    International Nuclear Information System (INIS)

    Lindman, E.L.

    1975-01-01

    Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics

  11. Wave equation tomography using the unwrapped phase - Analysis of the traveltime sensitivity kernels

    KAUST Repository

    Djebbi, Ramzi

    2013-01-01

    Full waveform inversion suffers from the high non-linearity in the misfit function, which causes the convergence to a local minimum. In the other hand, traveltime tomography has a quasi-linear misfit function but yields low- resolution models. Wave equation tomography (WET) tries to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. However, conventional (WET), based on the crosscorelaion lag, yields the popular hallow banana sensitivity kernel indicating that the measured wavefield at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, the sensitivity kernel reflects more the model-data dependency we grown accustom to in seismic inversion (even phase inversion). Demonstrations on synthetic and the Mamousi model support such assertions.

  12. An arbitrary-order staggered time integrator for the linear acoustic wave equation

    Science.gov (United States)

    Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

    2018-02-01

    We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

  13. An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

    KAUST Repository

    Zhan, Ge

    2013-02-19

    The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.

  14. An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

    International Nuclear Information System (INIS)

    Zhan, Ge; Pestana, Reynam C; Stoffa, Paul L

    2013-01-01

    The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward–backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. (paper)

  15. A new iterative solver for the time-harmonic wave equation

    NARCIS (Netherlands)

    Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.

    2006-01-01

    The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can

  16. Diffusion phenomenon for linear dissipative wave equations in an exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  17. On the wave equation with semilinear porous acoustic boundary conditions

    KAUST Repository

    Graber, Philip Jameson; Said-Houari, Belkacem

    2012-01-01

    The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

  18. Energy decay of a viscoelastic wave equation with supercritical nonlinearities

    Science.gov (United States)

    Guo, Yanqiu; Rammaha, Mohammad A.; Sakuntasathien, Sawanya

    2018-06-01

    This paper presents a study of the asymptotic behavior of the solutions for the history value problem of a viscoelastic wave equation which features a fading memory term as well as a supercritical source term and a frictional damping term: u_{tt}- k(0) Δ u - \\int \\limits _0^{&infty } k'(s) Δ u(t-s) ds +|u_t|^{m-1}u_t =|u|^{p-1}u, { in } Ω × (0,T), u(x,t)=u_0(x,t), \\quad { in } Ω × (-∞,0]), where Ω is a bounded domain in R^3 with a Dirichlét boundary condition and u_0 represents the history value. A suitable notion of a potential well is introduced for the system, and global existence of solutions is justified, provided that the history value u_0 is taken from a subset of the potential well. Also, uniform energy decay rate is obtained which depends on the relaxation kernel -k'(s) as well as the growth rate of the damping term. This manuscript complements our previous work (Guo et al. in J Differ Equ 257:3778-3812, 2014, J Differ Equ 262:1956-1979, 2017) where Hadamard well-posedness and the singularity formulation have been studied for the system. It is worth stressing the special features of the model, namely the source term here has a supercritical growth rate and the memory term accounts to the full past history that goes back to -∞.

  19. On the wave equation with semilinear porous acoustic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-05-01

    The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.

  20. On the wave equations with memory in noncylindrical domains

    Directory of Open Access Journals (Sweden)

    Mauro de Lima Santos

    2007-10-01

    Full Text Available In this paper we prove the exponential and polynomial decays rates in the case $n > 2$, as time approaches infinity of regular solutions of the wave equations with memory $$ u_{tt}-Delta u+int^{t}_{0}g(t-sDelta u(sds=0 quad mbox{in } widehat{Q} $$ where $widehat{Q}$ is a non cylindrical domains of $mathbb{R}^{n+1}$, $(nge1$. We show that the dissipation produced by memory effect is strong enough to produce exponential decay of solution provided the relaxation function $g$ also decays exponentially. When the relaxation function decay polynomially, we show that the solution decays polynomially with the same rate. For this we introduced a new multiplier that makes an important role in the obtaining of the exponential and polynomial decays of the energy of the system. Existence, uniqueness and regularity of solutions for any $n ge 1$ are investigated. The obtained result extends known results from cylindrical to non-cylindrical domains.

  1. Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz—Ladik—Lattice system

    International Nuclear Information System (INIS)

    Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao

    2013-01-01

    In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)

  2. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

    Science.gov (United States)

    Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

  3. Full Waveform Inversion of Diving & Reflected Waves based on Scale Separation for Velocity and Impedance Imaging

    Science.gov (United States)

    Brossier, Romain; Zhou, Wei; Operto, Stéphane; Virieux, Jean

    2015-04-01

    high wavenumber impedance model and low wavenumber velocity model is performed to iteratively improve subsurface models. References : Brossier, R., Operto, S. & Virieux, J., 2014. Velocity model building from seismic reflection data by full waveform inversion, Geophysical Prospecting, doi:10.1111/1365-2478.12190 Chavent, G., Clément, F. & Gomez, S., 1994.Automatic determination of velocities via migration-based traveltime waveform inversion: A synthetic data example, SEG Technical Program Expanded Abstracts 1994, pp. 1179--1182. Ma, Y. & Hale, D., 2013. Wave-equation reflection traveltime inversion with dynamic warping and full waveform inversion, Geophysics, 78(6), R223--R233. Symes, W.W. & Carazzone, J.J., 1991. Velocity inversion by differential semblance optimization, Geophysics, 56, 654--663. Virieux, J. & Operto, S., 2009. An overview of full waveform inversion in exploration geophysics, Geophysics, 74(6), WCC1--WCC26. Xu, S., Wang, D., Chen, F., Lambaré, G. & Zhang, Y., 2012. Inversion on reflected seismic wave, SEG Technical Program Expanded Abstracts 2012, pp. 1--7. Zhou, W., Brossier, R., Operto, S., & Virieux, J., 2014. Acoustic multiparameter full-waveform inversion through a hierachical scheme, in SEG Technical Program Expanded Abstracts 2014, pp. 1249--1253

  4. Inverse scattering and refraction corrected reflection for breast cancer imaging

    Science.gov (United States)

    Wiskin, J.; Borup, D.; Johnson, S.; Berggren, M.; Robinson, D.; Smith, J.; Chen, J.; Parisky, Y.; Klock, John

    2010-03-01

    Reflection ultrasound (US) has been utilized as an adjunct imaging modality for over 30 years. TechniScan, Inc. has developed unique, transmission and concomitant reflection algorithms which are used to reconstruct images from data gathered during a tomographic breast scanning process called Warm Bath Ultrasound (WBU™). The transmission algorithm yields high resolution, 3D, attenuation and speed of sound (SOS) images. The reflection algorithm is based on canonical ray tracing utilizing refraction correction via the SOS and attenuation reconstructions. The refraction correction reflection algorithm allows 360 degree compounding resulting in the reflection image. The requisite data are collected when scanning the entire breast in a 33° C water bath, on average in 8 minutes. This presentation explains how the data are collected and processed by the 3D transmission and reflection imaging mode algorithms. The processing is carried out using two NVIDIA® Tesla™ GPU processors, accessing data on a 4-TeraByte RAID. The WBU™ images are displayed in a DICOM viewer that allows registration of all three modalities. Several representative cases are presented to demonstrate potential diagnostic capability including: a cyst, fibroadenoma, and a carcinoma. WBU™ images (SOS, attenuation, and reflection modalities) are shown along with their respective mammograms and standard ultrasound images. In addition, anatomical studies are shown comparing WBU™ images and MRI images of a cadaver breast. This innovative technology is designed to provide additional tools in the armamentarium for diagnosis of breast disease.

  5. Concurrent reflectance imaging and microdialysis in the freely behaving cat

    DEFF Research Database (Denmark)

    Poe, G R; Nitz, D A; Rector, D M

    1996-01-01

    We present a method to perform simultaneous microdialysis with light reflectance imaging of neural activity in a discrete brain region of the freely behaving animal. We applied this method to the dorsal hippocampus of freely behaving cats to (1) measure extracellular glutamate and reflectance...... imaged neural activity. Sequential images showed that cocaine perfusion elicited a propagating reflectance change as cocaine reached the tissue. Microperfusion of hypo-osmotic solution ( - 100 mOsm), which increases cell volume, decreased reflectance. Microperfusion of hyperosmotic sucrose solutions...

  6. Lamont Doherty Seismic Reflection Scanned Images

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains single channel seismic reflection profiles as provided to NGDC by Lamont Doherty Earh Observatory (LDEO). The profiles were originally...

  7. Critical string wave equations and the QCD (U(N{sub c})) string. (Some comments)

    Energy Technology Data Exchange (ETDEWEB)

    Botelho, Luiz C.L. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Inst. de Matematica. Dept. de Matematica Aplicada], e-mail: botelho.luiz@superig.com.br

    2009-07-01

    We present a simple proof that self-avoiding fermionic strings solutions solve formally (in a Quantum Mechanical Framework) the QCD(U(N{sub c})) loop wave equation written in terms of random loops. (author)

  8. Numerical calculation of the cross section by the solution of the wave equation

    International Nuclear Information System (INIS)

    Drewko, J.

    1982-01-01

    A numerical method of solving of the wave equation is described for chosen vibrational eigenfunctions. A prepared program calculates the total cross sections for the resonant vibrational excitation for diatomic molecules on the basis of introduced molecular data. (author)

  9. Analysis and computation of the elastic wave equation with random coefficients

    KAUST Repository

    Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

    2015-01-01

    We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics

  10. Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

    KAUST Repository

    Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor

    2010-01-01

    In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.

  11. A stochastic collocation method for the second order wave equation with a discontinuous random speed

    KAUST Repository

    Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

    2012-01-01

    In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical

  12. THE EXPONENTIAL STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK

    Institute of Scientific and Technical Information of China (English)

    JIA CHAOHUA; FENG DEXING

    2005-01-01

    This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.

  13. Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

    KAUST Repository

    Jiang, Lijian

    2010-08-01

    In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.

  14. Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping

    Directory of Open Access Journals (Sweden)

    Jieqiong Wu

    2015-09-01

    Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.

  15. Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

    KAUST Repository

    Said-Houari, Belkacem

    2012-03-01

    In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.

  16. Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.

  17. Reflection symmetry-integrated image segmentation.

    Science.gov (United States)

    Sun, Yu; Bhanu, Bir

    2012-09-01

    This paper presents a new symmetry-integrated region-based image segmentation method. The method is developed to obtain improved image segmentation by exploiting image symmetry. It is realized by constructing a symmetry token that can be flexibly embedded into segmentation cues. Interesting points are initially extracted from an image by the SIFT operator and they are further refined for detecting the global bilateral symmetry. A symmetry affinity matrix is then computed using the symmetry axis and it is used explicitly as a constraint in a region growing algorithm in order to refine the symmetry of the segmented regions. A multi-objective genetic search finds the segmentation result with the highest performance for both segmentation and symmetry, which is close to the global optimum. The method has been investigated experimentally in challenging natural images and images containing man-made objects. It is shown that the proposed method outperforms current segmentation methods both with and without exploiting symmetry. A thorough experimental analysis indicates that symmetry plays an important role as a segmentation cue, in conjunction with other attributes like color and texture.

  18. Reflective optical imaging system for extreme ultraviolet wavelengths

    Science.gov (United States)

    Viswanathan, V.K.; Newnam, B.E.

    1993-05-18

    A projection reflection optical system has two mirrors in a coaxial, four reflection configuration to reproduce the image of an object. The mirrors have spherical reflection surfaces to provide a very high resolution of object feature wavelengths less than 200 [mu]m, and preferably less than 100 [mu]m. An image resolution of features less than 0.05-0.1 [mu]m, is obtained over a large area field; i.e., 25.4 mm [times] 25.4 mm, with a distortion less than 0.1 of the resolution over the image field.

  19. Automatic Wave Equation Migration Velocity Analysis by Focusing Subsurface Virtual Sources

    KAUST Repository

    Sun, Bingbing

    2017-11-03

    Macro velocity model building is important for subsequent pre-stack depth migration and full waveform inversion. Wave equation migration velocity analysis (WEMVA) utilizes the band-limited waveform to invert for the velocity. Normally, inversion would be implemented by focusing the subsurface offset common image gathers (SOCIGs). We re-examine this concept with a different perspective: In subsurface offset domain, using extended Born modeling, the recorded data can be considered as invariant with respect to the perturbation of the position of the virtual sources and velocity at the same time. A linear system connecting the perturbation of the position of those virtual sources and velocity is derived and solved subsequently by Conjugate Gradient method. In theory, the perturbation of the position of the virtual sources is given by the Rytov approximation. Thus, compared to the Born approximation, it relaxes the dependency on amplitude and makes the proposed method more applicable for real data. We demonstrate the effectiveness of the approach by applying the proposed method on both isotropic and anisotropic VTI synthetic data. A real dataset example verifies the robustness of the proposed method.

  20. Automatic Wave Equation Migration Velocity Analysis by Focusing Subsurface Virtual Sources

    KAUST Repository

    Sun, Bingbing; Alkhalifah, Tariq Ali

    2017-01-01

    Macro velocity model building is important for subsequent pre-stack depth migration and full waveform inversion. Wave equation migration velocity analysis (WEMVA) utilizes the band-limited waveform to invert for the velocity. Normally, inversion would be implemented by focusing the subsurface offset common image gathers (SOCIGs). We re-examine this concept with a different perspective: In subsurface offset domain, using extended Born modeling, the recorded data can be considered as invariant with respect to the perturbation of the position of the virtual sources and velocity at the same time. A linear system connecting the perturbation of the position of those virtual sources and velocity is derived and solved subsequently by Conjugate Gradient method. In theory, the perturbation of the position of the virtual sources is given by the Rytov approximation. Thus, compared to the Born approximation, it relaxes the dependency on amplitude and makes the proposed method more applicable for real data. We demonstrate the effectiveness of the approach by applying the proposed method on both isotropic and anisotropic VTI synthetic data. A real dataset example verifies the robustness of the proposed method.

  1. A simple polarized-based diffused reflectance colour imaging system

    African Journals Online (AJOL)

    A simple polarized-based diffuse reflectance imaging system has been developed. The system is designed for both in vivo and in vitro imaging of agricultural specimen in the visible region. The system uses a commercial web camera and a halogen lamp that makes it relatively simple and less expensive for diagnostic ...

  2. Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

    KAUST Repository

    Yu, Han

    2018-02-23

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

  3. Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

    Science.gov (United States)

    Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

    2018-04-01

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

  4. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    Science.gov (United States)

    Seadawy, Aly R.; Manafian, Jalil

    2018-03-01

    This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

  5. Reflective and Non-conscious Responses to Exercise Images.

    Science.gov (United States)

    Cope, Kathryn; Vandelanotte, Corneel; Short, Camille E; Conroy, David E; Rhodes, Ryan E; Jackson, Ben; Dimmock, James A; Rebar, Amanda L

    2017-01-01

    Images portraying exercise are commonly used to promote exercise behavior and to measure automatic associations of exercise (e.g., via implicit association tests). The effectiveness of these promotion efforts and the validity of measurement techniques partially rely on the untested assumption that the images being used are perceived by the general public as portrayals of exercise that is pleasant and motivating. The aim of this study was to investigate how content of images impacted people's automatic and reflective evaluations of exercise images. Participants ( N = 90) completed a response time categorization task (similar to the implicit association test) to capture how automatically people perceived each image as relevant to Exercise or Not exercise . Participants also self-reported their evaluations of the images using visual analog scales with the anchors: Exercise / Not exercise, Does not motivate me to exercise / Motivates me to exercise, Pleasant / Unpleasant , and Energizing/Deactivating . People tended to more strongly automatically associate images with exercise if the images were of an outdoor setting, presented sport (as opposed to active labor or gym-based) activities, and included young (as opposed to middle-aged) adults. People tended to reflectively find images of young adults more motivating and relevant to exercise than images of older adults. The content of exercise images is an often overlooked source of systematic variability that may impact measurement validity and intervention effectiveness.

  6. Reflective and Non-conscious Responses to Exercise Images

    Directory of Open Access Journals (Sweden)

    Kathryn Cope

    2018-01-01

    Full Text Available Images portraying exercise are commonly used to promote exercise behavior and to measure automatic associations of exercise (e.g., via implicit association tests. The effectiveness of these promotion efforts and the validity of measurement techniques partially rely on the untested assumption that the images being used are perceived by the general public as portrayals of exercise that is pleasant and motivating. The aim of this study was to investigate how content of images impacted people's automatic and reflective evaluations of exercise images. Participants (N = 90 completed a response time categorization task (similar to the implicit association test to capture how automatically people perceived each image as relevant to Exercise or Not exercise. Participants also self-reported their evaluations of the images using visual analog scales with the anchors: Exercise/Not exercise, Does not motivate me to exercise/Motivates me to exercise, Pleasant/Unpleasant, and Energizing/Deactivating. People tended to more strongly automatically associate images with exercise if the images were of an outdoor setting, presented sport (as opposed to active labor or gym-based activities, and included young (as opposed to middle-aged adults. People tended to reflectively find images of young adults more motivating and relevant to exercise than images of older adults. The content of exercise images is an often overlooked source of systematic variability that may impact measurement validity and intervention effectiveness.

  7. Continuous wave terahertz reflection imaging of human colorectal tissue

    Science.gov (United States)

    Doradla, Pallavi; Alavi, Karim; Joseph, Cecil S.; Giles, Robert H.

    2013-03-01

    Continuous wave terahertz (THz) imaging has the potential to offer a safe, non-ionizing, and nondestructive medical imaging modality for delineating colorectal cancer. Fresh excisions of normal colon tissue were obtained from surgeries performed at the University of Massachusetts Medical School, Worcester. Reflection measurements of thick sections of colorectal tissues, mounted in an aluminum sample holder, were obtained for both fresh and formalin fixed tissues. The two-dimensional reflection images were acquired by using an optically pumped far-infrared molecular gas laser operating at 584 GHz with liquid Helium cooled silicon bolometer detector. Using polarizers in the experiment both co-polarized and cross-polarized remittance form the samples was collected. Analysis of the images showed the importance of understanding the effects of formalin fixation while determining reflectance level of tissue response. The resulting co- and cross-polarized images of both normal and formalin fixed tissues showed uniform terahertz response over the entire sample area. Initial measurements indicated a co-polarized reflectance of 16%, and a cross-polarized reflectance of 0.55% from fresh excisions of normal colonic tissues.

  8. On the exact solutions of high order wave equations of KdV type (I)

    Science.gov (United States)

    Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

    2014-12-01

    In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

  9. Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

    Science.gov (United States)

    Novruzov, Emil

    2017-11-01

    This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

  10. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  11. Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

    Science.gov (United States)

    Miyazaki, Yutaka; Tsuchiya, Takao

    2012-07-01

    The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

  12. Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

    Directory of Open Access Journals (Sweden)

    M. Arshad

    Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

  13. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

    2013-01-01

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  14. A One-Dimensional Wave Equation with White Noise Boundary Condition

    International Nuclear Information System (INIS)

    Kim, Jong Uhn

    2006-01-01

    We discuss the Cauchy problem for a one-dimensional wave equation with white noise boundary condition. We also establish the existence of an invariant measure when the noise is additive. Similar problems for parabolic equations were discussed by several authors. To our knowledge, there is only one work which investigated the initial-boundary value problem for a wave equation with random noise at the boundary. We handle a more general case by a different method. Our result on the existence of an invariant measure relies on the author's recent work on a certain class of stochastic evolution equations

  15. Refraction traveltime tomography based on damped wave equation for irregular topographic model

    Science.gov (United States)

    Park, Yunhui; Pyun, Sukjoon

    2018-03-01

    Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography. This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem. As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography

  16. Hemispherical reflectance model for passive images in an outdoor environment.

    Science.gov (United States)

    Kim, Charles C; Thai, Bea; Yamaoka, Neil; Aboutalib, Omar

    2015-05-01

    We present a hemispherical reflectance model for simulating passive images in an outdoor environment where illumination is provided by natural sources such as the sun and the clouds. While the bidirectional reflectance distribution function (BRDF) accurately produces radiance from any objects after the illumination, using the BRDF in calculating radiance requires double integration. Replacing the BRDF by hemispherical reflectance under the natural sources transforms the double integration into a multiplication. This reduces both storage space and computation time. We present the formalism for the radiance of the scene using hemispherical reflectance instead of BRDF. This enables us to generate passive images in an outdoor environment taking advantage of the computational and storage efficiencies. We show some examples for illustration.

  17. Security authentication using the reflective glass pattern imaging effect.

    Science.gov (United States)

    Zhu, Ji Cheng; Shen, Su; Wu, Jian Hong

    2015-11-01

    The reflective glass pattern imaging effect is investigated experimentally for the utility in forming a synthetic 3D image as a security authentication device in this Letter. An array of homogeneously randomly distributed reflective elements and a corresponding micropattern array are integrated onto a thin layer of polyester film aiming to create a vivid image floating over a substrate surface, which can be clearly visible to the naked eye. By using the reflective-type configuration, the micro-optic system can be realized on a thinner substrate and is immune to external stain due to its flat working plane. A novel gravure-like doctor blading technique can realize a resolution up to 12,000 dpi and a stringent 2D alignment requirement should be imposed. Such devices can find applications in document security and banknotes or other valuable items to protect them against forgery.

  18. Gen-2 Hand-Held Optical Imager towards Cancer Imaging: Reflectance and Transillumination Phantom Studies

    Directory of Open Access Journals (Sweden)

    Anuradha Godavarty

    2012-02-01

    Full Text Available Hand-held near-infrared (NIR optical imagers are developed by various researchers towards non-invasive clinical breast imaging. Unlike these existing imagers that can perform only reflectance imaging, a generation-2 (Gen-2 hand-held optical imager has been recently developed to perform both reflectance and transillumination imaging. The unique forked design of the hand-held probe head(s allows for reflectance imaging (as in ultrasound and transillumination or compressed imaging (as in X-ray mammography. Phantom studies were performed to demonstrate two-dimensional (2D target detection via reflectance and transillumination imaging at various target depths (1–5 cm deep and using simultaneous multiple point illumination approach. It was observed that 0.45 cc targets were detected up to 5 cm deep during transillumination, but limited to 2.5 cm deep during reflectance imaging. Additionally, implementing appropriate data post-processing techniques along with a polynomial fitting approach, to plot 2D surface contours of the detected signal, yields distinct target detectability and localization. The ability of the gen-2 imager to perform both reflectance and transillumination imaging allows its direct comparison to ultrasound and X-ray mammography results, respectively, in future clinical breast imaging studies.

  19. Imaging Hybrid Photon Detectors with a Reflective Photocathode

    CERN Document Server

    Ferenc, D

    2000-01-01

    Modern epitaxially grown photocathodes, like GaAsP, bring a very high inherent quantum efficiency, but are rather expensive due to the complicated manufacturing and mounting process. We argue that such photocathodes could be used in reflective mode, in order to avoid the risky and expensive removal of the epitaxial growth substrate. Besides that the quantum efficiency should increase considerably. In this paper we present results of the development of large imaging Hybrid Photon Detectors (HPDs), particularly designed for such reflective photocathodes.

  20. Asymmetric systems described by a pair of local covariant wave equations

    Energy Technology Data Exchange (ETDEWEB)

    Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

    1979-07-16

    A class of asymmetric solutions of the integrability conditions for systems obeying the Leutwyler-Stern pair of covariant wave equations is obtained. The class of unequal-mass systems described by these solutions does not embed the particle-antiparticle system behaving as a relativistic harmonic oscillator.

  1. Poincare group and relativistic wave equations in 2+1 dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)

    1997-09-07

    Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)

  2. Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation

    Directory of Open Access Journals (Sweden)

    Gusein Sh. Guseinov

    2012-01-01

    Full Text Available Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.

  3. Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Claudio Cremaschini

    2017-07-01

    Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

  4. Stabilization of the Wave Equation with Boundary Time-Varying Delay

    Directory of Open Access Journals (Sweden)

    Hao Li

    2014-01-01

    Full Text Available We study the stabilization of the wave equation with variable coefficients in a bounded domain and a time-varying delay term in the time-varying, weakly nonlinear boundary feedbacks. By the Riemannian geometry methods and a suitable assumption of nonlinearity, we obtain the uniform decay of the energy of the closed loop system.

  5. On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

    Science.gov (United States)

    Chandran, Pallath

    2004-01-01

    The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

  6. Generalized internal long wave equations: construction, hamiltonian structure and conservation laws

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1982-01-01

    Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu

  7. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    Directory of Open Access Journals (Sweden)

    Aly R. Seadawy

    2018-03-01

    Full Text Available This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM in exactly solving a well-known nonlinear equation of partial differential equations (PDEs. In this respect, the longitudinal wave equation (LWE that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wave

  8. Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping

    International Nuclear Information System (INIS)

    Kaltenbacher, Barbara

    2010-01-01

    In this paper we show boundary observability and boundary stabilizability by linear feedbacks for a class of nonlinear wave equations including the undamped Westervelt model used in nonlinear acoustics. We prove local existence for undamped generalized Westervelt equations with homogeneous Dirichlet boundary conditions as well as global existence and exponential decay with absorbing type boundary conditions.

  9. Stabilization of wave equations with variable coefficient and delay in the dynamical boundary feedback

    Directory of Open Access Journals (Sweden)

    Dandan Guo

    2017-08-01

    Full Text Available In this article we consider the boundary stabilization of a wave equation with variable coefficients. This equation has an acceleration term and a delayed velocity term on the boundary. Under suitable geometric conditions, we obtain the exponential decay for the solutions. Our proof relies on the geometric multiplier method and the Lyapunov approach.

  10. A membrane wave equation for Q.C.D. (SU(infinity))

    International Nuclear Information System (INIS)

    Botelho, L.C.L.

    1988-01-01

    It is proposed a quantum membrane wave functional describing the interaction between a colored SU(N c ) membrane and a quantized Yang-Mills field. Additionally, its associated wave equation in the t'Hooft N c ->infinity limit is deduced. (A.C.A.S.) [pt

  11. Parsimonious wave-equation travel-time inversion for refraction waves

    KAUST Repository

    Fu, Lei

    2017-02-14

    We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

  12. Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

    Science.gov (United States)

    Przedborski, Michelle; Anco, Stephen C.

    2017-09-01

    A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

  13. Singular solitons and other solutions to a couple of nonlinear wave equations

    International Nuclear Information System (INIS)

    Inc Mustafa; Ulutaş Esma; Biswas Anjan

    2013-01-01

    This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method

  14. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    Chen Yunmei.

    1987-06-01

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  15. Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

    International Nuclear Information System (INIS)

    Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng

    2013-01-01

    In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)

  16. An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry

    Science.gov (United States)

    Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

    2005-12-01

    We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.

  17. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2Japon. 55 (2002) 33) plays an effective role.

  18. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong; Schuster, Gerard T.; Liu, Yike; Hanafy, Sherif M.; Li, Jing

    2016-01-01

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized

  19. Parsimonious wave-equation travel-time inversion for refraction waves

    KAUST Repository

    Fu, Lei; Hanafy, Sherif M.; Schuster, Gerard T.

    2017-01-01

    We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N

  20. Nonlinear and linear wave equations for propagation in media with frequency power law losses

    Science.gov (United States)

    Szabo, Thomas L.

    2003-10-01

    The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

  1. From Fermat principle to wave equation - quantization of 'particle mechanics of light'

    International Nuclear Information System (INIS)

    Ogawa, Naohisa

    2004-01-01

    The Fermat principle states that light chooses the temporally shortest path. The action for this 'motion' is the observed time, and it has no Lorentz invariance. In this Letter we show how this action can be obtained from a relativistic action of massive particle, and how the classical wave equation of light can be obtained from this action

  2. Detection of Lettuce Discoloration Using Hyperspectral Reflectance Imaging.

    Science.gov (United States)

    Mo, Changyeun; Kim, Giyoung; Lim, Jongguk; Kim, Moon S; Cho, Hyunjeong; Cho, Byoung-Kwan

    2015-11-20

    Rapid visible/near-infrared (VNIR) hyperspectral imaging methods, employing both a single waveband algorithm and multi-spectral algorithms, were developed in order to discrimination between sound and discolored lettuce. Reflectance spectra for sound and discolored lettuce surfaces were extracted from hyperspectral reflectance images obtained in the 400-1000 nm wavelength range. The optimal wavebands for discriminating between discolored and sound lettuce surfaces were determined using one-way analysis of variance. Multi-spectral imaging algorithms developed using ratio and subtraction functions resulted in enhanced classification accuracy of above 99.9% for discolored and sound areas on both adaxial and abaxial lettuce surfaces. Ratio imaging (RI) and subtraction imaging (SI) algorithms at wavelengths of 552/701 nm and 557-701 nm, respectively, exhibited better classification performances compared to results obtained for all possible two-waveband combinations. These results suggest that hyperspectral reflectance imaging techniques can potentially be used to discriminate between discolored and sound fresh-cut lettuce.

  3. Seismic reflection imaging with conventional and unconventional sources

    Science.gov (United States)

    Quiros Ugalde, Diego Alonso

    This manuscript reports the results of research using both conventional and unconventional energy sources as well as conventional and unconventional analysis to image crustal structure using reflected seismic waves. The work presented here includes the use of explosions to investigate the Taiwanese lithosphere, the use of 'noise' from railroads to investigate the shallow subsurface of the Rio Grande rift, and the use of microearthquakes to image subsurface structure near an active fault zone within the Appalachian mountains. Chapter 1 uses recordings from the land refraction and wide-angle reflection component of the Taiwan Integrated Geodynamic Research (TAIGER) project. The most prominent reflection feature imaged by these surveys is an anomalously strong reflector found in northeastern Taiwan. The goal of this chapter is to analyze the TAIGER recordings and to place the reflector into a geologic framework that fits with the modern tectonic kinematics of the region. Chapter 2 uses railroad traffic as a source for reflection profiling within the Rio Grande rift. Here the railroad recordings are treated in an analogous way to Vibroseis recordings. These results suggest that railroad noise in general can be a valuable new tool in imaging and characterizing the shallow subsurface in environmental and geotechnical studies. In chapters 3 and 4, earthquakes serve as the seismic imaging source. In these studies the methodology of Vertical Seismic Profiling (VSP) is borrowed from the oil and gas industry to develop reflection images. In chapter 3, a single earthquake is used to probe a small area beneath Waterboro, Maine. In chapter 4, the same method is applied to multiple earthquakes to take advantage of the increased redundancy that results from multiple events illuminating the same structure. The latter study demonstrates how dense arrays can be a powerful new tool for delineating, and monitoring temporal changes of deep structure in areas characterized by significant

  4. REFLECTANCE CALIBRATION SCHEME FOR AIRBORNE FRAME CAMERA IMAGES

    Directory of Open Access Journals (Sweden)

    U. Beisl

    2012-07-01

    Full Text Available The image quality of photogrammetric images is influenced by various effects from outside the camera. One effect is the scattered light from the atmosphere that lowers contrast in the images and creates a colour shift towards the blue. Another is the changing illumination during the day which results in changing image brightness within an image block. In addition, there is the so-called bidirectional reflectance of the ground (BRDF effects that is giving rise to a view and sun angle dependent brightness gradient in the image itself. To correct for the first two effects an atmospheric correction with reflectance calibration is chosen. The effects have been corrected successfully for ADS linescan sensor data by using a parametrization of the atmospheric quantities. Following Kaufman et al. the actual atmospheric condition is estimated by the brightness of a dark pixel taken from the image. The BRDF effects are corrected using a semi-empirical modelling of the brightness gradient. Both methods are now extended to frame cameras. Linescan sensors have a viewing geometry that is only dependent from the cross track view zenith angle. The difference for frame cameras now is to include the extra dimension of the view azimuth into the modelling. Since both the atmospheric correction and the BRDF correction require a model inversion with the help of image data, a different image sampling strategy is necessary which includes the azimuth angle dependence. For the atmospheric correction a sixth variable is added to the existing five variables visibility, view zenith angle, sun zenith angle, ground altitude, and flight altitude – thus multiplying the number of modelling input combinations for the offline-inversion. The parametrization has to reflect the view azimuth angle dependence. The BRDF model already contains the view azimuth dependence and is combined with a new sampling strategy.

  5. Specialized Color Targets for Spectral Reflectance Reconstruction of Magnified Images

    Science.gov (United States)

    Kruschwitz, Jennifer D. T.

    Digital images are used almost exclusively instead of film to capture visual information across many scientific fields. The colorimetric color representation within these digital images can be relayed from the digital counts produced by the camera with the use of a known color target. In image capture of magnified images, there is currently no reliable color target that can be used at multiple magnifications and give the user a solid understanding of the color ground truth within those images. The first part of this dissertation included the design, fabrication, and testing of a color target produced with optical interference coated microlenses for use in an off-axis illumination, compound microscope. An ideal target was designed to increase the color gamut for colorimetric imaging and provide the necessary "Block Dye" spectral reflectance profiles across the visible spectrum to reduce the number of color patches necessary for multiple filter imaging systems that rely on statistical models for spectral reflectance reconstruction. There are other scientific disciplines that can benefit from a specialized color target to determine the color ground truth in their magnified images and perform spectral estimation. Not every discipline has the luxury of having a multi-filter imaging system. The second part of this dissertation developed two unique ways of using an interference coated color mirror target: one that relies on multiple light-source angles, and one that leverages a dynamic color change with time. The source multi-angle technique would be used for the microelectronic discipline where the reconstructed spectral reflectance would be used to determine a dielectric film thickness on a silicon substrate, and the time varying technique would be used for a biomedical example to determine the thickness of human tear film.

  6. Automatic registration of terrestrial point cloud using panoramic reflectance images

    NARCIS (Netherlands)

    Kang, Z.

    2008-01-01

    Much attention is paid to registration of terrestrial point clouds nowadays. Research is carried out towards improved efficiency and automation of the registration process. This paper reports a new approach for point clouds registration utilizing reflectance panoramic images. The approach follows a

  7. One-Step Real-Image Reflection Holograms

    Science.gov (United States)

    Buah-Bassuah, Paul K.; Vannoni, Maurizio; Molesini, Giuseppe

    2007-01-01

    A holographic process is presented where the object is made of the real image produced by a two-mirror system. Single-step reflection hologram recording is achieved. Details of the process are given, optics concepts are outlined and demonstrative results are presented. (Contains 6 figures and 2 footnotes.)

  8. Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

    KAUST Repository

    Wang, T.; Cheng, J.B.; Guo, Qiang; Wang, C.L.

    2017-01-01

    Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive

  9. Robust reflective ghost imaging against different partially polarized thermal light

    Science.gov (United States)

    Li, Hong-Guo; Wang, Yan; Zhang, Rui-Xue; Zhang, De-Jian; Liu, Hong-Chao; Li, Zong-Guo; Xiong, Jun

    2018-03-01

    We theoretically study the influence of degree of polarization (DOP) of thermal light on the contrast-to-noise ratio (CNR) of the reflective ghost imaging (RGI), which is a novel and indirect imaging modality. An expression for the CNR of RGI with partially polarized thermal light is carefully derived, which suggests a weak dependence of CNR on the DOP, especially when the ratio of the object size to the speckle size of thermal light has a large value. Different from conventional imaging approaches, our work reveals that RGI is much more robust against the DOP of the light source, which thereby has advantages in practical applications, such as remote sensing.

  10. A Wide Spectral Range Reflectance and Luminescence Imaging System

    Directory of Open Access Journals (Sweden)

    Tapani Hirvonen

    2013-10-01

    Full Text Available In this study, we introduce a wide spectral range (200–2500 nm imaging system with a 250 μm minimum spatial resolution, which can be freely modified for a wide range of resolutions and measurement geometries. The system has been tested for reflectance and luminescence measurements, but can also be customized for transmittance measurements. This study includes the performance results of the developed system, as well as examples of spectral images. Discussion of the system relates it to existing systems and methods. The wide range spectral imaging system that has been developed is however highly customizable and has great potential in many practical applications.

  11. Superresolution Imaging Using Resonant Multiples

    KAUST Repository

    Guo, Bowen

    2017-12-22

    A resonant multiple is defined as a multiple reflection that revisits the same subsurface location along coincident reflection raypaths. We show that resonant first-order multiples can be migrated with either Kirchhoff or wave-equation migration methods to give images with approximately twice the spatial resolution compared to post-stack primary-reflection images. A moveout-correction stacking method is proposed to enhance the signal-to-noise ratios (SNRs) of the resonant multiples before superresolution migration. The effectiveness of this procedure is validated by synthetic and field data tests.

  12. Superresolution Imaging Using Resonant Multiples

    KAUST Repository

    Guo, Bowen; Schuster, Gerard T.

    2017-01-01

    A resonant multiple is defined as a multiple reflection that revisits the same subsurface location along coincident reflection raypaths. We show that resonant first-order multiples can be migrated with either Kirchhoff or wave-equation migration methods to give images with approximately twice the spatial resolution compared to post-stack primary-reflection images. A moveout-correction stacking method is proposed to enhance the signal-to-noise ratios (SNRs) of the resonant multiples before superresolution migration. The effectiveness of this procedure is validated by synthetic and field data tests.

  13. Identifiable images of bystanders extracted from corneal reflections.

    Directory of Open Access Journals (Sweden)

    Rob Jenkins

    Full Text Available Criminal investigations often use photographic evidence to identify suspects. Here we combined robust face perception and high-resolution photography to mine face photographs for hidden information. By zooming in on high-resolution face photographs, we were able to recover images of unseen bystanders from reflections in the subjects' eyes. To establish whether these bystanders could be identified from the reflection images, we presented them as stimuli in a face matching task (Experiment 1. Accuracy in the face matching task was well above chance (50%, despite the unpromising source of the stimuli. Participants who were unfamiliar with the bystanders' faces (n = 16 performed at 71% accuracy [t(15 = 7.64, p<.0001, d = 1.91], and participants who were familiar with the faces (n = 16 performed at 84% accuracy [t(15 = 11.15, p<.0001, d = 2.79]. In a test of spontaneous recognition (Experiment 2, observers could reliably name a familiar face from an eye reflection image. For crimes in which the victims are photographed (e.g., hostage taking, child sex abuse, reflections in the eyes of the photographic subject could help to identify perpetrators.

  14. Diffuse reflectance imaging: a tool for guided biopsy

    Science.gov (United States)

    Jayanthi, Jayaraj L.; Subhash, Narayanan; Manju, Stephen; Nisha, Unni G.; Beena, Valappil T.

    2012-01-01

    Accurate diagnosis of premalignant or malignant oral lesions depends on the quality of the biopsy, adequate clinical information and correct interpretation of the biopsy results. The major clinical challenge is to precisely locate the biopsy site in a clinically suspicious lesion. Dips due to oxygenated hemoglobin absorption have been noticed at 545 and 575 nm in the diffusely reflected white light spectra of oral mucosa and the intensity ratio R545/R575 has been found suited for early detection of oral pre-cancers. A multi-spectral diffuse reflectance (DR) imaging system has been developed consisting of an electron multiplying charge coupled device (EMCCD) camera and a liquid crystal tunable filter for guiding the clinician to an optimal biopsy site. Towards this DR images were recorded from 27 patients with potentially malignant lesions on their tongue (dorsal, lateral and ventral sides) and from 44 healthy controls at 545 and 575 nm with the DR imaging system. False colored ratio image R545/R575 of the lesion provides a visual discerning capability that helps in locating the most malignant site for biopsy. Histopathological report of guided biopsy showed that out of the 27 patients 16 were cancers, 9 pre-cancers and 2 lichen planus. In this clinical trial DR imaging has correctly guided 25 biopsy sites, yielding a sensitivity of 93% and a specificity of 98%, thereby establishing the potential of DR imaging as a tool for guided biopsy.

  15. Reflective terahertz (THz) imaging: system calibration using hydration phantoms

    Science.gov (United States)

    Bajwa, Neha; Garritano, James; Lee, Yoon Kyung; Tewari, Priyamvada; Sung, Shijun; Maccabi, Ashkan; Nowroozi, Bryan; Babakhanian, Meghedi; Sanghvi, Sajan; Singh, Rahul; Grundfest, Warren; Taylor, Zachary

    2013-02-01

    Terahertz (THz) hydration sensing continues to gain traction in the medical imaging community due to its unparalleled sensitivity to tissue water content. Rapid and accurate detection of fluid shifts following induction of thermal skin burns as well as remote corneal hydration sensing have been previously demonstrated in vivo using reflective, pulsed THz imaging. The hydration contrast sensing capabilities of this technology were recently confirmed in a parallel 7 Tesla Magnetic Resonance (MR) imaging study, in which burn areas are associated with increases in local mobile water content. Successful clinical translation of THz sensing, however, still requires quantitative assessments of system performance measurements, specifically hydration concentration sensitivity, with tissue substitutes. This research aims to calibrate the sensitivity of a novel, reflective THz system to tissue water content through the use of hydration phantoms for quantitative comparisons of THz hydration imagery.Gelatin phantoms were identified as an appropriate tissue-mimicking model for reflective THz applications, and gel composition, comprising mixtures of water and protein, was varied between 83% to 95% hydration, a physiologically relevant range. A comparison of four series of gelatin phantom studies demonstrated a positive linear relationship between THz reflectivity and water concentration, with statistically significant hydration sensitivities (p hydration). The THz-phantom interaction is simulated with a three-layer model using the Transfer Matrix Method with agreement in hydration trends. Having demonstrated the ability to accurately and noninvasively measure water content in tissue equivalent targets with high sensitivity, reflective THz imaging is explored as a potential tool for early detection and intervention of corneal pathologies.

  16. Reflective all-sky thermal infrared cloud imager.

    Science.gov (United States)

    Redman, Brian J; Shaw, Joseph A; Nugent, Paul W; Clark, R Trevor; Piazzolla, Sabino

    2018-04-30

    A reflective all-sky imaging system has been built using a long-wave infrared microbolometer camera and a reflective metal sphere. This compact system was developed for measuring spatial and temporal patterns of clouds and their optical depth in support of applications including Earth-space optical communications. The camera is mounted to the side of the reflective sphere to leave the zenith sky unobstructed. The resulting geometric distortion is removed through an angular map derived from a combination of checkerboard-target imaging, geometric ray tracing, and sun-location-based alignment. A tape of high-emissivity material on the side of the reflector acts as a reference that is used to estimate and remove thermal emission from the metal sphere. Once a bias that is under continuing study was removed, sky radiance measurements from the all-sky imager in the 8-14 μm wavelength range agreed to within 0.91 W/(m 2 sr) of measurements from a previously calibrated, lens-based infrared cloud imager over its 110° field of view.

  17. a Comparative Case Study of Reflection Seismic Imaging Method

    Science.gov (United States)

    Alamooti, M.; Aydin, A.

    2017-12-01

    Seismic imaging is the most common means of gathering information about subsurface structural features. The accuracy of seismic images may be highly variable depending on the complexity of the subsurface and on how seismic data is processed. One of the crucial steps in this process, especially in layered sequences with complicated structure, is the time and/or depth migration of seismic data.The primary purpose of the migration is to increase the spatial resolution of seismic images by repositioning the recorded seismic signal back to its original point of reflection in time/space, which enhances information about complex structure. In this study, our objective is to process a seismic data set (courtesy of the University of South Carolina) to generate an image on which the Magruder fault near Allendale SC can be clearly distinguished and its attitude can be accurately depicted. The data was gathered by common mid-point method with 60 geophones equally spaced along an about 550 m long traverse over a nearly flat ground. The results obtained from the application of different migration algorithms (including finite-difference and Kirchhoff) are compared in time and depth domains to investigate the efficiency of each algorithm in reducing the processing time and improving the accuracy of seismic images in reflecting the correct position of the Magruder fault.

  18. DIRC, the internally reflecting ring imaging Cherenkov detector for BABAR

    International Nuclear Information System (INIS)

    Adam, I.; Aston, D.

    1997-11-01

    The DIRC is a new type of Cherenkov imaging device that will be used for the first time in the BABAR detector at the asymmetric B-factory, PEP-II. It is based on total internal reflection and uses long, rectangular bars made from synthetic fused silica as Cherenkov radiator and light guide. The principles of the DIRC ring imaging Cherenkov technique are explained and results from the prototype program are presented. Its choice for the BABAR detector particle identification system is motivated, followed by a discussion of the quartz radiator properties and the detector design

  19. Iterative reflectivity-constrained velocity estimation for seismic imaging

    Science.gov (United States)

    Masaya, Shogo; Verschuur, D. J. Eric

    2018-03-01

    This paper proposes a reflectivity constraint for velocity estimation to optimally solve the inverse problem for active seismic imaging. This constraint is based on the velocity model derived from the definition of reflectivity and acoustic impedance. The constraint does not require any prior information of the subsurface and large extra computational costs, like the calculation of so-called Hessian matrices. We incorporate this constraint into the Joint Migration Inversion algorithm, which simultaneously estimates both the reflectivity and velocity model of the subsurface in an iterative process. Using so-called full wavefield modeling, the misfit between forward modeled and measured data is minimized. Numerical and field data examples are given to demonstrate the validity of our proposed algorithm in case accurate initial models and the low frequency components of observed seismic data are absent.

  20. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong

    2016-07-26

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

  1. Relativistic n-body wave equations in scalar quantum field theory

    International Nuclear Information System (INIS)

    Emami-Razavi, Mohsen

    2006-01-01

    The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields

  2. An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach

    KAUST Repository

    Asiri, Sharefa M.

    2013-05-25

    Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.

  3. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation

    Science.gov (United States)

    Jerke, Jonathan; Tymczak, C. J.; Poirier, Bill

    We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schrödinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation.

  4. Viscoacoustic wave-equation traveltime inversion with correct and incorrect attenuation profiles

    KAUST Repository

    Yu, Han

    2017-08-17

    A visco-acoustic wave-equation traveltime inversion method is presented that inverts for a shallow subsurface velocity distribution with correct and incorrect attenuation profiles. Similar to the classical wave equation traveltime inversion, this method applies the misfit functional that minimizes the first break differences between the observed and predicted data. Although, WT can partly avoid the cycle skipping problem, an initial velocity model approaches to the right or wrong velocity models under different setups of the attenuation profiles. However, with a Q model far away from the real model, the inverted tomogram is obviously different from the true velocity model while a small change of the Q model does not improve the inversion quality in a strong manner if low frequency information is not lost.

  5. Shock formation in small-data solutions to 3D quasilinear wave equations

    CERN Document Server

    Speck, Jared

    2016-01-01

    In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he prov...

  6. Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

    International Nuclear Information System (INIS)

    Wang Yun-Hu; Chen Yong

    2013-01-01

    We investigate the extended (2+1)-dimensional shallow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Bäcklund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method. (general)

  7. Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates

    Directory of Open Access Journals (Sweden)

    Povstenko YZ

    2011-01-01

    Full Text Available Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time , the Hankel transform with respect to the radial coordinate , the finite Fourier transform with respect to the angular coordinate , and the exponential Fourier transform with respect to the spatial coordinate . Numerical results are illustrated graphically.

  8. Travelling wave solutions for a surface wave equation in fluid mechanics

    Directory of Open Access Journals (Sweden)

    Tian Yi

    2016-01-01

    Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

  9. Global existence and decay of solutions of a nonlinear system of wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.

  10. A Laplace transform certified reduced basis method; application to the heat equation and wave equation

    OpenAIRE

    Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong

    2010-01-01

    We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...

  11. Well-posedness and exponential stability for a wave equation with nonlocal time-delay condition

    Directory of Open Access Journals (Sweden)

    Carlos Alberto Raposo

    2017-11-01

    Full Text Available Well-posedness and exponential stability of nonlocal time-delayed of a wave equation with a integral conditions of the 1st kind forms the center of this work. Through semigroup theory we prove the well-posedness by the Hille-Yosida theorem and the exponential stability exploring the dissipative properties of the linear operator associated to damped model using the Gearhart-Huang-Pruss theorem.

  12. THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION

    OpenAIRE

    Çenesiz, Yücel; Kurt, Ali

    2015-01-01

    – In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...

  13. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Sté phane; Said-Houari, Belkacem

    2011-01-01

    In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

  14. Soliton and periodic solutions for higher order wave equations of KdV type (I)

    International Nuclear Information System (INIS)

    Khuri, S.A.

    2005-01-01

    The aim of the paper is twofold. First, a new ansaetze is introduced for the construction of exact solutions for higher order wave equations of KdV type (I). We show the existence of a class of discontinuous soliton solutions with infinite spikes. Second, the projective Riccati technique is implemented as an alternate approach for obtaining new exact solutions, solitary solutions, and periodic wave solutions

  15. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2011-12-01

    In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

  16. Global existence and decay of solutions of a nonlinear system of wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-03-01

    This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.

  17. Optimization method for identifying the source term in an inverse wave equation

    Directory of Open Access Journals (Sweden)

    Arumugam Deiveegan

    2017-08-01

    Full Text Available In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.

  18. Non-periodic homogenization of 3-D elastic media for the seismic wave equation

    Science.gov (United States)

    Cupillard, Paul; Capdeville, Yann

    2018-05-01

    Because seismic waves have a limited frequency spectrum, the velocity structure of the Earth that can be extracted from seismic records has a limited resolution. As a consequence, one obtains smooth images from waveform inversion, although the Earth holds discontinuities and small scales of various natures. Within the last decade, the non-periodic homogenization method shed light on how seismic waves interact with small geological heterogeneities and `see' upscaled properties. This theory enables us to compute long-wave equivalent density and elastic coefficients of any media, with no constraint on the size, the shape and the contrast of the heterogeneities. In particular, the homogenization leads to the apparent, structure-induced anisotropy. In this paper, we implement this method in 3-D and show 3-D tests for the very first time. The non-periodic homogenization relies on an asymptotic expansion of the displacement and the stress involved in the elastic wave equation. Limiting ourselves to the order 0, we show that the practical computation of an upscaled elastic tensor basically requires (i) to solve an elastostatic problem and (ii) to low-pass filter the strain and the stress associated with the obtained solution. The elastostatic problem consists in finding the displacements due to local unit strains acting in all directions within the medium to upscale. This is solved using a parallel, highly optimized finite-element code. As for the filtering, we rely on the finite-element quadrature to perform the convolution in the space domain. We end up with an efficient numerical tool that we apply on various 3-D models to test the accuracy and the benefit of the homogenization. In the case of a finely layered model, our method agrees with results derived from Backus. In a more challenging model composed by a million of small cubes, waveforms computed in the homogenized medium fit reference waveforms very well. Both direct phases and complex diffracted waves are

  19. Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

    Science.gov (United States)

    Su, Bo; Tuo, Xianguo; Xu, Ling

    2017-08-01

    Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

  20. Theory of reflectivity blurring in seismic depth imaging

    Science.gov (United States)

    Thomson, C. J.; Kitchenside, P. W.; Fletcher, R. P.

    2016-05-01

    A subsurface extended image gather obtained during controlled-source depth imaging yields a blurred kernel of an interface reflection operator. This reflectivity kernel or reflection function is comprised of the interface plane-wave reflection coefficients and so, in principle, the gather contains amplitude versus offset or angle information. We present a modelling theory for extended image gathers that accounts for variable illumination and blurring, under the assumption of a good migration-velocity model. The method involves forward modelling as well as migration or back propagation so as to define a receiver-side blurring function, which contains the effects of the detector array for a given shot. Composition with the modelled incident wave and summation over shots then yields an overall blurring function that relates the reflectivity to the extended image gather obtained from field data. The spatial evolution or instability of blurring functions is a key concept and there is generally not just spatial blurring in the apparent reflectivity, but also slowness or angle blurring. Gridded blurring functions can be estimated with, for example, a reverse-time migration modelling engine. A calibration step is required to account for ad hoc band limitedness in the modelling and the method also exploits blurring-function reciprocity. To demonstrate the concepts, we show numerical examples of various quantities using the well-known SIGSBEE test model and a simple salt-body overburden model, both for 2-D. The moderately strong slowness/angle blurring in the latter model suggests that the effect on amplitude versus offset or angle analysis should be considered in more realistic structures. Although the description and examples are for 2-D, the extension to 3-D is conceptually straightforward. The computational cost of overall blurring functions implies their targeted use for the foreseeable future, for example, in reservoir characterization. The description is for scalar

  1. CMP reflection imaging via interferometry of distributed subsurface sources

    Science.gov (United States)

    Kim, D.; Brown, L. D.; Quiros, D. A.

    2015-12-01

    The theoretical foundations of recovering body wave energy via seismic interferometry are well established. However in practice, such recovery remains problematic. Here, synthetic seismograms computed for subsurface sources are used to evaluate the geometrical combinations of realistic ambient source and receiver distributions that result in useful recovery of virtual body waves. This study illustrates how surface receiver arrays that span a limited distribution suite of sources, can be processed to reproduce virtual shot gathers that result in CMP gathers which can be effectively stacked with traditional normal moveout corrections. To verify the feasibility of the approach in practice, seismic recordings of 50 aftershocks following the magnitude of 5.8 Virginia earthquake occurred in August, 2011 have been processed using seismic interferometry to produce seismic reflection images of the crustal structure above and beneath the aftershock cluster. Although monotonic noise proved to be problematic by significantly reducing the number of usable recordings, the edited dataset resulted in stacked seismic sections characterized by coherent reflections that resemble those seen on a nearby conventional reflection survey. In particular, "virtual" reflections at travel times of 3 to 4 seconds suggest reflector sat approximately 7 to 12 km depth that would seem to correspond to imbricate thrust structures formed during the Appalachian orogeny. The approach described here represents a promising new means of body wave imaging of 3D structure that can be applied to a wide array of geologic and energy problems. Unlike other imaging techniques using natural sources, this technique does not require precise source locations or times. It can thus exploit aftershocks too small for conventional analyses. This method can be applied to any type of microseismic cloud, whether tectonic, volcanic or man-made.

  2. Comparison of mouse mammary gland imaging techniques and applications: Reflectance confocal microscopy, GFP Imaging, and ultrasound

    International Nuclear Information System (INIS)

    Tilli, Maddalena T; Parrish, Angela R; Cotarla, Ion; Jones, Laundette P; Johnson, Michael D; Furth, Priscilla A

    2008-01-01

    Genetically engineered mouse models of mammary gland cancer enable the in vivo study of molecular mechanisms and signaling during development and cancer pathophysiology. However, traditional whole mount and histological imaging modalities are only applicable to non-viable tissue. We evaluated three techniques that can be quickly applied to living tissue for imaging normal and cancerous mammary gland: reflectance confocal microscopy, green fluorescent protein imaging, and ultrasound imaging. In the current study, reflectance confocal imaging offered the highest resolution and was used to optically section mammary ductal structures in the whole mammary gland. Glands remained viable in mammary gland whole organ culture when 1% acetic acid was used as a contrast agent. Our application of using green fluorescent protein expressing transgenic mice in our study allowed for whole mammary gland ductal structures imaging and enabled straightforward serial imaging of mammary gland ducts in whole organ culture to visualize the growth and differentiation process. Ultrasound imaging showed the lowest resolution. However, ultrasound was able to detect mammary preneoplastic lesions 0.2 mm in size and was used to follow cancer growth with serial imaging in living mice. In conclusion, each technique enabled serial imaging of living mammary tissue and visualization of growth and development, quickly and with minimal tissue preparation. The use of the higher resolution reflectance confocal and green fluorescent protein imaging techniques and lower resolution ultrasound were complementary

  3. Wave equation of a nonlinear triatomic molecule and the adiabatic correction to the Born--Oppenheimer approximation

    International Nuclear Information System (INIS)

    Bardo, R.D.; Wolfsberg, M.

    1977-01-01

    The wave equation for a nonlinear polyatomic molecule is formulated in molecule-fixed coordinates by a method originally due to Hirschfelder and Wigner. Application is made to a triatomic molecule, and the wave equation is explicitly presented in a useful molecule-fixed coordinate system. The formula for the adiabatic correction to the Born--Oppenheimer approximation for a triatomic molecule is obtained. The extension of the present formulation to larger polyatomic molecules is pointed out. Some terms in the triatomic molecule wave equation are discussed in detail

  4. Rapid prototyping of biomimetic vascular phantoms for hyperspectral reflectance imaging

    Science.gov (United States)

    Ghassemi, Pejhman; Wang, Jianting; Melchiorri, Anthony J.; Ramella-Roman, Jessica C.; Mathews, Scott A.; Coburn, James C.; Sorg, Brian S.; Chen, Yu; Joshua Pfefer, T.

    2015-12-01

    The emerging technique of rapid prototyping with three-dimensional (3-D) printers provides a simple yet revolutionary method for fabricating objects with arbitrary geometry. The use of 3-D printing for generating morphologically biomimetic tissue phantoms based on medical images represents a potentially major advance over existing phantom approaches. Toward the goal of image-defined phantoms, we converted a segmented fundus image of the human retina into a matrix format and edited it to achieve a geometry suitable for printing. Phantoms with vessel-simulating channels were then printed using a photoreactive resin providing biologically relevant turbidity, as determined by spectrophotometry. The morphology of printed vessels was validated by x-ray microcomputed tomography. Channels were filled with hemoglobin (Hb) solutions undergoing desaturation, and phantoms were imaged with a near-infrared hyperspectral reflectance imaging system. Additionally, a phantom was printed incorporating two disjoint vascular networks at different depths, each filled with Hb solutions at different saturation levels. Light propagation effects noted during these measurements-including the influence of vessel density and depth on Hb concentration and saturation estimates, and the effect of wavelength on vessel visualization depth-were evaluated. Overall, our findings indicated that 3-D-printed biomimetic phantoms hold significant potential as realistic and practical tools for elucidating light-tissue interactions and characterizing biophotonic system performance.

  5. Rapid prototyping of biomimetic vascular phantoms for hyperspectral reflectance imaging

    Science.gov (United States)

    Ghassemi, Pejhman; Wang, Jianting; Melchiorri, Anthony J.; Ramella-Roman, Jessica C.; Mathews, Scott A.; Coburn, James C.; Sorg, Brian S.; Chen, Yu; Joshua Pfefer, T.

    2015-01-01

    Abstract. The emerging technique of rapid prototyping with three-dimensional (3-D) printers provides a simple yet revolutionary method for fabricating objects with arbitrary geometry. The use of 3-D printing for generating morphologically biomimetic tissue phantoms based on medical images represents a potentially major advance over existing phantom approaches. Toward the goal of image-defined phantoms, we converted a segmented fundus image of the human retina into a matrix format and edited it to achieve a geometry suitable for printing. Phantoms with vessel-simulating channels were then printed using a photoreactive resin providing biologically relevant turbidity, as determined by spectrophotometry. The morphology of printed vessels was validated by x-ray microcomputed tomography. Channels were filled with hemoglobin (Hb) solutions undergoing desaturation, and phantoms were imaged with a near-infrared hyperspectral reflectance imaging system. Additionally, a phantom was printed incorporating two disjoint vascular networks at different depths, each filled with Hb solutions at different saturation levels. Light propagation effects noted during these measurements—including the influence of vessel density and depth on Hb concentration and saturation estimates, and the effect of wavelength on vessel visualization depth—were evaluated. Overall, our findings indicated that 3-D-printed biomimetic phantoms hold significant potential as realistic and practical tools for elucidating light–tissue interactions and characterizing biophotonic system performance. PMID:26662064

  6. Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

    Science.gov (United States)

    Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

    2015-12-01

    The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

  7. On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

    KAUST Repository

    Gao, Longfei; Ketcheson, David I.; Keyes, David E.

    2017-01-01

    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application

  8. Some exact solutions to the potential Kadomtsev-Petviashvili equation and to a system of shallow water wave equations

    International Nuclear Information System (INIS)

    Inan, Ibrahim E.; Kaya, Dogan

    2006-01-01

    In this Letter by considering an improved tanh function method, we found some exact solutions of the potential Kadomtsev-Petviashvili equation. Some exact solutions of the system of the shallow water wave equation were also found

  9. Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow

    KAUST Repository

    Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem

    2017-01-01

    In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations

  10. Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

    International Nuclear Information System (INIS)

    Carter, B.; McLenaghan, R.G.

    1982-01-01

    It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

  11. Accelerating 3D Elastic Wave Equations on Knights Landing based Intel Xeon Phi processors

    Science.gov (United States)

    Sourouri, Mohammed; Birger Raknes, Espen

    2017-04-01

    In advanced imaging methods like reverse-time migration (RTM) and full waveform inversion (FWI) the elastic wave equation (EWE) is numerically solved many times to create the seismic image or the elastic parameter model update. Thus, it is essential to optimize the solution time for solving the EWE as this will have a major impact on the total computational cost in running RTM or FWI. From a computational point of view applications implementing EWEs are associated with two major challenges. The first challenge is the amount of memory-bound computations involved, while the second challenge is the execution of such computations over very large datasets. So far, multi-core processors have not been able to tackle these two challenges, which eventually led to the adoption of accelerators such as Graphics Processing Units (GPUs). Compared to conventional CPUs, GPUs are densely populated with many floating-point units and fast memory, a type of architecture that has proven to map well to many scientific computations. Despite its architectural advantages, full-scale adoption of accelerators has yet to materialize. First, accelerators require a significant programming effort imposed by programming models such as CUDA or OpenCL. Second, accelerators come with a limited amount of memory, which also require explicit data transfers between the CPU and the accelerator over the slow PCI bus. The second generation of the Xeon Phi processor based on the Knights Landing (KNL) architecture, promises the computational capabilities of an accelerator but require the same programming effort as traditional multi-core processors. The high computational performance is realized through many integrated cores (number of cores and tiles and memory varies with the model) organized in tiles that are connected via a 2D mesh based interconnect. In contrary to accelerators, KNL is a self-hosted system, meaning explicit data transfers over the PCI bus are no longer required. However, like most

  12. A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

    Directory of Open Access Journals (Sweden)

    Liquan Mei

    2014-01-01

    Full Text Available A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.

  13. The high exponent limit $p \\to \\infty$ for the one-dimensional nonlinear wave equation

    OpenAIRE

    Tao, Terence

    2009-01-01

    We investigate the behaviour of solutions $\\phi = \\phi^{(p)}$ to the one-dimensional nonlinear wave equation $-\\phi_{tt} + \\phi_{xx} = -|\\phi|^{p-1} \\phi$ with initial data $\\phi(0,x) = \\phi_0(x)$, $\\phi_t(0,x) = \\phi_1(x)$, in the high exponent limit $p \\to \\infty$ (holding $\\phi_0, \\phi_1$ fixed). We show that if the initial data $\\phi_0, \\phi_1$ are smooth with $\\phi_0$ taking values in $(-1,1)$ and obey a mild non-degeneracy condition, then $\\phi$ converges locally uniformly to a piecewis...

  14. Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Sté phane; Said-Houari, Belkacem

    2013-01-01

    The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.

  15. Anomalies of the free loop wave equation in the WKB approximation

    International Nuclear Information System (INIS)

    Weisz, P.; Luescher, M.; Symanzik, K.

    1980-04-01

    We derive a well-defined, reparametrization invariant expression for the next to leading term in the small h/2π expansion of the Euclidean loop Green's functional PSI(C). To this order in h/2π, we then verify that PSI(C) satisfies a renormalized loop wave equation, which involves a number of local, but non-harmonic anomalous terms. Also, we find that the quantum fluctuations of the string give rise, in 3 + 1 dimensions, to a correction of the static quark potential by an attractive Coulomb potential of universal strength αsub(string) = π/12. (orig.)

  16. An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

    KAUST Repository

    Asiri, Sharefa M.; Zayane, Chadia; Laleg-Kirati, Taous-Meriem

    2015-01-01

    Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

  17. Two particles interacting via the Yukawa potential in the frame of a truly nonrelativistic wave equation

    International Nuclear Information System (INIS)

    Kukhtin, V.V.; Kuzmenko, M.V.

    2000-01-01

    Complete text of publication follows. Recent studies (1) have shown that the Schroedinger nonrelativistic wave equation for a system of interacting particles is not a rigorously nonrelativistic one since it is based on the implicit assumption that the interaction propagation velocity is a finite value, which implies commutativity of the operators of coordinates and momenta of different particles. The refusal from this assumption implies their noncommutativity, which allows one to construct a truly nonrelativistic nonlinear self-consistent wave equation for a system of interacting particles. In the frame of the advanced wave equation, we investigate the spectrum of bound states for the two-body problem with the Yukawa potential V(r) = -V 0 a exp(-r/a)/r as a function of parameters of the potential. A peculiar feature of the spectrum is the presence of a critical value of V 0 (with the fixed parameter a), above which the given bound state cannot exist. In the ground state with l = 0 at a critical value of V 0 , the mean distance between particles takes the least value equal to the Compton wavelength of the particle with reduced mass. We estimate the parameter of noncommutativity ε for the operators of the coordinate of one particle and of the momentum of other one ([χ 1 , p 2x ] = i(h/2π)m 2 /M x ε) for the bound state of a deuteron, for which we consider the lowest state with l = 0 as its ground state. The parameter a of the Yukawa potential is taken to be equal to the Compton wavelength of a pion, 1.41 fm. In order to obtain the binding energy of a deuteron E = -2.22452 MeV, the parameter V 0 has to equal 51.23 MeV. In this case, the parameter of noncommutativity ε for the operators of the coordinate of one particle and of the momentum of other one ε = 0.0011, i.e., the commutator is nonzero even for such a weakly bound system as a deuteron where particles are located outside the region of action of nuclear forces for a significant fraction of time. Moreover

  18. An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

    KAUST Repository

    Asiri, Sharefa M.

    2015-08-31

    Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

  19. New multidimensional partially integrable generalization of S-integrable N-wave equation

    International Nuclear Information System (INIS)

    Zenchuk, A. I.

    2007-01-01

    This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. The method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n. The associated solution space is not full, although it is parametrized by certain number of arbitrary functions of (n-1) variables. We consider four-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example

  20. Solving the KPI wave equation with a moving adaptive FEM grid

    Directory of Open Access Journals (Sweden)

    Granville Sewell

    2013-04-01

    Full Text Available The Kadomtsev-Petviashvili I (KPI equation is the difficult nonlinear wave equation $U_{xt} + 6U_x^2 + 6UU_{xx} + U_{xxxx} = 3U_{yy}.$ We solve this equation using PDE2D (www.pde2d.com with initial conditions consisting of two lump solitons, which collide and reseparate. Since the solution has steep, moving, peaks, an adaptive finite element grid is used with a grading which moves with the peaks.

  1. Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

    KAUST Repository

    Gerbi, Stéphane

    2013-01-15

    The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.

  2. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    KAUST Repository

    Li, Jing

    2017-08-17

    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  3. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    KAUST Repository

    Li, Jing; Schuster, Gerard T.; Lin, Fan-Chi; Alam, Amir

    2017-01-01

    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  4. Global Nonexistence of Solutions for Viscoelastic Wave Equations of Kirchhoff Type with High Energy

    Directory of Open Access Journals (Sweden)

    Gang Li

    2012-01-01

    Full Text Available We consider viscoelastic wave equations of the Kirchhoff type utt-M(∥∇u∥22Δu+∫0tg(t-sΔu(sds+ut=|u|p-1u with Dirichlet boundary conditions, where ∥⋅∥p denotes the norm in the Lebesgue space Lp. Under some suitable assumptions on g and the initial data, we establish a global nonexistence result for certain solutions with arbitrarily high energy, in the sense that lim⁡t→T*-(∥u(t∥22+∫0t∥u(s∥22ds=∞ for some 0

  5. Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

    Science.gov (United States)

    Baumeister, K. J.

    1983-01-01

    A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

  6. Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

    Science.gov (United States)

    Baumeiste, K. J.

    1983-01-01

    A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

  7. Solution of the nonrelativistic wave equation using the tridiagonal representation approach

    Science.gov (United States)

    Alhaidari, A. D.

    2017-07-01

    We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable problems in this approach is larger than the conventional class (see, for example, Table XII in the text). We also give very accurate results for cases where the wave operator matrix is not tridiagonal but its elements could be evaluated either exactly or numerically with high precision.

  8. The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

    International Nuclear Information System (INIS)

    Mourad, J.; Sazdjian, H.

    1994-01-01

    The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

  9. Integral representations of solutions of the wave equation based on relativistic wavelets

    International Nuclear Information System (INIS)

    Perel, Maria; Gorodnitskiy, Evgeny

    2012-01-01

    A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed. (paper)

  10. Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed

    Science.gov (United States)

    Ruzhansky, Michael; Tokmagambetov, Niyaz

    2017-12-01

    Given a Hilbert space H, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting on H. We consider the cases when the time-dependent propagation speed is regular, Hölder, and distributional. We also consider cases when it is strictly positive (strictly hyperbolic case) and when it is non-negative (weakly hyperbolic case). When the propagation speed is a distribution, we introduce the notion of "very weak solutions" to the Cauchy problem. We show that the Cauchy problem for the wave equation with the distributional coefficient has a unique "very weak solution" in an appropriate sense, which coincides with classical or distributional solutions when the latter exist. Examples include the harmonic and anharmonic oscillators, the Landau Hamiltonian on {R^n}, uniformly elliptic operators of different orders on domains, Hörmander's sums of squares on compact Lie groups and compact manifolds, operators on manifolds with boundary, and many others.

  11. The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

    International Nuclear Information System (INIS)

    Scully, M O

    2008-01-01

    The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

  12. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson; Said-Houari, Belkacem

    2012-01-01

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  13. General decay of solutions of a nonlinear system of viscoelastic wave equations

    KAUST Repository

    Said-Houari, Belkacem; Messaoudi, Salim A.; Guesmia, Aï ssa

    2011-01-01

    This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.

  14. Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations

    Science.gov (United States)

    Alzahrani, Mohammed A.; Gauthier, Robert C.

    2015-02-01

    For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.

  15. Linear and quadratic exponential modulation of the solutions of the paraxial wave equation

    International Nuclear Information System (INIS)

    Torre, A

    2010-01-01

    A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes

  16. Separation of variables for the nonlinear wave equation in polar coordinates

    International Nuclear Information System (INIS)

    Shermenev, Alexander

    2004-01-01

    Some classical types of nonlinear wave motion in polar coordinates are studied within quadratic approximation. When the nonlinear quadratic terms in the wave equation are arbitrary, the usual perturbation techniques used in polar coordinates leads to overdetermined systems of linear algebraic equations for the unknown coefficients. However, we show that these overdetermined systems are compatible with the special case of the nonlinear shallow water equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear shallow water equation that are periodic in time and found with the same accuracy as the equation is derived

  17. Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity

    Directory of Open Access Journals (Sweden)

    Gabriel Nguetseng

    2010-01-01

    Full Text Available The present work is devoted to the study of homogenization of the weakly damped wave equation ∫Ωρε∂2uε∂t2(t⋅υdx+2ε2μ∫ΩfεEij(∂uε∂t(tEij(υdx+ε2λ∫Ωfεdiv(∂uε∂t(tdiv υdx+ϑ∫Ωfεdiv(uε(tdivυdx=∫Ωf(t⋅υdx  for all υ=(υ1,υ2,υ3∈Vε(0

  18. General decay of solutions of a nonlinear system of viscoelastic wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2011-04-16

    This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.

  19. On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

    Science.gov (United States)

    Lupo, Umberto

    2018-04-01

    The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

  20. Existence and asymptotic stability of a viscoelastic wave equation with a delay

    KAUST Repository

    Kirane, Mokhtar

    2011-07-07

    In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem, together with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ1, μ2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. © 2011 Springer Basel AG.

  1. Existence and asymptotic behavior of the wave equation with dynamic boundary conditions

    KAUST Repository

    Graber, Philip Jameson

    2012-03-07

    The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.

  2. Existence and asymptotic stability of a viscoelastic wave equation with a delay

    KAUST Repository

    Kirane, Mokhtar; Said-Houari, Belkacem

    2011-01-01

    In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem, together with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ1, μ2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. © 2011 Springer Basel AG.

  3. Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N. Anders; Sjögreen, Björn

    2014-10-01

    Abstract

    We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more

  4. Cylindrical and spherical space equivalents to the plane wave expansion technique of Maxwell's wave equations

    Science.gov (United States)

    Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed

    2015-02-01

    The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.

  5. Analysis and Computation of Acoustic and Elastic Wave Equations in Random Media

    KAUST Repository

    Motamed, Mohammad

    2014-01-06

    We propose stochastic collocation methods for solving the second order acoustic and elastic wave equations in heterogeneous random media and subject to deterministic boundary and initial conditions [1, 4]. We assume that the medium consists of non-overlapping sub-domains with smooth interfaces. In each sub-domain, the materials coefficients are smooth and given or approximated by a finite number of random variable. One important example is wave propagation in multi-layered media with smooth interfaces. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems [2, 3], the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence is only algebraic. A fast spectral rate of convergence is still possible for some quantities of interest and for the wave solutions with particular types of data. We also show that the semi-discrete solution is analytic with respect to the random variables with the radius of analyticity proportional to the grid/mesh size h. We therefore obtain an exponential rate of convergence which deteriorates as the quantity h p gets smaller, with p representing the polynomial degree in the stochastic space. We have shown that analytical results and numerical examples are consistent and that the stochastic collocation method may be a valid alternative to the more traditional Monte Carlo method. Here we focus on the stochastic acoustic wave equation. Similar results are obtained for stochastic elastic equations.

  6. Introducing time-dependent molecular fields: a new derivation of the wave equations

    Science.gov (United States)

    Baer, Michael

    2018-02-01

    This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

  7. An improved method to estimate reflectance parameters for high dynamic range imaging

    Science.gov (United States)

    Li, Shiying; Deguchi, Koichiro; Li, Renfa; Manabe, Yoshitsugu; Chihara, Kunihiro

    2008-01-01

    Two methods are described to accurately estimate diffuse and specular reflectance parameters for colors, gloss intensity and surface roughness, over the dynamic range of the camera used to capture input images. Neither method needs to segment color areas on an image, or to reconstruct a high dynamic range (HDR) image. The second method improves on the first, bypassing the requirement for specific separation of diffuse and specular reflection components. For the latter method, diffuse and specular reflectance parameters are estimated separately, using the least squares method. Reflection values are initially assumed to be diffuse-only reflection components, and are subjected to the least squares method to estimate diffuse reflectance parameters. Specular reflection components, obtained by subtracting the computed diffuse reflection components from reflection values, are then subjected to a logarithmically transformed equation of the Torrance-Sparrow reflection model, and specular reflectance parameters for gloss intensity and surface roughness are finally estimated using the least squares method. Experiments were carried out using both methods, with simulation data at different saturation levels, generated according to the Lambert and Torrance-Sparrow reflection models, and the second method, with spectral images captured by an imaging spectrograph and a moving light source. Our results show that the second method can estimate the diffuse and specular reflectance parameters for colors, gloss intensity and surface roughness more accurately and faster than the first one, so that colors and gloss can be reproduced more efficiently for HDR imaging.

  8. Enface Thickness Mapping and Reflectance Imaging of Retinal Layers in Diabetic Retinopathy.

    Science.gov (United States)

    Francis, Andrew W; Wanek, Justin; Lim, Jennifer I; Shahidi, Mahnaz

    2015-01-01

    To present a method for image segmentation and generation of enface thickness maps and reflectance images of retinal layers in healthy and diabetic retinopathy (DR) subjects. High density spectral domain optical coherence tomography (SDOCT) images were acquired in 10 healthy and 4 DR subjects. Customized image analysis software identified 5 retinal cell layer interfaces and generated thickness maps and reflectance images of the total retina (TR), inner retina (IR), outer retina (OR), and the inner segment ellipsoid (ISe) band. Thickness maps in DR subjects were compared to those of healthy subjects by generating deviation maps which displayed retinal locations with thickness below, within, and above the normal 95% confidence interval. In healthy subjects, TR and IR thickness maps displayed the foveal depression and increased thickness in the parafoveal region. OR and ISe thickness maps showed increased thickness at the fovea, consistent with normal retinal anatomy. In DR subjects, thickening and thinning in localized regions were demonstrated on TR, IR, OR, and ISe thickness maps, corresponding to retinal edema and atrophy, respectively. TR and OR reflectance images showed reduced reflectivity in regions of increased thickness. Hard exudates appeared as hyper-reflective spots in IR reflectance images and casted shadows on the deeper OR and ISe reflectance images. The ISe reflectance image clearly showed the presence of focal laser scars. Enface thickness mapping and reflectance imaging of retinal layers is a potentially useful method for quantifying the spatial and axial extent of pathologies due to DR.

  9. About the use of reflectance terminology in imaging spectroscopy

    NARCIS (Netherlands)

    Schaepman-Strub, G.; Schaepman, M.E.; Dangel, S.; Painter, T.; Martonchik, J.

    2005-01-01

    Analysing databases, field and airborne spectrometer data, modelling studies and publications, a lack of consistency in the use of definitions and terminology of reflectance quantities can be observed. One example is the term `BRDF¿ (bidirectional reflectance distribution function) assigned to

  10. Azimuth and angle gathers from wave equation imaging in VTI media

    KAUST Repository

    Alkhalifah, Tariq Ali; Fomel, Sergey B.

    2009-01-01

    by the need to properly estimate multiple anisotropic parameters for a proper representation of the medium. We extract angle gathers for each downward-continuation step from converting offset-space-frequency planes into angle-space planes simultaneously

  11. Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Dumitru Baleanu

    2014-01-01

    Full Text Available We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

  12. A Semilinear Wave Equation with a Boundary Condition of Many-Point Type: Global Existence and Stability of Weak Solutions

    Directory of Open Access Journals (Sweden)

    Giai Giang Vo

    2015-01-01

    Full Text Available This paper is devoted to the study of a wave equation with a boundary condition of many-point type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established.

  13. Ray-tracing traveltime tomography versus wave-equation traveltime inversion for near-surface seismic land data

    KAUST Repository

    Fu, Lei; Hanafy, Sherif M.

    2017-01-01

    . This initial starting model can be obtained by inverting traveltimes with ray-tracing traveltime tomography (RT) or wave-equation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the first

  14. Image-based reflectance conversion of ASTER and IKONOS ...

    African Journals Online (AJOL)

    Spectral signatures derived from different image-based models for ASTER and IKONOS were inspected visually as first departure. This was followed by comparison of the total accuracy and Kappa index computed from supervised classification of images that were derived from different image-based atmospheric correction ...

  15. A vector field method on the distorted Fourier side and decay for wave equations with potentials

    CERN Document Server

    Donninger, Roland

    2016-01-01

    The authors study the Cauchy problem for the one-dimensional wave equation \\partial_t^2 u(t,x)-\\partial_x^2 u(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)\\sim -\\tfrac14 |x|^{-2}\\mbox{ as } |x|\\to \\infty. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t\\partial_t+x\\partial_x, where the latter are obtained by employing a vector field method on the âeoedistortedâe Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, âeoeCodimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski spaceâe, preprint arXiv:1310.5606 (2013).

  16. Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions

    Directory of Open Access Journals (Sweden)

    Nguyen Thanh Long

    2005-12-01

    Full Text Available In this paper we consider the nonlinear wave equation problem $$displaylines{ u_{tt}-Big(|u|_0^2,|u_{r}|_0^2ig(u_{rr}+frac{1}{r}u_{r} =f(r,t,u,u_{r},quad 0less than r less than 1,; 0 less than t less than T, ig|lim_{ro 0^+}sqrt{r}u_{r}(r,tig| less than infty, u_{r}(1,t+hu(1,t=0, u(r,0=widetilde{u}_0(r, u_{t}(r,0=widetilde{u}_1(r. }$$ To this problem, we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved, in weighted Sobolev using standard compactness arguments. In the latter part, we give sufficient conditions for quadratic convergence to the solution of the original problem, for an autonomous right-hand side independent on $u_{r}$ and a coefficient function $B$ of the form $B=B(|u|_0^2=b_0+|u|_0^2$ with $b_0$ greater than 0.

  17. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem

    2012-09-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  18. Energy decay for wave equations of phi-Laplacian type with weakly nonlinear dissipation

    Directory of Open Access Journals (Sweden)

    Aissa Guesmia

    2008-08-01

    Full Text Available In this paper, first we prove the existence of global solutions in Sobolev spaces for the initial boundary value problem of the wave equation of $phi$-Laplacian with a general dissipation of the form $$ (|u'|^{l-2}u''-Delta_{phi}u+sigma(t g(u'=0 quadext{in } Omegaimes mathbb{R}_+ , $$ where $Delta_{phi}=sum_{i=1}^n partial_{x_i}igl(phi (|partial_{x_i}|^2partial_{x_i}igr$. Then we prove general stability estimates using multiplier method and general weighted integral inequalities proved by the second author in [18]. Without imposing any growth condition at the origin on $g$ and $phi$, we show that the energy of the system is bounded above by a quantity, depending on $phi$, $sigma$ and $g$, which tends to zero (as time approaches infinity. These estimates allows us to consider large class of functions $g$ and $phi$ with general growth at the origin. We give some examples to illustrate how to derive from our general estimates the polynomial, exponential or logarithmic decay. The results of this paper improve and generalize many existing results in the literature, and generate some interesting open problems.

  19. Nonlinear dynamics of vortices in ultraclean type-II superconductors: Integrable wave equations in cylindrical geometry

    International Nuclear Information System (INIS)

    Coffey, M.W.

    1996-01-01

    Due to their short coherence lengths and relatively large energy gaps, the high-transition temperature superconductors are very likely candidates as ultraclean materials at low temperature. This class of materials features significantly modified vortex dynamics, with very little dissipation at low temperature. The motion is then dominated by wave propagation, being in general nonlinear. Here two-dimensional vortex motion is investigated in the ultraclean regime for a superconductor described in cylindrical geometry. The small-amplitude limit is assumed, and the focus is on the long-wavelength limit. Results for both zero and nonzero Hall force are presented, with the effects of nonlocal vortex interaction and vortex inertia being included within London theory. Linear and nonlinear problems are studied, with a predisposition toward the more analytically tractable situations. For a nonlinear problem in 2+1 dimensions, the cylindrical Kadomtsev-Petviashvili equation is derived. Hall angle measurements on high-T c superconductors indicate the need to investigate the properties of such a completely integrable wave equation. copyright 1996 The American Physical Society

  20. Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

    Energy Technology Data Exchange (ETDEWEB)

    Múnera, Héctor A., E-mail: hmunera@hotmail.com [Centro Internacional de Física (CIF), Apartado Aéreo 4948, Bogotá, Colombia, South America (Colombia); Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America (Colombia)

    2016-07-07

    It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.

  1. A simple finite-difference scheme for handling topography with the first-order wave equation

    Science.gov (United States)

    Mulder, W. A.; Huiskes, M. J.

    2017-07-01

    One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.

  2. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    KAUST Repository

    Said-Houari, Belkacem; Nascimento, Flá vio A Falcã o

    2012-01-01

    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.

  3. Analysis and computation of the elastic wave equation with random coefficients

    KAUST Repository

    Motamed, Mohammad

    2015-10-21

    We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest. We study the convergence rate of the error in the stochastic collocation method. In particular, we show that, the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space, which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest. We demonstrate that a fast rate of convergence is possible in two cases: for the elastic wave solutions with high regular data; and for some high regular quantities of interest even in the presence of low regular data. We perform numerical examples, including a simplified earthquake, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo sampling method for approximating quantities with high stochastic regularity.

  4. Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations

    Science.gov (United States)

    Bonnasse-Gahot, Marie; Calandra, Henri; Diaz, Julien; Lanteri, Stéphane

    2018-04-01

    Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the 3-D case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of the so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study an HDG method for the resolution of the frequency-domain elastic wave equations in the 2-D case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system.

  5. A stochastic collocation method for the second order wave equation with a discontinuous random speed

    KAUST Repository

    Motamed, Mohammad

    2012-08-31

    In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.

  6. A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

    KAUST Repository

    Duru, Kenneth

    2014-01-01

    A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.

  7. WAVE EQUATION DATUMING TO CORRECT TOPOGRAPHY EFFECT ON FOOTHILL SEISMIC DATA

    Directory of Open Access Journals (Sweden)

    Montes Vides Luis Alfredo

    2005-08-01

    Full Text Available The current seismic processing applies Static Corrections to overcome the effects associated to rough topography, based in the assumption that velocity in near surface is lower than in the substratum, which force going up rays travel near to vertical. However, when the velocity contrast between these layers is not large enough, the trajectory of the up going rays deviate from vertical raveling the reflectors erroneously. A better alternative to correct this is to continue the wave field to a datum, because it does not assume vertical ray trajectory and solves the acoustic wave equation to extrapolate sources and receivers. The Kirchhoff approach was tested in synthetic shots continuing their wave field to a datum and finally it was applied instead of Static Corrections in real data acquired in foothill zones. First shot and receiver gathers were downward continued to the base of weathering layer and later upward continued to a final flat datum. Comparing the obtained results we observed that continuation approach provides a noticeable enhancement of reflectors in seismic records, displaying a better continuity of the reflectors and an increment in frequency content.

  8. Initial-value problem for the 1-D wave equation in an inhomogeneous medium

    International Nuclear Information System (INIS)

    Sedlacek, Z.; Roberts, B.; Adam, J.A.

    1986-03-01

    A complete mathematical analysis of oscillations of an inhomogeneous medium described by a wave equation with a space-dependent coefficient is given. The initial-value problem is solved both by the Laplace transform and by normal-mode analysis and the equivalency of both approaches is demonstrated. The Green function of the problem is a double-valued function of the complex frequency, analytic in the upper and lower halves of the complex frequency plane (the ''physical'' sheet of its Riemann surface) with discontinuity on the whole real axis, corresponding to the continuous frequency spectrum of the physical system in question. The Green function has complex poles on analytic continuation onto the ''unphysical'' sheet of its Riemann surface. This makes it possible, by inverting the Laplace transform, to interpret the solution of the initial-value problem in terms of ''damped'' eigenmodes. The continuum eigenmodes can be constructed directly and are also recovered by integrating the Green function in the complex frequency plane along a closed contour enclosing the spectrum. Their orthogonality and completeness is proved. The solution of the initial-value problem synthesized from the continuum eigenmodes can be interpreted in terms of travelling disturbances scattered by inhomogeneity. (author)

  9. Calculation of coherent synchrotron radiation in toroidal waveguides by paraxial wave equation

    Directory of Open Access Journals (Sweden)

    D. R. Gillingham

    2007-05-01

    Full Text Available A new technique for the simulation of coherent synchrotron radiation (CSR and space-charge fields from a single electron bunch in straight or toroidal rectangular waveguide sections has been developed. It is based on the integration of the paraxial approximation to the wave equations, using the perturbation technique where the bending radius is large compared to the dimension of the waveguide. We have implemented an unconditionally stable integration method in the time domain with transparent boundary conditions that allows the use of a minimally sized computational domain about the bunch. This technique explicitly enforces the causality condition so that no portion of the fields can propagate faster than the speed of light, can be used with arbitrary three-dimensional charge distributions, and contains corrections for finite energy. We have also developed a method for the calculation of the transverse forces within the bunch including space-charge. This method has been developed for incorporation with a particle-in-cell code so that we may self-consistently model CSR and space-charge in combinations of bending sections with a fully dynamic electron bunch in an efficient manner. In this paper we describe the model and methods for calculation of the fields in detail and compare results to theory wherever possible.

  10. Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

    Science.gov (United States)

    Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

    2013-09-01

    Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

  11. Reflection-artifact-free photoacoustic imaging using PAFUSion (photoacoustic-guided focused ultrasound)

    Science.gov (United States)

    Kuniyil Ajith Singh, Mithun; Jaeger, Michael; Frenz, Martin; Steenbergen, Wiendelt

    2016-03-01

    Reflection artifacts caused by acoustic inhomogeneities are a main challenge to deep-tissue photoacoustic imaging. Photoacoustic transients generated by the skin surface and superficial vasculature will propagate into the tissue and reflect back from echogenic structures to generate reflection artifacts. These artifacts can cause problems in image interpretation and limit imaging depth. In its basic version, PAFUSion mimics the inward travelling wave-field from blood vessel-like PA sources by applying focused ultrasound pulses, and thus provides a way to identify reflection artifacts. In this work, we demonstrate reflection artifact correction in addition to identification, towards obtaining an artifact-free photoacoustic image. In view of clinical applications, we implemented an improved version of PAFUSion in which photoacoustic data is backpropagated to imitate the inward travelling wave-field and thus the reflection artifacts of a more arbitrary distribution of PA sources that also includes the skin melanin layer. The backpropagation is performed in a synthetic way based on the pulse-echo acquisitions after transmission on each single element of the transducer array. We present a phantom experiment and initial in vivo measurements on human volunteers where we demonstrate significant reflection artifact reduction using our technique. The results provide a direct confirmation that reflection artifacts are prominent in clinical epi-photoacoustic imaging, and that PAFUSion can reduce these artifacts significantly to improve the deep-tissue photoacoustic imaging.

  12. A Novel 3D Viscoelastic Acoustic Wave Equation Based Update Method for Reservoir History Matching

    KAUST Repository

    Katterbauer, Klemens

    2014-12-10

    The oil and gas industry has been revolutionized within the last decade, with horizontal drilling and hydraulic fracturing enabling the extraction of huge amounts of shale gas in areas previously considered impossible and the recovering of hydrocarbons in harsh environments like the arctic or in previously unimaginable depths like the off-shore exploration in the South China sea and Gulf of Mexico. With the development of 4D seismic, engineers and scientists have been enabled to map the evolution of fluid fronts within the reservoir and determine the displacement caused by the injected fluids. This in turn has led to enhanced production strategies, cost reduction and increased profits. Conventional approaches to incorporate seismic data into the history matching process have been to invert these data for constraints that are subsequently employed in the history matching process. This approach makes the incorporation computationally expensive and requires a lot of manual processing for obtaining the correct interpretation due to the potential artifacts that are generated by the generally ill-conditioned inversion problems. I have presented here a novel approach via including the time-lapse cross-well seismic survey data directly into the history matching process. The generated time-lapse seismic data are obtained from the full wave 3D viscoelastic acoustic wave equation. Furthermore an extensive analysis has been performed showing the robustness of the method and enhanced forecastability of the critical reservoir parameters, reducing uncertainties and exhibiting the benefits of a full wave 3D seismic approach. Finally, the improved performance has been statistically confirmed. The improvements illustrate the significant improvements in forecasting that are obtained via readily available seismic data without the need for inversion. This further optimizes oil production in addition to increasing return-on-investment on oil & gas field development projects, especially

  13. Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

    Science.gov (United States)

    Jun, Li; Huicheng, Yin

    2018-05-01

    The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

  14. A spectral image processing algorithm for evaluating the influence of the illuminants on the reconstructed reflectance

    Science.gov (United States)

    Toadere, Florin

    2017-12-01

    A spectral image processing algorithm that allows the illumination of the scene with different illuminants together with the reconstruction of the scene's reflectance is presented. Color checker spectral image and CIE A (warm light 2700 K), D65 (cold light 6500 K) and Cree TW Series LED T8 (4000 K) are employed for scene illumination. Illuminants used in the simulations have different spectra and, as a result of their illumination, the colors of the scene change. The influence of the illuminants on the reconstruction of the scene's reflectance is estimated. Demonstrative images and reflectance showing the operation of the algorithm are illustrated.

  15. Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

    Institute of Scientific and Technical Information of China (English)

    Tang Wen-Lin; Tian Gui-Hua

    2011-01-01

    The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

  16. Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow

    KAUST Repository

    Asiri, Sharefa M.

    2017-10-19

    In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations of blood mass density. The method is described and its performance is assessed through some numerical simulations. The robustness of the method in presence of noise is also studied.

  17. A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

    Science.gov (United States)

    Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

    2012-12-11

    The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

  18. How one can construct a consistent relativistic quantum mechanics on the base of a relativistic wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica

    2000-07-01

    Full text follows: There is a common opinion that the construction of a consistent relativistic quantum mechanics on the base of a relativistic wave equation meets well-known difficulties related to the existence of infinite number of negative energy levels, to the existence of negative vector norms, and so on, which may be only solved in a second-quantized theory, see, for example, two basic papers devoted to the problem L.Foldy, S.Wouthuysen, Phys. Rep.78 (1950) 29; H.Feshbach, F.Villars, Rev. Mod. Phys. 30 (1958) 24, whose arguments are repeated in all handbooks in relativistic quantum theory. Even Dirac trying to solve the problem had turned last years to infinite-component relativistic wave equations, see P.A.M. Dirac, Proc. R. Soc. London, A328 (1972) 1. We believe that a consistent relativistic quantum mechanics may be constructed on the base of an extended (charge symmetric) equation, which unite both a relativistic wave equation for a particle and for an antiparticle. We present explicitly the corresponding construction, see for details hep-th/0003112. We support such a construction by two demonstrations: first, in course of a careful canonical quantization of the corresponding classical action of a relativistic particle we arrive just to such a consistent quantum mechanics; second, we demonstrate that a reduction of the QFT of a corresponding field (scalar, spinor, etc.) to one-particle sector, if such a reduction may be done, present namely this quantum mechanics. (author)

  19. Reflections

    Directory of Open Access Journals (Sweden)

    Joanne Embree

    2001-01-01

    Full Text Available Ideally, editorials are written one to two months before publication in the Journal. It was my turn to write this one. I had planned to write the first draft the evening after my clinic on Tuesday, September 11. It didn't get done that night or during the next week. Somehow, the topic that I had originally chosen just didn't seem that important anymore as I, along my friends and colleagues, reflected on the changes that the events of that day were likely to have on our lives.

  20. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Synthetic and field data examples

    KAUST Repository

    Zhang, Sanzong; Luo, Yi; Schuster, Gerard T.

    2015-01-01

    . The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime

  1. Reflecting the divine image: The crux of Umunthu in contemporary ...

    African Journals Online (AJOL)

    ... implications of the nature of the image of God in humans; thereby pointing out that .... cradle of African thinking and acting. It implies the unity of ... Umunthu is a worldview that is commonly captured ... humanity has been a big quest. .... Calling on the Jewish, Muslim and Palestinian leaders, based on humanity created in ...

  2. Polarization resolved imaging with a reflection near-field optical microscope

    DEFF Research Database (Denmark)

    Bozhevolnyi, Sergey I.; Xiao, Mufei; Hvam, Jørn Märcher

    1999-01-01

    Using a rigorous microscopic point-dipole description of probe-sample interactions, we study imaging with a reflection scanning near-field optical microscope. Optical content, topographical artifacts, sensitivity window-i.e., the scale on which near-field optical images represent mainly optical...... configuration is preferable to the cross-linear one, since it ensures more isotropic (in the surface plane) near-field imaging of surface features. The numerical results are supported with experimental near-field images obtained by using a reflection microscope with an uncoated fiber tip....

  3. DIRC dreams: research directions for the next generation of internally reflected imaging counters

    International Nuclear Information System (INIS)

    Ratcliff, Blair N.; Spanier, Stefan

    1999-01-01

    Some conceptual design features of the total internally reflecting, imaging Cherenkov counter (DIRC) are described. Limits of the DIRC approach to particle identification, and a few features of alternative DIRC designs, are briefly explored

  4. BOREAS RSS-19 1996 CASI At-Sensor Radiance and Reflectance Images

    Data.gov (United States)

    National Aeronautics and Space Administration — CASI images from the Chieftain Navaho aircraft collected in order to observe the seasonal change in the radiometric reflectance properties of the boreal forest...

  5. BOREAS RSS-19 1996 CASI At-Sensor Radiance and Reflectance Images

    Data.gov (United States)

    National Aeronautics and Space Administration — ABSTRACT: CASI images from the Chieftain Navaho aircraft collected in order to observe the seasonal change in the radiometric reflectance properties of the boreal...

  6. BOREAS RSS-19 1994 CASI At-Sensor Radiance and Reflectance Images

    Data.gov (United States)

    National Aeronautics and Space Administration — ABSTRACT: CASI images from the Chieftain Navaho aircraft taken in order to observe the seasonal change in the radiometric reflectance properties of the boreal forest...

  7. BOREAS RSS-19 1994 CASI At-Sensor Radiance and Reflectance Images

    Data.gov (United States)

    National Aeronautics and Space Administration — CASI images from the Chieftain Navaho aircraft taken in order to observe the seasonal change in the radiometric reflectance properties of the boreal forest...

  8. Diagnosing hypoxia in murine models of rheumatoid arthritis from reflectance multispectral images

    Science.gov (United States)

    Glinton, Sophie; Naylor, Amy J.; Claridge, Ela

    2017-07-01

    Spectra computed from multispectral images of murine models of Rheumatoid Arthritis show a characteristic decrease in reflectance within the 600-800nm region which is indicative of the reduction in blood oxygenation and is consistent with hypoxia.

  9. DIRC Dreams Redux: Research Directions for the Next Generation of Internally Reflected Imaging Counters

    Energy Technology Data Exchange (ETDEWEB)

    Ratcliff, Blair N

    2001-09-18

    Some general conceptual design features of total internally reflecting, imaging Cherenkov counters (DIRCs) are described. Limits of the DIRC approach to particle identification and a few features of alternative DIRC designs are briefly explored.

  10. DCT-Based Characterization of Milk Products Using Diffuse Reflectance Images

    DEFF Research Database (Denmark)

    Sharifzadeh, Sara; Skytte, Jacob Lercke; Clemmensen, Line Katrine Harder

    2013-01-01

    We propose to use the two-dimensional Discrete Cosine Transform (DCT) for decomposition of diffuse reflectance images of laser illumination on milk products in different wavelengths. Based on the prior knowledge about the characteristics of the images, the initial feature vectors are formed at ea...... discriminate milk from yogurt products better....

  11. Cellular features of psoriatic skin: imaging and quantification using in vivo reflectance confocal microscopy

    NARCIS (Netherlands)

    Wolberink, E.A.W.; Erp, P.E.J. van; Teussink, M.M.; Kerkhof, P.C.M. van de; Gerritsen, M.J.P.

    2011-01-01

    BACKGROUND: In vivo reflectance confocal microscopy (RCM) is a novel, exciting imaging technique. It provides images of cell-and tissue structures and dynamics in situ, in real time, without the need for ex vivo tissue samples. RCM visualizes the superficial part of human skin up to a depth of 250

  12. Non-invasive detection of murals with pulsed terahertz reflected imaging system

    Science.gov (United States)

    Yuan, Minjie; Sun, Wenfeng; Wang, Xinke; Ye, Jiasheng; Wang, Sen; Zhang, Qunxi; Zhang, Yan

    2015-11-01

    Pulsed terahertz reflected imaging technology has been expected to have great potential for the non-invasive analysis of artworks. In this paper, three types of defects hidden in the plaster used to simulate the cases of defects in the murals, have been investigated by a pulsed terahertz reflected imaging system. These preset defects include a circular groove, a cross-shaped slit and a piece of "Y-type" metal plate built in the plaster. With the terahertz reflective tomography, information about defects has been determined involving the thickness from the surface of sample to the built-in defect, the profile and distribution of the defect. Additionally, three-dimensional analyses have been performed in order to reveal the internal structure of defects. Terahertz reflective imaging can be applied to the defect investigation of the murals.

  13. Properties of light reflected from road signs in active imaging for driving safety

    Science.gov (United States)

    Halstuch, Aviran; Yitzhaky, Yitzhak

    2007-10-01

    Night-vision systems in vehicles are a new emerging technology. A crucial problem in active (illumination-based) systems is distortion of images by saturation and blooming, due to strong retro-reflections from road signs. In this work we quantified this phenomenon. We measured the Mueller matrices and the polarization state of the reflected light from three different types of road signs commonly used. Measurements of the reflected intensity were taken also with respect to the angle of reflection. We found that different types of signs have different reflection properties. It is concluded from our measurements that the optimal solution for attenuating the retro-reflected intensity is using a linear horizontal polarized light source and a linear vertical polarizer. Unfortunately, while the performance of this solution is good for two types of road signs, it is less efficient for the third sign type.

  14. Global well-posedness for the radial defocusing cubic wave equation on $R^3$ and for rough data

    Directory of Open Access Journals (Sweden)

    Tristan Roy

    2007-11-01

    Full Text Available We prove global well-posedness for the radial defocusing cubic wave equation $$displaylines{ partial_{tt} u - Delta u = -u^{3} cr u(0,x = u_{0}(x cr partial_{t} u(0,x = u_{1}(x }$$ with data $(u_0, u_1 in H^{s} imes H^{s-1}$, $1 > s >7/10$. The proof relies upon a Morawetz-Strauss-type inequality that allows us to control the growth of an almost conserved quantity.

  15. Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

    Science.gov (United States)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

  16. Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

    Directory of Open Access Journals (Sweden)

    Weiguo Rui

    2014-01-01

    Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

  17. Application of fractional derivative with exponential law to bi-fractional-order wave equation with frictional memory kernel

    Science.gov (United States)

    Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.

    2017-12-01

    Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.

  18. Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

    Science.gov (United States)

    Ryo, Ikehata

    Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

  19. Polarized near-infrared autofluorescence imaging combined with near-infrared diffuse reflectance imaging for improving colonic cancer detection.

    Science.gov (United States)

    Shao, Xiaozhuo; Zheng, Wei; Huang, Zhiwei

    2010-11-08

    We evaluate the diagnostic feasibility of the integrated polarized near-infrared (NIR) autofluorescence (AF) and NIR diffuse reflectance (DR) imaging technique developed for colonic cancer detection. A total of 48 paired colonic tissue specimens (normal vs. cancer) were measured using the integrated NIR DR (850-1100 nm) and NIR AF imaging at the 785 nm laser excitation. The results showed that NIR AF intensities of cancer tissues are significantly lower than those of normal tissues (ppolarization conditions gives a higher diagnostic accuracy (of ~92-94%) compared to non-polarized NIR AF imaging or NIR DR imaging. Further, the ratio imaging of NIR DR to NIR AF with polarization provides the best diagnostic accuracy (of ~96%) among the NIR AF and NIR DR imaging techniques. This work suggests that the integrated NIR AF/DR imaging under polarization condition has the potential to improve the early diagnosis and detection of malignant lesions in the colon.

  20. Forme Fruste Keratoconus Imaging and Validation via Novel Multi-Spot Reflection Topography

    Directory of Open Access Journals (Sweden)

    Anastasios John Kanellopoulos

    2013-10-01

    Full Text Available Background/Aims: This case report aims to evaluate safety, efficacy and applicability of anterior surface imaging in a patient with forme fruste keratoconus (FFKC based on a novel multi-spot, multicolor light-emitting-diode (LED tear film-reflection imaging technology Case Description: A 45-year-old male patient, clinically diagnosed with FFKC, with highly asymmetric manifestation between his eyes, was subjected to the multicolor-spot reflection topography. We investigated elevation and sagittal curvature maps comparatively with the multicolor-spot reflection topographer, a Placido topographer and a Scheimpflug imaging system. For the right eye, steep and flat keratometry values were 41.92 and 41.05 D with the multicolor spot-reflection topographer, 42.30 and 42.08 D with the Placido, and 41.95 and 41.19 D with the Scheimpflug system. For the left eye, steep and flat keratometry values were 41.86 and 41.19 D with the multicolor spot-reflection topographer, 42.06 and 41.66 D with the Placido topographer, and 41.96 and 41.66 D with the Scheimpflug camera. Average repeatability of the keratometry measurements was ±0.35 D for the multicolor spot-reflection topographer, ±0.30 D for the Placido, and ±0.25 D for the Scheimpflug camera. Very good agreement between the instruments was demonstrated on the elevation and curvature maps. Conclusion: The ease of use and the comparable results offered by the multicolor spot-reflection topographer, in comparison to established Placido and Scheimpflug imaging, as well as the increased predictability that may be offered by the multicolor spot-reflection topographer, may hold promise for wider clinical application, such as screening of young adults for early keratoconus and, in a much wider perspective, potential candidates for laser corneal refractive surgery.

  1. Watch your step! A frustrated total internal reflection approach to forensic footwear imaging.

    Science.gov (United States)

    Needham, J A; Sharp, J S

    2016-02-16

    Forensic image retrieval and processing are vital tools in the fight against crime e.g. during fingerprint capture. However, despite recent advances in machine vision technology and image processing techniques (and contrary to the claims of popular fiction) forensic image retrieval is still widely being performed using outdated practices involving inkpads and paper. Ongoing changes in government policy, increasing crime rates and the reduction of forensic service budgets increasingly require that evidence be gathered and processed more rapidly and efficiently. A consequence of this is that new, low-cost imaging technologies are required to simultaneously increase the quality and throughput of the processing of evidence. This is particularly true in the burgeoning field of forensic footwear analysis, where images of shoe prints are being used to link individuals to crime scenes. Here we describe one such approach based upon frustrated total internal reflection imaging that can be used to acquire images of regions where shoes contact rigid surfaces.

  2. Watch your step! A frustrated total internal reflection approach to forensic footwear imaging

    Science.gov (United States)

    Needham, J. A.; Sharp, J. S.

    2016-02-01

    Forensic image retrieval and processing are vital tools in the fight against crime e.g. during fingerprint capture. However, despite recent advances in machine vision technology and image processing techniques (and contrary to the claims of popular fiction) forensic image retrieval is still widely being performed using outdated practices involving inkpads and paper. Ongoing changes in government policy, increasing crime rates and the reduction of forensic service budgets increasingly require that evidence be gathered and processed more rapidly and efficiently. A consequence of this is that new, low-cost imaging technologies are required to simultaneously increase the quality and throughput of the processing of evidence. This is particularly true in the burgeoning field of forensic footwear analysis, where images of shoe prints are being used to link individuals to crime scenes. Here we describe one such approach based upon frustrated total internal reflection imaging that can be used to acquire images of regions where shoes contact rigid surfaces.

  3. Non-destructive quality evaluation of pepper (Capsicum annuum L.) seeds using LED-induced hyperspectral reflectance imaging

    Science.gov (United States)

    In this study, we develop a viability evaluation method for pepper (Capsicum annuum L.) seed based on hyperspectral reflectance imaging. The reflectance spectra of pepper seeds in the 400–700 nm range are collected from hyperspectral reflectance images obtained using blue, green, and red LED illumin...

  4. SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

    KAUST Repository

    Gao, Longfei

    2018-02-16

    We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

  5. High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

    Science.gov (United States)

    Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.

    2018-01-01

    High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.

  6. Imaging of Volume Phase Gratings in a Photosensitive Polymer, Recorded in Transmission and Reflection Geometry

    Directory of Open Access Journals (Sweden)

    Tina Sabel

    2014-02-01

    Full Text Available Volume phase gratings, recorded in a photosensitive polymer by two-beam interference exposure, are studied by means of optical microscopy. Transmission gratings and reflection gratings, with periods in the order of 10 μm down to 130 nm, were investigated. Mapping of holograms by means of imaging in sectional view is introduced to study reflection-type gratings, evading the resolution limit of classical optical microscopy. In addition, this technique is applied to examine so-called parasitic gratings, arising from interference from the incident reference beam and the reflected signal beam. The appearance and possible avoidance of such unintentionally recorded secondary structures is discussed.

  7. [A Method to Reconstruct Surface Reflectance Spectrum from Multispectral Image Based on Canopy Radiation Transfer Model].

    Science.gov (United States)

    Zhao, Yong-guang; Ma, Ling-ling; Li, Chuan-rong; Zhu, Xiao-hua; Tang, Ling-li

    2015-07-01

    Due to the lack of enough spectral bands for multi-spectral sensor, it is difficult to reconstruct surface retlectance spectrum from finite spectral information acquired by multi-spectral instrument. Here, taking into full account of the heterogeneity of pixel from remote sensing image, a method is proposed to simulate hyperspectral data from multispectral data based on canopy radiation transfer model. This method first assumes the mixed pixels contain two types of land cover, i.e., vegetation and soil. The sensitive parameters of Soil-Leaf-Canopy (SLC) model and a soil ratio factor were retrieved from multi-spectral data based on Look-Up Table (LUT) technology. Then, by combined with a soil ratio factor, all the parameters were input into the SLC model to simulate the surface reflectance spectrum from 400 to 2 400 nm. Taking Landsat Enhanced Thematic Mapper Plus (ETM+) image as reference image, the surface reflectance spectrum was simulated. The simulated reflectance spectrum revealed different feature information of different surface types. To test the performance of this method, the simulated reflectance spectrum was convolved with the Landsat ETM + spectral response curves and Moderate Resolution Imaging Spectrometer (MODIS) spectral response curves to obtain the simulated Landsat ETM+ and MODIS image. Finally, the simulated Landsat ETM+ and MODIS images were compared with the observed Landsat ETM+ and MODIS images. The results generally showed high correction coefficients (Landsat: 0.90-0.99, MODIS: 0.74-0.85) between most simulated bands and observed bands and indicated that the simulated reflectance spectrum was well simulated and reliable.

  8. Phase resolved and coherence gated en face reflection imaging of multilayered embryonal carcinoma cells

    Science.gov (United States)

    Yamauchi, Toyohiko; Fukami, Tadashi; Iwai, Hidenao; Yamashita, Yutaka

    2012-03-01

    Embryonal carcinoma (EC) cells, which are cell lines derived from teratocarcinomas, have characteristics in common with stem cells and differentiate into many kinds of functional cells. Similar to embryonic stem (ES) cells, undifferentiated EC cells form multi-layered spheroids. In order to visualize the three-dimensional structure of multilayered EC cells without labeling, we employed full-field interference microscopy with the aid of a low-coherence quantitative phase microscope, which is a reflection-type interference microscope employing the digital holographic technique with a low-coherent light source. Owing to the low-coherency of the light-source (halogen lamp), only the light reflected from reflective surface at a specific sectioning height generates an interference image on the CCD camera. P19CL6 EC cells, derived from mouse teratocarcinomas, formed spheroids that are about 50 to 200 micrometers in diameter. Since the height of each cell is around 10 micrometers, it is assumed that each spheroid has 5 to 20 cell layers. The P19CL6 spheroids were imaged in an upright configuration and the horizontally sectioned reflection images of the sample were obtained by sequentially and vertically scanning the zero-path-length height. Our results show the threedimensional structure of the spheroids, in which plasma and nuclear membranes were distinguishably imaged. The results imply that our technique is further capable of imaging induced pluripotent stem (iPS) cells for the assessment of cell properties including their pluripotency.

  9. A New Wave Equation Based Source Location Method with Full-waveform Inversion

    KAUST Repository

    Wu, Zedong

    2017-05-26

    Locating the source of a passively recorded seismic event is still a challenging problem, especially when the velocity is unknown. Many imaging approaches to focus the image do not address the velocity issue and result in images plagued with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using an extended source. At the later stages the focusing of the image dominates the inversion allowing for high resolution source and velocity inversion. We also compute the source location explicitly and numerical tests show that we obtain good estimates of the source locations with this approach.

  10. Contribution of Reflection Terahertz Time Domain-Imaging (THz-TDI) to Imaging Analysis of Artworks

    DEFF Research Database (Denmark)

    Dandolo, Corinna Ludovica Koch; Fukunaga, Kaori; Kohzuma, Y.

    Different kind s of artefacts (easel painting, panel paintings and Asian lacquerwares) have been scanned by THz - TDI and results have been compared with those obtained by others standard imaging techniques (x-ray radiography, cross sectional imaging, technical photography) .......Different kind s of artefacts (easel painting, panel paintings and Asian lacquerwares) have been scanned by THz - TDI and results have been compared with those obtained by others standard imaging techniques (x-ray radiography, cross sectional imaging, technical photography) ....

  11. Registration of eye reflection and scene images using an aspherical eye model.

    Science.gov (United States)

    Nakazawa, Atsushi; Nitschke, Christian; Nishida, Toyoaki

    2016-11-01

    This paper introduces an image registration algorithm between an eye reflection and a scene image. Although there are currently a large number of image registration algorithms, this task remains difficult due to nonlinear distortions at the eye surface and large amounts of noise, such as iris texture, eyelids, eyelashes, and their shadows. To overcome this issue, we developed an image registration method combining an aspherical eye model that simulates nonlinear distortions considering eye geometry and a two-step iterative registration strategy that obtains dense correspondence of the feature points to achieve accurate image registrations for the entire image region. We obtained a database of eye reflection and scene images featuring four subjects in indoor and outdoor scenes and compared the registration performance with different asphericity conditions. Results showed that the proposed approach can perform accurate registration with an average accuracy of 1.05 deg by using the aspherical cornea model. This work is relevant for eye image analysis in general, enabling novel applications and scenarios.

  12. Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

    KAUST Repository

    Dutta, Gaurav; Lu, Kai; Wang, Xin; Schuster, Gerard T.

    2013-01-01

    Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images

  13. Automated cart with VIS/NIR hyperspectral reflectance and fluorescence imaging capabilities

    Science.gov (United States)

    A system to take high-resolution VIS/NIR hyperspectral reflectance and fluorescence images in outdoor fields using ambient lighting or a pulsed laser (355 nm), respectively, for illumination was designed, built, and tested. Components of the system include a semi-autonomous cart, a gated-intensified...

  14. Bright Retinal Lesions Detection using Colour Fundus Images Containing Reflective Features

    Energy Technology Data Exchange (ETDEWEB)

    Giancardo, Luca [ORNL; Karnowski, Thomas Paul [ORNL; Chaum, Edward [ORNL; Meriaudeau, Fabrice [ORNL; Tobin Jr, Kenneth William [ORNL; Li, Yaquin [University of Tennessee, Knoxville (UTK)

    2009-01-01

    In the last years the research community has developed many techniques to detect and diagnose diabetic retinopathy with retinal fundus images. This is a necessary step for the implementation of a large scale screening effort in rural areas where ophthalmologists are not available. In the United States of America, the incidence of diabetes is worryingly increasing among the young population. Retina fundus images of patients younger than 20 years old present a high amount of reflection due to the Nerve Fibre Layer (NFL), the younger the patient the more these reflections are visible. To our knowledge we are not aware of algorithms able to explicitly deal with this type of reflection artefact. This paper presents a technique to detect bright lesions also in patients with a high degree of reflective NFL. First, the candidate bright lesions are detected using image equalization and relatively simple histogram analysis. Then, a classifier is trained using texture descriptor (Multi-scale Local Binary Patterns) and other features in order to remove the false positives in the lesion detection. Finally, the area of the lesions is used to diagnose diabetic retinopathy. Our database consists of 33 images from a telemedicine network currently developed. When determining moderate to high diabetic retinopathy using the bright lesions detected the algorithm achieves a sensitivity of 100% at a specificity of 100% using hold-one-out testing.

  15. Total Internal Reflection Fluorescence Microscopy Imaging-Guided Confocal Single-Molecule Fluorescence Spectroscopy

    OpenAIRE

    Zheng, Desheng; Kaldaras, Leonora; Lu, H. Peter

    2013-01-01

    We have developed an integrated spectroscopy system combining total internal reflection fluorescence microscopy imaging with confocal single-molecule fluorescence spectroscopy for two-dimensional interfaces. This spectroscopy approach is capable of both multiple molecules simultaneously sampling and in situ confocal fluorescence dynamics analyses of individual molecules of interest. We have demonstrated the calibration with fluorescent microspheres, and carried out single-molecule spectroscop...

  16. Macro Photography for Reflectance Transformation Imaging: A Practical Guide to the Highlights Method

    Directory of Open Access Journals (Sweden)

    Antonino Cosentino

    2014-11-01

    Full Text Available Reflectance Transformation Imaging (RTI is increasingly being used for art documentation and analysis and it can be successful also for the examination of features on the order of hundreds of microns. This paper evaluates some macro scale photography methods specifically for RTI employing the Highlights method for documenting sub-millimeter details. This RTI technique consists in including one reflective sphere in the scene photographed so that the processing software can calculate for each photo the direction of the light source from its reflection on the sphere. RTI documentation can be performed also with an RTI dome, but the Highlights method is preferred because is more mobile and more affordable. This technique is demonstrated in the documentation of some prints ranging from the XV to the XX century from to the Ingels collection in Sweden. The images are here examined and discussed, showing the application of macro RTI for identifying features of prints.

  17. Pixel Statistical Analysis of Diabetic vs. Non-diabetic Foot-Sole Spectral Terahertz Reflection Images

    Science.gov (United States)

    Hernandez-Cardoso, G. G.; Alfaro-Gomez, M.; Rojas-Landeros, S. C.; Salas-Gutierrez, I.; Castro-Camus, E.

    2018-03-01

    In this article, we present a series of hydration mapping images of the foot soles of diabetic and non-diabetic subjects measured by terahertz reflectance. In addition to the hydration images, we present a series of RYG-color-coded (red yellow green) images where pixels are assigned one of the three colors in order to easily identify areas in risk of ulceration. We also present the statistics of the number of pixels with each color as a potential quantitative indicator for diabetic foot-syndrome deterioration.

  18. A new time–space domain high-order finite-difference method for the acoustic wave equation

    KAUST Repository

    Liu, Yang; Sen, Mrinal K.

    2009-01-01

    A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

  19. A new time–space domain high-order finite-difference method for the acoustic wave equation

    KAUST Repository

    Liu, Yang

    2009-12-01

    A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

  20. Attenuated total reflection-Fourier transform infrared imaging of large areas using inverted prism crystals and combining imaging and mapping.

    Science.gov (United States)

    Chan, K L Andrew; Kazarian, Sergei G

    2008-10-01

    Attenuated total reflection-Fourier transform infrared (ATR-FT-IR) imaging is a very useful tool for capturing chemical images of various materials due to the simple sample preparation and the ability to measure wet samples or samples in an aqueous environment. However, the size of the array detector used for image acquisition is often limited and there is usually a trade off between spatial resolution and the field of view (FOV). The combination of mapping and imaging can be used to acquire images with a larger FOV without sacrificing spatial resolution. Previous attempts have demonstrated this using an infrared microscope and a Germanium hemispherical ATR crystal to achieve images of up to 2.5 mm x 2.5 mm but with varying spatial resolution and depth of penetration across the imaged area. In this paper, we demonstrate a combination of mapping and imaging with a different approach using an external optics housing for large ATR accessories and inverted ATR prisms to achieve ATR-FT-IR images with a large FOV and reasonable spatial resolution. The results have shown that a FOV of 10 mm x 14 mm can be obtained with a spatial resolution of approximately 40-60 microm when using an accessory that gives no magnification. A FOV of 1.3 mm x 1.3 mm can be obtained with spatial resolution of approximately 15-20 microm when using a diamond ATR imaging accessory with 4x magnification. No significant change in image quality such as spatial resolution or depth of penetration has been observed across the whole FOV with this method and the measurement time was approximately 15 minutes for an image consisting of 16 image tiles.

  1. LSB-based Steganography Using Reflected Gray Code for Color Quantum Images

    Science.gov (United States)

    Li, Panchi; Lu, Aiping

    2018-02-01

    At present, the classical least-significant-bit (LSB) based image steganography has been extended to quantum image processing. For the existing LSB-based quantum image steganography schemes, the embedding capacity is no more than 3 bits per pixel. Therefore, it is meaningful to study how to improve the embedding capacity of quantum image steganography. This work presents a novel LSB-based steganography using reflected Gray code for colored quantum images, and the embedding capacity of this scheme is up to 4 bits per pixel. In proposed scheme, the secret qubit sequence is considered as a sequence of 4-bit segments. For the four bits in each segment, the first bit is embedded in the second LSB of B channel of the cover image, and and the remaining three bits are embedded in LSB of RGB channels of each color pixel simultaneously using reflected-Gray code to determine the embedded bit from secret information. Following the transforming rule, the LSB of stego-image are not always same as the secret bits and the differences are up to almost 50%. Experimental results confirm that the proposed scheme shows good performance and outperforms the previous ones currently found in the literature in terms of embedding capacity.

  2. Expanding the Caring Lens: Nursing and Medical Students Reflecting on Images of Older People.

    Science.gov (United States)

    Brand, Gabrielle; Miller, Karen; Saunders, Rosemary; Dugmore, Helen; Etherton-Beer, Christopher

    2016-01-01

    In changing higher education environments, health profession's educators have been increasingly challenged to prepare future health professionals to care for aging populations. This article reports on an exploratory, mixed-method research study that used an innovative photo-elicitation technique and interprofessional small-group work in the classroom to enhance the reflective learning experience of medical and nursing students. Data were collected from pre- and postquestionnaires and focus groups to explore shifts in perceptions toward older persons following the reflective learning session. The qualitative data revealed how using visual images of older persons provides a valuable learning space for reflection. Students found meaning in their own learning by creating shared storylines that challenged their perceptions of older people and themselves as future health professionals. These data support the use of visual methodologies to enhance engagement, reflection, and challenge students to explore and deepen their understanding in gerontology.

  3. Imaging rat esophagus using combination of reflectance confocal and multiphoton microscopy

    International Nuclear Information System (INIS)

    Zhuo, S M; Chen, J X; Jiang, X S; Lu, K C; Xie, S S

    2008-01-01

    We combine reflectance confocal microscopy (RCM) with multiphoton microscopy (MPM) to image rat esophagus. The two imaging modalities allow detection of layered–resolved complementary information from esophagus. In the keratinizing layer, the keratinocytes boundaries can be characterized by RCM, while the keratinocytes cytoplasm (keratin) can be further imaged by multiphoton autofluorescence signal. In the epithelium, the epithelial cellular boundaries and nucleus can be detected by RCM, and MPM can be used for imaging epithelial cell cytoplasm and monitoring metabolic state of epithelium. In the stroma, multiphoton autofluorescence signal is used to image elastin and second harmonic generation signal is utilized to detect collagen, while RCM is used to determine the optical property of stroma. Overall, these results suggest that the combination of RCM and MPM has potential to provide more important and comprehensive information for early diagnosis of esophageal cancer

  4. Reflection tomography from pre-stack migrated images; Tomographie de reflexion a partir des images migrees avant addition

    Energy Technology Data Exchange (ETDEWEB)

    Adler, F

    1996-10-29

    The application of reflection tomography to data from complex geological structures is very interesting in the hydrocarbons exploration. Indeed, it contributes to localize the hydrocarbons potential traps. The used reflection tomography method is faced with two major difficulties. Travel time picking is difficult or impossible in seismic time sections. The processing of multiple arrival travel times needs an adequate formulation of reflection tomography. In order to solve the first problem, we adopt the approach of the SMART (Sequential Migration Aided Reflection Tomography) method which is an original method for the implementation of migration velocity analysis. The velocity model is automatically calculated by reflection tomography. The kinematic data set for reflection tomography is constructed from pre-stack depth-migrated images that are interpreted in the chosen migration configuration. For the implementation of the SMART method in the common-offset domain, we propose an original formulation of reflection tomography that takes multiple arrival travel times, which are calculated from common-offset migrated images, into account. In this new formulation, we look for a model such that a modelling, which consists in shooting in this model from the source locations with some ray parameters at the source, matches some emergence conditions: for each offset, the rays emerge at the receiver locations (given by the offset) with the same travel times and the same travel time slopes as observed in the associated common-offset section. These conditions constitute the kinematic data set for tomographic inversion. The common-offset travel time slope is the difference between the ray parameter at the receiver and the ray parameter at the source. Therefore, the ray parameter at the source is an unknown and has to be determined together with the model parameters during inversion. (author)

  5. On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

    KAUST Repository

    Gao, Longfei

    2017-10-26

    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

  6. New high accuracy super stable alternating direction implicit methods for two and three dimensional hyperbolic damped wave equations

    Directory of Open Access Journals (Sweden)

    R.K. Mohanty

    2014-01-01

    Full Text Available In this paper, we report new three level implicit super stable methods of order two in time and four in space for the solution of hyperbolic damped wave equations in one, two and three space dimensions subject to given appropriate initial and Dirichlet boundary conditions. We use uniform grid points both in time and space directions. Our methods behave like fourth order accurate, when grid size in time-direction is directly proportional to the square of grid size in space-direction. The proposed methods are super stable. The resulting system of algebraic equations is solved by the Gauss elimination method. We discuss new alternating direction implicit (ADI methods for two and three dimensional problems. Numerical results and the graphical representation of numerical solution are presented to illustrate the accuracy of the proposed methods.

  7. The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

    Directory of Open Access Journals (Sweden)

    H. O. Bakodah

    2013-01-01

    Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

  8. On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

    Science.gov (United States)

    Gao, Longfei; Ketcheson, David; Keyes, David

    2018-02-01

    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

  9. The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

  10. Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available In the solution of boundary value problems, usually zero eigenvalue is ignored. This case also happens in calculating the eigenvalues of matrices, so that we would often like to find the nonzero solutions of the linear system A X = λ X when λ ≠ 0 . But λ = 0 implies that det A = 0 for X ≠ 0 and then the rank of matrix A is reduced at least one degree. This comment can similarly be stated for boundary value problems. In other words, if at least one of the eigens of equations related to the main problem is considered zero, then one of the solutions will be specified in advance. By using this note, first we study a class of special functions and then apply it for the potential, heat, and wave equations in spherical coordinate. In this way, some practical examples are also given.

  11. An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong; Zhang Hongqing

    2005-01-01

    With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

  12. The features of inclined force acting on 1D homogeneous elastic lumped line and corresponding modernisation of the wave equations

    CERN Document Server

    Karavashkin, S B

    2002-01-01

    We analyse the exact analytical solutions for 1D elastic lumped lines under action of an external force inclined to the line axis. We show that in this case an inclined wave being described by an implicit function propagates along the line. We extend this conclusion both to free vibrations and to distributed lines. We prove that the presented solution in the form of implicit function is a generalizing for the wave equation. When taken into consideration exactly, the dynamical processes pattern leads to the conclusion that the divergence of a vector in dynamical fields is not zero but proportional to the scalar product of the partial derivative of the given vector with respect to time into the wave propagation direction vector.

  13. A New Wave Equation Based Source Location Method with Full-waveform Inversion

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2017-01-01

    with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using

  14. Solution of Full Wave Equation for Global Modes in Small Aspect Ratio Tokamaks with Non-Circular Cross-Section

    International Nuclear Information System (INIS)

    Burma, C.; Cuperman, S.; Komoshvili, K.

    1998-01-01

    The wave equation for strongly toroidal small aspect ratio (spherical) tokamaks with non-circular cross-section is properly formulated and solved for global waves, in the Alfven frequency range. The current-carrying toroidal plasma is surrounded by a helical sheet-current antenna, which is enclosed within a perfectly conducting wall. The problem is formulated in terms of the vector and scalar potentials (A,Φ), thus avoiding the numerical solution occurring in the case of (E,B) formulation. Adequate boundary conditions are applied at the vacuum - metallic wall interface and the magnetic axis. A recently derived dielectric tensor-operator, able to describe the anisotropic plasma response in spherical tokamaks, is used for this purpose; except for its linear character, no physical or geometrical limitations are imposed on it. The equilibrium profiles (magnetic field, pressure and current) are obtained from a numerical solution of the Grad-Shafranov equation. Specifically, the wave equation is solved by the aid of a numerical code we developed for the present problem, based on the well documented 2(1/2)D finite element solver proposed by E.G. Sewell. With the definitions V i (θ,ρ) = U i (-θ,ρ) (V i U i = A j , Φ; j = ρ,φ,θ), our code solves simultaneously 16 second order partial differential equations (eight equations for each of real and imaginary set of functions V i , U i ). A systematic analysis of the solutions obtained for various values and combinations of wavenumbers and frequencies in the Alfven range is presented

  15. Improving Image Matching by Reducing Surface Reflections Using Polarising Filter Techniques

    Science.gov (United States)

    Conen, N.; Hastedt, H.; Kahmen, O.; Luhmann, T.

    2018-05-01

    In dense stereo matching applications surface reflections may lead to incorrect measurements and blunders in the resulting point cloud. To overcome the problem of disturbing reflexions polarising filters can be mounted on the camera lens and light source. Reflections in the images can be suppressed by crossing the polarising direction of the filters leading to homogeneous illuminated images and better matching results. However, the filter may influence the camera's orientation parameters as well as the measuring accuracy. To quantify these effects, a calibration and an accuracy analysis is conducted within a spatial test arrangement according to the German guideline VDI/VDE 2634.1 (2002) using a DSLR with and without polarising filter. In a second test, the interior orientation is analysed in more detail. The results do not show significant changes of the measuring accuracy in object space and only very small changes of the interior orientation (Δc ≤ 4 μm) with the polarising filter in use. Since in medical applications many tiny reflections are present and impede robust surface measurements, a prototypic trinocular endoscope is equipped with polarising technique. The interior and relative orientation is determined and analysed. The advantage of the polarising technique for medical image matching is shown in an experiment with a moistened pig kidney. The accuracy and completeness of the resulting point cloud can be improved clearly when using polarising filters. Furthermore, an accuracy analysis using a laser triangulation system is performed and the special reflection properties of metallic surfaces are presented.

  16. Kinematics of reflections in subsurface offset and angle-domain image gathers

    Science.gov (United States)

    Dafni, Raanan; Symes, William W.

    2018-05-01

    Seismic migration in the angle-domain generates multiple images of the earth's interior in which reflection takes place at different scattering-angles. Mechanically, the angle-dependent reflection is restricted to happen instantaneously and at a fixed point in space: Incident wave hits a discontinuity in the subsurface media and instantly generates a scattered wave at the same common point of interaction. Alternatively, the angle-domain image may be associated with space-shift (regarded as subsurface offset) extended migration that artificially splits the reflection geometry. Meaning that, incident and scattered waves interact at some offset distance. The geometric differences between the two approaches amount to a contradictory angle-domain behaviour, and unlike kinematic description. We present a phase space depiction of migration methods extended by the peculiar subsurface offset split and stress its profound dissimilarity. In spite of being in radical contradiction with the general physics, the subsurface offset reveals a link to some valuable angle-domain quantities, via post-migration transformations. The angle quantities are indicated by the direction normal to the subsurface offset extended image. They specifically define the local dip and scattering angles if the velocity at the split reflection coordinates is the same for incident and scattered wave pairs. Otherwise, the reflector normal is not a bisector of the opening angle, but of the corresponding slowness vectors. This evidence, together with the distinguished geometry configuration, fundamentally differentiates the angle-domain decomposition based on the subsurface offset split from the conventional decomposition at a common reflection point. An asymptotic simulation of angle-domain moveout curves in layered media exposes the notion of split versus common reflection point geometry. Traveltime inversion methods that involve the subsurface offset extended migration must accommodate the split geometry

  17. A comparison of hair colour measurement by digital image analysis with reflective spectrophotometry.

    Science.gov (United States)

    Vaughn, Michelle R; van Oorschot, Roland A H; Baindur-Hudson, Swati

    2009-01-10

    While reflective spectrophotometry is an established method for measuring macroscopic hair colour, it can be cumbersome to use on a large number of individuals and not all reflective spectrophotometry instruments are easily portable. This study investigates the use of digital photographs to measure hair colour and compares its use to reflective spectrophotometry. An understanding of the accuracy of colour determination by these methods is of relevance when undertaking specific investigations, such as those on the genetics of hair colour. Measurements of hair colour may also be of assistance in cases where a photograph is the only evidence of hair colour available (e.g. surveillance). Using the CIE L(*)a(*)b(*) colour space, the hair colour of 134 individuals of European ancestry was measured by both reflective spectrophotometry and by digital image analysis (in V++). A moderate correlation was found along all three colour axes, with Pearson correlation coefficients of 0.625, 0.593 and 0.513 for L(*), a(*) and b(*) respectively (p-values=0.000), with means being significantly overestimated by digital image analysis for all three colour components (by an average of 33.42, 3.38 and 8.00 for L(*), a(*) and b(*) respectively). When using digital image data to group individuals into clusters previously determined by reflective spectrophotometric analysis using a discriminant analysis, individuals were classified into the correct clusters 85.8% of the time when there were two clusters. The percentage of cases correctly classified decreases as the number of clusters increases. It is concluded that, although more convenient, hair colour measurement from digital images has limited use in situations requiring accurate and consistent measurements.

  18. Correction for reflected sky radiance in low-altitude coastal hyperspectral images.

    Science.gov (United States)

    Kim, Minsu; Park, Joong Yong; Kopilevich, Yuri; Tuell, Grady; Philpot, William

    2013-11-10

    Low-altitude coastal hyperspectral imagery is sensitive to reflections of sky radiance at the water surface. Even in the absence of sun glint, and for a calm water surface, the wide range of viewing angles may result in pronounced, low-frequency variations of the reflected sky radiance across the scan line depending on the solar position. The variation in reflected sky radiance can be obscured by strong high-spatial-frequency sun glint and at high altitude by path radiance. However, at low altitudes, the low-spatial-frequency sky radiance effect is frequently significant and is not removed effectively by the typical corrections for sun glint. The reflected sky radiance from the water surface observed by a low-altitude sensor can be modeled in the first approximation as the sum of multiple-scattered Rayleigh path radiance and the single-scattered direct-solar-beam radiance by the aerosol in the lower atmosphere. The path radiance from zenith to the half field of view (FOV) of a typical airborne spectroradiometer has relatively minimal variation and its reflected radiance to detector array results in a flat base. Therefore the along-track variation is mostly contributed by the forward single-scattered solar-beam radiance. The scattered solar-beam radiances arrive at the water surface with different incident angles. Thus the reflected radiance received at the detector array corresponds to a certain scattering angle, and its variation is most effectively parameterized using the downward scattering angle (DSA) of the solar beam. Computation of the DSA must account for the roll, pitch, and heading of the platform and the viewing geometry of the sensor along with the solar ephemeris. Once the DSA image is calculated, the near-infrared (NIR) radiance from selected water scan lines are compared, and a relationship between DSA and NIR radiance is derived. We then apply the relationship to the entire DSA image to create an NIR reference image. Using the NIR reference image

  19. State-dependent cellular activity patterns of the cat paraventricular hypothalamus measured by reflectance imaging

    DEFF Research Database (Denmark)

    Kristensen, Morten Pilgaard; Rector, D M; Poe, G R

    1996-01-01

    Activity within the cat paraventricular hypothalamus (PVH) during sleep and waking states was measured by quantifying intrinsic tissue reflectivity. A fiber optic probe consisting of a 1.0 mm coherent image conduit, surrounded by plastic fibers which conducted 660 nm source light, was attached...... to a charge-coupled device camera, and positioned over the PVH in five cats. Electrodes for assessing state variables, including electroencephalographic activity, eye movement, and somatic muscle tone were also placed. After surgical recovery, reflected light intensity was measured continuously at 2.5 Hz...

  20. Imaging the dorsal hippocampus: light reflectance relationships to electroencephalographic patterns during sleep

    DEFF Research Database (Denmark)

    Rector, D M; Poe, G R; Kristensen, Morten Pilgaard

    1995-01-01

    We assessed the correspondence of 660 nm light reflectance changes from the dorsal hippocampus with slow wave electroencephalographic (EEG) activity during quiet sleep (QS) and rapid eye movement (REM) sleep in four cats. An optic probe, attached to a charge-coupled-device (CCD) video camera...... as EEG changes. Dividing the image into 10 subregions revealed that reflectance changes at the rhythmical slow wave activity band (RSA, 4-6 Hz) persisted in localized regions during QS and REM sleep, but regional changes showed considerable wave-by-wave independence between areas and from slow wave...

  1. Reflective THz and MR imaging of burn wounds: a potential clinical validation of THz contrast mechanisms

    Science.gov (United States)

    Bajwa, Neha; Nowroozi, Bryan; Sung, Shijun; Garritano, James; Maccabi, Ashkan; Tewari, Priyamvada; Culjat, Martin; Singh, Rahul; Alger, Jeffry; Grundfest, Warren; Taylor, Zachary

    2012-10-01

    Terahertz (THz) imaging is an expanding area of research in the field of medical imaging due to its high sensitivity to changes in tissue water content. Previously reported in vivo rat studies demonstrate that spatially resolved hydration mapping with THz illumination can be used to rapidly and accurately detect fluid shifts following induction of burns and provide highly resolved spatial and temporal characterization of edematous tissue. THz imagery of partial and full thickness burn wounds acquired by our group correlate well with burn severity and suggest that hydration gradients are responsible for the observed contrast. This research aims to confirm the dominant contrast mechanism of THz burn imaging using a clinically accepted diagnostic method that relies on tissue water content for contrast generation to support the translation of this technology to clinical application. The hydration contrast sensing capabilities of magnetic resonance imaging (MRI), specifically T2 relaxation times and proton density values N(H), are well established and provide measures of mobile water content, lending MRI as a suitable method to validate hydration states of skin burns. This paper presents correlational studies performed with MR imaging of ex vivo porcine skin that confirm tissue hydration as the principal sensing mechanism in THz burn imaging. Insights from this preliminary research will be used to lay the groundwork for future, parallel MRI and THz imaging of in vivo rat models to further substantiate the clinical efficacy of reflective THz imaging in burn wound care.

  2. Nondestructive Evaluation of Carbon Fiber Reinforced Polymer Composites Using Reflective Terahertz Imaging

    Directory of Open Access Journals (Sweden)

    Jin Zhang

    2016-06-01

    Full Text Available Terahertz (THz time-domain spectroscopy (TDS imaging is considered a nondestructive evaluation method for composite materials used for examining various defects of carbon fiber reinforced polymer (CFRP composites and fire-retardant coatings in the reflective imaging modality. We demonstrate that hidden defects simulated by Teflon artificial inserts are imaged clearly in the perpendicular polarization mode. The THz TDS technique is also used to measure the thickness of thin fire-retardant coatings on CFRP composites with a typical accuracy of about 10 micrometers. In addition, coating debonding is successfully imaged based on the time-delay difference of the time-domain waveforms between closely adhered and debonded sample locations.

  3. DETERMINING SPECTRAL REFLECTANCE COEFFICIENTS FROM HYPERSPECTRAL IMAGES OBTAINED FROM LOW ALTITUDES

    Directory of Open Access Journals (Sweden)

    P. Walczykowski

    2016-06-01

    Full Text Available Remote Sensing plays very important role in many different study fields, like hydrology, crop management, environmental and ecosystem studies. For all mentioned areas of interest different remote sensing and image processing techniques, such as: image classification (object and pixel- based, object identification, change detection, etc. can be applied. Most of this techniques use spectral reflectance coefficients as the basis for the identification and distinction of different objects and materials, e.g. monitoring of vegetation stress, identification of water pollutants, yield identification, etc. Spectral characteristics are usually acquired using discrete methods such as spectrometric measurements in both laboratory and field conditions. Such measurements however can be very time consuming, which has led many international researchers to investigate the reliability and accuracy of using image-based methods. According to published and ongoing studies, in order to acquire these spectral characteristics from images, it is necessary to have hyperspectral data. The presented article describes a series of experiments conducted using the push-broom Headwall MicroHyperspec A-series VNIR. This hyperspectral scanner allows for registration of images with more than 300 spectral channels with a 1.9 nm spectral bandwidth in the 380- 1000 nm range. The aim of these experiments was to establish a methodology for acquiring spectral reflectance characteristics of different forms of land cover using such sensor. All research work was conducted in controlled conditions from low altitudes. Hyperspectral images obtained with this specific type of sensor requires a unique approach in terms of post-processing, especially radiometric correction. Large amounts of acquired imagery data allowed the authors to establish a new post- processing approach. The developed methodology allowed the authors to obtain spectral reflectance coefficients from a hyperspectral sensor

  4. Determining Spectral Reflectance Coefficients from Hyperspectral Images Obtained from Low Altitudes

    Science.gov (United States)

    Walczykowski, P.; Jenerowicz, A.; Orych, A.; Siok, K.

    2016-06-01

    Remote Sensing plays very important role in many different study fields, like hydrology, crop management, environmental and ecosystem studies. For all mentioned areas of interest different remote sensing and image processing techniques, such as: image classification (object and pixel- based), object identification, change detection, etc. can be applied. Most of this techniques use spectral reflectance coefficients as the basis for the identification and distinction of different objects and materials, e.g. monitoring of vegetation stress, identification of water pollutants, yield identification, etc. Spectral characteristics are usually acquired using discrete methods such as spectrometric measurements in both laboratory and field conditions. Such measurements however can be very time consuming, which has led many international researchers to investigate the reliability and accuracy of using image-based methods. According to published and ongoing studies, in order to acquire these spectral characteristics from images, it is necessary to have hyperspectral data. The presented article describes a series of experiments conducted using the push-broom Headwall MicroHyperspec A-series VNIR. This hyperspectral scanner allows for registration of images with more than 300 spectral channels with a 1.9 nm spectral bandwidth in the 380- 1000 nm range. The aim of these experiments was to establish a methodology for acquiring spectral reflectance characteristics of different forms of land cover using such sensor. All research work was conducted in controlled conditions from low altitudes. Hyperspectral images obtained with this specific type of sensor requires a unique approach in terms of post-processing, especially radiometric correction. Large amounts of acquired imagery data allowed the authors to establish a new post- processing approach. The developed methodology allowed the authors to obtain spectral reflectance coefficients from a hyperspectral sensor mounted on an

  5. REFLECTIONS ON IMAGE AND PHOTOGRAPHY: possibilities in research and teaching of Physical Education

    Directory of Open Access Journals (Sweden)

    Mariana Mendonça Lisboa

    2010-12-01

    Full Text Available Starting this reflexion from the theoretical contributions such as Guy Debord and Susan Sontag to have a critical understanding of our reality, mediated by images, we intend, throughout this article, to reflect to the reader, some ability to think and work at school with images in educational processes and research, especially Physical Education. Is it possible their use? What can be the interests? How of photography can be enhanced and theoretical-methodologically thought over the educational and scientific practices that have commitment with social changes? These are the main considerations that we give as a challenge to be assumed by researchers/teachers.

  6. Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

    KAUST Repository

    Dutta, Gaurav

    2014-10-01

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as Qp-LSRTM. During the leastsquares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that Qp-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of Qp-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and Qp errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

  7. Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

    KAUST Repository

    Dutta, Gaurav; Schuster, Gerard T.

    2014-01-01

    Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as Qp-LSRTM. During the leastsquares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that Qp-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of Qp-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and Qp errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

  8. A direct reflection OLVF debris detector based on dark-field imaging

    Science.gov (United States)

    Li, Bo; Xi, Yinhu; Feng, Song; Mao, Junhong; Xie, You-Bai

    2018-06-01

    To solve the problems of monitoring wear debris in black oil, a direct reflection online visual ferrograph (OLVF) debris detector is presented. In current OLVF detectors, a reflected light source is used. The emitted light is reflected by wear debris directly instead of passing through the lube oil. Therefore, the transparency of the lube oil ceases to matter. Two experiments were conducted to validate the wear debris imaging feasibility and effectiveness of the newly developed detector. The results show that the visual feature information of the wear debris can be reliably obtained from black oil by this detector, and it can also be used to track the fast-changing wear of tribopairs at different wear stages. To the best of our knowledge, to date there is no other report for solving this issue.

  9. Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method

    Directory of Open Access Journals (Sweden)

    Yoshihisa Aizu

    2013-06-01

    Full Text Available A multi-spectral diffuse reflectance imaging method based on a single snap shot of Red-Green-Blue images acquired with the exposure time of 65 ms (15 fps was investigated for estimating melanin concentration, blood concentration, and oxygen saturation in human skin tissue. The technique utilizes the Wiener estimation method to deduce spectral reflectance images instantaneously from an RGB image. Using the resultant absorbance spectrum as a response variable and the extinction coefficients of melanin, oxygenated hemoglobin and deoxygenated hemoglobin as predictor variables, multiple regression analysis provides regression coefficients. Concentrations of melanin and total blood are then determined from the regression coefficients using conversion vectors that are numerically deduced in advance by the Monte Carlo simulations for light transport in skin. Oxygen saturation is obtained directly from the regression coefficients. Experiments with a tissue-like agar gel phantom validated the method. In vivo experiments on fingers during upper limb occlusion demonstrated the ability of the method to evaluate physiological reactions of human skin.

  10. Combined analysis of surface reflection imaging and vertical seismic profiling at Yucca Mountain, Nevada

    International Nuclear Information System (INIS)

    Daley, T.M.; Majer, E.L.; Karageorgi, E.

    1994-08-01

    This report presents results from surface and borehole seismic profiling performed by the Lawrence Berkeley Laboratory (LBL) on Yucca Mountain. This work was performed as part of the site characterization effort for the potential high-level nuclear waste repository. Their objective was to provide seismic imaging from the near surface (200 to 300 ft. depth) to the repository horizon and below, if possible. Among the issues addressed by this seismic imaging work are location and depth of fracturing and faulting, geologic identification of reflecting horizons, and spatial continuity of reflecting horizons. The authors believe their results are generally positive, with tome specific successes. This was the first attempt at this scale using modem seismic imaging techniques to determine geologic features on Yucca Mountain. The principle purpose of this report is to present the interpretation of the seismic reflection section in a geologic context. Three surface reflection profiles were acquired and processed as part of this study. Because of environmental concerns, all three lines were on preexisting roads. Line 1 crossed the mapped surface trace of the Ghost Dance fault and it was intended to study the dip and depth extent of the fault system. Line 2 was acquired along Drill Hole wash and was intended to help the ESF north ramp design activities. Line 3 was acquired along Yucca Crest and was designed to image geologic horizons which were thought to be less faulted along the ridge. Unfortunately, line 3 proved to have poor data quality, in part because of winds, poor field conditions and limited time. Their processing and interpretation efforts were focused on lines 1 and 2 and their associated VSP studies

  11. Artificial neural networks based estimation of optical parameters by diffuse reflectance imaging under in vitro conditions

    Directory of Open Access Journals (Sweden)

    Mahmut Ozan Gökkan

    2017-01-01

    Full Text Available Optical parameters (properties of tissue-mimicking phantoms are determined through noninvasive optical imaging. Objective of this study is to decompose obtained diffuse reflectance into these optical properties such as absorption and scattering coefficients. To do so, transmission spectroscopy is firstly used to measure the coefficients via an experimental setup. Next, the optical properties of each characterized phantom are input for Monte Carlo (MC simulations to get diffuse reflectance. Also, a surface image for each single phantom with its known optical properties is obliquely captured due to reflectance-based geometrical setup using CMOS camera that is positioned at 5∘ angle to the phantoms. For the illumination of light, a laser light source at 633nm wavelength is preferred, because optical properties of different components in a biological tissue on that wavelength are nonoverlapped. During in vitro measurements, we prepared 30 different mixture samples adding clinoleic intravenous lipid emulsion (CILE and evans blue (EB dye into a distilled water. Finally, all obtained diffuse reflectance values are used to estimate the optical coefficients by artificial neural networks (ANNs in inverse modeling. For a biological tissue it is found that the simulated and measured values in our results are in good agreement.

  12. Classification of peacock feather reflectance using principal component analysis similarity factors from multispectral imaging data.

    Science.gov (United States)

    Medina, José M; Díaz, José A; Vukusic, Pete

    2015-04-20

    Iridescent structural colors in biology exhibit sophisticated spatially-varying reflectance properties that depend on both the illumination and viewing angles. The classification of such spectral and spatial information in iridescent structurally colored surfaces is important to elucidate the functional role of irregularity and to improve understanding of color pattern formation at different length scales. In this study, we propose a non-invasive method for the spectral classification of spatial reflectance patterns at the micron scale based on the multispectral imaging technique and the principal component analysis similarity factor (PCASF). We demonstrate the effectiveness of this approach and its component methods by detailing its use in the study of the angle-dependent reflectance properties of Pavo cristatus (the common peacock) feathers, a species of peafowl very well known to exhibit bright and saturated iridescent colors. We show that multispectral reflectance imaging and PCASF approaches can be used as effective tools for spectral recognition of iridescent patterns in the visible spectrum and provide meaningful information for spectral classification of the irregularity of the microstructure in iridescent plumage.

  13. Electronic spreadsheet to acquire the reflectance from the TM and ETM+ Landsat images

    Directory of Open Access Journals (Sweden)

    Antonio R. Formaggio

    2005-08-01

    Full Text Available The reflectance of agricultural cultures and other terrestrial surface "targets" is an intrinsic parameter of these targets, so in many situations, it must be used instead of the values of "gray levels" that is found in the satellite images. In order to get reflectance values, it is necessary to eliminate the atmospheric interference and to make a set of calculations that uses sensor parameters and information regarding the original image. The automation of this procedure has the advantage to speed up the process and to reduce the possibility of errors during calculations. The objective of this paper is to present an electronic spreadsheet that simplifies and automatizes the transformation of the digital numbers of the TM/Landsat-5 and ETM+/Landsat-7 images into reflectance. The method employed for atmospheric correction was the dark object subtraction (DOS. The electronic spreadsheet described here is freely available to users and can be downloaded at the following website: http://www.dsr.inpe.br/Calculo_Reflectancia.xls.

  14. Progress in reflectance confocal microscopy for imaging oral tissues in vivo

    Science.gov (United States)

    Peterson, Gary; Zanoni, Daniella K.; Migliacci, Jocelyn; Cordova, Miguel; Rajadhyaksha, Milind; Patel, Snehal

    2016-02-01

    We report progress in development and feasibility testing of reflectance confocal microscopy (RCM) for imaging in the oral cavity of humans. We adapted a small rigid relay telescope (120mm long x 14mm diameter) and a small water immersion objective lens (12mm diameter, NA 0.7) to a commercial handheld RCM scanner (Vivascope 3000, Caliber ID, Rochester NY). This scanner is designed for imaging skin but we adapted the front end (the objective lens and the stepper motor that axially translates) for intra-oral use. This adaption required a new approach to address the loss of the automated stepper motor for acquisition of images in depth. A helical spring-like cap (with a coverslip to contact tissue) was designed for approximately 150 um of travel. Additionally other methods for focusing optics were designed and evaluated. The relay telescope optics is being tested in a clinical setting. With the capture of video and "video-mosaicing", extended areas can be imaged. The feasibility of imaging oral tissues was initially investigated in volunteers. RCM imaging in buccal mucosa in vivo shows nuclear and cellular detail in the epithelium and epithelial junction, and connective tissue and blood flow in the underlying lamina propria. Similar detail, including filiform and fungiform papillae, can be seen on the tongue in vivo. Clinical testing during head and neck surgery is now in progress and patients are being imaged for both normal tissue and cancerous margins in lip and tongue mucosa.

  15. On the time-stepping stability of continuous mass-lumped and discontinuous Galerkin finite elements for the 3D acoustic wave equation

    NARCIS (Netherlands)

    Zhebel, E.; Minisini, S.; Mulder, W.A.

    2012-01-01

    We solve the three-dimensional acoustic wave equation, discretized on tetrahedral meshes. Two methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method (SIP-DG). Combining the spatial discretization with the leap-frog

  16. Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra

    Science.gov (United States)

    Medina, José M.; Pereira, Luís M.; Correia, Hélder T.; Nascimento, Sérgio M. C.

    2011-07-01

    We report a hyperspectral imaging system to measure the reflectance spectra of real human irises with high spatial resolution. A set of ocular prosthesis was used as the control condition. Reflectance data were decorrelated by the principal-component analysis. The main conclusion is that spectral complexity of the human iris is considerable: between 9 and 11 principal components are necessary to account for 99% of the cumulative variance in human irises. Correcting image misalignments associated with spontaneous ocular movements did not influence this result. The data also suggests a correlation between the first principal component and different levels of melanin present in the irises. It was also found that although the spectral characteristics of the first five principal components were not affected by the radial and angular position of the selected iridal areas, they affect the higher-order ones, suggesting a possible influence of the iris texture. The results show that hyperspectral imaging in the iris, together with adequate spectroscopic analyses provide more information than conventional colorimetric methods, making hyperspectral imaging suitable for the characterization of melanin and the noninvasive diagnosis of ocular diseases and iris color.

  17. Diffuse reflectance imaging for non-melanoma skin cancer detection using laser feedback interferometry

    Science.gov (United States)

    Mowla, Alireza; Taimre, Thomas; Lim, Yah L.; Bertling, Karl; Wilson, Stephen J.; Prow, Tarl W.; Soyer, H. P.; Rakić, Aleksandar D.

    2016-04-01

    We propose a compact, self-aligned, low-cost, and versatile infrared diffuse-reflectance laser imaging system using a laser feedback interferometry technique with possible applications in in vivo biological tissue imaging and skin cancer detection. We examine the proposed technique experimentally using a three-layer agar skin phantom. A cylindrical region with a scattering rate lower than that of the surrounding normal tissue was used as a model for a non-melanoma skin tumour. The same structure was implemented in a Monte Carlo computational model. The experimental results agree well with the Monte Carlo simulations validating the theoretical basis of the technique. Results prove the applicability of the proposed technique for biological tissue imaging, with the capability of depth sectioning and a penetration depth of well over 1.2 mm into the skin phantom.

  18. Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment.

    Science.gov (United States)

    Li, Zexiao; Liu, Xianlei; Fang, Fengzhou; Zhang, Xiaodong; Zeng, Zhen; Zhu, Linlin; Yan, Ning

    2018-03-19

    Multi-reflective imaging systems find wide applications in optical imaging and space detection. However, it is faced with difficulties in adjusting the freeform mirrors with high accuracy to guarantee the optical function. Motivated by this, an alignment-free manufacture approach is proposed to machine the optical system. The direct optical performance-guided manufacture route is established without measuring the form error of freeform optics. An analytical model is established to investigate the effects of machine errors to serve the error identification and compensation in machining. Based on the integrated manufactured system, an ingenious self-designed testing configuration is constructed to evaluate the optical performance by directly measuring the wavefront aberration. Experiments are carried out to manufacture a three-mirror anastigmat, surface topographical details and optical performance shows agreement to the designed expectation. The final system works as an off-axis infrared imaging system. Results validate the feasibility of the proposed method to achieve excellent optical application.

  19. IMPROVING IMAGE MATCHING BY REDUCING SURFACE REFLECTIONS USING POLARISING FILTER TECHNIQUES

    Directory of Open Access Journals (Sweden)

    N. Conen

    2018-05-01

    Full Text Available In dense stereo matching applications surface reflections may lead to incorrect measurements and blunders in the resulting point cloud. To overcome the problem of disturbing reflexions polarising filters can be mounted on the camera lens and light source. Reflections in the images can be suppressed by crossing the polarising direction of the filters leading to homogeneous illuminated images and better matching results. However, the filter may influence the camera’s orientation parameters as well as the measuring accuracy. To quantify these effects, a calibration and an accuracy analysis is conducted within a spatial test arrangement according to the German guideline VDI/VDE 2634.1 (2002 using a DSLR with and without polarising filter. In a second test, the interior orientation is analysed in more detail. The results do not show significant changes of the measuring accuracy in object space and only very small changes of the interior orientation (Δc ≤ 4 μm with the polarising filter in use. Since in medical applications many tiny reflections are present and impede robust surface measurements, a prototypic trinocular endoscope is equipped with polarising technique. The interior and relative orientation is determined and analysed. The advantage of the polarising technique for medical image matching is shown in an experiment with a moistened pig kidney. The accuracy and completeness of the resulting point cloud can be improved clearly when using polarising filters. Furthermore, an accuracy analysis using a laser triangulation system is performed and the special reflection properties of metallic surfaces are presented.

  20. Delay and Standard Deviation Beamforming to Enhance Specular Reflections in Ultrasound Imaging.

    Science.gov (United States)

    Bandaru, Raja Sekhar; Sornes, Anders Rasmus; Hermans, Jeroen; Samset, Eigil; D'hooge, Jan

    2016-12-01

    Although interventional devices, such as needles, guide wires, and catheters, are best visualized by X-ray, real-time volumetric echography could offer an attractive alternative as it avoids ionizing radiation; it provides good soft tissue contrast, and it is mobile and relatively cheap. Unfortunately, as echography is traditionally used to image soft tissue and blood flow, the appearance of interventional devices in conventional ultrasound images remains relatively poor, which is a major obstacle toward ultrasound-guided interventions. The objective of this paper was therefore to enhance the appearance of interventional devices in ultrasound images. Thereto, a modified ultrasound beamforming process using conventional-focused transmit beams is proposed that exploits the properties of received signals containing specular reflections (as arising from these devices). This new beamforming approach referred to as delay and standard deviation beamforming (DASD) was quantitatively tested using simulated as well as experimental data using a linear array transducer. Furthermore, the influence of different imaging settings (i.e., transmit focus, imaging depth, and scan angle) on the obtained image contrast was evaluated. The study showed that the image contrast of specular regions improved by 5-30 dB using DASD beamforming compared with traditional delay and sum (DAS) beamforming. The highest gain in contrast was observed when the interventional device was tilted away from being orthogonal to the transmit beam, which is a major limitation in standard DAS imaging. As such, the proposed beamforming methodology can offer an improved visualization of interventional devices in the ultrasound image with potential implications for ultrasound-guided interventions.

  1. Accessible biometrics: A frustrated total internal reflection approach to imaging fingerprints.

    Science.gov (United States)

    Smith, Nathan D; Sharp, James S

    2017-05-01

    Fingerprints are widely used as a means of identifying persons of interest because of the highly individual nature of the spatial distribution and types of features (or minuta) found on the surface of a finger. This individuality has led to their wide application in the comparison of fingerprints found at crime scenes with those taken from known offenders and suspects in custody. However, despite recent advances in machine vision technology and image processing techniques, fingerprint evidence is still widely being collected using outdated practices involving ink and paper - a process that can be both time consuming and expensive. Reduction of forensic service budgets increasingly requires that evidence be gathered and processed more rapidly and efficiently. However, many of the existing digital fingerprint acquisition devices have proven too expensive to roll out on a large scale. As a result new, low-cost imaging technologies are required to increase the quality and throughput of the processing of fingerprint evidence. Here we describe an inexpensive approach to digital fingerprint acquisition that is based upon frustrated total internal reflection imaging. The quality and resolution of the images produced are shown to be as good as those currently acquired using ink and paper based methods. The same imaging technique is also shown to be capable of imaging powdered fingerprints that have been lifted from a crime scene using adhesive tape or gel lifters. Copyright © 2017 The Chartered Society of Forensic Sciences. Published by Elsevier B.V. All rights reserved.

  2. In vivo inflammation mapping of periodontal disease based on diffuse reflectance spectral imaging: a clinical study

    Science.gov (United States)

    Prasanth, Chandra Sekhar; Betsy, Joseph; Jayanthi, Jayaraj L.; Nisha, Unni G.; Prasantila, Janam; Subhash, Narayanan

    2013-02-01

    Since conventional techniques using periodontal probes have inherent drawbacks in the diagnosis of different grades of gingival inflammation, development of noninvasive screening devices becomes significant. Diffuse reflectance (DR) spectra recorded with white light illumination is utilized to detect periodontal inflammation from the oxygenated hemoglobin absorption ratio R620/R575. A multispectral imaging system is utilized to record narrow-band DR images at 575 and 620 nm from the anterior sextant of the gingivia of 15 healthy volunteers and 25 patients (N=40). An experienced periodontist assesses the level of gingival inflammation at each site through periodontal probing and assigns diagnosis as healthy, mild, moderate, or severe inflammation. The DR image ratio R620/R575 computed for each pixel (8-μm resolution) from the monochrome images is pseudo-color-mapped to identify gingival inflammation sites. The DR image ratio values at each site are compared with clinical diagnosis to estimate the specificity and sensitivity of the DR imaging technique in inflammation mapping. The high diagnostic accuracy is utilized to detect underlying inflammation in six patients with a previous history of periodontitis.

  3. A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation

    KAUST Repository

    Liu, Yang; Sen, Mrinal K.

    2010-01-01

    We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.

  4. A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation

    KAUST Repository

    Liu, Yang

    2010-03-01

    We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.

  5. REFLECT: Logiciel de restitution des reflectances au sol pour l'amelioration de la qualite de l'information extraite des images satellitales a haute resolution spatiale

    Science.gov (United States)

    Bouroubi, Mohamed Yacine

    Multi-spectral satellite imagery, especially at high spatial resolution (finer than 30 m on the ground), represents an invaluable source of information for decision making in various domains in connection with natural resources management, environment preservation or urban planning and management. The mapping scales may range from local (finer resolution than 5 m) to regional (resolution coarser than 5m). The images are characterized by objects reflectance in the electromagnetic spectrum witch represents the key information in many applications. However, satellite sensor measurements are also affected by parasite input due to illumination and observation conditions, to the atmosphere, to topography and to sensor properties. Two questions have oriented this research. What is the best approach to retrieve surface reflectance with the measured values while taking into account these parasite factors? Is this retrieval a sine qua non condition for reliable image information extraction for the diverse domains of application for the images (mapping, environmental monitoring, landscape change detection, resources inventory, etc.)? The goals we have delineated for this research are as follow: (1) Develop software to retrieve ground reflectance while taking into account the aspects mentioned earlier. This software had to be modular enough to allow improvement and adaptation to diverse remote sensing application problems; and (2) Apply this software in various context (urban, agricultural, forest) and analyse results to evaluate the accuracy gain of extracted information from remote sensing imagery transformed in ground reflectance images to demonstrate the necessity of operating in this way, whatever the type of application. During this research, we have developed a tool to retrieve ground reflectance (the new version of the REFLECT software). This software is based on the formulas (and routines) of the 6S code (Second Simulation of Satellite Signal in the Solar Spectrum

  6. [Insert Image Here]: A Reflection on the Ethics of Imagery in a Critical Pedagogy for the Humanities

    Science.gov (United States)

    Carniel, Jessica

    2018-01-01

    Using the controversial image of Syrian toddler Alan Kurdi as its provocation, this paper reflects upon the ethics of images used in teaching in a time of high-volume image circulation via social media, as well as a time when debates about content and trigger warnings are starting to gain more traction in the Australian tertiary sector. It…

  7. Automatic and improved radiometric correction of Landsat imagery using reference values from MODIS surface reflectance images

    Science.gov (United States)

    Pons, X.; Pesquer, L.; Cristóbal, J.; González-Guerrero, O.

    2014-12-01

    Radiometric correction is a prerequisite for generating high-quality scientific data, making it possible to discriminate between product artefacts and real changes in Earth processes as well as accurately produce land cover maps and detect changes. This work contributes to the automatic generation of surface reflectance products for Landsat satellite series. Surface reflectances are generated by a new approach developed from a previous simplified radiometric (atmospheric + topographic) correction model. The proposed model keeps the core of the old model (incidence angles and cast-shadows through a digital elevation model [DEM], Earth-Sun distance, etc.) and adds new characteristics to enhance and automatize ground reflectance retrieval. The new model includes the following new features: (1) A fitting model based on reference values from pseudoinvariant areas that have been automatically extracted from existing reflectance products (Terra MODIS MOD09GA) that were selected also automatically by applying quality criteria that include a geostatistical pattern model. This guarantees the consistency of the internal and external series, making it unnecessary to provide extra atmospheric data for the acquisition date and time, dark objects or dense vegetation. (2) A spatial model for atmospheric optical depth that uses detailed DEM and MODTRAN simulations. (3) It is designed so that large time-series of images can be processed automatically to produce consistent Landsat surface reflectance time-series. (4) The approach can handle most images, acquired now or in the past, regardless of the processing system, with the exception of those with extremely high cloud coverage. The new methodology has been successfully applied to a series of near 300 images of the same area including MSS, TM and ETM+ imagery as well as to different formats and processing systems (LPGS and NLAPS from the USGS; CEOS from ESA) for different degrees of cloud coverage (up to 60%) and SLC

  8. Guided wave imaging of oblique reflecting interfaces in pipes using common-source synthetic focusing

    Science.gov (United States)

    Sun, Zeqing; Sun, Anyu; Ju, Bing-Feng

    2018-04-01

    Cross-mode-family mode conversion and secondary reflection of guided waves in pipes complicate the processing of guided waves signals, and can cause false detection. In this paper, filters operating in the spectral domain of wavenumber, circumferential order and frequency are designed to suppress the signal components of unwanted mode-family and unwanted traveling direction. Common-source synthetic focusing is used to reconstruct defect images from the guided wave signals. Simulations of the reflections from linear oblique defects and a semicircle defect are separately implemented. Defect images, which are reconstructed from the simulation results under different excitation conditions, are comparatively studied in terms of axial resolution, reflection amplitude, detectable oblique angle and so on. Further, the proposed method is experimentally validated by detecting linear cracks with various oblique angles (10-40°). The proposed method relies on the guided wave signals that are captured during 2-D scanning of a cylindrical area on the pipe. The redundancy of the signals is analyzed to reduce the time-consumption of the scanning process and to enhance the practicability of the proposed method.

  9. MBR-SIFT: A mirror reflected invariant feature descriptor using a binary representation for image matching.

    Directory of Open Access Journals (Sweden)

    Mingzhe Su

    Full Text Available The traditional scale invariant feature transform (SIFT method can extract distinctive features for image matching. However, it is extremely time-consuming in SIFT matching because of the use of the Euclidean distance measure. Recently, many binary SIFT (BSIFT methods have been developed to improve matching efficiency; however, none of them is invariant to mirror reflection. To address these problems, in this paper, we present a horizontal or vertical mirror reflection invariant binary descriptor named MBR-SIFT, in addition to a novel image matching approach. First, 16 cells in the local region around the SIFT keypoint are reorganized, and then the 128-dimensional vector of the SIFT descriptor is transformed into a reconstructed vector according to eight directions. Finally, the MBR-SIFT descriptor is obtained after binarization and reverse coding. To improve the matching speed and accuracy, a fast matching algorithm that includes a coarse-to-fine two-step matching strategy in addition to two similarity measures for the MBR-SIFT descriptor are proposed. Experimental results on the UKBench dataset show that the proposed method not only solves the problem of mirror reflection, but also ensures desirable matching accuracy and speed.

  10. MBR-SIFT: A mirror reflected invariant feature descriptor using a binary representation for image matching.

    Science.gov (United States)

    Su, Mingzhe; Ma, Yan; Zhang, Xiangfen; Wang, Yan; Zhang, Yuping

    2017-01-01

    The traditional scale invariant feature transform (SIFT) method can extract distinctive features for image matching. However, it is extremely time-consuming in SIFT matching because of the use of the Euclidean distance measure. Recently, many binary SIFT (BSIFT) methods have been developed to improve matching efficiency; however, none of them is invariant to mirror reflection. To address these problems, in this paper, we present a horizontal or vertical mirror reflection invariant binary descriptor named MBR-SIFT, in addition to a novel image matching approach. First, 16 cells in the local region around the SIFT keypoint are reorganized, and then the 128-dimensional vector of the SIFT descriptor is transformed into a reconstructed vector according to eight directions. Finally, the MBR-SIFT descriptor is obtained after binarization and reverse coding. To improve the matching speed and accuracy, a fast matching algorithm that includes a coarse-to-fine two-step matching strategy in addition to two similarity measures for the MBR-SIFT descriptor are proposed. Experimental results on the UKBench dataset show that the proposed method not only solves the problem of mirror reflection, but also ensures desirable matching accuracy and speed.

  11. A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

    Science.gov (United States)

    Macías-Díaz, J. E.

    2017-12-01

    In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

  12. An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

    Science.gov (United States)

    Macías-Díaz, J. E.

    2018-06-01

    In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.

  13. Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

    Science.gov (United States)

    Kanagawa, Tetsuya

    2015-05-01

    This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

  14. Ray-tracing traveltime tomography versus wave-equation traveltime inversion for near-surface seismic land data

    KAUST Repository

    Fu, Lei

    2017-05-11

    Full-waveform inversion of land seismic data tends to get stuck in a local minimum associated with the waveform misfit function. This problem can be partly mitigated by using an initial velocity model that is close to the true velocity model. This initial starting model can be obtained by inverting traveltimes with ray-tracing traveltime tomography (RT) or wave-equation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the first-arrival traveltimes, and empirical tests suggest that RT is more sensitive to the additive noise in the input data than WT. We present two examples of applying WT and RT to land seismic data acquired in western Saudi Arabia. One of the seismic experiments investigated the water-table depth, and the other one attempted to detect the location of a buried fault. The seismic land data were inverted by WT and RT to generate the P-velocity tomograms, from which we can clearly identify the water table depth along the seismic survey line in the first example and the fault location in the second example.

  15. On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

    Science.gov (United States)

    van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

    2018-06-01

    In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

  16. Solution of the Helmholtz-Poincare Wave Equation using the coupled boundary integral equations and optimal surface eigenfunctions

    International Nuclear Information System (INIS)

    Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.

    1992-01-01

    The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented

  17. Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations

    International Nuclear Information System (INIS)

    Godinho, Cresus F.L.; Weberszpil, J.; Helayël-Neto, J.A.

    2012-01-01

    In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.

  18. High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling.

    Science.gov (United States)

    Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R

    2014-04-13

    We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685-6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension ( r + 1) D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over [Formula: see text] for r ⩽ 100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin-Voigt and Maxwell-Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.

  19. A two-component wave equation for particles of spin 1/2 and non-zero rest mass

    International Nuclear Information System (INIS)

    Srivastava, T.

    1981-11-01

    We have discussed here the qualifications of the equation (delta 0 +sigmasup(k)deltasub(k))psi = -kappaTpsi, where deltasub(μ) is identical to delta/deltaxsup(μ), sigmasup(k) are the Pauli spin matrices, T is the linear operator which changes the sign of t, kappa=m 0 c/(h/2π) and psi a function with two components, as a suitable wave equation for a spin 1/2 particle with non-zero rest mass. We have established that both components of all its solutions satisfy the Klein-Gordon equation and that a 1-1 correspondence can be set up between its solutions and the positive energy solutions of the Dirac equation which preserves inner products (suitably defined for our case). We have then gone on to show covariance under transformations of the proper Lorentz group as also under space and time inversions and translations. Eigenfunctions of energy-momentum and spin have been explicitly found and it is shown that causality is preserved and a Green's function exists. A list appears, at the end, of points to be discussed in Part II of this paper, points which, it is hoped, will complete the acceptability of the theory. (author)

  20. Wave equations on a de Sitter fiber bundle. [Semiclassical wave function, bundle space, L-S coupling

    Energy Technology Data Exchange (ETDEWEB)

    Drechsler, W [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)

    1975-01-01

    A gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the Lsub(4,1) de Sitter group. An internal variable xi, varying in the fiber over a space-time point x, is introduced as a means to describe - with the help of a semiclassical wave function psi(x,xi) defined on the bundle space - the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for psi(x,xi) are established which are of integro-differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.

  1. Analysis of the validity of the asymptotic techniques in the lower hybrid wave equation solution for reactor applications

    International Nuclear Information System (INIS)

    Cardinali, A.; Morini, L.; Castaldo, C.; Cesario, R.; Zonca, F.

    2007-01-01

    Knowing that the lower hybrid (LH) wave propagation in tokamak plasmas can be correctly described with a full wave approach only, based on fully numerical techniques or on semianalytical approaches, in this paper, the LH wave equation is asymptotically solved via the Wentzel-Kramers-Brillouin (WKB) method for the first two orders of the expansion parameter, obtaining governing equations for the phase at the lowest and for the amplitude at the next order. The nonlinear partial differential equation (PDE) for the phase is solved in a pseudotoroidal geometry (circular and concentric magnetic surfaces) by the method of characteristics. The associated system of ordinary differential equations for the position and the wavenumber is obtained and analytically solved by choosing an appropriate expansion parameter. The quasilinear PDE for the WKB amplitude is also solved analytically, allowing us to reconstruct the wave electric field inside the plasma. The solution is also obtained numerically and compared with the analytical solution. A discussion of the validity limits of the WKB method is also given on the basis of the obtained results

  2. Seismic reflection data imaging and interpretation from Braniewo2014 experiment using additional wide-angle refraction and reflection and well-logs data

    Science.gov (United States)

    Trzeciak, Maciej; Majdański, Mariusz; Białas, Sebastian; Gaczyński, Edward; Maksym, Andrzej

    2015-04-01

    Braniewo2014 reflection and refraction experiment was realized in cooperation between Polish Oil and Gas Company (PGNiG) and the Institute of Geophysics (IGF), Polish Academy of Sciences, near the locality of Braniewo in northern Poland. PGNiG realized a 20-km-long reflection profile, using vibroseis and dynamite shooting; the aim of the reflection survey was to characterise Silurian shale gas reservoir. IGF deployed 59 seismic stations along this profile and registered additional full-spread wide-angle refraction and reflection data, with offsets up to 12 km; maximum offsets from the seismic reflection survey was 3 km. To improve the velocity information two velocity logs from near deep boreholes were used. The main goal of the joint reflection-refraction interpretation was to find relations between velocity field from reflection velocity analysis and refraction tomography, and to build a velocity model which would be consistent for both, reflection and refraction, datasets. In this paper we present imaging results and velocity models from Braniewo2014 experiment and the methodology we used.

  3. Refractive Index Imaging of Cells with Variable-Angle Near-Total Internal Reflection (TIR) Microscopy.

    Science.gov (United States)

    Bohannon, Kevin P; Holz, Ronald W; Axelrod, Daniel

    2017-10-01

    The refractive index in the interior of single cells affects the evanescent field depth in quantitative studies using total internal reflection (TIR) fluorescence, but often that index is not well known. We here present method to measure and spatially map the absolute index of refraction in a microscopic sample, by imaging a collimated light beam reflected from the substrate/buffer/cell interference at variable angles of incidence. Above the TIR critical angle (which is a strong function of refractive index), the reflection is 100%, but in the immediate sub-critical angle zone, the reflection intensity is a very strong ascending function of incidence angle. By analyzing the angular position of that edge at each location in the field of view, the local refractive index can be estimated. In addition, by analyzing the steepness of the edge, the distance-to-substrate can be determined. We apply the technique to liquid calibration samples, silica beads, cultured Chinese hamster ovary cells, and primary culture chromaffin cells. The optical technique suffers from decremented lateral resolution, scattering, and interference artifacts. However, it still provides reasonable results for both refractive index (~1.38) and for distance-to-substrate (~150 nm) for the cells, as well as a lateral resolution to about 1 µm.

  4. Simultaneous in vivo imaging of diffuse optical reflectance, optoacoustic pressure and ultrasonic scattering (Conference Presentation)

    Science.gov (United States)

    Subochev, Pavel V.; Orlova, Anna G.; Turchin, Ilya V.

    2017-03-01

    We will present reflection-mode bioimaging system providing complementary optical, photoacsoutic and acoustic measurements by acoustic detector after each laser pulse with 2kHz repetition rate. The photons absorbed within the biological tissue provide optoacoustic (OA) signals, the photons absorbed by the external electrode of a detector provide the measurable diffuse reflectance (DR) from the sample and the probing ultrasonic (US) pulse. To demonstrate the in vivo capabilities of the system we performed complementary DR/OA/US imaging of small laboratory animals and human palm with 3.5mm/50μm/35μm lateral resolution at up to 3 mm diagnostic depth. Functional OA and DR imaging demonstrated the levels of tissue vascularization and blood supply. Structural US imaging was essential for understanding the position of vessels and zones with different perfusion. Before BiOS-2017 we plan to accomplish more in vivo experiments validating the developed triple-modality system as diagnostic tool to detect vascularization as well as mechanisms of vascular changes when monitoring response to therapy.

  5. State-dependent cellular activity patterns of the cat paraventricular hypothalamus measured by reflectance imaging

    DEFF Research Database (Denmark)

    Kristensen, Morten Pilgaard; Rector, D M; Poe, G R

    1996-01-01

    Activity within the cat paraventricular hypothalamus (PVH) during sleep and waking states was measured by quantifying intrinsic tissue reflectivity. A fiber optic probe consisting of a 1.0 mm coherent image conduit, surrounded by plastic fibers which conducted 660 nm source light, was attached...... to a charge-coupled device camera, and positioned over the PVH in five cats. Electrodes for assessing state variables, including electroencephalographic activity, eye movement, and somatic muscle tone were also placed. After surgical recovery, reflected light intensity was measured continuously at 2.5 Hz...... changes with behavioral state in a regionally specific manner, and that overall activity increases during quiet sleep, and is even more enhanced in active sleep. PVH activation could be expected to stimulate pituitary release of adrenocorticotropic hormone (ACTH) and affect input to autonomic regulatory...

  6. Active laser radar (lidar) for measurement of corresponding height and reflectance images

    Science.gov (United States)

    Froehlich, Christoph; Mettenleiter, M.; Haertl, F.

    1997-08-01

    For the survey and inspection of environmental objects, a non-tactile, robust and precise imaging of height and depth is the basis sensor technology. For visual inspection,surface classification, and documentation purposes, however, additional information concerning reflectance of measured objects is necessary. High-speed acquisition of both geometric and visual information is achieved by means of an active laser radar, supporting consistent 3D height and 2D reflectance images. The laser radar is an optical-wavelength system, and is comparable to devices built by ERIM, Odetics, and Perceptron, measuring the range between sensor and target surfaces as well as the reflectance of the target surface, which corresponds to the magnitude of the back scattered laser energy. In contrast to these range sensing devices, the laser radar under consideration is designed for high speed and precise operation in both indoor and outdoor environments, emitting a minimum of near-IR laser energy. It integrates a laser range measurement system and a mechanical deflection system for 3D environmental measurements. This paper reports on design details of the laser radar for surface inspection tasks. It outlines the performance requirements and introduces the measurement principle. The hardware design, including the main modules, such as the laser head, the high frequency unit, the laser beam deflection system, and the digital signal processing unit are discussed.the signal processing unit consists of dedicated signal processors for real-time sensor data preprocessing as well as a sensor computer for high-level image analysis and feature extraction. The paper focuses on performance data of the system, including noise, drift over time, precision, and accuracy with measurements. It discuses the influences of ambient light, surface material of the target, and ambient temperature for range accuracy and range precision. Furthermore, experimental results from inspection of buildings, monuments

  7. Imaging the spectral reflectance properties of bipolar radiofrequency-fused bowel tissue

    Science.gov (United States)

    Clancy, Neil T.; Arya, Shobhit; Stoyanov, Danail; Du, Xiaofei; Hanna, George B.; Elson, Daniel S.

    2015-07-01

    Delivery of radiofrequency (RF) electrical energy is used during surgery to heat and seal tissue, such as vessels, allowing resection without blood loss. Recent work has suggested that this approach may be extended to allow surgical attachment of larger tissue segments for applications such as bowel anastomosis. In a large series of porcine surgical procedures bipolar RF energy was used to resect and re-seal the small bowel in vivo with a commercial tissue fusion device (Ligasure; Covidien PLC, USA). The tissue was then imaged with a multispectral imaging laparoscope to obtain a spectral datacube comprising both fused and healthy tissue. Maps of blood volume, oxygen saturation and scattering power were derived from the measured reflectance spectra using an optimised light-tissue interaction model. A 60% increase in reflectance of visible light (460-700 nm) was observed after fusion, with the tissue taking on a white appearance. Despite this the distinctive shape of the haemoglobin absorption spectrum was still noticeable in the 460-600 nm wavelength range. Scattering power increased in the fused region in comparison to normal serosa, while blood volume and oxygen saturation decreased. Observed fusion-induced changes in the reflectance spectrum are consistent with the biophysical changes induced through tissue denaturation and increased collagen cross-linking. The multispectral imager allows mapping of the spatial extent of these changes and classification of the zone of damaged tissue. Further analysis of the spectral data in parallel with histopathological examination of excised specimens will allow correlation of the optical property changes with microscopic alterations in tissue structure.

  8. Magnetic fields and star formation: evidence from imaging polarimetry of the Serpens Reflection Nebula

    Energy Technology Data Exchange (ETDEWEB)

    Warren-Smith, R F; Draper, P W; Scarrott, S M

    1987-08-01

    CCD imaging of the Serpens bipolar reflection nebula shows it to be surrounded by dark material having spiral density structure. Multi-colour polarization mapping also reveals details of the surrounding magnetic field, indicating that this also has spiral structure. These observations are discussed along with current ideas about the role of magnetic fields during star formation. An interpretation involving the non-axisymmetric magnetically braked collapse of a protostellar cloud is proposed and a resulting magnetic field configuration is described which can account for the observations. Evidence is also discussed for the formation of a binary star system within the nebula, resulting from the fragmentation of a magnetized protostellar disc.

  9. Polarization-based and specular-reflection-based noncontact latent fingerprint imaging and lifting

    Science.gov (United States)

    Lin, Shih-Schön; Yemelyanov, Konstantin M.; Pugh, Edward N., Jr.; Engheta, Nader

    2006-09-01

    In forensic science the finger marks left unintentionally by people at a crime scene are referred to as latent fingerprints. Most existing techniques to detect and lift latent fingerprints require application of a certain material directly onto the exhibit. The chemical and physical processing applied to the fingerprint potentially degrades or prevents further forensic testing on the same evidence sample. Many existing methods also have deleterious side effects. We introduce a method to detect and extract latent fingerprint images without applying any powder or chemicals on the object. Our method is based on the optical phenomena of polarization and specular reflection together with the physiology of fingerprint formation. The recovered image quality is comparable to existing methods. In some cases, such as the sticky side of tape, our method shows unique advantages.

  10. Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue

    International Nuclear Information System (INIS)

    Woodward, Ruth M; Cole, Bryan E; Wallace, Vincent P; Pye, Richard J; Arnone, Donald D; Linfield, Edmund H; Pepper, Michael

    2002-01-01

    We demonstrate the application of terahertz pulse imaging (TPI) in reflection geometry for the study of skin tissue and related cancers both in vitro and in vivo. The sensitivity of terahertz radiation to polar molecules, such as water, makes TPI suitable for studying the hydration levels in the skin and the determination of the lateral spread of skin cancer pre-operatively. By studying the terahertz pulse shape in the time domain we have been able to differentiate between diseased and normal tissue for the study of basal cell carcinoma (BCC). Basal cell carcinoma has shown a positive terahertz contrast, and inflammation and scar tissue a negative terahertz contrast compared to normal tissue. In vivo measurements on the stratum corneum have enabled visualization of the stratum corneum-epidermis interface and the study of skin hydration levels. These results demonstrate the potential of terahertz pulse imaging for the study of skin tissue and its related disorders, both in vitro and in vivo

  11. Combining total internal reflection sum frequency spectroscopy spectral imaging and confocal fluorescence microscopy.

    Science.gov (United States)

    Allgeyer, Edward S; Sterling, Sarah M; Gunewardene, Mudalige S; Hess, Samuel T; Neivandt, David J; Mason, Michael D

    2015-01-27

    Understanding surface and interfacial lateral organization in material and biological systems is critical in nearly every field of science. The continued development of tools and techniques viable for elucidation of interfacial and surface information is therefore necessary to address new questions and further current investigations. Sum frequency spectroscopy (SFS) is a label-free, nonlinear optical technique with inherent surface specificity that can yield critical organizational information on interfacial species. Unfortunately, SFS provides no spatial information on a surface; small scale heterogeneities that may exist are averaged over the large areas typically probed. Over the past decade, this has begun to be addressed with the advent of SFS microscopy. Here we detail the construction and function of a total internal reflection (TIR) SFS spectral and confocal fluorescence imaging microscope directly amenable to surface investigations. This instrument combines, for the first time, sample scanning TIR-SFS imaging with confocal fluorescence microscopy.

  12. Benney's long wave equations

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1979-01-01

    Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

  13. Near-Infrared Confocal Laser Reflectance Cytoarchitectural Imaging of the Substantia Nigra and Cerebellum in the Fresh Human Cadaver.

    Science.gov (United States)

    Cheyuo, Cletus; Grand, Walter; Balos, Lucia L

    2017-01-01

    Cytoarchitectural neuroimaging remains critical for diagnosis of many brain diseases. Fluorescent dye-enhanced, near-infrared confocal in situ cellular imaging of the brain has been reported. However, impermeability of the blood-brain barrier to most fluorescent dyes limits clinical utility of this modality. The differential degree of reflectance from brain tissue with unenhanced near-infrared imaging may represent an alternative technique for in situ cytoarchitectural neuroimaging. We assessed the utility of unenhanced near-infrared confocal laser reflectance imaging of the cytoarchitecture of the cerebellum and substantia nigra in 2 fresh human cadaver brains using a confocal near-infrared laser probe. Cellular images based on near-infrared differential reflectance were captured at depths of 20-180 μm from the brain surface. Parts of the cerebellum and substantia nigra imaged using the probe were subsequently excised and stained with hematoxylin and eosin for histologic correlation. Near-infrared reflectance imaging revealed the 3-layered cytoarchitecture of the cerebellum, with Purkinje cells appearing hyperreflectant. In the substantia nigra, neurons appeared hyporeflectant with hyperreflectant neuromelanin cytoplasmic inclusions. Cytoarchitecture of the cerebellum and substantia nigra revealed on near-infrared imaging closely correlated with the histology on hematoxylin-eosin staining. We showed that unenhanced near-infrared reflectance imaging of fresh human cadaver brain can reliably identify and distinguish neurons and detailed cytoarchitecture of the cerebellum and substantia nigra. Copyright © 2016 Elsevier Inc. All rights reserved.

  14. Automated Cart with VIS/NIR Hyperspectral Reflectance and Fluorescence Imaging Capabilities

    Directory of Open Access Journals (Sweden)

    Alan M. Lefcourt

    2016-12-01

    Full Text Available A system to take high-resolution Visible/Near Infra-Red (VIS/NIR hyperspectral reflectance and fluorescence images in outdoor fields using ambient lighting or a pulsed laser (355 nm, respectively, for illumination purposes was designed, built, and tested. Components of the system include a semi-autonomous cart, a gated-intensified camera, a spectral adapter, a frequency-triple Nd:YAG (Neodymium-doped Yttrium Aluminium Garnet laser, and optics to convert the Gaussian laser beam into a line-illumination source. The front wheels of the cart are independently powered by stepper motors that support stepping or continuous motion. When stepping, a spreadsheet is used to program parameters of image sets to be acquired at each step. For example, the spreadsheet can be used to set delays before the start of image acquisitions, acquisition times, and laser attenuation. One possible use of this functionality would be to establish acquisition parameters to facilitate the measurement of fluorescence decay-curve characteristics. The laser and camera are mounted on an aluminum plate that allows the optics to be calibrated in a laboratory setting and then moved to the cart. The system was validated by acquiring images of fluorescence responses of spinach leaves and dairy manure.

  15. New light on ion channel imaging by total internal reflection fluorescence (TIRF) microscopy.

    Science.gov (United States)

    Yamamura, Hisao; Suzuki, Yoshiaki; Imaizumi, Yuji

    2015-05-01

    Ion channels play pivotal roles in a wide variety of cellular functions; therefore, their physiological characteristics, pharmacological responses, and molecular structures have been extensively investigated. However, the mobility of an ion channel itself in the cell membrane has not been examined in as much detail. A total internal reflection fluorescence (TIRF) microscope allows fluorophores to be imaged in a restricted region within an evanescent field of less than 200 nm from the interface of the coverslip and plasma membrane in living cells. Thus the TIRF microscope is useful for selectively visualizing the plasmalemmal surface and subplasmalemmal zone. In this review, we focused on a single-molecule analysis of the dynamic movement of ion channels in the plasma membrane using TIRF microscopy. We also described two single-molecule imaging techniques under TIRF microscopy: fluorescence resonance energy transfer (FRET) for the identification of molecules that interact with ion channels, and subunit counting for the determination of subunit stoichiometry in a functional channel. TIRF imaging can also be used to analyze spatiotemporal Ca(2+) events in the subplasmalemma. Single-molecule analyses of ion channels and localized Ca(2+) signals based on TIRF imaging provide beneficial pharmacological and physiological information concerning the functions of ion channels. Copyright © 2015 The Authors. Production and hosting by Elsevier B.V. All rights reserved.

  16. Deep Interior Mission: Imaging the Interior of Near-Earth Asteroids Using Radio Reflection Tomography

    Science.gov (United States)

    Safaeinili, A.; Asphaug, E.; Belton, M.; Klaasen, K.; Ostro, S.; Plaut, J.; Yeomans, D.

    2004-12-01

    Near-Earth asteroids are important exploration targets since they provide clues to the evolution of the solar system. They are also of interest since they present a clear danger to Earth in the future. Our mission objective is to image the internal structure of two NEOs using radio reflection tomography (RRT), in order to explore the record of asteroid origin and impact evolution, and to test the fundamental hypothesis that these important members of the solar system are rubble piles rather than consolidated bodies. Our mission's RRT technique is analogous to doing a ``CAT scan" of the asteroid from orbit. Closely sampled radar echoes are processed to yield volumetric maps of mechanical and compositional boundaries, and measure interior material dielectric properties. The RRT instrument is a radar that operates at 5 and 15 MHz with two 30-m (tip-to-tip) dipole antennas that are used in a cross-dipole configuration. The radar transmitter and receiver electronics have heritage from JPL's MARSIS contribution to Mars Express, and the antenna is similar to systems used in IMAGE and LACE missions. The 5-MHz channel is designed to penetrate >1 km of basaltic rock, and 15-MHz penetrates a few hundred meters or more. In addition to RRT volumetric imaging, we use a redundant color cameras to explore the surface expressions of unit boundaries, in order to relate interior radar imaging to what is observable from spacecraft imaging and from Earth. The camera also yields stereo color imaging for geology and RRT-related compositional analysis. Gravity and high fidelity geodesy are used to explore how interior structure is expressed in shape, density, mass distribution and spin. Deep interior has two targets (S-type 1999 ND43 and V-type Nyx ) whose composition bracket the diversity of solar system materials that we are likely to encounter, and are richly complementary.

  17. Asymmetry quantification from reflectance images of orthotic patients using structural similarity metrics

    Science.gov (United States)

    Boucher, Marc-Antoine; Watts, Nicolas; Gremillet, Frederic; Legare, Philippe; Kadoury, Samuel

    2018-02-01

    Pathologies like plantar fasciitis, a common soft tissue disorder of the foot, is frequently associated with older age, high BMI and little exercise. Like other pathologies associated with the foot, the knee or hip, foot orthoses can help the patient's posture and recent techniques allow the creation of personalized foot orthoses based on 3D foot model that are fitted with high accuracy to the foot surface. In order to assess the efficacy of the personalized orthoses on the patient's pose and balance, depth images with reflectance camera filters are acquired in order to evaluate the posture of the patient before and after the use of the orthoses. Images are analysed by clinicians to assess the region asymmetry and posture changes. However, this remains a subjective evaluation and a quantifiable measurement is required to follow patient progression. In this paper, we present a novel tool to assess and quantify the asymmetry of body regions using a color-based structural similarity metric calculated from paired regions. This provides a quantitative measure to evaluate the effect of the personalized orthoses on the patient. A user-friendly interface allows the user to select an area of the body and automatically generate a symmetry axis, along with a measure of asymmetry measuring reflectance variations from the skin. The tool was validated on 30 patients, demonstrating an 83% agreement rate compare to clinical observations.

  18. On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation

    Directory of Open Access Journals (Sweden)

    Yuri Luchko

    2017-12-01

    Full Text Available In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

  19. Evaluating visibility of age spot and freckle based on simulated spectral reflectance distribution and facial color image

    Science.gov (United States)

    Hirose, Misa; Toyota, Saori; Tsumura, Norimichi

    2018-02-01

    In this research, we evaluate the visibility of age spot and freckle with changing the blood volume based on simulated spectral reflectance distribution and the actual facial color images, and compare these results. First, we generate three types of spatial distribution of age spot and freckle in patch-like images based on the simulated spectral reflectance. The spectral reflectance is simulated using Monte Carlo simulation of light transport in multi-layered tissue. Next, we reconstruct the facial color image with changing the blood volume. We acquire the concentration distribution of melanin, hemoglobin and shading components by applying the independent component analysis on a facial color image. We reproduce images using the obtained melanin and shading concentration and the changed hemoglobin concentration. Finally, we evaluate the visibility of pigmentations using simulated spectral reflectance distribution and facial color images. In the result of simulated spectral reflectance distribution, we found that the visibility became lower as the blood volume increases. However, we can see that a specific blood volume reduces the visibility of the actual pigmentations from the result of the facial color images.

  20. Generalization of Bateman-Hillion progressive wave and Bessel-Gauss pulse solutions of the wave equation via a separation of variables

    CERN Document Server

    Kiselev, A

    2003-01-01

    Two new families of exact solutions of the wave equation u sub x sub x + u sub y sub y + u sub z sub z - c sup - sup 2 u sub t sub t = 0 generalizing Bessel-Gauss pulses and Bateman-Hillion relatively undistorted progressive waves, respectively are presented. In each of these families new simple solutions describing localized wave propagation are found. The approach is based on a kind of separation of variables. (letter to the editor)

  1. A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yong Chen; Qi Wang

    2005-01-01

    In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained

  2. Ultraviolet Imaging Telescope images of the reflection nebula NGC 7023 - Derivation of ultraviolet scattering properties of dust grains

    Science.gov (United States)

    Witt, Adolf N.; Petersohn, Jens K.; Bohlin, Ralph C.; O'Connell, Robert W.; Roberts, Morton S.; Smith, Andrew M.; Stecher, Theodore P.

    1992-01-01

    The Ultraviolet Imaging Telescope as part of the Astro-1 mission, was used to obtain high-resolution surface brightness distribution data in six ultraviolet wavelength bands for the bright reflection nebula NGC 7023. From the quantitative comparison of the measured surface brightness gradients ratios of nebular to stellar flux, and detail radial surface brightness profiles with corresponding data from the visible, two major conclusions results: (1) the scattering in the near- and far-ultraviolet in this nebula is more strongly forward-directed than in the visible; (2) the dust albedo in the ultraviolet for wavelengths not less than 140 nm is identical to that in the visible, with the exception of the 220 nm bump in the extinction curve. In the wavelengths region of the bump, the albedo is reduced by 25 to 30 percent in comparison with wavelengths regions both shorter and longer. This lower albedo is expected, if the bump is a pure absorption feature.

  3. Computational study on full-wave inversion based on the acoustic wave-equation; Onkyoha hado hoteishiki full wave inversion no model keisan ni yoru kento

    Energy Technology Data Exchange (ETDEWEB)

    Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan); Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering

    1996-10-01

    The effect of initial models on full-wave inversion (FWI) analysis based on acoustic wave-equation was studied for elastic wave tomography of underground structures. At present, travel time inversion using initial motion travel time is generally used, and inverse analysis is conducted using the concept `ray,` assuming very high wave frequency. Although this method can derive stable solutions relatively unaffected by initial model, it uses only the data of initial motion travel time. FWI calculates theoretical waveform at each receiver using all of observed waveforms as data by wave equation modeling where 2-D underground structure is calculated by difference calculus under the assumption that wave propagation is described by wave equation of P wave. Although it is a weak point that FWI is easily affected by noises in an initial model and data, it is featured by high resolution of solutions. This method offers very excellent convergence as a proper initial model is used, resulting in sufficient performance, however, it is strongly affected by initial model. 2 refs., 7 figs., 1 tab.

  4. On image pre-processing for PIV of sinlge- and two-phase flows over reflecting objects

    NARCIS (Netherlands)

    Deen, N.G.; Willems, P.; van Sint Annaland, M.; Kuipers, J.A.M.; Lammertink, Rob G.H.; Kemperman, Antonius J.B.; Wessling, Matthias; van der Meer, Walterus Gijsbertus Joseph

    2010-01-01

    A novel image pre-processing scheme for PIV of single- and two-phase flows over reflecting objects which does not require the use of additional hardware is discussed. The approach for single-phase flow consists of image normalization and intensity stretching followed by background subtraction. For

  5. Separation of irradiance and reflectance from observed color images by logarithmical nonlinear diffusion process

    Science.gov (United States)

    Saito, Takahiro; Takahashi, Hiromi; Komatsu, Takashi

    2006-02-01

    The Retinex theory was first proposed by Land, and deals with separation of irradiance from reflectance in an observed image. The separation problem is an ill-posed problem. Land and others proposed various Retinex separation algorithms. Recently, Kimmel and others proposed a variational framework that unifies the previous Retinex algorithms such as the Poisson-equation-type Retinex algorithms developed by Horn and others, and presented a Retinex separation algorithm with the time-evolution of a linear diffusion process. However, the Kimmel's separation algorithm cannot achieve physically rational separation, if true irradiance varies among color channels. To cope with this problem, we introduce a nonlinear diffusion process into the time-evolution. Moreover, as to its extension to color images, we present two approaches to treat color channels: the independent approach to treat each color channel separately and the collective approach to treat all color channels collectively. The latter approach outperforms the former. Furthermore, we apply our separation algorithm to a high quality chroma key in which before combining a foreground frame and a background frame into an output image a color of each pixel in the foreground frame are spatially adaptively corrected through transformation of the separated irradiance. Experiments demonstrate superiority of our separation algorithm over the Kimmel's separation algorithm.

  6. Development of algorithms for detecting citrus canker based on hyperspectral reflectance imaging.

    Science.gov (United States)

    Li, Jiangbo; Rao, Xiuqin; Ying, Yibin

    2012-01-15

    Automated discrimination of fruits with canker from other fruit with normal surface and different type of peel defects has become a helpful task to enhance the competitiveness and profitability of the citrus industry. Over the last several years, hyperspectral imaging technology has received increasing attention in the agricultural products inspection field. This paper studied the feasibility of classification of citrus canker from other peel conditions including normal surface and nine peel defects by hyperspectal imaging. A combination algorithm based on principal component analysis and the two-band ratio (Q(687/630)) method was proposed. Since fewer wavelengths were desired in order to develop a rapid multispectral imaging system, the canker classification performance of the two-band ratio (Q(687/630)) method alone was also evaluated. The proposed combination approach and two-band ratio method alone resulted in overall classification accuracy for training set samples and test set samples of 99.5%, 84.5% and 98.2%, 82.9%, respectively. The proposed combination approach was more efficient for classifying canker against various conditions under reflectance hyperspectral imagery. However, the two-band ratio (Q(687/630)) method alone also demonstrated effectiveness in discriminating citrus canker from normal fruit and other peel diseases except for copper burn and anthracnose. Copyright © 2011 Society of Chemical Industry.

  7. Visualizing Ebolavirus Particles Using Single-Particle Interferometric Reflectance Imaging Sensor (SP-IRIS).

    Science.gov (United States)

    Carter, Erik P; Seymour, Elif Ç; Scherr, Steven M; Daaboul, George G; Freedman, David S; Selim Ünlü, M; Connor, John H

    2017-01-01

    This chapter describes an approach for the label-free imaging and quantification of intact Ebola virus (EBOV) and EBOV viruslike particles (VLPs) using a light microscopy technique. In this technique, individual virus particles are captured onto a silicon chip that has been printed with spots of virus-specific capture antibodies. These captured virions are then detected using an optical approach called interference reflectance imaging. This approach allows for the detection of each virus particle that is captured on an antibody spot and can resolve the filamentous structure of EBOV VLPs without the need for electron microscopy. Capture of VLPs and virions can be done from a variety of sample types ranging from tissue culture medium to blood. The technique also allows automated quantitative analysis of the number of virions captured. This can be used to identify the virus concentration in an unknown sample. In addition, this technique offers the opportunity to easily image virions captured from native solutions without the need for additional labeling approaches while offering a means of assessing the range of particle sizes and morphologies in a quantitative manner.

  8. Attenuated total internal reflection infrared microspectroscopic imaging using a large-radius germanium internal reflection element and a linear array detector.

    Science.gov (United States)

    Patterson, Brian M; Havrilla, George J

    2006-11-01

    The number of techniques and instruments available for Fourier transform infrared (FT-IR) microspectroscopic imaging has grown significantly over the past few years. Attenuated total internal reflectance (ATR) FT-IR microspectroscopy reduces sample preparation time and has simplified the analysis of many difficult samples. FT-IR imaging has become a powerful analytical tool using either a focal plane array or a linear array detector, especially when coupled with a chemometric analysis package. The field of view of the ATR-IR microspectroscopic imaging area can be greatly increased from 300 x 300 microm to 2500 x 2500 microm using a larger internal reflection element of 12.5 mm radius instead of the typical 1.5 mm radius. This gives an area increase of 70x before aberrant effects become too great. Parameters evaluated include the change in penetration depth as a function of beam displacement, measurements of the active area, magnification factor, and change in spatial resolution over the imaging area. Drawbacks such as large file size will also be discussed. This technique has been successfully applied to the FT-IR imaging of polydimethylsiloxane foam cross-sections, latent human fingerprints, and a model inorganic mixture, which demonstrates the usefulness of the method for pharmaceuticals.

  9. Deep Interior: Radio Reflection Tomographic Imaging of Earth-Crossing Asteroids

    Science.gov (United States)

    Asphaug, E.; Belton, M.; Safaeinili, A.; Klaasen, K.; Ostro, S.; Yeomans, D.; Plaut, J.

    2004-12-01

    Near-Earth Objects (NEOs) present an important scientific question and an intriguing space hazard. They are scrutinized by a number of large, dedicated groundbased telescopes, and their diverse compositions are represented by thousands of well-studied meteorites. A successful program of NEO spacecraft exploration has begun, and we are proposing Deep Interior as the next logical step. Our mission objective is to image the deep interior structure of two NEOs using radio reflection tomography (RRT), in order to explore the record of asteroid origin and impact evolution, and to test the fundamental hypothesis that these important members of the solar system are rubble piles rather than consolidated bodies. Asteroid Interiors. Our mission's RRT technique is like a CAT scan from orbit. Closely sampled radar echoes yield volumetric maps of mechanical and compositional boundaries, and measure interior material dielectric properties. Exteriors. We use color imaging to explore the surface expressions of unit boundaries, in order to relate interior radar imaging to what is observable from spacecraft imaging and from Earth. Gravity and high fidelity geodesy are used to explore how interior structure is expressed in shape, density, mass distribution and spin. Diversity. We first visit a common, primitive, S-type asteroid. We next visit an asteroid that was perhaps blasted from the surface of a differentiated asteroid. We attain an up-close and inside look at two taxonomic archetypes spanning an important range of NEO mass and spin rate. Scientific focus is achieved by keeping our payload simple: Radar. A 30-m (tip-to-tip) cross-dipole antenna system operates at 5 and 15-MHz, with electronics heritage from JPL's MARSIS contribution to Mars Express, and antenna heritage from IMAGE and LACE. The 5-MHz channel is designed to penetrate >1 km of basaltic rock, and 15-MHz penetrates a few 100 m or more. They bracket the diversity of solar system materials that we are likely to

  10. Label free imaging of cell-substrate contacts by holographic total internal reflection microscopy.

    Science.gov (United States)

    Mandracchia, Biagio; Gennari, Oriella; Marchesano, Valentina; Paturzo, Melania; Ferraro, Pietro

    2017-09-01

    The study of cell adhesion contacts is pivotal to understand cell mechanics and interaction at substrates or chemical and physical stimuli. We designed and built a HoloTIR microscope for label-free quantitative phase imaging of total internal reflection. Here we show for the first time that HoloTIR is a good choice for label-free study of focal contacts and of cell/substrate interaction as its sensitivity is enhanced in comparison with standard TIR microscopy. Finally, the simplicity of implementation and relative low cost, due to the requirement of less optical components, make HoloTIR a reasonable alternative, or even an addition, to TIRF microscopy for mapping cell/substratum topography. As a proof of concept, we studied the formation of focal contacts of fibroblasts on three substrates with different levels of affinity for cell adhesion. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  11. Imaging Early Steps of Sindbis Virus Infection by Total Internal Reflection Fluorescence Microscopy

    Directory of Open Access Journals (Sweden)

    Youling Gu

    2011-01-01

    Full Text Available Sindbis virus (SINV is an alphavirus that has a broad host range and has been widely used as a vector for recombinant gene transduction, DNA-based vaccine production, and oncolytic cancer therapy. The mechanism of SINV entry into host cells has yet to be fully understood. In this paper, we used single virus tracking under total internal reflection fluorescence microscopy (TIRFM to investigate SINV attachment to cell surface. Biotinylated viral particles were labeled with quantum dots, which retained viral viability and infectivity. By time-lapse imaging, we showed that the SINV exhibited a heterogeneous dynamics on the surface of the host cells. Analysis of SINV motility demonstrated a two-step attachment reaction. Moreover, dual color TIRFM of GFP-Rab5 and SINV suggested that the virus was targeted to the early endosomes after endocytosis. These findings demonstrate the utility of quantum dot labeling in studying the early steps and behavior of SINV infection.

  12. Image analysis using reflected light: an underutilized tool for interpreting magnetic fabrics

    Science.gov (United States)

    Waters-Tormey, C. L.; Liner, T.; Miller, B.; Kelso, P. R.

    2010-12-01

    Grain shape fabric analysis is one of the most common tools used to compare magnetic fabric and handsample scale rock fabric. Usually, this image analysis uses photomicrographs taken under plane or polarized light, which may be problematic if there are several dominant magnetic carriers (e.g., magnetite and pyrrhotite). The method developed for this study uses reflected light photomicrographs, and is effective in assessing the relative contribution of different phases to the opaque mineral shape-preferred orientation (SPO). Mosaics of high-resolution photomicrographs are first assembled and processed in Adobe Photoshop®. The Adobe Illustrator® “Live Trace” tool, whose settings can be optimized for reflected light images, completes initial automatic grain tracing and phase separation. Checking and re-classification of phases using reflected light properties and trace editing occurs manually. Phase identification is confirmed by microprobe or quantitative EDS, after which grain traces are easily reclassified as needed. Traces are imported into SPO2003 (Launeau and Robin, 2005) for SPO analysis. The combination of image resolution and magnification used here includes grains down to 10 microns. This work is part of an ongoing study examining fabric development across strain gradients in the granulite facies Capricorn ridge shear zone exposed in the Mt. Hay block of central Australia (Waters-Tormey et al., 2009). Strain marker shape fabrics, mesoscale structures, and strain localization adjacent to major lithologic boundaries all indicate that the deformation involved flattening, but that components of the deformation have been partitioned into different lithological domains. Thin sections were taken from the two gabbroic map units which volumetrically dominate the shear zone (northern and southern) using samples with similar outcrop fabric intensity. Prior thermomagnetic analyses indicate these units contain magnetite ± titanomagnetite ± ilmenite ± pyrrhotite

  13. Interferometric Reflectance Imaging Sensor (IRIS—A Platform Technology for Multiplexed Diagnostics and Digital Detection

    Directory of Open Access Journals (Sweden)

    Oguzhan Avci

    2015-07-01

    Full Text Available Over the last decade, the growing need in disease diagnostics has stimulated rapid development of new technologies with unprecedented capabilities. Recent emerging infectious diseases and epidemics have revealed the shortcomings of existing diagnostics tools, and the necessity for further improvements. Optical biosensors can lay the foundations for future generation diagnostics by providing means to detect biomarkers in a highly sensitive, specific, quantitative and multiplexed fashion. Here, we review an optical sensing technology, Interferometric Reflectance Imaging Sensor (IRIS, and the relevant features of this multifunctional platform for quantitative, label-free and dynamic detection. We discuss two distinct modalities for IRIS: (i low-magnification (ensemble biomolecular mass measurements and (ii high-magnification (digital detection of individual nanoparticles along with their applications, including label-free detection of multiplexed protein chips, measurement of single nucleotide polymorphism, quantification of transcription factor DNA binding, and high sensitivity digital sensing and characterization of nanoparticles and viruses.

  14. High frequency asymptotic solutions of the reduced wave equation on infinite regions with non-convex boundaries

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    Bloom Clifford O.

    1996-01-01

    Full Text Available The asymptotic behavior as λ → ∞ of the function U ( x , λ that satisfies the reduced wave equation L λ [ U ] = ∇ ⋅ ( E ( x ∇ U + λ 2 N 2 ( x U = 0 on an infinite 3-dimensional region, a Dirichlet condition on ∂ V , and an outgoing radiation condition is investigated. A function U N ( x , λ is constructed that is a global approximate solution as λ → ∞ of the problem satisfied by U ( x , λ . An estimate for W N ( x , λ = U ( x , λ − U N ( x , λ on V is obtained, which implies that U N ( x , λ is a uniform asymptotic approximation of U ( x , λ as λ → ∞ , with an error that tends to zero as rapidly as λ − N ( N = 1 , 2 , 3 , ... . This is done by applying a priori estimates of the function W N ( x , λ in terms of its boundary values, and the L 2 norm of r L λ [ W N ( x , λ ] on V . It is assumed that E ( x , N ( x , ∂ V and the boundary data are smooth, that E ( x − I and N ( x − 1 tend to zero algebraically fast as r → ∞ , and finally that E ( x and N ( x are slowly varying; ∂ V may be finite or infinite. The solution U ( x , λ can be interpreted as a scalar potential of a high frequency acoustic or electromagnetic field radiating from the boundary of an impenetrable object of general shape. The energy of the field propagates through an inhomogeneous, anisotropic medium; the rays along which it propagates may form caustics. The approximate solution (potential derived in this paper is defined on and in a neighborhood of any such caustic, and can be used to connect local “geometrical optics” type approximate solutions that hold on caustic free subsets of V .The result of this paper generalizes previous work of Bloom and Kazarinoff [C. O. BLOOM and N. D. KAZARINOFF, Short Wave Radiation Problems in Inhomogeneous Media: Asymptotic Solutions, SPRINGER VERLAG, NEW YORK, NY, 1976].

  15. Virtual source reflection imaging of the Socorro Magma Body, New Mexico, using a dense seismic array

    Science.gov (United States)

    Finlay, T. S.; Worthington, L. L.; Schmandt, B.; Hansen, S. M.; Bilek, S. L.; Aster, R. C.; Ranasinghe, N. R.

    2017-12-01

    The Socorro Magma Body (SMB) is one of the largest known actively inflating continental magmatic intrusions. Previous studies have relied on sparse instrument coverage to determine its spatial extent, depth, and seismic signature, which characterized the body as a thin sill with a surface at 19 km below the Earth's surface. However, over the last two decades, InSAR and magneto-telluric (MT) studies have shed new light on the SMB and invigorated the scientific debate of the spatial distribution and uplift rate of the SMB. We return to seismic imaging of the SMB with the Sevilleta Array, a 12-day deployment of approximately 800 vertical component, 10-Hz geophones north of Socorro, New Mexico above and around the estimated northern half of the SMB. Teleseismic virtual source reflection profiling (TVR) employs the free surface reflection off of a teleseismic P as a virtual source in dense arrays, and has been used successfully to image basin structure and the Moho in multiple tectonic environments. The Sevilleta Array recorded 62 teleseismic events greater than M5. Applying TVR to the data collected by the Sevilleta Array, we present stacks from four events that produced the with high signal-to-noise ratios and simple source-time functions: the February 11, 2015 M6.7 in northern Argentina, the February 19, 2015 M5.4 in Kamchatka, Russia, and the February 21, 2015 M5.1 and February 22, 2015 M5.5 in western Colombia. Preliminary results suggest eastward-dipping reflectors at approximately 5 km depth near the Sierra Ladrones range in the northwestern corner of the array. Further analysis will focus on creating profiles across the area of maximum SMB uplift and constraining basin geometry.

  16. Mapping Reflectance Anisotropy of a Potato Canopy Using Aerial Images Acquired with an Unmanned Aerial Vehicle

    Directory of Open Access Journals (Sweden)

    Peter P. J. Roosjen

    2017-04-01

    Full Text Available Viewing and illumination geometry has a strong influence on optical measurements of natural surfaces due to their anisotropic reflectance properties. Typically, cameras on-board unmanned aerial vehicles (UAVs are affected by this because of their relatively large field of view (FOV and thus large range of viewing angles. In this study, we investigated the magnitude of reflectance anisotropy effects in the 500–900 nm range, captured by a frame camera mounted on a UAV during a standard mapping flight. After orthorectification and georeferencing of the images collected by the camera, we calculated the viewing geometry of all observations of each georeferenced ground pixel, forming a dataset with multi-angular observations. We performed UAV flights on two days during the summer of 2016 over an experimental potato field where different zones in the field received different nitrogen fertilization treatments. These fertilization levels caused variation in potato plant growth and thereby differences in structural properties such as leaf area index (LAI and canopy cover. We fitted the Rahman–Pinty–Verstraete (RPV model through the multi-angular observations of each ground pixel to quantify, interpret, and visualize the anisotropy patterns in our study area. The Θ parameter of the RPV model, which controls the proportion of forward and backward scattering, showed strong correlation with canopy cover, where in general an increase in canopy cover resulted in a reduction of backward scattering intensity, indicating that reflectance anisotropy contains information on canopy structure. In this paper, we demonstrated that anisotropy data can be extracted from measurements using a frame camera, collected during a typical UAV mapping flight. Future research will focus on how to use the anisotropy signal as a source of information for estimation of physical vegetation properties.

  17. Improved classification and visualization of healthy and pathological hard dental tissues by modeling specular reflections in NIR hyperspectral images

    Science.gov (United States)

    Usenik, Peter; Bürmen, Miran; Fidler, Aleš; Pernuš, Franjo; Likar, Boštjan

    2012-03-01

    Despite major improvements in dental healthcare and technology, dental caries remains one of the most prevalent chronic diseases of modern society. The initial stages of dental caries are characterized by demineralization of enamel crystals, commonly known as white spots, which are difficult to diagnose. Near-infrared (NIR) hyperspectral imaging is a new promising technique for early detection of demineralization which can classify healthy and pathological dental tissues. However, due to non-ideal illumination of the tooth surface the hyperspectral images can exhibit specular reflections, in particular around the edges and the ridges of the teeth. These reflections significantly affect the performance of automated classification and visualization methods. Cross polarized imaging setup can effectively remove the specular reflections, however is due to the complexity and other imaging setup limitations not always possible. In this paper, we propose an alternative approach based on modeling the specular reflections of hard dental tissues, which significantly improves the classification accuracy in the presence of specular reflections. The method was evaluated on five extracted human teeth with corresponding gold standard for 6 different healthy and pathological hard dental tissues including enamel, dentin, calculus, dentin caries, enamel caries and demineralized regions. Principal component analysis (PCA) was used for multivariate local modeling of healthy and pathological dental tissues. The classification was performed by employing multiple discriminant analysis. Based on the obtained results we believe the proposed method can be considered as an effective alternative to the complex cross polarized imaging setups.

  18. Reflection imaging of the Moon's interior using deep-moonquake seismic interferometry

    Science.gov (United States)

    Nishitsuji, Yohei; Rowe, C. A.; Wapenaar, Kees; Draganov, Deyan

    2016-04-01

    The internal structure of the Moon has been investigated over many years using a variety of seismic methods, such as travel time analysis, receiver functions, and tomography. Here we propose to apply body-wave seismic interferometry to deep moonquakes in order to retrieve zero-offset reflection responses (and thus images) beneath the Apollo stations on the nearside of the Moon from virtual sources colocated with the stations. This method is called deep-moonquake seismic interferometry (DMSI). Our results show a laterally coherent acoustic boundary around 50 km depth beneath all four Apollo stations. We interpret this boundary as the lunar seismic Moho. This depth agrees with Japan Aerospace Exploration Agency's (JAXA) SELenological and Engineering Explorer (SELENE) result and previous travel time analysis at the Apollo 12/14 sites. The deeper part of the image we obtain from DMSI shows laterally incoherent structures. Such lateral inhomogeneity we interpret as representing a zone characterized by strong scattering and constant apparent seismic velocity at our resolution scale (0.2-2.0 Hz).

  19. Automatic luminous reflections detector using global threshold with increased luminosity contrast in images

    Science.gov (United States)

    Silva, Ricardo Petri; Naozuka, Gustavo Taiji; Mastelini, Saulo Martiello; Felinto, Alan Salvany

    2018-01-01

    The incidence of luminous reflections (LR) in captured images can interfere with the color of the affected regions. These regions tend to oversaturate, becoming whitish and, consequently, losing the original color information of the scene. Decision processes that employ images acquired from digital cameras can be impaired by the LR incidence. Such applications include real-time video surgeries, facial, and ocular recognition. This work proposes an algorithm called contrast enhancement of potential LR regions, which is a preprocessing to increase the contrast of potential LR regions, in order to improve the performance of automatic LR detectors. In addition, three automatic detectors were compared with and without the employment of our preprocessing method. The first one is a technique already consolidated in the literature called the Chang-Tseng threshold. We propose two automatic detectors called adapted histogram peak and global threshold. We employed four performance metrics to evaluate the detectors, namely, accuracy, precision, exactitude, and root mean square error. The exactitude metric is developed by this work. Thus, a manually defined reference model was created. The global threshold detector combined with our preprocessing method presented the best results, with an average exactitude rate of 82.47%.

  20. BMI and WHR Are Reflected in Female Facial Shape and Texture: A Geometric Morphometric Image Analysis.

    Directory of Open Access Journals (Sweden)

    Christine Mayer

    Full Text Available Facial markers of body composition are frequently studied in evolutionary psychology and are important in computational and forensic face recognition. We assessed the association of body mass index (BMI and waist-to-hip ratio (WHR with facial shape and texture (color pattern in a sample of young Middle European women by a combination of geometric morphometrics and image analysis. Faces of women with high BMI had a wider and rounder facial outline relative to the size of the eyes and lips, and relatively lower eyebrows. Furthermore, women with high BMI had a brighter and more reddish skin color than women with lower BMI. The same facial features were associated with WHR, even though BMI and WHR were only moderately correlated. Yet BMI was better predictable than WHR from facial attributes. After leave-one-out cross-validation, we were able to predict 25% of variation in BMI and 10% of variation in WHR by facial shape. Facial texture predicted only about 3-10% of variation in BMI and WHR. This indicates that facial shape primarily reflects total fat proportion, rather than the distribution of fat within the body. The association of reddish facial texture in high-BMI women may be mediated by increased blood pressure and superficial blood flow as well as diet. Our study elucidates how geometric morphometric image analysis serves to quantify the effect of biological factors such as BMI and WHR to facial shape and color, which in turn contributes to social perception.

  1. Extending Whole Slide Imaging: Color Darkfield Internal Reflection Illumination (DIRI for Biological Applications.

    Directory of Open Access Journals (Sweden)

    Yoshihiro Kawano

    Full Text Available Whole slide imaging (WSI is a useful tool for multi-modal imaging, and in our work, we have often combined WSI with darkfield microscopy. However, traditional darkfield microscopy cannot use a single condenser to support high- and low-numerical-aperture objectives, which limits the modality of WSI. To overcome this limitation, we previously developed a darkfield internal reflection illumination (DIRI microscope using white light-emitting diodes (LEDs. Although the developed DIRI is useful for biological applications, substantial problems remain to be resolved. In this study, we propose a novel illumination technique called color DIRI. The use of three-color LEDs dramatically improves the capability of the system, such that color DIRI (1 enables optimization of the illumination color; (2 can be combined with an oil objective lens; (3 can produce fluorescence excitation illumination; (4 can adjust the wavelength of light to avoid cell damage or reactions; and (5 can be used as a photostimulator. These results clearly illustrate that the proposed color DIRI can significantly extend WSI modalities for biological applications.

  2. Direct visualization of polarization reversal of organic ferroelectric memory transistor by using charge modulated reflectance imaging

    Science.gov (United States)

    Otsuka, Takako; Taguchi, Dai; Manaka, Takaaki; Iwamoto, Mitsumasa

    2017-11-01

    By using the charge modulated reflectance (CMR) imaging technique, charge distribution in the pentacene organic field-effect transistor (OFET) with a ferroelectric gate insulator [P(VDF-TrFE)] was investigated in terms of polarization reversal of the P(VDF-TrFE) layer. We studied the polarization reversal process and the carrier spreading process in the OFET channel. The I-V measurement showed a hysteresis behavior caused by the spontaneous polarization of P(VDF-TrFE), but the hysteresis I-V curve changes depending on the applied drain bias, possibly due to the gradual shift of the polarization reversal position in the OFET channel. CMR imaging visualized the gradual shift of the polarization reversal position and showed that the electrostatic field formed by the polarization of P(VDF-TrFE) contributes to hole and electron injection into the pentacene layer and the carrier distribution is significantly dependent on the direction of the polarization. The polarization reversal position in the channel region is governed by the electrostatic potential, and it happens where the potential reaches the coercive voltage of P(VDF-TrFE). The transmission line model developed on the basis of the Maxwell-Wagner effect element analysis well accounts for this polarization reversal process in the OFET channel.

  3. Diffuse reflectance spectroscopy and optical polarization imaging of in-vivo biological tissue

    Science.gov (United States)

    Mora-Núñez, A.; Castillejos, Y.; García-Torales, G.; Martínez-Ponce, G.

    2013-11-01

    A number of optical techniques have been reported in the scientific literature as accomplishable methodologies to diagnose diseases in biological tissue, for instance, diffuse reflectance spectroscopy (DRS) and optical polarization imaging (OPI). The skin is the largest organ in the body and consists of three primary layers, namely, the epidermis (the outermost layer exposed to the world), the dermis, and the hypodermis. The epidermis changes from to site to site, mainly because of difference in hydration. A lower water content increase light scattering and reduce the penetration depth of radiation. In this work, two hairless mice have been selected to evaluate their skin features by using DRS and OPI. Four areas of the specimen body were chosen to realize the comparison: back, abdomen, tail, and head. From DRS, it was possible to distinguish the skin nature because of different blood irrigation at dermis. In the other hand, OPI shows pseudo-depolarizing regions in the measured Mueller images related to a spatially varying propagation of the scattered light. This provides information about the cell size in the irradiated skin.

  4. Characterization of hydrogel microstructure using laser tweezers particle tracking and confocal reflection imaging

    International Nuclear Information System (INIS)

    Kotlarchyk, M A; Botvinick, E L; Putnam, A J

    2010-01-01

    Hydrogels are commonly used as extracellular matrix mimetics for applications in tissue engineering and increasingly as cell culture platforms with which to study the influence of biophysical and biochemical cues on cell function in 3D. In recent years, a significant number of studies have focused on linking substrate mechanical properties to cell function using standard methodologies to characterize the bulk mechanical properties of the hydrogel substrates. However, current understanding of the correlations between the microstructural mechanical properties of hydrogels and cell function in 3D is poor, in part because of a lack of appropriate techniques. Here we have utilized a laser tracking system, based on passive optical microrheology instrumentation, to characterize the microstructure of viscoelastic fibrin clots. Trajectories and mean square displacements were observed as bioinert PEGylated (PEG: polyethylene glycol) microspheres (1, 2 or 4.7 μm in diameter) diffused within confined pores created by the protein phase of fibrin hydrogels. Complementary confocal reflection imaging revealed microstructures comprised of a highly heterogeneous fibrin network with a wide range of pore sizes. As the protein concentration of fibrin gels was increased, our quantitative laser tracking measurements showed a corresponding decrease in particle mean square displacements with greater resolution and sensitivity than conventional imaging techniques. This platform-independent method will enable a more complete understanding of how changes in substrate mechanical properties simultaneously influence other microenvironmental parameters in 3D cultures.

  5. Nonlinear reflection of shock shear waves in soft elastic media.

    Science.gov (United States)

    Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

    2010-02-01

    For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

  6. Imaging spin filter for electrons based on specular reflection from iridium (001)

    Energy Technology Data Exchange (ETDEWEB)

    Kutnyakhov, D.; Lushchyk, P. [Johannes Gutenberg-Universität, Institut für Physik, 55099 Mainz (Germany); Fognini, A.; Perriard, D. [Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich (Switzerland); Kolbe, M.; Medjanik, K.; Fedchenko, E.; Nepijko, S.A.; Elmers, H.J. [Johannes Gutenberg-Universität, Institut für Physik, 55099 Mainz (Germany); Salvatella, G.; Stieger, C.; Gort, R.; Bähler, T.; Michlmayer, T.; Acremann, Y.; Vaterlaus, A. [Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich (Switzerland); Giebels, F.; Gollisch, H.; Feder, R. [Universität Duisburg-Essen, Theoretische Festkörperphysik, 47057 Duisburg (Germany); Tusche, C. [Max Planck-Institut für Mikrostrukturphysik, 06120 Halle (Germany); and others

    2013-07-15

    As Stern–Gerlach type spin filters do not work with electrons, spin analysis of electron beams is accomplished by spin-dependent scattering processes based on spin–orbit or exchange interaction. Existing polarimeters are single-channel devices characterized by an inherently low figure of merit (FoM) of typically 10{sup −4}–10{sup −3}. This single-channel approach is not compatible with parallel imaging microscopes and also not with modern electron spectrometers that acquire a certain energy and angular interval simultaneously. We present a novel type of polarimeter that can transport a full image by making use of k-parallel conservation in low-energy electron diffraction. We studied specular reflection from Ir (001) because this spin-filter crystal provides a high analyzing power combined with a “lifetime” in UHV of a full day. One good working point is centered at 39 eV scattering energy with a broad maximum of 5 eV usable width. A second one at about 10 eV shows a narrower profile but much higher FoM. A relativistic layer-KKR SPLEED calculation shows good agreement with measurements. - Highlights: • Novel type of spin polarimeter can transport a full image by making use of k{sup →}{sub ||} conservation in LEED. • When combined with a hemispherical analyzer, it acquires a certain energy and angular interval simultaneously. • Ir (001) based spin-filter provides a high analyzing power combined with a “lifetime” in UHV of a full day. • Parallel spin detection improves spin polarimeter efficiency by orders of magnitude. • A relativistic layer-KKR SPLEED calculation shows good agreement with measurements.

  7. Radio Spectral Imaging of Reflective MHD Waves during the Impulsive Phase of a Solar Flare

    Science.gov (United States)

    Yu, S.; Chen, B.; Reeves, K.

    2017-12-01

    We report a new type of coherent radio bursts observed by the Karl G. Jansky Very Large Array (VLA) in 1-2 GHz during the impulsive phase of a two-ribbon flare on 2014 November 1, which we interpret as MHD waves reflected near the footpoint of flaring loops. In the dynamic spectrum, this burst starts with a positive frequency drift toward higher frequencies until it slows down near its highest-frequency boundary. Then it turns over and drifts toward lower frequencies. The frequency drift rate in its descending and ascending branch is between 50-150 MHz/s, which is much slower than type III radio bursts associated with fast electron beams but close to the well-known intermediate drift bursts, or fiber bursts, which are usually attributed to propagating whistler or Alfvenic waves. Thanks to VLA's unique capability of imaging with spectrometer-like temporal and spectral resolution (50 ms and 2 MHz), we are able to obtain an image of the radio source at every time and frequency in the dynamic spectrum where the burst is present and trace its spatial evolution. From the imaging results, we find that the radio source firstly moves downward toward one of the flaring ribbons before it "bounces off" at the lowest height (corresponding to the turnover frequency in the dynamic spectrum) and moves upward again. The measured speed in projection is at the order of 1-2 Mm/s, which is characteristic of Alfvenic or fast-mode MHD waves in the low corona. We conclude that the radio burst is emitted by trapped nonthermal electrons in the flaring loop carried along by a large-scale MHD wave. The waves are probably launched during the eruption of a magnetic flux rope in the flare impulsive phase.

  8. Analysis of Properties of Reflectance Reference Targets for Permanent Radiometric Test Sites of High Resolution Airborne Imaging Systems

    Directory of Open Access Journals (Sweden)

    Eero Ahokas

    2010-08-01

    Full Text Available Reliable and optimal exploitation of rapidly developing airborne imaging methods requires geometric and radiometric quality assurance of production systems in operational conditions. Permanent test sites are the most promising approach for cost-efficient performance assessment. Optimal construction of permanent radiometric test sites for high resolution airborne imaging systems is an unresolved issue. The objective of this study was to assess the performance of commercially available gravels and painted and unpainted concrete targets for permanent, open-air radiometric test sites under sub-optimal climate conditions in Southern Finland. The reflectance spectrum and reflectance anisotropy and their stability were characterized during the summer of 2009. The management of reflectance anisotropy and stability were shown to be the key issues for better than 5% reflectance accuracy.

  9. Investigating the use of terahertz pulsed time domain reflection imaging for the study of fabric layers of an Egyptian mummy

    Science.gov (United States)

    Fukunaga, K.; Cortes, E.; Cosentino, A.; Stã¼nkel, I.; Leona, M.; Duling, N.; Mininberg, D. T.

    2011-08-01

    This paper reports the first use of terahertz time domain reflection imaging involving textiles on part of a complete human mummy, still in original wrapping. X-ray technique has been used extensively to investigate anatomical features, since X-ray pass through the wrapping. Terahertz waves, on the other hand, can penetrate into non-metallic materials and its reflection depends on the refractive index of materials at the interface, such as textiles and the air. The mummy of Kharushere (ca. 945-712 B.C.) was examined by using Terahertz time domain reflection imaging in the Egyptian galleries of The Metropolitan Museum of Art. Experimental results suggest that the Terahetz imaging is a promising technique for probing the fabric layers surrounding Egyptian mummies, although it is still very limited in its current state. In the future it could become a useful complement to CT scanning when materials with low radiographic density and contrast are being investigated

  10. High-resolution optical coherence tomography, autofluorescence, and infrared reflectance imaging in Sjögren reticular dystrophy.

    Science.gov (United States)

    Schauwvlieghe, Pieter-Paul; Torre, Kara Della; Coppieters, Frauke; Van Hoey, Anneleen; De Baere, Elfride; De Zaeytijd, Julie; Leroy, Bart P; Brodie, Scott E

    2013-01-01

    To describe the phenotype of three cases of Sjögren reticular dystrophy in detail, including high-resolution optical coherence tomography, autofluorescence imaging, and near-infrared reflectance imaging. Two unrelated teenagers were independently referred for ophthalmologic evaluation. Both underwent a full ophthalmologic workup, including electrophysiologic and extensive imaging with spectral-domain optical coherence tomography, autofluorescence imaging, and near-infrared reflectance imaging. In addition, mutation screening of ABCA4, PRPH2, and the mitochondrial tRNA gene was performed in Patient 1. Subsequently, the teenage sister of Patient 2 was examined. Strikingly similar phenotypes were present in these three patients. Fundoscopy showed bilateral foveal pigment alterations, and a lobular network of deep retinal, pigmented deposits throughout the posterior pole, tapering toward the midperiphery, with relative sparing of the immediate perifoveal macula and peripapillary area. This network is mildly to moderately hyperautofluorescent on autofluorescence and bright on near-infrared reflectance imaging. Optical coherence tomography showed abnormalities of the retinal pigment epithelium-Bruch membrane complex, photoreceptor outer segments, and photoreceptor inner/outer segment interface. The results of retinal function test were entirely normal. No molecular cause was detected in Patient 1. Imaging suggested that the lobular network of deep retinal deposits in Sjögren reticular dystrophy is the result of accumulation of both pigment and lipofuscin between photoreceptors and retinal pigment epithelium, as well as within the retinal pigment epithelium.

  11. Seismic imaging of sandbox experiments – laboratory hardware setup and first reflection seismic sections

    Directory of Open Access Journals (Sweden)

    C. M. Krawczyk

    2013-02-01

    Full Text Available With the study and technical development introduced here, we combine analogue sandbox simulation techniques with seismic physical modelling of sandbox models. For that purpose, we designed and developed a new mini-seismic facility for laboratory use, comprising a seismic tank, a PC-driven control unit, a positioning system, and piezoelectric transducers used here for the first time in an array mode. To assess the possibilities and limits of seismic imaging of small-scale structures in sandbox models, different geometry setups were tested in the first 2-D experiments that also tested the proper functioning of the device and studied the seismo-elastic properties of the granular media used. Simple two-layer models of different materials and layer thicknesses as well as a more complex model comprising channels and shear zones were tested using different acquisition geometries and signal properties. We suggest using well sorted and well rounded grains with little surface roughness (glass beads. Source receiver-offsets less than 14 cm for imaging structures as small as 2.0–1.5 mm size have proven feasible. This is the best compromise between wide beam and high energy output, and is applicable with a consistent waveform. Resolution of the interfaces of layers of granular materials depends on the interface preparation rather than on the material itself. Flat grading of interfaces and powder coverage yields the clearest interface reflections. Finally, sandbox seismic sections provide images of high quality showing constant thickness layers as well as predefined channel structures and indications of the fault traces from shear zones. Since these were artificially introduced in our test models, they can be regarded as zones of disturbance rather than tectonic shear zones characterized by decompaction. The multiple-offset surveying introduced here, improves the quality with respect to S / N ratio and source signature even more; the maximum depth

  12. Comparative study between fundus autofluorescence and red reflectance imaging of choroidal nevi using ultra-wide-field scanning laser ophthalmoscopy.

    Science.gov (United States)

    Zapata, Miguel Angel; Leila, Mahmoud; Teixidor, Teresa; Garcia-Arumi, Jose

    2015-06-01

    To explore the utility of fundus autofluorescence (FAF) and red reflectance (RR) imaging using ultra-wide-field scanning laser ophthalmoscope in choroidal nevi. Retrospective observational case study reviewing clinical data, color, FAF, and RR images of patients with choroidal nevi and comparing the findings. The ultra-wide-field scanning laser ophthalmoscope uses green laser 532 nm and red laser 633 nm that enabled FAF and RR imaging, respectively in separate channels. Superimposition of both images yielded a composite color image. The study included 46 eyes of 45 patients. Nevi were unilateral in 44 patients (98%). Forty-one nevi (89.1%) were located temporally between the macula and the equator. All nevi (100%) were deeply pigmented. The most frequent surface changes were lipofuscin pigments, zones of retinal pigment epithelium atrophy, and retinal pigment epithelium pigment clumps in 31 (67.3%), 18 (39.1%), and 8 eyes (17.3%), respectively. Color photographs were superior to FAF in detecting nevus boundaries and surface changes. Red reflectance correlated strongly with color images, although the nevus boundaries and surface changes were better delineated in RR mode. Red reflectance was superior to FAF in delineating the boundaries and surface changes of the nevus; clear visibility (3+) for RR versus no or poor visibility (0/1+) for FAF. Nevertheless, the areas of retinal pigment epithelium atrophy were better delineated in FAF mode; clear visibility (3+) for FAF versus poor visibility (1+) for FAF. Red reflectance imaging is more sensitive than conventional photography for follow-up of choroidal nevi. Fundus autofluorescence should be considered only as a complementary tool to RR imaging.

  13. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    International Nuclear Information System (INIS)

    Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

    2009-01-01

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  14. A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

    Directory of Open Access Journals (Sweden)

    Venu Gopal

    2014-07-01

    Full Text Available In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k2 + h4 based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

  15. Infrared Imaging of Cotton Fiber Bundles Using a Focal Plane Array Detector and a Single Reflectance Accessory

    Directory of Open Access Journals (Sweden)

    Michael Santiago Cintrón

    2016-11-01

    Full Text Available Infrared imaging is gaining attention as a technique used in the examination of cotton fibers. This type of imaging combines spectral analysis with spatial resolution to create visual images that examine sample composition and distribution. Herein, we report on the use of an infrared instrument equipped with a reflection accessory and an array detector system for the examination of cotton fiber bundles. Cotton vibrational spectra and chemical images were acquired by grouping pixels in the detector array. This technique reduced spectral noise and was employed to visualize cell wall development in cotton fibers bundles. Fourier transform infrared spectra reveal band changes in the C–O bending region that matched previous studies. Imaging studies were quick, relied on small amounts of sample and provided a distribution of the cotton fiber cell wall composition. Thus, imaging of cotton bundles with an infrared detector array has potential for use in cotton fiber examinations.

  16. On-line, continuous monitoring in solar cell and fuel cell manufacturing using spectral reflectance imaging

    Energy Technology Data Exchange (ETDEWEB)

    Sopori, Bhushan; Rupnowski, Przemyslaw; Ulsh, Michael

    2016-01-12

    A monitoring system 100 comprising a material transport system 104 providing for the transportation of a substantially planar material 102, 107 through the monitoring zone 103 of the monitoring system 100. The system 100 also includes a line camera 106 positioned to obtain multiple line images across a width of the material 102, 107 as it is transported through the monitoring zone 103. The system 100 further includes an illumination source 108 providing for the illumination of the material 102, 107 transported through the monitoring zone 103 such that light reflected in a direction normal to the substantially planar surface of the material 102, 107 is detected by the line camera 106. A data processing system 110 is also provided in digital communication with the line camera 106. The data processing system 110 is configured to receive data output from the line camera 106 and further configured to calculate and provide substantially contemporaneous information relating to a quality parameter of the material 102, 107. Also disclosed are methods of monitoring a quality parameter of a material.

  17. Characterization of NPP Visible/Infrared Imager Radiometer Suite (VIIRS) Reflective Solar Bands Dual Gain Anomaly

    Science.gov (United States)

    Lee, Shihyan; McIntire, Jeff; Oudari, Hassan

    2012-01-01

    The Visible/Infrared Imager Radiometer Suite (VIIRS) contains six dual gain bands in the reflective solar spectrum. The dual gain bands are designed to switch gain mode at pre-defined thresholds to achieve high resolution at low radiances while maintaining the required dynamic range for science. During pre-launch testing, an anomaly in the electronic response before transitioning from high to low gain was discovered and characterized. On-orbit, the anomaly was confirmed using MODIS data collected during Simultaneous Nadir Overpasses (SNOs). The analysis of the Earth scene data shows that dual gain anomaly can be determined at the orbital basis. To characterize the dual gain anomaly, the anomaly region and electronic offsets were tracked per week during the first 8 month of VIIRS operation. The temporal analysis shows the anomaly region can drift 20 DN and is impacted by detectors DC Restore. The estimated anomaly flagging regions cover 2.5 % of the high gain dynamic range and are consistent with prelaunch and on-orbit LUT. The prelaunch results had a smaller anomaly range (30-50 DN) and are likely the results of more stable electronics from the shorter data collection time. Finally, this study suggests future calibration efforts to focus on the anomaly's impact on science products and possible correction method to reduce uncertainties.

  18. Echo intensity obtained from ultrasonography images reflecting muscle strength in elderly men

    Directory of Open Access Journals (Sweden)

    Watanabe Y

    2013-07-01

    Full Text Available Yuya Watanabe,1 Yosuke Yamada,1,2 Yoshihiro Fukumoto,3 Tatsuro Ishihara,4 Keiichi Yokoyama,1 Tsukasa Yoshida,1 Motoko Miyake,1 Emi Yamagata,5 Misaka Kimura1 1Laboratory of Sports and Health Science, Kyoto Prefectural University of Medicine, Kyoto, Japan; 2Research Fellow, Japan Society for the Promotion of Science, Tokyo, Japan; 3Faculty of Rehabilitation, Kobe Gakuin University, Kobe, Japan; 4Faculty of Health and Sports Science, Doshisha University, Kyoto, Japan; 5Laboratory of Gerontological Nursing, Kyoto Prefectural University of Medicine, Kyoto, Japan Background: It is well known that loss of muscle mass (quantitative change is a major change that occurs with aging. Qualitative changes in skeletal muscle, such as increased intramuscular fat, also occur as one ages. Enhanced echo intensity (EI on ultrasonography images of skeletal muscle is believed to reflect muscle quality. Recent studies evaluating the quality of skeletal muscle using computer-aided gray scale analysis showed that EI is associated with muscle strength independently of age or muscle size in middle-aged and elderly women. The aim of the present study was to investigate whether muscle quality based on EI is associated with muscle strength independently of muscle size for elderly men. Methods: A total of 184 elderly men (65–91 years living independently in Kyoto, Japan, participated in this study. The EI, muscle thickness (MT, and subcutaneous fat thickness (FT of the anterior compartment of the right thigh were determined by assessing ultrasonography images. The maximum isometric torque of knee extension at a knee angle of 90° was measured. Results: The EI showed a significant negative correlation with muscle strength (r = -0.333, P < 0.001. Multivariate regression analysis revealed that the MT and EI of the knee extensor muscle were independently associated with maximum isometric knee extension strength. Even when partial correlation analysis was performed with age

  19. Total internal reflection fluorescence (TIRF) microscopy for real-time imaging of nanoparticle-cell plasma membrane interaction

    DEFF Research Database (Denmark)

    Parhamifar, Ladan; Moghimi, Seyed Moien

    2012-01-01

    Nanoparticulate systems are widely used for site-specific drug and gene delivery as well as for medical imaging. The mode of nanoparticle-cell interaction may have a significant effect on the pathway of nanoparticle internalization and subsequent intracellular trafficking. Total internal reflection...

  20. Bild, Bildung and the 'Romance of the Soul': Reflections upon the Image of Meister Eckhart

    Science.gov (United States)

    Hedley, Douglas

    2018-01-01

    In this article, the "Bild" or image of the sculptor used by Plotinus and adapted by his Christian follower Meister Eckhart forms the basis of a reflection on the religious or otherworldly dimension in ethics (as opposed to a reductionist or functionalist conception of ethics with its focus on human happiness in the sense of worldly…

  1. Image potential effect on the specular reflection coefficient of alkali ions scattered from a nickel surface at low energy

    International Nuclear Information System (INIS)

    Zemih, R.; Boudjema, M.; Benazeth, C.; Boudouma, Y.; Chami, A.C.

    2002-01-01

    The resonant charge exchange in the incoming path of alkali ions scattered at low energy from a polycrystalline nickel surface is studied by using the image effect occurring at glancing incidence (2-10 deg. from the surface plane) and for specular reflection. The part of the experimental artefacts (geometrical factor, surface roughness ...) is extracted from the reflection coefficient of almost completely neutralised projectiles (He + or Ne + ) compared with the coefficient obtained from numerical simulations (TRIM and MARLOWE codes). The present model explains very well the lowering of the reflection coefficient measured at grazing incidence (below 4 deg.). Furthermore, the optimised values of the charge fraction in the incoming path and the image potential are in agreement with the theoretical calculations in the case of Na + /Ni at 4 keV

  2. Darkfield adapter for whole slide imaging: adapting a darkfield internal reflection illumination system to extend WSI applications.

    Directory of Open Access Journals (Sweden)

    Yoshihiro Kawano

    Full Text Available We present a new method for whole slide darkfield imaging. Whole Slide Imaging (WSI, also sometimes called virtual slide or virtual microscopy technology, produces images that simultaneously provide high resolution and a wide field of observation that can encompass the entire section, extending far beyond any single field of view. For example, a brain slice can be imaged so that both overall morphology and individual neuronal detail can be seen. We extended the capabilities of traditional whole slide systems and developed a prototype system for darkfield internal reflection illumination (DIRI. Our darkfield system uses an ultra-thin light-emitting diode (LED light source to illuminate slide specimens from the edge of the slide. We used a new type of side illumination, a variation on the internal reflection method, to illuminate the specimen and create a darkfield image. This system has four main advantages over traditional darkfield: (1 no oil condenser is required for high resolution imaging (2 there is less scatter from dust and dirt on the slide specimen (3 there is less halo, providing a more natural darkfield contrast image, and (4 the motorized system produces darkfield, brightfield and fluorescence images. The WSI method sometimes allows us to image using fewer stains. For instance, diaminobenzidine (DAB and fluorescent staining are helpful tools for observing protein localization and volume in tissues. However, these methods usually require counter-staining in order to visualize tissue structure, limiting the accuracy of localization of labeled cells within the complex multiple regions of typical neurohistological preparations. Darkfield imaging works on the basis of light scattering from refractive index mismatches in the sample. It is a label-free method of producing contrast in a sample. We propose that adapting darkfield imaging to WSI is very useful, particularly when researchers require additional structural information without the

  3. Short-time asymptotics of the two-dimensional wave equation for an annular vibrating membrane with applications in the mathematical physics

    International Nuclear Information System (INIS)

    Zayed, E.M.E.

    2004-01-01

    We study the influence of a finite container on an ideal gas using the wave equation approach. The asymptotic expansion of the trace of the wave kernel μ-circumflex(t)=Σ υ=1 ∞ exp(-itμ υ 1/2 ) for small vertical bar t vertical bar and i=√-1, where {μ ν } ν=1 ∞ are the eigenvalues of the negative Laplacian -Δ=-Σ k=1 2 (((∂)/(∂x k ))) 2 in the (x 1 ,x 2 )-plane, is studied for an annular vibrating membrane Ω in R 2 together with its smooth inner boundary ∂Ω 1 and its smooth outer boundary ∂Ω 2 , where a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Γ j (j=1,...,m) of ∂Ω 1 and on the piecewise smooth components Γ j (j=m+1,...,n) of ∂Ω 2 such that ∂Ω 1 =union j=1 m Γ j and ∂Ω 2 =union j=m+1 n Γ j is considered. The basic problem is to extract information on the geometry of the annular vibrating membrane Ω from complete knowledge of its eigenvalues using the wave equation approach by analyzing the asymptotic expansions of the spectral function μ-circumflex(t) for small vertical bar t vertical bar. Some applications of μ-circumflex(t) for an ideal gas enclosed in the general annular bounded domain Ω are given.

  4. An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

    Science.gov (United States)

    Manning, Robert M.

    2004-01-01

    The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

  5. Single view reflectance capture using multiplexed scattering and time-of-flight imaging

    OpenAIRE

    Zhao, Shuang; Velten, Andreas; Raskar, Ramesh; Bala, Kavita; Naik, Nikhil Deepak

    2011-01-01

    This paper introduces the concept of time-of-flight reflectance estimation, and demonstrates a new technique that allows a camera to rapidly acquire reflectance properties of objects from a single view-point, over relatively long distances and without encircling equipment. We measure material properties by indirectly illuminating an object by a laser source, and observing its reflected light indirectly using a time-of-flight camera. The configuration collectively acquires dense angular, but l...

  6. Non-Destructive Quality Evaluation of Pepper (Capsicum annuum L. Seeds Using LED-Induced Hyperspectral Reflectance Imaging

    Directory of Open Access Journals (Sweden)

    Changyeun Mo

    2014-04-01

    Full Text Available In this study, we developed a viability evaluation method for pepper (Capsicum annuum L. seeds based on hyperspectral reflectance imaging. The reflectance spectra of pepper seeds in the 400–700 nm range are collected from hyperspectral reflectance images obtained using blue, green, and red LED illumination. A partial least squares–discriminant analysis (PLS-DA model is developed to classify viable and non-viable seeds. Four spectral ranges generated with four types of LEDs (blue, green, red, and RGB, which were pretreated using various methods, are investigated to develop the classification models. The optimal PLS-DA model based on the standard normal variate for RGB LED illumination (400–700 nm yields discrimination accuracies of 96.7% and 99.4% for viable seeds and nonviable seeds, respectively. The use of images based on the PLS-DA model with the first-order derivative of a 31.5-nm gap for red LED illumination (600–700 nm yields 100% discrimination accuracy for both viable and nonviable seeds. The results indicate that a hyperspectral imaging technique based on LED light can be potentially applied to high-quality pepper seed sorting.

  7. Exploration of a Polarized Surface Bidirectional Reflectance Model Using the Ground-Based Multiangle SpectroPolarimetric Imager

    Directory of Open Access Journals (Sweden)

    David J. Diner

    2012-12-01

    Full Text Available Accurate characterization of surface reflection is essential for retrieval of aerosols using downward-looking remote sensors. In this paper, observations from the Ground-based Multiangle SpectroPolarimetric Imager (GroundMSPI are used to evaluate a surface polarized bidirectional reflectance distribution function (PBRDF model. GroundMSPI is an eight-band spectropolarimetric camera mounted on a rotating gimbal to acquire pushbroom imagery of outdoor landscapes. The camera uses a very accurate photoelastic-modulator-based polarimetric imaging technique to acquire Stokes vector measurements in three of the instrument’s bands (470, 660, and 865 nm. A description of the instrument is presented, and observations of selected targets within a scene acquired on 6 January 2010 are analyzed. Data collected during the course of the day as the Sun moved across the sky provided a range of illumination geometries that facilitated evaluation of the surface model, which is comprised of a volumetric reflection term represented by the modified Rahman-Pinty-Verstraete function plus a specular reflection term generated by a randomly oriented array of Fresnel-reflecting microfacets. While the model is fairly successful in predicting the polarized reflection from two grass targets in the scene, it does a poorer job for two manmade targets (a parking lot and a truck roof, possibly due to their greater degree of geometric organization. Several empirical adjustments to the model are explored and lead to improved fits to the data. For all targets, the data support the notion of spectral invariance in the angular shape of the unpolarized and polarized surface reflection. As noted by others, this behavior provides valuable constraints on the aerosol retrieval problem, and highlights the importance of multiangle observations.

  8. The wave equation in Friedmann-Robertson-Walker space-times and asymptotics of the intensity and distance relationship of a localised source

    Science.gov (United States)

    Starko, Darij; Craig, Walter

    2018-04-01

    Variations in redshift measurements of Type 1a supernovae and intensity observations from large sky surveys are an indicator of a component of acceleration in the rate of expansion of space-time. A key factor in the measurements is the intensity-distance relation for Maxwell's equations in Friedmann-Robertson-Walker (FRW) space-times. In view of future measurements of the decay of other fields on astronomical time and spatial scales, we determine the asymptotic behavior of the intensity-distance relationship for the solution of the wave equation in space-times with an FRW metric. This builds on previous work done on initial value problems for the wave equation in FRW space-time [Abbasi, B. and Craig, W., Proc. R. Soc. London, Ser. A 470, 20140361 (2014)]. In this paper, we focus on the precise intensity decay rates of the special cases for curvature k = 0 and k = -1, as well as giving a general derivation of the wave solution for -∞ 0} where t0 represents the time of an initial emission source, relative to the Big Bang singularity at t = 0. The initial data [g(x), h(x)] are assumed to be compactly supported; supp(g, h) ⊆ BR(0) and terms in the expression for the fundamental solution for the wave equation with the slowest decay rate are retained. The intensities calculated for coordinate time {t : t > 0} contain correction terms proportional to the ratio of t0 and the time differences ρ = t - t0. For the case of general curvature k, these expressions for the intensity reduce by scaling to the same form as for k = -1, from which we deduce the general formula. We note that for typical astronomical events such as Type 1a supernovae, the first order correction term for all curvatures -∞ < k < 0 is on the order of 10-4 smaller than the zeroth order term. These correction terms are small but may be significant in applications to alternative observations of cosmological space-time expansion rates.

  9. Reflective photovoltaics

    Energy Technology Data Exchange (ETDEWEB)

    Lentine, Anthony L.; Nielson, Gregory N.; Cruz-Campa, Jose Luis; Okandan, Murat; Goeke, Ronald S.

    2018-03-06

    A photovoltaic module includes colorized reflective photovoltaic cells that act as pixels. The colorized reflective photovoltaic cells are arranged so that reflections from the photovoltaic cells or pixels visually combine into an image on the photovoltaic module. The colorized photovoltaic cell or pixel is composed of a set of 100 to 256 base color sub-pixel reflective segments or sub-pixels. The color of each pixel is determined by the combination of base color sub-pixels forming the pixel. As a result, each pixel can have a wide variety of colors using a set of base colors, which are created, from sub-pixel reflective segments having standard film thicknesses.

  10. Autofluorescence Imaging With Near-Infrared Excitation:Normalization by Reflectance to Reduce Signal From Choroidal Fluorophores

    Science.gov (United States)

    Cideciyan, Artur V.; Swider, Malgorzata; Jacobson, Samuel G.

    2015-01-01

    Purpose. We previously developed reduced-illuminance autofluorescence imaging (RAFI) methods involving near-infrared (NIR) excitation to image melanin-based fluorophores and short-wavelength (SW) excitation to image lipofuscin-based flurophores. Here, we propose to normalize NIR-RAFI in order to increase the relative contribution of retinal pigment epithelium (RPE) fluorophores. Methods. Retinal imaging was performed with a standard protocol holding system parameters invariant in healthy subjects and in patients. Normalized NIR-RAFI was derived by dividing NIR-RAFI signal by NIR reflectance point-by-point after image registration. Results. Regions of RPE atrophy in Stargardt disease, AMD, retinitis pigmentosa, choroideremia, and Leber congenital amaurosis as defined by low signal on SW-RAFI could correspond to a wide range of signal on NIR-RAFI depending on the contribution from the choroidal component. Retinal pigment epithelium atrophy tended to always correspond to high signal on NIR reflectance. Normalizing NIR-RAFI reduced the choroidal component of the signal in regions of atrophy. Quantitative evaluation of RPE atrophy area showed no significant differences between SW-RAFI and normalized NIR-RAFI. Conclusions. Imaging of RPE atrophy using lipofuscin-based AF imaging has become the gold standard. However, this technique involves bright SW lights that are uncomfortable and may accelerate the rate of disease progression in vulnerable retinas. The NIR-RAFI method developed here is a melanin-based alternative that is not absorbed by opsins and bisretinoid moieties, and is comfortable to view. Further development of this method may result in a nonmydriatic and comfortable imaging method to quantify RPE atrophy extent and its expansion rate. PMID:26024124

  11. Application of Reflectance Transformation Imaging Technique to Improve Automated Edge Detection in a Fossilized Oyster Reef

    Science.gov (United States)

    Djuricic, Ana; Puttonen, Eetu; Harzhauser, Mathias; Dorninger, Peter; Székely, Balázs; Mandic, Oleg; Nothegger, Clemens; Molnár, Gábor; Pfeifer, Norbert

    2016-04-01

    The world's largest fossilized oyster reef is located in Stetten, Lower Austria excavated during field campaigns of the Natural History Museum Vienna between 2005 and 2008. It is studied in paleontology to learn about change in climate from past events. In order to support this study, a laser scanning and photogrammetric campaign was organized in 2014 for 3D documentation of the large and complex site. The 3D point clouds and high resolution images from this field campaign are visualized by photogrammetric methods in form of digital surface models (DSM, 1 mm resolution) and orthophoto (0.5 mm resolution) to help paleontological interpretation of data. Due to size of the reef, automated analysis techniques are needed to interpret all digital data obtained from the field. One of the key components in successful automation is detection of oyster shell edges. We have tested Reflectance Transformation Imaging (RTI) to visualize the reef data sets for end-users through a cultural heritage viewing interface (RTIViewer). The implementation includes a Lambert shading method to visualize DSMs derived from terrestrial laser scanning using scientific software OPALS. In contrast to shaded RTI no devices consisting of a hardware system with LED lights, or a body to rotate the light source around the object are needed. The gray value for a given shaded pixel is related to the angle between light source and the normal at that position. Brighter values correspond to the slope surfaces facing the light source. Increasing of zenith angle results in internal shading all over the reef surface. In total, oyster reef surface contains 81 DSMs with 3 m x 2 m each. Their surface was illuminated by moving the virtual sun every 30 degrees (12 azimuth angles from 20-350) and every 20 degrees (4 zenith angles from 20-80). This technique provides paleontologists an interactive approach to virtually inspect the oyster reef, and to interpret the shell surface by changing the light source direction

  12. An analysis of Richard Prince's "Lake Resort Nurse": using an image to expose and critically reflect on stereotypes in nursing.

    Science.gov (United States)

    Holmes, Vicki C

    2012-01-01

    Our interactions with images, created and viewed within contexts, are a significant means through which we construct and interpret our values and beliefs. Nurses' efforts at monitoring images to encourage accurate portrayals of nurses' work have had little influence on the way nurses are represented or the inherent ability of images to shape perceptions of nurses' work. One explanation for this lack of influence is that viewers do not closely attend to the ways in which we make meaning of everyday images. This inattention creates passive viewers, vulnerable to and more likely to internalize messages (G. Dines & J. Humez, 2011). Misunderstandings about nursing leave nurses vulnerable to contexts and influence the outcomes of at least 2 issues, the nursing shortage and the provision of quality care. Prince, in his painting "Lake Resort Nurse," utilizes the artistic strategies of expressionism, appropriation, and reflexivity to expose stereotypes and provides an opportunity for reflection on the potential impact these stereotypes have on the profession. He provides a means through which we can recognize that images are significant contributors to how understandings of nursing and nurses are shaped. New understandings of nursing, gained through reflection and dialog, subsequently influences perceptions of the value of nurses' work and their contribution to health care. Copyright © 2012 Elsevier Inc. All rights reserved.

  13. Sub-wavelength imaging by depolarization in a reflection near-field optical microscope using an uncoated fiber probe

    DEFF Research Database (Denmark)

    Madsen, Steen; Bozhevolnyi, Sergey I.; Hvam, Jørn Märcher

    1998-01-01

    We present a reflection scanning near-field optical microscope utilizing counter-directional light propagation in an uncoated fiber probe, cross-polarized detection and shear-force feedback. Topographical and near-field optical imaging with a scanning speed of up to 10 mu m/s and a lateral...... resolution better than 40 nm are demonstrated with a latex projection test sample. Determination of the optical resolution as well as correlation between topographical and near-field optical images are discussed. (C) 1998 Elsevier Science B.V....

  14. Infrared images of reflection nebulae and Orion's bar: Fluorescent molecular hydrogen and the 3.3 micron feature

    International Nuclear Information System (INIS)

    Burton, M.G.; Moorhouse, A.; Brand, P.W.J.L.; Roche, P.F.; Geballe, T.R.

    1989-01-01

    Images were obtained of the (fluorescent) molecular hydrogen 1-0 S(1) line, and of the 3.3 micron emission feature, in Orion's Bar and three reflection nebulae. The emission from these species appears to come from the same spatial locations in all sources observed. This suggests that the 3.3 micron feature is excited by the same energetic UV-photons which cause the molecular hydrogen to fluoresce

  15. Analysis of In-Situ Spectral Reflectance of Sago and Other Palms: Implications for Their Detection in Optical Satellite Images

    Science.gov (United States)

    Rendon Santillan, Jojene; Makinano-Santillan, Meriam

    2018-04-01

    We present a characterization, comparison and analysis of in-situ spectral reflectance of Sago and other palms (coconut, oil palm and nipa) to ascertain on which part of the electromagnetic spectrum these palms are distinguishable from each other. The analysis also aims to reveal information that will assist in selecting which band to use when mapping Sago palms using the images acquired by these sensors. The datasets used in the analysis consisted of averaged spectral reflectance curves of each palm species measured within the 345-1045 nm wavelength range using an Ocean Optics USB4000-VIS-NIR Miniature Fiber Optic Spectrometer. This in-situ reflectance data was also resampled to match the spectral response of the 4 bands of ALOS AVNIR-2, 3 bands of ASTER VNIR, 4 bands of Landsat 7 ETM+, 5 bands of Landsat 8, and 8 bands of Worldview-2 (WV2). Examination of the spectral reflectance curves showed that the near infra-red region, specifically at 770, 800 and 875 nm, provides the best wavelengths where Sago palms can be distinguished from other palms. The resampling of the in-situ reflectance spectra to match the spectral response of optical sensors made possible the analysis of the differences in reflectance values of Sago and other palms in different bands of the sensors. Overall, the knowledge learned from the analysis can be useful in the actual analysis of optical satellite images, specifically in determining which band to include or to exclude, or whether to use all bands of a sensor in discriminating and mapping Sago palms.

  16. ANALYSIS OF IN-SITU SPECTRAL REFLECTANCE OF SAGO AND OTHER PALMS: IMPLICATIONS FOR THEIR DETECTION IN OPTICAL SATELLITE IMAGES

    Directory of Open Access Journals (Sweden)

    J. R. Santillan

    2018-04-01

    Full Text Available We present a characterization, comparison and analysis of in-situ spectral reflectance of Sago and other palms (coconut, oil palm and nipa to ascertain on which part of the electromagnetic spectrum these palms are distinguishable from each other. The analysis also aims to reveal information that will assist in selecting which band to use when mapping Sago palms using the images acquired by these sensors. The datasets used in the analysis consisted of averaged spectral reflectance curves of each palm species measured within the 345–1045 nm wavelength range using an Ocean Optics USB4000-VIS-NIR Miniature Fiber Optic Spectrometer. This in-situ reflectance data was also resampled to match the spectral response of the 4 bands of ALOS AVNIR-2, 3 bands of ASTER VNIR, 4 bands of Landsat 7 ETM+, 5 bands of Landsat 8, and 8 bands of Worldview-2 (WV2. Examination of the spectral reflectance curves showed that the near infra-red region, specifically at 770, 800 and 875 nm, provides the best wavelengths where Sago palms can be distinguished from other palms. The resampling of the in-situ reflectance spectra to match the spectral response of optical sensors made possible the analysis of the differences in reflectance values of Sago and other palms in different bands of the sensors. Overall, the knowledge learned from the analysis can be useful in the actual analysis of optical satellite images, specifically in determining which band to include or to exclude, or whether to use all bands of a sensor in discriminating and mapping Sago palms.

  17. VIIRSN Level-3 Standard Mapped Image, Remote Sensing Reflectance at 671 nm, 8 Day, 4km

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — NOAA CoastWatch distributes Remote sensing reflectance (671 nm) data from the NPP-suomi spacecraft. Measurements are gathered by the VIIRS instrument carried aboard...

  18. Differential field equations for the MHD waves and wave equation of Alfven; Las ecuaciones diferenciales de campo para las ondas MHD y la ecuacion de onda de Alfven

    Energy Technology Data Exchange (ETDEWEB)

    Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)

    2001-02-01

    In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.

  19. Superresolution Imaging Using Resonant Multiples and Plane-wave Migration Velocity Analysis

    KAUST Repository

    Guo, Bowen

    2017-08-28

    Seismic imaging is a technique that uses seismic echoes to map and detect underground geological structures. The conventional seismic image has the resolution limit of λ/2, where λ is the wavelength associated with the seismic waves propagating in the subsurface. To exceed this resolution limit, this thesis develops a new imaging method using resonant multiples, which produces superresolution images with twice or even more the spatial resolution compared to the conventional primary reflection image. A resonant multiple is defined as a seismic reflection that revisits the same subsurface location along coincident reflection raypath. This reverberated raypath is the reason for superresolution imaging because it increases the differences in reflection times associated with subtle changes in the spatial location of the reflector. For the practical implementation of superresolution imaging, I develop a post-stack migration technique that first enhances the signal-to-noise ratios (SNRs) of resonant multiples by a moveout-correction stacking method, and then migrates the post-stacked resonant multiples with the associated Kirchhoff or wave-equation migration formula. I show with synthetic and field data examples that the first-order resonant multiple image has about twice the spatial resolution compared to the primary reflection image. Besides resolution, the correct estimate of the subsurface velocity is crucial for determining the correct depth of reflectors. Towards this goal, wave-equation migration velocity analysis (WEMVA) is an image-domain method which inverts for the velocity model that maximizes the similarity of common image gathers (CIGs). Conventional WEMVA based on subsurface-offset, angle domain or time-lag CIGs requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, I present a new WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce the

  20. Preliminary investigations into macroscopic attenuated total reflection-fourier transform infrared imaging of intact spherical domains: spatial resolution and image distortion.

    Science.gov (United States)

    Everall, Neil J; Priestnall, Ian M; Clarke, Fiona; Jayes, Linda; Poulter, Graham; Coombs, David; George, Michael W

    2009-03-01

    This paper describes preliminary investigations into the spatial resolution of macro attenuated total reflection (ATR) Fourier transform infrared (FT-IR) imaging and the distortions that arise when imaging intact, convex domains, using spheres as an extreme example. The competing effects of shallow evanescent wave penetration and blurring due to finite spatial resolution meant that spheres within the range 20-140 microm all appeared to be approximately the same size ( approximately 30-35 microm) when imaged with a numerical aperture (NA) of approximately 0.2. A very simple model was developed that predicted this extreme insensitivity to particle size. On the basis of these studies, it is anticipated that ATR imaging at this NA will be insensitive to the size of intact highly convex objects. A higher numerical aperture device should give a better estimate of the size of small spheres, owing to superior spatial resolution, but large spheres should still appear undersized due to the shallow sampling depth. An estimate of the point spread function (PSF) was required in order to develop and apply the model. The PSF was measured by imaging a sharp interface; assuming an Airy profile, the PSF width (distance from central maximum to first minimum) was estimated to be approximately 20 and 30 microm for IR bands at 1600 and 1000 cm(-1), respectively. This work has two significant limitations. First, underestimation of domain size only arises when imaging intact convex objects; if surfaces are prepared that randomly and representatively section through domains, the images can be analyzed to calculate parameters such as domain size, area, and volume. Second, the model ignores reflection and refraction and assumes weak absorption; hence, the predicted intensity profiles are not expected to be accurate; they merely give a rough estimate of the apparent sphere size. Much further work is required to place the field of quantitative ATR-FT-IR imaging on a sound basis.