The small data solutions of general 3-D quasilinear wave equations. II
NASA Astrophysics Data System (ADS)
Ding, Bingbing; Witt, Ingo; Yin, Huicheng
2016-07-01
This paper is a continuation of the work in [8], where the authors established the global existence of smooth small data solutions to the general 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 when the weak null condition holds. In the present paper, we show that the smooth small data solutions of equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied, moreover, a precise blowup time is completely determined. Therefore, collecting the main results in this paper and [8], we have given a basically complete study on the blowup or global existence of small data solutions to the 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0.
NASA Astrophysics Data System (ADS)
Vidal, A.; San-Blas, A. A.; Quesada-Pereira, F. D.; Pérez-Soler, J.; Gil, J.; Vicente, C.; Gimeno, B.; Boria, V. E.
2015-07-01
A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RME technique. The developed tool also provides an accurate computation of the electromagnetic fields at an arbitrary observation point of the considered device, so it can be used for predicting high-power breakdown phenomena. In order to validate the accuracy and efficiency of this novel approach, several new designs of band-pass waveguides filters are presented. The obtained results (S-parameters and electromagnetic fields) are successfully compared both to experimental data and to numerical simulations provided by a commercial software based on the finite element technique. The results obtained show that the new technique is specially suitable for the efficient full-wave analysis of complex waveguide devices considering an integrated coaxial excitation, where the coaxial probes may be in contact with the metallic insets of the component.
3D Elastic Seismic Wave Propagation Code
Energy Science and Technology Software Center (ESTSC)
1998-09-23
E3D is capable of simulating seismic wave propagation in a 3D heterogeneous earth. Seismic waves are initiated by earthquake, explosive, and/or other sources. These waves propagate through a 3D geologic model, and are simulated as synthetic seismograms or other graphical output.
Finite-difference solutions of the 3-D eikonal equation
Fei, Tong; Fehler, M.C.; Hildebrand, S.T.
1995-12-31
Prestack Kirchhoff depth migration requires the computation of traveltimes from surface source and receiver locations to subsurface image locations. In 3-D problems, computational efficiency becomes important. Finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference method for computing the first arrival traveltime by solving the eikonal equation has been developed in Cartesian coordinates. The method, which is unconditionally stable and computationally efficient, can handle instabilities due to caustics and provide information about head waves. The comparison of finite-difference solutions of the acoustic wave equation with the traveltime solutions from the eikonal equation in various structure models demonstrate that the method developed here can provide correct first arrival traveltime information even in areas of complex velocity structure.
Numerical simulation of 3D breaking waves
NASA Astrophysics Data System (ADS)
Fraunie, Philippe; Golay, Frederic
2015-04-01
Numerical methods dealing with two phase flows basically can be classified in two ways : the "interface tracking" methods when the two phases are resolved separately including boundary conditions fixed at the interface and the "interface capturing" methods when a single flow is considered with variable density. Physical and numerical properties of the two approaches are discussed, based on some numerical experiments performed concerning 3D breaking waves. Acknowledgements : This research was supported by the Modtercom program of Region PACA.
Two-equation turbulence modeling for 3-D hypersonic flows
NASA Technical Reports Server (NTRS)
Bardina, J. E.; Coakley, T. J.; Marvin, J. G.
1992-01-01
An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.
Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo
2013-01-01
We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085
Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo
2013-02-15
We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085
NASA Astrophysics Data System (ADS)
Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo
2013-02-01
We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems.
Derivation of new 3D discrete ordinate equations
Ahrens, C. D.
2012-07-01
The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)
A note on singularities of the 3-D Euler equation
NASA Technical Reports Server (NTRS)
Tanveer, S.
1994-01-01
In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.
Simulation of 3D Global Wave Propagation Through Geodynamic Models
NASA Astrophysics Data System (ADS)
Schuberth, B.; Piazzoni, A.; Bunge, H.; Igel, H.; Steinle-Neumann, G.
2005-12-01
This project aims at a better understanding of the forward problem of global 3D wave propagation. We use the spectral element program "SPECFEM3D" (Komatitsch and Tromp, 2002a,b) with varying input models of seismic velocities derived from mantle convection simulations (Bunge et al., 2002). The purpose of this approach is to obtain seismic velocity models independently from seismological studies. In this way one can test the effects of varying parameters of the mantle convection models on the seismic wave field. In order to obtain the seismic velocities from the temperature field of the geodynamical simulations we follow a mineral physics approach. Assuming a certain mantle composition (e.g. pyrolite with CMASF composition) we compute the stable phases for each depth (i.e. pressure) and temperature by system Gibbs free energy minimization. Elastic moduli and density are calculated from the equations of state of the stable mineral phases. For this we use a mineral physics database derived from calorimetric experiments (enthalphy and entropy of formation, heat capacity) and EOS parameters.
3D Ultrasonic Wave Simulations for Structural Health Monitoring
NASA Technical Reports Server (NTRS)
Campbell, Leckey Cara A/; Miler, Corey A.; Hinders, Mark K.
2011-01-01
Structural health monitoring (SHM) for the detection of damage in aerospace materials is an important area of research at NASA. Ultrasonic guided Lamb waves are a promising SHM damage detection technique since the waves can propagate long distances. For complicated flaw geometries experimental signals can be difficult to interpret. High performance computing can now handle full 3-dimensional (3D) simulations of elastic wave propagation in materials. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate ultrasound scattering from flaws in materials. EFIT results have been compared to experimental data and the simulations provide unique insight into details of the wave behavior. This type of insight is useful for developing optimized experimental SHM techniques. 3D EFIT can also be expanded to model wave propagation and scattering in anisotropic composite materials.
A parallel algorithm for solving the 3d Schroedinger equation
Strickland, Michael; Yager-Elorriaga, David
2010-08-20
We describe a parallel algorithm for solving the time-independent 3d Schroedinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between computational nodes. We demonstrate that the compute time, t, scales inversely with the number of computational nodes as t {proportional_to} (N{sub nodes}){sup -0.95} {sup {+-} 0.04}. This makes it possible to solve the 3d Schroedinger equation on extremely large spatial lattices using a small computing cluster. In addition, we present a new method for precisely determining the energy eigenvalues and wavefunctions of quantum states based on a symmetry constraint on the FDTD initial condition. Finally, we discuss the usage of multi-resolution techniques in order to speed up convergence on extremely large lattices.
Numerical simulation of vortex breakdown via 3-D Euler equations
NASA Astrophysics Data System (ADS)
Le, T. H.; Mege, P.; Morchoisne, Y.
1990-06-01
The long term goal is the modeling of vortex breakdown that occurs in some aerodynamic configurations at high angle of attack, (i.e., fighters with highly swept delta wings or missiles). A numerical simulation was made based on solving the 3-D Euler equations for an usteady incompressible flow. Preliminary results were obtained using a pressure-velocity formulation with periodic boundary conditions, the Euler equations being discretized by 2nd order finite difference schemes. The continuation to this work by implementing more realistic boundary conditions and 4th order finite difference discretization schemes are presented.
3D Guided Wave Motion Analysis on Laminated Composites
NASA Technical Reports Server (NTRS)
Tian, Zhenhua; Leckey, Cara; Yu, Lingyu
2013-01-01
Ultrasonic guided waves have proved useful for structural health monitoring (SHM) and nondestructive evaluation (NDE) due to their ability to propagate long distances with less energy loss compared to bulk waves and due to their sensitivity to small defects in the structure. Analysis of actively transmitted ultrasonic signals has long been used to detect and assess damage. However, there remain many challenging tasks for guided wave based SHM due to the complexity involved with propagating guided waves, especially in the case of composite materials. The multimodal nature of the ultrasonic guided waves complicates the related damage analysis. This paper presents results from parallel 3D elastodynamic finite integration technique (EFIT) simulations used to acquire 3D wave motion in the subject laminated carbon fiber reinforced polymer composites. The acquired 3D wave motion is then analyzed by frequency-wavenumber analysis to study the wave propagation and interaction in the composite laminate. The frequency-wavenumber analysis enables the study of individual modes and visualization of mode conversion. Delamination damage has been incorporated into the EFIT model to generate "damaged" data. The potential for damage detection in laminated composites is discussed in the end.
Potentially singular solutions of the 3D axisymmetric Euler equations
Luo, Guo; Hou, Thomas Y.
2014-01-01
The question of finite-time blowup of the 3D incompressible Euler equations is numerically investigated in a periodic cylinder with solid boundaries. Using rotational symmetry, the equations are discretized in the (2D) meridian plane on an adaptive (moving) mesh and is integrated in time with adaptively chosen time steps. The vorticity is observed to develop a ring-singularity on the solid boundary with a growth proportional to ∼(ts − t)−2.46, where ts ∼ 0.0035056 is the estimated singularity time. A local analysis also suggests the existence of a self-similar blowup. The simulations stop at τ2 = 0.003505 at which time the vorticity amplifies by more than (3 × 108)-fold and the maximum mesh resolution exceeds (3 × 1012)2. The vorticity vector is observed to maintain four significant digits throughout the computations. PMID:25157172
Modeling tree crown dynamics with 3D partial differential equations.
Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry
2014-01-01
We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications. PMID:25101095
Cari, C. Suparmi, A.
2014-09-30
Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.
Wave-CAIPI for Highly Accelerated 3D Imaging
Bilgic, Berkin; Gagoski, Borjan A.; Cauley, Stephen F.; Fan, Audrey P.; Polimeni, Jonathan R.; Grant, P. Ellen; Wald, Lawrence L.; Setsompop, Kawin
2014-01-01
Purpose To introduce the Wave-CAIPI (Controlled Aliasing in Parallel Imaging) acquisition and reconstruction technique for highly accelerated 3D imaging with negligible g-factor and artifact penalties. Methods The Wave-CAIPI 3D acquisition involves playing sinusoidal gy and gz gradients during the readout of each kx encoding line, while modifying the 3D phase encoding strategy to incur inter-slice shifts as in 2D-CAIPI acquisitions. The resulting acquisition spreads the aliasing evenly in all spatial directions, thereby taking full advantage of 3D coil sensitivity distribution. By expressing the voxel spreading effect as a convolution in image space, an efficient reconstruction scheme that does not require data gridding is proposed. Rapid acquisition and high quality image reconstruction with Wave-CAIPI is demonstrated for high-resolution magnitude and phase imaging and Quantitative Susceptibility Mapping (QSM). Results Wave-CAIPI enables full-brain gradient echo (GRE) acquisition at 1 mm isotropic voxel size and R=3×3 acceleration with maximum g-factors of 1.08 at 3T, and 1.05 at 7T. Relative to the other advanced Cartesian encoding strategies 2D-CAIPI and Bunched Phase Encoding, Wave-CAIPI yields up to 2-fold reduction in maximum g-factor for 9-fold acceleration at both field strengths. Conclusion Wave-CAIPI allows highly accelerated 3D acquisitions with low artifact and negligible g-factor penalties, and may facilitate clinical application of high-resolution volumetric imaging. PMID:24986223
Equations on knot polynomials and 3d/5d duality
Mironov, A.; Morozov, A.
2012-09-24
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.
3-D FDTD simulation of shear waves for evaluation of complex modulus imaging.
Orescanin, Marko; Wang, Yue; Insana, Michael
2011-02-01
The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity. PMID:21342824
Quasi-regular solutions to a class of 3D degenerating hyperbolic equations
NASA Astrophysics Data System (ADS)
Hristov, T. D.; Popivanov, N. I.; Schneider, M.
2012-11-01
In the fifties M. Protter stated new three-dimensional (3D) boundary value problems (BVP) for mixed type equations of first kind. For hyperbolic-elliptic equations they are multidimensional analogue of the classical two-dimensional (2D) Morawetz-Guderley transonic problem. Up to now, in this case, not a single example of nontrivial solution to the new problem, neither a general existence result is known. The difficulties appear even for BVP in the hyperbolic part of the domain, that were formulated by Protter for weakly hyperbolic equations. In that case the Protter problems are 3D analogues of the plane Darboux or Cauchy-Goursat problems. It is interesting that in contrast to the planar problems the new 3D problems are strongly ill-posed. Some of the Protter problems for degenerating hyperbolic equation without lower order terms or even for the usual wave equation have infinite-dimensional kernels. Therefore there are infinitely many orthogonality conditions for classical solvability of their adjiont problems. So it is interesting to obtain results for uniqueness of solutions adding first order terms in the equation. In the present paper we do this and find conditions for coefficients under which we prove uniqueness of quasi-regular solutions to the Protter problems.
Shao, Yan-Lin Faltinsen, Odd M.
2014-10-01
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
Instability and Wave Propagation in Structured 3D Composites
NASA Astrophysics Data System (ADS)
Kaynia, Narges; Fang, Nicholas X.; Boyce, Mary C.
2014-03-01
Many structured composites found in nature possess undulating and wrinkled interfacial layers that regulate mechanical, chemical, acoustic, adhesive, thermal, electrical and optical functions of the material. This research focused on the complex instability and wrinkling pattern arising in 3D structured composites and the effect of the buckling pattern on the overall structural response. The 3D structured composites consisted of stiffer plates supported by soft matrix on both sides. Compression beyond the critical strain led to complex buckling patterns in the initially straight plates. The motivation of our work is to elaborate the formation of a system of prescribed periodic scatterers (metamaterials) due to buckling, and their effect to interfere wave propagation through the metamaterial structures. Such metamaterials made from elastomers enable large reversible deformation and, as a result, significant changes of the wave propagation properties. We developed analytical and finite element models to capture various aspects of the instability mechanism. Mechanical experiments were designed to further explore the modeling results. The ability to actively alter the 3D composite structure can enable on-demand tunability of many different functions, such as active control of wave propagation to create band-gaps and waveguides.
Xiong, Z.; Tripp, A.C.
1994-12-31
This paper presents an integral equation algorithm for 3D EM modeling at high frequencies for applications in engineering an environmental studies. The integral equation method remains the same for low and high frequencies, but the dominant roles of the displacements currents complicate both numerical treatments and interpretations. With singularity extraction technique they successively extended the application of the Hankel filtering technique to the computation of Hankel integrals occurring in high frequency EM modeling. Time domain results are calculated from frequency domain results via Fourier transforms. While frequency domain data are not obvious for interpretations, time domain data show wave-like pictures that resemble seismograms. Both 1D and 3D numerical results show clearly the layer interfaces.
Protrusive waves guide 3D cell migration along nanofibers
Guetta-Terrier, Charlotte; Monzo, Pascale; Zhu, Jie; Long, Hongyan; Venkatraman, Lakshmi; Zhou, Yue; Wang, PeiPei; Chew, Sing Yian; Mogilner, Alexander
2015-01-01
In vivo, cells migrate on complex three-dimensional (3D) fibrous matrices, which has made investigation of the key molecular and physical mechanisms that drive cell migration difficult. Using reductionist approaches based on 3D electrospun fibers, we report for various cell types that single-cell migration along fibronectin-coated nanofibers is associated with lateral actin-based waves. These cyclical waves have a fin-like shape and propagate up to several hundred micrometers from the cell body, extending the leading edge and promoting highly persistent directional movement. Cells generate these waves through balanced activation of the Rac1/N-WASP/Arp2/3 and Rho/formins pathways. The waves originate from one major adhesion site at leading end of the cell body, which is linked through actomyosin contractility to another site at the back of the cell, allowing force generation, matrix deformation and cell translocation. By combining experimental and modeling data, we demonstrate that cell migration in a fibrous environment requires the formation and propagation of dynamic, actin based fin-like protrusions. PMID:26553933
3D modeling of ultrasonic wave interaction with disbonds and weak bonds
NASA Astrophysics Data System (ADS)
Leckey, C.; Hinders, M.
2012-05-01
Ultrasonic techniques, such as the use of guided waves, can be ideal for finding damage in the plate and pipe-like structures used in aerospace applications. However, the interaction of waves with real flaw types and geometries can lead to experimental signals that are difficult to interpret. 3-dimensional (3D) elastic wave simulations can be a powerful tool in understanding the complicated wave scattering involved in flaw detection and for optimizing experimental techniques. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate Lamb wave scattering from realistic flaws. This paper discusses simulation results for an aluminum-aluminum diffusion disbond and an aluminum-epoxy disbond and compares results from the disbond case to the common artificial flaw type of a flat-bottom hole. The paper also discusses the potential for extending the 3D EFIT equations to incorporate physics-based weak bond models for simulating wave scattering from weak adhesive bonds.
3D Modeling of Ultrasonic Wave Interaction with Disbonds and Weak Bonds
NASA Technical Reports Server (NTRS)
Leckey, C.; Hinders, M.
2011-01-01
Ultrasonic techniques, such as the use of guided waves, can be ideal for finding damage in the plate and pipe-like structures used in aerospace applications. However, the interaction of waves with real flaw types and geometries can lead to experimental signals that are difficult to interpret. 3-dimensional (3D) elastic wave simulations can be a powerful tool in understanding the complicated wave scattering involved in flaw detection and for optimizing experimental techniques. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate Lamb wave scattering from realistic flaws. This paper discusses simulation results for an aluminum-aluminum diffusion disbond and an aluminum-epoxy disbond and compares results from the disbond case to the common artificial flaw type of a flat-bottom hole. The paper also discusses the potential for extending the 3D EFIT equations to incorporate physics-based weak bond models for simulating wave scattering from weak adhesive bonds.
Analytical and numerical aspects in solving the controlled 3D Gross-Pitaevskii equation
Fedele, R.; Jovanovic, D.; De Nicola, S.; Eliasson, B.; Shukla, P. K.
2009-11-10
The results of recently developed investigations, that have been carried out within the framework of the controlling potential method (CPM), are reviewed. This method allows one to decompose a three dimensional (3D) Gross-Pitaevskii equation (GPE) into the pair of coupled Schroedinger-type equations. Under suitable mathematical conditions, the solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schroedinger equation (the transverse component of the GPE) coupled with a 1D nonlinear Schroedinger equation (the longitudinal component of the GPE). Such decomposition allows one to cast the solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. It is shown that the CPM can be used to obtain a new class of three-dimensional solitary waves solutions of the GPE, which governs the dynamics of Bose-Einstein condensates. By imposing an external controlling potential, the desired time-dependent shape of the localized BECs is obtained. The stability of the exact solutions was checked with direct simulations of the time -dependent, three-dimensional GPE. Our simulations show that the localized condensates are stable with respect to perturbed initial conditions.
A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations
NASA Astrophysics Data System (ADS)
Georges, Gabriel; Breil, Jérôme; Maire, Pierre-Henri
2016-01-01
Solving the gas dynamics equations under the Lagrangian formalism enables to simulate complex flows with strong shock waves. This formulation is well suited to the simulation of multi-material compressible fluid flows such as those encountered in the domain of High Energy Density Physics (HEDP). These types of flows are characterized by complex 3D structures such as hydrodynamic instabilities (Richtmyer-Meshkov, Rayleigh-Taylor, etc.). Recently, the 3D extension of different Lagrangian schemes has been proposed and appears to be challenging. More precisely, the definition of the cell geometry in the 3D space through the treatment of its non-planar faces and the limiting of a reconstructed field in 3D in the case of a second-order extension are of great interest. This paper proposes two new methods to solve these problems. A systematic and symmetric geometrical decomposition of polyhedral cells is presented. This method enables to define a discrete divergence operator leading to the respect of the Geometric Conservation Law (GCL). Moreover, a multi-dimensional minmod limiter is proposed. This new limiter constructs, from nodal gradients, a cell gradient which enables to ensure the monotonicity of the numerical solution even in presence of strong discontinuity. These new ingredients are employed into a cell-centered Lagrangian scheme. Robustness and accuracy are assessed against various representative test cases.
Numerical investigation of wave attenuation by vegetation using a 3D RANS model
NASA Astrophysics Data System (ADS)
Marsooli, Reza; Wu, Weiming
2014-12-01
Vegetation has been recognized as an important natural shoreline protection against storm surges and waves. Understanding of wave-vegetation interaction is essential for assessing the ability of vegetation patches, such as wetlands, to mitigate storm damages. In this study the wave attenuation by vegetation is investigated numerically using a 3-D model which solves the Reynolds-Averaged Navier-Stokes equations (RANS) by means of a finite-volume method based on collocated hexahedron mesh. A mixing length model is used for turbulence closure of the RANS equations. The water surface boundary is tracked using the Volume-of-Fluid (VOF) method with the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) to solve the VOF advection equation. The presence of vegetation is taken into account by adding the vegetation drag and inertia forces to the momentum equations. The model is validated by several laboratory experiments of short wave propagation through vegetation over flat and sloping beds. The comparisons show good agreement between the measured data and calculated results, but the swaying motion of flexible vegetation which is neglected in this study can influence the accuracy of the wave height predictions. The model is then applied to one of the validation tests with different vegetation properties, revealing that the wave height attenuation by vegetation depends not only on the wave conditions, but also the vegetation characteristics such as vegetation height and density.
Subduction zone guided waves: 3D modelling and attenuation effects
NASA Astrophysics Data System (ADS)
Garth, T.; Rietbrock, A.
2013-12-01
Waveform modelling is an important tool for understanding complex seismic structures such as subduction zone waveguides. These structures are often simplified to 2D structures for modelling purposes to reduce computational costs. In the case of subduction zone waveguide affects, 2D models have shown that dispersed arrivals are caused by a low velocity waveguide, inferred to be subducted oceanic crust and/or hydrated outer rise normal faults. However, due to the 2D modelling limitations the inferred seismic properties such as velocity contrast and waveguide thickness are still debated. Here we test these limitations with full 3D waveform modelling. For waveguide effects to be observable the waveform must be accurately modelled to relatively high frequencies (> 2 Hz). This requires a small grid spacing due to the high seismic velocities present in subduction zones. A large area must be modelled as well due to the long propagation distances (400 - 600 km) of waves interacting with subduction zone waveguides. The combination of the large model area and small grid spacing required means that these simulations require a large amount of computational resources, only available at high performance computational centres like the UK National super computer HECTOR (used in this study). To minimize the cost of modelling for such a large area, the width of the model area perpendicular to the subduction trench (the y-direction) is made as small as possible. This reduces the overall volume of the 3D model domain. Therefore the wave field is simulated in a model ';corridor' of the subduction zone velocity structure. This introduces new potential sources of error particularly from grazing wave side reflections in the y-direction. Various dampening methods are explored to reduce these grazing side reflections, including perfectly matched layers (PML) and more traditional exponential dampening layers. Defining a corridor model allows waveguide affects to be modelled up to at least 2
3D WKB solution for fast magnetoacoustic wave behaviour around an X-line
NASA Astrophysics Data System (ADS)
McLaughlin, J. A.; Botha, G. J. J.; Régnier, S.; Spoors, D. L.
2016-06-01
Context. We study the propagation of a fast magnetoacoustic wave in a 3D magnetic field created from two magnetic dipoles. The magnetic topology contains an X-line. Aims: We aim to contribute to the overall understanding of MHD wave propagation within inhomogeneous media, specifically around X-lines. Methods: We investigate the linearised, 3D MHD equations under the assumptions of ideal and cold plasma. We utilise the WKB approximation and Charpit's method during our investigation. Results: It is found that the behaviour of the fast magnetoacoustic wave is entirely dictated by the local, inhomogeneous, equilibrium Alfvén speed profile. All parts of the wave experience refraction during propagation, where the magnitude of the refraction effect depends on the location of an individual wave element within the inhomogeneous magnetic field. The X-line, along which the Alfvén speed is identically zero, acts as a focus for the refraction effect. There are two main types of wave behaviour: part of the wave is either trapped by the X-line or escapes the system, and there exists a critical starting region around the X-line that divides these two types of behaviour. For the set-up investigated, it is found that 15.5% of the fast wave energy is trapped by the X-line. Conclusions: We conclude that linear, β = 0 fast magnetoacoustic waves can accumulate along X-lines and thus these will be specific locations of fast wave energy deposition and thus preferential heating. The work here highlights the importance of understanding the magnetic topology of a system. We also demonstrate how the 3D WKB technique described in this paper can be applied to other magnetic configurations.
ADVANCED WAVE-EQUATION MIGRATION
L. HUANG; M. C. FEHLER
2000-12-01
Wave-equation migration methods can more accurately account for complex wave phenomena than ray-tracing-based Kirchhoff methods that are based on the high-frequency asymptotic approximation of waves. With steadily increasing speed of massively parallel computers, wave-equation migration methods are becoming more and more feasible and attractive for imaging complex 3D structures. We present an overview of several efficient and accurate wave-equation-based migration methods that we have recently developed. The methods are implemented in the frequency-space and frequency-wavenumber domains and hence they are called dual-domain methods. In the methods, we make use of different approximate solutions of the scalar-wave equation in heterogeneous media to recursively downward continue wavefields. The approximations used within each extrapolation interval include the Born, quasi-Born, and Rytov approximations. In one of our dual-domain methods, we use an optimized expansion of the square-root operator in the one-way wave equation to minimize the phase error for a given model. This leads to a globally optimized Fourier finite-difference method that is a hybrid split-step Fourier and finite-difference scheme. Migration examples demonstrate that our dual-domain migration methods provide more accurate images than those obtained using the split-step Fourier scheme. The Born-based, quasi-Born-based, and Rytov-based methods are suitable for imaging complex structures whose lateral variations are moderate, such as the Marmousi model. For this model, the computational cost of the Born-based method is almost the same as the split-step Fourier scheme, while other methods takes approximately 15-50% more computational time. The globally optimized Fourier finite-difference method significantly improves the accuracy of the split-step Fourier method for imaging structures having strong lateral velocity variations, such as the SEG/EAGE salt model, at an approximately 30% greater
An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations
NASA Astrophysics Data System (ADS)
Helzel, Christiane; Rossmanith, James A.; Taetz, Bertram
2011-05-01
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [J.A. Rossmanith, An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows, SIAM J. Sci. Comput. 28 (2006) 1766], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J.O. Langseth, R.J. LeVeque, A wave propagation method for threedimensional hyperbolic conservation laws, J. Comput. Phys. 165 (2000) 126]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The
Upscaling small heterogeneities for seismic wave propagation in 3D complex media
NASA Astrophysics Data System (ADS)
Cupillard, P.; Capdeville, Y.
2012-04-01
Seismic waves propagating in the Earth are affected by different sizes of heterogeneities. When modelling these waves (using numerical methods such as the SEM), taking into account heterogeneities that are much smaller than the minimum wavelength is a challenge because meshing small heterogeneities often requires important efforts and leads to high numerical costs. In this work, we present a technique which allows to upscale the small heterogeneities that can lie in an elastic medium. This technique yields a smooth effective medium and effective equations. We describe its implementation in the 3D case and we show relevant examples.
Gravitational Wave Signals from 2D and 3D Core Collapse Supernova Explosions
NASA Astrophysics Data System (ADS)
Yakunin, Konstantin; Mezzacappa, Anthony; Marronetti, Pedro; Bruenn, Stephen; Hix, W. Raphael; Lentz, Eric J.; Messer, O. E. Bronson; Harris, J. Austin; Endeve, Eirik; Blondin, John
2016-03-01
We study two- and three-dimensional (2D and 3D) core-collapse supernovae (CCSN) using our first-principles CCSN simulations performed with the neutrino hydrodynamics code CHIMERA. The following physics is included: Newtonian hydrodynamics with a nuclear equation of state capable of describing matter in both NSE and non-NSE, MGFLD neutrino transport with realistic neutrino interactions, an effective GR gravitational potential, and a nuclear reaction network. Both our 2D and 3D models achieve explosion, which in turn enables us to determine their complete gravitational wave signals. In this talk, we present them, and we analyze the similarities and differences between the 2D and 3D signals.
Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises
Albeverio, Sergio; Debussche, Arnaud; Xu Lihu
2012-10-15
We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes being forced) via a Kolmogorov equation approach.
Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves.
Driben, Rodislav; Meier, Torsten
2014-10-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse. PMID:25360922
On the Implementation of 3D Galerkin Boundary Integral Equations
Nintcheu Fata, Sylvain; Gray, Leonard J
2010-01-01
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.
A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
NASA Astrophysics Data System (ADS)
Stolk, Christiaan C.
2016-06-01
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.
Study of nonlinear 3-D evolution of kinetic Alfvén wave and fluctuation spectra
NASA Astrophysics Data System (ADS)
Sharma, Prachi; Yadav, Nitin; Sharma, R. P.
2015-11-01
Waves and instabilities play a very crucial role in astrophysical plasmas e.g. solar wind, Geospace etc. The main objective of current study is to investigate the importance of nonlinear processes associated with kinetic Alfvén waves (KAWs) in order to understand the physical mechanism behind the magnetopause turbulence. Numerical simulation of the coupled equations guiding the dynamics of three dimensionally propagating kinetic Alfvén wave (KAW) and slow magnetosonic wave has been performed for intermediate beta plasma (i.e. me/mi ≪ β < 1, where β is thermal to magnetic pressure ratio) applicable to the magnetopause. A simplified semi-analytical model based on paraxial approach has also been developed. We have examined the field localization and associated power spectrum of 3-D kinetic Alfvén wave for this nonlinear interaction. Governing dynamical equations of KAW and slow magnetosonic wave get coupled when the ponderomotive force arising due to pump KAW is taken into account while studying the slow magnetosonic wave dynamics. The numerical prediction of power law scaling is just consistent with the observation of THEMIS spacecraft in the magnetopause.
Spatial parallelism of a 3D finite difference, velocity-stress elastic wave propagation code
Minkoff, S.E.
1999-12-01
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, finite difference simulations for 3D elastic wave propagation are expensive. The authors model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code
MINKOFF,SUSAN E.
1999-12-09
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
2D/1D approximations to the 3D neutron transport equation. I: Theory
Kelley, B. W.; Larsen, E. W.
2013-07-01
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
ATHENA 3D: A finite element code for ultrasonic wave propagation
NASA Astrophysics Data System (ADS)
Rose, C.; Rupin, F.; Fouquet, T.; Chassignole, B.
2014-04-01
The understanding of wave propagation phenomena requires use of robust numerical models. 3D finite element (FE) models are generally prohibitively time consuming. However, advances in computing processor speed and memory allow them to be more and more competitive. In this context, EDF R&D developed the 3D version of the well-validated FE code ATHENA2D. The code is dedicated to the simulation of wave propagation in all kinds of elastic media and in particular, heterogeneous and anisotropic materials like welds. It is based on solving elastodynamic equations in the calculation zone expressed in terms of stress and particle velocities. The particularity of the code relies on the fact that the discretization of the calculation domain uses a Cartesian regular 3D mesh while the defect of complex geometry can be described using a separate (2D) mesh using the fictitious domains method. This allows combining the rapidity of regular meshes computation with the capability of modelling arbitrary shaped defects. Furthermore, the calculation domain is discretized with a quasi-explicit time evolution scheme. Thereby only local linear systems of small size have to be solved. The final step to reduce the computation time relies on the fact that ATHENA3D has been parallelized and adapted to the use of HPC resources. In this paper, the validation of the 3D FE model is discussed. A cross-validation of ATHENA 3D and CIVA is proposed for several inspection configurations. The performances in terms of calculation time are also presented in the cases of both local computer and computation cluster use.
3D simulation of seismic wave propagation around a tunnel using the spectral element method
NASA Astrophysics Data System (ADS)
Lambrecht, L.; Friederich, W.
2010-05-01
We model seismic wave propagation in the environment of a tunnel for later application to reconnaissance. Elastic wave propagation can be simulated by different numerical techniques such as finite differences and pseudospectral methods. Their disadvantage is the lack of accuracy on free surfaces, numerical dispersion and inflexibility of the mesh. Here we use the software package SPECFEM3D_SESAME in an svn development version, which is based on the spectral element method (SEM) and can handle complex mesh geometries. A weak form of the elastic wave equation leads to a linear system of equations with a diagonal mass matrix, where the free surface boundary of the tunnel can be treated under realistic conditions and can be effectively implemented in parallel. We have designed a 3D external mesh including a tunnel and realistic features such as layers and holes to simulate elastic wave propagation in the zone around the tunnel. The source is acting at the tunnel surface so that we excite Rayleigh waves which propagate to the front face of the tunnel. A conversion takes place and a high amplitude S-wave is radiated in the direction of the tunnel axis. Reflections from perturbations in front of the tunnel can be measured by receivers implemented on the tunnel face. For a shallow tunnel the land surface has high influence on the wave propagation. By implementing additional receivers at this surface we intent to improve the prediction. It shows that the SEM is very capable to handle the complex geometry of the model and especially incorporates the free surfaces of the model.
Numerical homogenization for seismic wave propagation in 3D geological media
NASA Astrophysics Data System (ADS)
Cupillard, P.; Capdeville, Y.; Botella, A.
2014-12-01
Despite the important increase of the computational power in the last decades, simulating the seismic wave propagation through realistic geological models is still a challenge. By realistic models we here mean 3D media in which a broad variety (in terms of amplitude and extent) of heterogeneities lies, including discontinuities with complex geometry such as faulted and folded horizons, intrusive geological contacts and fault systems. To perform accurate numerical simulations, these discontinuities require complicated meshes which usually contain extremely small elements, yielding large, sometimes prohibitive, computation costs. Fortunately, the recent development of the non-periodic homogenization technique now enables to overcome this problem by computing smooth equivalent models for which a coarse mesh is sufficient to get an accurate wavefield. In this work, we present an efficient implementation of the technique which now allows for the homogenization of large 3D geological models. This implementation relies on a tetrahedral finite-element solution of the elasto-static equation behind the homogenization problem. Because this equation is time-independent, solving it is numerically cheaper than solving the wave equation, but it nevertheless requires some care because of the large size of the stiffness matrix arising from the fine mesh of realistic geological structures. A domain decomposition is therefore adopted. In our strategy, the obtained sub-domains overlap but they are independent so the solution within each of them can be computed either in series or in parallel. In addition, well-balanced loads, efficient search algorithms and multithreading are implemented to speed up the computation. The resulting code enables the homogenization of 3D elastic media in a time that is neglectable with respect to the simulation time of the wave propagation within. This is illustrated through a sub-surface model of the Furfooz karstic region, Belgium.
3D frequency-domain finite-difference modeling of acoustic wave propagation
NASA Astrophysics Data System (ADS)
Operto, S.; Virieux, J.
2006-12-01
We present a 3D frequency-domain finite-difference method for acoustic wave propagation modeling. This method is developed as a tool to perform 3D frequency-domain full-waveform inversion of wide-angle seismic data. For wide-angle data, frequency-domain full-waveform inversion can be applied only to few discrete frequencies to develop reliable velocity model. Frequency-domain finite-difference (FD) modeling of wave propagation requires resolution of a huge sparse system of linear equations. If this system can be solved with a direct method, solutions for multiple sources can be computed efficiently once the underlying matrix has been factorized. The drawback of the direct method is the memory requirement resulting from the fill-in of the matrix during factorization. We assess in this study whether representative problems can be addressed in 3D geometry with such approach. We start from the velocity-stress formulation of the 3D acoustic wave equation. The spatial derivatives are discretized with second-order accurate staggered-grid stencil on different coordinate systems such that the axis span over as many directions as possible. Once the discrete equations were developed on each coordinate system, the particle velocity fields are eliminated from the first-order hyperbolic system (following the so-called parsimonious staggered-grid method) leading to second-order elliptic wave equations in pressure. The second-order wave equations discretized on each coordinate system are combined linearly to mitigate the numerical anisotropy. Secondly, grid dispersion is minimized by replacing the mass term at the collocation point by its weighted averaging over all the grid points of the stencil. Use of second-order accurate staggered- grid stencil allows to reduce the bandwidth of the matrix to be factorized. The final stencil incorporates 27 points. Absorbing conditions are PML. The system is solved using the parallel direct solver MUMPS developed for distributed
A support-operator method for viscoelastic wave modelling in 3-D heterogeneous media
NASA Astrophysics Data System (ADS)
Ely, Geoffrey P.; Day, Steven M.; Minster, Jean-Bernard
2008-01-01
We apply the method of support operators (SOM) to solve the 3-D, viscoelastic equations of motion for use in earthquake simulations. SOM is a generalized finite-difference method that can utilize meshes of arbitrary structure and incorporate irregular geometry. Our implementation uses a 3-D, logically rectangular, hexahedral mesh. Calculations are second-order in space and time. A correction term is employed for suppression of spurious zero-energy modes (hourglass oscillations). We develop a free surface boundary condition, and an absorbing boundary condition using the method of perfectly matched layers (PML). Numerical tests using a layered material model in a highly deformed mesh show good agreement with the frequency-wavenumber method, for resolutions greater than 10 nodes per wavelength. We also test a vertically incident P wave on a semi-circular canyon, for which results match boundary integral solutions at resolutions greater that 20 nodes per wavelength. We also demonstrate excellent parallel scalability of our code.
On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame
NASA Technical Reports Server (NTRS)
Mahalov, A.
1994-01-01
The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).
2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons
Kelley, B. W.; Collins, B.; Larsen, E. W.
2013-07-01
In a companion paper [1], (i) several new '2D/1D equations' are introduced as accurate approximations to the 3D Boltzmann transport equation, (ii) the simplest of these approximate equations is systematically discretized, and (iii) a theoretically stable iteration scheme is developed to solve the discrete equations. In this paper, numerical results are presented that confirm the theoretical predictions made in [1]. (authors)
Acoustic wave-equation-based earthquake location
NASA Astrophysics Data System (ADS)
Tong, Ping; Yang, Dinghui; Liu, Qinya; Yang, Xu; Harris, Jerry
2016-04-01
We present a novel earthquake location method using acoustic wave-equation-based traveltime inversion. The linear relationship between the location perturbation (δt0, δxs) and the resulting traveltime residual δt of a particular seismic phase, represented by the traveltime sensitivity kernel K(t0, xs) with respect to the earthquake location (t0, xs), is theoretically derived based on the adjoint method. Traveltime sensitivity kernel K(t0, xs) is formulated as a convolution between the forward and adjoint wavefields, which are calculated by numerically solving two acoustic wave equations. The advantage of this newly derived traveltime kernel is that it not only takes into account the earthquake-receiver geometry but also accurately honours the complexity of the velocity model. The earthquake location is obtained by solving a regularized least-squares problem. In 3-D realistic applications, it is computationally expensive to conduct full wave simulations. Therefore, we propose a 2.5-D approach which assumes the forward and adjoint wave simulations within a 2-D vertical plane passing through the earthquake and receiver. Various synthetic examples show the accuracy of this acoustic wave-equation-based earthquake location method. The accuracy and efficiency of the 2.5-D approach for 3-D earthquake location are further verified by its application to the 2004 Big Bear earthquake in Southern California.
On the Dynamic Programming Approach for the 3D Navier-Stokes Equations
Manca, Luigi
2008-06-15
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.
Joint inversion of 3D crustal structure with ambient noise and earthquake body wave travel time
NASA Astrophysics Data System (ADS)
Li, Z.; Ni, S.; Chong, J.; Wang, X.
2012-12-01
Surface wave tomography based on the noise correlation function of seismic ambient noise has been widely used in studies of crustal and mantle structure . However, the periods of surface wave dispersions in the ambient noise tomography are typically less than 40 s, which limits its resolution on the lower crust. Travel times of earthquake body waves, such as Sg and SmS, could provide additional constraints to the crustal structure, especially to the lower crust due to the ray paths of SmS traveling through the lower crust twice. Here, we proposed a joint inversion method for 3D crustal structure with ambient noise and earthquake body wave travel time data, with the goal of providing better constraints and resolutions on the whole crust. We constructed the linear equations for joint inversion of crustal S velocity structure with the surface wave dispersion and body wave travel time data, and solved the equations with LSQR algorithm. Different weighting and damping factors, together with smoothing constraints, are adopted for surface wave dispersion and body wave travel time data to fit both dataset simultaneously. Synthetics experiments showed that the joint inversion could resolve the crust structure better than sole tomography of ambient noise or body wave travel time. We conducted the joint inversion around the Yangtze block in the eastern China. Rayleigh wave dispersions are extracted from the seismic ambient noise tomography by Zheng et al (2011) in this area. The body waves (e.g., Sg, SmS, Sn) are coherent to be identified and their travel times are measured with accuracy from high quality waveforms of some recent local earthquakes in this area. In order to minimize the travel time uncertainties, the focal depth and epicenter of these local earthquakes were resolved by depth phases and temporary aftershock observations. The result from joint inversion suggests that the crustal velocity structure, especially the lower crust, was well improved, which not only
Characteristics of Oceanic Waves Caused by Landslides: Insights from 3D-Hydrocode Modeling
NASA Astrophysics Data System (ADS)
Elbeshausen, D.; Wünnemann, K.; Weiss, R.
2008-12-01
In an experimental framework, the generation of tsunami waves can be considered as a two-dimensional or three-dimensional problem by finding the respective geometry of the experimental set up. In nature, of course, it is a fully three-dimensional problem. The generation of tsunami waves caused by landslides (submarine and subaerial) must be approached as a dynamical problem. The understanding of the slide body's dynamics plays a key role in understanding the generated waves. Numerical calculations are a standard tool in tsunami science as the propagation of long waves can be tackled with depth-averaged equations. These classical models have often been used for modeling the propagation and run up of those tsunami waves caused by earthquakes. Tsunamis generated during slide motion are different. They are shorter and have larger amplitudes. It could be demonstrated in respective laboratory experiments and two dimensional numerical studies that in the initial phase the behavior of the waves is very complex, resulting in wave breaking and plunging. We conducted hydrocode simulations to model the generation of tsunami by slide in two dimensions. Results could show the complexity of the initial wave evolution as well as the development of the slide body itself. As an extension to these two-dimensional simulations, we now consider the three-dimensional problem and reveal some differences to the two-dimensional results. For this purpose we are using iSALE-3D, a multi- material, multi-rheology hydrocode capable of studying landslide processes in both two and three dimensions. iSALE-3D has been originally developed to study shock waves and high pressure scenarios like meteorite impacts or explosions and has been successfully validated against theoretical and experimental results as well as other numerical codes. Previous studies revealed differences in the formation and propagation of oceanic waves caused by meteorite impacts at different angles of incidence. Hence, for
A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
Riyanti, C.D. . E-mail: C.D.Riyanti@tudelft.nl; Kononov, A.; Erlangga, Y.A.; Vuik, C.; Oosterlee, C.W.; Plessix, R.-E.; Mulder, W.A.
2007-05-20
We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.
Mach-wave coherence in 3D media with random heterogeneities
NASA Astrophysics Data System (ADS)
Vyas, Jagdish C.; Mai, P. Martin; Galis, Martin; Dunham, Eric M.; Imperatori, Walter
2016-04-01
We investigate Mach-waves coherence for complex super-shear ruptures embedded in 3D random media that lead to seismic scattering. We simulate Mach-wave using kinematic earthquake sources that include fault-regions over which the rupture propagates at super-shear speed. The local slip rate is modeled with the regularized Yoffe function. The medium heterogeneities are characterized by Von Karman correlation function. We consider various realizations of 3D random media from combinations of different values of correlation length (0.5 km, 2 km, 5 km), standard deviation (5%, 10%, 15%) and Hurst exponent (0.2). Simulations in a homogeneous medium serve as a reference case. The ground-motion simulations (maximum resolved frequency of 5 Hz) are conducted by solving the elasto-dynamic equations of motions using a generalized finite-difference method, assuming a vertical strike-slip fault. The seismic wavefield is sampled at numerous locations within the Mach-cone region to study the properties and evolution of the Mach-waves in scattering media. We find that the medium scattering from random heterogeneities significantly diminishes the coherence of Mach-wave in terms of both amplitude and frequencies. We observe that Mach-waves are considerably scattered at distances RJB > 20 km (and beyond) for random media with standard deviation 10%. The scattering efficiency of the medium for small Hurst exponents (H <= 0.2) is mainly controlled by the standard deviation of the velocity heterogeneities, rather than their correlation length, as both theoretical considerations and numerical experiments indicate. Based on our simulations, we propose that local super-shear ruptures may be more common in nature then reported, but are very difficult to detect due to the strong seismic scattering. We suggest that if an earthquake is recorded within 10-15 km fault perpendicular distance and has high PGA, then inversion should be carried out by allowing rupture speed variations from sub
3D Numerical Simulation on the Sloshing Waves Excited by the Seismic Shacking
NASA Astrophysics Data System (ADS)
Zhang, Lin; Wu, Tso-Ren
2016-04-01
In the event of 2015 Nepal earthquake, a video clip broadcasted worldwide showed a violent water spilling in a hotel swimming pool. This sloshing phenomenon indicates a potential water loss in the sensitive facilities, e.g. the spent fuel pools in nuclear power plant, has to be taken into account carefully under the consideration of seismic-induced ground acceleration. In the previous studies, the simulation of sloshing mainly focused on the pressure force on the structure by using a simplified Spring-Mass Method developed in the field of solid mechanics. However, restricted by the assumptions of plane water surface and limited wave height, significant error will be made in evaluating the amount of water loss in the tank. In this paper, the computational fluid dynamical model, Splash3D, was adopted for studying the sloshing problem accurately. Splash3D solved 3D Navier-Stokes Equation directly with Large-Eddy Simulation (LES) turbulent closure. The Volume-of-fluid (VOF) method with piecewise linear interface calculation (PLIC) was used to track the complex breaking water surface. The time series acceleration of a design seismic was loaded to excite the water. With few restrictions from the assumptions, the accuracy of the simulation results were improved dramatically. A series model validations were conducted by compared to a 2D theoretical solution, and a 3D experimental data. Good comparisons can be seen. After the validation, we performed the simulation for considering a sloshing case in a rectangular water tank with a dimension of 12 m long, 8 m wide, 8 m deep, which contained water with 7 m in depth. The seismic movement was imported by considering time-series acceleration in three dimensions, which were about 0.5 g to 1.2 g in the horizontal directions, and 0.3 g to 1 g in the vertical direction. We focused the discussions on the kinematics of the water surface, wave breaking, velocity field, pressure field, water force on the side walls, and, most
Solitons and nonlinear wave equations
Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.
1982-01-01
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.
Optimization of one-way wave equations.
Lee, M.W.; Suh, S.Y.
1985-01-01
The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors
Simulation of 3D Seismic Wave Propagation with Volcano Topography
NASA Astrophysics Data System (ADS)
Ripperger, J.; Igel, H.; Wassermann, J.
2001-12-01
We investigate the possibilities of using three-dimensional finite difference (FD) methods for numerical simulation of the seismic wave field at active volcanoes. We put special emphasis on the implementation of the boundary conditions for free surface topography. We compare two different approaches to solve the free surface boundary conditions. The algorithms are implemented on parallel hardware and have been tested for correctness and stability. We apply them to smooth artificial topographies and to the real topography of Mount Merapi, Indonesia. We conclude, that grid stretching type methods (e.g. Hestholm & Ruud, 1994) are not well suited for realistic volcano topography as they tend to become unstable for large topographic gradients. The representation of topography through staircase shaped grids (Ohminato & Chouet, 1997) results in stable calculations, while demanding very fine gridding. The simulations show the effects of a three-dimensional surface topography on elastic wave propagation. Ground motion at the surface is severely affected by topography. If neglected, this may jeopardize attempts to determine source location by analyzing particle motion. Numerical studies like this can help to understand wave propagation phenomena observed on field recordings in volcano seismology. Future studies will aim at separating the wave effects of internal scattering, topography and sources (tremors, tectonic events, pyroclastic flows).
Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.
2000-01-01
USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.
NASA Astrophysics Data System (ADS)
Velioǧlu, Deniz; Cevdet Yalçıner, Ahmet; Zaytsev, Andrey
2016-04-01
Tsunamis are huge waves with long wave periods and wave lengths that can cause great devastation and loss of life when they strike a coast. The interest in experimental and numerical modeling of tsunami propagation and inundation increased considerably after the 2011 Great East Japan earthquake. In this study, two numerical codes, FLOW 3D and NAMI DANCE, that analyze tsunami propagation and inundation patterns are considered. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. NAMI DANCE uses finite difference computational method to solve 2D depth-averaged linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In order to validate these two codes and analyze the differences between 3D-NS and 2D depth-averaged NSWE equations, two benchmark problems are applied. One benchmark problem investigates the runup of long waves over a complex 3D beach. The experimental setup is a 1:400 scale model of Monai Valley located on the west coast of Okushiri Island, Japan. Other benchmark problem is discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. It is a field dataset, recording the Japan 2011 tsunami in Hilo Harbor, Hawaii. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. The differences between 3D-NS and 2D depth-averaged NSWE equations are highlighted. All results are presented with discussions and comparisons. Acknowledgements: Partial support by Japan-Turkey Joint Research Project by JICA on earthquakes and tsunamis in Marmara Region (JICA SATREPS - MarDiM Project), 603839 ASTARTE Project of EU, UDAP-C-12-14 project of AFAD Turkey, 108Y227, 113M556 and 213M534 projects of TUBITAK Turkey, RAPSODI (CONCERT_Dis-021) of CONCERT
Global regular solutions for the 3D Kawahara equation posed on unbounded domains
NASA Astrophysics Data System (ADS)
Larkin, Nikolai A.; Simões, Márcio Hiran
2016-08-01
An initial boundary value problem for the 3D Kawahara equation posed on a channel-type domain was considered. The existence and uniqueness results for global regular solutions as well as exponential decay of small solutions in the H 2-norm were established.
Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on unbounded domains
NASA Astrophysics Data System (ADS)
Larkin, N. A.
2015-09-01
An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on unbounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the H2-norm for small initial data are proven.
A research of 3D gravity inversion based on the recovery of sparse underdetermined linear equations
NASA Astrophysics Data System (ADS)
Zhaohai, M.
2014-12-01
Because of the properties of gravity data, it is made difficult to solve the problem of multiple solutions. There are two main types of 3D gravity inversion methods：One of two methods is based on the improvement of the instability of the sensitive matrix, solving the problem of multiple solutions and instability in 3D gravity inversion. Another is to join weight function into the 3D gravity inversion iteration. Through constant iteration, it can renewal density values and weight function to achieve the purpose to solve the multiple solutions and instability of the 3D gravity data inversion. Thanks to the sparse nature of the solutions of 3D gravity data inversions, we can transform it into a sparse equation. Then, through solving the sparse equations, we can get perfect 3D gravity inversion results. The main principle is based on zero norm of sparse matrix solution of the equation. Zero norm is mainly to solve the nonzero solution of the sparse matrix. However, the method of this article adopted is same as the principle of zero norm. But the method is the opposite of zero norm to obtain zero value solution. Through the form of a Gaussian fitting solution of the zero norm, we can find the solution by using regularization principle. Moreover, this method has been proved that it had a certain resistance to random noise in the mathematics, and it was more suitable than zero norm for the solution of the geophysical data. 3D gravity which is adopted in this article can well identify abnormal body density distribution characteristics, and it can also recognize the space position of abnormal distribution very well. We can take advantage of the density of the upper and lower limit penalty function to make each rectangular residual density within a reasonable range. Finally, this 3D gravity inversion is applied to a variety of combination model test, such as a single straight three-dimensional model, the adjacent straight three-dimensional model and Y three
3D dynamic simulation of crack propagation in extracorporeal shock wave lithotripsy
NASA Astrophysics Data System (ADS)
Wijerathne, M. L. L.; Hori, Muneo; Sakaguchi, Hide; Oguni, Kenji
2010-06-01
Some experimental observations of Shock Wave Lithotripsy(SWL), which include 3D dynamic crack propagation, are simulated with the aim of reproducing fragmentation of kidney stones with SWL. Extracorporeal shock wave lithotripsy (ESWL) is the fragmentation of kidney stones by focusing an ultrasonic pressure pulse onto the stones. 3D models with fine discretization are used to accurately capture the high amplitude shear shock waves. For solving the resulting large scale dynamic crack propagation problem, PDS-FEM is used; it provides numerically efficient failure treatments. With a distributed memory parallel code of PDS-FEM, experimentally observed 3D photoelastic images of transient stress waves and crack patterns in cylindrical samples are successfully reproduced. The numerical crack patterns are in good agreement with the experimental ones, quantitatively. The results shows that the high amplitude shear waves induced in solid, by the lithotriptor generated shock wave, play a dominant role in stone fragmentation.
Ott, C D; Dimmelmeier, H; Marek, A; Janka, H-T; Hawke, I; Zink, B; Schnetter, E
2007-06-29
We present 2D and 3D simulations of the collapse of rotating stellar iron cores in general relativity employing a nuclear equation of state and an approximate treatment of deleptonization. We compare fully general relativistic and conformally flat evolutions and find that the latter treatment is sufficiently accurate for the core-collapse supernova problem. We focus on gravitational wave (GW) emission from rotating collapse, bounce, and early postbounce phases. Our results indicate that the GW signature of these phases is much more generic than previously estimated. We also track the growth of a nonaxisymmetric instability in one model, leading to strong narrow-band GW emission. PMID:17678077
Upper Semicontinuity of Pullback Attractors for the 3D Nonautonomous Benjamin-Bona-Mahony Equations
Yang, Xinguang; Wang, Xiaosong; Zhang, Lingrui
2014-01-01
We will study the upper semicontinuity of pullback attractors for the 3D nonautonomouss Benjamin-Bona-Mahony equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors 𝒜 ε(t) of equation ut-Δut-νΔu+∇·F→(u)=ɛg(x,t), x ∈ Ω, converge to the global attractor 𝒜 of the above-mentioned equation with ε = 0 for any t ∈ ℝ. PMID:24790585
Recasting the 3D Wigner-Liouville equation with spectral components of the force
NASA Astrophysics Data System (ADS)
van de Put, Maarten; Sorée, Bart; Magnus, Wim
The phasespace approach to many-body quantum mechanics, by means of the Wigner-function is interesting through its connection to classical mechanics. Time-evolution of any statistical distribution of states under influence of a (time-dependent) Hamiltonian is obtained through use of the Wigner-Liouville equation. The standard form of this equation contains two 3D integrals, over the entire phase space. As a result, this form emphasizes the non-locality of the interaction of the potential, but lacks simplicity and ease of understanding. Furthermore, the integrals make numerical solution of the Wigner-Liouville equation challenging. We present an alternative form to the Wigner-Liouville equation based on the force rather than the potential, in alignment with the classical Boltzmann equation. Decomposition of the force in its spectral components yields a simpler form of the Wigner-Liouville equation. This new form has only one 3D integral over the spectral force components, and is local in position, simplifying both interpretation and numerical implementation. Because of its use of the force, it straightforwardly reduces to the Boltzmann equation under classical conditions.
Equation-of-State Test Suite for the DYNA3D Code
Benjamin, Russell D.
2015-11-05
This document describes the creation and implementation of a test suite for the Equationof- State models in the DYNA3D code. A customized input deck has been created for each model, as well as a script that extracts the relevant data from the high-speed edit file created by DYNA3D. Each equation-of-state model is broken apart and individual elements of the model are tested, as well as testing the entire model. The input deck for each model is described and the results of the tests are discussed. The intent of this work is to add this test suite to the validation suite presently used for DYNA3D.
Characterizing the propagation of gravity waves in 3D nonlinear simulations of solar-like stars
NASA Astrophysics Data System (ADS)
Alvan, L.; Strugarek, A.; Brun, A. S.; Mathis, S.; Garcia, R. A.
2015-09-01
Context. The revolution of helio- and asteroseismology provides access to the detailed properties of stellar interiors by studying the star's oscillation modes. Among them, gravity (g) modes are formed by constructive interferences between progressive internal gravity waves (IGWs), propagating in stellar radiative zones. Our new 3D nonlinear simulations of the interior of a solar-like star allows us to study the excitation, propagation, and dissipation of these waves. Aims: The aim of this article is to clarify our understanding of the behavior of IGWs in a 3D radiative zone and to provide a clear overview of their properties. Methods: We use a method of frequency filtering that reveals the path of individual gravity waves of different frequencies in the radiative zone. Results: We are able to identify the region of propagation of different waves in 2D and 3D, to compare them to the linear raytracing theory and to distinguish between propagative and standing waves (g-modes). We also show that the energy carried by waves is distributed in different planes in the sphere, depending on their azimuthal wave number. Conclusions: We are able to isolate individual IGWs from a complex spectrum and to study their propagation in space and time. In particular, we highlight in this paper the necessity of studying the propagation of waves in 3D spherical geometry, since the distribution of their energy is not equipartitioned in the sphere.
NuSol - Numerical solver for the 3D stationary nuclear Schrödinger equation
NASA Astrophysics Data System (ADS)
Graen, Timo; Grubmüller, Helmut
2016-01-01
The classification of short hydrogen bonds depends on several factors including the shape and energy spacing between the nuclear eigenstates of the hydrogen. Here, we describe the NuSol program in which three classes of algorithms were implemented to solve the 1D, 2D and 3D time independent nuclear Schrödinger equation. The Schrödinger equation was solved using the finite differences based Numerov's method which was extended to higher dimensions, the more accurate pseudo-spectral Chebyshev collocation method and the sinc discrete variable representation by Colbert and Miller. NuSol can be applied to solve the Schrödinger equation for arbitrary analytical or numerical potentials with focus on nuclei bound by the potential of their molecular environment. We validated the methods against literature values for the 2D Henon-Heiles potential, the 3D linearly coupled sextic oscillators and applied them to study hydrogen bonding in the malonaldehyde derivate 4-cyano-2,2,6,6-tetramethyl-3,5-heptanedione. With NuSol, the extent of nuclear delocalization in a given molecular potential can directly be calculated without relying on linear reaction coordinates in 3D molecular space.
Propagation of Electromagnetic Waves in 3D Opal-based Magnetophotonic Crystals
NASA Astrophysics Data System (ADS)
Pardavi-Horvath, Martha; Makeeva, Galina S.; Golovanov, Oleg A.; Rinkevich, Anatolii B.
2013-03-01
Opals, a class of self-organized 3D nanostructures, are typical representatives of photonic bandgap structures. The voids inside of the opal structure of close packed SiO2 spheres can be infiltrated by a magnetic material, creating magnetically tunable magnetophotonic crystals with interesting and potentially useful properties at GHz and THz frequencies. The propagation of electromagnetic waves at microwave frequencies was investigated numerically in SiO2 opal based magnetic nanostructures, using rigorous mathematical models to solve Maxwell's equations complemented by the Landau-Lifshitz equation with electrodynamic boundary conditions. The numerical approach is based on Galerkin's projection method using the decomposition algorithm on autonomous blocks with Floquet channels. The opal structure consists of SiO2 nanospheres, with inter-sphere voids infiltrated with nanoparticles of Ni-Zn ferrites. Both the opal matrix and the ferrite are assumed to be lossy. A model, taking into account the real structure of the ferrite particles in the opal's voids was developed to simulate the measured FMR lineshape of the ferrite infiltrated opal. The numerical technique shows an excellent agreement when applied to model recent experimental data on similar ferrite opals.
Some Properties of the M3D-C1 Form of the 3D Magnetohydrodynamics Equations
J. Breslau, N. Ferraro, S. Jardin
2009-07-10
We introduce a set of scalar variables and projection operators for the vector momentum and magnetic field evolution equations that have several unique and desirable properties, making them a preferred system for solving the magnetohydrodynamics equations in a torus with a strong toroidal magnetic field. We derive a "weak form" of these equations that explicitly conserves energy and is suitable for a Galerkin finite element formulation provided the basis elements have C1 continuity. Systems of reduced equations are discussed, along with their energy conservation properties. An implicit time advance is presented that adds diagonally dominant self-adjoint energy terms to the mass matrix to obtain numerical stability.
Benchmarks of 3D Laplace Equation Solvers in a Cubic Configuration for Streamer Simulation
NASA Astrophysics Data System (ADS)
Joseph-Marie, Plewa; Olivier, Ducasse; Philippe, Dessante; Carolyn, Jacobs; Olivier, Eichwald; Nicolas, Renon; Mohammed, Yousfi
2016-05-01
The aim of this paper is to test a developed SOR R&B method using the Chebyshev accelerator algorithm to solve the Laplace equation in a cubic 3D configuration. Comparisons are made in terms of precision and computing time with other elliptic equation solvers proposed in the open source LIS library. The first results, obtained by using a single core on a HPC, show that the developed SOR R&B method is efficient when the spectral radius needed for the Chebyshev acceleration is carefully pre-estimated. Preliminary results obtained with a parallelized code using the MPI library are also discussed when the calculation is distributed over one hundred cores.
A least-squares finite element method for 3D incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
Solution of the Skyrme HF + BCS equation on a 3D mesh
NASA Astrophysics Data System (ADS)
Bonche, P.; Flocard, H.; Heenen, P. H.
2005-09-01
Over the years, the ev8 code has been a very useful tool for the study of nuclear mean-field theory. Its main characteristic is that it solves the Hartree-Fock plus BCS equations for Skyrme type functionals via a discretization of the individual wave-functions on a three-dimensional Cartesian mesh. This allows maximal flexibility in the determination of the nuclear shape by the variational process. For instance, the same mesh can be used to describe the oblate deformed, spherical, prolate deformed, superdeformed and fission configurations of a given nucleus. The quadrupole constraining operator yielding the deformation energy curve covering all these configurations is included in ev8. This version of the code is restricted to even-even nuclei. Program summaryTitle of program:ev8 Catalogue identifier:ADWA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWA Licensing provisions: none Computers on which the program has been tested: HP-RX4640, Compaq-Digital Alpha GS140, has run on several other platforms Computer for which the program is designed and others on which is has been tested:Unix, Linux Operating systems or monitors under which the program has been tested:FORTRAN-90 Programming language used:depends on problem; example given requires 60 MB Memory required to execute with typical data:yes No. of lines in distributed program, including test data, etc.:11 524 No. of bytes in distributed program, including test data, etc.:89 949 Distribution format:tar.gzip file Nature of the physical problem:By means of the Hartree-Fock plus BCS method using Skyrme type functionals, ev8 allows a study of the evolution of the binding energy of even-even nuclei for various shapes determined by the most general quadrupole constraint. Solution method:The program expands the single-particle wave-functions on a 3D Cartesian mesh. The nonlinear mean-field equations are solved by the
A novel numerical flux for the 3D Euler equations with general equation of state
NASA Astrophysics Data System (ADS)
Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik
2015-12-01
Here we extend the flux vector splitting approach recently proposed in E.F. Toro and M.E. Vázquez-Cendón (2012) [42]. The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
Seismic waves in 3-D: from mantle asymmetries to reliable seismic hazard assessment
NASA Astrophysics Data System (ADS)
Panza, Giuliano F.; Romanelli, Fabio
2014-10-01
A global cross-section of the Earth parallel to the tectonic equator (TE) path, the great circle representing the equator of net lithosphere rotation, shows a difference in shear wave velocities between the western and eastern flanks of the three major oceanic rift basins. The low-velocity layer in the upper asthenosphere, at a depth range of 120 to 200 km, is assumed to represent the decoupling between the lithosphere and the underlying mantle. Along the TE-perturbed (TE-pert) path, a ubiquitous LVZ, about 1,000-km-wide and 100-km-thick, occurs in the asthenosphere. The existence of the TE-pert is a necessary prerequisite for the existence of a continuous global flow within the Earth. Ground-shaking scenarios were constructed using a scenario-based method for seismic hazard analysis (NDSHA), using realistic and duly validated synthetic time series, and generating a data bank of several thousands of seismograms that account for source, propagation, and site effects. Accordingly, with basic self-organized criticality concepts, NDSHA permits the integration of available information provided by the most updated seismological, geological, geophysical, and geotechnical databases for the site of interest, as well as advanced physical modeling techniques, to provide a reliable and robust background for the development of a design basis for cultural heritage and civil infrastructures. Estimates of seismic hazard obtained using the NDSHA and standard probabilistic approaches are compared for the Italian territory, and a case-study is discussed. In order to enable a reliable estimation of the ground motion response to an earthquake, three-dimensional velocity models have to be considered, resulting in a new, very efficient, analytical procedure for computing the broadband seismic wave-field in a 3-D anelastic Earth model.
A fast rebinning algorithm for 3D positron emission tomography using John's equation
NASA Astrophysics Data System (ADS)
Defrise, Michel; Liu, Xuan
1999-08-01
Volume imaging in positron emission tomography (PET) requires the inversion of the three-dimensional (3D) x-ray transform. The usual solution to this problem is based on 3D filtered-backprojection (FBP), but is slow. Alternative methods have been proposed which factor the 3D data into independent 2D data sets corresponding to the 2D Radon transforms of a stack of parallel slices. Each slice is then reconstructed using 2D FBP. These so-called rebinning methods are numerically efficient but are approximate. In this paper a new exact rebinning method is derived by exploiting the fact that the 3D x-ray transform of a function is the solution to the second-order partial differential equation first studied by John. The method is proposed for two sampling schemes, one corresponding to a pair of infinite plane detectors and another one corresponding to a cylindrical multi-ring PET scanner. The new FORE-J algorithm has been implemented for this latter geometry and was compared with the approximate Fourier rebinning algorithm FORE and with another exact rebinning algorithm, FOREX. Results with simulated data demonstrate a significant improvement in accuracy compared to FORE, while the reconstruction time is doubled. Compared to FOREX, the FORE-J algorithm is slightly less accurate but more than three times faster.
Wave-equation Based Earthquake Location
NASA Astrophysics Data System (ADS)
Tong, P.; Yang, D.; Yang, X.; Chen, J.; Harris, J.
2014-12-01
Precisely locating earthquakes is fundamentally important for studying earthquake physics, fault orientations and Earth's deformation. In industry, accurately determining hypocenters of microseismic events triggered in the course of a hydraulic fracturing treatment can help improve the production of oil and gas from unconventional reservoirs. We develop a novel earthquake location method based on solving full wave equations to accurately locate earthquakes (including microseismic earthquakes) in complex and heterogeneous structures. Traveltime residuals or differential traveltime measurements with the waveform cross-correlation technique are iteratively inverted to obtain the locations of earthquakes. The inversion process involves the computation of the Fréchet derivative with respect to the source (earthquake) location via the interaction between a forward wavefield emitting from the source to the receiver and an adjoint wavefield reversely propagating from the receiver to the source. When there is a source perturbation, the Fréchet derivative not only measures the influence of source location but also the effects of heterogeneity, anisotropy and attenuation of the subsurface structure on the arrival of seismic wave at the receiver. This is essential for the accuracy of earthquake location in complex media. In addition, to reduce the computational cost, we can first assume that seismic wave only propagates in a vertical plane passing through the source and the receiver. The forward wavefield, adjoint wavefield and Fréchet derivative with respect to the source location are all computed in a 2D vertical plane. By transferring the Fréchet derivative along the horizontal direction of the 2D plane into the ones along Latitude and Longitude coordinates or local 3D Cartesian coordinates, the source location can be updated in a 3D geometry. The earthquake location obtained with this combined 2D-3D approach can then be used as the initial location for a true 3D wave-equation
Field structure of collapsing wave packets in 3D strong Langmuir turbulence
NASA Technical Reports Server (NTRS)
Newman, D. L.; Robinson, P. A.; Goldman, M. V.
1989-01-01
A simple model is constructed for the electric fields in the collapsing wave packets found in 3D simulations of driven and damped isotropic strong Langmuir turbulence. This model, based on a spherical-harmonic decomposition of the electrostatic potential, accounts for the distribution of wave-packet shapes observed in the simulations, particularly the predominance of oblate wave packets. In contrast with predictions for undamped and undriven subsonic collapse of scalar fields, oblate vector-field wave packets do not flatten during collapse but, instead, remain approximately self-similar and rigid.
Luquet, David; Marchiano, Régis; Coulouvrat, François
2015-10-28
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
NASA Astrophysics Data System (ADS)
Luquet, David; Marchiano, Régis; Coulouvrat, François
2015-10-01
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
Nonhydrostatic granular flow over 3-D terrain: New Boussinesq-type gravity waves?
NASA Astrophysics Data System (ADS)
Castro-Orgaz, Oscar; Hutter, Kolumban; Giraldez, Juan V.; Hager, Willi H.
2015-01-01
granular mass flow is a basic step in the prediction and control of natural or man-made disasters related to avalanches on the Earth. Savage and Hutter (1989) pioneered the mathematical modeling of these geophysical flows introducing Saint-Venant-type mass and momentum depth-averaged hydrostatic equations using the continuum mechanics approach. However, Denlinger and Iverson (2004) found that vertical accelerations in granular mass flows are of the same order as the gravity acceleration, requiring the consideration of nonhydrostatic modeling of granular mass flows. Although free surface water flow simulations based on nonhydrostatic depth-averaged models are commonly used since the works of Boussinesq (1872, 1877), they have not yet been applied to the modeling of debris flow. Can granular mass flow be described by Boussinesq-type gravity waves? This is a fundamental question to which an answer is required, given the potential to expand the successful Boussinesq-type water theory to granular flow over 3-D terrain. This issue is explored in this work by generalizing the basic Boussinesq-type theory used in civil and coastal engineering for more than a century to an arbitrary granular mass flow using the continuum mechanics approach. Using simple test cases, it is demonstrated that the above question can be answered in the affirmative way, thereby opening a new framework for the physical and mathematical modeling of granular mass flow in geophysics, whereby the effect of vertical motion is mathematically included without the need of ad hoc assumptions.
Efficient solution on solving 3D Maxwell equations using stable semi-implicit splitting method
NASA Astrophysics Data System (ADS)
Cen, Wei; Gu, Ning
2016-05-01
In this paper, we propose an efficient solution on solving 3-dimensional (3D) time-domain Maxwell equations using the semi-implicit Crank-Nicholson (CN) method for time domain discretization with advantage of unconditional time stability. By applying the idea of fractional steps method (FSM) to the CN scheme, the proposed method provides a much simpler and efficient implementation than a direct implementation of the CN scheme. Compared with the alternating-direction implicit (ADI) method and explicit finite-difference time-domain approach (FDTD), it significantly saves the computational resource like memory and CPU time while remains similar numerical accuracy.
Fast and Robust Sixth Order Multigrid Computation for 3D Convection Diffusion Equation.
Wang, Yin; Zhang, Jun
2010-10-15
We present a sixth order explicit compact finite difference scheme to solve the three dimensional (3D) convection diffusion equation. We first use multiscale multigrid method to solve the linear systems arising from a 19-point fourth order discretization scheme to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator based interpolation scheme combined with an extrapolation technique is used to approximate the sixth order accurate solution on the fine grid. Since the multigrid method using a standard point relaxation smoother may fail to achieve the optimal grid independent convergence rate for solving convection diffusion equation with a high Reynolds number, we implement the plane relaxation smoother in the multigrid solver to achieve better grid independency. Supporting numerical results are presented to demonstrate the efficiency and accuracy of the sixth order compact scheme (SOC), compared with the previously published fourth order compact scheme (FOC). PMID:21151737
A CNN-based approach to integrate the 3-D turbolent diffusion equation
NASA Astrophysics Data System (ADS)
Nunnari, G.
2003-04-01
The paper deals with the integration of the 3-D turbulent diffusion equation. This problem is relevant in several application fields including fluid dynamics, air/water pollution, volcanic ash emissions and industrial hazard assessment. As it is well known numerical solution of such a kind of equation is very time consuming even by using modern digital computers and this represents a short-coming for on-line applications. To overcome this drawback a Cellular Neural Network Approach is proposed in this paper. CNN's proposed by Chua and Yang in 1988 are massive parallel analog non-linear circuits with local interconnections between the computing elements that allow very fast distributed computations. Nowadays several producers of semiconductors such as SGS-Thomson are producing on chip CNN's so that their massive use for heavy computing applications is expected in the near future. In the paper the methodological background of the proposed approach will be outlined. Further some results both in terms of accuracy and computation time will be presented also in comparison with traditional three-dimensional computation schemes. Some results obtained to model 3-D pollution problems in the industrial area of Siracusa (Italy), characterised by a large concentration of petrol-chemical plants, will be presented.
Fast Wave Trains Associated with Solar Eruptions: Insights from 3D Thermodynamic MHD Simulations
NASA Astrophysics Data System (ADS)
Downs, C.; Liu, W.; Torok, T.; Linker, J.; Mikic, Z.; Ofman, L.
2015-12-01
EUV imaging observations during the SDO/AIA era have provided new insights into a variety of wave phenomena occurring in the low solar corona. One example is the observation of quasi-periodic, fast-propagating wave trains that are associated with solar eruptions, including flares and CMEs. While there has been considerable progress in understanding such waves from both an observational and theoretical perspective, it remains a challenge to pin down their physical origin. In this work, we detail our results from a case-study 3D thermodynamic MHD simulation of a coronal mass ejection where quasi-periodic wave trains are generated during the simulated eruption. We find a direct correlation between the onset of non-steady reconnection in the flare current sheet and the generation of quasi-periodic wave train signatures when patchy, collimated downflows interact with the flare arcade. Via forward modeling of SDO/AIA observables, we explore how the appearance of the wave trains is affected by line-of-sight integration and the multi-thermal nature of the coronal medium. We also examine how the wave trains themselves are channeled by natural waveguides formed in 3D by the non-uniform background magnetic field. While the physical association of the reconnection dynamics to the generation of quasi-periodic wave trains appears to be a compelling result, unanswered questions posed from recent observations as well as future prospects will be discussed.
New equations to calculate 3D joint centres in the lower extremities.
Sandau, Martin; Heimbürger, Rikke V; Villa, Chiara; Jensen, Karl E; Moeslund, Thomas B; Aanæs, Henrik; Alkjær, Tine; Simonsen, Erik B
2015-10-01
Biomechanical movement analysis in 3D requires estimation of joint centres in the lower extremities and this estimation is based on extrapolation from markers placed on anatomical landmarks. The purpose of the present study was to quantify the accuracy of three established set of equations and provide new improved equations to predict the joint centre locations. The 'true' joint centres of the knee and ankle joint were obtained in vivo by MRI scans on 10 male subjects whereas the 'true' hip joint centre was obtained in 10 male and 10 female cadavers by CT scans. For the hip joint the errors ranged from 26.7 (8.9) to 29.6 (7.5) mm, for the knee joint 5.8 (3.1) to 22.6 (3.3) mm and for the ankle joint 14.4 (2.2) to 27.0 (4.6) mm. This differed significantly from the improved equations by which the error for the hip joint ranged from 8.2 (3.6) to 11.6 (5.6) mm, for the knee joint from 2.9 (2.1) to 4.7 (2.5) mm and for the ankle joint from 3.4 (1.3) to 4.1 (2.0) mm. The coefficients in the new hip joint equations differed significantly between sexes. This difference depends on anatomical differences of the male and female pelvis. PMID:26320760
Vdovin V.L.
2005-08-15
In this report we describe theory and 3D full wave code description for the wave excitation, propagation and absorption in 3-dimensional (3D) stellarator equilibrium high beta plasma in ion cyclotron frequency range (ICRF). This theory forms a basis for a 3D code creation, urgently needed for the ICRF heating scenarios development for the operated LHD, constructed W7-X, NCSX and projected CSX3 stellarators, as well for re evaluation of ICRF scenarios in operated tokamaks and in the ITER . The theory solves the 3D Maxwell-Vlasov antenna-plasma-conducting shell boundary value problem in the non-orthogonal flux coordinates ({Psi}, {theta}, {var_phi}), {Psi} being magnetic flux function, {theta} and {var_phi} being the poloidal and toroidal angles, respectively. All basic physics, like wave refraction, reflection and diffraction are self consistently included, along with the fundamental ion and ion minority cyclotron resonances, two ion hybrid resonance, electron Landau and TTMP absorption. Antenna reactive impedance and loading resistance are also calculated and urgently needed for an antenna -generator matching. This is accomplished in a real confining magnetic field being varying in a plasma major radius direction, in toroidal and poloidal directions, through making use of the hot dense plasma wave induced currents with account to the finite Larmor radius effects. We expand the solution in Fourier series over the toroidal ({var_phi}) and poloidal ({theta}) angles and solve resulting ordinary differential equations in a radial like {Psi}-coordinate by finite difference method. The constructed discretization scheme is divergent-free one, thus retaining the basic properties of original equations. The Fourier expansion over the angle coordinates has given to us the possibility to correctly construct the ''parallel'' wave number k{sub //}, and thereby to correctly describe the ICRF waves absorption by a hot plasma. The toroidal harmonics are tightly coupled with each
NASA Astrophysics Data System (ADS)
Chen, Duan; Cai, Wei; Zinser, Brian; Cho, Min Hyung
2016-09-01
In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for a large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for cubes, spheres and cylinders, that are frequently encountered in the design of meta-materials. The resulting Nyström VIE method is shown to have high accuracy with a small number of collocation points and demonstrates p-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic, spherical, and cylindrical shapes validate the efficiency and accuracy of the proposed method.
Importance of a 3D forward modeling tool for surface wave analysis methods
NASA Astrophysics Data System (ADS)
Pageot, Damien; Le Feuvre, Mathieu; Donatienne, Leparoux; Philippe, Côte; Yann, Capdeville
2016-04-01
Since a few years, seismic surface waves analysis methods (SWM) have been widely developed and tested in the context of subsurface characterization and have demonstrated their effectiveness for sounding and monitoring purposes, e.g., high-resolution tomography of the principal geological units of California or real time monitoring of the Piton de la Fournaise volcano. Historically, these methods are mostly developed under the assumption of semi-infinite 1D layered medium without topography. The forward modeling is generally based on Thomson-Haskell matrix based modeling algorithm and the inversion is driven by Monte-Carlo sampling. Given their efficiency, SWM have been transfered to several scale of which civil engineering structures in order to, e.g., determine the so-called V s30 parameter or assess other critical constructional parameters in pavement engineering. However, at this scale, many structures may often exhibit 3D surface variations which drastically limit the efficiency of SWM application. Indeed, even in the case of an homogeneous structure, 3D geometry can bias the dispersion diagram of Rayleigh waves up to obtain discontinuous phase velocity curves which drastically impact the 1D mean velocity model obtained from dispersion inversion. Taking advantages of high-performance computing center accessibility and wave propagation modeling algorithm development, it is now possible to consider the use of a 3D elastic forward modeling algorithm instead of Thomson-Haskell method in the SWM inversion process. We use a parallelized 3D elastic modeling code based on the spectral element method which allows to obtain accurate synthetic data with very low numerical dispersion and a reasonable numerical cost. In this study, we choose dike embankments as an illustrative example. We first show that their longitudinal geometry may have a significant effect on dispersion diagrams of Rayleigh waves. Then, we demonstrate the necessity of 3D elastic modeling as a forward
Computational time analysis of the numerical solution of 3D electrostatic Poisson's equation
NASA Astrophysics Data System (ADS)
Kamboh, Shakeel Ahmed; Labadin, Jane; Rigit, Andrew Ragai Henri; Ling, Tech Chaw; Amur, Khuda Bux; Chaudhary, Muhammad Tayyab
2015-05-01
3D Poisson's equation is solved numerically to simulate the electric potential in a prototype design of electrohydrodynamic (EHD) ion-drag micropump. Finite difference method (FDM) is employed to discretize the governing equation. The system of linear equations resulting from FDM is solved iteratively by using the sequential Jacobi (SJ) and sequential Gauss-Seidel (SGS) methods, simulation results are also compared to examine the difference between the results. The main objective was to analyze the computational time required by both the methods with respect to different grid sizes and parallelize the Jacobi method to reduce the computational time. In common, the SGS method is faster than the SJ method but the data parallelism of Jacobi method may produce good speedup over SGS method. In this study, the feasibility of using parallel Jacobi (PJ) method is attempted in relation to SGS method. MATLAB Parallel/Distributed computing environment is used and a parallel code for SJ method is implemented. It was found that for small grid size the SGS method remains dominant over SJ method and PJ method while for large grid size both the sequential methods may take nearly too much processing time to converge. Yet, the PJ method reduces computational time to some extent for large grid sizes.
NASA Astrophysics Data System (ADS)
Tago, J.; Cruz-Atienza, V. M.; Etienne, V.; Virieux, J.; Benjemaa, M.; Sanchez-Sesma, F. J.
2010-12-01
Simulating any realistic seismic scenario requires incorporating physical basis into the model. Considering both the dynamics of the rupture process and the anelastic attenuation of seismic waves is essential to this purpose and, therefore, we choose to extend the hp-adaptive Discontinuous Galerkin finite-element method to integrate these physical aspects. The 3D elastodynamic equations in an unstructured tetrahedral mesh are solved with a second-order time marching approach in a high-performance computing environment. The first extension incorporates the viscoelastic rheology so that the intrinsic attenuation of the medium is considered in terms of frequency dependent quality factors (Q). On the other hand, the extension related to dynamic rupture is integrated through explicit boundary conditions over the crack surface. For this visco-elastodynamic formulation, we introduce an original discrete scheme that preserves the optimal code performance of the elastodynamic equations. A set of relaxation mechanisms describes the behavior of a generalized Maxwell body. We approximate almost constant Q in a wide frequency range by selecting both suitable relaxation frequencies and anelastic coefficients characterizing these mechanisms. In order to do so, we solve an optimization problem which is critical to minimize the amount of relaxation mechanisms. Two strategies are explored: 1) a least squares method and 2) a genetic algorithm (GA). We found that the improvement provided by the heuristic GA method is negligible. Both optimization strategies yield Q values within the 5% of the target constant Q mechanism. Anelastic functions (i.e. memory variables) are introduced to efficiently evaluate the time convolution terms involved in the constitutive equations and thus to minimize the computational cost. The incorporation of anelastic functions implies new terms with ordinary differential equations in the mathematical formulation. We solve these equations using the same order
The Vajont disaster: a 3D numerical simulation for the slide and the waves
NASA Astrophysics Data System (ADS)
Rubino, Angelo; Androsov, Alexey; Vacondio, Renato; Zanchettin, Davide; Voltzinger, Naum
2016-04-01
A very high resolution O(5 m), 3D hydrostatic nonlinear numerical model was used to simulate the dynamics of both the slide and the surface waves produced during the Vajont disaster (north Italy, 1963), one of the major landslide-induced tsunamis ever documented. Different simulated wave phenomena like, e.g., maximum run-up on the opposite shore, maximum height, and water velocity were analyzed and compared with data available in literature, including the results of a fully 3D simulation obtained with a Smoothed Particle Hydrodynamic code. The difference between measured and simulated after-slide bathymetries was calculated and used in an attempt to quantify the relative magnitude and extension of rigid and fluid motion components during the event.
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1988-01-01
An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.
Wave equation on spherically symmetric Lorentzian metrics
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.
2011-06-15
Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.
Nonlinear Evolution of a 3D Inertial Alfvén Wave and Its Implication in Particle Acceleration
NASA Astrophysics Data System (ADS)
Sharma, Prachi; Yadav, Nitin; Sharma, R. P.
2016-03-01
A simulation based on a pseudo-spectral method has been performed in order to study particle acceleration. A model for the acceleration of charged particles by field localization is developed for the low-β plasma. For this purpose, a fractional diffusion approach has been employed. The nonlinear interaction between a 3D inertial Alfvén wave and a slow magnetosonic wave has been examined, and the dynamical equations of these two waves in the presence of ponderomotive nonlinearity have been solved numerically. The nonlinear evolution of the inertial Alfvén wave in the presence of slow magnetosonic wave undergoes a filamentation instability and results in field intensity localization. The results obtained show the localization and power spectrum of inertial Alfvén wave due to nonlinear coupling. The scaling obtained after the first break point of the magnetic power spectrum has been used to calculate the formation of the thermal tail of energetic particles in the solar corona.
A Self-Consistent Beam Loaded Travelling Wave Accelerator Model for use in TRACE-3D
NASA Astrophysics Data System (ADS)
Lampel, M. C.
1997-05-01
An optics model of a constant gradient traveling wave (CGTW) accelerator structure has been implemented for TRACE-3D. TRACE-3D is an envelope code including space charge that is used to model bunched beams in magnetic transport systems and radio frequency (rf) accelerators when the effects of beam current might be significant. The new matrix model has been developed to allow incorporation of particle beam loading (current) effects on the accelerator gradient and the accelerator structure's beam focusing properties in a self-consistent manner. The beam loaded electric field for a CGTW accelerator structure is constant for only a particular design current (e.g., 0 current), otherwise it can be written as a function of accelerator attenuation and axial position along the structure. The variation of the electric field through the structure has been taken into account in the new model. CGTW structures differ substantially in focusing properties and beam loading properties from standing wave structures. Examples will be presented using the new TW model, propagating electron beams with different currents through the Stanford Linear Accelerator Center's 3 m structure. The results will be compared to the zero current TW structure model in TRANSPORT and the Tank model (a standing wave structure model) in TRACE-3D. A computer demonstration of the code with the new element will also be presented.
Ocular surface temperature: a 3D FEM prediction using bioheat equation.
Ng, E Y K; Ooi, E H
2007-06-01
Computational and mathematical human eye models from previous studies which were constructed in two-dimensions (2D) did not give a precise representation of the actual human eye. This work is an extension from an earlier published work on the 2D model. In this paper, a 3D FEM model of the human eye is simulated for the steady state temperature distribution during normal condition and during electromagnetic (EM) wave radiation. Results show a discrepancy of 0.49% for a normal condition as opposed to 1.9% of a 2D model when compared to experimental results from open literatures. Investigations on the EM wave radiations found an average power absorption density of 15,151 and 22,145 Wm(-3) for the 750 and 1500 MHz radiation, respectively. A peak temperature of 38.18( composite function)C was predicted for the 750 MHz radiation while 41.19( composite function)C was computed for the 1500 MHz radiation. These temperatures are in reasonable agreement with the simulated results computed by another report in the past. PMID:17034781
NASA Astrophysics Data System (ADS)
Wang, S.; De Hoop, M. V.; Xia, J.; Li, X.
2011-12-01
We consider the modeling of elastic seismic wave propagation on a rectangular domain via the discretization and solution of the inhomogeneous coupled Helmholtz equation in 3D, by exploiting a parallel multifrontal sparse direct solver equipped with Hierarchically Semi-Separable (HSS) structure to reduce the computational complexity and storage. In particular, we are concerned with solving this equation on a large domain, for a large number of different forcing terms in the context of seismic problems in general, and modeling in particular. We resort to a parsimonious mixed grid finite differences scheme for discretizing the Helmholtz operator and Perfect Matched Layer boundaries, resulting in a non-Hermitian matrix. We make use of a nested dissection based domain decomposition, and introduce an approximate direct solver by developing a parallel HSS matrix compression, factorization, and solution approach. We cast our massive parallelization in the framework of the multifrontal method. The assembly tree is partitioned into local trees and a global tree. The local trees are eliminated independently in each processor, while the global tree is eliminated through massive communication. The solver for the inhomogeneous equation is a parallel hybrid between multifrontal and HSS structure. The computational complexity associated with the factorization is almost linear with the size of the Helmholtz matrix. Our numerical approach can be compared with the spectral element method in 3D seismic applications.
NASA Astrophysics Data System (ADS)
Belashov, Vasily
We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega
Implicit scheme for Maxwell equations solution in case of flat 3D domains
NASA Astrophysics Data System (ADS)
Boronina, Marina; Vshivkov, Vitaly
2016-02-01
We present a new finite-difference scheme for Maxwell's equations solution for three-dimensional domains with different scales in different directions. The stability condition of the standard leap-frog scheme requires decreasing of the time-step with decreasing of the minimal spatial step, which depends on the minimal domain size. We overcome the conditional stability by modifying the standard scheme adding implicitness in the direction of the smallest size. The new scheme satisfies the Gauss law for the electric and magnetic fields in the final- differences. The approximation order, the maintenance of the wave amplitude and propagation speed, the invariance of the wave propagation on angle with the coordinate axes are analyzed.
NASA Astrophysics Data System (ADS)
Lieske, Mike; Schlurmann, Torsten
2016-04-01
INTRODUCTION & MOTIVATION The design of structures in coastal and offshore areas and their maintenance are key components of coastal protection. Usually, assessments of processes and loads on coastal structures are derived from experiments with flow and wave parameters in separate physical models. However, Peregrin (1976) already points out that processes in natural shallow coastal waters flow and sea state processes do not occur separately, but influence each other nonlinearly. Kemp & Simons (1982) perform 2D laboratory tests and study the interactions between a turbulent flow and following waves. They highlight the significance of wave-induced changes in the current properties, especially in the mean flow profiles, and draw attention to turbulent fluctuations and bottom shear stresses. Kemp & Simons (1983) also study these processes and features with opposing waves. Studies on the wave-current interaction in three-dimensional space for a certain wave height, wave period and water depth were conducted by MacIver et al. (2006). The research focus is set on the investigation of long-crested waves on obliquely opposing and following currents in the new 3D wave-current basin. METHODOLOGY In a first step the flow analysis without waves is carried out and includes measurements of flow profiles in the sweet spot of the basin at predefined measurement positions. Five measuring points in the water column have been delineated in different water depths in order to obtain vertical flow profiles. For the characterization of the undisturbed flow properties in the basin, an uniformly distributed flow was generated in the wave basin. In the second step wave analysis without current, the unidirectional wave propagation and wave height were investigated for long-crested waves in intermediate wave conditions. In the sweet spot of the wave basin waves with three different wave directions, three wave periods and uniform wave steepness were examined. For evaluation, we applied a common
On the Finite-Time Splash and Splat Singularities for the 3-D Free-Surface Euler Equations
NASA Astrophysics Data System (ADS)
Coutand, Daniel; Shkoller, Steve
2014-01-01
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in Castro et al. (Splash singularity for water waves, http://arxiv.org/abs/1106.2120v2, 2011), wherein the evolving 2-D hypersurface, the moving boundary of the fluid domain, self-intersects at a point (or on surface). Such singularities can occur when the crest of a breaking wave falls unto its trough, or in the study of drop impact upon liquid surfaces. Our approach is founded upon the Lagrangian description of the free-boundary problem, combined with a novel approximation scheme of a finite collection of local coordinate charts; as such we are able to analyze a rather general set of geometries for the evolving 2-D free-surface of the fluid. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems, including compressible flows, plasmas, as well as the inclusion of surface tension effects.
An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids
NASA Astrophysics Data System (ADS)
Kokonkov, N. I.; Nikolaeva, O. V.
2015-10-01
A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.
3D resolution tests of two-plane wave approach using synthetic seismograms
NASA Astrophysics Data System (ADS)
Ceylan, S.; Larmat, C. S.; Sandvol, E. A.
2012-12-01
Two-plane wave tomography (TPWT) is becoming a standard approach to obtain fundamental mode Rayleigh wave phase velocities for a variety of tectonic settings. A recent study by Ceylan et al. (2012) has applied this method to eastern Tibet, using data from INDEPTH-IV and Namche-Barwa seismic experiments. The TPWT assumes that distortion of wavefronts at each station can be expressed as the sum of two plane waves. However, there is currently no robust or complete resolution test for TPWT, to address its limitations such as wavefront healing. In this study, we test the capabilities of TPWT and resolution of INDEPTH-IV seismic experiment, by performing 3D resolution tests using synthetic seismograms. Utilizing SPECFEM3D software, we compute synthetic data sets resolving periods down to ~30 s. We implement a checkerboard upper mantle (for depths between 50 and 650 km) with variable cell sizes, superimposed to PREM as the background model. We then calculate fundamental mode surface wave phase velocities using TPWT for periods between 33-143 seconds, using synthetic seismograms computed from our three dimensional hypothetical model. Assuming a constant Poisson's ratio, we use partial derivatives from Saito (1988) to invert for shear wave velocities. We show that the combination of TPWT and Saito (1988) methods is capable of retrieving anomalies down to depths of ~200 km for Rayleigh waves. Below these depths, we observe evidence of both lateral and vertical smearing. We also find that the traditional method for estimating the resolution of TPWT consistently overestimates phase velocity resolutions. Love waves exhibit adequate resolution down to depths of ~100 km. At depths greater than 100 km, smearing is more evident in SH wave results than those of SV waves. Increased smearing of SH waves is most probably due to propagation characteristics and shallower sensitivity of Love waves. Our results imply that TPWT can be applied to Love waves, making future investigations of
Multiple-mode Lamb wave scattering simulations using 3D elastodynamic finite integration technique.
Leckey, Cara A C; Rogge, Matthew D; Miller, Corey A; Hinders, Mark K
2012-02-01
We have implemented three-dimensional (3D) elastodynamic finite integration technique (EFIT) simulations to model Lamb wave scattering for two flaw-types in an aircraft-grade aluminum plate, a rounded rectangle flat-bottom hole and a disbond of the same shape. The plate thickness and flaws explored in this work include frequency-thickness regions where several Lamb wave modes exist and sometimes overlap in phase and/or group velocity. For the case of the flat-bottom hole the depth was incrementally increased to explore progressive changes in multiple-mode Lamb wave scattering due to the damage. The flat-bottom hole simulation results have been compared to experimental data and are shown to provide key insight for this well-defined experimental case by explaining unexpected results in experimental waveforms. For the rounded rectangle disbond flaw, which would be difficult to implement experimentally, we found that Lamb wave behavior differed significantly from the flat-bottom hole flaw. Most of the literature in this field is restricted to low frequency-thickness regions due to difficulties in interpreting data when multiple modes exist. We found that benchmarked 3D EFIT simulations can yield an understanding of scattering behavior for these higher frequency-thickness regions and in cases that would be difficult to set up experimentally. Additionally, our results show that 2D simulations would not have been sufficient for modeling the complicated scattering that occurred. PMID:21908011
3-D P Wave Velocity Structure of Marmara Region Using Local Earthquake Tomography
NASA Astrophysics Data System (ADS)
Işık, S. E.; Gurbuz, C.
2014-12-01
The 3D P wave velocity model of upper and lower crust of the Marmara Region between 40.200- 41.200N and 26.500- 30.500E is obtained by tomographic inversion (Simulps) of 47034 P wave arrivals of local earthquakes recorded at 90 land stations between October 2009 and December 2012 and 30 OBO stations and 14162 shot arrivals recorded at 35 OBO stations (Seismarmara Survey, 2001). We first obtained a 1D minimum model with Velest code in order to obtain an initial model for 3D inversion with 648 well located earthquakes located within the study area. After several 3D inversion trials we decided to create a more adequate initial model for 3D inversion. Choosing the initial model we estimated the 3D P wave velocity model representing the whole region both for land and sea. The results are tested by making Checkerboard , Restoring Resolution and Characteristic Tests, and the reliable areas of the resulting model is defined in terms of RDE, DWS, SF and Hit count distributions. By taking cross sections from the resulting model we observed the vertical velocity change along profiles crossing both land and sea. All the profiles crossing the basins showed that the high velocities of lower crust make extensions towards the basin area which looks like the force that gives a shape to the basins. These extensions of lower crust towards the basins appeared with an average velocity of 6.3 km/s which might be the result of the deformation due the shearing in the region. It is also interpreted that the development of these high velocities coincide with the development of the basins. Thus, both the basins and the high velocity zones around them might be resulted from the entrance of the NAF into the Marmara Sea and at the same time a shear regime was dominated due to the resistance of the northern Marmara Region (Yılmaz, 2010). The seismicity is observed between 5 km and 15 km after the 3D location of the earthquakes. The locations of the earthquakes improved and the seismogenic zone
NASA Astrophysics Data System (ADS)
Wilder, F. D.; Ergun, R.; Goodrich, K.; Malaspina, D.; Eriksson, S.; Stawarz, J. E.; Sturner, A. P.; Holmes, J.; Burch, J. L.; Torbert, R. B.; Phan, T.; Le Contel, O.; Goldman, M. V.; Newman, D. L.; Lindqvist, P. A.; Khotyaintsev, Y. V.; Strangeway, R. J.; Russell, C. T.; Giles, B. L.; Pollock, C. J.
2015-12-01
The phenomenon of magnetic reconnection, especially at electron scales, is still poorly understood. One process that warrants further investigation is the role of wave phenomenon in mediating magnetic reconnection. Previous observations have shown the presence of electrostatic solitary waves (ESWs) as well as whistler mode waves near the dayside reconnection site. Additionally, recent simulations have suggested that whistler waves might be generated by electron phase space holes associated with ESWs as they propagate along the magnetic separatrix towards the diffusion region. Other observations have shown ESWs with distinct speeds and time scales, suggesting that different instabilities generate the ESWs. NASA's recently launched Magnetospheric Multiscale (MMS) mission presents a unique opportunity to investigate the roles of wave phenomena, such as ESWs and whistlers, in asymmetric reconnection at the dayside magnetopause. We will present 3-D electric and magnetic field data from magnetopause crossings by MMS during its first dayside science phase. Burst mode wave data and electron distributions from all four spacecraft will be analyzed to investigate the origin of these wave phenomena, as well as their impact on the reconnection electric field.
Simulating Seismic Wave Propagation in 3-D Structure: A Case Study For Istanbul City
NASA Astrophysics Data System (ADS)
Yelkenci, Seda; Aktar, Mustafa
2013-04-01
Investigation of the wave propagation around the Marmara Sea, in particular for the city of Istanbul is critical because this target area is identified as one of the megacities with the highest seismic risk in the world. This study makes an attempt for creating an integrated 3D seismic/geologic model and precise understanding of 3-D wave propagation in the city of Istanbul. The approach is based on generating synthetic seismograms using realistic velocity structures as well as accurate location, focal mechanism and source parameters of reference earthquakes. The modarate size reference earthquakes occured in the Marmara Sea and were recorded by the National Seismic Network of Turkey as well as the network of Istanbul Early Warning and Rapid Response System. The seismograms are simulated by means of a 3-D finite difference method operated on parallel processing environment. In the content of creating a robust velocity model; 1D velocity models which are derived fom previous crustal studies of Marmara region such as refraction seismic and receiver functions have been conducted firstly for depths greater than 1km. Velocity structure in shallower part of the study region is then derived from recent geophysical and geotechnical surveys. To construct 3-D model from the obtained 1-D model data, a variety of interpolation methods are considered. According to the observations on amplitude and arrival time based on comparison of simulated seismograms, the considered velocity model is refined the way that S delay times are compensated. Another important task of this work is an application of the finite difference method to estimate three-dimensional seismic responses for a specified basin structure including soft sediments with low shear velocities in respect of the surrounded area in the Asian part of Istanbul. The analysis performed both in the time and frequency domain, helps in understanding of the comprehensive wave propagation characteristics and the distribution of
3D P-Wave Velocity Structure of the Deep Galicia Rifted Margin
NASA Astrophysics Data System (ADS)
Bayrakci, Gaye; Minshull, Timothy; Davy, Richard; Sawyer, Dale; Klaeschen, Dirk; Papenberg, Cord; Reston, Timothy; Shillington, Donna; Ranero, Cesar
2015-04-01
The combined wide-angle reflection-refraction and multi-channel seismic (MCS) experiment, Galicia 3D, was carried out in 2013 at the Galicia rifted margin in the northeast Atlantic Ocean, west of Spain. The main geological features within the 64 by 20 km (1280 km²) 3D box investigated by the survey are the peridotite ridge (PR), the fault bounded, rotated basement blocks and the S reflector, which has been interpreted to be a low angle detachment fault. 44 short period four-component ocean bottom seismometers and 28 ocean bottom hydrophones were deployed in the 3D box. 3D MCS profiles sampling the whole box were acquired with two airgun arrays of 3300 cu.in. fired alternately every 37.5 m. We present the results from 3D first-arrival time tomography that constrains the P-wave velocity in the 3D box, for the entire depth sampled by reflection data. Results are validated by synthetic tests and by the comparison with Galicia 3D MCS lines. The main outcomes are as follows: 1- The 3.5 km/s iso-velocity contour mimics the top of the acoustic basement observed on MCS profiles. Block bounding faults are imaged as velocity contrasts and basement blocks exhibit 3D topographic variations. 2- On the southern profiles, the top of the PR rises up to 5.5 km depth whereas, 20 km northward, its basement expression (at 6.5 km depth) nearly disappears. 3- The 6.5 km/s iso-velocity contour matches the topography of the S reflector where the latter is visible on MCS profiles. Within a depth interval of 0.6 km (in average), velocities beneath the S reflector increase from 6.5 km/s to 7 km/s, which would correspond to a decrease in the degree of serpentinization from ~45 % to ~30 % if these velocity variations are caused solely by variations in hydration. At the intersections between the block bounding normal faults and the S reflector, this decrease happens over a larger depth interval (> 1 km), suggesting that faults act as conduit for the water flow in the upper mantle.
Concealed threat detection with the IRAD sub-millimeter wave 3D imaging radar
NASA Astrophysics Data System (ADS)
Robertson, Duncan A.; Cassidy, Scott L.; Jones, Ben; Clark, Anthony
2014-06-01
Sub-millimeter wave 3D imaging radar is a promising technology for the stand-off detection of threats concealed on people. The IRAD 340 GHz 3D imaging radar uses polarization intensity information to identify signatures associated with concealed threats. We report on an extensive trials program which has been carried out involving dozens of individual subjects wearing a variety of different clothing to evaluate the detection of a wide range of threat and benign items. We have developed an automatic algorithm to run on the radar which yields a level of anomaly indication in real time. Statistical analysis of the large volume of recorded data has enabled performance metrics for the radar system to be evaluated.
Efficient 3D/1D self-consistent integral-equation analysis of ICRH antennae
NASA Astrophysics Data System (ADS)
Maggiora, R.; Vecchi, G.; Lancellotti, V.; Kyrytsya, V.
2004-08-01
This work presents a comprehensive account of the theory and implementation of a method for the self-consistent numerical analysis of plasma-facing ion-cyclotron resonance heating (ICRH) antenna arrays. The method is based on the integral-equation formulation of the boundary-value problem, solved via a weighted-residual scheme. The antenna geometry (including Faraday shield bars and a recess box) is fairly general and three-dimensional (3D), and the plasma is in the one-dimensional (1D) 'slab' approximation; finite-Larmor radius effects, as well as plasma density and temperature gradients, are considered. Feeding via the voltages in the access coaxial lines is self-consistently accounted throughout and the impedance or scattering matrix of the antenna array obtained therefrom. The problem is formulated in both the dual space (physical) and spectral (wavenumber) domains, which allows the extraction and simple handling of the terms that slow the convergence in the spectral domain usually employed. This paper includes validation tests of the developed code against measured data, both in vacuo and in the presence of plasma. An example of application to a complex geometry is also given.
NASA Astrophysics Data System (ADS)
Abdi, Daniel S.; Giraldo, Francis X.
2016-09-01
A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods, namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine how classical CG that uses a global storage scheme can be constructed within the DG framework using constraint imposition techniques commonly used in the finite element literature. Then, we implement and test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the case of explicit time integration and a diagonal mass matrix. Constructing CG within the DG framework allows CG to benefit from the desirable properties of DG such as, easier hp-refinement, better stability etc. Moreover, this representation allows for regional mixing of CG and DG depending on the flow regime in an area. The different flavors of CG and DG in the unified implementation are then tested for accuracy and performance using a suite of benchmark problems representative of cloud-resolving scale, meso-scale and global-scale atmospheric dynamics. The value of our unified approach is that we are able to show how to carry both CG and DG methods within the same code and also offer a simple recipe for modifying an existing CG code to DG and vice versa.
An efficient flexible-order model for 3D nonlinear water waves
Engsig-Karup, A.P. Bingham, H.B.; Lindberg, O.
2009-04-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.
NASA Astrophysics Data System (ADS)
Woodbury, D.; Kubota, S.; Johnson, I.
2014-10-01
Computer simulations of electromagnetic wave propagation in magnetized plasmas are an important tool for both plasma heating and diagnostics. For active millimeter-wave and microwave diagnostics, accurately modeling the evolution of the beam parameters for launched, reflected or scattered waves in a toroidal plasma requires that calculations be done using the full 3-D geometry. Previously, we reported on the application of GPGPU (General-Purpose computing on Graphics Processing Units) to a 3-D vacuum Maxwell code using the FDTD (Finite-Difference Time-Domain) method. Tests were done for Gaussian beam propagation with a hard source antenna, utilizing the parallel processing capabilities of the NVIDIA K20M. In the current study, we have modified the 3-D code to include a soft source antenna and an induced current density based on the cold plasma approximation. Results from Gaussian beam propagation in an inhomogeneous anisotropic plasma, along with comparisons to ray- and beam-tracing calculations will be presented. Additional enhancements, such as advanced coding techniques for improved speedup, will also be investigated. Supported by U.S. DoE Grant DE-FG02-99-ER54527 and in part by the U.S. DoE, Office of Science, WDTS under the Science Undergraduate Laboratory Internship program.
3D Simulation of an Audible Ultrasonic Electrolarynx Using Difference Waves
Mills, Patrick; Zara, Jason
2014-01-01
A total laryngectomy removes the vocal folds which are fundamental in forming voiced sounds that make speech possible. Although implanted prosthetics are commonly used in developed countries, simple handheld vibrating electrolarynxes are still common worldwide. These devices are easy to use but suffer from many drawbacks including dedication of a hand, mechanical sounding voice, and sound leakage. To address some of these drawbacks, we introduce a novel electrolarynx that uses vibro-acoustic interference of dual ultrasonic waves to generate an audible fundamental frequency. A 3D simulation of the principles of the device is presented in this paper. PMID:25401965
3D rendering of passive millimeter-wave scenes using modified open source software
NASA Astrophysics Data System (ADS)
Murakowski, Maciej; Wilson, John; Murakowski, Janusz; Schneider, Garrett; Schuetz, Christopher; Prather, Dennis
2011-05-01
As millimeter-wave imaging technology becomes more mature, several applications are emerging for which this technology may be useful. However, effectively predicting the nuances of millimeter-wave phenomenology on the usefulness for a given application remains a challenge. To this end, an accurate millimeter-wave scene simulator would have tremendous value in predicting imager requirements for a given application. Herein, we present a passive millimeter-wave scene simulator built on the open-source 3d modeling software Blender. We describe the changes made to the Blender rendering engine to make it suitable for this purpose, including physically accurate reflections at each material interface, volumetric absorption and scattering, and tracking of both s and p polarizations. In addition, we have incorporated a mmW material database and world model that emulates the effects of cold sky profiles for varying weather conditions and frequencies of operation. The images produced by this model have been validated against calibrated experimental imagery captured by a passive scanning millimeter-wave imager for maritime, desert, and standoff detection applications.
Wave optics theory and 3-D deconvolution for the light field microscope
Broxton, Michael; Grosenick, Logan; Yang, Samuel; Cohen, Noy; Andalman, Aaron; Deisseroth, Karl; Levoy, Marc
2013-01-01
Light field microscopy is a new technique for high-speed volumetric imaging of weakly scattering or fluorescent specimens. It employs an array of microlenses to trade off spatial resolution against angular resolution, thereby allowing a 4-D light field to be captured using a single photographic exposure without the need for scanning. The recorded light field can then be used to computationally reconstruct a full volume. In this paper, we present an optical model for light field microscopy based on wave optics, instead of previously reported ray optics models. We also present a 3-D deconvolution method for light field microscopy that is able to reconstruct volumes at higher spatial resolution, and with better optical sectioning, than previously reported. To accomplish this, we take advantage of the dense spatio-angular sampling provided by a microlens array at axial positions away from the native object plane. This dense sampling permits us to decode aliasing present in the light field to reconstruct high-frequency information. We formulate our method as an inverse problem for reconstructing the 3-D volume, which we solve using a GPU-accelerated iterative algorithm. Theoretical limits on the depth-dependent lateral resolution of the reconstructed volumes are derived. We show that these limits are in good agreement with experimental results on a standard USAF 1951 resolution target. Finally, we present 3-D reconstructions of pollen grains that demonstrate the improvements in fidelity made possible by our method. PMID:24150383
Solving tolerancing and 3D beam shaping problems by multifunctional wave optical design
NASA Astrophysics Data System (ADS)
Buehling, Sven; Wyrowski, Frank
2000-10-01
A strategy for designing optical systems that are optimized for multiple optical functions on the basis of wave optics is presented. Each optical function is composed of an input field, a set of fixed system parameters, and a merit function. A design algorithm is proposed which is applicable for optical systems consisting of an transmission operator followed by an arbitrary linear operator. The goal is to find the transmission operator which is optimal for all optical functions simultaneously. In later design steps, the found transmission operator can be transformed to real optical elements, for instance by using the thin element approximation. It is shown that the algorithm is efficiently applicable by investigating two sample applications for multifunctional wave optical design: the design of tolerant systems and 3D beam shaping.
Does the Wave Equation Really Work?
ERIC Educational Resources Information Center
Armstead, Donald C.; Karls, Michael A.
2006-01-01
The wave equation is a classic partial differential equation that one encounters in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating string. Using a video camera and Wave-in-Motion software to record displacement data from a vibrating string or spring,…
NASA Astrophysics Data System (ADS)
Crosta, G.; Imposimato, S.; Roddeman, D.; Frattini, P.
2012-04-01
Fast moving landslides can be originated along slopes in mountainous terrains with natural and artificial lakes, or fjords at the slope foot. This landslides can reach extremely high speed and the impact with the immobile reservoir water can be influenced by the local topography and the landslide mass profile. The impact can generate large impulse waves and landslide tsunami. Initiation, propagation and runup are the three phases that need to be considered. The landslide evolution and the consequent wave can be controlled by the initial mass position (subaerial, partially or completely submerged), the landslide speed, the type of material, the subaerial and subaqueous slope geometry, the landslide depth and length at the impact, and the water depth. Extreme events have been caused by subaerial landslides: the 1963 Vajont rockslide (Italy), the 1958 Lituya Bay event (Alaska), the Tafjord and the Loen multiple events event (Norway), also from volcanic collapses (Hawaii and Canary islands). Various researchers completed a systematic experimental work on 2D and 3D wave generation and propagation (Kamphuis and Bowering, 1970; Huber, 1980; Müller, 1995; Huber and Hager, 1997; Fritz, 2002; Zweifel, 2004; Panizzo et al., 2005; Heller, 2007; Heller and Kinnear, 2010; Sælevik et al., 2009), using both rigid blocks and deformable granular" masses. Model data and results have been used to calibrate and validate numerical modelling tools (Harbitz, 1992; Jiang and LeBlond, 1993; Grilli et al., 2002; Grilli and Watts, 2005; Lynett and Liu, 2005; Tinti et al., 2006; Abadie et al., 2010) generally considering simplified rheologies (e.g. viscous rheologies) for subaerial subaqueous spreading. We use a FEM code (Roddeman, 2011; Crosta et al., 2006, 2009, 2010, 2011) adopting an Eulerian-Lagrangian approach to give accurate results for large deformations. We model both 2D and fully 3D events considering different settings. The material is considered as a fully deformable elasto
Development of a GPU-Accelerated 3-D Full-Wave Code for Reflectometry Simulations
NASA Astrophysics Data System (ADS)
Reuther, K. S.; Kubota, S.; Feibush, E.; Johnson, I.
2013-10-01
1-D and 2-D full-wave codes used as synthetic diagnostics in microwave reflectometry are standard tools for understanding electron density fluctuations in fusion plasmas. The accuracy of the code depends on how well the wave properties along the ignored dimensions can be pre-specified or neglected. In a toroidal magnetic geometry, such assumptions are never strictly correct and ray tracing has shown that beam propagation is inherently a 3-D problem. Previously, we reported on the application of GPGPU's (General-Purpose computing on Graphics Processing Units) to a 2-D FDTD (Finite-Difference Time-Domain) code ported to utilize the parallel processing capabilities of the NVIDIA C870 and C1060. Here, we report on the development of a FDTD code for 3-D problems. Initial tests will use NVIDIA's M2070 GPU and concentrate on the launching and propagation of Gaussian beams in free space. If available, results using a plasma target will also be presented. Performance will be compared with previous generations of GPGPU cards as well as with NVIDIA's newest K20C GPU. Finally, the possibility of utilizing multiple GPGPU cards in a cluster environment or in a single node will also be discussed. Supported by U.S. DoE Grants DE-FG02-99-ER54527 and DE-AC02-09CH11466 and the DoE National Undergraduate Fusion Fellowship.
Nondiffracting accelerating wave packets of Maxwell's equations.
Kaminer, Ido; Bekenstein, Rivka; Nemirovsky, Jonathan; Segev, Mordechai
2012-04-20
We present the nondiffracting spatially accelerating solutions of the Maxwell equations. Such beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams to the full domain of the wave equation. For both TE and TM polarizations, the beams exhibit shape-preserving bending which can have subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°. We show that these accelerating beams are self-healing, analyze their properties, and find the new class of accelerating breathers: self-bending beams of periodically oscillating shapes. Finally, we emphasize that in their scalar form, these beams are the exact solutions for nondispersive accelerating wave packets of the most common wave equation describing time-harmonic waves. As such, this work has profound implications to many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes. PMID:22680719
NASA Astrophysics Data System (ADS)
Plotnikov, Illya; Vourlidas, Angelos; Tylka, Allan J.; Pinto, Rui; Rouillard, Alexis; Tirole, Margot
2016-07-01
Identifying the physical mechanisms that produce the most energetic particles is a long-standing observational and theoretical challenge in astrophysics. Strong pressure waves have been proposed as efficient accelerators both in the solar and astrophysical contexts via various mechanisms such as diffusive-shock/shock-drift acceleration and betatron effects. In diffusive-shock acceleration, the efficacy of the process relies on shock waves being super-critical or moving several times faster than the characteristic speed of the medium they propagate through (a high Alfven Mach number) and on the orientation of the magnetic field upstream of the shock front. High-cadence, multipoint imaging using the NASA STEREO, SOHO and SDO spacecrafts now permits the 3-D reconstruction of pressure waves formed during the eruption of coronal mass ejections. Using these unprecedented capabilities, some recent studies have provided new insights on the timing and longitudinal extent of solar energetic particles, including the first derivations of the time-dependent 3-dimensional distribution of the expansion speed and Mach numbers of coronal shock waves. We will review these recent developments by focusing on particle events that occurred between 2011 and 2015. These new techniques also provide the opportunity to investigate the enigmatic long-duration gamma ray events.
3D laboratory experiments on a system of low-crested breakwaters under oblique wave attack
NASA Astrophysics Data System (ADS)
Papacharalampous, Georgia; Karantinos, Michalis; Giantsi, Theodora; Moutzouris, Constantinos
2016-04-01
Low-crested breakwaters are being increasingly used for shore protection. Hydrodynamics around coastal structures are complicated and have not been fully understood. A series of large scale (1:40) 3D laboratory experiments were carried out in the Laboratory of Harbour Works, National Technical University of Athens to investigate the wave disturbance around a system of two non-parallel to the shoreline breakwaters. The structures were of the type of low-crested, permeable and attacked by obliquely incident waves. Three different water depths were tested in the basin with a range of various different spectra. The transmission and reflection coefficients were measured in the middle of each breakwater. For this purpose, 1 gauge and 4 gauges (in line) were placed on the landward and seaward side of each breakwater respectively. The effect of diffraction is incorporate at the measured wave heights. The measured coefficients are being compared to their corresponding estimated using existing empirical formulas. Most of those formulas neglect wave obliquity.
A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero magnetic diffusivity
NASA Astrophysics Data System (ADS)
Gala, Sadek; Ragusa, Maria Alessandra
2016-06-01
In this work, we show that a smooth solution of the 3D MHD equations with zero magnetic diffusivity in the whole space ℝ3 breaks down if and only if a certain norm of the magnetic field blows up at the same time.
NASA Technical Reports Server (NTRS)
Kwak, D.
1994-01-01
INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far
3D surface-wave tomography in the central Baltic Shield
NASA Astrophysics Data System (ADS)
Bruneton, M.; Pedersen, H. A.; Farra, V.; Svekalapko Seismic Tomography Working Group
2003-04-01
The main objective of the SVEKALAPKO deep seismic experiment was to image in details the lithosphere-asthenosphere system of the central Baltic Shield, therefore enhancing our knowledge of the structure and evolution of cratonic lithosphere. During the experiment a regular 2D grid of 46 broad-band stations covered the southern part of Finland. This exceptional stations distribution made it possible to undertake a high precision surface-wave tomography. We developed a technique based on paraxial ray tracing to obtain 2D phase-velocity maps as a function of frequency which can subsequently be inverted for the 3D structure. The major improvement is that we jointly inverted for the velocity model under the array and the shape of incoming wave fronts, therefore reducing artifacts due to structure outside the study region. The data set included carefully selected fundamental mode Rayleigh wave arrival times of 69 teleseismic events, computed using Wiener filtering. An average dispersion curve was obtained imposing the phase-velocity to be quasi constant. It leads to shear-wave velocities for the lithospheric mantle 4% faster than standard Earth model ak135. The inversion of the same data set was also conducted using weaker constraints to obtain the lateral variations of the phase-velocity at each frequency and subsequently of the shear-wave velocity as a function of depth. Three Vs profiles were computed respectively in the Karelian Archean province, in the Proterozoic Svekofennia, and at the suture between the two domains. They showed significant variations, the higher lithospheric velocities were seen in the proterozoic domain, a low velocity zone was necessary only in the suture zone. Our results showed that chemical changes are maintained within the lithosphere over extended periods of time.
System-in-package LTCC platform for 3D RF to millimeter wave
NASA Astrophysics Data System (ADS)
Vähä-Heikkilä, T.; Lahti, M.
2011-04-01
This presentation shows recent trends and results in 3D Low Temperature Co-Fired Ceramics (LTCC) modules in applications from RF to millimeter waves. The system-in-package LTCC platform is a true three dimensional module technology. LTCC is a lightweight multi-layer technology having typically 6-20 ceramic layers and metallizations between. The metallization levels i.e different metal layers can be patterned and connected together with metal vias. Passive devices can also be fabricated on LTCC while active devices and other chips are connected with flip-chip, wire bonding or soldering. In addition to passives directly fabricated to LTCC, several different technologies/ chips can be hybrid integrated to the same module. LTCC platform is also well suited for the realization of antenna arrays for microwave and millimeter wave applications. Potential applications are ranging from short range communications to space and radars. VTT has designed, fabricated and characterized microwave and millimeter wave packages for Radio Frequency (RF) Micro Electro Mechanical Systems (MEMS) as well as active devices. Also, several types of system-in-package modules have been realized containing hybrid integrated CMOS and GaAs MMICs and antenna arrays.
A 3D MPI-Parallel GPU-accelerated framework for simulating ocean wave energy converters
NASA Astrophysics Data System (ADS)
Pathak, Ashish; Raessi, Mehdi
2015-11-01
We present an MPI-parallel GPU-accelerated computational framework for studying the interaction between ocean waves and wave energy converters (WECs). The computational framework captures the viscous effects, nonlinear fluid-structure interaction (FSI), and breaking of waves around the structure, which cannot be captured in many potential flow solvers commonly used for WEC simulations. The full Navier-Stokes equations are solved using the two-step projection method, which is accelerated by porting the pressure Poisson equation to GPUs. The FSI is captured using the numerically stable fictitious domain method. A novel three-phase interface reconstruction algorithm is used to resolve three phases in a VOF-PLIC context. A consistent mass and momentum transport approach enables simulations at high density ratios. The accuracy of the overall framework is demonstrated via an array of test cases. Numerical simulations of the interaction between ocean waves and WECs are presented. Funding from the National Science Foundation CBET-1236462 grant is gratefully acknowledged.
Electronic representation of wave equation
NASA Astrophysics Data System (ADS)
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
On the Global Regularity of a Helical-Decimated Version of the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Biferale, Luca; Titi, Edriss S.
2013-06-01
We study the global regularity, for all time and all initial data in H 1/2, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L 2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H 1/2-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H 1/2 and the time average of the square of the H 3/2 norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato (Arch. Ration. Mech. Anal. 16:269-315, 1964; Rend. Semin. Mat. Univ. Padova 32:243-260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences.
3D P and S Wave Velocity Structure and Tremor Locations in the Parkfield Region
NASA Astrophysics Data System (ADS)
Zeng, X.; Thurber, C. H.; Shelly, D. R.; Bennington, N. L.; Cochran, E. S.; Harrington, R. M.
2014-12-01
We have assembled a new dataset to refine the 3D seismic velocity model in the Parkfield region. The S arrivals from 184 earthquakes recorded by the Parkfield Experiment to Record MIcroseismicity and Tremor array (PERMIT) during 2010-2011 were picked by a new S wave picker, which is based on machine learning. 74 blasts have been assigned to four quarries, whose locations were identified with Google Earth. About 1000 P and S wave arrivals from these blasts at permanent seismic network were also incorporated. Low frequency earthquakes (LFEs) occurring within non-volcanic tremor (NVT) are valuable for improving the precision of NVT location and the seismic velocity model at greater depths. Based on previous work (Shelley and Hardebeck, 2010), waveforms of hundreds of LFEs in same family were stacked to improve signal qualify. In a previous study (McClement et al., 2013), stacked traces of more than 30 LFE families at the Parkfileld Array Seismic Observatory (PASO) have been picked. We expanded our work to include LFEs recorded by the PERMIT array. The time-frequency Phase Weight Stacking (tf-PWS) method was introduced to improve the stack quality, as direct stacking does not produce clear S-wave arrivals on the PERMIT stations. This technique uses the coherence of the instantaneous phase among the stacked signals to enhance the signal-to-noise ratio (SNR) of the stack. We found that it is extremely effective for picking LFE arrivals (Thurber et al., 2014). More than 500 P and about 1000 S arrivals from 58 LFE families were picked at the PERMIT and PASO arrays. Since the depths of LFEs are much deeper than earthquakes, we are able to extend model resolution to lower crustal depths. Both P and S wave velocity structure have been obtained with the tomoDD method. The result suggests that there is a low velocity zone (LVZ) in the lower crust and the location of the LVZ is consistent with the high conductivity zone beneath the southern segment of the Rinconada fault that
NASA Astrophysics Data System (ADS)
Bayrakci, Gaye; Minshull, Timothy A.; Davy, Richard G.; Karplus, Marianne S.; Kaeschen, Dirk; Papenberg, Cord; Krabbenhoeft, Anne; Sawyer, Dale; Reston, Timothy J.; Shillington, Donna J.; Ranero, César R.
2014-05-01
Galicia 3D, a reflection-refraction and long offset seismic experiment was carried out from May through September 2013, at the Galicia rifted margin (in the northeast Atlantic Ocean, west of Spain) as a collaboration between US, UK, German and Spanish groups. The 3D multichannel seismic acquisition conducted by R/V Marcus Langseth covered a 64 km by 20 km (1280 km2) zone where the main geological features are the Peridotite Ridge (PR), composed of serpentinized peridotite and thought be upper mantle exhumed to the seafloor during rifting, and the S reflector which has been interpreted to be a low angle detachment fault overlain by fault bounded, rotated, continental crustal blocks. In the 3D box, two airgun arrays of 3300 cu.in. were fired alternately (in flip-flop configuration) every 37.5 m. All shots are recorded by 44 short period four component ocean bottom seismometers (OBS) and 26 ocean bottom hydrophones (OBH) deployed and recovered by R/V Poseidon, as well as four 6 km hydrophone streamers with 12.5 m channel spacing towed by R/V Marcus Langseth. We present the preliminary results of the first arrival time tomography study which is carried out with a subset of the wide-angle dataset, in order to generate a 3D P-wave velocity volume for the entire depth sampled by the reflection data. After the relocation of OBSs and OBHs, an automatic first-arrival time picking approach is applied to a subset of the dataset, which comprises more than 5.5 million source-receiver pairs. Then, the first-arrival times are checked visually, in 3-dimensions. The a priori model used for the first-arrival time tomography is built up using information from previous seismic surveys carried out at the Galicia margin (e.g. ISE, 1997). The FAST algorithm of Zelt and Barton (1998) is used for the first-arrival time inversion. The 3D P-wave velocity volume can be used in interpreting the reflection dataset, as a starting point for migration, to quantify the thinning of the crustal layers
Effect of spatial dispersion on transient acoustic wave propagation in 3D.
Every, A G
2006-12-22
Spatial dispersion is the variation of wave speed with wavelength. It sets in when the acoustic wavelength approaches the natural scale of length of the medium, which could, for example, be the lattice constant of a crystal, the repeat distance in a superlattice, or the grain size in a granular material. In centrosymmetric media, the first onset of dispersion is accommodated by the introduction of fourth order spatial derivatives into the wave equation. These lead to a correction to the phase velocity which is quadratic in the spatial frequency. This paper treats the effect of spatial dispersion on the point force elastodynamic Green's functions of solids. The effects of dispersion are shown to be most pronounced in the vicinity of wave arrivals. These lose their singular form, and are transformed into wave trains known as quasi-arrivals. The step and ramp function wave arrivals are treated, and it is shown that their unfolded quasi-arrival forms can be expressed in terms of integrals involving the Airy function. PMID:16828830
On Blowup in Supercritical Wave Equations
NASA Astrophysics Data System (ADS)
Donninger, Roland; Schörkhuber, Birgit
2016-03-01
We study the blowup behavior for the focusing energy-supercritical semilinear wave equation in 3 space dimensions without symmetry assumptions on the data. We prove the stability in {H^2× H^1} of the ODE blowup profile.
Finite Element Code For 3D-Hydraulic Fracture Propagation Equations (3-layer).
Energy Science and Technology Software Center (ESTSC)
1992-03-24
HYFRACP3D is a finite element program for simulation of a pseudo three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and winglength over time for a hydraulic fracture propagating in a three-layered system of rocks with variable rock mechanics properties.
Intersymbol Interference Investigations Using a 3D Time-Dependent Traveling Wave Tube Model
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Andro, Monty; Downey, Alan (Technical Monitor)
2001-01-01
For the first time, a physics based computational model has been used to provide a direct description of the effects of the TWT (Traveling Wave Tube) on modulated digital signals. The TWT model comprehensively takes into account the effects of frequency dependent AM/AM and AM/PM conversion; gain and phase ripple; drive-induced oscillations; harmonic generation; intermodulation products; and backward waves. Thus, signal integrity can be investigated in the presence of these sources of potential distortion as a function of the physical geometry of the high power amplifier and the operational digital signal. This method promises superior predictive fidelity compared to methods using TWT models based on swept amplitude and/or swept frequency data. The fully three-dimensional (3D), time-dependent, TWT interaction model using the electromagnetic code MAFIA is presented. This model is used to investigate assumptions made in TWT black box models used in communication system level simulations. In addition, digital signal performance, including intersymbol interference (ISI), is compared using direct data input into the MAFIA model and using the system level analysis tool, SPW (Signal Processing Worksystem).
Intersymbol Interference Investigations Using a 3D Time-Dependent Traveling Wave Tube Model
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Andro, Monty
2002-01-01
For the first time, a time-dependent, physics-based computational model has been used to provide a direct description of the effects of the traveling wave tube amplifier (TWTA) on modulated digital signals. The TWT model comprehensively takes into account the effects of frequency dependent AM/AM and AM/PM conversion; gain and phase ripple; drive-induced oscillations; harmonic generation; intermodulation products; and backward waves. Thus, signal integrity can be investigated in the presence of these sources of potential distortion as a function of the physical geometry and operating characteristics of the high power amplifier and the operational digital signal. This method promises superior predictive fidelity compared to methods using TWT models based on swept- amplitude and/or swept-frequency data. First, the TWT model using the three dimensional (3D) electromagnetic code MAFIA is presented. Then, this comprehensive model is used to investigate approximations made in conventional TWT black-box models used in communication system level simulations. To quantitatively demonstrate the effects these approximations have on digital signal performance predictions, including intersymbol interference (ISI), the MAFIA results are compared to the system level analysis tool, Signal Processing Workstation (SPW), using high order modulation schemes including 16 and 64-QAM.
Modeling Recent Large Earthquakes Using the 3-D Global Wave Field
NASA Astrophysics Data System (ADS)
Hjörleifsdóttir, V.; Kanamori, H.; Tromp, J.
2003-04-01
We use the spectral-element method (SEM) to accurately compute waveforms at periods of 40 s and longer for three recent large earthquakes using 3D Earth models and finite source models. The M_w~7.6, Jan~26, 2001, Bhuj, India event had a small rupture area and is well modeled at long periods with a point source. We use this event as a calibration event to investigate the effects of 3-D Earth models on the waveforms. The M_w~7.9, Nov~11, 2001, Kunlun, China, event exhibits a large directivity (an asymmetry in the radiation pattern) even at periods longer than 200~s. We used the source time function determined by Kikuchi and Yamanaka (2001) and the overall pattern of slip distribution determined by Lin et al. to guide the wave-form modeling. The large directivity is consistent with a long fault, at least 300 km, and an average rupture speed of 3±0.3~km/s. The directivity at long periods is not sensitive to variations in the rupture speed along strike as long as the average rupture speed is constant. Thus, local variations in rupture speed cannot be ruled out. The rupture speed is a key parameter for estimating the fracture energy of earthquakes. The M_w~8.1, March~25, 1998, event near the Balleny Islands on the Antarctic Plate exhibits large directivity in long period surface waves, similar to the Kunlun event. Many slip models have been obtained from body waves for this earthquake (Kuge et al. (1999), Nettles et al. (1999), Antolik et al. (2000), Henry et al. (2000) and Tsuboi et al. (2000)). We used the slip model from Henry et al. to compute SEM waveforms for this event. The synthetic waveforms show a good fit to the data at periods from 40-200~s, but the amplitude and directivity at longer periods are significantly smaller than observed. Henry et al. suggest that this event comprised two subevents with one triggering the other at a distance of 100 km. To explain the observed directivity however, a significant amount of slip is required between the two subevents
NASA Astrophysics Data System (ADS)
Zhdanov, M. S.; Cuma, M.; Black, N.; Wilson, G. A.
2009-12-01
The marine controlled source electromagnetic (MCSEM) method has become widely used in offshore oil and gas exploration. Interpretation of MCSEM data is still a very challenging problem, especially if one would like to take into account the realistic 3D structure of the subsurface. The inversion of MCSEM data is complicated by the fact that the EM response of a hydrocarbon-bearing reservoir is very weak in comparison with the background EM fields generated by an electric dipole transmitter in complex geoelectrical structures formed by a conductive sea-water layer and the terranes beneath it. In this paper, we present a review of the recent developments in the area of large-scale 3D EM forward modeling and inversion. Our approach is based on using a new integral form of Maxwell’s equations allowing for an inhomogeneous background conductivity, which results in a numerically effective integral representation for 3D EM field. This representation provides an efficient tool for the solution of 3D EM inverse problems. To obtain a robust inverse model of the conductivity distribution, we apply regularization based on a focusing stabilizing functional which allows for the recovery of models with both smooth and sharp geoelectrical boundaries. The method is implemented in a fully parallel computer code, which makes it possible to run large-scale 3D inversions on grids with millions of inversion cells. This new technique can be effectively used for active EM detection and monitoring of the subsurface targets.
NASA Astrophysics Data System (ADS)
Hu, Y.; Ji, Y.; Egbert, G. D.
2015-12-01
The fictitious time domain method (FTD), based on the correspondence principle for wave and diffusion fields, has been developed and used over the past few years primarily for marine electromagnetic (EM) modeling. Here we present results of our efforts to apply the FTD approach to land and airborne TEM problems which can reduce the computer time several orders of magnitude and preserve high accuracy. In contrast to the marine case, where sources are in the conductive sea water, we must model the EM fields in the air; to allow for topography air layers must be explicitly included in the computational domain. Furthermore, because sources for most TEM applications generally must be modeled as finite loops, it is useful to solve directly for the impulse response appropriate to the problem geometry, instead of the point-source Green functions typically used for marine problems. Our approach can be summarized as follows: (1) The EM diffusion equation is transformed to a fictitious wave equation. (2) The FTD wave equation is solved with an explicit finite difference time-stepping scheme, with CPML (Convolutional PML) boundary conditions for the whole computational domain including the air and earth , with FTD domain source corresponding to the actual transmitter geometry. Resistivity of the air layers is kept as low as possible, to compromise between efficiency (longer fictitious time step) and accuracy. We have generally found a host/air resistivity contrast of 10-3 is sufficient. (3)A "Modified" Fourier Transform (MFT) allow us recover system's impulse response from the fictitious time domain to the diffusion (frequency) domain. (4) The result is multiplied by the Fourier transformation （FT） of the real source current avoiding time consuming convolutions in the time domain. (5) The inverse FT is employed to get the final full waveform and full time response of the system in the time domain. In general, this method can be used to efficiently solve most time-domain EM
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
Viscous Boussinesq equations for internal waves
NASA Astrophysics Data System (ADS)
Liu, Chi-Min
2016-04-01
In this poster, Boussinesq wave equations for internal wave propagation in a two-fluid system bounded by two impermeable plates are derived and analyzed. Using the perturbation method as well as the Padé approximation, a set of three equations accurate up to the fourth order are derived and displayed by three unknowns: the interfacial elevation, upper and lower velocity potentials at arbitrary vertical positions. No limitation on nonlinearity is made while weakly dispersive effects are originally considered in the derivation. The derived equations are examined by comparing its dispersion relation with those of existing models to verify the accuracy. The results show that present model equations provide an excellent base for simulating internal waves not only in shallower configuration but also medium configuration.
Quantitative analysis of accuracy of seismic wave-propagation codes in 3D random scattering media
NASA Astrophysics Data System (ADS)
Galis, Martin; Imperatori, Walter; Mai, P. Martin
2013-04-01
Several recent verification studies (e.g. Day et al., 2001; Bielak et al., 2010, Chaljub et al., 2010) have demonstrated the importance of assessing the accuracy of available numerical tools at low frequency in presence of large-scale features (basins, topography, etc.). The fast progress in high-performance computing, including efficient optimization of numerical codes on petascale supercomputers, has permitted the simulation of 3D seismic wave propagation at frequencies of engineering interest (up to 10Hz) in highly heterogeneous media (e.g. Hartzell et al, 2010; Imperatori and Mai, 2013). However, high frequency numerical simulations involving random scattering media, characterized by small-scale heterogeneities, are much more challenging for most numerical methods, and their verification may therefore be even more crucial than in the low-frequency case. Our goal is to quantitatively compare the accuracy and the behavior of three different numerical codes for seismic wave propagation in 3D random scattering media at high frequency. We deploy a point source with omega-squared spectrum, and focus on the near-source region, being of great interest in strong motion seismology. We use two codes based on finite-difference method (FD1 and FD2) and one code based on support-operator method (SO). Both FD1 and FD2 are 4-th order staggered-grid finite-difference codes (for FD1 see Olsen et al., 2009; for FD2 see Moczo et al., 2007). The FD1 and FD2 codes are characterized by slightly different medium representations, since FD1 uses point values of material parameters in each FD-cell, while FD2 uses the effective material parameters at each grid-point (Moczo et al., 2002). SO is 2-nd order support-operator method (Ely et al., 2008). We considered models with random velocity perturbations described by van Karman correlation function with different correlation lengths and different standard deviations. Our results show significant variability in both phase and amplitude as
Anomalously low amplitude of S waves produced by the 3D structures in the lower mantle
NASA Astrophysics Data System (ADS)
To, Akiko; Capdeville, Yann; Romanowicz, Barbara
2016-07-01
Direct S and Sdiff phases with anomalously low amplitudes are recorded for the earthquakes in Papua New Guinea by seismographs in northern America. According to the prediction by a standard 1D model, the amplitudes are the lowest at stations in southern California, at a distance and azimuth of around 95° and 55°, respectively, from the earthquake. The amplitude anomaly is more prominent at frequencies higher than 0.03 Hz. We checked and ruled out the possibility of the anomalies appearing because of the errors in the focal mechanism used in the reference synthetic waveform calculations. The observed anomaly distribution changes drastically with a relatively small shift in the location of the earthquake. The observations indicate that the amplitude reduction is likely due to the 3D shear velocity (Vs) structure, which deflects the wave energy away from the original ray paths. Moreover, some previous studies suggested that some of the S and Sdiff phases in our dataset are followed by a prominent postcursor and show a large travel time delay, which was explained by placing a large ultra-low velocity zone (ULVZ) located on the core-mantle boundary southwest of Hawaii. In this study, we evaluated the extent of amplitude anomalies that can be explained by the lower mantle structures in the existing models, including the previously proposed ULVZ. In addition, we modified and tested some models and searched for the possible causes of low amplitudes. Full 3D synthetic waveforms were calculated and compared with the observations. Our results show that while the existing models explain the trends of the observed amplitude anomalies, the size of such anomalies remain under-predicted especially at large distances. Adding a low velocity zone, which is spatially larger and has less Vs reduction than ULVZ, on the southwest side of ULVZ, contributes to explain the low amplitudes observed at distances larger than 100° from the earthquake. The newly proposed low velocity zone
NASA Astrophysics Data System (ADS)
Polkowski, Marcin; Grad, Marek
2015-04-01
The 3D P-wave seismic velocity model was obtained by combining data from multiple studies during past 50 years. Data sources included refraction seismology, reflection seismology, geological boreholes, vertical seismic profiling, magnetotellurics and gravimetry. Use of many data sources allowed creation of detailed 3D P-wave velocity model that reaches to depth of 60 km and includes 6-layers of sediments and 3-layers of the crust. Purpose of this study is to analyze how 3D model influences local (accuracy of location and source time estimation for local events), regional (identification of wide-angle seismic phases) and global (teleseismic tomography) seismic travel times. Additionally we compare results of forward seismic wave propagation with signals observed on short period and broadband stations. National Science Centre Poland provided financial support for this work by NCN grant DEC-2011/02/A/ST10/00284.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
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.
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
3D Anisotropic structure of the south-central Mongolia from Rayleigh and Love wave tomography
NASA Astrophysics Data System (ADS)
Yu, D.; Wu, Q.; Montagner, J. P.
2014-12-01
A better understanding of the geodynamics of the crust and mantle below Baikal-Mongolia is required to identify the role of mantle processes versus that of far-field tectonic effects from India-Asia collision. Anisotropy tomography can provide new perspective to the continental growth mechanism. In order to study the 3D anisotropic structure of the upper mantle in the south-central Mongolia, we collected the vertical and transverse components of seismograms recorded at 69 broadband seismic stations. We have measured inter-station phase velocities of 7181 Rayleigh waves and 901 Love waves using the frequency-time analysis of wavelet transformation method for the fundamental mode at period range 10~80s. The lateral phase velocity variations are computed by using a regionalization method. These phase velocities have been inverted to obtain the first anisotropic model including Sv velocities, azimuthal and radial anisotropy. The Middle Gobi is associated with low velocity. Based on the distribution of the Cenozoic basalts in the Middle Gobi, it refers that the low velocity anomaly is related to the Cenozoic volcanism. In the northern domain, near to Baikal zone, the azimuthal anisotropy is normal to the Baikal rift and consistent with the fast direction of previous SKS splitting measurements. In the South Gobi, north to Main Mongolian Lineament, the azimuthal anisotropy is NEE-SWW in the crust and NW-SE in the mantle. It indicates that the crust and mantle are decoupled. We propose that the crustal deformation is related to the far-field effects of India-Asia collision and that the mantle flow is correlated with the Baikal rift activity. Further study in process will provide more evidence and insight to better understand the geodynamics in this region.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
NASA Astrophysics Data System (ADS)
Frisch, Uriel; Villone, Barbara
2014-09-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century - besides Hankel, foremost by George Stokes and Maurice Lévy - and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
Helical localized wave solutions of the scalar wave equation.
Overfelt, P L
2001-08-01
A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch. PMID:11488494
Characterization of an SRF gun: a 3D full wave simulation
Wang, E.; Ben-Zvi, I.; Wang, J.
2011-03-28
We characterized a BNL 1.3GHz half-cell SRF gun is tested for GaAs photocathode. The gun already was simulated several years ago via two-dimensional (2D) numerical codes (i.e., Superfish and Parmela) with and without the beam. In this paper, we discuss our investigation of its characteristics using a three dimensional (3D) full-wave code (CST STUDIO SUITE{trademark}).The input/pickup couplers are sited symmetrically on the same side of the gun at an angle of 180{sup o}. In particular, the inner conductor of the pickup coupler is considerably shorter than that of the input coupler. We evaluated the cross-talk between the beam (trajectory) and the signal on the input coupler compared our findings with published results based on analytical models. The CST STUDIO SUITE{trademark} also was used to predict the field within the cavity; particularly, a combination of transient/eigenmode solvers was employed to accurately construct the RF field for the particles, which also includes the effects of the couplers. Finally, we explored the beam's dynamics with a particle in cell (PIC) simulation, validated the results and compare them with 2D code result.
Understanding the core-halo relation of quantum wave dark matter from 3D simulations.
Schive, Hsi-Yu; Liao, Ming-Hsuan; Woo, Tak-Pong; Wong, Shing-Kwong; Chiueh, Tzihong; Broadhurst, Tom; Hwang, W-Y Pauchy
2014-12-31
We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter, described by the Schrödinger-Poisson (SP) equation with a particle mass ∼10(-22) eV. A distinct gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark matter scenarios. Furthermore, we show that each solitonic core is surrounded by an extended halo composed of large fluctuating dark matter granules which modulate the halo density on a scale comparable to the diameter of the solitonic core. The scaling symmetry of the SP equation and the uncertainty principle tightly relate the core mass to the halo specific energy, which, in the context of cosmological structure formation, leads to a simple scaling between core mass (Mc) and halo mass (Mh), Mc∝a(-1/2)Mh(1/3), where a is the cosmic scale factor. We verify this scaling relation by (i) examining the internal structure of a statistical sample of virialized halos that form in our 3D cosmological simulations and by (ii) merging multiple solitons to create individual virialized objects. Sufficient simulation resolution is achieved by adaptive mesh refinement and graphic processing units acceleration. From this scaling relation, present dwarf satellite galaxies are predicted to have kiloparsec-sized cores and a minimum mass of ∼10(8)M⊙, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of 2×10(12)M⊙ at z=8 should have massive solitonic cores of ∼2×10(9)M⊙ within ∼60 pc. Such cores can provide a favorable local environment for funneling the gas that leads to the prompt formation of early stellar spheroids and quasars. PMID:25615301
A lattice-Boltzmann scheme of the Navier-Stokes equations on a 3D cuboid lattice
NASA Astrophysics Data System (ADS)
Min, Haoda; Peng, Cheng; Wang, Lian-Ping
2015-11-01
The standard lattice-Boltzmann method (LBM) for fluid flow simulation is based on a square (in 2D) or cubic (in 3D) lattice grids. Recently, two new lattice Boltzmann schemes have been developed on a 2D rectangular grid using the MRT (multiple-relaxation-time) collision model, by adding a free parameter in the definition of moments or by extending the equilibrium moments. Here we developed a lattice Boltzmann model on 3D cuboid lattice, namely, a lattice grid with different grid lengths in different spatial directions. We designed our MRT-LBM model by matching the moment equations from the Chapman-Enskog expansion with the Navier-Stokes equations. The model guarantees correct hydrodynamics. A second-order term is added to the equilibrium moments in order to restore the isotropy of viscosity on a cuboid lattice. The form and the coefficients of the extended equilibrium moments are determined through an inverse design process. An additional benefit of the model is that the viscosity can be adjusted independent of the stress-moment relaxation parameter, thus improving the numerical stability of the model. The resulting cuboid MRT-LBM model is then validated through benchmark simulations using laminar channel flow, turbulent channel flow, and the 3D Taylor-Green vortex flow.
The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations
NASA Astrophysics Data System (ADS)
Ben Hassen, M. F.; Erhard, K.; Potthast, R.
2006-02-01
We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.
Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes
NASA Technical Reports Server (NTRS)
Marx, Yves P.
1990-01-01
An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.
NASA Astrophysics Data System (ADS)
Lee, H.; Min, D.; Lim, S.; Yang, J.; Kwon, B.; Yoo, H.
2009-12-01
In a conventional marine seismic data analysis, pressure data have been usually interpreted on the basis of acoustic wave equation. The acoustic wave equation, however, only deals with P-wave propagation, and it cannot correctly describe the wave propagation in acoustic-elastic (fluid-solid) coupled media. Recently, in 4C OBC survey (4-component ocean bottom cable), it is possible to acquire both pressure and 3-component displacements (measured at the sea-bottom). Combining pressure and displacement data allows us to interpret subsurface structures more accurately. In order to accurately simulate wave propagation in fluid-solid coupled media, we need an acoustic-elastic coupled modeling algorithm, which deals with displacements in elastic region and pressure in acoustic region. For waveform inversion and reverse-time migration that require a great number of forward modeling, it is essential to develop an efficient scheme that reduces computing time and computer core memory. In this study, we present a 3D time-domain acoustic-elastic coupled modeling algorithm on the basis of the cell-based finite difference method. The cell-based method has proven to properly describe the free-surface boundary, which indicates that it will also properly describe the fluid-solid interface boundaries. In the acoustic-elastic coupled modeling, we first compose cell-based finite differences individually for the 3D acoustic and elastic media, and then combine the differences using the fluid-solid interface boundary conditions. Considering that the 2D acoustic-elastic coupled modeling algorithm gives numerical solutions comparable to analytic solutions, we expect that the 3D acoustic-elastic coupled modeling will correctly describe wave propagation in the fluid-solid coupled media. We apply our algorithm to 3D horizontal two- and three-layer models. Numerical experiments show that the cell-based coupled modeling algorithm properly describes S- and converted waves as well as P-waves. The
Scattering and coupling effects of electromagnetic waves in 3D networks of spheres
NASA Astrophysics Data System (ADS)
Defos Du Rau, M.; Pessan, F.; Ruffie, G.; Vignéras-Lefebvre, V.; Parneix, J. P.
1998-01-01
In this paper, the problem of electromagnetic scattering from a 3D system of spheres is considered and an iterative solution that accounts for multiple scattering is proposed. The Mie formalism used for a single sphere is extended to account for multiple scattered fields between several particles. The translational addition theorems for spherical wave functions are used to express the electromagnetic field scattered by a sphere S_i in terms of an incident field for a sphere S_k in a spherical coordinates system attached to the sphere S_k. In this work, the numerical convergence of the method is discussed and associated computational times are given. Numerical computations including Radar Cross Section (RCS) and radiation patterns for various 3D configurations are presented. Some of them are compared with free-space measurements made in the 8 to 100 GHz frequency band using vectorial network analyzers. 11.55.-m S-matrix theory; analytic structure of amplitudes Cet article étudie la diffusion des ondes électromagnétiques par des réseaux tridimensionnels de sphères et propose une méthode itérative pour prendre en compte les effets de multidiffusion. Le formalisme de Mie utilisé dans le cas d'une sphère est étendu pour calculer les champs "multidiffusés" entre plusieurs particules. Les théorèmes d'addition et de translation des fonctions d'onde sphériques sont utilisés pour exprimer le champ diffusé par une sphère S_i comme étant incident sur une sphère S_k, dans un système de coordonnées sphériques lié au centre de S_k. La convergence numérique de la méthode est discutée et des temps de calcul sont donnés. Des résultats numériques tels que des Surfaces Équivalentes Radar (SER) et des diagrammes de rayonnement pour différentes configurations tridimensionnelles sont montrés. Certains d'entre eux sont comparés à des mesures en espace libre faites à l'aide d'analyseurs de réseaux vectoriels dans la bande de fréquence 8{-}100 GHz.
NASA Astrophysics Data System (ADS)
Mulder, W. A.; Zhebel, E.; Minisini, S.
2014-02-01
We analyse the time-stepping stability for the 3-D acoustic wave equation, discretized on tetrahedral meshes. Two types of methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method. Combining the spatial discretization with the leap-frog time-stepping scheme, which is second-order accurate and conditionally stable, leads to a fully explicit scheme. We provide estimates of its stability limit for simple cases, namely, the reference element with Neumann boundary conditions, its distorted version of arbitrary shape, the unit cube that can be partitioned into six tetrahedra with periodic boundary conditions and its distortions. The Courant-Friedrichs-Lewy stability limit contains an element diameter for which we considered different options. The one based on the sum of the eigenvalues of the spatial operator for the first-degree mass-lumped element gives the best results. It resembles the diameter of the inscribed sphere but is slightly easier to compute. The stability estimates show that the mass-lumped continuous and the discontinuous Galerkin finite elements of degree 2 have comparable stability conditions, whereas the mass-lumped elements of degree one and three allow for larger time steps.
Gabor Wave Packet Method to Solve Plasma Wave Equations
A. Pletzer; C.K. Phillips; D.N. Smithe
2003-06-18
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.
Space–time fractional Zener wave equation
Atanackovic, T.M.; Janev, M.; Oparnica, Lj.; Pilipovic, S.; Zorica, D.
2015-01-01
The space–time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented. PMID:25663807
SHEAR WAVE SEISMIC STUDY COMPARING 9C3D SV AND SH IMAGES WITH 3C3D C-WAVE IMAGES
John Beecherl; Bob A. Hardage
2004-07-01
The objective of this study was to compare the relative merits of shear-wave (S-wave) seismic data acquired with nine-component (9-C) technology and with three-component (3-C) technology. The original proposal was written as if the investigation would be restricted to a single 9-C seismic survey in southwest Kansas (the Ashland survey), on the basis of the assumption that both 9-C and 3-C S-wave images could be created from that one data set. The Ashland survey was designed as a 9-C seismic program. We found that although the acquisition geometry was adequate for 9-C data analysis, the source-receiver geometry did not allow 3-C data to be extracted on an equitable and competitive basis with 9-C data. To do a fair assessment of the relative value of 9-C and 3-C seismic S-wave data, we expanded the study beyond the Ashland survey and included multicomponent seismic data from surveys done in a variety of basins. These additional data were made available through the Bureau of Economic Geology, our research subcontractor. Bureau scientists have added theoretical analyses to this report that provide valuable insights into several key distinctions between 9-C and 3-C seismic data. These theoretical considerations about distinctions between 3-C and 9-C S-wave data are presented first, followed by a discussion of differences between processing 9-C common-midpoint data and 3-C common-conversion-point data. Examples of 9-C and 3-C data are illustrated and discussed in the last part of the report. The key findings of this study are that each S-wave mode (SH-SH, SV-SV, or PSV) involves a different subsurface illumination pattern and a different reflectivity behavior and that each mode senses a different Earth fabric along its propagation path because of the unique orientation of its particle-displacement vector. As a result of the distinct orientation of each mode's particle-displacement vector, one mode may react to a critical geologic condition in a more optimal way than do
On Energy Cascades in the Forced 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Dascaliuc, R.; Grujić, Z.
2016-02-01
We show—in the framework of physical scales and (K_1,K_2) -averages—that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier-Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws—in terms of Grashof number—for kinetic energy, energy flux, and energy dissipation rate. These are used to improve our sufficient condition for forced cascades in physical scales.
On Energy Cascades in the Forced 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Dascaliuc, R.; Grujić, Z.
2016-06-01
We show—in the framework of physical scales and (K_1,K_2)-averages—that Kolmogorov's dissipation law combined with the smallness condition on a Taylor length scale is sufficient to guarantee energy cascades in the forced Navier-Stokes equations. Moreover, in the periodic case we establish restrictive scaling laws—in terms of Grashof number—for kinetic energy, energy flux, and energy dissipation rate. These are used to improve our sufficient condition for forced cascades in physical scales.
Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver
NASA Technical Reports Server (NTRS)
Kim, S.-W.
1991-01-01
A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.
NASA Astrophysics Data System (ADS)
Tong, Ping; Komatitsch, Dimitri; Tseng, Tai-Lin; Hung, Shu-Huei; Chen, Chin-Wu; Basini, Piero; Liu, Qinya
2014-10-01
We present a three-dimensional (3-D) hybrid method that interfaces the spectral-element method (SEM) with the frequency-wave number (FK) technique to model the propagation of teleseismic plane waves beneath seismic arrays. The accuracy of the resulting 3-D SEM-FK hybrid method is benchmarked against semianalytical FK solutions for 1-D models. The accuracy of 2.5-D modeling based on 2-D SEM-FK hybrid method is also investigated through comparisons to this 3-D hybrid method. Synthetic examples for structural models of the Alaska subduction zone and the central Tibet crust show that this method is capable of accurately capturing interactions between incident plane waves and local heterogeneities. This hybrid method presents an essential tool for the receiver function and scattering imaging community to verify and further improve their techniques. These numerical examples also show the promising future of the 3-D SEM-FK hybrid method in high-resolution regional seismic imaging based on waveform inversions of converted/scattered waves recorded by seismic array.
Dispersion equation of gravito-MHD waves
NASA Astrophysics Data System (ADS)
Jovanović, Gordana
2016-03-01
We derive the dispersion equation for gravito-MHD waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. In the present model the sound and the Alfvén speeds are constant. It is known that in this model analytical solutions can be obtained for linearized perturbations. There are three modes propagating in the considered plasma: the fast, the slow and the Alfvén mode, all modified by gravity. In the extreme short wavelength limit, these waves propagate in a locally uniform plasma. The waves with larger wavelengths will be affected by the nonuniformity of the medium resulting from the action of gravitational force ρg. In the case without magnetic field these waves become gravito-acoustic waves.
Singular boundary method using time-dependent fundamental solution for scalar wave equations
NASA Astrophysics Data System (ADS)
Chen, Wen; Li, Junpu; Fu, Zhuojia
2016-07-01
This study makes the first attempt to extend the meshless boundary-discretization singular boundary method (SBM) with time-dependent fundamental solution to two-dimensional and three-dimensional scalar wave equation upon Dirichlet boundary condition. The two empirical formulas are also proposed to determine the source intensity factors. In 2D problems, the fundamental solution integrating along with time is applied. In 3D problems, a time-successive evaluation approach without complicated mathematical transform is proposed. Numerical investigations show that the present SBM methodology produces the accurate results for 2D and 3D time-dependent wave problems with varied velocities c and wave numbers k.
Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.
Kelly, James F; McGough, Robert J
2016-08-01
The Caputo fractional wave equation [Geophys. J. R. Astron. Soc. 13, 529-539 (1967)] models power-law attenuation and dispersion for both viscoelastic and ultrasound wave propagation. The Caputo model can be derived from an underlying fractional constitutive equation and is causal. In this study, an approximate analytical time-domain Green's function is derived for the Caputo equation in three dimensions (3D) for power law exponents greater than one. The Green's function consists of a shifted and scaled maximally skewed stable distribution multiplied by a spherical spreading factor 1/(4πR). The approximate one dimensional (1D) and two dimensional (2D) Green's functions are also computed in terms of stable distributions. Finally, this Green's function is decomposed into a loss component and a diffraction component, revealing that the Caputo wave equation may be approximated by a coupled lossless wave equation and a fractional diffusion equation. PMID:27586735
Controlled-aperture wave-equation migration
Huang, L.; Fehler, Michael C.; Sun, H.; Li, Z.
2003-01-01
We present a controlled-aperture wave-equation migration method that no1 only can reduce migration artiracts due to limited recording aperlurcs and determine image weights to balance the efl'ects of limited-aperture illumination, but also can improve thc migration accuracy by reducing the slowness perturbations within thc controlled migration regions. The method consists of two steps: migration aperture scan and controlled-aperture migration. Migration apertures for a sparse distribution of shots arc determined using wave-equation migration, and those for the other shots are obtained by interpolation. During the final controlled-aperture niigration step, we can select a reference slowness in c;ontrollecl regions of the slowness model to reduce slowncss perturbations, and consequently increase the accuracy of wave-equation migration inel hods that makc use of reference slownesses. In addition, the computation in the space domain during wavefield downward continuation is needed to be conducted only within the controlled apertures and therefore, the computational cost of controlled-aperture migration step (without including migration aperture scan) is less than the corresponding uncontrolled-aperture migration. Finally, we can use the efficient split-step Fourier approach for migration-aperture scan, then use other, more accurate though more expensive, wave-equation migration methods to perform thc final controlled-apertio.ee migration to produce the most accurate image.
NASA Astrophysics Data System (ADS)
Green, A.; Gribenko, A.; Cuma, M.; Zhdanov, M. S.
2008-12-01
In this paper we apply 3D inversion to MT data collected in Oregon as a part of the EarthScope project. We use the integral equation method as a forward modeling engine. Quasi-analytical approximation with a variable background (QAVB) method of Frechet derivative calculation is applied. This technique allows us to simplify the inversion algorithm and to use just one forward modeling on every iteration step. The receiver footprint approach considerably reduces the computational resources needed to invert the large volumes of data covering vast areas. The data set, which was used in the inversion, was obtained through the Incorporated Research Institutions for Seismology (IRIS). The long-period MT data was collected in Eastern Oregon in 2006. The inverted electrical conductivity distribution agrees reasonably well with geological features of the region as well as with 3D MT inversion results obtained by other researchers. The geoelectrical model of the Oregon deep interior produced by 3D inversion indicates several lithospheres' electrical conductivity anomalies, including a linear zone marked by low-high conductivity transition along the Klamath Blue Mountain Lineament associated with a linear trend of gravity minima. High electrical conductivity values occur in the upper crust under the accreted terrains in the Blue Mountains region.
3D Hot Test Simulations of a 220 GHz Folded Waveguide Traveling Wave Tube Using a CFDTD PIC Method
NASA Astrophysics Data System (ADS)
Lin, Ming-Chieh; Song, Heather
2015-11-01
Millimeter or sub-THz wave sources centered at 220 GHz is of interest due to the potential for its commercial and military applications including high resolution radar, remote sensing, and high-data-rate communications. It has been demonstrated via 3D cold test finite element method (FEM) simulations that a folded waveguide traveling wave tube (FWTWT) can be designed and optimized at this frequency range with a small signal gain of 18 dB over a comparatively broad (-3 dB) bandwidth of ~ 10%. On the other hand, 3D hot test simulations of a V-band ladder TWT have been successfully demonstrated using a conformal finite-difference time-domain (CFDTD) particle-in-cell (PIC) method for center frequency of 50 GHz. In the present work, the 220 GHz FWTWT designs have been reviewed and studied. 3D Cold test simulations using both the CFDTD and FEM methods have been carried out and compared with each other as basis for 3D hot test CFDTD PIC simulations. The preliminary simulation result shows that the gain-bandwidth features at 220 GHz are achievable while carefully avoiding beam interceptions. Our study shows that the interaction characteristics are very sensitive to the operating beam parameters. Detail simulation results and discussions will be presented.
Local existence and Gevrey regularity of 3-D Navier-Stokes equations with ℓp initial data
NASA Astrophysics Data System (ADS)
Biswas, Animikh
We obtain local existence and Gevrey regularity of 3-D periodic Navier-Stokes equations in case the sequence of Fourier coefficients of the initial data is in ℓp (p<3/2). The ℓp norm of the sequence of Fourier coefficients of the solution and its analogous Gevrey norm remains bounded on a time interval whose length depends only on the size of the body force and the ℓp norm of the Fourier coefficient sequence of the initial data. The control on the Gevrey norm produces explicit estimates on the analyticity radius of the solution as in Foias and Temam (J. Funct. Anal. 87 (1989) 359-369). The results provide an alternate approach in estimating the space-analyticity radius of solutions to Navier-Stokes equations than the one presented by Grujić and Kukavica (J. Funct. Anal. 152 (1998) 447-466).
Recent advances in Runge-Kutta schemes for solving 3-D Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Wedan, Bruce W.; Abid, Ridha
1989-01-01
A thin-layer Navier-Stokes has been developed for solving high Reynolds number, turbulent flows past aircraft components under transonic flow conditions. The computer code has been validated through data comparisons for flow past isolated wings, wing-body configurations, prolate spheroids and wings mounted inside wind-tunnels. The basic code employs an explicit Runge-Kutta time-stepping scheme to obtain steady state solution to the unsteady governing equations. Significant gain in the efficiency of the code has been obtained by implementing a multigrid acceleration technique to achieve steady-state solutions. The improved efficiency of the code has made it feasible to conduct grid-refinement and turbulence model studies in a reasonable amount of computer time. The non-equilibrium turbulence model of Johnson and King has been extended to three-dimensional flows and excellent agreement with pressure data has been obtained for transonic separated flow over a transport type of wing.
Absence of Critical Points of Solutions to the Helmholtz Equation in 3D
NASA Astrophysics Data System (ADS)
Alberti, Giovanni S.
2016-05-01
The focus of this paper is to show the absence of critical points for the solutions to the Helmholtz equation in a bounded domain {Ωsubset{R}3} , given by div(a nabla u_{ω}g)-ω qu_{ω}g=0&quad {in Ω,} u_{ω}g=g&quad{on partialΩ.} We prove that for an admissible g there exists a finite set of frequencies K in a given interval and an open cover {overline{Ω}=\\cup_{ωin K} Ω_{ω}} such that {|nabla u_{ω}g(x)| > 0} for every {ωin K} and {xinΩ_{ω}} . The set K is explicitly constructed. If the spectrum of this problem is simple, which is true for a generic domain {Ω} , the admissibility condition on g is a generic property.
Statistical shape analysis using 3D Poisson equation-A quantitatively validated approach.
Gao, Yi; Bouix, Sylvain
2016-05-01
Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures. PMID:26874288
On the Helicity in 3D-Periodic Navier-Stokes Equations II: The Statistical Case
NASA Astrophysics Data System (ADS)
Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil
2009-09-01
We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present. Our collaborator and friend Basil Nicolaenko passed away in September of 2007, after this work was completed. Honoring his contribution and friendship, we dedicate this article to him.
A Laplacian Equation Method for Numerical Generation of Boundary-Fitted 3D Orthogonal Grids
NASA Astrophysics Data System (ADS)
Theodoropoulos, T.; Bergeles, G. C.
1989-06-01
A sethod for generating boundary fitted orthogonal curvilinear grids in 3-dimensional space is described. The mapping between the curvilinear coordinates and the Cartesian coordinates is provided by a set of Laplace equations which, expressed in curvilinear coordinates, involve the components of the metric tensor and are therefore non-linear and coupled. An iterative algorithm is described, which achieves a numerical solution. Grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery, and for other engineering applications can be constructed using the proposed method. Various examples are presented and plotted in perspective, and data for the assessment of the properties of the resulting meshes is provided.
Ultra Deep Wave Equation Imaging and Illumination
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).
3D millimeter wave imaging of vertical cracks and its application for the inspection of HDPE pipes
NASA Astrophysics Data System (ADS)
Ghasr, Mohammad Tayeb; Ying, Kuang; Zoughi, Reza
2014-02-01
Robust detection of vertical cracks in high-density polyethylene (HDPE) pipes is a challenging task for the majority of nondestructive testing (NDT) techniques. Vertical cracks are specifically referred to those whose largest planar view is parallel to the signal direction of propagation, leaving very little signal to be scattered for detection. In such pipes this commonly occurs between two pipes sections when thermally or adhesively joined. This work presents the utility and efficacy of three-dimensional (3D) millimeter wave holographical imaging based on synthetic aperture radar (SAR) algorithm for imaging such cracks. Such a 3D millimeter wave image can readily represent the type, size, and location of various flaws within a structure. Two-dimensional (2D) slices of the 3D image, at different orientations, can also be readily produced showing the cross-sectional views of the structure and flaws, further aiding in identifying, and sizing a flaw or vertical crack. Imaging results for planner and curved (pipe section) specimen with machined flaws are presented. These images are produced using a novel field-portable, small, and low-cost wideband millimeter-wave reflectometer capable of rapid 3D image production.
NASA Technical Reports Server (NTRS)
Temmer, M.; Veronig, A. M.; Gopalswamy, N.; Yashiro, S.
2011-01-01
We study the kinematical characteristics and 3D geometry of a large-scale coronal wave that occurred in association with the 26 April 2008 flare-CME event. The wave was observed with the EUVI instruments aboard both STEREO spacecraft (STEREO-A and STEREO-B) with a mean speed of approx 240 km/s. The wave is more pronounced in the eastern propagation direction, and is thus, better observable in STEREO-B images. From STEREO-B observations we derive two separate initiation centers for the wave, and their locations fit with the coronal dimming regions. Assuming a simple geometry of the wave we reconstruct its 3D nature from combined STEREO-A and STEREO-B observations. We find that the wave structure is asymmetric with an inclination toward East. The associated CME has a deprojected speed of approx 750 +/- 50 km/s, and it shows a non-radial outward motion toward the East with respect to the underlying source region location. Applying the forward fitting model developed by Thernisien, Howard, and Vourlidas we derive the CME flux rope position on the solar surface to be close to the dimming regions. We conclude that the expanding flanks of the CME most likely drive and shape the coronal wave.
Calculation of a simulated 3-D high speed inlet using the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Knight, D. D.
1983-01-01
A hybrid numerical algorithm, developed to solve the full three-dimensional Navier-Stokes equations, is applied to the computation of the flowfield in a simulated three-dimensional high speed aircraft inlet at a Mach number of 2.5 and Reynolds number of 1.4 x 10 to the 7th based on inlet length. The numerical algorithm incorporates a coordinate transformation in order to handle general flow geometries, and utilizes the algebraic turbulent eddy viscosity model of Baldwin and Lomax. The hybrid algorithm has been vectorized on the CDC CYBER 203 computer using the SL/1 vector programming language developed at NASA Langley. The computed results are compared with experimental measurements of the ramp and cowl static pressures, and boundary layer pitot profiles. The results are also compared with a previous two-dimensional Navier-Stokes computation of the same configuration. The agreement with the experimental data is generally good; however, additional improvements in turbulence modeling are needed.
A New Global Model for 3-D variations in P Wave Speed in Earth's Mantle
NASA Astrophysics Data System (ADS)
Karason, H.; van der Hilst, R. D.; Li, C.
2003-12-01
In an effort to improve the resolution of mantle structure we have combined complementary data sets of short- and long period (absolute and differential) travel time residuals. Our new model is based on short period P (N\\~7.7x10**6), pP (N\\~2.3x10**5), and PKP (N\\~16x10**4) data from the catalog by Engdahl et al (BSSA, 1998), short-period PKP differential times (N\\~1600) measured by McSweeney & Creager, and long-period differential PP-P times - N\\~20,000 measured by Bolton & Masters and N\\~18,000 by Ritsema - and Pdiff-PKP (N\\~560) measured by Wysession. Inversion tests, spectral analysis, and comparison with geology indicate that the large-scale upper mantle structure is better constrained with the addition of PP-P, whereas the Pdiff and PKP data help constrain deep mantle structure (Karason & Van der Hilst, JGR, 2001). The long period data were measured by cross-correlation. We solved the system of equations using 400 iterations of the iterative algorithm LSQR For the short period (1 Hz) data we use a high frequency approximation and trace rays through a fine grid of constant slowness cells to invert for mantle structure. For low frequency Pdiff and PP data we account for sensitivity to structure away from the optical ray path with 3-D Frechet derivatives (sensitivity kernels) estimated from single forward scattering and projected onto basis functions (constant slowness blocks) used for model parameterization. With such kernels the low frequency data can constrain long wavelength heterogeneity without keeping the short period data from mapping details in densely sampled regions. In addition to finite frequency sensitivity kernels we optimized the localization by using a parameterization that adapts to spatial resolution, with small cells in regions of dense sampling and larger cells in regions where sampling is more sparse (the total number of cells was \\~ 350,000). Finally, we corrected all travel times and surface reflections for lateral variations in
NASA Astrophysics Data System (ADS)
Gabl, R.; Seibl, J.; Gems, B.; Aufleger, M.
2015-12-01
The impact of an avalanche in a reservoir induces impulse waves, which pose a threat to population and infrastructure. For a good approximation of the generated wave height and length as well as the resulting overtopping volume over structures and dams, formulas, which are based on different simplifying assumptions, can be used. Further project-specific investigations by means of a scale model test or numerical simulations are advisable for complex reservoirs as well as the inclusion of hydraulic structures such as spillways. This paper presents a new approach for a 3-D numerical simulation of the avalanche impact in a reservoir. In this model concept the energy and mass of the avalanche are represented by accelerated water on the actual hill slope. Instead of snow, only water and air are used to simulate the moving avalanche with the software FLOW-3D. A significant advantage of this assumption is the self-adaptation of the model avalanche onto the terrain. In order to reach good comparability of the results with existing research at ETH Zürich, a simplified reservoir geometry is investigated. Thus, a reference case has been analysed including a variation of three geometry parameters (still water depth in the reservoir, freeboard of the dam and reservoir width). There was a good agreement of the overtopping volume at the dam between the presented 3-D numerical approach and the literature equations. Nevertheless, an extended parameter variation as well as a comparison with natural data should be considered as further research topics.
NASA Astrophysics Data System (ADS)
Gumerov, Nail A.; Karavaev, Alexey V.; Surjalal Sharma, A.; Shao, Xi; Papadopoulos, Konstantinos D.
2011-04-01
Efficient spectral and pseudospectral algorithms for simulation of linear and nonlinear 3D whistler waves in a cold electron plasma are developed. These algorithms are applied to the simulation of whistler waves generated by loop antennas and spheromak-like stationary waves of considerable amplitude. The algorithms are linearly stable and show good stability properties for computations of nonlinear waves over tens of thousands of time steps. Additional speedups by factors of 10-20 (comparing single core CPU and one GPU) are achieved by using graphics processors (GPUs), which enable efficient numerical simulation of the wave propagation on relatively high resolution meshes (tens of millions nodes) in personal computing environment. Comparisons of the numerical results with analytical solutions and experiments show good agreement. The limitations of the codes and the performance of the GPU computing are discussed.
Homentcovschi, Dorel; Miles, Ronald N.
2008-01-01
An analysis is presented of the diffraction of a pressure wave by a periodic grating including the influence of the air viscosity. The direction of the incoming pressure wave is arbitrary. As opposed to the classical nonviscous case, the problem cannot be reduced to a plane problem having a definite 3-D character. The system of partial differential equations used for solving the problem consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to a system of two hypersingular integral equations for determining the velocity components in the slits’ plane and a hypersingular integral equation for the normal component of velocity. These equations are solved by using Galerkin’s method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in MEMS technology. In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The analysis indicates that the openings in the screen should be on the order of 10 microns in order to avoid excessive attenuation of the signal. This paper also provides the variation of the transmission coefficient with frequency in the acoustical domain. PMID:19122753
NASA Astrophysics Data System (ADS)
Pankratov, Oleg; Kuvshinov, Alexey
2016-01-01
second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach.
Internal waves patterns in the wake of a 3D body towed in a two-layer fluid
NASA Astrophysics Data System (ADS)
Lacaze, Laurent; Mercier, Matthieu; Thual, Olivier; Paci, Alexandre
2014-11-01
Stratified flows over obstacles are important features in meteorology and oceanography. The characterization of these flows is crucial in order to propose models of geophysical processes such as mixing and ocean circulation or orographic drag in the atmosphere. For some specific stratification profiles, the energy of internal waves generated by the obstacle can be trapped at a given depth, at the base of the oceanic mixing layer or at the top of the atmospheric boundary layer for instance. This scenario can be modelled by a two-layer stratified fluid for which gravity waves spread at the interface between the two layers. The work presented here focuses on a two-layer flow over a 3D obstacle, or equivalently, an obstacle towed in a fluid at rest. Experiments performed both in the large-scale flume of CNRM-GAME Toulouse (METEO-FRANCE & CNRS) and in a smaller tank apparatus, are presented with a specific attention on the measurement of the 3D wave patterns. A non-hydrostatic linear analysis is used to describe the observed wave patterns. The experiments highlight the strong influence of the Froude number on the generated waves. More specifically, we investigate the nature of the wake angle obtained from the wave pattern, and discuss a transition from Kelvin to Mach angle.
Spectral element modeling of 3D wave propagation in the Earth: the graver part of the spectrum
NASA Astrophysics Data System (ADS)
Chaljub, E.; Valette, B.
2003-04-01
The Spectral Element Method (SEM) has been recently established as a new reference to compute synthetic seismograms in 3D models of the Earth. So far, all the studies involving the SEM have been performed within the Cowling approximation, i. e. neglecting the variations of the gravity field during wave propagation. For low-frequency studies (typically less than 5 mHz) the previous assumption fails and the complete treatment of self-gravitation has to be considered. This requires the introduction of the mass redistribution potential (MRP) which has to satisfy Poisson's equation everywhere in space. Unlike spherical harmonics approaches, the use of a grid based method does not provide a natural framework for the resolution of the exterior problem. However, we show that a Dirichlet-to-Neumann operator at the surface of the Earth provides a simple and efficient solution to this problem. A special attention is needed for the fluid parts to avoid spurious oscillations. To this end, we introduce a general two-potentials formulation which allows to take any density stratification into account. Contrary to other studies that considered the velocity potential, our decomposition is applied to the displacement field in order to obtain natural solid-fluid boundary conditions for the MRP. At each time step, the MRP is computed from the displacement field through a preconditioned conjugate gradient algorithm. This procedure has to be accurate enough in order to ensure a stable calculation on long time series. Some examples of synthetic seismograms computed in spherical Earth models illustrate the accuracy of our approach.
NASA Astrophysics Data System (ADS)
Shi, Jian; Zhang, Qian
2016-03-01
A uniqueness result of weak solution for the 3D viscous magneto-hydrodynamics equations in {B^1_{infty,infty}} is proved by means of the Fourier localization technique and the losing derivative estimates.
Conformally invariant wave equations for massless particles
NASA Astrophysics Data System (ADS)
McLennan, James A.
1984-07-01
The invariance of wave equations for massless particles under conformal transformations of space-time is briefly summarized. Particular attention is given to a recent paper by Bracken and Jessup in which it is claimed that results obtained by the author are in error. Their paper contains several misleading statements based on a misreading of the author's paper, and in addition an argument of theirs, intended to show error, is itself invalid. Their claims of error on the author's part are therefore unfounded.
NASA Astrophysics Data System (ADS)
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Ibraheem, S. O.
1993-01-01
The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.
NASA Astrophysics Data System (ADS)
Newton, W. G.; Stone, J. R.; Mezzacappa, A.
2006-09-01
First results from a fully self-consistent, temperature-dependent equation of state that spans the density range of neutron stars and supernova cores above neutron drip density are presented. The equation of state (EoS) is calculated using a mean-field Hartree-Fock method in three dimensions (3D). The nuclear interaction is represented by the phenomenological Skyrme model in this work, but the EoS can be obtained in our framework for any suitable form of the nucleon-nucleon effective interaction. The scheme we employ naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state is calculated across phase transitions without recourse to interpolation techniques between density regimes described by different physical models. EoS tables are calculated in the wide range of densities, temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000 processors simultaneously.
NASA Astrophysics Data System (ADS)
Uhrig, Matthias P.; Kim, Jin-Yeon; Jacobs, Laurence J.
2016-02-01
This research presents a 3D numerical finite element (FE) model which, previously developed, precisely simulates non-contact, air-coupled measurements of nonlinear Rayleigh wave propagation. The commercial FE-solver ABAQUS is used to perform the simulations. First, frequency dependent pressure wave attenuation is investigated numerically to reconstruct the sound pressure distribution along the active surface of the non-contact receiver. Second, constitutive law and excitation source properties are optimized to match nonlinear ultrasonic experimental data. Finally, the FE-model data are fit with analytical solutions showing a good agreement and thus, indicating the significance of the study performed.
NASA Astrophysics Data System (ADS)
Obermann, Anne; Planès, Thomas; Hadziioannou, Céline; Campillo, Michel
2016-07-01
In the context of seismic monitoring, recent studies made successful use of seismic coda waves to locate medium changes on the horizontal plane. Locating the depth of the changes, however, remains a challenge. In this paper, we use 3-D wavefield simulations to address two problems: firstly, we evaluate the contribution of surface and body wave sensitivity to a change at depth. We introduce a thin layer with a perturbed velocity at different depths and measure the apparent relative velocity changes due to this layer at different times in the coda and for different degrees of heterogeneity of the model. We show that the depth sensitivity can be modelled as a linear combination of body- and surface-wave sensitivity. The lapse-time dependent sensitivity ratio of body waves and surface waves can be used to build 3-D sensitivity kernels for imaging purposes. Secondly, we compare the lapse-time behavior in the presence of a perturbation in horizontal and vertical slabs to address, for instance, the origin of the velocity changes detected after large earthquakes.
An IPOT meshless method using DC PSE approximation for fluid flow equations in 2D and 3D geometries
NASA Astrophysics Data System (ADS)
Bourantas, G. C.; Loukopoulos, V. C.; Skouras, E. D.; Burganos, V. N.; Nikiforidis, G. C.
2016-06-01
Navier-Stokes (N-S) equations, in their primitive variable (u-v-p) formulation, are numerically solved using the Implicit Potential (IPOT) numerical scheme in the context of strong form Meshless Point Collocation (MPC) method. The unknown field functions are computed using the Discretization Correction Particle Strength Exchange (DC PSE) approximation method. The latter makes use of discrete moment conditions to derive the operator kernels, which leads to low condition number for the moment matrix compared to other meshless interpolation methods and increased stability for the numerical solution. The proposed meshless scheme is applied on 2D and 3D spatial domains, using uniform or irregular set of nodes to represent the domain. The numerical results obtained are compared against those obtained using well-established methods.
Prediction of Tsunami Waves and Runup Generated by 3d Granular Landslides
NASA Astrophysics Data System (ADS)
Mohammed, F.; Fritz, H. M.
2008-12-01
Subaerial and submarine landslides can trigger tsunamis with locally high amplitudes and runup, which can cause devastating effects in the near field region. The 50th anniversary of the Lituya Bay 1958 landslide impact generated mega tsunami recalls the largest tsunami runup of 524m in recorded history. In contrast to earthquake generated tsunamis, landslide generated tsunami sources are not confined to active tectonic regions and therefore are of particular importance for the Atlantic Ocean. Landslide generated tsunamis were studied in the three dimensional NEES tsunami wave basin TWB at OSU based on the generalized Froude similarity. A novel pneumatic landslide generator was deployed to control the landslide geometry and kinematics. Granular materials were used to model deformable landslides. Measurement techniques such as particle image velocimetry (PIV), multiple above and underwater video cameras, multiple acoustic transducer arrays (MTA), as well as resistance wave and runup gauges were applied. The wave generation was characterized by an extremely unsteady three phase flow consisting of the slide granulate, water and air entrained into the flow. The underwater cameras and the MTA provide data on the landslide deformation as it impacts the water surface, penetrates the water and finally deposits on the bottom of the basin. The influence of the landslide volume, shape and the impact speed on the generated tsunami wave characteristics were extensively studied. The experimental data provides prediction models for the generated tsunami wave characteristics based on the initial landslide characteristics and the final slide deposits. PIV provided instantaneous surface velocity vector fields, which gave insight into the kinematics of the landslide and wave generation process. At high impact velocities flow separation occurred on the slide shoulder resulting in a hydrodynamic impact crater. The recorded wave profiles yielded information on the wave propagation and
3D finite element modelling of guided wave scattering at delaminations in composites
NASA Astrophysics Data System (ADS)
Murat, Bibi Intan Suraya; Fromme, Paul
2016-02-01
Carbon fiber laminate composites are increasingly used for aerospace structures as they offer a number of advantages including a good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, delaminations can occur, reducing the load carrying capacity of the structure. Efficient nondestructive testing of composite panels can be achieved using guided ultrasonic waves propagating along the structure. The guided wave (A0 Lamb wave mode) scattering at delaminations was modeled using full three-dimensional Finite Element (FE) simulations. The influence of the delamination size was systematically investigated from a parameter study. A significant influence of the delamination width on the guided wave scattering was found, especially on the angular dependency of the scattered guided wave amplitude. The sensitivity of guided ultrasonic waves for the detection of delamination damage in composite panels is discussed.
WaveQ3D: Fast and accurate acoustic transmission loss (TL) eigenrays, in littoral environments
NASA Astrophysics Data System (ADS)
Reilly, Sean M.
This study defines a new 3D Gaussian ray bundling acoustic transmission loss model in geodetic coordinates: latitude, longitude, and altitude. This approach is designed to lower the computation burden of computing accurate environmental effects in sonar training application by eliminating the need to transform the ocean environment into a collection of Nx2D Cartesian radials. This approach also improves model accuracy by incorporating real world 3D effects, like horizontal refraction, into the model. This study starts with derivations for a 3D variant of Gaussian ray bundles in this coordinate system. To verify the accuracy of this approach, acoustic propagation predictions of transmission loss, time of arrival, and propagation direction are compared to analytic solutions and other models. To validate the model's ability to predict real world phenomena, predictions of transmission loss and propagation direction are compared to at-sea measurements, in an environment where strong horizontal refraction effect have been observed. This model has been integrated into U.S. Navy active sonar training system applications, where testing has demonstrated its ability to improve transmission loss calculation speed without sacrificing accuracy.
Analysis of non linear partially standing waves from 3D velocity measurements
NASA Astrophysics Data System (ADS)
Drevard, D.; Rey, V.; Svendsen, Ib; Fraunie, P.
2003-04-01
Surface gravity waves in the ocean exhibit an energy spectrum distributed in both frequency and direction of propagation. Wave data collection is of great importance in coastal zones for engineering and scientific studies. In particular, partially standing waves measurements near coastal structures and steep or barred beaches may be a requirement, for instance for morphodynamic studies. The aim of the present study is the analysis of partially standing surface waves icluding non-linear effects. According to 1st order Stokes theory, synchronous measurements of horizontal and vertical velocity components allow calculation of rate of standing waves (Drevard et al, 2003). In the present study, it is demonstrated that for deep water conditions, partially standing 2nd order Stokes waves induced velocity field is still represented by the 1st order solution for the velocity potential contrary to the surface elevation which exhibits harmonic components. For intermediate water depth, harmonic components appear not only in the surface elevation but also in the velocity fields, but their weight remains much smaller, because of the vertical decreasing wave induced motion. For irregular waves, the influence of the spectrum width on the non-linear effects in the analysis is discussed. Keywords: Wave measurements ; reflection ; non-linear effects Acknowledgements: This work was initiated during the stay of Prof. Ib Svendsen, as invited Professor, at LSEET in autumn 2002. This study is carried out in the framework of the Scientific French National Programmes PNEC ART7 and PATOM. Their financial supports are acknowledged References: Drevard, D., Meuret, A., Rey, V. Piazzola, J. And Dolle, A.. (2002). "Partially reflected waves measurements using Acoustic Doppler Velocimeter (ADV)", Submitted to ISOPE 03, Honolulu, Hawaii, May 2003.
NASA Astrophysics Data System (ADS)
Deng, Y.; Ebert-Uphoff, I.; Chen, J.
2015-12-01
Causal discovery seeks to discover potential cause-effect relationships from observational data. Here we adopt the idea of interpreting large-scale atmospheric dynamical processes, particularly those tied to propagation of large-scale waves, as information flow around the globe, which can then be calculated using causal discovery methods. We apply a well-established causal discovery algorithm - based on constraint-based structure learning of probabilistic graphical models - toward 51 years of 6-hourly, atmospheric isobaric-level geopotential height data to construct the first-ever graphs of 3D information flow in the atmosphere. These graphs are created globally for different seasons and their connection to phase/energy propagation of atmospheric waves are investigated. Specifically, we examine the information flows 1) in the topical region that represent horizontal and vertical propagations of Kelvin and Rossby-gravity waves whose associated momentum transfer are known to play a key role in the Quasi-Biennial Oscillation (QBO), and 2) in the northern extratropics that represent propagations of planetary-scale waves whose heat/momentum fluxes are responsible for vacillations in the polar stratospheric vortex and occurrences of extreme events such as the stratospheric sudden warming. The sensitivity of the constructed graphs of 3D information flow to data resolution and pre-processing methods (e.g., spatial and temporal filtering) will be discussed.
Wang, Tao; Green, Ryan; Nair, Rajesh Ramakrishnan; Howell, Mark; Mohapatra, Subhra; Guldiken, Rasim; Mohapatra, Shyam Sundar
2015-01-01
Detection and quantification of cell viability and growth in two-dimensional (2D) and three-dimensional (3D) cell cultures commonly involve harvesting of cells and therefore requires a parallel set-up of several replicates for time-lapse or dose–response studies. Thus, developing a non-invasive and touch-free detection of cell growth in longitudinal studies of 3D tumor spheroid cultures or of stem cell regeneration remains a major unmet need. Since surface acoustic waves (SAWs) permit mass loading-based biosensing and have been touted due to their many advantages including low cost, small size and ease of assembly, we examined the potential of SAW-biosensing to detect and quantify cell growth. Herein, we demonstrate that a shear horizontal-surface acoustic waves (SH-SAW) device comprising two pairs of resonators consisting of interdigital transducers and reflecting fingers can be used to quantify mass loading by the cells in suspension as well as within a 3D cell culture platform. A 3D COMSOL model was built to simulate the mass loading response of increasing concentrations of cells in suspension in the polydimethylsiloxane (PDMS) well in order to predict the characteristics and optimize the design of the SH-SAW biosensor. The simulated relative frequency shift from the two oscillatory circuit systems (one of which functions as control) were found to be concordant to experimental data generated with RAW264.7 macrophage and A549 cancer cells. In addition, results showed that SAW measurements per se did not affect viability of cells. Further, SH-SAW biosensing was applied to A549 cells cultured on a 3D electrospun nanofiber scaffold that generate tumor spheroids (tumoroids) and the results showed the device's ability to detect changes in tumor spheroid growth over the course of eight days. Taken together, these results demonstrate the use of SH-SAW device for detection and quantification of cell growth changes over time in 2D suspension cultures and in 3D cell
Wang, Tao; Green, Ryan; Nair, Rajesh Ramakrishnan; Howell, Mark; Mohapatra, Subhra; Guldiken, Rasim; Mohapatra, Shyam Sundar
2015-01-01
Detection and quantification of cell viability and growth in two-dimensional (2D) and three-dimensional (3D) cell cultures commonly involve harvesting of cells and therefore requires a parallel set-up of several replicates for time-lapse or dose-response studies. Thus, developing a non-invasive and touch-free detection of cell growth in longitudinal studies of 3D tumor spheroid cultures or of stem cell regeneration remains a major unmet need. Since surface acoustic waves (SAWs) permit mass loading-based biosensing and have been touted due to their many advantages including low cost, small size and ease of assembly, we examined the potential of SAW-biosensing to detect and quantify cell growth. Herein, we demonstrate that a shear horizontal-surface acoustic waves (SH-SAW) device comprising two pairs of resonators consisting of interdigital transducers and reflecting fingers can be used to quantify mass loading by the cells in suspension as well as within a 3D cell culture platform. A 3D COMSOL model was built to simulate the mass loading response of increasing concentrations of cells in suspension in the polydimethylsiloxane (PDMS) well in order to predict the characteristics and optimize the design of the SH-SAW biosensor. The simulated relative frequency shift from the two oscillatory circuit systems (one of which functions as control) were found to be concordant to experimental data generated with RAW264.7 macrophage and A549 cancer cells. In addition, results showed that SAW measurements per se did not affect viability of cells. Further, SH-SAW biosensing was applied to A549 cells cultured on a 3D electrospun nanofiber scaffold that generate tumor spheroids (tumoroids) and the results showed the device's ability to detect changes in tumor spheroid growth over the course of eight days. Taken together, these results demonstrate the use of SH-SAW device for detection and quantification of cell growth changes over time in 2D suspension cultures and in 3D cell
NASA Astrophysics Data System (ADS)
Lin, C. W.; Wu, T. R.; Chuang, M. H.; Tsai, Y. L.
2015-12-01
The wind in Taiwan Strait is strong and stable which offers an opportunity to build offshore wind farms. However, frequently visited typhoons and strong ocean current require more attentions on the wave force and local scour around the foundation of the turbine piles. In this paper, we introduce an in-house, multi-phase CFD model, Splash3D, for solving the flow field with breaking wave, strong turbulent, and scour phenomena. Splash3D solves Navier-Stokes Equation with Large-Eddy Simulation (LES) for the fluid domain, and uses volume of fluid (VOF) with piecewise linear interface reconstruction (PLIC) method to describe the break free-surface. The waves were generated inside the computational domain by internal wave maker with a mass-source function. This function is designed to adequately simulate the wave condition under observed extreme events based on JONSWAP spectrum and dispersion relationship. Dirichlet velocity boundary condition is assigned at the upper stream boundary to induce the ocean current. At the downstream face, the sponge-layer method combined with pressure Dirichlet boundary condition is specified for dissipating waves and conducting current out of the domain. Numerical pressure gauges are uniformly set on the structure surface to obtain the force distribution on the structure. As for the local scour around the foundation, we developed Discontinuous Bi-viscous Model (DBM) for the development of the scour hole. Model validations were presented as well. The force distribution under observed irregular wave condition was extracted by the irregular-surface force extraction (ISFE) method, which provides a fast and elegant way to integrate the force acting on the surface of irregular structure. From the Simulation results, we found that the total force is mainly induced by the impinging waves, and the force from the ocean current is about 2 order of magnitude smaller than the wave force. We also found the dynamic pressure, wave height, and the
NASA Astrophysics Data System (ADS)
Montiel, F.; Squire, V. A.
2013-12-01
A new ocean wave/sea-ice interaction model is proposed that simulates how a directional wave spectrum evolves as it travels through a realistic marginal ice zone (MIZ), where wave/ice dynamics are entirely governed by coherent conservative wave scattering effects. Field experiments conducted by Wadhams et al. (1986) in the Greenland Sea generated important data on wave attenuation in the MIZ and, particularly, on whether the wave spectrum spreads directionally or collimates with distance from the ice edge. The data suggest that angular isotropy, arising from multiple scattering by ice floes, occurs close to the edge and thenceforth dominates wave propagation throughout the MIZ. Although several attempts have been made to replicate this finding theoretically, including by the use of numerical models, none have confronted this problem in a 3D MIZ with fully randomised floe distribution properties. We construct such a model by subdividing the discontinuous ice cover into adjacent infinite slabs of finite width parallel to the ice edge. Each slab contains an arbitrary (but finite) number of circular ice floes with randomly distributed properties. Ice floes are modeled as thin elastic plates with uniform thickness and finite draught. We consider a directional wave spectrum with harmonic time dependence incident on the MIZ from the open ocean, defined as a continuous superposition of plane waves traveling at different angles. The scattering problem within each slab is then solved using Graf's interaction theory for an arbitrary incident directional plane wave spectrum. Using an appropriate integral representation of the Hankel function of the first kind (see Cincotti et al., 1993), we map the outgoing circular wave field from each floe on the slab boundaries into a directional spectrum of plane waves, which characterizes the slab reflected and transmitted fields. Discretizing the angular spectrum, we can obtain a scattering matrix for each slab. Standard recursive
NASA Astrophysics Data System (ADS)
Sidler, Rolf; Carcione, José M.; Holliger, Klaus
2014-02-01
We present a novel approach for the comprehensive, flexible and accurate simulation of poroelastic wave propagation in 3-D cylindrical coordinates. An important application of this method is the realistic modelling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, as of yet largely unresolved, problem in exploration geophysics. To this end, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the centre followed by the mudcake and/or casing, and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction and Fourier expansions in the vertical and azimuthal directions as well as a Runge-Kutta integration scheme for the time evolution. Trigonometric interpolation and a domain decomposition method based on the method of characteristics are used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces as well as to reduce the number of gridpoints in the innermost domain for computational efficiency. We apply this novel modelling approach to the particularly challenging scenario of near-surface borehole environments. To this end, we compare 3-D heterogeneous and corresponding rotationally invariant simulations, assess the sensitivity of Stoneley waves to formation permeability in the presence of a casing and evaluate the effects of an excavation damage zone behind a casing on sonic log recordings. Our results indicate that only first arrival times of fast modes are reasonably well described by rotationally invariant approximations of 3-D heterogenous media. We also find that Stoneley waves are indeed remarkably sensitive to the average permeability behind a perforated PVC casing, and that the presence of an excavation damage zone behind a casing tends to dominate the overall signature of recorded seismograms.
NASA Astrophysics Data System (ADS)
Parisi, Laura; Ferreira, Ana M. G.
2016-04-01
The surface wave full ray theory (FRT) is an efficient tool to calculate synthetic waveforms of surface waves. It combines the concept of local modes with exact ray tracing as a function of frequency, providing a more complete description of surface wave propagation than the widely used great circle approximation (GCA). The purpose of this study is to evaluate the ability of the FRT approach to model teleseismic long-period surface waveforms (T ˜ 45-150 s) in the context of current 3-D Earth models to empirically assess its validity domain and its scope for future studies in seismic tomography. To achieve this goal, we compute vertical and horizontal component fundamental mode synthetic Rayleigh waveforms using the FRT, which are compared with calculations using the highly accurate spectral element method. We use 13 global earth models including 3-D crustal and mantle structure, which are derived by successively varying the strength and lengthscale of heterogeneity in current tomographic models. For completeness, GCA waveforms are also compared with the spectral element method. We find that the FRT accurately predicts the phase and amplitude of long-period Rayleigh waves (T ˜ 45-150 s) for almost all the models considered, with errors in the modelling of the phase (amplitude) of Rayleigh waves being smaller than 5 per cent (10 per cent) in most cases. The largest errors in phase and amplitude are observed for T ˜ 45 s and for the three roughest earth models considered that exhibit shear wave anomalies of up to ˜20 per cent, which is much larger than in current global tomographic models. In addition, we find that overall the GCA does not predict Rayleigh wave amplitudes well, except for the longest wave periods (T ˜ 150 s) and the smoothest models considered. Although the GCA accurately predicts Rayleigh wave phase for current earth models such as S20RTS and S40RTS, FRT's phase errors are smaller, notably for the shortest wave periods considered (T ˜ 45 s and
Skin-friction measurements in a 3-D, supersonic shock-wave/boundary-layer interaction
NASA Astrophysics Data System (ADS)
Wideman, Jeffrey Kenneth
An experimental study has been conducted in a three-dimensional, supersonic shockwave/boundary-layer interaction (3-D SW/BLI) with the intent of providing accurate experimental data for turbulence modeling and computational fluid dynamics (CFD) code validation. The experiment was performed in the High Reynolds Channel 1 (HRCI) wind tunnel at NASA Ames Research Center. The test was conducted at a Mach number of M(sub infinity) = 2.89 and at a Reynolds number of Re = 15 x 106/m. The model consisted of a sting-supported cylinder aligned with the tunnel axis and a 20 deg half-angle conical flare offset 1.27 cm from the cylinder centerline. The generated shock system was verified to be steady by schlieren visualization. The highlight of the study was the acquisition of 3-D skin-friction data by a laser interferometric skin friction (LISF) meter. Surface pressure measurements were obtained in 15 deg intervals around the cylinder and flare. Additional measurements included surface oil flow and laser light sheet illumination which were used to document the flow topology. Skin-friction measurements are proving to be a very challenging test of a CFD code predictive capability. However, at the present time there is a very limited amount of accurate skin-friction data in complex flows such as in 3-D SW/BLI. The LISF technique is advantageous as compared to other skin-friction measurement techniques for application in complex flows like the present since it is non-intrusive and is capable of performing measurements in flows with large shear and pressure gradients where the reliability of other techniques is questionable. Thus, the prevent skin-friction data will prove valuable to turbulence modeling and CFD code validation efforts.
Propagation of 3D nonlinear waves over complex bathymetry using a High-Order Spectral method
NASA Astrophysics Data System (ADS)
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2016-04-01
Scattering of regular and irregular surface gravity waves propagating over a region of arbitrary three-dimensional varying bathymetry is considered here. The three-dimensional High-Order Spectral method (HOS) with an extension to account for a variable bathymetry is used. The efficiency of the model has been proved to be conserved even with this extension. The method is first applied to a bathymetry consisting of an elliptical lens, as used in the Vincent and Briggs (1989) experiment. Incident waves passing across the lens are transformed and a strong convergence region is observed after the elliptical mound. The wave amplification depends on the incident wave. Numerical results for regular and irregular waves are analysed and compared with other methods and experimental data demonstrating the efficiency and practical applicability of the present approach. Then the method is used to model waves propagating over a real bathymetry: the canyons of Scripps/La Jolla in California. The implementation of this complex bathymetry in the model is presented, as well as the first results achieved. They will be compared to the ones obtained with another numerical model.
NASA Astrophysics Data System (ADS)
Bennis, A.; Ardhuin, F.; Dumas, F.; Bonneton, P.
2010-12-01
The interaction of waves with three-dimensional current structure is investigated using a two-way coupled modelling system combining MARS3D (Lazure and Dumas 2008) with WAVEWATCH III (Tolman 2008, Ardhuin et al. 2009) , a wave model (NOAA/NCEP, Tolman 2008). After a basic validation in two dimensions, the flow model MARS3D was adapted with three options that solve for the total momentum (Mellor 2003, 2008) or the quasi-Eulerian momentum (Ardhuin et al. 2008b). Adiabatic model results show that, as expected from theory (Ardhuin et al. 2008a), the total momentum fluxes parameterized by Mellor are not self-consistent and can lead to very large errors (Bennis and Ardhuin 2010). We thus use the model option to solve for the quasi-Eulerian momentum, including sources of momentum and turbulent kinetic energy (TKE). The influence of these TKE sources is investigated in the case of the NSTS experiment (Thornton and Guza, 1986). The feedback of the currents on the waves is negligible in this case. The sources of TKE from wave breaking and wave bottom friction are found to have strong influence on the bottom friction, in a way consistent with the parameterizations by Longuet-Higgins (1970) and Mellor (2002). The complete model is then applied to a real case of a large rip current on the South-West coast of France (Bruneau et al., Cont. Shelf Res. 2009). The breaking of waves on the opposed current generates a strong coupling on the rip current that partially controls the strength of the current and it three-dimensional shape.
Conducting a 3D Converted Shear Wave Project to Reduce Exploration Risk at Wister, CA
Matlick, Skip; Walsh, Patrick; Rhodes, Greg; Fercho, Steven
2015-06-30
Ormat sited 2 full-size exploration wells based on 3D seismic interpretation of fractures, prior drilling results, and temperature anomaly. The wells indicated commercial temperatures (>300 F), but almost no permeability, despite one of the wells being drilled within 820 ft of an older exploration well with reported indications of permeability. Following completion of the second well in 2012, Ormat undertook a lengthy program to 1) evaluate the lack of observed permeability, 2) estimate the likelihood of finding permeability with additional drilling, and 3) estimate resource size based on an anticipated extent of permeability.
Display depth analyses with the wave aberration for the auto-stereoscopic 3D display
NASA Astrophysics Data System (ADS)
Gao, Xin; Sang, Xinzhu; Yu, Xunbo; Chen, Duo; Chen, Zhidong; Zhang, Wanlu; Yan, Binbin; Yuan, Jinhui; Wang, Kuiru; Yu, Chongxiu; Dou, Wenhua; Xiao, Liquan
2016-07-01
Because the aberration severely affects the display performances of the auto-stereoscopic 3D display, the diffraction theory is used to analyze the diffraction field distribution and the display depth through aberration analysis. Based on the proposed method, the display depth of central and marginal reconstructed images is discussed. The experimental results agree with the theoretical analyses. Increasing the viewing distance or decreasing the lens aperture can improve the display depth. Different viewing distances and the LCD with two lens-arrays are used to verify the conclusion.
Emergence of wave equations from quantum geometry
NASA Astrophysics Data System (ADS)
Majid, Shahn
2012-10-01
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
Emergence of wave equations from quantum geometry
Majid, Shahn
2012-09-24
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
A dispersive wave equation using nonlocal elasticity
NASA Astrophysics Data System (ADS)
Challamel, Noël; Rakotomanana, Lalaonirina; Le Marrec, Loïc
2009-08-01
Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This Note investigates a model of wave propagation in a nonlocal elastic material. We show that a dispersive wave equation is obtained from a nonlocal elastic constitutive law, based on a mixture of a local and a nonlocal strain. This model comprises both the classical gradient model and the Eringen's integral model. The dynamic properties of the model are discussed, and corroborate well some recent theoretical studies published to unify both static and dynamics gradient elasticity theories. Moreover, an excellent matching of the dispersive curve of the Born-Kármán model of lattice dynamics is obtained with such nonlocal model. To cite this article: N. Challamel et al., C. R. Mecanique 337 (2009).
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
SAFE-3D analysis of a piezoelectric transducer to excite guided waves in a rail web
NASA Astrophysics Data System (ADS)
Ramatlo, Dineo A.; Long, Craig S.; Loveday, Philip W.; Wilke, Daniel N.
2016-02-01
Our existing Ultrasonic Broken Rail Detection system detects complete breaks and primarily uses a propagating mode with energy concentrated in the head of the rail. Previous experimental studies have demonstrated that a mode with energy concentrated in the head of the rail, is capable of detecting weld reflections at long distances. Exploiting a mode with energy concentrated in the web of the rail would allow us to effectively detect defects in the web of the rail and could also help to distinguish between reflections from welds and cracks. In this paper, we will demonstrate the analysis of a piezoelectric transducer attached to the rail web. The forced response at different frequencies is computed by the Semi-Analytical Finite Element (SAFE) method and compared to a full three-dimensional finite element method using ABAQUS. The SAFE method only requires the rail track cross-section to be meshed using two-dimensional elements. The ABAQUS model in turn requires a full three-dimensional discretisation of the rail track. The SAFE approach can yield poor predictions at cut-on frequencies associated with other modes in the rail. Problematic frequencies are identified and a suitable frequency range identified for transducer design. The forced response results of the two methods were found to be in good agreement with each other. We then use a previously developed SAFE-3D method to analyse a practical transducer over the selected frequency range. The results obtained from the SAFE-3D method are in good agreement with experimental measurements.
Rigas, Fotis; Sklavounos, Spyros
2005-05-20
Accidental blast wave generation and propagation in the surroundings poses severe threats for people and property. The prediction of overpressure maxima and its change with time at specified distances can lead to useful conclusions in quantitative risk analysis applications. In this paper, the use of a computational fluid dynamics (CFD) code CFX-5.6 on dense explosive detonation events is described. The work deals with the three-dimensional simulation of overpressure wave propagation generated by the detonation of a dense explosive within a small-scale branched tunnel. It also aids at validating the code against published experimental data as well as to study the way that the resulting shock wave propagates in a confined space configuration. Predicted overpressure histories were plotted and compared versus experimental measurements showing a reasonably good agreement. Overpressure maxima and corresponding times were found close to the measured ones confirming that CFDs may constitute a useful tool in explosion hazard assessment procedures. Moreover, it was found that blast wave propagates preserving supersonic speed along the tunnel accompanied by high overpressure levels, and indicating that space confinement favors the formation and maintenance of a shock rather than a weak pressure wave. PMID:15885402
NASA Astrophysics Data System (ADS)
Liu, Yang; Sen, Mrinal K.
2011-09-01
Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations. Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of
NASA Astrophysics Data System (ADS)
Simpson, J. J.; Taflove, A.
2005-12-01
We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A
Real-time 3D millimeter wave imaging based FMCW using GGD focal plane array as detectors
NASA Astrophysics Data System (ADS)
Levanon, Assaf; Rozban, Daniel; Kopeika, Natan S.; Yitzhaky, Yitzhak; Abramovich, Amir
2014-03-01
Millimeter wave (MMW) imaging systems are required for applications in medicine, communications, homeland security, and space technology. This is because there is no known ionization hazard for biological tissue, and atmospheric attenuation in this range of the spectrum is relatively low. The lack of inexpensive room temperature imaging systems makes it difficult to give a suitable MMW system for many of the above applications. 3D MMW imaging system based on chirp radar was studied previously using a scanning imaging system of a single detector. The system presented here proposes to employ a chirp radar method with a Glow Discharge Detector (GDD) Focal Plane Array (FPA) of plasma based detectors. Each point on the object corresponds to a point in the image and includes the distance information. This will enable 3D MMW imaging. The radar system requires that the millimeter wave detector (GDD) will be able to operate as a heterodyne detector. Since the source of radiation is a frequency modulated continuous wave (FMCW), the detected signal as a result of heterodyne detection gives the object's depth information according to value of difference frequency, in addition to the reflectance of the image. In this work we experimentally demonstrate the feasibility of implementing an imaging system based on radar principles and FPA of GDD devices. This imaging system is shown to be capable of imaging objects from distances of at least 10 meters.
NASA Astrophysics Data System (ADS)
Xie, J.; Yang, Y.; Ni, S.; Zhao, K.
2015-12-01
In the past decade, ambient noise tomography (ANT) has become an estimated method to construct the earth's interior structures thanks to its advantage in extracting surface waves from cross-correlations of ambient noise without using earthquake data. However, most of previous ambient noise tomography studies concentrate on short and intermediate periods (<50sec) due to the dominant energy of the microseism at these periods. Studies of long period surface waves from cross-correlation of ambient noise are limited. In this study, we verify the accuracy of the long period (50-250sec) surface wave (Rayleigh wave) from ambient noise by comparing both dispersion curves and seismic waveforms from ambient noise with those from earthquake records quantitatively. After that, we calculate vertical-vertical cross-correlation functions among more than1800 USArray Transportable Array stations and extract high quality interstation phase velocity dispersion curves from them at 10-200 sec periods. Then, we adopt a finite frequency ambient noise tomography method based on Born approximation to obtain high resolution phase velocity maps using the obtained dispersion measurements at 10-150 sec periods. Afterward, we extract local dispersion curves from these dispersion maps and invert them for 1D shear wave velocity profiles at individual grids using a Bayesian Monte Carlo method. Finally, a 3D shear velocity model is constructed by assembling all the 1D Vs profiles. Our 3D model is overall similar to other models constructed using earthquake surface waves and body waves. In summary, we demonstrate that the long period surface waves can be extracted from ambient noise, and the long period dispersion measurements from ambient noise are as accurate as those from earthquake data and can be used to construct 3D lithospheric structure from surface down to lithosphere/asthenosphere depths.
Fatigue crack detection in metallic structures with Lamb waves and 3D laser vibrometry
NASA Astrophysics Data System (ADS)
Staszewski, W. J.; Lee, B. C.; Traynor, R.
2007-03-01
The paper presents the application of ultrasonic guided waves for fatigue crack detection in metallic structures. The study involves a simple fatigue test performed to introduce a crack into an aluminium plate. Lamb waves generated by a low-profile, surface-bonded piezoceramic transducer are sensed using a tri-axis, multi-position scanning laser vibrometer. The results demonstrate the potential of laser vibrometry for simple, rapid and robust detection of fatigue cracks in metallic structures. The method could be used in quality inspection and in-service maintenance of metallic structures in aerospace, civil and mechanical engineering industries.
Non-linear 3D Born Shear Wave Tomography in Southeastern Asia
NASA Astrophysics Data System (ADS)
Cao, A.; Panning, M.; Kim, A.; Romanowicz, B.
2007-12-01
We have developed a 3D radially anisotropic shear velocity model of the upper mantle in southeastern Asia from the inversion of long period seismic multimode waveforms. Our approach is based on normal mode perturbation theory, specifically, on a recent modification of the Born approximation, which we call "N-Born", and which includes a non-linear term that allows the accurate inclusion of accumulated phase shifts which arise when the wavepath traverses a spatially extended region with a smooth velocity anomaly of constant sign. We apply the N-Born approximation in the forward modeling part and calculate linear 3D Born kernels in the inverse part. Our starting model is a 3D radially anisotropic model which we derived from a large dataset of teleseismic multimode long period waveforms in the period range 60 to 400 s, using a finite-frequency 2D approximation (NACT, Li and Romanowicz, 1995). This model covered a larger region of East Asia (longitude 30 to 150 degrees and latitude -10 to 60 degrees), while our N-Born model is restricted to a smaller subregion (longitude 75 to 150 degrees and latitude 0 to 45 degrees) for computational efficiency. In this subregion, our N-Born isotropic and anisotropic models are both parameterized at relatively short wavelengths corresponding to a spherical spline level 6 (~200km). Our N-Born model can fit waveforms as well as the NACT model, with up to ~ 83% variance reduction. While the models agree in general, the N-Born isotropic model shows a stronger fast velocity anomaly beneath the Tibetan plateau in the depth range of 150 km to 250 km, which disappears at greater depth, consistent with other studies. More importantly, the N-Born anisotropic model can recover well the downwelling structure associated with subducted slabs. Beneath the Tibet plateau, radial anisotropy shows VSH>VSV, which is indicative of horizontal rather than vertical flow and may help distinguish between end member models of the tectonics of Tibet.
NASA Astrophysics Data System (ADS)
Greenhalgh, Stewart; Zhou, Bing; Maurer, Hansruedi
2010-05-01
We have developed a modified version of the spectral element method (SEM), called the Gaussian Quadrature Grid (GQG) approach, for frequency domain 3D seismic modelling in arbitrary heterogeneous, anisotropic media. The model may incorporate an arbitrary free-surface topography and irregular subsurface interfaces. Unlike the SEM ,it does not require a powerful mesh generator such as the Delauney Triangular or TetGen. Rather, the GQG approach replaces the element mesh with Gaussian quadrature abscissae to directly sample the physical properties of the model parameters and compute the weighted residual or variational integral. This renders the model discretisation simple and easily matched to the model topography, as well as direct control of the model paramterisation for subsequent inversion. In addition, it offers high accuracy in numerical modelling provided that an appropriate density of the Gaussian quadrature abscissae is employed. The second innovation of the GQG is the incorporation of a new implementation of perfectly matched layers to suppress artificial reflections from the domain margins. We employ PML model parameters (specified complex valued density and elastic moduli) rather than explicitly solving the governing wave equation with a complex co-ordinate system as in conventional approaches. Such an implementation is simple, general, effective and easily extendable to any class of anisotropy and other numerical modelling methods. The accuracy of the GQG approach is controlled by the number of Gaussian quadrature points per minimum wavelength, the so-called sampling density. The optimal sampling density should be the one which enables high definition of geological characteristics and high precision of the variational integral evaluation and spatial differentiation. Our experiments show that satisfactory results can be obtained using sampling densities of 5 points per minimum wavelength. Efficiency of the GQG approach mainly depends on the linear
Internal wave attractors examined using laboratory experiments and 3D numerical simulations
NASA Astrophysics Data System (ADS)
Brouzet, C.; Sibgatullin, I. N.; Scolan, H.; Ermanyuk, E. V.; Dauxois, T.
2016-04-01
In the present paper, we combine numerical and experimental approaches to study the dynamics of stable and unstable internal wave attractors. The problem is considered in a classic trapezoidal setup filled with a uniformly stratified fluid. Energy is injected into the system at global scale by the small-amplitude motion of a vertical wall. Wave motion in the test tank is measured with the help of conventional synthetic schlieren and PIV techniques. The numerical setup closely reproduces the experimental one in terms of geometry and the operational range of the Reynolds and Schmidt numbers. The spectral element method is used as a numerical tool to simulate the nonlinear dynamics of a viscous salt-stratified fluid. We show that the results of three-dimensional calculations are in excellent qualitative and quantitative agreement with the experimental data, including the spatial and temporal parameters of the secondary waves produced by triadic resonance instability. Further, we explore experimentally and numerically the effect of lateral walls on secondary currents and spanwise distribution of velocity amplitudes in the wave beams. Finally, we test the assumption of a bidimensional flow and estimate the error made in synthetic schlieren measurements due to this assumption.
Summary of work on shock wave feature extraction in 3-D datasets
NASA Technical Reports Server (NTRS)
Hesselink, Lambertus (Principal Investigator)
1996-01-01
A method for extracting and visualizing shock waves from three dimensional data-sets is discussed. Issues concerning computation time, robustness to numerical perturbations, and noise introduction are considered and compared with other methods. Finally, results using this method are discussed.
NASA Astrophysics Data System (ADS)
Gainullin, I. K.; Sonkin, M. A.
2015-03-01
A parallelized three-dimensional (3D) time-dependent Schrodinger equation (TDSE) solver for one-electron systems is presented in this paper. The TDSE Solver is based on the finite-difference method (FDM) in Cartesian coordinates and uses a simple and explicit leap-frog numerical scheme. The simplicity of the numerical method provides very efficient parallelization and high performance of calculations using Graphics Processing Units (GPUs). For example, calculation of 106 time-steps on the 1000ṡ1000ṡ1000 numerical grid (109 points) takes only 16 hours on 16 Tesla M2090 GPUs. The TDSE Solver demonstrates scalability (parallel efficiency) close to 100% with some limitations on the problem size. The TDSE Solver is validated by calculation of energy eigenstates of the hydrogen atom (13.55 eV) and affinity level of H- ion (0.75 eV). The comparison with other TDSE solvers shows that a GPU-based TDSE Solver is 3 times faster for the problems of the same size and with the same cost of computational resources. The usage of a non-regular Cartesian grid or problem-specific non-Cartesian coordinates increases this benefit up to 10 times. The TDSE Solver was applied to the calculation of the resonant charge transfer (RCT) in nanosystems, including several related physical problems, such as electron capture during H+-H0 collision and electron tunneling between H- ion and thin metallic island film.
NASA Astrophysics Data System (ADS)
Zhai, Cuili; Zhang, Ting
2015-09-01
In this article, we consider the global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity. More precisely, assuming a 0 ∈ B˙ q , 1 /3 q ( R 3 ) and u 0 = ( u0 h , u0 3 ) ∈ B˙ p , 1 - 1 + /3 p ( R 3 ) for p, q ∈ (1, 6) with sup ( /1 p , /1 q ) ≤ /1 3 + inf ( /1 p , /1 q ) , we prove that if C a↑0↑ B˙q1/3 q α (↑u0 3↑ B˙ p , 1 - 1 + /3 p/μ + 1 ) ≤ 1 , /C μ (↑u0 h↑ B˙ p , 1 - 1 + /3 p + ↑u03↑ B˙ p , 1 - 1 + /3 p 1 - α ↑u0h↑ B˙ p , 1 - 1 + /3 p α) ≤ 1 , then the system has a unique global solution a ∈ C ˜ ( [ 0 , ∞ ) ; B˙ q , 1 /3 q ( R 3 ) ) , u ∈ C ˜ ( [ 0 , ∞ ) ; B˙ p , 1 - 1 + /3 p ( R 3 ) ) ∩ L 1 ( R + ; B˙ p , 1 1 + /3 p ( R 3 ) ) . It improves the recent result of M. Paicu and P. Zhang [J. Funct. Anal. 262, 3556-3584 (2012)], where the exponent form of the initial smallness condition is replaced by a polynomial form.
Miles, A R; Edwards, M J; Greenough, J A
2004-11-08
Perturbations on an interface driven by a strong blast wave grow in time due to a combination of Rayleigh-Taylor, Richtmyer-Meshkov, and decompression effects. In this paper, results from three-dimensional numerical simulations of such a system under drive conditions to be attainable on the National Ignition Facility [E. M. Campbell, Laser Part. Beams, 9(2), 209 (1991)] are presented. Using the multi-physics, adaptive mesh refinement, higher order Godunov Eulerian hydrocode, Raptor [L. H. Howell and J.A. Greenough, J. Comp. Phys. 184, 53 (2003)], the late nonlinear instability evolution, including transition to turbulence, is considered for various multimode perturbation spectra. The 3D post-transition state differs from the 2D result, but the process of transition proceeds similarly in both 2D and 3D. The turbulent mixing transition results in a reduction in the growth rate of the mixing layer relative to its pre-transition value and, in the case of the bubble front, relative to the 2D result. The post-transition spike front velocity is approximately the same in 2D and 3D. Implications for hydrodynamic mixing in core-collapse supernova are discussed.
Weak concentration and wave operator for a 3D coupled nonlinear Schrödinger system
NASA Astrophysics Data System (ADS)
Pastor, Ademir
2015-02-01
Reported in this paper are results concerning the Cauchy problem and the dynamics for a cubic nonlinear Schrödinger system arising in nonlinear optics. A sharp criterion is given concerned with the dichotomy global existence versus finite time blow-up. When a radial solution blows up in finite time, we prove the concentration in the critical Lebesgue space. Sufficient condition for the scattering and the construction of the wave operator in the energy space is also provided.
Generation of field-aligned currents and Alfven waves by 3D magnetic reconnection
Ma, Z.W.; Lee, L.C.; Otto, A.
1995-07-01
The authors have carried out a three-dimensional compressible MHD simulation to study the generation of field-aligned currents (FAC`s) and Alfven waves by magnetic reconnection for locally antiparallel magnetic fields across the current sheet. Reconnection is triggered by a localized resistivity. The results indicate that both FAC`s and Alfven waves are generated by the three-dimensional reconnection process. Two pairs of FAC`s are generated on each side of current sheet. The polarities of the resulting FAC pair in the leading bulge region are opposite to those of a FAC pair in the trailing quasi-steady region. It is further found that a large portion of the FAC`s ({approximately}40%) is located in the closed field line region. They examine the Walen relation between FAC and parallel vorticity and find that Alfven waves are generated and propagate away from the reconnection site. They discuss the relevance of the results to the observed Region 1 FAC`s at noon. 15 refs., 4 figs.
NASA Astrophysics Data System (ADS)
Xu, Feixiang; Zou, Qiushun; Zhou, Quancheng; Wang, Tongbiao; Yu, Tianbao; Liu, Nianhua
2016-05-01
We report that self-imaging effect still can be achieved in photonic quasicrystal waveguides (PtQCWs) just as it does in photonic crystal waveguides. As a possible application of the results, a new kind of compact 3 dB PtQCWs-based power splitters based on this effect for terahertz waves with symmetric interference is presented and analyzed. The finite element method is used to calculate the distributions of stable-state electric field and evaluate transmission efficiency of these structures. The calculated results show that the proposed device provides a new compact model for exporting efficiently THz wave with a broad bandwidth to two channels averagely and can be extended to new designs of PtQCW devices.
Kokeyama, Keiko; Sato, Shuichi; Nishizawa, Atsushi; Kawamura, Seiji; Chen, Yanbei; Sugamoto, Akio
2009-10-23
The displacement- and frequency-noise-free interferometer (DFI) is a multiple laser interferometer array for gravitational-wave detection free from both the displacement noise of optics and laser frequency noise. So far, partial experimental demonstrations of the DFI have been done in 2D table top experiments. In this Letter, we report the complete demonstration of a 3D DFI. The DFI consists of four Mach-Zehnder interferometers with four mirrors and two beam splitters The attained maximum suppression of the displacement noise of both mirrors and beam splitters was 40 dB at about 50 MHz. The nonvanishing DFI response to a gravitational wave was successfully confirmed using multiple electro-optic modulators and computing methods. PMID:19905742
Full 3D dispersion curve solutions for guided waves in generally anisotropic media
NASA Astrophysics Data System (ADS)
Hernando Quintanilla, F.; Lowe, M. J. S.; Craster, R. V.
2016-02-01
Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.
NASA Technical Reports Server (NTRS)
Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.
1994-01-01
A three-dimensional computational fluid dynamics code, RPLUS3D, which was developed for the reactive propulsive flows of ramjets and scramjets, was validated for glancing shock wave-boundary layer interactions. Both laminar and turbulent flows were studied. A supersonic flow over a wedge mounted on a flat plate was numerically simulated. For the laminar case, the static pressure distribution, velocity vectors, and particle traces on the flat plate were obtained. For turbulent flow, both the Baldwin-Lomax and Chien two-equation turbulent models were used. The static pressure distributions, pitot pressure, and yaw angle profiles were computed. In addition, the velocity vectors and particle traces on the flat plate were also obtained from the computed solution. Overall, the computed results for both laminar and turbulent cases compared very well with the experimentally obtained data.
NASA Astrophysics Data System (ADS)
Chen, Kai-Xun; Chen, Po-Fei; Liang, Wen-Tzong; Chen, Li-Wei; Gung, YuanCheng
2015-04-01
The Yilan Plain (YP) in NE Taiwan locates on the western YP of the Okinawa Trough and displays high geothermal gradients with abundant hot springs, likely resulting from magmatism associated with the back-arc spreading as attested by the offshore volcanic island (Kueishantao). YP features NS distinctive characteristics that the South YP exhibits thin top sedimentary layer, high on-land seismicity and significant SE movements, relative those of the northern counterpart. A dense network (~2.5 km station interval) of 89 Texan instruments was deployed in Aug. 2014, covering most of the YP and its vicinity. The ray path coverage density of each 0.015 degree cells are greater than 150 km that could provide the robustness assessment of tomographic results. We analyze ambient noise signals to invert a high-resolution 3D S-wave model for shallow velocity structures in and around YP. The aim is to investigate the velocity anomalies corresponding to geothermal resources and the NS geological distinctions aforementioned. We apply the Welch's method to generate empirical Rayleigh wave Green's functions between two stations records of continuous vertical components. The group velocities of thus derived functions are then obtained by the multiple-filter analysis technique measured at the frequency range between 0.25 and 1 Hz. Finally, we implement a wavelet-based multi-scale parameterization technique to construct 3D model of S-wave velocity. Our first month results exhibit low velocity in the plain, corresponding existing sediments, those of whole YP show low velocity offshore YP and those of high-resolution south YP reveal stark velocity contrast across the Sanshin fault. Key words: ambient seismic noises, Welch's method, S-wave, Yilan Plain
Imaging of 3D Ocean Turbulence Microstructure Using Low Frequency Acoustic Waves
NASA Astrophysics Data System (ADS)
Minakov, Alexander; Kolyukhin, Dmitriy; Keers, Henk
2015-04-01
In the past decade the technique of imaging the ocean structure with low-frequency signal (Hz), produced by air-guns and typically employed during conventional multichannel seismic data acquisition, has emerged. The method is based on extracting and stacking the acoustic energy back-scattered by the ocean temperature and salinity micro- and meso-structure (1 - 100 meters). However, a good understanding of the link between the scattered wavefield utilized by the seismic oceanography and physical processes in the ocean is still lacking. We describe theory and the numerical implementation of a 3D time-dependent stochastic model of ocean turbulence. The velocity and temperature are simulated as homogeneous Gaussian isotropic random fields with the Kolmogorov-Obukhov energy spectrum in the inertial subrange. Numerical modeling technique is employed for sampling of realizations of random fields with a given spatial-temporal spectral tensor. The model used is shown to be representative for a wide range of scales. Using this model, we provide a framework to solve the forward and inverse acoustic scattering problem using marine seismic data. Our full-waveform inversion method is based on the ray-Born approximation which is specifically suitable for the modelling of small velocity perturbations in the ocean. This is illustrated by showing a good match between synthetic seismograms computed using ray-Born and synthetic seismograms produced with a more computationally expensive finite-difference method.
NASA Astrophysics Data System (ADS)
Huang, Qinghua; Li, Zhanhui; Wang, Yanbin
2010-12-01
We presented a parallel 3-D staggered grid pseudospectral time domain (PSTD) method for simulating ground-penetrating radar (GPR) wave propagation. We took the staggered grid method to weaken the global effect in PSTD and developed a modified fast Fourier transform (FFT) spatial derivative operator to eliminate the wraparound effect due to the implicit periodical boundary condition in FFT operator. After the above improvements, we achieved the parallel PSTD computation based on an overlap domain decomposition method without any absorbing condition for each subdomain, which can significantly reduce the required grids in each overlap subdomain comparing with other proposed algorithms. We test our parallel technique for some numerical models and obtained consistent results with the analytical ones and/or those of the nonparallel PSTD method. The above numerical tests showed that our parallel PSTD algorithm is effective in simulating 3-D GPR wave propagation, with merits of saving computation time, as well as more flexibility in dealing with complicated models without losing the accuracy. The application of our parallel PSTD method in applied geophysics and paleoseismology based on GPR data confirmed the efficiency of our algorithm and its potential applications in various subdisciplines of solid earth geophysics. This study would also provide a useful parallel PSTD approach to the simulation of other geophysical problems on distributed memory PC cluster.
NASA Astrophysics Data System (ADS)
Luo, Cong; Friederich, Wolfgang
2016-04-01
Realistic shallow seismic wave propagation simulation is an important tool for studying induced seismicity (e.g., during geothermal energy development). However over a long time, there is a significant problem which constrains computational seismologists from performing a successful simulation conveniently: pre-processing. Conventional pre-processing has often turned out to be inefficient and unrobust because of the miscellaneous operations, considerable complexity and insufficiency of available tools. An integrated web-based platform for shallow seismic wave propagation simulation has been built. It is aiming at providing a user-friendly pre-processing solution, and cloud-based simulation abilities. The main features of the platform for the user include: revised digital elevation model (DEM) retrieving and processing mechanism; generation of multi-layered 3D shallow Earth model geometry (the computational domain) with user specified surface topography based on the DEM; visualization of the geometry before the simulation; a pipeline from geometry to fully customizable hexahedral element mesh generation; customization and running the simulation on our HPC; post-processing and retrieval of the results over cloud. Regarding the computational aspect, currently the widely accepted specfem3D is chosen as the computational package; packages using different types of elements can be integrated as well in the future. According to our trial simulation experiments, this web-based platform has produced accurate waveforms while significantly simplifying and enhancing the pre-processing and improving the simulation success rate.
P-wave tomography for 3-D radial and azimuthal anisotropy of Tohoku and Kyushu subduction zones
NASA Astrophysics Data System (ADS)
Wang, Jian; Zhao, Dapeng
2013-06-01
We determined high-resolution P-wave tomography for 3-D radial and azimuthal anisotropy of the Tohoku and Kyushu subduction zones using a large number of high-quality arrival-time data of local earthquakes recorded by the dense seismic network on the Japan Islands. Trench-normal P-wave fast-velocity directions (FVDs) are revealed in the backarc mantle wedge in both Tohoku and Kyushu, which are consistent with the model of slab-driven corner flow. Trench-parallel FVDs with amplitude <4 per cent appear in the forearc mantle wedge under Tohoku and Kyushu, suggesting the existence of B-type olivine fabric there. Trench-parallel FVDs are also visible in the mantle wedge under the volcanic front in Tohoku but not in Kyushu, suggesting that 3-D flow may exist in the mantle wedge under Tohoku and the 3-D flow is affected by the subduction rate of the oceanic plate. Negative radial anisotropy (i.e. vertical velocity being faster than horizontal velocity) is revealed in the low-velocity zones in the mantle wedge under the arc volcanoes in Tohoku and Kyushu as well as in the low-velocity zones below the Philippine Sea slab under Kyushu, which may reflect hot upwelling flows and transitions of olivine fabrics with the presence of water in the upper mantle. Trench-parallel FVDs and positive radial anisotropy (i.e. horizontal velocity being faster than vertical velocity) are revealed in the subducting Pacific slab under Tohoku and the Philippine Sea slab under Kyushu, suggesting that the slabs keep their frozen-in anisotropy formed at the mid-ocean ridge or that the slab anisotropy is induced by the lattice-preferred orientation of the B-type olivine.
NASA Astrophysics Data System (ADS)
Todoriki, M.; Furumura, T.; Maeda, T.
2013-12-01
We have studied the effect of topography and a seawater layer on the propagation of seismic wave propagation towards the realization of a high-resolution 3D FDM simulation of strong ground motions expected from future large subduction zone earthquakes along the Nankai Trough. Although most of the former studies on seismic wave propagation simulation did not consider a seawater layer in their simulation model, some of the recent studies claimed the importance of topography and a seawater layer on the simulation of strong ground motions (e.g., Petukhin et al., 2010; Nakamura, 2012; Maeda et al., 2013). In this study, we examined the effect of these two features on seismic wave propagation by introducing the high-resolution topography with a seawater layer over a wide frequency band. The area of 3D FDM simulation is 1200 km x 1000 km for horizontal directions and 200 km in depth, which covers entirely the area of southwestern Japan centered at 136E and 34.8N. This model was discretized with small grid interval of 0.5 km in horizontal direction and 0.25 km in depth. We used 2400 nodes of the K-computer, which is about 2.9% of its total resources, with a total memory of 1TB. We used a 3D velocity model of Koketsu et al. (2008) and an original source-rupture model from a recent study on the expansion of source-rupture area of the 1707 Hoei earthquake (Furumura et al., 2011). The result of simulation shows that the effect of a seawater layer on ground motion is small in almost all parts of Japan Island with a change of the seismic wave amplitude of less than +-20%. However, around the Northern Kanto area characterized by a belt-shaped anomalous zone, the amplitude of ground motion grows twice as large as that without seawater. This was possibly brought about from amplification of the amplitudes of surface waves generated on the Philippine Sea plate in the Suruga Trough located in the eastern end of the Nankai Trough. It is quite likely that the amplitude of surface wave