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.
Reduced integral order 3D scalar wave integral equation Derivation and BEM approach
NASA Astrophysics Data System (ADS)
Lee, HyunSuk
The Boundary Element Method (BEM) is a numerical method to solve partial differential equations (PDEs), which is derived from the integral equation (IE) that can be developed from certain PDEs. Among IEs, the 3D transient wave integral equation has a very special property which makes it distinguished from other integral equations; Dirac-delta and its derivative delta‧ appear in the fundamental-solution (or kernel-function). These delta and delta‧ generalized functions have continuity C-2 and C-3, respectively, and become a major hurdle for BEM implementation, because many numerical methods including BEM are based on the idea of continuity. More specifically, the integrands (kernel - shape function products) in the 3D transient wave IE become discontinuous (C-2 and C-3) and make numerical integration difficult. There are several existing approaches to overcome the delta difficulty, but none use the character of the Dirac-delta to cancel the integral. In this dissertation, a new method called the "Reduced order wave integral equation (Reduced IE)" is developed to deal with the difficulty in the 3D transient wave problem. In this approach, the sifting properties of delta and delta‧ are used to cancel an integration. As a result, smooth integrands are derived and the integral orders are reduced by one. Smooth integrands result in the more efficient and accurate numerical integration. In addition, there is no more coupling between the space-element size and time-step size. Non-zero initial condition (IC) can be considered also. Furthermore, space integrals need to be performed once, not per time-step. All of this reduces dramatically the computational requirement. As a result, the computation order for both time and space are reduced by 1 and one obtains an O(M N2) method, where M is the number of time steps and N is the number of spatial nodes on the boundary of the problem domain. A numerical approach to deal with the reduced IE is also suggested, and a simple
Wave Equation Based 3d Imaging of Ultrasonic Data, Theory and Practice
NASA Astrophysics Data System (ADS)
Pörtzgen, N.; Baardman, R.; Verschuur, D. J.; Gisolf, A.
2008-02-01
Non-destructive inspection (NDI) based on ultrasonic wave propagation is a well known method for the detection of defects in steel components such as girth welds. Although the detection of defects can be done reliably, characterization and sizing of defects remain problematic. For accurate sizing, 2D imaging techniques with ultrasonic array measurements have been developed and demonstrated in practice. With advances in computer technology and ultrasonic array design, the step towards 3D imaging also becomes feasible. This paper describes a 3D imaging procedure that consists of two 2D imaging steps in two orthogonal directions (the `two-pass' method). The procedure will be illustrated with real data obtained from ultrasonic linear array measurements. For 3D imaging, measurements over a surface area are required. Therefore, the linear array was shifted with small increments in the perpendicular direction to cover a surface area. In the direction parallel to the linear array (the `in-line' direction), all combinations of source-receiver elements were measured. This was repeated for a sufficient number of positions in the direction perpendicular to the linear array (the `cross-line' direction). The measurements were taken from carbon steel test pieces and an actual weld with an intentional defect (an embedded tungsten fragment). Significantly improved resolution in the cross-line direction was obtained as a result of the cross-line aperture synthesis.
Laplace-domain wave-equation modeling and full waveform inversion in 3D isotropic elastic media
NASA Astrophysics Data System (ADS)
Son, Woohyun; Pyun, Sukjoon; Shin, Changsoo; Kim, Han-Joon
2014-06-01
The 3D elastic problem has not been widely studied because of the computational burden. Over the past few years, 3D elastic full waveform inversion (FWI) techniques in the time and frequency domains have been proposed by some researchers based on developments in computer science. However, these techniques still have the non-uniqueness and high nonlinearity problems. In this paper, we propose a 3D elastic FWI algorithm in the Laplace domain that can mitigate these problems. To efficiently solve the impedance matrix, we adopt a first-order absorbing boundary condition that results in a symmetric system. A conjugate gradient (CG) solver can be used because the Laplace-domain wave equation is naturally positive definite. We apply the Jacobi preconditioner to increase the convergence speed. We identify the permissible range of Laplace damping constants through dispersion analysis and accuracy tests. We perform the Laplace-domain FWI based on a logarithmic objective function, and the inversion examples are designed for a land setting, which means that the source is vertically excited and multi-component data are considered. The inversion results indicate that the inversion that uses only the vertical component performs slightly better than the multi-component inversion. This unexpected result is obtained partly because we use a vertically polarized source. We analyze the residuals and Frechet derivatives for each component to examine the characteristics of the Laplace-domain multi-component FWI. The results indicate that the residuals and Frechet derivatives for the horizontal component have a singularity problem. The numerical examples demonstrate that the singularity problem is related to the directivity of the displacement and to taking the logarithm of Laplace-domain wave fields. To avoid this singularity problem, we use a simple method that excludes the data near the singular region. Although we can use either simultaneous or sequential strategies to invert the
3D Elastic Seismic Wave Propagation Code
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.
NASA Astrophysics Data System (ADS)
Botseas, George; Lee, Ding; King, David
1987-08-01
A computer model is developed for implementing the Lee-Saad-Schultz (LSS) method for solving the LSS Three-dimensional wide angle wave equation. The model is designed to predict propagation loss in range-, depth-, and azimuthal-dependent ocean environments. Computational speed is favorable since the Lee-Saad-Schultz method requires only solving two tri-diagonal systems of equations for each step marched forward in range. A test problem is included for demonstrating accuracy and the capabilities of the model. The model is written in Fortran for a VAX 11/780 computer.
Dual Variational Principles for 3-D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Liu, G. L.
Just recently the exact variational principles (VP) of the full 3-D Navier-Stokes equations of viscous flow have been successfully established for the first time by the present author by means of a systematic reversed deduction method via the undetermined function. As a continuation and further development of that - a pair of new dual (reciprocal)VP is generated herein by means of the Friedrichs involutory transformation. These VP have the advantage over the previous ones that they possess apparent physical meaning of energy, providing a new rigorous theoretical basis for the finite element analysis of 3-D viscous flow.
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.
NASA Astrophysics Data System (ADS)
Zhu, Liang-sheng; Yu, Long-fei
2016-10-01
Aimed at the hydrodynamic response for marine structures slamming into water, based on the mechanism analysis to the slamming process, and by combining 3D N-S equation and k- ɛ turbulent kinetic equation with structure fully 6DOF motion equation, a mathematical model for the wind-fluid-solid interaction is established in 3D marine structure slamming wave at free poses and wind-wave-flow complex environments. Compared with the results of physical model test, the numerical results from the slamming wave well correspond with the experimental results. Through the mathematical model, the wave-making issue of 3D marine structure at initial pose falls into water in different complex wind, wave and flow environments is investigated. The research results show that various kinds of natural factors and structure initial poses have different influence on the slamming wave, and there is an obvious rule in this process.
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.
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
Potentially singular solutions of the 3D axisymmetric Euler equations.
Luo, Guo; Hou, Thomas Y
2014-09-01
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 τ(2) = 0.003505 at which time the vorticity amplifies by more than (3 × 10(8))-fold and the maximum mesh resolution exceeds (3 × 10(12))(2). The vorticity vector is observed to maintain four significant digits throughout the computations.
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.
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.
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.
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.
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.
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.
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; Ladoux, Benoit; Gauthier, Nils C
2015-11-01
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.
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.
Inhomogeneous Media 3D EM Modeling with Integral Equation Method
NASA Astrophysics Data System (ADS)
di, Q.; Wang, R.; An, Z.; Fu, C.; Xu, C.
2010-12-01
In general, only the half space of earth is considered in electromagnetic exploration. However, for the long bipole source, because the length is close to the height of ionosphere and also most offsets between source and receivers are equal or larger than the height of ionosphere, the effect of ionosphere on the electromagnetic (EM) field should be considered when observation is carried at a very far (about several thousands kilometers) location away from the source. At this point the problem becomes one which should contain ionosphere, atmosphere and earth that is “earth-ionosphere” case. There are a few of literatures to report the electromagnetic field results which is including ionosphere, atmosphere and earth media at the same time. We firstly calculate the electromagnetic fields with the traditional controlled source (CSEM) configuration using integral equation (IE) method for a three layers earth-ionosphere model. The modeling results agree well with the half space analytical results because the effect of ionosphere for this small scale bipole source can be ignorable. The comparison of small scale three layers earth-ionosphere modeling and half space analytical resolution shows that the IE method can be used to modeling the EM fields for long bipole large offset configuration. In order to discuss EM fields’ characteristics for complicate earth-ionosphere media excited by long bipole source in the far-field and wave-guide zones, we first modeled the decay characters of electromagnetic fields for three layers earth-ionosphere model. Because of the effect of ionosphere, the earth-ionosphere electromagnetic fields’ decay curves with given frequency show that there should be an extra wave guide zone for long bipole artificial source, and there are many different characters between this extra zone and far field zone. They are: 1) the amplitudes of EM fields decay much slower; 2) the polarization patterns change; 3) the positions better to measure Zxy and
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.
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.
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.
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.
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.
GPU Accelerated Spectral Element Methods: 3D Euler equations
NASA Astrophysics Data System (ADS)
Abdi, D. S.; Wilcox, L.; Giraldo, F.; Warburton, T.
2015-12-01
A GPU accelerated nodal discontinuous Galerkin method for the solution of three dimensional Euler equations is presented. The Euler equations are nonlinear hyperbolic equations that are widely used in Numerical Weather Prediction (NWP). Therefore, acceleration of the method plays an important practical role in not only getting daily forecasts faster but also in obtaining more accurate (high resolution) results. The equation sets used in our atomospheric model NUMA (non-hydrostatic unified model of the atmosphere) take into consideration non-hydrostatic effects that become more important with high resolution. We use algorithms suitable for the single instruction multiple thread (SIMT) architecture of GPUs to accelerate solution by an order of magnitude (20x) relative to CPU implementation. For portability to heterogeneous computing environment, we use a new programming language OCCA, which can be cross-compiled to either OpenCL, CUDA or OpenMP at runtime. Finally, the accuracy and performance of our GPU implementations are veried using several benchmark problems representative of different scales of atmospheric dynamics.
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.
A 3D unstructured non-hydrostatic ocean model for internal waves
NASA Astrophysics Data System (ADS)
Ai, Congfang; Ding, Weiye
2016-10-01
A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max-min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max-min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model's capability to resolve internal waves relating to complex non-hydrostatic phenomena.
A 3D unstructured non-hydrostatic ocean model for internal waves
NASA Astrophysics Data System (ADS)
Ai, Congfang; Ding, Weiye
2016-08-01
A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max-min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max-min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model's capability to resolve internal waves relating to complex non-hydrostatic phenomena.
Navier-Stokes equations in 3D thin domains with Navier friction boundary condition
NASA Astrophysics Data System (ADS)
Hu, Changbing
In this article we study the 3D Navier-Stokes equations with Navier friction boundary condition in thin domains. We prove the global existence of strong solutions to the 3D Navier-Stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small. We generalize the techniques developed to study the 3D Navier-Stokes equations in thin domains, see [G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains I: Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993) 503-568; G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains II: Global regularity of spatially periodic conditions, in: Nonlinear Partial Differential Equations and Their Application, College de France Seminar, vol. XI, Longman, Harlow, 1994, pp. 205-247; R. Temam, M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996) 499-546; R. Temam, M. Ziane, Navier-Stokes equations in thin spherical shells, in: Optimization Methods in Partial Differential Equations, in: Contemp. Math., vol. 209, Amer. Math. Soc., Providence, RI, 1996, pp. 281-314], to the Navier friction boundary condition by introducing a new average operator M in the thin direction according to the spectral decomposition of the Stokes operator A. Our analysis hinges on the refined investigation of the eigenvalue problem corresponding to the Stokes operator A with Navier friction boundary condition.
A global 3-D MHD model of the solar wind with Alfven waves
NASA Technical Reports Server (NTRS)
Usmanov, A. V.
1995-01-01
A fully three-dimensional solar wind model that incorporates momentum and heat addition from Alfven waves is developed. The proposed model upgrades the previous one by considering self-consistently the total system consisting of Alfven waves propagating outward from the Sun and the mean polytropic solar wind flow. The simulation region extends from the coronal base (1 R(sub s) out to beyond 1 AU. The fully 3-D MHD equations written in spherical coordinates are solved in the frame of reference corotating with the Sun. At the inner boundary, the photospheric magnetic field observations are taken as boundary condition and wave energy influx is prescribed to be proportional to the magnetic field strength. The results of the model application for several time intervals are presented.
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).
3D Solitons of Capillary-Gravity and Flexural-Gravity Waves
NASA Astrophysics Data System (ADS)
Alam, Reza
2013-11-01
In the context of nonlinear water wave theory an intriguing question has always been if fully-localized 3D wave structures, counterparts of 2D solitons, can exist. These structures are important because, if exist, they can transport mass, momentum and energy over long distances. For pure gravity waves this possibility is already ruled out, but- as we will discuss- few limiting cases of capillary-gravity and flexural-gravity wave equations admit such solutions in the form of dromions and lumps. Here we show that weakly nonlinear flexural-gravity wave packets, such as those propagating on the surface of ice-covered waters, admit three-dimensional fully localized solutions in the form of dromions. This study is motivated by observations of (relatively) large amplitude localized waves deep inside the ice-pack in polar waters. For capillary-gravity wave classical theory obtains dromions for shallow-water and strong surface tension (Bond number, Bo, greater than 1/3). Here we show that capillary-gravity dromions exist beyond this limit for a broad range of finite water depths as well as for sub-critical Bond numbers, i.e. for Bo < 1/3.
A 3D S-wave model of the Valhall subsurface from ambient seismic noise tomography
NASA Astrophysics Data System (ADS)
Mordret, A.; Landes, M.; Shapiro, N.; Singh, S. C.; Roux, P.
2013-12-01
We present a depth inversion of Scholte wave group and phase velocity maps obtained from cross-correlation of 6.5 hours of noise data from the Valhall Life of Field Seismic (LoFS) network. We computed 2 690 040 vertical-vertical component cross-correlations from the 2320 available sensors, turning each sensor into a virtual source emitting Scholte waves. We used a traditional straight-ray surface-wave tomography to compute the group velocity map. The phase velocity maps have been computed using the Eikonal tomography method. For every virtual source, we measured the Scholte wave phase travel times to all other stations and interpolated them on a regular grid. This phase travel-time surface is inverted into phase velocity map via applying the eikonal equation. The contributions from all 2320 virtual sources are stacked to create the final phase velocity map of the Valhall subsurface. Scholte wave isotropic phase velocity maps at periods between 0.65 s and 1.6 s show a coherent geomorphological pattern dominated by paleo-channels in the shallower part. We also retrieved the azimuthal anisotropy and its lateral variations showing a characteristic elliptical pattern around the central exploitation platform. The inversion of these maps in depth using the Neighbourhood Algorithm allowed us to create a high resolution 3D S-wave model of the first 600 m of the Valhall subsurface and to precise the locations of geological structures at depth. These results would have important implication for shear wave statics and monitoring of sea-floor subsidence due to oil extraction. The 3D model could also be a good candidate for a starting model used in full-waveform inversions.
NASA Astrophysics Data System (ADS)
Leng, Kuangdai; Nissen-Meyer, Tarje; van Driel, Martin
2016-09-01
We present a new, computationally efficient numerical method to simulate global seismic wave propagation in realistic 3-D Earth models. We characterize the azimuthal dependence of 3-D wavefields in terms of Fourier series, such that the 3-D equations of motion reduce to an algebraic system of coupled 2-D meridian equations, which is then solved by a 2-D spectral element method (SEM). Computational efficiency of such a hybrid method stems from lateral smoothness of 3-D Earth models and axial singularity of seismic point sources, which jointly confine the Fourier modes of wavefields to a few lower orders. We show novel benchmarks for global wave solutions in 3-D structures between our method and an independent, fully discretized 3-D SEM with remarkable agreement. Performance comparisons are carried out on three state-of-the-art tomography models, with seismic period ranging from 34s down to 11s. It turns out that our method has run up to two orders of magnitude faster than the 3-D SEM, featured by a computational advantage expanding with seismic frequency.
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.
Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method
NASA Astrophysics Data System (ADS)
Kruglyakov, M.; Geraskin, A.; Kuvshinov, A.
2016-11-01
We present a novel, open source 3-D MT forward solver based on a method of integral equations (IE) with contracting kernel. Special attention in the solver is paid to accurate calculations of Green's functions and their integrals which are cornerstones of any IE solution. The solver supports massive parallelization and is able to deal with highly detailed and contrasting models. We report results of a 3-D numerical experiment aimed at analyzing the accuracy and scalability of the code.
NASA Astrophysics Data System (ADS)
Kimoto, K.; Hirose, S.
2002-05-01
This paper presents a boundary integral equation method for 3D ultrasonic scattering problems in a fluid-loaded elastic half space. Since full scale of numerical calculation using finite element or boundary element method is still very expensive, we formulate a boundary integral equation for the scattered field, which is amenable to numerical treatment. In order to solve the problem using the integral equation, however, the wave field without scattering objects, so-called free field need to be given in advance. We calculate the free field by the plane wave spectral method where the asymptotic approximation is introduced for computational efficiency. To show the efficiency of our method, scattering by a spherical cavity near fluid-solid interface is solved and the validity of the results is discussed.
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
Analysis of wave propagation in periodic 3D waveguides
NASA Astrophysics Data System (ADS)
Schaal, Christoph; Bischoff, Stefan; Gaul, Lothar
2013-11-01
Structural Health Monitoring (SHM) is a growing research field in the realm of civil engineering. SHM concepts are implemented using integrated sensors and actuators to evaluate the state of a structure. Within this work, wave-based techniques are addressed. Dispersion effects for propagating waves in waveguides of different materials are analyzed for various different cross-sections. Since analytical theory is limited, a general approach based on the Waveguide Finite Element Method is applied. Numerical results are verified experimentally.
Parallel 3D Simulation of Seismic Wave Propagation in the Structure of Nobi Plain, Central Japan
NASA Astrophysics Data System (ADS)
Kotani, A.; Furumura, T.; Hirahara, K.
2003-12-01
We performed large-scale parallel simulations of the seismic wave propagation to understand the complex wave behavior in the 3D basin structure of the Nobi Plain, which is one of the high population cities in central Japan. In this area, many large earthquakes occurred in the past, such as the 1891 Nobi earthquake (M8.0), the 1944 Tonankai earthquake (M7.9) and the 1945 Mikawa earthquake (M6.8). In order to mitigate the potential disasters for future earthquakes, 3D subsurface structure of Nobi Plain has recently been investigated by local governments. We referred to this model together with bouguer anomaly data to construct a detail 3D basin structure model for Nobi plain, and conducted computer simulations of ground motions. We first evaluated the ground motions for two small earthquakes (M4~5); one occurred just beneath the basin edge at west, and the other occurred at south. The ground motions from these earthquakes were well recorded by the strong motion networks; K-net, Kik-net, and seismic intensity instruments operated by local governments. We compare the observed seismograms with simulations to validate the 3D model. For the 3D simulation we sliced the 3D model into a number of layers to assign to many processors for concurrent computing. The equation of motions are solved using a high order (32nd) staggered-grid FDM in horizontal directions, and a conventional (4th-order) FDM in vertical direction with the MPI inter-processor communications between neighbor region. The simulation model is 128km by 128km by 43km, which is discritized at variable grid size of 62.5-125m in horizontal directions and of 31.25-62.5m in vertical direction. We assigned a minimum shear wave velocity is Vs=0.4km/s, at the top of the sedimentary basin. The seismic sources for the small events are approximated by double-couple point source and we simulate the seismic wave propagation at maximum frequency of 2Hz. We used the Earth Simulator (JAMSTEC, Yokohama Inst) to conduct such
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
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.
Wang, Shen; Huang, Songling; Zhao, Wei; Wei, Zheng
2015-02-01
In this paper, SH (shear horizontal) guided waves propagating in the circumferential direction of pipeline are modeled in 3 dimensions, with the aim for axial cracking detection implementation in ILI (in-line inspection) tools in mind. A theoretical formulation is given first, followed by an explanation about the 3D numerical modeling work. Displacement wave structures from the simulation and dispersion equation are compared to verify the effectiveness of the FEM package. Transverse slots along the axial direction are modeled to simulate axial cracking. Reflection and transmission coefficients curves are obtained to provide insight in using circumferential SH guided waves for quantitative testing of axial pipeline cracking.
Martingale solutions and Markov selection of stochastic 3D Navier-Stokes equations with jump
NASA Astrophysics Data System (ADS)
Dong, Zhao; Zhai, Jianliang
2011-03-01
In this paper, we study the existence of martingale solutions of stochastic 3D Navier-Stokes equations with jump, and following Flandoli and Romito (2008) [7] and Goldys et al. (2009) [8], we prove the existence of Markov selections for the martingale solutions.
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
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
NASA Astrophysics Data System (ADS)
Wang, Yueqing; Wu, Guisheng; Chen, Zhenyang
The complex astigmatic wave, which imitates the 3-D beam in high-frequency, is an effective method to analyze the electromagnetic characters of the 3-D arbitrarily curved radome. A number of calculations for the ellipsoidal sandwich radome are performed, and the stereoscopic graphics of the results are constructed. Comparing with the experiments, it is shown that this method can be used to simplify analysis and optimization design for many kinds of 3-D radome.
Rayleigh Wave Numerical Dispersion in a 3D Finite-Difference Algorithm
NASA Astrophysics Data System (ADS)
Preston, L. A.; Aldridge, D. F.
2010-12-01
A Rayleigh wave propagates laterally without dispersion in the vicinity of the plane stress-free surface of a homogeneous and isotropic elastic halfspace. The phase speed is independent of frequency and depends only on the Poisson ratio of the medium. However, after temporal and spatial discretization, a Rayleigh wave simulated by a 3D staggered-grid finite-difference (FD) seismic wave propagation algorithm suffers from frequency- and direction-dependent numerical dispersion. The magnitude of this dispersion depends critically on FD algorithm implementation details. Nevertheless, proper gridding can control numerical dispersion to within an acceptable level, leading to accurate Rayleigh wave simulations. Many investigators have derived dispersion relations appropriate for body wave propagation by various FD algorithms. However, the situation for surface waves is less well-studied. We have devised a numerical search procedure to estimate Rayleigh phase speed and group speed curves for 3D O(2,2) and O(2,4) staggered-grid FD algorithms. In contrast with the continuous time-space situation (where phase speed is obtained by extracting the appropriate root of the Rayleigh cubic), we cannot develop a closed-form mathematical formula governing the phase speed. Rather, we numerically seek the particular phase speed that leads to a solution of the discrete wave propagation equations, while holding medium properties, frequency, horizontal propagation direction, and gridding intervals fixed. Group speed is then obtained by numerically differentiating the phase speed with respect to frequency. The problem is formulated for an explicit stress-free surface positioned at two different levels within the staggered spatial grid. Additionally, an interesting variant involving zero-valued medium properties above the surface is addressed. We refer to the latter as an implicit free surface. Our preliminary conclusion is that an explicit free surface, implemented with O(4) spatial FD
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.
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
On a particular solution to the 3D Navier-Stokes equations for liquids with cavitation
NASA Astrophysics Data System (ADS)
Rabinowitch, Alexander S.
2016-08-01
The 3D Navier-Stokes equations for incompressible viscous liquids are examined. In the axially symmetric case, they are represented in the form of three nonlinear partial differential equations. These equations are studied and their particular solution is found. In it, the velocity components are sinusoidal in the direction of their axis of symmetry. As to the pressure, it can reach a sufficiently small value at which the phenomenon of cavitation takes place in a liquid. The found solution describes some flows of viscous liquids outside vapor-filled regions in them.
Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves.
Xavier, Jolly; Vyas, Sunil; Senthilkumaran, Paramasivam; Joseph, Joby
2012-04-20
As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.
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.
3D mapping of elastic modulus using shear wave optical micro-elastography
Zhu, Jiang; Qi, Li; Miao, Yusi; Ma, Teng; Dai, Cuixia; Qu, Yueqiao; He, Youmin; Gao, Yiwei; Zhou, Qifa; Chen, Zhongping
2016-01-01
Elastography provides a powerful tool for histopathological identification and clinical diagnosis based on information from tissue stiffness. Benefiting from high resolution, three-dimensional (3D), and noninvasive optical coherence tomography (OCT), optical micro-elastography has the ability to determine elastic properties with a resolution of ~10 μm in a 3D specimen. The shear wave velocity measurement can be used to quantify the elastic modulus. However, in current methods, shear waves are measured near the surface with an interference of surface waves. In this study, we developed acoustic radiation force (ARF) orthogonal excitation optical coherence elastography (ARFOE-OCE) to visualize shear waves in 3D. This method uses acoustic force perpendicular to the OCT beam to excite shear waves in internal specimens and uses Doppler variance method to visualize shear wave propagation in 3D. The measured propagation of shear waves agrees well with the simulation results obtained from finite element analysis (FEA). Orthogonal acoustic excitation allows this method to measure the shear modulus in a deeper specimen which extends the elasticity measurement range beyond the OCT imaging depth. The results show that the ARFOE-OCE system has the ability to noninvasively determine the 3D elastic map. PMID:27762276
Sky3D: Time-dependent Hartree-Fock equation solver
NASA Astrophysics Data System (ADS)
Maruhn, J. A.; Reinhard, P.-G.; Stevenson, P. D.; Umar, A. S.
2016-09-01
Written in Fortran 90, Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code can be easily modified to include additional physics or special analysis of the results and requires LAPACK and FFTW3.
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.
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.
Generalized solutions to Protter problems for 3-D Keldysh type equations
NASA Astrophysics Data System (ADS)
Hristov, T.; Popivanov, N.; Schneider, M.
2014-12-01
Some three-dimensional boundary value problems for equations of Keldysh type are studied. Such type problems, but for equations of Tricomi type are stated by M. H. Protter [25] as 3-D analogues of Darboux or Cauchy-Goursat plane problems. It is well known that in contrast of well-posedness of 2D problems, the Protter problems are strongly ill-posed. In [12] Protter problem for Keldysh type equations is formulated and it is shown that it is not correctly set since the homogeneous adjoint problem has infinitely many nontrivial classical solutions. In the present paper a notion for generalized solution to Protter problem for Keldysh type equations is introduced. Further, results for existence and uniqueness of such solution are obtained.
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.
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.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Barati, Mohammad Reza
2016-09-01
This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori-Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton's principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.
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.
FGG-NUFFT-Based Method for Near-Field 3-D Imaging Using Millimeter Waves
Kan, Yingzhi; Zhu, Yongfeng; Tang, Liang; Fu, Qiang; Pei, Hucheng
2016-01-01
In this paper, to deal with the concealed target detection problem, an accurate and efficient algorithm for near-field millimeter wave three-dimensional (3-D) imaging is proposed that uses a two-dimensional (2-D) plane antenna array. First, a two-dimensional fast Fourier transform (FFT) is performed on the scattered data along the antenna array plane. Then, a phase shift is performed to compensate for the spherical wave effect. Finally, fast Gaussian gridding based nonuniform FFT (FGG-NUFFT) combined with 2-D inverse FFT (IFFT) is performed on the nonuniform 3-D spatial spectrum in the frequency wavenumber domain to achieve 3-D imaging. The conventional method for near-field 3-D imaging uses Stolt interpolation to obtain uniform spatial spectrum samples and performs 3-D IFFT to reconstruct a 3-D image. Compared with the conventional method, our FGG-NUFFT based method is comparable in both efficiency and accuracy in the full sampled case and can obtain more accurate images with less clutter and fewer noisy artifacts in the down-sampled case, which are good properties for practical applications. Both simulation and experimental results demonstrate that the FGG-NUFFT-based near-field 3-D imaging algorithm can have better imaging performance than the conventional method for down-sampled measurements. PMID:27657066
Numerical Investigation of 3D multichannel analysis of surface wave method
NASA Astrophysics Data System (ADS)
Wang, Limin; Xu, Yixian; Luo, Yinhe
2015-08-01
Multichannel analysis of surface wave (MASW) method is an efficient tool to obtain near-surface S-wave velocity, and it has gained popularity in engineering practice. Up to now, most examples of using the MASW technique are focused on 2D models or data from a 1D linear receiver spread. We propose a 3D MASW scheme. A finite-difference (FD) method is used to investigate the method using linear and fan-shaped receiver spreads. Results show that the 3D topography strongly affects propagation of Rayleigh waves. The energy concentration of dispersion image is distorted and bifurcated because of the influence of free-surface topography. These effects are reduced with the 3D MASW method. Lastly we investigate the relation between the array size and the resolution of dispersion measurement.
3D Staggered-Grid Finite-Difference Simulation of Acoustic Waves in Turbulent Moving Media
NASA Astrophysics Data System (ADS)
Symons, N. P.; Aldridge, D. F.; Marlin, D.; Wilson, D. K.; Sullivan, P.; Ostashev, V.
2003-12-01
Acoustic wave propagation in a three-dimensional heterogeneous moving atmosphere is accurately simulated with a numerical algorithm recently developed under the DOD Common High Performance Computing Software Support Initiative (CHSSI). Sound waves within such a dynamic environment are mathematically described by a set of four, coupled, first-order partial differential equations governing small-amplitude fluctuations in pressure and particle velocity. The system is rigorously derived from fundamental principles of continuum mechanics, ideal-fluid constitutive relations, and reasonable assumptions that the ambient atmospheric motion is adiabatic and divergence-free. An explicit, time-domain, finite-difference (FD) numerical scheme is used to solve the system for both pressure and particle velocity wavefields. The atmosphere is characterized by 3D gridded models of sound speed, mass density, and the three components of the wind velocity vector. Dependent variables are stored on staggered spatial and temporal grids, and centered FD operators possess 2nd-order and 4th-order space/time accuracy. Accurate sound wave simulation is achieved provided grid intervals are chosen appropriately. The gridding must be fine enough to reduce numerical dispersion artifacts to an acceptable level and maintain stability. The algorithm is designed to execute on parallel computational platforms by utilizing a spatial domain-decomposition strategy. Currently, the algorithm has been validated on four different computational platforms, and parallel scalability of approximately 85% has been demonstrated. Comparisons with analytic solutions for uniform and vertically stratified wind models indicate that the FD algorithm generates accurate results with either a vanishing pressure or vanishing vertical-particle velocity boundary condition. Simulations are performed using a kinematic turbulence wind profile developed with the quasi-wavelet method. In addition, preliminary results are presented
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.
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
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
Wave equations for pulse propagation
NASA Astrophysics Data System (ADS)
Shore, B. W.
1987-06-01
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity.
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.
Global regularity to the 3D MHD equations with large initial data in bounded domains
NASA Astrophysics Data System (ADS)
Yu, Haibo
2016-08-01
This paper considers the global regularity to the 3D incompressible MHD equations with large initial data in bounded domains. Let μ, ν, u, and b denote the viscosity coefficient, magnetic diffusivity, velocity field, and magnetic field, respectively. We construct new systems for (u - b) and (u + b) to overcome the difficulties caused by the large initial data. It is shown that ↑" separators=" ( u , b ) ↑ H 1 is globally bounded as long as ↑" separators=" ( u0 - b 0 ) ↑ H 1 + |" separators=" μ - ν | ( μ + ν ) - 1 or ↑" separators=" ( u0 + b 0 ) ↑ H 1 + |" separators=" μ - ν | ( μ + ν ) - 1 is sufficiently small, which indicates that the Navier-Stokes equations can be regularized by the magnetic field.
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.
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.
Second order Method for Solving 3D Elasticity Equations with Complex Interfaces
Wang, Bao; Xia, Kelin; Wei, Guo-Wei
2015-01-01
Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422
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
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
Linear superposition solutions to nonlinear wave equations
NASA Astrophysics Data System (ADS)
Liu, Yu
2012-11-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.
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.
Anisotropic Regularity Conditions for the Suitable Weak Solutions to the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Wang, Yanqing; Wu, Gang
2016-07-01
We are concerned with the problem, originated from Seregin (159-200, 2007), Seregin (J. Math. Sci. 143: 2961-2968, 2007), Seregin (Russ. Math. Surv. 62:149-168, 2007), what are minimal sufficiently conditions for the regularity of suitable weak solutions to the 3D Navier-Stokes equations. We prove some interior regularity criteria, in terms of either one component of the velocity with sufficiently small local scaled norm and the rest part with bounded local scaled norm, or horizontal part of the vorticity with sufficiently small local scaled norm and the vertical part with bounded local scaled norm. It is also shown that only the smallness on the local scaled L 2 norm of horizontal gradient without any other condition on the vertical gradient can still ensure the regularity of suitable weak solutions. All these conclusions improve pervious results on the local scaled norm type regularity conditions.
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.
A time-space domain stereo finite difference method for 3D scalar wave propagation
NASA Astrophysics Data System (ADS)
Chen, Yushu; Yang, Guangwen; Ma, Xiao; He, Conghui; Song, Guojie
2016-11-01
The time-space domain finite difference methods reduce numerical dispersion effectively by minimizing the error in the joint time-space domain. However, their interpolating coefficients are related with the Courant numbers, leading to significantly extra time costs for loading the coefficients consecutively according to velocity in heterogeneous models. In the present study, we develop a time-space domain stereo finite difference (TSSFD) method for 3D scalar wave equation. The method propagates both the displacements and their gradients simultaneously to keep more information of the wavefields, and minimizes the maximum phase velocity error directly using constant interpolation coefficients for different Courant numbers. We obtain the optimal constant coefficients by combining the truncated Taylor series approximation and the time-space domain optimization, and adjust the coefficients to improve the stability condition. Subsequent investigation shows that the TSSFD can suppress numerical dispersion effectively with high computational efficiency. The maximum phase velocity error of the TSSFD is just 3.09% even with only 2 sampling points per minimum wavelength when the Courant number is 0.4. Numerical experiments show that to generate wavefields with no visible numerical dispersion, the computational efficiency of the TSSFD is 576.9%, 193.5%, 699.0%, and 191.6% of those of the 4th-order and 8th-order Lax-Wendroff correction (LWC) method, the 4th-order staggered grid method (SG), and the 8th-order optimal finite difference method (OFD), respectively. Meanwhile, the TSSFD is compatible to the unsplit convolutional perfectly matched layer (CPML) boundary condition for absorbing artificial boundaries. The efficiency and capability to handle complex velocity models make it an attractive tool in imaging methods such as acoustic reverse time migration (RTM).
Green's Functions of Wave Equations in
NASA Astrophysics Data System (ADS)
Deng, Shijin; Wang, Weike; Yu, Shih-Hsien
2015-06-01
We study the d'Alembert equation with a boundary. We introduce the notions of Rayleigh surface wave operators, delayed/advanced mirror images, wave recombinations, and wave cancellations. This allows us to obtain the complete and simple formula of the Green's functions for the wave equation with the presence of various boundary conditions. We are able to determine whether a Rayleigh surface wave is active or virtual, and study the lacunas of the wave equation in three dimensional with the presence of a boundary in the case of a virtual Rayleigh surface wave.
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.
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.
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.
3-D wave propagation solution of a stable resonator, free-electron laser
NASA Astrophysics Data System (ADS)
Bhowmik, A.; Cover, R. A.; Labbe, R. H.
1983-11-01
Rigorous numerical solutions of a stable resonator, free-electron laser are obtained using 3-D wave propagation algorithms in the presence of a radially and azimuthally varying gain. Assumptions of this time-independent formulation of the loaded-resonator cavity are discussed. Wave propagation in the cavity is performed by computing numerically the Fresnel-Kirchoff diffraction integral by the Gardner-Fresnel-Kirchoff algorithm. Results of steady-state numerical iterative solutions, in which both the gain and the optical fields achieve self-consistency throughout the resonator, are presented. These consist of: (1) mode pattern and (2) variations in gain with variations in the resonator parameters.
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.
Properties of lower-hybrid range wave activity at reconnection jet edge: 3D PIC simulations
NASA Astrophysics Data System (ADS)
Divin, Andrey; Khotyaintsev, Yuri; Vaivads, Andris; Andre, Mats; Lapenta, Giovanni; Markidis, Stefano
2014-05-01
Reconnection fronts are areas of intense currents and enhanced wave activity, since magnetic flux and plasma are piled up there when the accelerated flow encounters denser ambient current sheet. Observations and numerical simulations show that the fronts generate a variety of waves ranging from MHD frequencies up to lower hybrid frequency and above. In the present study we use 2D and 3D Particle-in-Cell (PIC) simulations to investigate the properties of the lower hybrid range waves developing at hot reconnected plasma - current sheet interface. Calculations are performed using implicit parallel code iPIC3D starting from conventional Harris current sheet. Initial evolution of the jet is simulated using 2D approach to save computational time, but 3D calculations are implemented at later stages in order to observe instability linear stage, saturation and transition to turbulence. Properties of the linear stage match closely theoretical predictions for the lower hybrid drift instability. During saturation, the mode produces intense electric fields (several Alfvén in electric fields normalized unit) that can provide an additional mechanism of electron heating at reconnection jet fronts.
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.
Implementation of 3D wave forcing terms in the HYbrid Coordinate Ocean Model
NASA Astrophysics Data System (ADS)
Ody, Cédric; Filipot, Jean-François; Pichon, Annick; Lathuilière, Cyril; Baraille, Rémy
2013-04-01
Waves may influence the circulation in coastal regions at temporal and spatial scales that are larger than the periods and wavelengths of the waves respectively. The setup of the mean sea surface level or longshore currents are two examples of coastal processes that are generated by the mean effects of waves. Although simple models have been shown to provide reasonable estimates of setup and mean currents, the prediction of such wave-induced mechanisms has been improved since the recent development of theories on 3D wave-current interactions. Amongst these theories, the works of Ardhuin et al. (2008) and Mc Williams et al. (2004) give rise to forcing terms that may be used in existing circulation models. Under some assumptions on the shear of the mean current, the two previous works derive similar expressions for the wave forcing terms. In this talk, we will detail and discuss the implementation of these 3D terms in the HYbrid Coordinate Ocean Model (HYCOM, Bleck 2002). We will focus in particular on the hybrid and layered features of the code. The hybrid coordinate, which allows to use distinct vertical coordinates in a same simulation, requires to reformulate the wave forcing terms with a generalised vertical coordinate. Then, these terms must be averaged on each layer of the water column. Two academic tests are investigated to validate the numerical implementation : the gently sloping bottom of Ardhuin (2008) and the plane beach of Haas and Warner (2009). Forcing terms are calculated with simple numerical methods under classical assumptions on conservation of wave properties. The results obtained with distinct configurations are shown to agree with the analytical or numerical known solutions. To conclude, we will discuss the impact of wetting and drying in numerical simulations.
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.
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
STOCHASTIC SOLUTIONS FOR FRACTIONAL WAVE EQUATIONS
MEERSCHAERT, MARK M.; SCHILLING, RENÉ L.; SIKORSKII, ALLA
2014-01-01
A fractional wave equation replaces the second time derivative by a Caputo derivative of order between one and two. In this paper, we show that the fractional wave equation governs a stochastic model for wave propagation, with deterministic time replaced by the inverse of a stable subordinator whose index is one half the order of the fractional time derivative. PMID:26146456
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
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.
Role of 3d-dispersive Alfven waves in coronal heating
NASA Astrophysics Data System (ADS)
Sharma, R. P.; Yadav, N.; Pathak, N.
2014-05-01
Coronal heating is one of the unresolved puzzles in solar physics from decades. In the present paper we have investigated the dynamics of vortices to apprehend coronal heating problem. A three dimensional (3d) model has been developed to study propagation of dispersive Alfvén waves (DAWs) in presence of ion acoustic waves which results in excitation of DAW and evolution of vortices. Taking ponderomotive nonlinearity into account, development of these vortices has been studied. There are observations of such vortices in the chromosphere, transition region and also in the lower solar corona. These structures may play an important role in transferring energy from lower solar atmosphere to corona and result in coronal heating. Nonlinear interaction of these waves is studied in view of recent simulation work and observations of giant magnetic tornadoes in solar corona and lower atmosphere of sun by solar dynamical observatory (SDO).
3D P-Wave Velocity Structure of the Deep Galicia Rifted Margin
NASA Astrophysics Data System (ADS)
Bayrakci, G.; Minshull, T. A.; Davy, R. G.; Sawyer, D. S.; Klaeschen, D.; Papenberg, C. A.; Reston, T. J.; Shillington, D. J.; Ranero, C. R.
2014-12-01
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.
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.
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.
3D SPH numerical simulation of the wave generated by the Vajont rockslide
NASA Astrophysics Data System (ADS)
Vacondio, R.; Mignosa, P.; Pagani, S.
2013-09-01
A 3D numerical modeling of the wave generated by the Vajont slide, one of the most destructive ever occurred, is presented in this paper. A meshless Lagrangian Smoothed Particle Hydrodynamics (SPH) technique was adopted to simulate the highly fragmented violent flow generated by the falling slide in the artificial reservoir. The speed-up achievable via General Purpose Graphic Processing Units (GP-GPU) allowed to adopt the adequate resolution to describe the phenomenon. The comparison with the data available in literature showed that the results of the numerical simulation reproduce satisfactorily the maximum run-up, also the water surface elevation in the residual lake after the event. Moreover, the 3D velocity field of the flow during the event and the discharge hydrograph which overtopped the dam, were obtained.
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.
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
Nonlinear Evolution of 3D Drift-Ion-Sound Standing Waves
NASA Astrophysics Data System (ADS)
Taranov, Volodymyr
2000-10-01
Drift waves play an important role in transport processes in plasmas [1]. Detailed investigation of their stability must include an account of the coupling to ion-sound waves [2]. General properties of the model [2] were studied in [3], stability analysis was done in [4], but linear drift dispersion effects were neglected. Incorrectness of this neglect was emphasized in [5]. In the present work, evolution of spatially periodic 3D standing waves is studied. All physical effects contained in the model [2] are taken into account, namely additional vortex nonlinearity and dispersion effects due to the emission of coupled drift and ion-sound waves. For the waves of small but finite amplitude, perturbation theory based on multiple-time-scale formalism is built. Second and third order in amplitude effects are discussed. References [1] Horton W. 1999. Rev.Mod.Phys. 3. 735. [2] Meiss J.D. and W.Horton. 1983. Phys.Fluids 26. 990. [3] Nycander J. 1994. Chaos 4. 253. [4] Akerstedt H.O., J.Nycander and V.P.Pavlenko. 1996. Phys.Plasmas 3. 160. [5] Goloborod'ko V.Ya., V.B.Taranov. 1999. J. of Plasma and Fusion Res. SERIES 2. 335.
Separation of Lamb waves modes using polarization filter of 3D laser measured signals
NASA Astrophysics Data System (ADS)
Ambrozinski, Lukasz; Stepinski, Tadeusz; Uhl, Tadeusz
2015-04-01
Interpretation of Lamb waves signals can rise serious difficulties due to their multi-modal nature. Different modes propagating with different velocities can be misleading with damage reflected components. As a solution to this problem we propose a technique capable of modes separation based on a polarization filter. Both S0 and A0 Lamb modes exhibit elliptical polarization, however, their polarization parameters, i.e. the ratios of in-plane and out-of-plane displacements and phase-shifts between these components are different. Furthermore, these parameters can be considered constant in a narrow frequency band. Therefore, if the vertical and horizontal components of the wave motion are available, it is possible to apply signal processing technique referred to as oblique polarization filter. This operation is based on phase-shifts and amplifications of the in- and out-of-plane components, which results in orthogonal, linearly polarized A0 and S0 waves signals. In this paper the proposed technique will be illustrated using both numerical simulations and experimental data. The simulations of wave propagation were performed using local interaction simulation approach (LISA) assuming isotropic material. The experiments were performed using 3D laser scanning Doppler vibrometer that allowed to capture the in-plane and out-of-plane wave components.
NASA Astrophysics Data System (ADS)
Haney, M. M.; Aldridge, D. F.; Symons, N. P.
2005-12-01
Numerical solution of partial differential equations by explicit, time-domain, finite-difference (FD) methods entails approximating temporal and spatial derivatives by discrete function differences. Thus, the solution of the difference equation will not be identical to the solution of the underlying differential equation. Solution accuracy degrades if temporal and spatial gridding intervals are too large. Overly coarse spatial gridding leads to spurious artifacts in the calculated results referred to as numerical dispersion, whereas coarse temporal sampling may produce numerical instability (manifest as unbounded growth in the calculations as FD timestepping proceeds). Quantitative conditions for minimizing dispersion and avoiding instability are developed by deriving the dispersion relation appropriate for the discrete difference equation (or coupled system of difference equations) under examination. A dispersion relation appropriate for FD solution of the 3D velocity-stress system of isotropic elastodynamics, on staggered temporal and spatial grids, is developed. The relation applies to either compressional or shear wave propagation, and reduces to the proper form for acoustic propagation in the limit of vanishing shear modulus. A stability condition and a plane-wave phase-speed formula follow as consequences of the dispersion relation. The mathematical procedure utilized for the derivation is a modern variant of classical von Neumann analysis, and involves a 4D discrete space/time Fourier transform of the nine, coupled, FD updating formulae for particle velocity vector and stress tensor components. The method is generalized to seismic wave propagation within anelastic and poroelastic media, as well as sound wave propagation within a uniformly-moving atmosphere. A significant extension of the approach yields a stability condition for wave propagation across an interface between dissimilar media with strong material contrast (e.g., the earth's surface, the seabed
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
A 3-D enlarged cell technique (ECT) for elastic wave modelling of a curved free surface
NASA Astrophysics Data System (ADS)
Wei, Songlin; Zhou, Jianyang; Zhuang, Mingwei; Liu, Qing Huo
2016-09-01
The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of its structured grid. In this work, an improved, stable and accurate 3-D FDTD method for elastic wave modelling on a curved free surface is developed based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the mean time, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability by enlarging small irregular cells into adjacent cells under the condition of conservation of force. This method is verified by several 3-D numerical examples. Results show that the method is stable at the Courant stability limit for a regular FDTD grid, and has much higher accuracy than the conventional FDTD method.
A 3-D enlarged cell technique (ECT) for elastic wave modelling of a curved free surface
NASA Astrophysics Data System (ADS)
Wei, Songlin; Zhou, Jianyang; Zhuang, Mingwei; Liu, Qing Huo
2016-07-01
The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of its structured grid. In this work, an improved, stable and accurate 3-D FDTD method for elastic wave modelling on a curved free surface is developed based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the mean time, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability by enlarging small irregular cells into adjacent cells under the condition of conservation of force. This method is verified by several 3-D numerical examples. Results show that the method is stable at the Courant stability limit for a regular FDTD grid, and has much higher accuracy than the conventional FDTD method.
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.
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.
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.
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
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.
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
NASA Astrophysics Data System (ADS)
Yoshizawa, K.
2014-10-01
A new radially anisotropic shear wave speed model for the Australasian region is constructed from multi-mode phase dispersion of Love and Rayleigh waves. An automated waveform fitting technique based on a global optimization with the Neighbourhood Algorithm allows the exploitation of large numbers of three-component broad-band seismograms to extract path-specific dispersion curves covering the entire continent. A 3-D shear wave model is constructed including radial anisotropy from a set of multi-mode phase speed maps for both Love and Rayleigh waves. These maps are derived from an iterative inversion scheme incorporating the effects of ray-path bending due to lateral heterogeneity, as well as the finite frequency of the surface waves for each mode. The new S wave speed model exhibits major tectonic features of this region that are in good agreement with earlier shear wave models derived primarily from Rayleigh waves. The lateral variations of depth and thickness of the lithosphere-asthenosphere transition (LAT) are estimated from the isotropic (Voigt average) S wave speed model and its vertical gradient, which reveals correlations between the lateral variations of the LAT and radial anisotropy. The thickness of the LAT is very large beneath the Archean cratons in western Australia, whereas that in south Australia is thinner. The radial anisotropy model shows faster SH wave speed than SV beneath eastern Australia and the Coral Sea at the lithospheric depth. The faster SH anomaly in the lithosphere is also seen in the suture zone between the three cratonic blocks of Australia. One of the most conspicuous features of fast SH anisotropy is found in the asthenosphere beneath the central Australia, suggesting anisotropy induced by shear flow in the asthenosphere beneath the fast drifting Australian continent.
Zhu, Meiling; Leighton, Glenn
2008-11-01
Accurate performance evaluation is crucial to the design and development of macro/micro-sized piezoelectric devices, and key to this is the proper use of the stiffness/ compliance and piezoelectric coefficients of the piezoelectric ceramics involved. Although the literature points out effective piezoelectric coefficients e(31,f) and d(33,f) for thin film materials and reduced dimensionality of equations for bulk material, the elastic and piezoelectric coefficients remain unchanged from the 3-D equations in most reported 1-D and 2-D analyses of the macro/micro-sized devices involving the e form of the constitutive equations. The use of unchanged coefficients leads to variations between numerically predicted and experimental results in most devices. To understand effects of the dimensional reduction from 3-D to 2-D and 1-D on stiffness/compliance and piezoelectric coefficients, this paper derives the 2-D and 1-D constitutive equations from the 3-D equations, focusing on the discussion of often-required device configurations for sensor and actuator design and analysis. Two modified coefficients are proposed, termed reduced and enhanced, which enable better understanding of effects of the dimensional reduction and also effects on the design and analysis of sensors and actuators.
Li Benwen Tian Shuai; Sun Yasong; Hu, Zhang-Mao
2010-02-20
The Schur-decomposition for three-dimensional matrix equations is developed and used to directly solve the radiative discrete ordinates equations which are discretized by Chebyshev collocation spectral method. Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented. The numerical results show the good accuracy of spectral method based on direct solvers. The CPU time cost comparisons against the resolutions between these three methods are made using MATLAB and FORTRAN 95 computer languages separately. The results show that the CPU time cost of Chebyshev collocation spectral method with 3D Schur-decomposition solver is the least, and almost only one thirtieth to one fiftieth CPU time is needed when using the spectral method with 3D Schur-decomposition solver compared with the standard discrete ordinates 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.
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.
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.
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.
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
Finite Element Code For 3D-Hydraulic Fracture Propagation Equations (3-layer).
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.
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
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.
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)
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
Du, Qi-Shi; Liu, Peng-Jun; Huang, Ri-Bo
2008-02-01
In this study the excess chemical potential of the integral equation theory, 3D-RISM-HNC [Q. Du, Q. Wei, J. Phys. Chem. B 107 (2003) 13463-13470], is visualized in three-dimensional form and localized at interaction sites of solute molecule. Taking the advantage of reference interaction site model (RISM), the calculation equations of chemical excess potential are reformulized according to the solute interaction sites s in molecular space. Consequently the solvation free energy is localized at every interaction site of solute molecule. For visualization of the 3D-RISM-HNC calculation results, the excess chemical potentials are described using radial and three-dimensional diagrams. It is found that the radial diagrams of the excess chemical potentials are more sensitive to the bridge functions than the radial diagrams of solvent site density distributions. The diagrams of average excess chemical potential provide useful information of solute-solvent electrostatic and van der Waals interactions. The local description of solvation free energy at active sites of solute in 3D-RISM-HNC may broaden the application scope of statistical mechanical integral equation theory in solution chemistry and life science.
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.
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
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.
NASA Astrophysics Data System (ADS)
Chinta, Prashanth K.; Mayer, K.; Langenberg, K. J.
2012-05-01
Nondestructive Evaluation (NDE) of elastic anisotropic media is very complex because of directional dependency of elastic stiffness tensor. Modeling of elastic waves in such materials gives us intuitive knowledge about the propagation and scattering phenomena. The wave propagation in three dimensional space in anisotropic media gives us the deep insight of the transition of the different elastic wave modes i.e. mode conversion, and scattering of these waves because of inhomogeneities present in the material. The numerical tool Three Dimensional-Elastodynamic Finite Integration Technique (3D-EFIT) has been proved to be a very efficient tool for the modeling of elastic waves in very complex geometries. The 3D-EFIT is validated using the analytical approach based on the Radon transform. The simulation results of 3D-EFIT applied to inhomogeneous austenitic steel welds and wood structures are presented. In the first application the geometry consists of an austenitic steel weld that joins two isotropic steel blocks. The vertical transversal isotropic (VTI) austenitic steel is used. The convolutional perfectly matched layers are applied at the boundaries that are supported by isotropic steel. In the second application the wave propagation in the orthotropic wooden structure with an air cavity inside is investigated. The wave propagation results are illustrated using time domain elastic wave snapshots.
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.
New aspects of whistler waves driven by an electron beam studied by a 3-D electromagnetic code
NASA Technical Reports Server (NTRS)
Nishikawa, Ken-Ichi; Buneman, Oscar; Neubert, Torsten
1994-01-01
We have restudied electron beam driven whistler waves with a 3-D electromagnetic particle code. The simulation results show electromagnetic whistler wave emissions and electrostatic beam modes like those observed in the Spacelab 2 electron beam experiment. It has been suggested in the past that the spatial bunching of beam electrons associated with the beam mode may directly generate whistler waves. However, the simulation results indicate several inconsistencies with this picture: (1) whistler waves continue to be generated even after the beam mode space charge modulation looses its coherence, (2) the parallel (to the background magnetic field) wavelength of the whistler wave is longer than that of the beam instability, and (3) the parallel phase velocity of the whistler wave is smaller than that of the beam mode. The complex structure of the whistler waves in the vicinity of the beam suggest that the transverse motion (gyration) of the beam and background electrons is also involved in the generation of whistler waves.
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.
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.
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.
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
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.
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.
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
Flow effects of blood constitutive equations in 3D models of vascular anomalies
NASA Astrophysics Data System (ADS)
Neofytou, Panagiotis; Tsangaris, Sokrates
2006-06-01
The effects of different blood rheological models are investigated numerically utilizing two three- dimensional (3D) models of vascular anomalies, namely a stenosis and an abdominal aortic aneurysm model. The employed CFD code incorporates the SIMPLE scheme in conjunction with the finite-volume method with collocated arrangement of variables. The approximation of the convection terms is carried out using the QUICK differencing scheme, whereas the code enables also multi-block computations, which are useful in order to cope with the two-block grid structure of the current computational domain. Three non-Newtonian models are employed, namely the Casson, Power-Law and Quemada models, which have been introduced in the past for modelling the rheological behaviour of blood and cover both the viscous as well as the two-phase character of blood. In view of the haemodynamical mechanisms related to abnormalities in the vascular network and the role of the wall shear stress in initiating and further developing of arterial diseases, the present study focuses on the 3D flow field and in particular on the distribution as well as on both low and high values of the wall shear stress in the vicinity of the anomaly. Finally, a comparison is made between the effects of each rheological model on the aforementioned parameters. Results show marked differences between simulating blood as Newtonian and non-Newtonian fluid and furthermore the Power-Law model exhibits different behaviour in all cases compared to the other models whereas Quemada and Casson models exhibit similar behaviour in the case of the stenosis but different behaviour in the case of the aneurysm.
Carmona, Guillaume; Perera, Upamali; Gillett, Cheryl; Naba, Alexandra; Law, Ah-Lai; Sharma, Ved P.; Wang, Jian; Wyckoff, Jeffrey; Balsamo, Michele; Mosis, Fuad; De Piano, Mario; Monypenny, James; Woodman, Natalie; McConnell, Russell E.; Mouneimne, Ghassan; Van Hemelrijck, Mieke; Cao, Yihai; Condeelis, John; Hynes, Richard O.; Gertler, Frank B.; Krause, Matthias
2016-01-01
Cancer invasion is a hallmark of metastasis. The mesenchymal mode of cancer cell invasion is mediated by elongated membrane protrusions driven by the assembly of branched F-actin networks. How deregulation of actin regulators promotes cancer cell invasion is still enigmatic. We report that increased expression and membrane localization of the actin regulator Lamellipodin correlates with reduced metastasis-free survival and poor prognosis in breast cancer patients. In agreement we find that Lamellipodin depletion reduced lung metastasis in an orthotopic mouse breast cancer model. Invasive 3D cancer cell migration as well as invadopodia formation, and matrix degradation were impaired upon Lamellipodin depletion. Mechanistically, we show that Lamellipodin promotes invasive 3D cancer cell migration via both actin-elongating Ena/VASP proteins and the Scar/WAVE complex, which stimulates actin branching. In contrast, Lamellipodin interaction with Scar/WAVE but not Ena/VASP is required for random 2D cell migration. We identify a phosphorylation-dependent mechanism that regulates selective recruitment of these effectors to Lamellipodin: Abl-mediated Lamellipodin phosphorylation promotes its association with both Scar/WAVE and Ena/VASP, while Src-dependent phosphorylation enhances binding to Scar/WAVE but not Ena/VASP. Through these selective, regulated interactions Lamellipodin mediates directional sensing of EGF gradients and invasive 3D migration of breast cancer cells. Our findings imply that increased Lamellipodin levels enhance Ena/VASP and Scar/WAVE activities at the plasma membrane to promote 3D invasion and metastasis. PMID:26996666
NASA Astrophysics Data System (ADS)
Guo, Z.; Xiong, S. M.
2015-05-01
An algorithm comprising adaptive mesh refinement (AMR) and parallel (Para-) computing capabilities was developed to efficiently solve the coupled phase field equations in 3-D. The AMR was achieved based on a gradient criterion and the point clustering algorithm introduced by Berger (1991). To reduce the time for mesh generation, a dynamic regridding approach was developed based on the magnitude of the maximum phase advancing velocity. Local data at each computing process was then constructed and parallel computation was realized based on the hierarchical grid structure created during the AMR. Numerical tests and simulations on single and multi-dendrite growth were performed and results show that the proposed algorithm could shorten the computing time for 3-D phase field simulation for about two orders of magnitude and enable one to gain much more insight in understanding the underlying physics during dendrite growth in solidification.
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.
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.
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
Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows
NASA Technical Reports Server (NTRS)
Hsu, C.-H.; Chen, Y.-M.; Liu, C. H.
1990-01-01
A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.
Rigorous 3-D coupled wave diffraction analysis of multiple superposed gratings in anisotropic media.
Glytsis, E N; Gaylord, T K
1989-06-15
The diffraction by two planar slanted fringe gratings superposed in the same volume of an anisotropic medium is treated using rigorous 3-D vector coupled wave analysis. Arbitrary angle of incidence and polarization are included. Both phase and/or amplitude slanted gratings in anisotropic media are treated in the analysis. The external boundary regions can be either isotropic (for bulk applications) or uniaxial anisotropic (for integrated applications). Both forward- and backward-diffracted orders are characterized by a number pair (i(l),i(2)), where i(l) and i(2) are integers. The Floquet condition is discussed for the case of two superposed gratings. When the external regions are anisotropic, each diffracted order has an ordinary (O), and an extraordinary (E) component. The analysis is also generalized for an arbitrary number of superposed gratings. The numerical complexity is discussed. In the case of equal grating periodicities along the boundaries, the diffracted orders become degenerate in the external regions. In this case, an alternative analysis that utilizes a cascaded stack of unslanted gratings can be used. Limiting cases are also presented. The various Bragg conditions are identified and quantified. Sample calculations presented include the quantification of the crosstalk between two superposed gratings, the evaluation of the effects of coupled Bragg conditions in beam combining applications, design and analysis of a beam splitter and a beam combiner, demonstration of the use of a cascaded stack of unslanted gratings of constant modulation to represent two superposed gratings that have the same periodicity along the boundaries, and finally evaluation of the effect of the phase difference between two gratings. The same analysis applies in the limiting cases of isotropic materials, single slanted gratings, etc. Applications of this analysis include optical storage, optical digital truth table look-up processing, neural nets, optical interconnects, beam
Singular boundary method using time-dependent fundamental solution for scalar wave equations
NASA Astrophysics Data System (ADS)
Chen, Wen; Li, Junpu; Fu, Zhuojia
2016-11-01
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.
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
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.
Absence of Critical Points of Solutions to the Helmholtz Equation in 3D
NASA Astrophysics Data System (ADS)
Alberti, Giovanni S.
2016-11-01
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.
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).
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.
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.
Smith, S.A. )
1996-01-01
Quantitative 3-D geological models of Shell's Niger delta reservoirs are now routinely used for well and field development planning, simulation input and reserves booking. A review of these models, built with Shell's reservoir modelling package Geocap, has highlighted the successes and potential pitfalls of 3D reservoir modelling and has led to a template for better modelling of wave-dominated deltaic reservoirs. The key issues fall into two categories. The first concerns the use of soft geological knowledge. Conceptual models are a prerequisite for quality 3-D reservoir models and meaningful results can be obtained only if the geologist has a mental 3-D picture(s) of the reservoir which is used to steer the modelling. The decision to use stochastic techniques is crucial. In wave-dominated deltaic reservoirs, uncertainty may be better handled by a series of deterministic scenarios rather than many stochastic realizations. Sequence stratigraphic correlation tools and the definition of meaningful and recognizable facies types and flow units also determine the quality of the model. Integration between the petroleum engineering disciplines is the second category. The interface with the reservoir engineer is particularly important; the relevant level of geological detail must be identified and preserved during upscaling and flow simulation. Reservoir engineering and seismological data must be used to refine or validate alternative scenarios in an iterative loop. 3-D modelling is a tremendous business opportunity, but it demands more geological skills as well as a fully integrated, multidisciplinary approach.
Smith, S.A.
1996-12-31
Quantitative 3-D geological models of Shell`s Niger delta reservoirs are now routinely used for well and field development planning, simulation input and reserves booking. A review of these models, built with Shell`s reservoir modelling package Geocap, has highlighted the successes and potential pitfalls of 3D reservoir modelling and has led to a template for better modelling of wave-dominated deltaic reservoirs. The key issues fall into two categories. The first concerns the use of soft geological knowledge. Conceptual models are a prerequisite for quality 3-D reservoir models and meaningful results can be obtained only if the geologist has a mental 3-D picture(s) of the reservoir which is used to steer the modelling. The decision to use stochastic techniques is crucial. In wave-dominated deltaic reservoirs, uncertainty may be better handled by a series of deterministic scenarios rather than many stochastic realizations. Sequence stratigraphic correlation tools and the definition of meaningful and recognizable facies types and flow units also determine the quality of the model. Integration between the petroleum engineering disciplines is the second category. The interface with the reservoir engineer is particularly important; the relevant level of geological detail must be identified and preserved during upscaling and flow simulation. Reservoir engineering and seismological data must be used to refine or validate alternative scenarios in an iterative loop. 3-D modelling is a tremendous business opportunity, but it demands more geological skills as well as a fully integrated, multidisciplinary approach.
Multistep and Multistage Boundary Integral Methods for the Wave Equation
NASA Astrophysics Data System (ADS)
Banjai, Lehel
2009-09-01
We describe how time-discretized wave equation in a homogeneous medium can be solved by boundary integral methods. The time discretization can be a multistep, Runge-Kutta, or a more general multistep-multistage method. The resulting convolutional system of boundary integral equations falls in the family of convolution quadratures of Ch. Lubich. In this work our aim is to discuss a new technique for efficiently solving the discrete convolutional system and to present large scale 3D numerical experiments with a wide range of time-discretizations that have up to now not appeared in print. One of the conclusions is that Runge-Kutta methods are often the method of choice even at low accuracy; yet, in connection with hyperbolic problems BDF (backward difference formulas) have been predominant in the literature on convolution quadrature.
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).
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.
3D Discontinuous Galerkin elastic seismic wave modeling based upon a grid injection method
NASA Astrophysics Data System (ADS)
Monteiller, V.
2015-12-01
Full waveform inversion (FWI) is a seismic imaging method that estimates thesub-surface physical properties with a spatial resolution of the order of thewavelength. FWI is generally recast as the iterative optimization of anobjective function that measures the distance between modeled and recordeddata. In the framework of local descent methods, FWI requires to perform atleast two seismic modelings per source and per FWI iteration.Due to the resulting computational burden, applications of elastic FWI have been usuallyrestricted to 2D geometries. Despite the continuous growth of high-performancecomputing facilities, application of 3D elastic FWI to real-scale problemsremain computationally too expensive. To perform elastic seismic modeling with a reasonable amount of time, weconsider a reduced computational domain embedded in a larger background modelin which seismic sources are located. Our aim is to compute repeatedly thefull wavefield in the targeted domain after model alteration, once theincident wavefield has been computed once for all in the background model. Toachieve this goal, we use a grid injection method referred to as the Total-Field/Scattered-Field (TF/SF) technique in theelectromagnetic community. We implemented the Total-Field/Scattered-Field approach in theDiscontinuous Galerkin Finite Element method (DG-FEM) that is used to performmodeling in the local domain. We show how to interface the DG-FEM with any modeling engine (analytical solution, finite difference or finite elements methods) that is suitable for the background simulation. One advantage of the Total-Field/Scattered-Field approach is related to thefact that the scattered wavefield instead of the full wavefield enter thePMLs, hence making more efficient the absorption of the outgoing waves at theouter edges of the computational domain. The domain reduction in which theDG-FEM is applied allows us to use modest computational resources opening theway for high-resolution imaging by full
A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations
NASA Technical Reports Server (NTRS)
Liu, Yen; Kwak, Dochan (Technical Monitor)
1995-01-01
A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind
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)
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.
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.
Carmona, G; Perera, U; Gillett, C; Naba, A; Law, A-L; Sharma, V P; Wang, J; Wyckoff, J; Balsamo, M; Mosis, F; De Piano, M; Monypenny, J; Woodman, N; McConnell, R E; Mouneimne, G; Van Hemelrijck, M; Cao, Y; Condeelis, J; Hynes, R O; Gertler, F B; Krause, M
2016-09-29
Cancer invasion is a hallmark of metastasis. The mesenchymal mode of cancer cell invasion is mediated by elongated membrane protrusions driven by the assembly of branched F-actin networks. How deregulation of actin regulators promotes cancer cell invasion is still enigmatic. We report that increased expression and membrane localization of the actin regulator Lamellipodin correlate with reduced metastasis-free survival and poor prognosis in breast cancer patients. In agreement, we find that Lamellipodin depletion reduced lung metastasis in an orthotopic mouse breast cancer model. Invasive 3D cancer cell migration as well as invadopodia formation and matrix degradation was impaired upon Lamellipodin depletion. Mechanistically, we show that Lamellipodin promotes invasive 3D cancer cell migration via both actin-elongating Ena/VASP proteins and the Scar/WAVE complex, which stimulates actin branching. In contrast, Lamellipodin interaction with Scar/WAVE but not with Ena/VASP is required for random 2D cell migration. We identified a phosphorylation-dependent mechanism that regulates selective recruitment of these effectors to Lamellipodin: Abl-mediated Lamellipodin phosphorylation promotes its association with both Scar/WAVE and Ena/VASP, whereas Src-dependent phosphorylation enhances binding to Scar/WAVE but not to Ena/VASP. Through these selective, regulated interactions Lamellipodin mediates directional sensing of epidermal growth factor (EGF) gradients and invasive 3D migration of breast cancer cells. Our findings imply that increased Lamellipodin levels enhance Ena/VASP and Scar/WAVE activities at the plasma membrane to promote 3D invasion and metastasis.
Relativistic wave equations: an operational approach
NASA Astrophysics Data System (ADS)
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
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)
Harris, Julius E.; Iyer, Venkit; Radwan, Samir
1987-01-01
The application of stability theory in Laminar Flow Control (LFC) research requires that density and velocity profiles be specified throughout the viscous flow field of interest. These profile values must be as numerically accurate as possible and free of any numerically induced oscillations. Guidelines for the present research project are presented: develop an efficient and accurate procedure for solving the 3-D boundary layer equation for aerospace configurations; develop an interface program to couple selected 3-D inviscid programs that span the subsonic to hypersonic Mach number range; and document and release software to the LFC community. The interface program was found to be a dependable approach for developing a user friendly procedure for generating the boundary-layer grid and transforming an inviscid solution from a relatively coarse grid to a sufficiently fine boundary-layer grid. The boundary-layer program was shown to be fourth-order accurate in the direction normal to the wall boundary and second-order accurate in planes parallel to the boundary. The fourth-order accuracy allows accurate calculations with as few as one-fifth the number of grid points required for conventional second-order schemes.
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.
NASA Astrophysics Data System (ADS)
Obermann, Anne; Planès, Thomas; Hadziioannou, Céline; Campillo, Michel
2016-10-01
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: first, 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. Second, we compare the lapse-time behaviour 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.
Far field expansion for anisotropic wave equations
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Hagstrom, Thomas
1989-01-01
A necessary ingredient for the numerical simulation of many time dependent phenomena in acoustics and aerodynamics is the imposition of accurate radiation conditions at artificial boundaries. The asymptotic analysis of propagating waves provides a rational approach to the development of such conditions. A far field asymptotic expansion of solutions of anisotropic wave equations is derived. This generalizes the well known Friedlander expansion for the standard wave operator. The expansion is used to derive a hierarchy of radiation conditions of increasing accuracy. Two numerical experiments are given to illustrate the utility of this approach. The first application is the study of unsteady vortical disturbances impinging on a flat plate; the second is the simulation of inviscid flow past an impulsively started cylinder.
Stability of Traveling Waves of Nonlinear Schrödinger Equation with Nonzero Condition at Infinity
NASA Astrophysics Data System (ADS)
Lin, Zhiwu; Wang, Zhengping; Zeng, Chongchun
2016-10-01
We study the stability of traveling waves of the nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physical models for this are the Gross-Pitaevskii (GP) equation and the cubic-quintic equation. First, under a non-degeneracy condition we prove a sharp instability criterion for 3D traveling waves of (GP), which had been conjectured in the physical literature. This result is also extended for general nonlinearity and higher dimensions, including 4D (GP) and 3D cubic-quintic equations. Second, for cubic-quintic type nonlinearity, we construct slow traveling waves and prove their nonlinear instability in any dimension. For dimension two, the non-degeneracy condition is also proved for these slow traveling waves. For general traveling waves without vortices (that is nonvanishing) and with general nonlinearity in any dimension, we find a sharp condition for linear instability. Third, we prove that any 2D traveling wave of (GP) is transversally unstable, and we find the sharp interval of unstable transversal wave numbers. Near unstable traveling waves of all of the above cases, we construct unstable and stable invariant manifolds.
NASA Astrophysics Data System (ADS)
Jalali, A.; Hulsen, M. A.; Norouzi, M.; Kayhani, M. H.
2013-05-01
This paper presents a numerical simulation of the developing flow and heat transfer of a viscoelastic fluid in a rectangular duct. In fully developed flow of a viscoelastic fluid in a non-circular duct, secondary flows normal to the flow direction are expected to enhance the rate of heat and mass transfer. On the other hand, properties such as viscosity, thermal conductivity, specific heat and relaxation time of the fluid are a function of temperature. Therefore, we developed a numerical model which solves the flow and energy equation simultaneously in three dimensional form. We included several equations of state to model the temperature dependency of the fluid parameters. The current paper is one of the first studies which present a 3D numerical simulation for developing viscoelastic duct flow that takes the dependency of flow parameters to the temperature into account. The rheological constitutive equation of the fluid is a common form of the Phan-Thien Tanner (PTT) model, which embodies both influences of elasticity and shear thinning in viscosity. The governing equations are discretized using the FTCS finite difference method on a staggered mesh. The marker-and-cell method is also employed to allocate the parameters on the staggered mesh, and static pressure is calculated using the artificial compressibility approach during the numerical simulation. In addition to report the results of flow and heat transfer in the developing region, the effect of some dimensionless parameters on the flow and heat transfer has also been investigated. The results are in a good agreement with the results reported by others in this field.
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.
Exact semiclassical wave equation for stochastic quantum optics
NASA Astrophysics Data System (ADS)
Diósi, Lajos
1996-02-01
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the framework of the stochastic wave equation model. We stress in such a way that the concept of stochastic wave equations is not to be restricted to the widely used Markovian approximation.
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.
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
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
Wang, Tao; Green, Ryan; Nair, Rajesh Ramakrishnan; Howell, Mark; Mohapatra, Subhra; Guldiken, Rasim; Mohapatra, Shyam Sundar
2015-12-19
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
3D crustal structure of the Alpine belt and foreland basins as imaged by ambient-noise surface wave
NASA Astrophysics Data System (ADS)
Molinari, Irene; Morelli, Andrea; Cardi, Riccardo; Boschi, Lapo; Poli, Piero; Kissling, Edi
2016-04-01
We derive a 3-D crustal structure (S wave velocity) underneath northern Italy and the wider Alpine region, from an extensive data set of measurements of Rayleigh-wave phase- and group-velocities from ambient noise correlation among all seismographic stations available to date in the region, via a constrained tomographic inversion made to honor detailed active source reflection/refraction profiles and other geological information. We first derive a regional-scale surface wave tomography from ambient-noise-based phase- and group- surface wave velocity observations (Verbeke et al., 2012). Our regional 3D model (Molinari et al., 2015) shows the low velocity area beneath the Po Plain and the Molasse basin; the contrast between the low-velocity crust of the Adriatic domain and the high-velocity crust of the Tyrrhenian domain is clearly seen, as well as an almost uniform crystalline crust beneath the Alpine belt. However, higher frequency data can be exploited to achieve higher resolution images of the Po Plain and Alpine foreland 3D crustal structure. We collected and analyze one year of noise records (2011) of ~100 North Italy seismic broadband stations, we derive the Green functions between each couple of stations and we measure the phase- and group-Rayleigh wave velocity. We conduct a suite of linear least squares inversion of both phase- and group-velocity data, resulting in 2-D maps of Rayleigh-wave phase and group velocity at periods between 3 and 40s with a resolution of 0.1x0.1 degrees. The maps are then inverted to get the 3D structure with unprecedented details. We present here our results, we compare them with other studies, and we discuss geological/geodynamical implications. We believe that such a model stands for the most up-to-date seismological information on the crustal structure of the Alpine belt and foreland basins, and it can represent a reliable reference for further, more detailed, studies to come, based on the high seismograph station density
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
Chang, Mei-Chu; Tsai, Ya-Yi; I, Lin
2013-08-15
We experimentally demonstrate the direct observation of defect mediated wave turbulence with fluctuating defects and low amplitude hole filaments, from a 3D self-excited plane dust acoustic wave in a dusty plasma by reducing dissipation. The waveform undulation is found to be the origin for the amplitude and the phase modulations of the local dust density oscillation, the broadening of the sharp peaks in the frequency spectrum, and the fluctuating defects. The corrugated wave crest surface also causes the observed high and low density patches in the transverse (xy) plane. Low oscillation amplitude spots (holes) share the same positions with the defects. Their trajectories in the xyt space appear in the form of chaotic filaments without long term predictability, through uncertain pair generation, propagation, and pair annihilation.
Fast wave current drive modeling using the combined RANT3D and PICES Codes
NASA Astrophysics Data System (ADS)
Jaeger, E. F.; Murakami, M.; Stallings, D. C.; Carter, M. D.; Wang, C. Y.; Galambos, J. D.; Batchelor, D. B.; Baity, F. W.; Bell, G. L.; Wilgen, J. B.; Chiu, S. C.; DeGrassie, J. S.; Forest, C. B.; Kupfer, K.; Petty, C. C.; Pinsker, R. T.; Prater, R.; Lohr, J.; Lee, K. M.
1996-02-01
Two numerical codes are combined to give a theoretical estimate of the current drive and direct electron heating by fast waves launched from phased antenna arrays on the DIII-D tokamak. Results are compared with experiment.
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.
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.
NASA Astrophysics Data System (ADS)
Viveros, U.; Sanchez-Sesma, F. J.; Luzon, F.
2001-12-01
The scattering of elastic waves by various types of cracks is an important engineering problem. From a physical point of view the question that arises is up to what degree will a local perturbation in a medium modifies the scattered wave field. For instance, in the seismic monitoring to enhance oil recovery (due to extensive presence of cracks and cavities) a crucial problem is to determine zones where there are physical property changes. Modelling such highly heterogeneous media is critical to increased production from oil and gas. In order to study scattering effects caused by arbitrary-shaped cracks a simplified indirect boundary element method (BEM) is used to compute the seismic response of a 3-D crack under incident elastic P and S waves. The method is based on the integral representation for scattered elastic waves using single layer boundary sources. This approach is called indirect BEM in the literature as the sources strengths should be obtained as an intermediate step. Scattered waves are constructed at the boundaries from which they radiate. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Boundary conditions lead to a system of integral for boundary sources. A simplified discretization scheme is used. It is based on the approximate rectification of the surfaces involved using circles for the numerical and analytical integration of the exact Green's function for the unbounded elastic space. Radiation patterns for penny-shaped and croissant-shaped cracks are explored. The scattering effects of the elastic waves in a homogeneous isotropic infinite elastic medium with a 3-D crack are displayed in both frequency and time domains.
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.
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.
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.
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
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)
Bisrat, Shishay T.; DeShon, Heather R.; Pesicek, Jeremy; Thurber, Clifford
2014-01-01
A three-dimensional (3-D), high-resolution P wave seismic attenuation model for the New Madrid Seismic Zone (NMSZ) is determined using P wave path attenuation (t*) values of small-magnitude earthquakes (MD < 3.9). Events were recorded at 89 broadband and short-period seismometers of the Cooperative New Madrid Seismic Zone Network and 40 short-period seismometers of the Portable Array for Numerical Data Acquisition experiment. The amplitude spectra of all the earthquakes are simultaneously inverted for source, path (t*), and site parameters. The t* values are inverted for QP using local earthquake tomography methods and a known 3-D P wave velocity model for the region. The four major seismicity arms of the NMSZ exhibit reduced QP (higher attenuation) than the surrounding crust. The highest attenuation anomalies coincide with areas of previously reported high swarm activity attributed to fluid-rich fractures along the southeast extension of the Reelfoot fault. The QP results are consistent with previous attenuation studies in the region, which showed that active fault zones and fractured crust in the NMSZ are highly attenuating.
NASA Astrophysics Data System (ADS)
Ayers, J.; Owens, C. T.; Liu, K. C.; Swenson, E.; Ghoshal, A.; Weiss, V.
2013-01-01
The application of guided waves to interrogate remote areas of structural components has been researched extensively in characterizing damage. However, there exists a sparsity of work in using piezoelectric transducer-generated guided waves as a method of assessing stress intensity factors (SIF). This quantitative information enables accurate estimation of the remaining life of metallic structures exhibiting cracks, such as military and commercial transport vehicles. The proposed full wavefield approach, based on 3D laser vibrometry and piezoelectric transducer-generated guided waves, provides a practical means for estimation of dynamic stress intensity factors (DSIF) through local strain energy mapping via the J-integral. Strain energies and traction vectors can be conveniently estimated from wavefield data recorded using 3D laser vibrometry, through interpolation and subsequent spatial differentiation of the response field. Upon estimation of the Jintegral, it is possible to obtain the corresponding DSIF terms. For this study, the experimental test matrix consists of aluminum plates with manufactured defects representing canonical elliptical crack geometries under uniaxial tension that are excited by surface mounted piezoelectric actuators. The defects' major to minor axes ratios vary from unity to approximately 133. Finite element simulations are compared to experimental results and the relative magnitudes of the J-integrals are examined.
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)
Barnoncel, David; Staszewski, Wieslaw J.; Schell, Jochen; Peres, Patrick
2013-04-01
Reusable Launch Vehicles are often used in space applications to guarantee space exploration with reduced costs. These structures often use components from newly developed materials. It is inevitable that reliable inspection methods will be required for quality control and maintenance of such structures to avoid potential damage. This paper describes some initial results from evaluation tests based on Lamb waves for damage detection of Reusable Launch Vehicle composite components. Low-profile, surface-bonded piezoceramic transducers were used for Lamb wave generation. Non-contact measurements of Lamb wave responses were taken by a laser vibrometer. The results presented in this paper demonstrate the great potential of the method for quality inspection and structural damage detection of space composite structures.
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.
NASA Astrophysics Data System (ADS)
Zhengyong, R.; Jingtian, T.; Changsheng, L.; Xiao, X.
2007-12-01
Although adaptive finite-element (AFE) analysis is becoming more and more focused in scientific and engineering fields, its efficient implementations are remain to be a discussed problem as its more complex procedures. In this paper, we propose a clear C++ framework implementation to show the powerful properties of Object-oriented philosophy (OOP) in designing such complex adaptive procedure. In terms of the modal functions of OOP language, the whole adaptive system is divided into several separate parts such as the mesh generation or refinement, a-posterior error estimator, adaptive strategy and the final post processing. After proper designs are locally performed on these separate modals, a connected framework of adaptive procedure is formed finally. Based on the general elliptic deferential equation, little efforts should be added in the adaptive framework to do practical simulations. To show the preferable properties of OOP adaptive designing, two numerical examples are tested. The first one is the 3D direct current resistivity problem in which the powerful framework is efficiently shown as only little divisions are added. And then, in the second induced polarization£¨IP£©exploration case, new adaptive procedure is easily added which adequately shows the strong extendibility and re-usage of OOP language. Finally we believe based on the modal framework adaptive implementation by OOP methodology, more advanced adaptive analysis system will be available in future.
Analysis of wall shear stress around a competitive swimmer using 3D Navier-Stokes equations in CFD.
Popa, C V; Zaidi, H; Arfaoui, A; Polidori, G; Taiar, R; Fohanno, S
2011-01-01
This paper deals with the flow dynamics around a competitive swimmer during underwater glide phases occurring at the start and at every turn. The influence of the head position, namely lifted up, aligned and lowered, on the wall shear stress and the static pressure distributions is analyzed. The problem is considered as 3D and in steady hydrodynamic state. Three velocities (1.4 m/s, 2.2 m/s and 3.1 m/s) that correspond to inter-regional, national and international swimming levels are studied. The flow around the swimmer is assumed turbulent. The Reynolds-averaged Navier-Stokes (RANS) equations are solved with the standard k-ω turbulent model by using the CFD (computational fluid dynamics) numerical method based on a volume control approach. Numerical simulations are carried out with the ANSYS FLUENT® CFD code. The results show that the wall shear stress increases with the velocity and consequently the drag force opposing the movement of the swimmer increases as well. Also, high wall shear stresses are observed in the areas where the body shape, globally rigid in form, presents complex surface geometries such as the head, shoulders, buttocks, heel and chest.
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.
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.
A faster aggregation for 3D fast evanescent wave solvers using rotations
Bogaert, Ignace Pissoort, Davy; Olyslager, Femke
2007-11-10
A novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented. The new method calculates the six plane wave radiation patterns from a multipole expansion (aggregation) and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns. It is faster than the direct approach for multipole orders larger than one, and becomes six times faster for large multipole orders. The method relies on a connection between the discretizations of the six integral representations, and on the fact that the Wigner D-matrices become diagonal for rotations around the z-axis. The proposed technique can also be extended to the vectorial case in two different ways, one of which is very similar to the scalar case. The other method relies on a Beltrami decomposition of the fields and is faster than the direct approach for any multipole order. This decomposition is also not limited to evanescent wave solvers, but can be used in any vectorial multilevel fast multipole algorithm.
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.
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.
Wave-equation based traveltime seismic tomography - Part 1: Method
NASA Astrophysics Data System (ADS)
Tong, P.; Zhao, D.; Yang, D.; Yang, X.; Chen, J.; Liu, Q.
2014-08-01
In this paper, we propose a wave-equation based traveltime seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the traveltime residual Δt = Tobs - Tsyn and the relative velocity perturbation δc(x) / c(x) connected by a finite-frequency traveltime sensitivity kernel K(x) is theoretically derived using the adjoint method. To accurately calculate the traveltime residual Δt, two automatic arrival-time picking techniques including the envelop energy ratio method and the combined ray and cross-correlation method are then developed to compute the arrival times Tsyn for synthetic seismograms. The arrival times Tobs of observed seismograms are usually determined by manual hand picking in real applications. Traveltime sensitivity kernel K(x) is constructed by convolving a forward wavefield u(t,x) with an adjoint wavefield q(t,x). The calculations of synthetic seismograms and sensitivity kernels rely on forward modelling. To make it computationally feasible for tomographic problems involving a large number of seismic records, the forward problem is solved in the two-dimensional (2-D) vertical plane passing through the source and the receiver by a high-order central difference method. The final model is parameterized on 3-D regular grid (inversion) nodes with variable spacings, while model values on each 2-D forward modelling node are linearly interpolated by the values at its eight surrounding 3-D inversion grid nodes. Finally, the tomographic inverse problem is formulated as a regularized optimization problem, which can be iteratively solved by either the LSQR solver or a non-linear conjugate-gradient method. To provide some insights into future 3-D tomographic inversions, Fréchet kernels for different seismic phases are also demonstrated in this study.
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.
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
Investigating a clay landslide site using 3D P-wave reflection seismics in Lilla Edet, Sweden
NASA Astrophysics Data System (ADS)
Lundberg, E.; Malehmir, A.; Juhlin, C.; Bastani, M.
2012-04-01
Landslides are one of the most commonly occurring natural disasters. Global damages range in the billions of dollars and cost hundreds of lives each year; Sweden is not an exception. The main objectives of this geohazard-related project are (1) to improve the understanding of the geometrical shape and structure of clay areas, (2) to develop tools for monitoring changes in their geometry and physical properties as critical factors for landslide triggering, and (3) to provide robust analytical methods for assessing risks associated with clay landslides both in short and long terms. The project is sponsored by the Geoscientists Without Borders (GWB) Program of the Society of Exploration Geophysicists and is multidisciplinary, involving several geophysical methods such as ground gravity and magnetics, geoelectrics, controlled source/radio magnetotellurics, as well as reflection/refraction seismic methods (both P- and S-wave source and receivers). The test site is located on the shoreline of the Göta river that runs from lake Vänern to Göteborg on the southwest coast. The Göta river is the largest river in Sweden and follows the Götaälv Zone, which is an approximately 4 km wide fault zone dipping towards the west. The 3D seismic survey covers a large landslide scar that occurred about 30-40 years ago. The main objective of the 3D seismic is to image the bedrock topography in detail and possibly define layering in the sediments above. The 3D seismic data were acquired in September 2011 using a weight-drop source, 4 m geophone spacing and 20 m line spacing with the source activated at most geophone positions. Ten lines with 60 geophones on each line were shot in two overlapping patches. The preliminary results are encouraging and depict the bedrock topography at 100-150 ms or about 70-100 m. The central line in the 3D seismic survey is overlapped by a longer 2D reflection seismic profile, acquired using a dynamite source. The 2D reflection stack, as well as a travel
NASA Astrophysics Data System (ADS)
Zhang, M. Y.; Li, Y. S.
1997-08-01
A third-generation wind wave model based on the energy balance equation taking into account the effects of time-varying currents and coupled dynamically with a semi-implicit three-dimensional hydrodynamic model incorporating the influences of time- and space-varying vertical eddy viscosity, bottom topography and wave-current interactions is presented in this paper. The wave model is synchronously coupled with the three-dimensional hydrodynamic model through the surface atmospheric turbulent boundary layer and the bottom boundary layer. The theory of Janssen (1991) (in Journal of Physical Oceanography21, 1631-1642) is used to incorporate the effects of waves on the surface boundary layer, while the theory of Grant and Maddsen (1979) [in Journal of Geophysical Research (Oceans)84, 1797-1808], which was used by Signell et al. (1990) (in Journal of Geophysical Research95, 9671-9678) on the bottom boundary layer for constant waves, is modified for the inclusion of time-varying waves. The mutual influences between waves and currents are investigated through an idealized continental shelf case and hindcastings of storm events in the sea area adjacent to Hong Kong in the northern South China Sea. Calculations are compared with other computed results and observations. Calculations show that the wave-dependent surface stress incorporated in the three-dimensional hydrodynamic model has significant impact on water surface velocities and surface elevations (over 10% higher). The inclusion of wave-dependent bottom stress also shows some effects; however, in the presence of the wave-dependent surface stress, its effect on surge levels becomes negligible. The effect of currents on waves amounts to the reduction of the significant wave height by about 8% and less for wave mean periods. However, the inclusion of the wave-dependent bottom stress in the three-dimensional hydrodynamic model has little effect on wave characteristics whether or not the wave-dependent surface stress is
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.
NASA Astrophysics Data System (ADS)
Matsuda, Takashi S.; Nakamura, Takuji; Murphy, Damian; Tsutsumi, Masaki; Moffat-Griffin, Tracy; Zhao, Yucheng; Pautet, Pierre-Dominique; Ejiri, Mitsumu K.; Taylor, Michael
2016-07-01
ANGWIN (Antarctic Gravity Wave Imaging/Instrument Network) is an international airglow imager/instrument network in the Antarctic, which commenced observations in 2011. It seeks to reveal characteristics of mesospheric gravity waves, and to study sources, propagation, breaking of the gravity waves over the Antarctic and the effects on general circulation and upper atmosphere. In this study, we compared distributions of horizontal phase velocity of the gravity waves at around 90 km altitude observed in the mesospheric airglow imaging over different locations using our new statistical analysis method of 3-D Fourier transform, developed by Matsuda et al. (2014). Results from the airglow imagers at four stations at Syowa (69S, 40E), Halley (76S, 27W), Davis (69S, 78E) and McMurdo (78S, 156E) out of the ANGWIN imagers have been compared, for the observation period between April 6 and May 21 in 2013. In addition to the horizontal distribution of propagation and phase speed, gravity wave energies have been quantitatively compared, indicating a smaller GW activity in higher latitude stations. We further investigated frequency dependence of gravity wave propagation direction, as well as nightly variation of the gravity wave direction and correlation with the background wind variations. We found that variation of propagation direction is partly due to the effect of background wind in the middle atmosphere, but variation of wave sources could play important role as well. Secondary wave generation is also needed to explain the observed results.
The Rossby wave instability and planet formation: 3D numerical simulations
NASA Astrophysics Data System (ADS)
Méheut, H.; Casse, F.; Varnière, P.; Tagger, M.
2008-11-01
Models of planet formation do not explain yet the growth of planetesimals as in certain ranges of grain size collisions are too slow compared to estimated planet formation time. The Rossby wave instability (RWI) may solve this problem by the formation of Rossby vortices in the accretion disc, speeding up the accumulation of grains in their centre ( te{Peggy} ). Up to now, only two dimensions numerical studies of the RWI have been done. In this proceeding we present the results of three dimensions numerical simulations of the non-linear evolution of the RWI in a non magnetized disc and its vertical structure.
A full 3D plane-wave-expansion model for 1-3 piezoelectric composite structures.
Wilm, Mikaël; Ballandras, Sylvain; Laude, Vincent; Pastureaud, Thomas
2002-09-01
The plane-wave-expansion (PWE) approach dedicated to the simulation of periodic devices has been extended to 1-3 connectivity piezoelectric composite structures. The case of simple but actual piezoelectric composite structures is addressed, taking piezoelectricity, acoustic losses, and electrical excitation conditions rigorously into account. The material distribution is represented by using a bidimensional Fourier series and the electromechanical response is simulated using a Bloch-Floquet expansion together with the Fahmy-Adler formulation of the Christoffel problem. Application of the model to 1-3 connectivity piezoelectric composites is reported and compared to previously published analyses of this problem.
Extracting chemical information from plane wave calculations by a 3D 'fuzzy atoms' analysis
NASA Astrophysics Data System (ADS)
Bakó, I.; Stirling, A.; Seitsonen, A. P.; Mayer, I.
2013-03-01
Bond order and valence indices have been calculated by the method of the three-dimensional 'fuzzy atoms' analysis, using the numerical molecular orbitals obtained from plane wave DFT calculations, i.e., without introducing any external atom-centered functions. Weight functions of both Hirshfeld and Becke types have been applied. The results are rather close to the similar 'fuzzy atoms' ones obtained by using atom-centered basis sets and agree well with the chemical expectations, stressing the power of the genuine chemical concepts.
Measurement of near-wall 3D flow velocity from wave-guiding micro-pillars.
Bruecker, Christoph
2016-09-19
The measurement of near-wall flow in a plane close to the wall is achieved using the wave-guiding feature of transparent flexible micro-pillars which are attached in a 2D array to a surface and bend with the flow. Optical detection of bending from below the surface and application of auto-correlation methods provide mean and fluctuating part of the components of the wall-parallel velocity components. In addition, the wall-normal fluid motion is determined from spatial gradients in the array. The data provide the three-component velocity vector field in a plane close to the wall as well as their statistics.
ERIC Educational Resources Information Center
Merchant, Zahira; Goetz, Ernest T.; Keeney-Kennicutt, Wendy; Kwok, Oi-man; Cifuentes, Lauren; Davis, Trina J.
2012-01-01
We examined a model of the impact of a 3D desktop virtual reality environment on the learner characteristics (i.e. perceptual and psychological variables) that can enhance chemistry-related learning achievements in an introductory college chemistry class. The relationships between the 3D virtual reality features and the chemistry learning test as…
Wave Phase-Sensitive Transformation of 3d-Straining of Mechanical Fields
NASA Astrophysics Data System (ADS)
Smirnov, I. N.; Speranskiy, A. A.
2015-11-01
It is the area of research of oscillatory processes in elastic mechanical systems. Technical result of innovation is creation of spectral set of multidimensional images which reflect time-correlated three-dimensional vector parameters of metrological, and\\or estimated, and\\or design parameters of oscillations in mechanical systems. Reconstructed images of different dimensionality integrated in various combinations depending on their objective function can be used as homeostatic profile or cybernetic image of oscillatory processes in mechanical systems for an objective estimation of current operational conditions in real time. The innovation can be widely used to enhance the efficiency of monitoring and research of oscillation processes in mechanical systems (objects) in construction, mechanical engineering, acoustics, etc. Concept method of vector vibrometry based on application of vector 3D phase- sensitive vibro-transducers permits unique evaluation of real stressed-strained states of power aggregates and loaded constructions and opens fundamental innovation opportunities: conduct of continuous (on-line regime) reliable monitoring of turboagregates of electrical machines, compressor installations, bases, supports, pipe-lines and other objects subjected to damaging effect of vibrations; control of operational safety of technical systems at all the stages of life cycle including design, test production, tuning, testing, operational use, repairs and resource enlargement; creation of vibro-diagnostic systems of authentic non-destructive control of anisotropic characteristics of materials resistance of power aggregates and loaded constructions under outer effects and operational flaws. The described technology is revolutionary, universal and common for all branches of engineering industry and construction building objects.
3-D Modelling of Stretched Solitary Waves along Magnetic Field Lines
NASA Astrophysics Data System (ADS)
Muschietti, L.; Roth, I.; Carlson, C. W.; Berthomier, M.
2001-12-01
A model is presented for a new type of fast solitary waves which is observed by FAST in downward current regions of the auroral zone. The three-dimensional, coherent structures are electrostatic, have a positive potential, and move along the ambient magnetic field lines with speeds on the order of the electron drift. Their potential profile in the parallel direction, which can be directly measured, is flat-top whereby it cannot fit to the Gaussian shape used in previous work. Their potential profile in the perpendicular direction can only be inferred from a measured unipolar electric signal. We develop an extended BGK model which includes a flattened potential and an assumed cylindrical symmetry around a centric magnetic field line. The model envisions concentric shells of trapped electrons slowly drifting azimuthally while bouncing back and forth in the parallel direction. The electron dynamics is analysed in terms of three basic motions that occur on different time scales. These are defined by the cyclotron frequency Ω e, the bounce frequency ω b, and the azimuthal drift frequency ω γ , for which explicit analytical expressions are obtained. Subject to the ordering ω γ <<ωb<< Ωe, we calculate self-consistent distribution functions in terms of approximate constants of motion. Constraints on the parameters characterizing the amplitude and shape of the stretched solitary wave are discussed.
Wave equation modelling using Julia programming language
NASA Astrophysics Data System (ADS)
Kim, Ahreum; Ryu, Donghyun; Ha, Wansoo
2016-04-01
Julia is a young high-performance dynamic programming language for scientific computations. It provides an extensive mathematical function library, a clean syntax and its own parallel execution model. We developed 2d wave equation modeling programs using Julia and C programming languages and compared their performance. We used the same modeling algorithm for the two modeling programs. We used Julia version 0.3.9 in this comparison. We declared data type of function arguments and used inbounds macro in the Julia program. Numerical results showed that the C programs compiled with Intel and GNU compilers were faster than Julia program, about 18% and 7%, respectively. Taking the simplicity of dynamic programming language into consideration, Julia can be a novel alternative of existing statically typed programming languages.
LASTRAC.3d: Transition Prediction in 3D Boundary Layers
NASA Technical Reports Server (NTRS)
Chang, Chau-Lyan
2004-01-01
Langley Stability and Transition Analysis Code (LASTRAC) is a general-purpose, physics-based transition prediction code released by NASA for laminar flow control studies and transition research. This paper describes the LASTRAC extension to general three-dimensional (3D) boundary layers such as finite swept wings, cones, or bodies at an angle of attack. The stability problem is formulated by using a body-fitted nonorthogonal curvilinear coordinate system constructed on the body surface. The nonorthogonal coordinate system offers a variety of marching paths and spanwise waveforms. In the extreme case of an infinite swept wing boundary layer, marching with a nonorthogonal coordinate produces identical solutions to those obtained with an orthogonal coordinate system using the earlier release of LASTRAC. Several methods to formulate the 3D parabolized stability equations (PSE) are discussed. A surface-marching procedure akin to that for 3D boundary layer equations may be used to solve the 3D parabolized disturbance equations. On the other hand, the local line-marching PSE method, formulated as an easy extension from its 2D counterpart and capable of handling the spanwise mean flow and disturbance variation, offers an alternative. A linear stability theory or parabolized stability equations based N-factor analysis carried out along the streamline direction with a fixed wavelength and downstream-varying spanwise direction constitutes an efficient engineering approach to study instability wave evolution in a 3D boundary layer. The surface-marching PSE method enables a consistent treatment of the disturbance evolution along both streamwise and spanwise directions but requires more stringent initial conditions. Both PSE methods and the traditional LST approach are implemented in the LASTRAC.3d code. Several test cases for tapered or finite swept wings and cones at an angle of attack are discussed.
Measurement of near-wall 3D flow velocity from wave-guiding micro-pillars.
Bruecker, Christoph
2016-09-19
The measurement of near-wall flow in a plane close to the wall is achieved using the wave-guiding feature of transparent flexible micro-pillars which are attached in a 2D array to a surface and bend with the flow. Optical detection of bending from below the surface and application of auto-correlation methods provide mean and fluctuating part of the components of the wall-parallel velocity components. In addition, the wall-normal fluid motion is determined from spatial gradients in the array. The data provide the three-component velocity vector field in a plane close to the wall as well as their statistics. PMID:27661882
Skin-Friction Measurements in a 3-D, Supersonic Shock-Wave/Boundary-Layer Interaction
NASA Technical Reports Server (NTRS)
Wideman, J. K.; Brown, J. L.; Miles, J. B.; Ozcan, O.
1994-01-01
The experimental documentation of a three-dimensional shock-wave/boundary-layer interaction in a nominal Mach 3 cylinder, aligned with the free-stream flow, and 20 deg. half-angle conical flare offset 1.27 cm from the cylinder centerline. Surface oil flow, laser light sheet illumination, and schlieren were used to document the flow topology. The data includes surface-pressure and skin-friction measurements. A laser interferometric skin friction data. Included in the skin-friction data are measurements within separated regions and three-dimensional measurements in highly-swept regions. The skin-friction data will be particularly valuable in turbulence modeling and computational fluid dynamics validation.
3D Body Wave Velocity Tomography in Southern Peru: Seismotectonic Implications
NASA Astrophysics Data System (ADS)
Gallego, A.; Perez, J.; David, C.; Comte, D.; Charrier, R.; Dorbath, L.
2004-12-01
The studied region corresponds to the southern segment of the 1868 rupture area, that did not break with the last Mw=8.4 Arequipa earthquake in southern Peru. A temporary network of 19 short period, continuous recording seismic stations was deployed (16.5° -18.5° S; 69.5° -72° W) between December 2002-March 2003 in this region. The 1093 select events were used for a joint hypocentral and velocity structure inversion. The first obtained 1D velocity model was used as the initial model for the 3D inversion, consisting in 231 blocks distributed along layers separated by 10 km for depths lower than 80 km, and by 20 km for depths between 80 and 160 km. North of the Arica Bend, between the Coast and Andean Range the high Vp velocity and Vp/Vs ratio observed at depths lower than 10 km could represent the Precambrian basement uplifted by the Incapuquio sinistral fault system, which develops a positive flower structure typical for transpressional zones, that raised the basement. This behavior is in good agreement with the uplift of the Cambrian metamorphic complex, in the Precordillera south of the Arica Bend (northern Chile), by the west-vergent thrust system. Beneath the anomalous high velocities (between 20 and 30 km depth), a low velocity zone (Vp<4.5 km/s, and Vp/Vs<1.5) can be observed; this LVZ can be associated with a zone of continuous metamorphism and/or partial melting that the decouples the upper-crustal imbrication from a thickening lower-crust. The Wadati-Benioff zone exhibits a dip angle of about 20° between 10 to 60 km depth, and about 45° for depths higher than 80 km. The double seismic zone known for northern Chile is not present in southern Peru. Cross sections perpendicular to the trench, define a very active seismic zone which dips about 45° trenchward, and is almost perpendicular to the subducting slab between 0 and 60 km depths, similar to the one existing in northern Chile, but with a lower rate of seismicity; the higher activity of this zone
Capturing atmospheric effects on 3D millimeter wave radar propagation patterns
NASA Astrophysics Data System (ADS)
Cook, Richard D.; Fiorino, Steven T.; Keefer, Kevin J.; Stringer, Jeremy
2016-05-01
Traditional radar propagation modeling is done using a path transmittance with little to no input for weather and atmospheric conditions. As radar advances into the millimeter wave (MMW) regime, atmospheric effects such as attenuation and refraction become more pronounced than at traditional radar wavelengths. The DoD High Energy Laser Joint Technology Offices High Energy Laser End-to-End Operational Simulation (HELEEOS) in combination with the Laser Environmental Effects Definition and Reference (LEEDR) code have shown great promise simulating atmospheric effects on laser propagation. Indeed, the LEEDR radiative transfer code has been validated in the UV through RF. Our research attempts to apply these models to characterize the far field radar pattern in three dimensions as a signal propagates from an antenna towards a point in space. Furthermore, we do so using realistic three dimensional atmospheric profiles. The results from these simulations are compared to those from traditional radar propagation software packages. In summary, a fast running method has been investigated which can be incorporated into computational models to enhance understanding and prediction of MMW propagation through various atmospheric and weather conditions.
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.
1990-01-01
The development and applications of multiblock/multizone and adaptive grid methodologies for solving the three-dimensional simplified Navier-Stokes equations are described. Adaptive grid and multiblock/multizone approaches are introduced and applied to external and internal flow problems. These new implementations increase the capabilities and flexibility of the PAB3D code in solving flow problems associated with complex geometry.
3D ARGUS-ESP computations of vacuum eigenmodes for standing-wave and traveling-wave structures
Petillo, J.J.; Chernin, D.P.; Mondelli, A.A.
1996-12-31
The ARGUS-ESP code has been used to calculate electromagnetic vacuum eigenmodes, including dispersion diagrams, for both standing-wave and traveling-wave devices. Slow-wave structures, as used in microwave devices, are readily modeled with this code. ARGUS-ESP gives the designer the ability to do Numerical Cold Testing. For this presentation, the ARGUS electromagnetic eigenmode solver, ESP, is featured. This solver gives the user the capability to calculate cavity modes for general, arbitrarily-complicated, structures. The eigenmode solver uses a fraction of the CPU time that a time-domain calculation would take, and yields a much higher accuracy of solution. In particular, this rapid frequency domain algorithm has incorporated in it a phase-advance boundary condition that allows dispersion diagrams for devices to be readily determined, where only a single period of a structure needs to be gridded. Two examples of the application of this solver will be presented.
What's its wave? A 3D analysis of flying snake locomotion
NASA Astrophysics Data System (ADS)
Yeaton, Isaac J.; Baumgardner, Grant A.; Weiss, Talia M.; Nave, Gary; Ross, Shane D.; Socha, John J.
2015-11-01
Arboreal snakes of the genus Chrysopelea are the only known snakes to glide. To execute aerial locomotion, a snake jumps from a tree into the air while simultaneously flattening its body into an aerodynamically favorable shape. Snake gliding is distinguished by complex, three-dimensional body undulations resulting in a stable glide. However, these undulations have not been sufficiently characterized for a proper dynamical analysis. Here we ask, what is the body waveform employed during a glide, and how does this waveform enhance rotational stability? We report on recent glide experiments in which we recorded the three-dimensional body position during 8.5 m glides using a multi-camera motion-capture system. We quantify the body posture using complex modal analysis, which then serves as input in a variable-geometry rigid-body simulation of the snake while gliding. By separating the inertial and aerodynamic contributions in the equations of motion, we can now quantify the stability of the snake's `gait'. Supported by NSF 1351322.
FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.; Torrisi, M.; Tracinà, R.
2010-11-01
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.
Detection of hidden objects using a real-time 3-D millimeter-wave imaging system
NASA Astrophysics Data System (ADS)
Rozban, Daniel; Aharon, Avihai; Levanon, Assaf; Abramovich, Amir; Yitzhaky, Yitzhak; Kopeika, N. S.
2014-10-01
Millimeter (mm)and sub-mm wavelengths or terahertz (THz) band have several properties that motivate their use in imaging for security applications such as recognition of hidden objects, dangerous materials, aerosols, imaging through walls as in hostage situations, and also in bad weather conditions. There is no known ionization hazard for biological tissue, and atmospheric degradation of THz radiation is relatively low for practical imaging distances. We recently developed a new technology for the detection of THz radiation. This technology is based on very inexpensive plasma neon indicator lamps, also known as Glow Discharge Detector (GDD), that can be used as very sensitive THz radiation detectors. Using them, we designed and constructed a Focal Plane Array (FPA) and obtained recognizable2-dimensional THz images of both dielectric and metallic objects. Using THz wave it is shown here that even concealed weapons made of dielectric material can be detected. An example is an image of a knife concealed inside a leather bag and also under heavy clothing. Three-dimensional imaging using radar methods can enhance those images since it can allow the isolation of the concealed objects from the body and environmental clutter such as nearby furniture or other people. The GDDs enable direct heterodyning between the electric field of the target signal and the reference signal eliminating the requirement for expensive mixers, sources, and Low Noise Amplifiers (LNAs).We expanded the ability of the FPA so that we are able to obtain recognizable 2-dimensional THz images in real time. We show here that the THz detection of objects in three dimensions, using FMCW principles is also applicable in real time. This imaging system is also shown here to be capable of imaging objects from distances allowing standoff detection of suspicious objects and humans from large distances.
Guided-wave-based damage detection in a composite T-joint using 3D scanning laser Doppler vibrometer
NASA Astrophysics Data System (ADS)
Kolappan Geetha, Ganesh; Roy Mahapatra, D.; Srinivasan, Gopalakrishnan
2012-04-01
Composite T-joints are commonly used in modern composite airframe, pressure vessels and piping structures, mainly to increase the bending strength of the joint and prevents buckling of plates and shells, and in multi-cell thin-walled structures. Here we report a detailed study on the propagation of guided ultrasonic wave modes in a composite T-joint and their interactions with delamination in the co-cured co-bonded flange. A well designed guiding path is employed wherein the waves undergo a two step mode conversion process, one is due to the web and joint filler on the back face of the flange and the other is due to the delamination edges close to underneath the accessible surface of the flange. A 3D Laser Doppler Vibrometer is used to obtain the three components of surface displacements/velocities of the accessible face of the flange of the T-joint. The waves are launched by a piezo ceramic wafer bonded on to the back surface of the flange. What is novel in the proposed method is that the location of any change in material/geometric properties can be traced by computing a frequency domain power flow along a scan line. The scan line can be chosen over a grid either during scan or during post-processing of the scan data off-line. The proposed technique eliminates the necessity of baseline data and disassembly of structure for structural interrogation.
A coupled wave-3-D hydrodynamics model of the Taranto Sea (Italy): a multiple-nesting approach
NASA Astrophysics Data System (ADS)
Gaeta, Maria Gabriella; Samaras, Achilleas G.; Federico, Ivan; Archetti, Renata; Maicu, Francesco; Lorenzetti, Giuliano
2016-09-01
The present work describes an operational strategy for the development of a multiscale modeling system, based on a multiple-nesting approach and open-source numerical models. The strategy was applied and validated for the Gulf of Taranto in southern Italy, scaling large-scale oceanographic model results to high-resolution coupled wave-3-D hydrodynamics simulations for the area of Mar Grande in the Taranto Sea. The spatial and temporal high-resolution simulations were performed using the open-source TELEMAC suite, forced by wind data from the COSMO-ME database, boundary wave spectra from the RON buoy at Crotone and results from the Southern Adriatic Northern Ionian coastal Forecasting System (SANIFS) regarding sea levels and current fields. Model validation was carried out using data collected in the Mar Grande basin from a fixed monitoring station and during an oceanographic campaign in October 2014. The overall agreement between measurements and model results in terms of waves, sea levels, surface currents, circulation patterns and vertical velocity profiles is deemed to be satisfactory, and the methodology followed in the process can constitute a useful tool for both research and operational applications in the same field and as support of decisions for management and design of infrastructures.
NASA Astrophysics Data System (ADS)
Romanova, M. M.; Ustyugova, G. V.; Koldoba, A. V.; Lovelace, R. V. E.
2013-03-01
We report results of the first global three-dimensional (3D) magnetohydrodynamic (MHD) simulations of the waves excited in an accretion disc by a rotating star with a dipole magnetic field misaligned from the star's rotation axis (which is aligned with the disc axis). The main results are the following. (1) If the magnetosphere of the star corotates approximately with the inner disc, then we observe a strong one-armed bending wave (a warp). This warp corotates with the star and has a maximum amplitude between corotation radius and the radius of the vertical resonance. The disc's centre of mass can deviate from the equatorial plane up to the distance of zw ≈ 0.1r. However, the effective height of the warp can be larger, hw ≈ 0.3r, due to the finite thickness of the disc. Stars with a range of misalignment angles excite warps. However, the amplitude of the warps is larger for misalignment angles between 15° and 60°. The location and amplitude of the warp do not depend on viscosity, at least for relatively small values of the standard alpha-parameter, up to 0.08. (2) If the magnetosphere rotates slower than the inner disc, then a bending wave is excited at the disc-magnetosphere boundary, but does not form a large-scale warp. Instead, persistent, high-frequency oscillations become strong at the inner region of the disc. These are (a) trapped density waves which form inside the radius where the disc angular velocity has a maximum, and (b) inner bending waves which appear in the case of accretion through magnetic Rayleigh-Taylor instability. These two types of waves are connected with the inner disc and their frequencies will vary with accretion rate. Bending oscillations at lower frequencies are also excited including global oscillations of the disc. In cases where the simulation region is small, slowly precessing warp forms with the maximum amplitude at the vertical resonance. The present simulations are applicable to young stars, cataclysmic variables and
Hartzell, S.; Harmsen, S.; Williams, R.A.; Carver, D.; Frankel, A.; Choy, G.; Liu, P.-C.; Jachens, R.C.; Brocher, T.M.; Wentworth, C.M.
2006-01-01
A 3D seismic velocity and attenuation model is developed for Santa Clara Valley, California, and its surrounding uplands to predict ground motions from scenario earthquakes. The model is developed using a variety of geologic and geophysical data. Our starting point is a 3D geologic model developed primarily from geologic mapping and gravity and magnetic surveys. An initial velocity model is constructed by using seismic velocities from boreholes, reflection/refraction lines, and spatial autocorrelation microtremor surveys. This model is further refined and the seismic attenuation is estimated through waveform modeling of weak motions from small local events and strong-ground motion from the 1989 Loma Prieta earthquake. Waveforms are calculated to an upper frequency of 1 Hz using a parallelized finite-difference code that utilizes two regions with a factor of 3 difference in grid spacing to reduce memory requirements. Cenozoic basins trap and strongly amplify ground motions. This effect is particularly strong in the Evergreen Basin on the northeastern side of the Santa Clara Valley, where the steeply dipping Silver Creek fault forms the southwestern boundary of the basin. In comparison, the Cupertino Basin on the southwestern side of the valley has a more moderate response, which is attributed to a greater age and velocity of the Cenozoic fill. Surface waves play a major role in the ground motion of sedimentary basins, and they are seen to strongly develop along the western margins of the Santa Clara Valley for our simulation of the Loma Prieta earthquake.
NASA Astrophysics Data System (ADS)
Michaud, H.; Marsaleix, P.; Leredde, Y.; Estournel, C.; Bourrin, F.; Lyard, F.; Mayet, C.; Ardhuin, F.
2012-04-01
We implement the new set of equations of Bennis et al. (2011) which use the glm2z-RANS theory (Ardhuin et al., 2008) to take into account the impact of waves into the 3D circulation model SYMPHONIE (Marsaleix et al., 2008, 2009). These adiabatic equations are completed by additional parameterizations of wave breaking, bottom friction and wave-enhanced vertical mixing, making the forcing valid from the surf zone through to the open ocean. The wave forcing is performed by WAVEWATCH III® (Tolman 2008; Ardhuin et al., 2010) for the realistic cases and SWAN (Booij et al., 1999) for the academic cases. Firstly, the model is tested in two academic cases. In the first case, it is compared with other models for a plane beach test case, previously tested by Haas and Warner (2009) and Uchiyama et al. (2010). Then, a comparison is made with the laboratory measurements of Haller et al. (2002) of a barred beach with channels. Results fit with previous simulations performed by other models or with available observational data: the littoral drift and the vertical profiles of current or in the second case, the rip current are well reproduced. Finally, a realistic case of a winter storm over a coast of the Gulf of Lion (NW of the Mediterranean Sea) for which currents are available at different depths as well as an accurate bathymetric database of the 0-10m depth range, is simulated. A grid nesting approach is used to account for the different forcing acting at the different spatial scales. We use at the smaller scale a grid with a variable resolution. The model is successful to reproduce the powerful northward littoral drift in the 0-15m depth zone. More precisely, two distinct cases are identified: when waves have a normal angle of incidence with the coast, they are responsible for complex circulation cells and rip currents in the surf zone, and when they travel obliquely, they generate a northward littoral drift. These features are more complicated than in the test cases, due to
Joukar, Amin; Nammakie, Erfan; Niroomand-Oscuii, Hanieh
2015-01-01
The application of laser in ophthalmology and eye surgery is so widespread that hardly can anyone deny its importance. On the other hand, since the human eye is an organ susceptible to external factors such as heat waves, laser radiation rapidly increases the temperature of the eye and therefore the study of temperature distribution inside the eye under laser irradiation is crucial; but the use of experimental and invasive methods for measuring the temperature inside the eye is typically high-risk and hazardous. In this paper, using the three-dimensional finite element method, the distribution of heat transfer inside the eye under transient condition was studied through three different lasers named Nd:Yag, Nd:Yap and ArF. Considering the metabolic heat and blood perfusion rate in various regions of the eye, numerical solution of space-time dependant Pennes bioheat transfer equation has been applied in this study. Lambert-Beer's law has been used to model the absorption of laser energy inside the eye tissues. It should also be mentioned that the effect of the ambient temperature, tear evaporation rate, laser power and the pupil diameter on the temperature distribution have been studied. Also, temperature distribution inside the eye after applying each laser and temperature variations of six optional regions as functions of time have been investigated. The results show that these radiations cause temperature rise in various regions, which will in turn causes serious damages to the eye tissues. Investigating the temperature distribution inside the eye under the laser irradiation can be a useful tool to study and predict the thermal effects of laser radiation on the human eye and evaluate the risk involved in performing laser surgery.
High-order rogue waves for the Hirota equation
Li, Linjing; Wu, Zhiwei; Wang, Lihong; He, Jingsong
2013-07-15
The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures. -- Highlights: •The determinant representation of the N-fold Darboux transformation of the Hirota equation. •Properties of the fundamental pattern of the higher order rogue wave. •Ring structure and triangular structure of the higher order rogue waves.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2014-11-01
We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a one-parameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finite-time blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a well-known exact solution of 3D Euler equations [Gibbon et al., Physica D 132, 497 (1999)]. We discuss practical applications. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
Evolution equation for bidirectional surface waves in a convecting fluid
NASA Astrophysics Data System (ADS)
Depassier, M. C.
2006-10-01
Surface waves in a heated viscous fluid exhibit a long-wave oscillatory instability. The non-linear evolution of unidirectional waves is known to be described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the present work, we eliminate the restriction of unidirectional waves and find that the evolution of the wave is governed by a modified Boussinesq system. A perturbed Boussinesq equation of the form ytt-yxx-ɛ2[yxxtt+(y2)xx]+ɛ3[yxxt+yxxxxt+(y2)xxt]=0, which includes instability and dissipation, can be derived from this system.
Bifurcations of traveling wave solutions for an integrable equation
Li Jibin; Qiao Zhijun
2010-04-15
This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.
Kamon, M.; Phillips, J.R.
1994-12-31
In this paper techniques are presented for preconditioning equations generated by discretizing constrained vector integral equations associated with magnetoquasistatic analysis. Standard preconditioning approaches often fail on these problems. The authors present a specialized preconditioning technique and prove convergence bounds independent of the constraint equations and electromagnetic excitation frequency. Computational results from analyzing several electronic packaging examples are given to demonstrate that the new preconditioning approach can sometimes reduce the number of GMRES iterations by more than an order of magnitude.
NASA Astrophysics Data System (ADS)
Petrov, P.; Newman, G. A.
2010-12-01
-Fourier domain we had developed 3D code for full-wave field simulation in the elastic media which take into account nonlinearity introduced by free-surface effects. Our approach is based on the velocity-stress formulation. In the contrast to conventional formulation we defined the material properties such as density and Lame constants not at nodal points but within cells. This second order finite differences method formulated in the cell-based grid, generate numerical solutions compatible with analytical ones within the range errors determinate by dispersion analysis. Our simulator will be embedded in an inversion scheme for joint seismic- electromagnetic imaging. It also offers possibilities for preconditioning the seismic wave propagation problems in the frequency domain. References. Shin, C. & Cha, Y. (2009), Waveform inversion in the Laplace-Fourier domain, Geophys. J. Int. 177(3), 1067- 1079. Shin, C. & Cha, Y. H. (2008), Waveform inversion in the Laplace domain, Geophys. J. Int. 173(3), 922-931. Commer, M. & Newman, G. (2008), New advances in three-dimensional controlled-source electromagnetic inversion, Geophys. J. Int. 172(2), 513-535. Newman, G. A., Commer, M. & Carazzone, J. J. (2010), Imaging CSEM data in the presence of electrical anisotropy, Geophysics, in press.
PLOT3D/AMES, APOLLO UNIX VERSION USING GMR3D (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, APOLLO UNIX VERSION USING GMR3D (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
Exchange effects in Coulomb quantum plasmas: Dispersion of waves in 2D and 3D quantum plasmas
Andreev, Pavel A.
2014-11-15
We describe quantum hydrodynamic equations with the Coulomb exchange interaction for three and two dimensional plasmas. Explicit form of the force densities are derived. We present non-linear Schrödinger equations (NLSEs) for the Coulomb quantum plasmas with the exchange interaction. We show contribution of the exchange interaction in the dispersion of the Langmuir, and ion-acoustic waves. We consider influence of the spin polarization ratio on strength of the Coulomb exchange interaction. This is important since exchange interaction between particles with same spin direction and particles with opposite spin directions are different. At small particle concentrations n{sub 0}≪10{sup 25}cm{sup −3} and small polarization the exchange interaction gives small decrease of the Fermi pressure. With increase of polarization role the exchange interaction becomes more important, so that it can overcome the Fermi pressure. The exchange interaction also decreases contribution of the Langmuir frequency. Ion-acoustic waves do not exist in limit of large polarization since the exchange interaction changes the sign of pressure. At large particle concentrations n{sub 0}≫10{sup 25}cm{sup −3} the Fermi pressure prevails over the exchange interaction for all polarizations. We obtain a similar picture for two dimensional quantum plasmas.
Single integrodifferential wave equation for a Lévy walk
NASA Astrophysics Data System (ADS)
Fedotov, Sergei
2016-02-01
We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Lévy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Lévy walk. It is valid at all times, not only in the long time limit, and it does not involve any large-scale approximations. It generalizes the well-known telegraph or Cattaneo equation for the persistent random walk with the exponential switching time distribution. Several non-Markovian cases are considered when the particle's velocity alternates at the gamma and power-law distributed random times. In the strong anomalous case we obtain the asymptotic solution to the integrodifferential wave equation. We implement the nonlinear reaction term of Kolmogorov-Petrovsky-Piskounov type into our equation and develop the theory of wave propagation in reaction-transport systems involving Lévy diffusion.
3D P-Wave Velocity Structure of the Crust and Relocation of Earthquakes in 21 the Lushan Source Area
NASA Astrophysics Data System (ADS)
Yu, X.; Wang, X.; Zhang, W.
2014-12-01
The double difference seismic tomography method is applied to the absolute first arrival P wave arrival times and high quality relative P arrival times of the Lushan seismic sequence to determine the detailed crustal 3D P wave velocity structure and the hypocenter parameters in the Lushan seismic area. The results show that the Lushan mainshock locates at 30.28 N, 103.98 E, with the depth of 16.38 km. The leading edge of aftershock in the northeast of mainshock present a spade with a steep dip angle, the aftershocks' extended length is about 12 km. In the southwest of the Lushan mainshock, the leading edge of aftershock in low velocity zone slope gently, the aftershocks' extended length is about 23 km. The P wave velocity structure of the Lushan seismic area shows obviously lateral heterogeneity. The P wave velocity anomalies represent close relationship with topographic relief and geological structure. In Baoxing area the complex rocks correspond obvious high-velocity anomalies extending down to 15 km depth，while the Cenozoic rocks are correlated with low-velocity anomalies. Our high-resolution tomographic model not only displays the general features contained in the previous models, but also reveals some new features. An obvious high-velocity anomaly is visible in Daxing area. The high-velocity anomalies beneath Baoxing and Daxing connect each other in 10 km depth, which makes the contrast between high and low velocity anomalies more sharp. Above 20 km depth the velocity structure in southwest and northeast segment of the mainshock shows a big difference: low-velocity anomalies are dominated the southwest segment, while high-velocity anomalies rule the northeast segment. The Lushan mainshock locates at the leading edge of a low-velocity anomaly surrounded by the Baoxing and Daxing high-velocity anomalies. The Lushan aftershocks in southwest are distributed in low-velocity anomalies or the transition belt: the footwall represents low-velocity anomalies, while
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
NASA Astrophysics Data System (ADS)
Li, Y.; Han, B.; Métivier, L.; Brossier, R.
2016-09-01
We investigate an optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling. An anti-lumped mass strategy is incorporated to minimize the numerical dispersion. The optimal finite-difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity. An iterative damped least-squares method, the Levenberg-Marquardt algorithm, is utilized for the optimization. Dispersion analysis shows that the optimal fourth-order scheme presents less grid dispersion and anisotropy than the conventional fourth-order scheme with respect to different Poisson's ratios. Moreover, only 3.7 grid-points per minimum shear wavelength are required to keep the error of the group velocities below 1%. The memory cost is then greatly reduced due to a coarser sampling. A parallel iterative method named CARP-CG is used to solve the large ill-conditioned linear system for the frequency-domain modeling. Validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions. Compared with the conventional fourth-order scheme, the optimal scheme generates wavefields having smaller error under the same discretization setups. Profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions.
Hu, Youfan; Yang, Jin; Jing, Qingshen; Niu, Simiao; Wu, Wenzhuo; Wang, Zhong Lin
2013-11-26
An unstable mechanical structure that can self-balance when perturbed is a superior choice for vibration energy harvesting and vibration detection. In this work, a suspended 3D spiral structure is integrated with a triboelectric nanogenerator (TENG) for energy harvesting and sensor applications. The newly designed vertical contact-separation mode TENG has a wide working bandwidth of 30 Hz in low-frequency range with a maximum output power density of 2.76 W/m(2) on a load of 6 MΩ. The position of an in-plane vibration source was identified by placing TENGs at multiple positions as multichannel, self-powered active sensors, and the location of the vibration source was determined with an error less than 6%. The magnitude of the vibration is also measured by the output voltage and current signal of the TENG. By integrating the TENG inside a buoy ball, wave energy harvesting at water surface has been demonstrated and used for lighting illumination light, which shows great potential applications in marine science and environmental/infrastructure monitoring.
NASA Astrophysics Data System (ADS)
Pardo, F.; López, P.; Cabello, D.; Balsi, M.
2009-11-01
This paper targets the efficient computational solution of the heat transfer processes that take place in the soil and at the soil-air interface and its use in non-destructive evaluation (NDE) techniques. In particular, the problem of the detection of plastic antipersonnel mines is considered. To this aim we projected a 3D finite-difference (FD) thermal model of the soil on a FPGA platform using Handel-C and VHDL. A speedup factor of 34 over a purely software solution is achieved, obtaining processing times that permit the use of the system on the field.
Travelling wave solutions for higher-order wave equations of kdv type (iii).
Li, Jibin; Rui, Weigou; Long, Yao; He, Bin
2006-01-01
By using the theory of planar dynamical systems to the travelling wave equation of a higher order nonlinear wave equations of KdV type, the existence of smooth solitary wave, kink wave and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact explicit parametric representations of these waves are obtain. PMID:20361813
NASA Astrophysics Data System (ADS)
Yu, Xiangwei; Wang, Xiaona; Zhang, Wenbo
2016-04-01
Many researchers have investigated the Lushan source area with geological and geophysical approaches since the 2013 Lushan, China, earthquake happened. Compared with the previous tomographic studies, we have used a much large data set and an updated tomographic method to determine a small scale three-dimensional P wave velocity structure with spatial resolution less than 5km, which plays the important role for understanding the deep structure and the genetic mechanism beneath the Lushan area. The double difference seismic tomography method is applied to 50,711 absolute first arrival P wave arrival times and 7,294,691 high quality relative P arrival times of 5,285 events of Lushan seismic sequence to simultaneously determine the detailed crustal 3D P wave velocity structure and the hypocenter parameters in the Lushan seismic area. This method takes account of the path anomaly biases explicitly by making full use of valuable information of seismic wave propagation jointly with absolute and relative arrival time data. Our results show that the Lushan mainshock locates at 30.28N, 103.98E, with the depth of 16.38km. The front edge of aftershock in the northeast of mainshock present a spade with a steep dip angle, the aftershocks' extended length is about 12km. In the southwest of Lushan mainshock, the front edge of aftershock in low velocity zone slope gently, the aftershocks' extended length is about 23km. Our high-resolution tomographic model not only displays the general features contained in the previous models, but also reveals some new features. The Tianquan, Shuangshi and Daguan line lies in the transition zone between high velocity anomalies to the southeast and low velocity anomalies to the northwest at the ground surface. An obvious high-velocity anomaly is visible in Daxing area. With the depth increasing, Baoxing high velocity anomaly extends to Lingguan, while the southeast of the Tianquan, Shuangshi and Daguan line still shows low velocity. The high
NASA Astrophysics Data System (ADS)
da Silva, J. C. B.; Magalhaes, J. M.; Batista, M.; Gostiaux, L.; Gerkema, T.; New, A. L.
2013-03-01
spectral range 8-12 μm. With a nominal ground resolution of approximately 1.5 meters (at an altitude of 500 meters) it is capable to detect fine structure associated to turbulence. The LiDAR system that has been used is the Leica ALS50-II (1064nm) with a hit rate greater than 1 hit per square meter and a vertical resolution of approximately 15 cm. Both systems were available simultaneously, together with the hyperspectral system and the RCD105 39Mpx digital camera, integrated with the LiDAR navigation system. We analyse the airborne data together with a comprehensive dataset of satellite Synthetic Aperture Radar (SAR) that includes ENVISAT and TerraSAR-X images. In addition, in situ observations in the near-shore zone were obtained in a previous experiment (Project SPOTIWAVE-II POCI/MAR/57836/2004 funded by the Portuguese FCT) during the summer period in 2006. These included thermistor chain measurements along the water column that captured the vertical structure of shoaling internal (tidal) waves and ISWs close to the breaking point. The SAR and airborne images were obtained in light wind conditions, in the near-shore zone, and in the presence of ISWs. The LiDAR images revealed sub-surface structures (some 1-2 m below the sea surface) that were co-located with surface films. These film slicks were induced by the convergent fields of internal waves and upwelling fronts. Some of the sub-surface features were located over the front slopes of the internal waves, which coincides with the internal wave slick band visible in the aerial photos and hyperspectral systems. Our flight measurements revealed thermal features similar to “boils” of cold water within the wake of (admittedly breaking) internal waves. These features are consistent with the previous in situ measurements of breaking ISWs. In this paper we will show coincident multi-sensor airborne and satellite SAR observations that reveal the 3D structure of air bubble entrainment in the internal wave field and frontal
Late-time attractor for the cubic nonlinear wave equation
Szpak, Nikodem
2010-08-15
We apply our recently developed scaling technique for obtaining late-time asymptotics to the cubic nonlinear wave equation and explain the appearance and approach to the two-parameter attractor found recently by Bizon and Zenginoglu.
Asymptotic analysis of numerical wave propagation in finite difference equations
NASA Technical Reports Server (NTRS)
Giles, M.; Thompkins, W. T., Jr.
1983-01-01
An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.
On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Ibraheem, S. O.; Demuren, A. O.
1994-01-01
A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.
A wave equation interpolating between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.
2015-10-01
We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.
Travelling wave solution of the Buckley-Leverett equation
NASA Astrophysics Data System (ADS)
Tychkov, Sergey
2016-09-01
A two-dimensional Buckley-Leverett system governing motion of two-phase flow is considered. Travelling-wave solutions for these equations are found. Wavefronts of these solutions may be circles, lines and parabolae. Values of pressure and saturation on the wave fronts are found.
NASA Astrophysics Data System (ADS)
Lin, F. C.; Schmandt, B.
2015-12-01
Imaging the crust and lithosphere structure beneath North America is one of the primary targets for the NSF-funded EarthScope project. In this study, we apply the recently developed ambient noise and surface wave tomography methods to construct a detailed 3D crustal model across the entire contiguous US using USArray data between January 2007 and May 2015. By using both Rayleigh wave phase velocity and ellipticity measurements between 8 and 100 sec period, the shear velocity structure can be well resolved within the five crustal layers we modeled: three upper crust, one middle crust, and one lower crust. Clear correlations are observed between the resolved velocity anomalies and known geological features at all depths. In the uppermost crust, slow Vs anomalies are observed within major sedimentary environments such as the Williston Basin, Denver Basin, and Mississippi embayment, and fast Vs anomalies are observed in environments with deeply exhumed bedrock outcrops at the surface including the Laurentian Highlands, Ouachita-Ozark Interior Highlands, and Appalachian Highlands. In the deeper upper crust, slow anomalies are observed in deep sedimentary basins such as the Green River Basin, Appalachian Basin, Southern Oklahoma Aulacogen, and areas surrounding the Gulf of Mexico. Fast anomalies, on the other hand, are observed in the Colorado Plateau, within the Great Plains between the Front Ranges and Midcontinental Rift, and east of the Appalachian Mountains. At this depth, the Midcontinental Rift and Grenville Front clearly correlate well with various velocity structure boundaries. In the middle crust, slow anomalies are mostly observed in the tectonically active areas in the western US, but relatively slow anomalies are also observed southeast of the Precambrian Rift Margins. At this depth, fast anomalies are observed beneath various deep sedimentary basins such as the Southern Oklahoma Aulacogen, Appalachian Basin, and Central Valley. In the lower crust, a clear
NASA Astrophysics Data System (ADS)
Young, D. L.; Tsai, C. H.; Wu, C. S.
2015-11-01
An alternative vector potential formulation is used to solve the Navier-Stokes (N-S) equations in 3D incompressible viscous flow problems with and without through-flow boundaries. Difficulties of the vector potential formulation include the implementation of boundary conditions for through-flow boundaries and the numerical treatment of fourth-order partial differential equations. The advantages on the other hand are the automatic satisfaction of the continuity equation; and pressure is decoupled from the velocity. The objective of this paper is to introduce the appropriate gauge and boundary conditions on the vector potential formulation by a localized meshless method. To handle the divergence-free property, a Coulomb gauge condition is enforced on the vector potential to ensure its existence and uniqueness mathematically. We further improve the algorithm to through-flow problems for the boundary conditions of vector potential by introducing the concept of Stokes' theorem. Based on this innovation, there is no need to include an additional variable to tackle the through-flow fields. This process will greatly simplify the imposition of boundary conditions by the vector potential approach. Under certain conditions, the coupled fourth-order partial differential equations can be easily solved by using this meshless local differential quadrature (LDQ) method. Due to the LDQ capability to deal with the high order differential equations, this algorithm is very attractive to solve this fourth-order vector potential formulation for the N-S equations as comparing to the conventional numerical schemes such as finite element or finite difference methods. The proposed vector potential formulation is simpler and has improved accuracy and efficiency compared to other pressure-free or pressure-coupled algorithms. This investigation can be regarded as the first complete study to obtain the N-S solutions by vector potential formulation through a LDQ method. Two classic 3D benchmark
On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap
NASA Astrophysics Data System (ADS)
Chen, Xuwen
2013-11-01
We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.
Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.
2014-08-29
We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.
Doinikov, Alexander A; Novell, Anthony; Calmon, Pierre; Bouakaz, Ayache
2014-09-01
The purpose of this work is to validate, by comparing numerical and experimental results, the ability of the Westervelt equation to predict the behavior of ultrasound beams generated by phased-array transducers. To this end, the full Westervelt equation is solved numerically and the results obtained are compared with experimental measurements. The numerical implementation of the Westervelt equation is performed using the explicit finite-difference time-domain method on a three-dimensional Cartesian grid. The validation of the developed numerical code is first carried out by using experimental data obtained for two different focused circular transducers in the regimes of small-amplitude and finite-amplitude excitations. Then, the comparison of simulated and measured ultrasonic fields is extended to the case of a modified 32-element array transducer. It is shown that the developed code is capable of correctly predicting the behavior of the main lobe and the grating lobes in the cases of zero and nonzero steering angles for both the fundamental and the second-harmonic components.
Wave and pseudo-diffusion equations from squeezed states
NASA Technical Reports Server (NTRS)
Daboul, Jamil
1993-01-01
We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.
Imperfect Geometric Control and Overdamping for The Damped Wave Equation
NASA Astrophysics Data System (ADS)
Burq, Nicolas; Christianson, Hans
2015-05-01
We consider the damped wave equation on a manifold with imperfect geometric control. We show the sub-exponential energy decay estimate in (Christianson, J Funct Anal 258(3):1060-1065, 2010) is optimal in the case of one hyperbolic periodic geodesic. We show if the equation is overdamped, then the energy decays exponentially. Finally we show if the equation is overdamped but geometric control fails for one hyperbolic periodic geodesic, then nevertheless the energy decays exponentially.
NASA Astrophysics Data System (ADS)
Tsuzuki, Yutaka
2015-09-01
This paper is concerned with a system of heat equations with hysteresis and Navier-Stokes equations. In Tsuzuki (J Math Anal Appl 423:877-897, 2015) an existence result is obtained for the problem in a 2-dimensional domain with the Navier-Stokes equation in a weak sense. However the result does not include uniqueness for the problem due to the low regularity for solutions. This paper establishes existence and uniqueness in 2- and 3-dimensional domains with the Navier-Stokes equation in a stronger sense. Moreover this work decides required height of regularity for the initial data by introducing the fractional power of the Stokes operator.
NASA Astrophysics Data System (ADS)
Oieroset, M.; Sundkvist, D. J.; Chaston, C. C.; Phan, T. D.; Mozer, F.; McFadden, J. P.; Angelopoulos, V.; Andersson, L.; Eastwood, J. P.
2014-12-01
We have performed a detailed analysis of plasma and wave observations in a 3D magnetic flux rope encountered by the THEMIS spacecraft at the subsolar magnetopause. The extent of the flux rope was ˜270 ion skin depths in the outflow direction, and it was flanked by two active reconnection X lines producing colliding plasma jets in the flux rope core where ion heating and suprathermal electrons were observed. The colliding jet region was highly dynamic and characterized by the presence of high-frequency waves such as ion acoustic-like waves, electron holes, and whistler mode waves near the flux rope center and low-frequency kinetic Alfvén waves over a larger region. We will discuss possible links between these waves and particle heating.
A nonlinear wave equation in nonadiabatic flame propagation
Booty, M.R.; Matalon, M.; Matkowsky, B.J.
1988-06-01
The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.
Optimization of High-order Wave Equations for Multicore CPUs
Williams, Samuel
2011-11-01
This is a simple benchmark to guage the performance of a high-order isotropic wave equation grid. The code is optimized for both SSE and AVX and is parallelized using OpenMP (see Optimization section). Structurally, the benchmark begins, reads a few command-line parameters, allocates and pads the four arrays (current, last, next wave fields, and the spatially varying but isotropic velocity), initializes these arrays, then runs the benchmark proper. The code then benchmarks the naive, SSE (if supported), and AVX (if supported implementations) by applying the wave equation stencil 100 times and taking the average performance. Boundary conditions are ignored and would noiminally be implemented by the user. THus, the benchmark measures only the performance of the wave equation stencil and not a full simulation. The naive implementation is a quadruply (z,y,x, radius) nested loop that can handle arbitrarily order wave equations. The optimized (SSE/AVX) implentations are somewhat more complex as they operate on slabs and include a case statement to select an optimized inner loop depending on wave equation order.
Optimization of High-order Wave Equations for Multicore CPUs
2011-11-01
This is a simple benchmark to guage the performance of a high-order isotropic wave equation grid. The code is optimized for both SSE and AVX and is parallelized using OpenMP (see Optimization section). Structurally, the benchmark begins, reads a few command-line parameters, allocates and pads the four arrays (current, last, next wave fields, and the spatially varying but isotropic velocity), initializes these arrays, then runs the benchmark proper. The code then benchmarks the naive, SSEmore » (if supported), and AVX (if supported implementations) by applying the wave equation stencil 100 times and taking the average performance. Boundary conditions are ignored and would noiminally be implemented by the user. THus, the benchmark measures only the performance of the wave equation stencil and not a full simulation. The naive implementation is a quadruply (z,y,x, radius) nested loop that can handle arbitrarily order wave equations. The optimized (SSE/AVX) implentations are somewhat more complex as they operate on slabs and include a case statement to select an optimized inner loop depending on wave equation order.« less
Steady dark solitary waves emerging from wave-generated meanflow: the role of modulation equations.
Bridges, Thomas J
2005-09-01
Various classes of steady and unsteady dark solitary waves (DSWs) are known to exist in modulation equations for water waves in finite depth. However, there is a class of steady DSWS of the full water-wave problem which are missed by the classical modulation equations such as the Hasimoto-Ono, Benney-Roskes, and Davey-Stewartson. These steady DSWs, recently discovered by Bridges and Donaldson, are pervasive in finite depth, arise through secondary criticality of Stokes gravity waves, and are synchronized with the Stokes wave. In this paper, the role of DSWs in modulation equations for water waves is reappraised. The intrinsic unsteady nature of existing modulation equations filters out some interesting solutions. On the other hand, the geometry of DSWs in modulation equations is very similar to the full water wave problem and these geometrical properties are developed. A model equation is proposed which illustrates the general nature of the emergence of steady DSWs due to wave-generated mean flow coupled to a periodic wave. Although the existing modulation equations are intrinsically unsteady, it is shown that there are also important shortcomings when one wants to use them for stability analysis of DSWs.
Correlation equation for the marine drag coefficient and wave steepness
NASA Astrophysics Data System (ADS)
Foreman, Richard J.; Emeis, Stefan
2012-09-01
This work questions, starting from dimensional considerations, the generality of the belief that the marine drag coefficient levels off with increasing wind speed. Dimensional analysis shows that the drag coefficient scales with the wave steepness as opposed to a wave-age scaling. A correlation equation is employed here that uses wave steepness scaling at low aspect ratios (inverse wave steepnesses) and a constant drag coefficient at high aspect ratios. Invoked in support of the correlation are measurements sourced from the literature and at the FINO1 platform in the North Sea. The correlation equation is then applied to measurements recorded from buoys during the passage of hurricanes Rita, Katrina (2005) and Ike (2008). Results show that the correlation equation anticipates the expected levelling off in deeper water, but a drag coefficient more consistent with a Charnock type relation is also possible in more shallower water. Some suggestions are made for proceeding with a higher-order analysis than that conducted here.
NASA Technical Reports Server (NTRS)
Zhang, Jun; Ge, Lixin; Kouatchou, Jules
2000-01-01
A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.
NASA Astrophysics Data System (ADS)
Moczo, P.; Kristek, J.; Galis, M.; Chaljub, E.; Chen, X.; Zhang, Z.
2012-04-01
Numerical modeling of earthquake ground motion in sedimentary basins and valleys often has to account for the P-wave to S-wave speed ratios (VP/VS) as large as five and even larger, mainly in sediments below groundwater level. The ratio can attain values larger than 10 - the unconsolidated lake sediments in Ciudad de México are a good example. At the same time, accuracy of the numerical schemes with respect to VP/VS has not been sufficiently analyzed. The numerical schemes are often applied without adequate check of the accuracy. We present theoretical analysis and numerical comparison of 18 3D numerical time-domain explicit schemes for modeling seismic motion for their accuracy with the varying VP/VS. The schemes are based on the finite-difference, spectral-element, finite-element and discontinuous-Galerkin methods. All schemes are presented in a unified form. Theoretical analysis compares accuracy of the schemes in terms of local errors in amplitude and vector difference. In addition to the analysis we compare numerically simulated seismograms with exact solutions for canonical configurations. We compare accuracy of the schemes in terms of the local errors, grid dispersion and full wavefield simulations with respect to the structure of the numerical schemes.
Feher, L.; Link, G.; Thumm, M.
1996-12-31
Precise knowledge of millimeter-wave oven properties and design studies have to be obtained by 3D numerical field calculations. A simulation code solving the electromagnetic field problem based on a covariant raytracing scheme (MiRa-Code) has been developed. Time dependent electromagnetic field-material interactions during sintering as well as the heat transfer processes within the samples has been investigated. A numerical code solving the nonlinear heat transfer problem due to millimeter-wave heating has been developed (THESIS3D-Code). For a self consistent sintering simulation, a zip interface between both codes exchanging the time advancing fields and material parameters is implemented. Recent results and progress on calculations of field distributions in large overmoded resonators as well as results on modeling heating of materials with millimeter waves are presented in this paper. The calculations are compared to experiments.
Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan
2013-09-01
Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.
Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation
NASA Technical Reports Server (NTRS)
Spangler, Steven R.
1990-01-01
A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.
Rogue wave spectra of the Kundu-Eckhaus equation.
Bayındır, Cihan
2016-06-01
In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrödinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly differ from their NLSE analogs. A remarkable difference is the one-sided development of the triangular spectrum before the rogue wave becomes evident in time. Also we show that increasing the skewness of the rogue wave results in increased asymmetry in the triangular Fourier spectra. Additionally, the triangular spectra of the rogue waves of the KEE begin to develop at earlier stages of their development compared to their NLSE analogs, especially for larger skew angles. This feature may be used to enhance the early warning times of the rogue waves. However, we show that in a chaotic wave field with many spectral components the triangular spectra remain as the main attribute as a universal feature of the typical wave fields produced through modulation instability and characteristic features of the KEE's analytical rogue wave spectra may be suppressed in a realistic chaotic wave field. PMID:27415263
NASA Astrophysics Data System (ADS)
DeJong, Andrew
Numerical models of fluid-structure interaction have grown in importance due to increasing interest in environmental energy harvesting, airfoil-gust interactions, and bio-inspired formation flying. Powered by increasingly powerful parallel computers, such models seek to explain the fundamental physics behind the complex, unsteady fluid-structure phenomena. To this end, a high-fidelity computational model based on the high-order spectral difference method on 3D unstructured, dynamic meshes has been developed. The spectral difference method constructs continuous solution fields within each element with a Riemann solver to compute the inviscid fluxes at the element interfaces and an averaging mechanism to compute the viscous fluxes. This method has shown promise in the past as a highly accurate, yet sufficiently fast method for solving unsteady viscous compressible flows. The solver is monolithically coupled to the equations of motion of an elastically mounted 3-degree of freedom rigid bluff body undergoing flow-induced lift, drag, and torque. The mesh is deformed using 4 methods: an analytic function, Laplace equation, biharmonic equation, and a bi-elliptic equation with variable diffusivity. This single system of equations -- fluid and structure -- is advanced through time using a 5-stage, 4th-order Runge-Kutta scheme. Message Passing Interface is used to run the coupled system in parallel on up to 240 processors. The solver is validated against previously published numerical and experimental data for an elastically mounted cylinder. The effect of adding an upstream body and inducing wake galloping is observed.
Waves on a vortex filament: exact solutions of dynamical equations
NASA Astrophysics Data System (ADS)
Brugarino, Tommaso; Mongiovi, Maria Stella; Sciacca, Michele
2014-09-01
In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.
Waves on a vortex filament: exact solutions of dynamical equations
NASA Astrophysics Data System (ADS)
Brugarino, Tommaso; Mongiovi, Maria Stella; Sciacca, Michele
2015-06-01
In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.
Solitary waves of the rotation-modified Kadomtsev Petviashvili equation
NASA Astrophysics Data System (ADS)
Chen, Robin Ming; Mikyoung Hur, Vera; Liu, Yue
2008-12-01
The rotation-modified Kadomtsev-Petviashvili equation describes small-amplitude, long internal waves propagating in one primary direction in a rotating frame of reference. The main investigation is the existence and properties of its solitary waves. The existence and nonexistence results for the solitary waves are obtained, and their regularity and decay properties are established. Various characterizations are given for the ground states and their cylindrical symmetry is demonstrated. When the effects of rotation are weak, the energy minima constrained by constant momentum are shown to be nonlinearly stable. The weak rotation limit of solitary waves as the rotation parameter tends to zero is studied.
Solutions of the Maxwell equations and photon wave functions
Mohr, Peter J.
2010-03-15
Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.
NASA Astrophysics Data System (ADS)
Sosa, Anibal; Thompson, Lennox; Velasco, Aaron A.; Romero, Rodrigo; Herrmann, Robert B.
2014-09-01
The Southern terminus of the Rio Grande Rift region has been poorly defined in the geologic record, with few seismic studies that provide information on the deeper Rift structure. In consequence, important questions related to tectonic and lithospheric activity of the Rio Grande Rift remain unresolved. To address some of these geological questions, we collect and analyze seismic data from 147 EarthScope Transportable Array (USArray) and other seismic stations in the region, to develop a 3-D crust and upper mantle velocity model. We apply a constrained optimization approach for joint inversion of surface wave and receiver functions using seismic S wave velocities as a model parameter. In particular, we compute receiver functions stacks based on ray parameter, and invert them jointly with collected surface wave group velocity dispersion observations. The inversions estimate 1-D seismic S-wave velocity profiles to 300 km depth, which are then interpolated to a 3-D velocity model using a Bayesian kriging scheme. Our 3-D models show a thin lower velocity crust anomaly along the southeastern Rio Grande Rift, a persistent low velocity anomaly underneath the Colorado Plateau and Basin and Range province, and another one at depth beneath the Jemez lineament, and the southern RGR.
Finite element solution of 3-D turbulent Navier-Stokes equations for propeller-driven slender bodies
NASA Astrophysics Data System (ADS)
Thomas, Russell Hicks
1987-12-01
Three-dimensional turbulent flow over the aft end of a slender propeller driven body with the wake from a slender, planar appendage was calculated for 4 configurations. The finite element method in the form of the weak Galerkin formulation with the penalty method was used to solve the Reynolds averaged Navier-Stokes equations. The actual code was FIDAP, modified with a propeller body force and turbulence model, used for the solution. The turbulence model included an Inner Layer Integrated TKE model, and Outer Layer mixing length model, and a Planar Wake model. No separate boundary layer method was used for the body, rather modifications to the Integrated TKE model were made to account for the primary effects of the surface boundary layer on the flow. The flow was calculated at two levels of thrust and corresponding swirl, selfpropelled and 100 percent overthrust, as well as with selfpropelled thrust but no torque simulating an ideal rotor stator combination. Also, the selfpropelled case was calculated with a simplified turbulence model using only the Inner Layer and Planar Wake model. The results compared favorably with experiments.
D-wave charmonia η _{c2}(1^1D_2), ψ _2(1^3D_2), and ψ _3(1^3D_3) in B_c decays
NASA Astrophysics Data System (ADS)
Li, Qiang; Wang, Tianhong; Jiang, Yue; Yuan, Han; Wang, Guo-Li
2016-08-01
We study the semileptonic and nonleptonic decays of B_c meson to D-wave charmonia, namely, η _{c2}(1^1D_2), ψ _2(1^3D_2), and ψ _3(1^3D_3). In our calculations, the instantaneous Bethe-Salpeter method is applied to obtain the hadronic matrix elements. This method includes relativistic corrections which are important especially for the higher orbital excited states. For the semileptonic decay channels with electron as the final lepton, we get the branching ratios {B}[B_c → η _{c2}ebar{ν }_e] = 5.9^{-0.8}_{+1.0}× 10^{-4}, {B}[B_c → ψ _2ebar{ν }_e]=1.5^{-0.2}_{+0.3}× 10^{-4}, and {B}[B_c → ψ _3ebar{ν }_e]=3.5^{-0.6}_{+0.8}× 10^{-4}. The transition form factors, forward-backward asymmetries, and lepton spectra in these processes are also presented. For the nonleptonic decay channels, those with ρ as the lighter meson have the largest branching ratios, {B}[B_c → η _{c2}ρ ] = 8.1^{-1.0}_{+1.0}× 10^{-4}, {B}[B_c → ψ _2ρ ]=9.6^{-1.0}_{+1.0}× 10^{-5}, and {B}[B_c → ψ _3ρ ]=4.1^{-0.7}_{+0.8}× 10^{-4}.
NASA Astrophysics Data System (ADS)
Miah, Khalid; Bellefleur, Gilles
2014-05-01
The global demand for base metals, uranium and precious metals has been pushing mineral explorations at greater depth. Seismic techniques and surveys have become essential in finding and extracting mineral rich ore bodies, especially for deep VMS mining camps. Geophysical parameters collected from borehole logs and laboratory measurements of core samples provide preliminary information about the nature and type of subsurface lithologic units. Alteration halos formed during the hydrothermal alteration process contain ore bodies, which are of primary interests among geologists and mining industries. It is known that the alteration halos are easier to detect than the ore bodies itself. Many 3D geological models are merely projection of 2D surface geology based on outcrop inspections and geochemical analysis of a small number of core samples collected from the area. Since a large scale 3D multicomponent seismic survey can be prohibitively expensive, performance analysis of such geological models can be helpful in reducing exploration costs. In this abstract, we discussed challenges and constraints encountered in geophysical modelling of ore bodies and surrounding geologic structures from the available coarse 3D geological models of the Lalor Lake mining camp, located in northern Manitoba, Canada. Ore bodies in the Lalor lake VMS camp are rich in gold, zinc, lead and copper, and have an approximate weight of 27 Mt. For better understanding of physical parameters of these known ore bodies and potentially unknown ones at greater depth, we constructed a fine resolution 3D seismic model with dimensions: 2000 m (width), 2000 m (height), and 1500 m (vertical depth). Seismic properties (P-wave, S-wave velocities, and density) were assigned based on a previous rock properties study of the same mining camp. 3D finite-difference elastic wave propagation simulation was performed in the model using appropriate parameters. The generated synthetic 3D seismic data was then compared to
Blumberg, L.N.
1992-03-01
The authors have analyzed simulated magnetic measurements data for the SXLS bending magnet in a plane perpendicular to the reference axis at the magnet midpoint by fitting the data to an expansion solution of the 3-dimensional Laplace equation in curvilinear coordinates as proposed by Brown and Servranckx. The method of least squares is used to evaluate the expansion coefficients and their uncertainties, and compared to results from an FFT fit of 128 simulated data points on a 12-mm radius circle about the reference axis. They find that the FFT method gives smaller coefficient uncertainties that the Least Squares method when the data are within similar areas. The Least Squares method compares more favorably when a larger number of data points are used within a rectangular area of 30-mm vertical by 60-mm horizontal--perhaps the largest area within the 35-mm x 75-mm vacuum chamber for which data could be obtained. For a grid with 0.5-mm spacing within the 30 x 60 mm area the Least Squares fit gives much smaller uncertainties than the FFT. They are therefore in the favorable position of having two methods which can determine the multipole coefficients to much better accuracy than the tolerances specified to General Dynamics. The FFT method may be preferable since it requires only one Hall probe rather than the four envisioned for the least squares grid data. However least squares can attain better accuracy with fewer probe movements. The time factor in acquiring the data will likely be the determining factor in choice of method. They should further explore least squares analysis of a Fourier expansion of data on a circle or arc of a circle since that method gives coefficient uncertainties without need for multiple independent sets of data as needed by the FFT method.
Phase integral theory, coupled wave equations, and mode conversion.
Littlejohn, Robert G.; Flynn, William G.
1992-01-01
Phase integral or WKB theory is applied to multicomponent wave equations, i.e., wave equations in which the wave field is a vector, spinor, or tensor of some kind. Specific examples of physical interest often have special features that simplify their analysis, when compared with the general theory. The case of coupled channel equations in atomic or molecular scattering theory in the Born-Oppenheimer approximation is examined in this context. The problem of mode conversion, also called surface jumping or Landau-Zener-Stuckelberg transitions, is examined in the multidimensional case, and cast into normal form. The group theoretical principles of the normal form transformation are laid out, and shown to involve both the Lorentz group and the symplectic group. PMID:12779962
An Object Oriented, Finite Element Framework for Linear Wave Equations
Koning, Joseph M.
2004-03-01
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
NASA Astrophysics Data System (ADS)
Turchetti, G.; Rambaldi, S.; Bazzani, A.; Comunian, M.; Pisent, A.
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribition obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances.
Existence of solitary waves and periodic waves for a perturbed generalized BBM equation
NASA Astrophysics Data System (ADS)
Chen, Aiyong; Guo, Lina; Deng, Xijun
2016-11-01
The existence of solitary waves and periodic waves for a perturbed generalized BBM equation is established by using geometric singular perturbation theory. Attention goes to perturbations of the Hamiltonian vector field with an elliptic Hamiltonian of degree four, exhibiting a cuspidal loop. It is proven that the wave speed c0 (h) is decreasing on h ∈ [ 0 , 1 / 12 ] by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are given. Moreover, the relation between the wave speed and the wavelength of traveling waves is obtained.
Generalized relativistic wave equations with intrinsic maximum momentum
NASA Astrophysics Data System (ADS)
Ching, Chee Leong; Ng, Wei Khim
2014-05-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
The pulsating orb: solving the wave equation outside a ball
2016-01-01
Transient acoustic waves are generated by the oscillations of an object or are scattered by the object. This leads to initial-boundary value problems (IBVPs) for the wave equation. Basic properties of this equation are reviewed, with emphasis on characteristics, wavefronts and compatibility conditions. IBVPs are formulated and their properties reviewed, with emphasis on weak solutions and the constraints imposed by the underlying continuum mechanics. The use of the Laplace transform to treat the IBVPs is also reviewed, with emphasis on situations where the solution is discontinuous across wavefronts. All these notions are made explicit by solving simple IBVPs for a sphere in some detail. PMID:27279773
Fast numerical treatment of nonlinear wave equations by spectral methods
Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.
2011-02-15
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.
Nonlinear Generalized Hydrodynamic Wave Equations in Strongly Coupled Dusty Plasmas
Veeresha, B. M.; Sen, A.; Kaw, P. K.
2008-09-07
A set of nonlinear equations for the study of low frequency waves in a strongly coupled dusty plasma medium is derived using the phenomenological generalized hydrodynamic (GH) model and is used to study the modulational stability of dust acoustic waves to parallel perturbations. Dust compressibility contributions arising from strong Coulomb coupling effects are found to introduce significant modifications in the threshold and range of the instability domain.
Single integrodifferential wave equation for a Lévy walk.
Fedotov, Sergei
2016-02-01
We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Lévy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Lévy walk. It is valid at all times, not only in the long time limit, and it does not involve any large-scale approximations. It generalizes the well-known telegraph or Cattaneo equation for the persistent random walk with the exponential switching time distribution. Several non-Markovian cases are considered when the particle's velocity alternates at the gamma and power-law distributed random times. In the strong anomalous case we obtain the asymptotic solution to the integrodifferential wave equation. We implement the nonlinear reaction term of Kolmogorov-Petrovsky-Piskounov type into our equation and develop the theory of wave propagation in reaction-transport systems involving Lévy diffusion. PMID:26986271
Dao, Tien Tuan; Pouletaut, Philippe; Charleux, Fabrice; Tho, Marie-Christine Ho Ba; Bensamoun, Sabine
2014-01-01
The purpose of this study was to develop a subject specific finite element model derived from MRI images to numerically analyze the MRE (magnetic resonance elastography) shear wave propagation within skeletal thigh muscles. A sagittal T2 CUBE MRI sequence was performed on the 20-cm thigh segment of a healthy male subject. Skin, adipose tissue, femoral bone and 11 muscles were manually segmented in order to have 3D smoothed solid and meshed models. These tissues were modeled with different constitutive laws. A transient modal dynamics analysis was applied to simulate the shear wave propagation within the thigh tissues. The effects of MRE experimental parameters (frequency, force) and the muscle material properties (shear modulus: C10) were analyzed through the simulated shear wave displacement within the vastus medialis muscle. The results showed a plausible range of frequencies (from 90Hz to 120 Hz), which could be used for MRE muscle protocol. The wave amplitude increased with the level of the force, revealing the importance of the boundary condition. Moreover, different shear displacement patterns were obtained as a function of the muscle mechanical properties. The present study is the first to analyze the shear wave propagation in skeletal muscles using a 3D subject specific finite element model. This study could be of great value to assist the experimenters in the set-up of MRE protocols. PMID:25570875
Surface electromagnetic wave equations in a warm magnetized quantum plasma
Li, Chunhua; Yang, Weihong; Wu, Zhengwei; Chu, Paul K.
2014-07-15
Based on the single-fluid plasma model, a theoretical investigation of surface electromagnetic waves in a warm quantum magnetized inhomogeneous plasma is presented. The surface electromagnetic waves are assumed to propagate on the plane between a vacuum and a warm quantum magnetized plasma. The quantum magnetohydrodynamic model includes quantum diffraction effect (Bohm potential), and quantum statistical pressure is used to derive the new dispersion relation of surface electromagnetic waves. And the general dispersion relation is analyzed in some special cases of interest. It is shown that surface plasma oscillations can be propagated due to quantum effects, and the propagation velocity is enhanced. Furthermore, the external magnetic field has a significant effect on surface wave's dispersion equation. Our work should be of a useful tool for investigating the physical characteristic of surface waves and physical properties of the bounded quantum plasmas.
3D numerical simulation of laser-generated Lamb waves propagation in 2D acoustic black holes
NASA Astrophysics Data System (ADS)
Yan, Shiling; Lomonosov, Alexey M.; Shen, Zhonghua; Han, Bing
2015-05-01
Acoustic black holes have been widely used in damping structural vibration. In this work, the Lamb waves are utilized to evaluate the specified structure. The three-dimensional numerical model of acoustic black holes with parabolic profile was established. The propagation of laser-generated Lamb wave in two-dimensional acoustic black holes was numerically simulated using the finite element method. The results indicated that the incident wave was trapped by the structure obviously.
NASA Astrophysics Data System (ADS)
Porter, K.
2015-12-01
There are two common ways to create a ground-motion map for a hypothetical earthquake: using ground motion prediction equations (by far the more common of the two) and using 3-D physics-based modeling. The former is very familiar to engineers, the latter much less so, and the difference can present a problem because engineers tend to trust the familiar and distrust novelty. Maps for essentially the same hypothetical earthquake using the two different methods can look very different, while appearing to present the same information. Using one or the other can lead an engineer or disaster planner to very different estimates of damage and risk. The reasons have to do with depiction of variability, spatial correlation of shaking, the skewed distribution of real-world shaking, and the upward-curving relationship between shaking and damage. The scientists who develop the two kinds of map tend to specialize in one or the other and seem to defend their turf, which can aggravate the problem of clearly communicating with engineers.The USGS Science Application for Risk Reduction's (SAFRR) HayWired scenario has addressed the challenge of explaining to engineers the differences between the two maps, and why, in a disaster planning scenario, one might want to use the less-familiar 3-D map.
NASA Astrophysics Data System (ADS)
Xu, Hongrui; Luo, Yinhe; Chen, Chao; Xu, Yixian
2016-06-01
Eikonal tomography based on ambient noise data is one of the most effective methods to reveal shallow earth structures. By tracking surface wave phase fronts, constructing travel time surfaces, and computing the gradients of travel time surfaces to generate phase velocity maps, eikonal tomography avoids the ray tracing and matrix construction and inversion in the traditional surface wave tomography methods. In this study, we collect continuous ambient noise data recorded by a dense seismic array in Karamay, Xinjiang to construct a 3D model of shallow structures using eikonal tomography. The seismic array consists of 35 stations with shortest interstation distance close to 1 km. 890 empirical surface wave Green's functions (EGFs) between each station pair are retrieved by cross-correlating one or two months of continuous ambient noise data. From these EGFs, surface wave travel times in the frequency range of 1.8 to 4.0 Hz are measured by a frequency-time analysis technique (FTAN). Then, eikonal tomography is adopted to construct Rayleigh wave phase velocity maps and estimate the phase velocity uncertainties. Finally, we invert the obtained phase velocity dispersion curves for 1D shear velocity profiles and then assemble these 1D profiles to construct a 3D shear velocity model. Major velocity features of our 3D model are correlated well with the known geological features. A shallow east-west velocity discontinuity is observed, which clearly reflects the lithological change between Baogutu formation (C1b) and Xibeikulasi formation (C1x) of lower Carboniferous system. Low shear velocities are observed beneath the location of porphyry copper deposit (V), possibly related to stockwork fracture and hydrothermal brecciation developed during the intrusion of deep magma in forming the deposit.
Lattice Boltzmann model for generalized nonlinear wave equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2011-10-01
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.
A systematic exposition of the conservation equations for blast waves.
NASA Technical Reports Server (NTRS)
Oppenheim, A. K.; Lundstrom, E. A.; Kuhl, A. L.; Kamel, M. M.
1971-01-01
In order to provide a rational background for the analysis of experimental observations of blast wave phenomena, the conservation equations governing their nonsteady flow field are formulated in a general manner, without the usual restrictions imposed by an equation of state, and with proper account taken, by means of source terms, of other effects which, besides the inertial terms that conventionally dominate these equations, can affect the flow. Taking advantage of the fact that a blast wave can be generally considered as a spatially one-dimensional flow field whose nonsteady behavior can be regarded, consequently, as a function of just two independent variables, two generalized blast wave coordinates are introduced, one associated with the front of the blast wave and the other with its flow field. The conservation equations are accordingly transformed into this coordinate system, acquiring thereby a comprehensive character, in that they refer then to any frame of reference, being applicable, in particular, to problems involving either space or time profiles of the gas-dynamic parameters in the Eulerian system, or time profiles in the Lagrangian system.
Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
Holm, Sverre; Näsholm, Sven Peter
2014-04-01
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
Pierantozzi, T.; Vazquez, L.
2005-11-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
Pollitz, F.F.
2002-01-01
I present a new algorithm for calculating seismic wave propagation through a three-dimensional heterogeneous medium using the framework of mode coupling theory originally developed to perform very low frequency (f < ???0.01-0.05 Hz) seismic wavefield computation. It is a Greens function approach for multiple scattering within a defined volume and employs a truncated traveling wave basis set using the locked mode approximation. Interactions between incident and scattered wavefields are prescribed by mode coupling theory and account for the coupling among surface waves, body waves, and evanescent waves. The described algorithm is, in principle, applicable to global and regional wave propagation problems, but I focus on higher frequency (typically f ??????0.25 Hz) applications at regional and local distances where the locked mode approximation is best utilized and which involve wavefields strongly shaped by propagation through a highly heterogeneous crust. Synthetic examples are shown for P-SV-wave propagation through a semi-ellipsoidal basin and SH-wave propagation through a fault zone.
Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Cooper, Fred; Khare, Avinash; Mihaila, Bogdan; Saxena, Avadh
2010-09-01
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction g{2}/k+1(ΨΨ){k+1} , as well as a vector-vector self interaction g{2}/k+1(Ψγ{μ}ΨΨγ{μ}Ψ){1/2(k+1)} . We find the exact analytic form for solitary waves for arbitrary k and find that they are a generalization of the exact solutions for the nonlinear Schrödinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. We perform the nonrelativistic reduction and find the 1/2m correction to the NLSE, valid when |ω-m|<2m , where ω is the frequency of the solitary wave in the rest frame. We discuss the stability and blowup of solitary waves assuming the modified NLSE is valid and find that they should be stable for k<2 . PMID:21230200
Nonlinear waves in compressible shallow water magnetohydrodynemic equations
NASA Astrophysics Data System (ADS)
Klimachkov, Dmitry; Petrosyan, Arakel
2016-04-01
Compressible magnetohydrodynamic equations for a plasma in a gravity field with a free surface in shallow water approximation are obtained. Compressibility means that the pressure is a function of height. It is shown that classical shallow water incompressible magnetohydrodynamic equations are modified with a new argument instead of a layer height. We found all the simple discontinuous and continuous wave solutions for these equations, the wave velocities are obtained. Rankine-Hugoniot jump conditions for the velocities and magnetic field in the discontinuity are obtained. The Riemann problem for the arbitrary discontinuity is solved. It was found that the decay of arbitrary discontinuity causes five different configurations. For each configuration, we found the conditions necessary and sufficient for its implementation.
Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field.
Bayindir, Cihan
2016-03-01
In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.
Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field
NASA Astrophysics Data System (ADS)
Bayindir, Cihan
2016-03-01
In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k . The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k . Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.
Understanding Stokes forces in the wave-averaged equations
NASA Astrophysics Data System (ADS)
Suzuki, Nobuhiro; Fox-Kemper, Baylor
2016-05-01
The wave-averaged, or Craik-Leibovich, equations describe the dynamics of upper ocean flow interacting with nonbreaking, not steep, surface gravity waves. This paper formulates the wave effects in these equations in terms of three contributions to momentum: Stokes advection, Stokes Coriolis force, and Stokes shear force. Each contribution scales with a distinctive parameter. Moreover, these contributions affect the turbulence energetics differently from each other such that the classification of instabilities is possible accordingly. Stokes advection transfers energy between turbulence and Eulerian mean-flow kinetic energy, and its form also parallels the advection of tracers such as salinity, buoyancy, and potential vorticity. Stokes shear force transfers energy between turbulence and surface waves. The Stokes Coriolis force can also transfer energy between turbulence and waves, but this occurs only if the Stokes drift fluctuates. Furthermore, this formulation elucidates the unique nature of Stokes shear force and also allows direct comparison of Stokes shear force with buoyancy. As a result, the classic Langmuir instabilities of Craik and Leibovich, wave-balanced fronts and filaments, Stokes perturbations of symmetric and geostrophic instabilities, the wavy Ekman layer, and the wavy hydrostatic balance are framed in terms of intuitive physical balances.
Scalar Decomposition of the Electromagnetic Vector Wave Equation
NASA Astrophysics Data System (ADS)
Franke, Carlos Rodolfo
The accepted definition of separability of the electromagnetic vector wave equation requires that only one scalar field component exists in a scalar partial differential equation of no higher order than the second, for at least one of the scalar field components. The second order constraint so tightly restricts the mathematics that only the rectangular, the three cylindrical, and the spherical and conical coordinates can be separated. The constraint also permits separation of one scalar field component in prolate and oblate spheroidal coordinates, and paraboloidal coordinates, in that absence of azimuthal variations. The definition of separability makes it a particular attribute of a particular coordinate in a particular coordinate system, and not a general property of the coordinate system as a whole. The second order constraint on the scalar partial differential equation is now lifted, permitting the vector wave equation in any orthogonal curvilinear coordinate system to be completely separated into three scalar partial differential equations. The treatment is carried out for the circular-cylindrical and spherical coordinates, and the analysis indicates that the highest order of at least one of the uncoupled scalar partial differential equations in a given orthogonal curvilinear coordinate system is equal to twice the number of curvilinear coordinates.
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas.
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K
2010-06-01
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin- 1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin- 1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars. PMID:20866534
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas.
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K
2010-06-01
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin- 1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin- 1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
NASA Astrophysics Data System (ADS)
Wodo, Olga; Ganapathysubramanian, Baskar
2011-07-01
We present an efficient numerical framework for analyzing spinodal decomposition described by the Cahn-Hilliard equation. We focus on the analysis of various implicit time schemes for two and three dimensional problems. We demonstrate that significant computational gains can be obtained by applying embedded, higher order Runge-Kutta methods in a time adaptive setting. This allows accessing time-scales that vary by five orders of magnitude. In addition, we also formulate a set of test problems that isolate each of the sub-processes involved in spinodal decomposition: interface creation and bulky phase coarsening. We analyze the error fluctuations using these test problems on the split form of the Cahn-Hilliard equation solved using the finite element method with basis functions of different orders. Any scheme that ensures at least four elements per interface satisfactorily captures both sub-processes. Our findings show that linear basis functions have superior error-to-cost properties. This strategy - coupled with a domain decomposition based parallel implementation - let us notably augment the efficiency of a numerical Cahn-Hillard solver, and open new venues for its practical applications, especially when three dimensional problems are considered. We use this framework to address the isoperimetric problem of identifying local solutions in the periodic cube in three dimensions. The framework is able to generate all five hypothesized candidates for the local solution of periodic isoperimetric problem in 3D - sphere, cylinder, lamella, doubly periodic surface with genus two (Lawson surface) and triply periodic minimal surface (P Schwarz surface).
Data dependence for the amplitude equation of surface waves
NASA Astrophysics Data System (ADS)
Secchi, Paolo
2016-04-01
We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.
NASA Astrophysics Data System (ADS)
Cunningham, G.; Tu, W.; Chen, Y.; Reeves, G. D.; Henderson, M. G.; Baker, D. N.; Blake, J. B.; Spence, H.
2013-12-01
During the interval October 8-9, 2012, the phase-space density (PSD) of high-energy electrons exhibited a dropout preceding an intense enhancement observed by the MagEIS and REPT instruments aboard the Van Allen Probes. The evolution of the PSD suggests heating by chorus waves, which were observed to have high intensities at the time of the enhancement [1]. Although intense chorus waves were also observed during the first Dst dip on October 8, no PSD enhancement was observed at this time. We demonstrate a quantitative reproduction of the entire event that makes use of three recent modifications to the LANL DREAM3D diffusion code: 1) incorporation of a time-dependent, low-energy, boundary condition from the MagEIS instrument, 2) use of a time-dependent estimate of the chorus wave intensity derived from observations of POES low-energy electron precipitation, and 3) use of an estimate of the last closed drift shell, beyond which electrons are assumed to have a lifetime that is proportional to their drift period around earth. The key features of the event are quantitatively reproduced by the simulation, including the dropout on October 8, and a rapid increase in PSD early on October 9, with a peak near L*=4.2. The DREAM3D code predicts the dropout on October 8 because this feature is dominated by magnetospheric compression and outward radial diffusion-the L* of the last closed drift-shell reaches a minimum value of 5.33 at 1026 UT on October 8. We find that a ';statistical' wave model based on historical CRRES measurements binned in AE* does not reproduce the enhancement because the peak wave amplitudes are only a few 10's of pT, whereas an ';event-specific' model reproduces both the magnitude and timing of the enhancement very well, a s shown in the Figure, because the peak wave amplitudes are 10x higher. [1] 'Electron Acceleration in the Heart of the Van Allen Radiation Belts', G. D. Reeves et al., Science 1237743, Published online 25 July 2013 [DOI:10.1126/science
Broadband sub-millimeter wave amplifer module with 38dB gain and 8.3dB noise figure
NASA Astrophysics Data System (ADS)
Sarkozy, S.; Leong, K.; Lai, R.; Leakey, R.; Yoshida, W.; Mei, X.; Lee, J.; Liu, P.-H.; Gorospe, B.; Deal, W. R.
2011-05-01
Broadband sub-millimeter wave technology has received significant attention for potential applications in security, medical, and military imaging. Despite theoretical advantages of reduced size, weight, and power compared to current millimeter-wave systems, sub-millimeter-wave systems are hampered by a fundamental lack of amplification with sufficient gain and noise figure properties. We report on the development of a sub-millimeter wave amplifier module as part of a broadband pixel operating from 300-350 GHz, biased off of a single 2V power supply. Over this frequency range, > 38 dB gain and < 8.3 dB noise figure are obtained and represent the current state-of-art performance capabilities. The prototype pixel chain consists of two WR3 waveguide amplifier blocks, and a horn antenna and diode detector. The low noise amplifier Sub-Millimeter-wave Monolithic Integrated Circuit (SMMIC) was originally developed under the DARPA SWIFT and THz Electronics programs and is based on sub 50 nm Indium Arsenide Composite Channel (IACC) transistor technology with a projected maximum oscillation frequency fmax > 1.0 THz. This development and demonstration may bring to life future sub-millimeter-wave and THz applications such as solutions to brown-out problems, ultra-high bandwidth satellite communication cross-links, and future planetary exploration missions.
NASA Astrophysics Data System (ADS)
Gerke, Kirill; Vasilyev, Roman; Khirevich, Siarhei; Karsanina, Marina; Collins, Daniel; Korost, Dmitry; Mallants, Dirk
2015-04-01
In this contribution we introduce a novel free software which solves the Stokes equation to obtain velocity fields for low Reynolds-number flows within externally generated 3D pore geometries. Provided with velocity fields, one can calculate permeability for known pressure gradient boundary conditions via Darcy's equation. Finite-difference schemes of 2nd and 4th order of accuracy are used together with an artificial compressibility method to iteratively converge to a steady-state solution of Stokes' equation. This numerical approach is much faster and less computationally demanding than the majority of open-source or commercial softwares employing other algorithms (finite elements/volumes, lattice Boltzmann, etc.) The software consists of two parts: 1) a pre and post-processing graphical interface, and 2) a solver. The latter is efficiently parallelized to use any number of available cores (the speedup on 16 threads was up to 10-12 depending on hardware). Due to parallelization and memory optimization our software can be used to obtain solutions for 300x300x300 voxels geometries on modern desktop PCs. The software was successfully verified by testing it against lattice Boltzmann simulations and analytical solutions. To illustrate the software's applicability for numerous problems in Earth Sciences, a number of case studies have been developed: 1) identifying the representative elementary volume for permeability determination within a sandstone sample, 2) derivation of permeability/hydraulic conductivity values for rock and soil samples and comparing those with experimentally obtained values, 3) revealing the influence of the amount of fine-textured material such as clay on filtration properties of sandy soil. This work was partially supported by RSF grant 14-17-00658 (pore-scale modelling) and RFBR grants 13-04-00409-a and 13-05-01176-a.
NASA Astrophysics Data System (ADS)
Amor, Rumelo; Mahajan, Sumeet; Amos, William Bradshaw; McConnell, Gail
2014-12-01
Standing-wave excitation of fluorescence is highly desirable in optical microscopy because it improves the axial resolution. We demonstrate here that multiplanar excitation of fluorescence by a standing wave can be produced in a single-spot laser scanning microscope by placing a plane reflector close to the specimen. We report here a variation in the intensity of fluorescence of successive planes related to the Stokes shift of the dye. We show by the use of dyes specific for the cell membrane how standing-wave excitation can be exploited to generate precise contour maps of the surface membrane of red blood cells, with an axial resolution of ~90 nm. The method, which requires only the addition of a plane mirror to an existing confocal laser scanning microscope, may well prove useful in studying diseases which involve the red cell membrane, such as malaria.
Amor, Rumelo; Mahajan, Sumeet; Amos, William Bradshaw; McConnell, Gail
2014-12-08
Standing-wave excitation of fluorescence is highly desirable in optical microscopy because it improves the axial resolution. We demonstrate here that multiplanar excitation of fluorescence by a standing wave can be produced in a single-spot laser scanning microscope by placing a plane reflector close to the specimen. We report here a variation in the intensity of fluorescence of successive planes related to the Stokes shift of the dye. We show by the use of dyes specific for the cell membrane how standing-wave excitation can be exploited to generate precise contour maps of the surface membrane of red blood cells, with an axial resolution of ≈90 nm. The method, which requires only the addition of a plane mirror to an existing confocal laser scanning microscope, may well prove useful in studying diseases which involve the red cell membrane, such as malaria.
NASA Astrophysics Data System (ADS)
Lipatov, A. S.; Sibeck, D. G.
2016-09-01
We use a new hybrid kinetic model to simulate the response of ring current, outer radiation belt, and plasmaspheric particle populations to impulsive interplanetary shocks. Since particle distributions attending the interplanetary shock waves and in the ring current and radiation belts are non-Maxwellian, wave-particle interactions play a crucial role in energy transport within the inner magnetosphere. Finite gyroradius effects become important in mass loading the shock waves with the background plasma in the presence of higher energy ring current and radiation belt ions and electrons. Initial results show that shocks cause strong deformations in the global structure of the ring current, radiation belt, and plasmasphere. The ion velocity distribution functions at the shock front, in the ring current, and in the radiation belt help us determine energy transport through the Earth's inner magnetosphere.
Stochastic regulator theory for a class of abstract wave equations
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1991-01-01
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
Quaternion wave equations in curved space-time
NASA Technical Reports Server (NTRS)
Edmonds, J. D., Jr.
1974-01-01
The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.
NASA Astrophysics Data System (ADS)
Wawerzinek, B.; Ritter, J. R. R.; Roy, C.
2013-08-01
We analyse travel times of shear waves, which were recorded at the MAGNUS network, to determine the 3D shear wave velocity (vS) structure underneath Southern Scandinavia. The travel time residuals are corrected for the known crustal structure of Southern Norway and weighted to account for data quality and pick uncertainties. The resulting residual pattern of subvertically incident waves is very uniform and simple. It shows delayed arrivals underneath Southern Norway compared to fast arrivals underneath the Oslo Graben and the Baltic Shield. The 3D upper mantle vS structure underneath the station network is determined by performing non-linear travel time tomography. As expected from the residual pattern the resulting tomographic model shows a simple and continuous vS perturbation pattern: a negative vS anomaly is visible underneath Southern Norway relative to the Baltic Shield in the east with a contrast of up to 4% vS and a sharp W-E dipping transition zone. Reconstruction tests reveal besides vertical smearing a good lateral reconstruction of the dipping vS transition zone and suggest that a deep-seated anomaly at 330-410 km depth is real and not an inversion artefact. The upper part of the reduced vS anomaly underneath Southern Norway (down to 250 km depth) might be due to an increase in lithospheric thickness from the Caledonian Southern Scandes in the west towards the Proterozoic Baltic Shield in Sweden in the east. The deeper-seated negative vS anomaly (330-410 km depth) could be caused by a temperature anomaly possibly combined with effects due to fluids or hydrous minerals. The determined simple 3D vS structure underneath Southern Scandinavia indicates that mantle processes might influence and contribute to a Neogene uplift of Southern Norway.
Optically realizable localized wave solutions of the homogeneous scalar wave equation.
Reivelt, Kaido; Saari, Peeter
2002-04-01
One of the most frequently discussed problems in construction of localized wave (LW) solutions of the homogeneous scalar wave equation has been their energy content--the LW's generally have infinite energy content and special methods have to be used to obtain physically realizable wave fields. So far the problem has mainly been addressed as a pure mathematical one and the proposed LW's can hardly be implemented in optics. In this paper we propose an approach for constructing physically realizable LW's that have a transparent interpretation in terms of optical setups. It will be shown that such LW's can be derived as finite aperture approximations of fundamental LW's, the focus wave modes.
Bounded Error Schemes for the Wave Equation on Complex Domains
NASA Technical Reports Server (NTRS)
Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir
1998-01-01
This paper considers the application of the method of boundary penalty terms ("SAT") to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example, involving the solution of Maxwell's equations inside a 2-D circular wave-guide demonstrates the efficacy of this method in comparison to others (e.g. the staggered Yee scheme) - we achieve a decrease of two orders of magnitude in the level of the L2-error.
Electrostatic wave propagation and trapping near the magnetic equator
NASA Technical Reports Server (NTRS)
Barbosa, D. D.
1985-01-01
Results of a two-dimensional ray tracing computer code, based on Snell's law, for electrostatic wave propagation in a dipole magnetic field are discussed. A survey of possible ray paths varying a wide range of parameters is conducted for low-harmonic Bernstein modes in a high-density plasma. It is shown that the ray paths exhibit similarity with radial distance and that there exists the possibility of two classes of wave statistics of the equator: a broad emission region extending to about + or - 4 deg and a class of events restricted to the smaller region of 1-2 deg about the magnetic equator. The regulating parameter between these two types of events is the transition energy from the isotropic background electrons to the unstable distribution of superthermals. Ray paths for propagation in the magnetic equatorial plane are considered and an explanation is given for ray focusing in the equatorial plane based on electron gyroradius considerations.
Fast neural solution of a nonlinear wave equation
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad; Barhen, Jacob
1992-01-01
A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.
Fast Neural Solution Of A Nonlinear Wave Equation
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Toomarian, Nikzad
1996-01-01
Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
Non-Hermitian wave packet approximation of Bloch optical equations
Charron, Eric; Sukharev, Maxim
2013-01-14
We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation, and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method, one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schroedinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure, and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville-von Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.
NASA Astrophysics Data System (ADS)
Chen, Haopeng; Zhu, Liangbao; Su, Youjin
2016-08-01
We used teleseismic data recorded by a permanent seismic network in Yunnan, SE Tibet, and measured the interstation Rayleigh wave phase velocity between 10 and 60 s. A two-step inversion scheme was used to invert for the 3D S-wave velocity and azimuthal anisotropy structure of 10-110 km. The results show that there are two low velocity channels between depths of 20-30 km in Yunnan and that the fast axes are sub-parallel to the strikes of the low velocity channels, which supports the crustal flow model. The azimuthal anisotropy pattern is quite complicated and reveals a complex crust-mantle coupling mechanism in Yunnan. The N-S trending Lüzhijiang Fault separates the Dianzhong Block into two parts. In the western Dianzhong Block, the fast axis of the S-wave changes with depth, which indicates that the crust and the lithospheric mantle are decoupled. In the eastern Dianzhong Block and the western Yangtze Craton, the crust and the lithospheric mantle may be decoupled because of crustal flow, despite a coherent S-wave fast axis at depths of 10-110 km. In addition, the difference between the S-wave fast axis in the lithosphere and the SKS splitting measurement suggests that the lithosphere and the upper mantle are decoupled there. In the Baoshan Block, the stratified anisotropic pattern suggests that the crust and the upper mantle are decoupled.
Wave Equation of Three-Dimensional Skyrmion Line
NASA Astrophysics Data System (ADS)
Iwasaki, Junichi; Schütte, Christoph; Nagaosa, Naoto
2015-03-01
Magnetic skyrmion is a particle in magnets, which is now regarded as one of the most promising candidate for information career in future memory devices. In the bulk of chiral magnets, skyrmions form lines along the applied magnetic field. Previous studies report that the emergent magnetic monopoles are assocoated with the creation and annihilation of these lines. Here, we raise more fundamental question: how does the wave propagates in these one-dimensional ``strings''? Surprisingly, the numerical simulation reveals that the waves propagating in positive and negative directions are different. This asymmetric feature is described by magnon contribution, which has, in general, k-linear term in its dispersion relation under the Dzyaloshinskii-Moriya interaction. Starting from the action of the spin system in chiral magnets, we derive the wave equation of the skyrmion line.
Plasma wave interactions with energetic ions near the magnetic equator
NASA Technical Reports Server (NTRS)
Gurnett, D. A.
1975-01-01
An intense band of electromagnetic noise is frequently observed near the magnetic equatorial plane at radial distance from about 2 to 5 Re. Recent wideband wave-form measurements with the IMP-6 and Hawkeye-1 satellites have shown that the equatorial noise consists of a complex superposition of many harmonically spaced lines. Several distinctly different frequency spacings are often evident in the same spectrum. The frequency spacing typically ranges from a few Hz to a few tens of Hz. It is suggested that these waves are interacting with energetic protons, alpha particles, and other heavy ions trapped near the magnetic equator. The possible role these waves play in controlling the distribution of the energetic ions is considered.
Plasma wave interactions with energetic ions near the magnetic equator
NASA Technical Reports Server (NTRS)
Gurnett, D. A.
1976-01-01
An intense band of electromagnetic noise is frequently observed near the magnetic equatorial plane at radial distance from about 2 to 9 earth radii. Recent wide band wave form measurements with the Imp 6 and Hawkeye 1 satellites have shown that the equatorial noise consists of a complex superposition of many harmonically spaced lines. Several distinctly different frequency spacings are often evident in the same spectrum. The frequency spacing typically ranges from a few hertz to a few tens of hertz. The purpose of this paper is to suggest that these waves are interacting with energetic protons, alpha particles, and other heavy ions trapped near the magnetic equator. The possible role that these waves play in controlling the distribution of the energetic ions is considered.
NASA Technical Reports Server (NTRS)
Sakai, J. I.; Zhao, J.; Nishikawa, K.-I.
1994-01-01
We have shown that a current-carrying plasma loop can be heated by magnetic pinch driven by the pressure imbalance between inside and outside the loop, using a 3-dimensional electromagnetic (EM) particle code. Both electrons and ions in the loop can be heated in the direction perpendicular to the ambient magnetic field, therefore the perpendicular temperature can be increased about 10 times compared with the parallel temperature. This temperature anisotropy produced by the magnetic pinch heating can induce a plasma instability, by which high-frequency electromagnetic waves can be excited. The plasma current which is enhanced by the magnetic pinch can also excite a kinetic kink instability, which can heat ions perpendicular to the magnetic field. The heating mechanism of ions as well as the electromagnetic emission could be important for an understanding of the coronal loop heating and the electromagnetic wave emissions from active coronal regions.
On a class of nonlocal wave equations from applications
NASA Astrophysics Data System (ADS)
Beyer, Horst Reinhard; Aksoylu, Burak; Celiker, Fatih
2016-06-01
We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form a system of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain ℝn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.
Variational principle in optics II: Dissipative wave equations.
Rubinstein, Jacob; Wolansky, Gershon
2016-08-01
The problem of phase retrieval from intensity measurements is examined for the case of dissipative wave equations. Unlike the conservative case, it is not clear if and when the problem is solvable at all. We provide two solutions. First, it is shown that, for a certain class of dissipating potentials, the problem can be fully solved by converting it through a simple transformation to the framework of the weighted least action principle. Second, for all other dissipating potentials, a deep result from the theory of elliptic partial differential equations is used to show that the problem is always solvable up to a scaling of one of the measured intensities. Moreover, the solution in this general case can be obtained by solving a Monge-Ampere type differential equation. Two numerical examples are given to illustrate some of the theoretical considerations. PMID:27505643
3D-ambient noise Rayleigh wave tomography of Snæfellsjökull volcano, Iceland
NASA Astrophysics Data System (ADS)
Obermann, Anne; Lupi, Matteo; Mordret, Aurélien; Jakobsdóttir, Steinunn S.; Miller, Stephen A.
2016-05-01
From May to September 2013, 21 seismic stations were deployed around the Snæfellsjökull volcano, Iceland. We cross-correlate the five months of seismic noise and measure the Rayleigh wave group velocity dispersion curves to gain more information about the geological structure of the Snæfellsjökull volcano. In particular, we investigate the occurrence of seismic wave anomalies in the first 6 km of crust. We regionalize the group velocity dispersion curves into 2-D velocity maps between 0.9 and 4.8 s. With a neighborhood algorithm we then locally invert the velocity maps to obtain accurate shear-velocity models down to 6 km depth. Our study highlights three seismic wave anomalies. The deepest, located between approximately 3.3 and 5.5 km depth, is a high velocity anomaly, possibly representing a solidified magma chamber. The second anomaly is also a high velocity anomaly east of the central volcano that starts at the surface and reaches approximately 2.5 km depth. It may represent a gabbroic intrusion or a dense swarm of inclined magmatic sheets (similar to the dike swarms found in the ophiolites), typical of Icelandic volcanic systems. The third anomaly is a low velocity anomaly extending up to 1.5 km depth. This anomaly, located directly below the volcanic edifice, may be interpreted either as a shallow magmatic reservoir (typical of Icelandic central volcanoes), or alternatively as a shallow hydrothermal system developed above the cooling magmatic reservoir.
NASA Astrophysics Data System (ADS)
Lampson, Alan I.; Plummer, David N.; Erkkila, John H.; Crowell, Peter G.; Helms, Charles A.
1998-05-01
This paper describes a series of analyses using the 3-d MINT Navier-Stokes and OCELOT wave optics codes to calculate beam quality in a COIL laser cavity. To make this analysis tractable, the problem was broken into two contributions to the medium quality; that associated with microscale disturbances primarily from the transverse iodine injectors, and that associated with the macroscale including boundary layers and shock-like effects. Results for both microscale and macroscale medium quality are presented for the baseline layer operating point in terms of single pass wavefront error. These results show that the microscale optical path difference effects are 1D in nature and of low spatial order. The COIL medium quality is shown to be dominated by macroscale effects; primarily pressure waves generated from flow/boundary layer interactions on the cavity shrouds.
Ghosh, Aryya; Vaval, Nayana; Pal, Sourav
2015-07-14
Auger decay is an efficient ultrafast relaxation process of core-shell or inner-shell excited atom or molecule. Generally, it occurs in femto-second or even atto-second time domain. Direct measurement of lifetimes of Auger process of single ionized and double ionized inner-shell state of an atom or molecule is an extremely difficult task. In this paper, we have applied the highly correlated complex absorbing potential-equation-of-motion coupled cluster (CAP-EOMCC) approach which is a combination of CAP and EOMCC approach to calculate the lifetime of the states arising from 2p inner-shell ionization of an Ar atom and 3d inner-shell ionization of Kr atom. We have also calculated the lifetime of Ar{sup 2+}(2p{sup −1}3p{sup −1}) {sup 1}D, Ar{sup 2+}(2p{sup −1}3p{sup −1}) {sup 1}S, and Ar{sup 2+}(2p{sup −1}3s{sup −1}) {sup 1}P double ionized states. The predicted results are compared with the other theoretical results as well as experimental results available in the literature.
Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation
NASA Astrophysics Data System (ADS)
Huang, Xin
2016-06-01
We derive and study a general rational solution of a coupled defocusing Hirota equation which can be used to describe evolution of light in a two-mode fiber with defocusing Kerr effect and some certain high-order effects. We find some new excitation patterns in the model, such as M-shaped soliton, W-shaped soliton, anti-eye-shaped rogue wave and four-petaled flower rogue wave. The results are compared with the solutions obtained in other coupled systems like vector nonlinear Schrödinger equation, coupled focusing Hirota and Sasa-Satsuma equations. We explain the new characters by modulational instability properties. This further indicates that rational solution does not necessarily correspond to rogue wave excitation dynamics and the quantitative relation between nonlinear excitations and modulational instability should exist.
NASA Astrophysics Data System (ADS)
Zeng, Xiangfang; Thurber, Clifford H.; Shelly, David R.; Harrington, Rebecca M.; Cochran, Elizabeth S.; Bennington, Ninfa L.; Peterson, Dana; Guo, Bin; McClement, Kara
2016-09-01
To refine the 3-D seismic velocity model in the greater Parkfield, California region, a new data set including regular earthquakes, shots, quarry blasts and low-frequency earthquakes (LFEs) was assembled. Hundreds of traces of each LFE family at two temporary arrays were stacked with time-frequency domain phase weighted stacking method to improve signal-to-noise ratio. We extend our model resolution to lower crustal depth with LFE data. Our result images not only previously identified features but also low velocity zones (LVZs) in the area around the LFEs and the lower crust beneath the southern Rinconada Fault. The former LVZ is consistent with high fluid pressure that can account for several aspects of LFE behaviour. The latter LVZ is consistent with a high conductivity zone in magnetotelluric studies. A new Vs model was developed with S picks that were obtained with a new autopicker. At shallow depth, the low Vs areas underlie the strongest shaking areas in the 2004 Parkfield earthquake. We relocate LFE families and analyse the location uncertainties with the NonLinLoc and tomoDD codes. The two methods yield similar results.
Stability analysis of an interactive system of wave equation and heat equation with memory
NASA Astrophysics Data System (ADS)
Zhang, Qiong
2014-10-01
This paper is devoted to the stability analysis of an interaction system comprised of a wave equation and a heat equation with memory, where the hereditary heat conduction is due to Gurtin-Pipkin law or Coleman-Gurtin law. First, we show the strong asymptotic stability of solutions to this system. Then, the exponential stability of the interaction system is obtained when the hereditary heat conduction is of Gurtin-Pipkin type. Further, we show the lack of uniform decay of the interaction system when the heat conduction law is of Coleman-Gurtin type.
NASA Astrophysics Data System (ADS)
Simmons, N. A.; Myers, S. C.; Johannesson, G.; Matzel, E.
2011-12-01
LLNL-G3D is a global-scale model of P-wave velocity designed to accurately predict seismic travel times at regional and teleseismic distances simultaneously. The underlying goal of the model is to provide enhanced seismic event location capabilities. Previous versions of LLNL-G3D (versions 1 and 2) provide substantial improvements in event location accuracy via 3-D ray tracing. The latest models are based on ~2.7 million P and Pn arrivals that are re-processed using our global multi-event locator known as BayesLoc. Bayesloc is a formulation of the joint probability distribution across multiple-event location parameters, including hypocenters, travel time corrections, pick precision, and phase labels. Modeling the whole multiple-event system results in accurate locations and an internally consistent data set that is ideal for tomography. Our recently developed inversion approach (called Progressive Multi-level Tessellation Inversion or PMTI) captures regional trends and fine details where data warrant. Using PMTI, we model multiple heterogeneity scale lengths without defining parameter grids with variable densities based on some ad hoc criteria. LLNL-G3Dv3 (version 3) is produced with data generated with the BayesLoc procedure, recently modified to account for localized travel time trends via a multiple event clustering technique. We demonstrate the significance of BayesLoc processing, the impact on the resulting tomographic images, and the application of LLNL-G3D to seismic event location. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-491805.
Glushko, O; Meisels, R; Kuchar, F
2010-03-29
The plane-wave expansion method (PWEM), the multiple-scattering method (MSM) and the 3D finite-difference time-domain method (FDTD) are applied for simulations of propagation of electromagnetic waves through 3D colloidal photonic crystals. The system investigated is not a "usual" artificial opal with close-packed fcc lattice but a dilute bcc structure which occurs due to long-range repulsive interaction between electrically charged colloidal particles during the growth process. The basic optical properties of non-close-packed colloidal PhCs are explored by examining the band structure and reflection spectra for a bcc lattice of silica spheres in an aqueous medium. Finite size effects and correspondence between the Bragg model, band structure and reflection spectra are discussed. The effects of size, positional and missing-spheres disorder are investigated. In addition, by analyzing the results of experimental work we show that the fabricated structures have reduced plane-to-plane distance probably due to the effect of gravity during growth.
NASA Astrophysics Data System (ADS)
Harvey, R. W. (Bob); Petrov, Yu. V.; Jaeger, E. F.; Berry, L. A.; Bonoli, P. T.; Bader, A.
2015-11-01
A time-dependent simulation of C-Mod pulsed ICRF power is made calculating minority hydrogen ion distribution functions with the CQL3D-Hybrid-FOW finite-orbit-width Fokker-Planck code. ICRF fields are calculated with the AORSA full wave code, and RF diffusion coefficients are obtained from these fields using the DC Lorentz gyro-orbit code. Prior results with a zero-banana-width simulation using the CQL3D/AORSA/DC time-cycles showed a pronounced enhancement of the H distribution in the perpendicular velocity direction compared to results obtained from Stix's quasilinear theory, in general agreement with experiment. The present study compares the new FOW results, including relevant gyro-radius effects, to determine the importance of these effects on the the NPA synthetic diagnostic time-dependence. The new NPA results give increased agreement with experiment, particularly in the ramp-down time after the ICRF pulse. Funded, through subcontract with Massachusetts Institute of Technology, by USDOE sponsored SciDAC Center for Simulation of Wave-Plasma Interactions.
Spatial and temporal compact equations for water waves
NASA Astrophysics Data System (ADS)
Dyachenko, Alexander; Kachulin, Dmitriy; Zakharov, Vladimir
2016-04-01
A one-dimensional potential flow of an ideal incompressible fluid with a free surface in a gravity field is the Hamiltonian system with the Hamiltonian: H = 1/2intdxint-∞^η |nablaφ|^2dz + g/2ont η^2dxŗφ(x,z,t) - is the potential of the fluid, g - gravity acceleration, η(x,t) - surface profile Hamiltonian can be expanded as infinite series of steepness: {Ham4} H &=& H2 + H3 + H4 + dotsŗH2 &=& 1/2int (gη2 + ψ hat kψ) dx, ŗH3 &=& -1/2int \\{(hat kψ)2 -(ψ_x)^2}η dx,ŗH4 &=&1/2int {ψxx η2 hat kψ + ψ hat k(η hat k(η hat kψ))} dx. where hat k corresponds to the multiplication by |k| in Fourier space, ψ(x,t)= φ(x,η(x,t),t). This truncated Hamiltonian is enough for gravity waves of moderate amplitudes and can not be reduced. We have derived self-consistent compact equations, both spatial and temporal, for unidirectional water waves. Equations are written for normal complex variable c(x,t), not for ψ(x,t) and η(x,t). Hamiltonian for temporal compact equation can be written in x-space as following: {SPACE_C} H = intc^*hat V c dx + 1/2int [ i/4(c2 partial/partial x {c^*}2 - {c^*}2 partial/partial x c2)- |c|2 hat K(|c|^2) ]dx Here operator hat V in K-space is so that Vk = ω_k/k. If along with this to introduce Gardner-Zakharov-Faddeev bracket (for the analytic in the upper half-plane function) {GZF} partial^+x Leftrightarrow ikθk Hamiltonian for spatial compact equation is the following: {H24} &&H=1/gint1/ω|cω|2 dω +ŗ&+&1/2g^3int|c|^2(ddot c^*c + ddot c c^*)dt + i/g^2int |c|^2hatω(dot c c* - cdot c^*)dt. equation of motion is: {t-space} &&partial /partial xc +i/g partial^2/partial t^2c =ŗ&=& 1/2g^3partial^3/partial t3 [ partial^2/partial t^2(|c|^2c) +2 |c|^2ddot c +ddot c^*c2 ]+ŗ&+&i/g3 partial^3/partial t3 [ partial /partial t( chatω |c|^2) + dot c hatω |c|2 + c hatω(dot c c* - cdot c^*) ]. It solves the spatial Cauchy problem for surface gravity wave on the deep water. Main features of the equations are: Equations are written for
Hartzell, Stephen; Leeds, Alena L.; Ramirez-Guzman, Leonardo; Allen, James P.; Schmitt, Robert G.
2016-01-01
Thirty‐two accelerometers were deployed in the Livermore Valley, California, for approximately one year to study sedimentary basin effects. Many local and near‐regional earthquakes were recorded, including the 24 August 2014 Mw 6.0 Napa, California, earthquake. The resulting ground‐motion data set is used to quantify the seismic response of the Livermore basin, a major structural depression in the California Coast Range Province bounded by active faults. Site response is calculated by two methods: the reference‐site spectral ratio method and a source‐site spectral inversion method. Longer‐period (≥1 s) amplification factors follow the same general pattern as Bouguer gravity anomaly contours. Site response spectra are inverted for shallow shear‐wave velocity profiles, which are consistent with independent information. Frequency–wavenumber analysis is used to analyze plane‐wave propagation across the Livermore Valley and to identify basin‐edge‐induced surface waves with back azimuths different from the source back azimuth. Finite‐element simulations in a 3D velocity model of the region illustrate the generation of basin‐edge‐induced surface waves and point out strips of elevated ground velocities along the margins of the basin.
Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations
NASA Astrophysics Data System (ADS)
Tamilselvan, K.; Kanna, T.; Khare, Avinash
2016-10-01
We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on speed, pulse width and amplitude of the nonlinear waves is analyzed in detail. Particularly, a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behavior due to the presence of nonparaxial parameter.
Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation
NASA Astrophysics Data System (ADS)
Wang, X. P.; Ablowitz, M. J.; Segur, H.
1994-11-01
The solutions of a family of generalized Kadomtsev-Petviasvili equation in two diemnsions, ut+ umux+ uxxxx = σ2uyy, are studied with appropriate boundary conditions and constraints on the initial data for m in a dense set m ≥ 0 and for σ2 = 1. If m ≥ 4, then thé solution can blow up in finite time. We show that if 1 ≤ m ≤ 4, a solitary wave so exists which is unstable if m > {4}/{3}. In this and related problems, th e instability of solitary waves is associated with onset of wave collapse. We give numerical evidence to support this.
Approximate travelling waves for generalized KPP equations and classical mechanics
NASA Astrophysics Data System (ADS)
Elworthy, K. D.; Truman, A.; Zhao, H. Z.; Gaines, J. G.
1994-09-01
We consider the existence of approximate travelling waves of generalized Kolmogoroff, Petrovskii, Piscounoff (KPP) equations in which the initial distribution can depend on a small parameter mu which in the limit mu approaches 0 is the sum of some delta-functions or a step function. Using the method of Elworthy & Truman (1982) we construct a classical path which is the backward flow of a classical newtonian mechanics with given initial position and velocity before the time at which the caustic appears. By the Feynman-Kac formula and the Maruyana-Girsanov-Cameron-Martin transformation we obtain an identity from which, with a late caustic assumption, we see the propagation of the global wave front and the shape of the trough. Our theory shoes clearly how the initial distribution contributes to the propagation of the travelling wave. Finally, we prove a Huygens priciple for KPP equations on complete riemannian manifolds without cut locus, with some bounds on their volume element, in particular Cartan-Hadamard manifolds.
3D dimeron as a stable topological object
NASA Astrophysics Data System (ADS)
Yang, Shijie; Liu, Yongkai
2015-03-01
Searching for novel topological objects is always an intriguing task for scientists in various fields. We study a new three-dimensional (3D) topological structure called 3D dimeron in the trapped two-component Bose-Einstein condensates. The 3D dimeron differs to the conventional 3D skyrmion for the condensates hosting two interlocked vortex-rings. We demonstrate that the vortex-rings are connected by a singular string and the complexity constitutes a vortex-molecule. The stability is investigated through numerically evolving the Gross-Pitaevskii equations, giving a coherent Rabi coupling between the two components. Alternatively, we find that the stable 3D dimeron can be naturally generated from a vortex-free Gaussian wave packet via incorporating a synthetic non-Abelian gauge potential into the condensates. This work is supported by the NSF of China under Grant No. 11374036 and the National 973 program under Grant No. 2012CB821403.
NASA Astrophysics Data System (ADS)
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
3D Lithospheric Imaging by Time-Domain Full-Waveform Inversion of Teleseismic Body-Waves
NASA Astrophysics Data System (ADS)
Beller, S.; Monteiller, V.; Operto, S.; Nolet, G.; Combe, L.; Metivier, L.; Virieux, J.; Nissen-Meyer, T.; Paul, A.
2014-12-01
With the deployment of dense seismic arrays and the continuous growth of computing facilities, full-waveform inversion (FWI) of teleseismic data has become a method of choice for high-resolution lithospheric imaging. FWI can be recast as a local optimization problem that seeks to estimate Earth's elastic properties by iteratively minimizing the misfit function between observed and modeled seismograms.In passive teleseismic configurations, the seismic source no longer corresponds to a point source embedded in the targeted medium but rather corresponds to a wavefront incoming from the outside of the model. We develop a 3-dimensional time-domain full-waveform inversion program that is more designed for this configuration. The gradient of the misfit function is efficiently computed with the adjoint-state method. A velocity-stress finite-difference time-domain modeling engine, which is interfaced with the so-called total-field/scattered-field method, is used to propagate in the targeted medium the incident wavefield inferred from a global Earth simulation (AxiSEM). Such interfacing is required to account for the multiple arrivals in the incoming wavefield and the sphericity of the Earth. Despite the limited number of nearly plane-wave sources, the interaction of the incident wavefield with the topography (P-Sv conversions and P-P reflections acting as secondary sources) provides a suitable framework to record both transmitted wavefields and reflected wavefields from lithospheric reflectors. These recordings of both transmitted and reflected waves makes FWI amenable to a broadband-wavenumber (i.e., high resolution) reconstruction of the lithosphere.Feasibility of the method is assessed with a realistic synthetic model representative of the Western Alps. One key issue is the estimation of the temporal source excitation, as there might be some trade-off between the source estimation and the subsurface update. To avoid being trapped in a local minimum, we follow a
NASA Astrophysics Data System (ADS)
Marras, Simone; Giraldo, Francis X.
2015-02-01
The stabilization of high order spectral elements to solve the transport equations for tracers in the atmosphere remains an active topic of research among atmospheric modelers. This paper builds on our previous work on variational multiscale stabilization (VMS) and discontinuity capturing (DC) (Marras et al. (2012) [7]) and shows the applicability of VMS+DC to realistic atmospheric problems that involve physics coupling with phase change in the simulation of 3D deep convection. We show that the VMS+DC approach is a robust technique that can damp the high order modes characterizing the spectral element solution of complex coupled transport problems. The method has important properties that techniques of more common use often lack: 1) it is free of a user-defined parameter, 2) it is anisotropic in that it only acts along the flow direction, 3) it is numerically consistent, and 4) it can improve the monotonicity of high-order spectral elements. The proposed method is assessed by comparing the results against those obtained with a fourth-order hyper-viscosity programmed in the same code. The main conclusion that arises is that tuning can be fully avoided without loss of accuracy if the dissipative scheme is properly designed. Finally, the cost of parallel communication is that of a second order operator which means that fewer communications are required by VMS+DC than by a hyper-viscosity method; fewer communications translate into a faster and more scalable code, which is of vital importance as we approach the exascale range of computing.
Transport equations for linear surface waves with random underlying flows
NASA Astrophysics Data System (ADS)
Bal, Guillaume; Chou, Tom
1999-11-01
We define the Wigner distribution and use it to develop equations for linear surface capillary-gravity wave propagation in the transport regime. The energy density a(r, k) contained in waves propagating with wavevector k at field point r is given by dota(r,k) + nabla_k[U_⊥(r,z=0) \\cdotk + Ω(k)]\\cdotnabla_ra [13pt] \\: hspace1in - (nabla_r\\cdotU_⊥)a - nabla_r(k\\cdotU_⊥)\\cdotnabla_ka = Σ(δU^2) where U_⊥(r, z=0) is a slowly varying surface current, and Ω(k) = √(k^3+k)tanh kh is the free capillary-gravity dispersion relation. Note that nabla_r\\cdotU_⊥(r,z=0) neq 0, and that the surface currents exchange energy density with the propagating waves. When an additional weak random current √\\varepsilon δU(r/\\varepsilon) varying on the scale of k-1 is included, we find an additional scattering term Σ(δU^2) as a function of correlations in δU. Our results can be applied to the study of surface wave energy transport over a turbulent ocean.
Modulational instability in nonlinear nonlocal equations of regularized long wave type
NASA Astrophysics Data System (ADS)
Hur, Vera Mikyoung; Pandey, Ashish Kumar
2016-06-01
We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of Benjamin-Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations.
Regime independent coupled-wave equations in anisotropic photorefractive media
NASA Astrophysics Data System (ADS)
Daly, K. R.; D'Alessandro, G.; Kaczmarek, M.
2009-06-01
An extension to coupled wave theory suitable for all regimes of diffraction is presented. The model assumes that the refractive index grating has an arbitrary profile in one direction and is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms are considered and appropriate mismatch terms dealt with. It is shown that this model is analytically equivalent to both the Bragg and Raman-Nath regime coupling models under an appropriate set of assumptions. This model is applied to cases such as optical coupling in liquid crystal cells with photoconductive layers. Its predictions are successfully compared to finite element simulations of the full Maxwell’s equations.
Maxwell Equation for the Coupled Spin-Charge Wave Propagation
Bernevig, B.Andrei; Yu, Xiaowei; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-01-15
We show that the dissipationless spin current in the ground state of the Rashba model gives rise to a reactive coupling between the spin and charge propagation, which is formally identical to the coupling between the electric and the magnetic fields in the 2 + 1 dimensional Maxwell equation. This analogy leads to a remarkable prediction that a density packet can spontaneously split into two counter propagation packets, each carrying the opposite spins. In a certain parameter regime, the coupled spin and charge wave propagates like a transverse 'photon'. We propose both optical and purely electronic experiments to detect this effect.
NASA Astrophysics Data System (ADS)
Kawaguchi, Genta; Maesato, Mitsuhiko; Komatsu, Tokutaro; Imakubo, Tatsuro; Kitagawa, Hiroshi
2016-02-01
We present the results of high-pressure transport measurements on the anion-mixed molecular conductors (DIETSe)2M Br2Cl2 [DIETSe = diiodo(ethylenedithio)tetraselenafulvalene; M =Fe , Ga]. They undergo a metal-insulator (M-I) transition below 9 K at ambient pressure, which is suppressed by applying pressure, indicating a spin-density-wave (SDW) transition caused by a nesting instability of the quasi-one-dimensional (Q1D) Fermi surface, as observed in the parent compounds (DIETSe)2M Cl4 (M =Fe , Ga). In the metallic state, the existence of the Q1D Fermi surface is confirmed by observing the Lebed resonance. The critical pressures of the SDW, Pc, of the M Br2Cl2 (M =Fe , Ga) salts are significantly lower than those of the the M Cl4 (M = Fe, Ga) salts, suggesting chemical pressure effects. Above Pc, field-induced SDW transitions appear, as evidenced by kink structures in the magnetoresistance (MR) in both salts. The FeBr2Cl2 salt also shows antiferromagnetic (AF) ordering of d spins at 4 K, below which significant spin-charge coupling is observed. A large positive MR change up to 150% appears above the spin-flop field at high pressure. At low pressure, in particular below Pc, a dip or kink structure appears in MR at the spin-flop field, which shows unconventionally large hysteresis at low temperature (T <1 K). The hysteresis region clearly decreases with increasing pressure towards Pc, strongly indicating that the coexisting SDW plays an important role in the enhancement of magnetic hysteresis besides the random exchange interaction.
3D Elastic Wavefield Tomography
NASA Astrophysics Data System (ADS)
Guasch, L.; Warner, M.; Stekl, I.; Umpleby, A.; Shah, N.
2010-12-01
Wavefield tomography, or waveform inversion, aims to extract the maximum information from seismic data by matching trace by trace the response of the solid earth to seismic waves using numerical modelling tools. Its first formulation dates from the early 80's, when Albert Tarantola developed a solid theoretical basis that is still used today with little change. Due to computational limitations, the application of the method to 3D problems has been unaffordable until a few years ago, and then only under the acoustic approximation. Although acoustic wavefield tomography is widely used, a complete solution of the seismic inversion problem requires that we account properly for the physics of wave propagation, and so must include elastic effects. We have developed a 3D tomographic wavefield inversion code that incorporates the full elastic wave equation. The bottle neck of the different implementations is the forward modelling algorithm that generates the synthetic data to be compared with the field seismograms as well as the backpropagation of the residuals needed to form the direction update of the model parameters. Furthermore, one or two extra modelling runs are needed in order to calculate the step-length. Our approach uses a FD scheme explicit time-stepping by finite differences that are 4th order in space and 2nd order in time, which is a 3D version of the one developed by Jean Virieux in 1986. We chose the time domain because an explicit time scheme is much less demanding in terms of memory than its frequency domain analogue, although the discussion of wich domain is more efficient still remains open. We calculate the parameter gradients for Vp and Vs by correlating the normal and shear stress wavefields respectively. A straightforward application would lead to the storage of the wavefield at all grid points at each time-step. We tackled this problem using two different approaches. The first one makes better use of resources for small models of dimension equal
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Kreider, K. L.
1996-01-01
An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
NASA Astrophysics Data System (ADS)
Ando, Ryosuke
2016-11-01
The elastodynamic boundary integral equation method (BIEM) in real space and in the temporal domain is an accurate semi-analytical tool to investigate the earthquake rupture dynamics on non-planar faults. However, its heavy computational demand for a historic integral generally increases with a time complexity of O(MN3)for the number of time steps N and elements M due to volume integration in the causality cone. In this study, we introduce an efficient BIEM, termed the `Fast Domain Partitioning Method' (FDPM), which enables us to reduce the computation time to the order of the surface integral, O(MN2), without degrading the accuracy. The memory requirement is also reduced to O(M2) from O(M2N). FDPM uses the physical nature of Green's function for stress to partition the causality cone into the domains of the P and S wave fronts, the domain in-between the P and S wave fronts, and the domain of the static equilibrium, where the latter two domains exhibit simpler dependences on time and/or space. The scalability of this method is demonstrated on the large-scale parallel computing environments of distributed memory systems. It is also shown that FDPM enables an efficient use of memory storage, which makes it possible to reduce computation times to a previously unprecedented level. We thus present FDPM as a powerful tool to break through the current fundamental difficulties in running dynamic simulations of coseismic ruptures and earthquake cycles under realistic conditions of fault geometries.
Remarks on the asymptotic behavior of the solution to damped wave equations
NASA Astrophysics Data System (ADS)
Nishiyama, Hisashi
2016-10-01
We study the diffusion phenomena for damped wave equations. We prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent. As an application of our approach, we also study the asymptotic behavior of the damped wave equation in Euclidean space under the geometric control condition.
Global, uniform, asymptotic wave-equation solutions for large wavenumbers
NASA Astrophysics Data System (ADS)
Klauder, John R.
1987-11-01
For each of a large class of linear wave equations-relevant, for example, to very general acoustical or optical propagation problems-we develop within a single expression a global, uniform, asymptotic solution for large wavenumbers (small wavelengths) based on coherentstate transformation techniques. Such techniques effectively separate the configuration-space field into its orientational components, and are thus analogous to a phase-space description of rays by their position and direction. The resultant coherent-state approximation offers distinct advantages over more traditional asymptotic approximations based on direct or Fourier transform techniques. In particular, coherent-state methods lead to an everywhere well-defined approximation independent of the complexity of the caustic structure, independent of whether there are a few or a vast number of relevant rays, or even in shadow regions where no conventional rays exist. For propagation in random media it is shown that coherent-state techniques also offer certain advantages. Approximations are developed for wave equations in an arbitrary number of space dimensions for single component fields as well as multicomponent fields that, for example, can account for backscattering. It is noteworthy that the coherentstate asymptotic approximation should lend itself to numerical studies as well.
A Schamel equation for ion acoustic waves in superthermal plasmas
Williams, G. Kourakis, I.; Verheest, F.; Hellberg, M. A.; Anowar, M. G. M.
2014-09-15
An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u{sub 0}. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.
Coherent states, vacuum structure and infinite component relativistic wave equations
NASA Astrophysics Data System (ADS)
Cirilo-Lombardo, Diego Julio
2016-11-01
It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the transformations and symmetries involved in equations of such type corresponded to a particular representation of the Lorentz group. In this paper, we give the general solution to this problem emphasizing the interplay between the group structure, the corresponding algebra and the physical spectrum. This analysis is completed with a strong discussion and proving that: (i) the physical states are represented by coherent states; (ii) the solutions in [Yu. P. Stepanovsky, Nucl. Phys. B (Proc. Suppl.) 102 (2001) 407-411; 103 (2001) 407-411] are not general, (iii) the symmetries of the considered physical system in [Yu. P. Stepanovsky, Nucl. Phys. B (Proc. Suppl.) 102 (2001) 407-411; 103 (2001) 407-411] (equations and geometry) do not correspond to the Lorentz group but to the fourth covering: the Metaplectic group Mp(n).
Wave-equation-based travel-time seismic tomography - Part 1: Method
NASA Astrophysics Data System (ADS)
Tong, P.; Zhao, D.; Yang, D.; Yang, X.; Chen, J.; Liu, Q.
2014-11-01
In this paper, we propose a wave-equation-based travel-time seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the travel-time residual Δt = Tobs-Tsyn and the relative velocity perturbation δ c(x)/c(x) connected by a finite-frequency travel-time sensitivity kernel K(x) is theoretically derived using the adjoint method. To accurately calculate the travel-time residual Δt, two automatic arrival-time picking techniques including the envelop energy ratio method and the combined ray and cross-correlation method are then developed to compute the arrival times Tsyn for synthetic seismograms. The arrival times Tobs of observed seismograms are usually determined by manual hand picking in real applications. Travel-time sensitivity kernel K(x) is constructed by convolving a~forward wavefield u(t,x) with an adjoint wavefield q(t,x). The calculations of synthetic seismograms and sensitivity kernels rely on forward modeling. To make it computationally feasible for tomographic problems involving a large number of seismic records, the forward problem is solved in the two-dimensional (2-D) vertical plane passing through the source and the receiver by a high-order central difference method. The final model is parameterized on 3-D regular grid (inversion) nodes with variable spacings, while model values on each 2-D forward modeling node are linearly interpolated by the values at its eight surrounding 3-D inversion grid nodes. Finally, the tomographic inverse problem is formulated as a regularized optimization problem, which can be iteratively solved by either the LSQR solver or a~nonlinear conjugate-gradient method. To provide some insights into future 3-D tomographic inversions, Fréchet kernels for different seismic phases are also demonstrated in this study.
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-08-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
Wave-equation migration velocity inversion using passive seismic sources
NASA Astrophysics Data System (ADS)
Witten, B.; Shragge, J. C.
2015-12-01
Seismic monitoring at injection sites (e.g., CO2 sequestration, waste water disposal, hydraulic fracturing) has become an increasingly important tool for hazard identification and avoidance. The information obtained from this data is often limited to seismic event properties (e.g., location, approximate time, moment tensor), the accuracy of which greatly depends on the estimated elastic velocity models. However, creating accurate velocity models from passive array data remains a challenging problem. Common techniques rely on picking arrivals or matching waveforms requiring high signal-to-noise data that is often not available for the magnitude earthquakes observed over injection sites. We present a new method for obtaining elastic velocity information from earthquakes though full-wavefield wave-equation imaging and adjoint-state tomography. The technique exploits the fact that the P- and S-wave arrivals originate at the same time and location in the subsurface. We generate image volumes by back-propagating P- and S-wave data through initial Earth models and then applying a correlation-based extended-imaging condition. Energy focusing away from zero lag in the extended image volume is used as a (penalized) residual in an adjoint-state tomography scheme to update the P- and S-wave velocity models. We use an acousto-elastic approximation to greatly reduce the computational cost. Because the method requires neither an initial source location or origin time estimate nor picking of arrivals, it is suitable for low signal-to-noise datasets, such as microseismic data. Synthetic results show that with a realistic distribution of microseismic sources, P- and S-velocity perturbations can be recovered. Although demonstrated at an oil and gas reservoir scale, the technique can be applied to problems of all scales from geologic core samples to global seismology.
NASA Astrophysics Data System (ADS)
Hildebrandt, Andre; Alhaddad, Samer; Hammer, Manfred; Förstner, Jens
2016-02-01
Semi-guided light propagation across linear folds of slab waveguides is being considered. Radiation losses vanish beyond certain critical angles of incidence, as can be understood by arguments resembling Snell's law. One thus realizes lossless propagation through 90-degree corner configurations, where the remaining guided waves are still subject to pronounced reflection and polarization conversion. A step-like system of two of these sharp corners can then be viewed as a system akin to a Fabry-Perot interferometer, with two partial reflectors at a distance given by the vertical separation of the slab cores. The respective resonance effect enables full transmission of semiguided, laterally plane waves through the step structures. One obtains a configuration that optically connects guiding layers at different elevation levels in a 3-D integrated optical chip, without radiation losses, over large distances, and reasonably broadband. We show rigorous quasi-analytical results for typical high-contrast Si/SiO2 structures. Although the full-transmission effect requires a symmetric system, here realized by slab waveguides with a silicon core sandwiched between thick silica substrate and cover layers, simulations for configurations with air cover show that a certain asymmetry can well be afforded.
Wang, Yugang; Wu, Xinjun; Sun, Pengfei; Li, Jian
2015-02-03
Electromagnetic acoustic transducers (EMATs) can generate non-dispersive T(0,1) mode guided waves in a metallic pipe for nondestructive testing (NDT) by using a periodic permanent magnet (PPM) EMAT circular array. In order to enhance the excitation efficiency of the sensor, the effects of varying the number of elements of the array on the excitation efficiency is studied in this paper. The transduction process of the PPM EMAT array is studied based on 3-D finite element method (FEM). The passing signal amplitude of the torsional wave is obtained to represent the excitation efficiency of the sensor. Models with different numbers of elements are established and the results are compared to obtain an optimal element number. The simulation result is verified by experiments. It is shown that after optimization, the amplitudes of both the passing signal and defect signal with the optimal element number are increased by 29%, which verifies the feasibility of this optimal method. The essence of the optimization is to find the best match between the static magnetic field and the eddy current field in a limited circumferential space to obtain the maximum circumferential Lorentz force.
Wang, Yugang; Wu, Xinjun; Sun, Pengfei; Li, Jian
2015-01-01
Electromagnetic acoustic transducers (EMATs) can generate non-dispersive T(0,1) mode guided waves in a metallic pipe for nondestructive testing (NDT) by using a periodic permanent magnet (PPM) EMAT circular array. In order to enhance the excitation efficiency of the sensor, the effects of varying the number of elements of the array on the excitation efficiency is studied in this paper. The transduction process of the PPM EMAT array is studied based on 3-D finite element method (FEM). The passing signal amplitude of the torsional wave is obtained to represent the excitation efficiency of the sensor. Models with different numbers of elements are established and the results are compared to obtain an optimal element number. The simulation result is verified by experiments. It is shown that after optimization, the amplitudes of both the passing signal and defect signal with the optimal element number are increased by 29%, which verifies the feasibility of this optimal method. The essence of the optimization is to find the best match between the static magnetic field and the eddy current field in a limited circumferential space to obtain the maximum circumferential Lorentz force. PMID:25654722
NASA Astrophysics Data System (ADS)
Morales, L. E. A. P.; Aguirre, J.; Vazquez Rosas, R.; Suarez, G.; Contreras Ruiz-Esparza, M. G.; Farraz, I.
2014-12-01
Methods that use seismic noise or microtremors have become very useful tools worldwide due to its low costs, the relative simplicity in collecting data, the fact that these are non-invasive methods hence there is no need to alter or even perforate the study site, and also these methods require a relatively simple analysis procedure. Nevertheless the geological structures estimated by this methods are assumed to be parallel, isotropic and homogeneous layers. Consequently precision of the estimated structure is lower than that from conventional seismic methods. In the light of these facts this study aimed towards searching a new way to interpret the results obtained from seismic noise methods. In this study, seven triangular SPAC (Aki, 1957) arrays were performed in the city of Coatzacoalcos, Veracruz, varying in sizes from 10 to 100 meters. From the autocorrelation between the stations of each array, a Rayleigh wave phase velocity dispersion curve was calculated. Such dispersion curve was used to obtain a S wave parallel layers velocity (VS) structure for the study site. Subsequently the horizontal to vertical ratio of the spectrum of microtremors H/V (Nogoshi and Igarashi, 1971; Nakamura, 1989, 2000) was calculated for each vertex of the SPAC triangular arrays, and from the H/V spectrum the fundamental frequency was estimated for each vertex. By using the H/V spectral ratio curves interpreted as a proxy to the Rayleigh wave ellipticity curve, a series of VS structures were inverted for each vertex of the SPAC array. Lastly each VS structure was employed to calculate a 3D velocity model, in which the exploration depth was approximately 100 meters, and had a velocity range in between 206 (m/s) to 920 (m/s). The 3D model revealed a thinning of the low velocity layers. This proved to be in good agreement with the variation of the fundamental frequencies observed at each vertex. With the previous kind of analysis a preliminary model can be obtained as a first
On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes
ERIC Educational Resources Information Center
Chandran, Pallath
2004-01-01
The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…
New Travelling Solitary Wave and Periodic Solutions of the Generalized Kawahara Equation
Chen Huaitang; Yin Huicheng
2007-09-06
A simple elliptic equation method is used for constructing exact trevelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. With the aid of Maple, more new travelling solitary wave and periodic solutions are obtained for the generalized Kawahara equation.
Approximate solution to the scalar wave equation for optical waveguides.
Goyal, I C; Gallawa, R L; Ghatak, A K
1991-07-20
We consider an approximate solution to the wave equation appropriate to the optical waveguides encountered in practice. The refractive-index profile may be arbitrary, and the geometry may be two or three dimensional. A circular or a planar waveguide could thus be treated by this method. The technique is more accurate and more useful than the WKB method, which is often used in problems of this type, because the technique is valid even at the turning points, where the WKB solution fails. The fields and the propagation constants of the lowest-order modes for two profiles are calculated, and they compare well with the exact solutions. The solutions that we proposed are, in fact, not new. However, insofar as we know, they are unknown and unused by the optics community.
Standing waves for supercritical nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Dávila, Juan; del Pino, Manuel; Musso, Monica; Wei, Juncheng
Let V(x) be a non-negative, bounded potential in R, N⩾3 and p supercritical, p>{N+2}/{N-2}. We look for positive solutions of the standing-wave nonlinear Schrödinger equation Δu-V(x)u+u=0 in R, with u(x)→0 as |x|→+∞. We prove that if V(x)=o(|) as |x|→+∞, then for N⩾4 and p>{N+1}/{N-3} this problem admits a continuum of solutions. If in addition we have, for instance, V(x)=O(|) with μ>N, then this result still holds provided that N⩾3 and p>{N+2}/{N-2}. Other conditions for solvability, involving behavior of V at ∞, are also provided.
Extreme physical information and the nonlinear wave equation
NASA Astrophysics Data System (ADS)
Frieden, B. R.
1995-09-01
The nonlinear wave equation an be derived from a principle of extreme physical information (EPI) K. This is for a scenario where a probe electron moves through a medium in a weak magnetic field. The field is caused by a probabilistic line current source. Assume that the probability current density S of the electron is approximately constant, and directed parallel to the current source. Both the source probability amplitudes (rho) and the electron probability amplitudes (phi) are unknowns (called 'modes') of the problem. The net physical information K here consists of two components: functional K1[(phi) ] due to modes (phi) and K2[(rho) ] due to modes (rho) , respectively. To form K1[(phi) ], the Fisher information functional I1[(phi) ] for the electron modes is first constructed. This is of a fixed mathematical form. Then, a unitary transformation on (phi) to a physical space is sought that leaves I1 invariant, as form J1. This is, of course, the Fourier transformation, where the transform coordinates are momenta and I1 is essentially the mean-square electron momentum. Information K1[(phi) ] is then defined as (I1 - J1). Information K2 is formed similarly. The total information K is formed as the sum of the two components K1[(phi) ] and K2[(rho) ], by the additivity of Fisher information, and is then extremized in both (phi) and (rho) . Extremizing first in (rho) gives a Taylor series in powers of (phi) n*(phi) n, which is cut off at the quadratic term. Back-substituting this into the total Lagrangian gives one that is quadratic in (phi) n*(phi) n. Now varying (phi) * gives the required cubic wave equation in (phi) .
Green`s function implementation of common-offset, wave-equation migration
Ehinger, A.; Lailly, P.; Marfurt, K.J.
1996-11-01
Common-offset migration is extremely important in the context of migration velocity analysis (MVA) since it generates geologically interpretable migrated images. However, only a wave-equation-based migration handles multipathing of energy in contrast to the popular Kirchhoff migration with first-arrival traveltimes. The authors have combined the superior treatment of multipathing of energy by wave-equation-based migration with the advantages of the common-offset domain for MVA by implementing wave-equation migration algorithms via the use of finite-difference Green`s functions. With this technique, the authors are able to apply wave-equation migration in measurement configurations that are usually considered to be of the realm of Kirchhoff migration. In particular, wave-equation migration of common offset sections becomes feasible. The application of the wave-equation, common-offset migration algorithm to the Marmousi data set confirms the large increase in interpretability of individual migrated sections, for about twice the cost of standard wave-equation common-shot migration. The implementation of wave-equation migration via the Green`s functions is based on wavefield extrapolation via paraxial one-way wave equations. For these equations, theoretical results allow one to perform exact inverse extrapolation of wavefields.
Jarvis, Andrew J C; Cegla, Frederic B
2014-07-01
The challenge of accurately simulating how incident scalar waves interact with rough boundaries has made it an important area of research within many scientific disciplines. Conventional methods, which in the majority of cases focus only on scattering in two dimensions, often suffer from long simulation times or reduced accuracy, neglecting phenomena such as multiple scattering and surface self-shadowing. A simulation based on the scalar wave distributed point source method (DPSM) is presented as an alternative which is computationally more efficient than fully meshed numerical methods while obtaining greater accuracy than approximate analytical techniques. Comparison is made to simulated results obtained using the finite element method for a sinusoidally periodic surface where scattering only occurs in two dimensions, showing very good agreement (<0.2 dB). In addition to two-dimensional scattering, comparison to experimental results is also carried out for scattering in three dimensions when the surface has a Gaussian roughness distribution. Results indicate that for two-dimensional scattering and for rough surfaces with a correlation length equal to the incident wavelength (λ) and a root mean square height less than 0.2λ, the scalar wave approximation predicts reflected pulse shape change and envelope amplitudes generally to within 1 dB. Comparison between transducers within a three-element array also illustrate the sensitivity pulse amplitude can have to sensor position above a rough surface, differing by as much as 17 dB with a positional change of just 1.25λ. PMID:24960707
Jarvis, Andrew J C; Cegla, Frederic B
2014-07-01
The challenge of accurately simulating how incident scalar waves interact with rough boundaries has made it an important area of research within many scientific disciplines. Conventional methods, which in the majority of cases focus only on scattering in two dimensions, often suffer from long simulation times or reduced accuracy, neglecting phenomena such as multiple scattering and surface self-shadowing. A simulation based on the scalar wave distributed point source method (DPSM) is presented as an alternative which is computationally more efficient than fully meshed numerical methods while obtaining greater accuracy than approximate analytical techniques. Comparison is made to simulated results obtained using the finite element method for a sinusoidally periodic surface where scattering only occurs in two dimensions, showing very good agreement (<0.2 dB). In addition to two-dimensional scattering, comparison to experimental results is also carried out for scattering in three dimensions when the surface has a Gaussian roughness distribution. Results indicate that for two-dimensional scattering and for rough surfaces with a correlation length equal to the incident wavelength (λ) and a root mean square height less than 0.2λ, the scalar wave approximation predicts reflected pulse shape change and envelope amplitudes generally to within 1 dB. Comparison between transducers within a three-element array also illustrate the sensitivity pulse amplitude can have to sensor position above a rough surface, differing by as much as 17 dB with a positional change of just 1.25λ.
Wave equation-based reflection tomography of the 1992 Landers earthquake area
NASA Astrophysics Data System (ADS)
Huang, Xueyuan; Yang, Dinghui; Tong, Ping; Badal, José; Liu, Qinya
2016-03-01
In the framework of a recent wave equation-based traveltime seismic tomography, we show that incorporating Moho-reflected phases (PmP and SmS) in addition to the direct P and S phases can significantly increase tomography resolution in the lower crust and this may provide additional evidence to resolve important tectonic issues. To highlight the resolving power of the new strategy, we apply it in the region around the 1992 Landers earthquake (Mw = 7.3) in Southern California using seismic arrivals from local earthquakes, obtaining 3-D high-resolution P and S wave crustal velocity models and Poisson's ratio structures. In the upper crust, our method confirmed features that had been previously found. However, in the middle-to-lower crust, we found low-velocity anomalies on the southeastern section of the San Jacinto Fault and high Vp and low Vs structures to the west of the Big Bear earthquake, which may be related to upwelling of partial melt from the mantle.
NASA Astrophysics Data System (ADS)
Ishise, M.; Koketsu, K.; Miyake, H.
2008-12-01
Seismic anisotropy is one of key elements to understand geodynamics such as mantle convection, plate tectonics, and evolutional process of the crust. Thus, it is crucial to investigate seismic anisotropy in the subduction zone where various phenomena are attributed to dynamic processes caused by interaction among adjacent plates. Actually, recent studies of seismic anisotropy show that the determination of a 3D seismic anisotropy structure can be potential diagnostics of a geological lineament structure inside the crust, and probe earthquake rupture areas and rupture nucleation points. In this study, we have evaluated the three-dimensional (3D) P-wave anisotropic velocity structure in the Kii Peninsula, southwest Japan, as well as the isotropic velocity structure by P-wave travel times tomography. The study area lies on the Eurasian (Amulian) plate above the subducting Philippine Sea Plate. This belongs to an accretionary prism, which is being developed at the margin of the Asian Continent, and is characterized by E-W trending metamorphic belts including a segment of the active faults zone called the Median Tectonic Line (MTL). Additionally, the Kii Peninsula region is presumed to be source regions of megathrust earthquakes along the Nankai trough. The resultant images of both the isotropic and anisotropic tomography show that the upper crust is characterized by E-W trending structure similar to that of the geological structure over the peninsula region. Because deformation of the crust such as preferred mineral alignment and recrystallization associated with planar structures produces significant seismic anisotropy, the plausible factor of the crustal feature is interpreted as E-W orientation of the regional metamorphic belt. Furthermore, in the resultant tomographic image, the E-W trending pattern is found within the deeper crust. This fact indicates that the lineament structure is sustained in the deeper crust. Since our tomography has good resolution in the
NASA Astrophysics Data System (ADS)
Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian
2016-07-01
Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.
The zero dispersion limits of nonlinear wave equations
Tso, T.
1992-01-01
In chapter 2 the author uses functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schroedinger equation for initial data that satisfy some suitable conditions. In chapter 3 the energy estimates are used to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H[sup 3](R) as [epsilon] [yields] 0; also, it is shown that the strong L[sup 2](R)-limit of the solutions of the BBM equation as [epsilon] [yields] 0 before a critical time. In chapter 4 the author uses the Whitham modulation theory and averaging method to find the 2[pi]-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. It is shown that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, the relations are studied of the KdV equation and the mKdV equation. Finally, the author studies the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.
Exact solutions for two nonlinear wave equations with nonlinear terms of any order
NASA Astrophysics Data System (ADS)
Chen, Yong; Li, Biao; Zhang, Hongqing
2005-03-01
In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin-Bona-Mahony (BBM) equation and the generalized Burgers-Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported.
Sub- and superluminal kink-like waves in the kinetic limit of Maxwell-Bloch equations
NASA Astrophysics Data System (ADS)
Janowicz, Maciej; Holthaus, Martin
2011-01-01
Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level Maxwell-Bloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the Lambert-Beer law. Those solitary waves can propagate with either sub- or superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained.
NASA Astrophysics Data System (ADS)
Bekki, Naoaki; Shintani, Seine A.
2015-12-01
We consider the Rayleigh-Lamb-type equation for propagating pulsive waves excited by aortic-valve closure at end-systole in the human heart wall. We theoretically investigate the transcendental dispersion equation of pulsive waves for the asymmetrical zero-order mode of the Lamb wave. We analytically find a simple dispersion equation with a universal constant for a small Lamb wavenumber. We show that the simple dispersion equation can qualitatively explain the myocardial noninvasive measurements in vivo of pulsive waves in the human heart wall. We can also consistently estimate the viscoelastic constant of the myocardium in the human heart wall using the simple dispersion equation for a small Lamb wavenumber instead of using a complex nonlinear optimization.
Compacton-like wave and kink-like wave solutions of the generalized KP-MEW (2, 2) equation
NASA Astrophysics Data System (ADS)
Li, Shaoyong; Song, Ming
2014-03-01
Using a bifurcation method and a numerical simulation approach of dynamical systems, we study the generalized KP-MEW(2, 2) equation (ut + (u2)x + (u2)xxt)x + uyy = 0. Two types of bounded traveling waves are found, that is, a compacton-like wave and a kink-like wave. The planar graphs of the compacton-like and kink-like waves are simulated using the software Maple. Exact implicit or parameter expressions of these solutions are given.
A Wave Equation Migration Method for Receiver Function Imaging
NASA Astrophysics Data System (ADS)
Chen, L.; Wen, L.; Zheng, T.
2004-12-01
A wave equation based poststack depth migration method is proposed to image the crustal and upper mantle structures using teleseismic receiver functions. By utilizing a frequency-wavenumber domain one-way phase-screen propagator for wavefield extrapolation in the migration scheme, the common conversion point (CCP) stacked receiver functions are backward propagated to construct the subsurface structural images. Synthetic experiments demonstrate the validity of the migration method for a variety of laterally heterogeneous models. The migrated images show considerable improvement over the CCP images in recovering the structural features. The phase-screen propagator migration method proves to be particularly useful for imaging complex structures and deep discontinuities overlain by strong shallow anomalies, because of its capability of handling lateral velocity variations. Influences of several factors on the image quality of the poststack migration are further investigated, including inter-station spacing, noise level of the data, velocity model used in migration, and earthquake distribution (incident direction of source fields). Theoretical derivation and numerical results suggest that both the CCP stacking and the poststack migration of receiver functions need to be designed in a target-oriented way for reliable and efficient imaging, and special consideration on earthquake distribution is particularly required in designing seismic experiments if structures of large dips are present. The proposed wav equation migration scheme is applied to image the Earth's internal structures using a number of dense field data sets collected at many seismic arrays in Asia. The constructed images reveal several interesting subsurface structures of the study regions and synthetic tests indicate that those subsurface features are well resolved by the seismic data. Significant improvements of the image quality demonstrate the great potential and flexibility of the proposed migration
Pretend model of traveling wave solution of two-dimensional K-dV equation
NASA Astrophysics Data System (ADS)
Karim, Md Rezaul; Alim, Md Abdul; Andallah, Laek Sazzad
2013-11-01
Traveling wave resolution of Korteweg-de Vries (K-dV) solitary and numerical estimation of analytic solutions have been studied in this paper for imaginary concept. Pretend model of traveling wave deals with giant waves or series of waves created by an undersea earthquake, volcanic eruption or landslide. The concept of traveling wave is frequently used by mariners and in coastal, ocean and naval engineering. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by Pang et al. (Appl. Math. Mech-Engl. Ed 31(7):929-936, 2010). We have solved the imaginary part of exact traveling wave equations analytically, and numerical results of time-dependent wave solutions have been presented graphically. This procedure has a potential to be used in more complex system for other types of K-dV equations.
NASA Astrophysics Data System (ADS)
Hanson-Hedgecock, S.; Wagner, L.; Fouch, M. J.; James, D. E.
2011-12-01
We present the results of inversions for 3D shear velocity structure of the crust and uppermost mantle beneath the High Lava Plains, Oregon using data from ~300 broadband stations of the High Lava Plains seismic experiment and the EarthScope/USArray Transportable Array (TA). The High Lava Plains (HLP) is a WNW progressive silicic volcanism, initiated ~14.5 Ma near the Owyhee Plateau and is currently active at the Newberry caldera. The Yellowstone Snake River Plain (YSRP) volcanic track is temporally contemporaneous with the HLP, but trends to the northeast, parallel to North American plate motion. The cause of volcanism along the HLP is debated and has been variously attributed to Basin and Range extension, back-arc extension, rollback of the subducting Juan de Fuca plate, and an intra-continental hotspot/plume source. Additionally the relationship between the HLP, YSRP, and Columbia River Basalts (CRB), the three major post-17Ma intracontinental volcanic provinces of the Pacific Northwest, is not well understood. The 3D shear velocity structure of the crust and uppermost mantle to ~65km depth is determined from fundamental mode Rayleigh wave ambient noise phase velocity maps at periods up to 40s. The use of ambient noise tomography with the dense station spacing of the combined High Lava Plains seismic experiment and the EarthScope/USArray Transportable Array (TA) datasets allows the shallow structure of the High Lava Plains to be imaged in finer detail than previous ANT studies that focused on the entire western United States. In the crust, low velocities in central Oregon are observed in association with the Brothers Fault Zone, Jordan and Diamond Craters and Steens Mountain regions in addition to the strong low velocity zone associated with the Cascades to the west. To the east of the HLP, low velocities are observed to about 10km depth in the western SRP. In the eastern SRP we observe a shallow veneer of low velocities underlain by a ~10km thick high velocity
NASA Astrophysics Data System (ADS)
Cárdenas-Soto, M.; Valdes, J. E.; Escobedo-Zenil, D.
2013-05-01
In June 2006, the base of the artificial lake in Chapultepec Park collapsed. 20 thousand liters of water were filtered to the ground through a crack increasing the dimensions of initial gap. Studies indicated that the collapse was due to saturated material associated with a sudden and massive water filtration process. Geological studies indicates that all the area of this section the subsoil is composed of vulcano-sedimentary materials that were economically exploited in the mid-20th century, leaving a series of underground mines that were rehabilitated for the construction of the Park. Currently, the Lake is rehabilitated and running for recreational activities. In this study we have applied two methods of seismic noise correlation; seismic interferometry (SI) in time domain and the Spatial Power Auto Correlation (SPAC) in frequency domain, in order to explore the 3D subsoil velocity structure. The aim is to highlight major variations in velocity that can be associated with irregularities in the subsoil that may pose a risk to the stability of the Lake. For this purpose we use 96 vertical geophones of 4.5 Hz with 5-m spacing that conform a semi-circular array that provide a length of 480 m around the lake zone. For both correlation methods, we extract the phase velocity associated with the dispersion characteristics between each pair of stations in the frequency range from 4 to 12 Hz. In the SPAC method the process was through the dispersion curve, and in SI method we use the time delay of the maximum amplitude in the correlation pulse, which was previously filtered in multiple frequency bands. The results of both processes were captured in 3D velocity volumes (in the case SI a process of traveltime tomography was applied). We observed that in the frequency range from 6 to 8 Hz, appear irregular structures, with high velocity contrast in relation with the shear wave velocity of surface layer (ten thick m of saturated sediments). One of these anomalies is related
NASA Astrophysics Data System (ADS)
Pletinckx, D.
2011-09-01
The current 3D hype creates a lot of interest in 3D. People go to 3D movies, but are we ready to use 3D in our homes, in our offices, in our communication? Are we ready to deliver real 3D to a general public and use interactive 3D in a meaningful way to enjoy, learn, communicate? The CARARE project is realising this for the moment in the domain of monuments and archaeology, so that real 3D of archaeological sites and European monuments will be available to the general public by 2012. There are several aspects to this endeavour. First of all is the technical aspect of flawlessly delivering 3D content over all platforms and operating systems, without installing software. We have currently a working solution in PDF, but HTML5 will probably be the future. Secondly, there is still little knowledge on how to create 3D learning objects, 3D tourist information or 3D scholarly communication. We are still in a prototype phase when it comes to integrate 3D objects in physical or virtual museums. Nevertheless, Europeana has a tremendous potential as a multi-facetted virtual museum. Finally, 3D has a large potential to act as a hub of information, linking to related 2D imagery, texts, video, sound. We describe how to create such rich, explorable 3D objects that can be used intuitively by the generic Europeana user and what metadata is needed to support the semantic linking.
NASA Astrophysics Data System (ADS)
Sabetkar, Akbar; Dorranian, Davoud
2015-08-01
In this paper, our attention is first concentrated on obliquely propagating properties of low-frequency (ω ≪ ωcd) "fast" and "slow" dust acoustic waves, in the linear regime, in dusty electronegative plasmas with Maxwellian electrons, kappa distributed positive ions, negative ions (following the combination of kappa-Schamel distribution), and negatively charged dust particles. So, an explicit expression for dispersion relation is derived by linearizing a set of dust-fluid equations. The results show that wave frequency ω in long and short-wavelengths limit is conspicuously affected by physical parameters, namely, positive to negative temperature ion ratio (βp), trapping parameter of negative ions (μ), magnitude of the magnetic field B0 (via ωcd), superthermal index ( κn,κp ), and positive ion to dust density ratio (δp). The signature of the penultimate parameter (i.e., κn) on wave frequency reveals that the frequency gap between the modes reduces (escalates) for k
New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia
The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.
On the solution of the generalized wave and generalized sine-Gordon equations
NASA Technical Reports Server (NTRS)
Ablowitz, M. J.; Beals, R.; Tenenblat, K.
1986-01-01
The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.
NASA Technical Reports Server (NTRS)
Lee, L. C.
1974-01-01
The propagation of waves in a random medium is studied in the 'quasi-optics' and the 'Markov random process' approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of moment equations with different transverse coordinates and different wave numbers is then obtained from the Fokker-Planck equation of the characteristic functional. The application of those results to the pulse smearing of the pulsar signal and the frequency correlation function of the wave intensity in interstellar scintillation is briefly discussed.
Numerical solution of Maxwell's Wave Equation in an Axisymmetric Curved Space-Time
NASA Astrophysics Data System (ADS)
Otu, Joseph
2002-03-01
Using an exact Weyl metric with a quadrupole moment, a wave equation valid in flat space-time was derived from the covariant Maxwell's equations in curved space-time. The curvature effects are shown to represent a medium with an effective but variable index of refraction. Numerical solution of the wave equation is studied. The solution shows that the wave amplitude is unchanged as the wave propagates into a stronger gravitational field. However, the frequency changes in a way that is consistent with the analytic solution^1, and as predicted by the gravitational red-shift phenomenon. ^1 J. O. Otu, Bull. of the APS, Vol. 44, No. 1, 676(1999).
Two kinds of peaked solitary waves of the KdV, BBM and Boussinesq equations
NASA Astrophysics Data System (ADS)
Liao, ShiJun
2012-12-01
It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves, which have been not reported for other mainstream models of shallow water waves. In this letter, the closed-form solutions of peaked solitary waves of the KdV equation, the BBM equation and the Boussinesq equation are given for the first time. All of them have either a peakon or an anti-peakon. Each of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and could be understood as weak solution. Therefore, the peaked solitary waves might be common for most of shallow water wave models, no matter whether or not they are integrable and/or admit breaking-wave solutions.
A solution scheme for the Euler equations based on a multi-dimensional wave model
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.; Barth, Timothy J.; Parpia, Ijaz H.
1993-01-01
A scheme for the solution of scalar advection on an unstructured mesh has been developed, tested, and extended to the Euler equations. The scheme preserves a linear function exactly, and yields nearly monotone results. The flux function associated with the Euler scheme is based on a discrete 'wave model' for the system of equations. The wave model decomposes the solution gradient at a location into shear waves, entropy waves and acoustic waves and calculates the speeds, strengths and directions associated with the waves. The approach differs from typical flux-difference splitting schemes in that the waves are not assumed to propagate normal to the faces of the control volumes; directions of propagation of the waves are instead computed from solution-gradient information. Results are shown for three test cases, and two different wave models. The results are compared to those from other approaches, including MUSCL and Galerkin least squares schemes.
Spectral methods for the wave equation in second-order form
Taylor, Nicholas W.; Teukolsky, Saul A.; Kidder, Lawrence E.
2010-07-15
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semidiscrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multidomain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.
A quartic dispersion equation for internal gravity waves in the thermosphere
NASA Technical Reports Server (NTRS)
Hickey, M. P.; Cole, K. D.
1987-01-01
A new quartic dispersion equation in the square of the complex vertical wave number is derived by employing the 'shallow atmosphere' approximation and an ion drag approximation. These approximations allow the coefficients of the quartic equation to be given in terms of the corresponding cubic equation (which neglects the Coriolis force and the zonal ion drag component), but modified to take into account these neglected effects. Coupling between the extraordinary viscosity wave mode and the other three wave modes is highlighted and numerical solutions are compared for this quartic equation, an exact eighth order equation and the cubic equation. For the first time the validity of using the 'shallow atmosphere' approximation to describe internal gravity wave motions is demonstrated.
PLOT3D/AMES, DEC VAX VMS VERSION USING DISSPLA (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, DEC VAX VMS VERSION USING DISSPLA (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P. G.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
On the Stability of Self-Similar Solutions to Nonlinear Wave Equations
NASA Astrophysics Data System (ADS)
Costin, Ovidiu; Donninger, Roland; Glogić, Irfan; Huang, Min
2016-04-01
We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.
New solitary wave solutions of some nonlinear evolution equations with distinct physical structures
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Chun, Changbum
2008-12-01
In this paper, we obtain solitary wave solutions for some nonlinear partial differential equations. The Exp-function method is used to establish solitary wave solutions for Calogero-Bogoyavlenskii-Schiff and general modified Degasperis-Procesi and Camassa-Holm equations. The result shows that the Exp-function method yields new and more general solutions. Moreover, this method with the aid of symbolic computation provides a very effective and powerful mathematical tool for solving nonlinear evolution equations arising in mathematical physics.
Synchronization of traveling waves in a dispersive system of weakly coupled equations
NASA Astrophysics Data System (ADS)
Makridin, Z. V.; Makarenko, N. I.
2016-06-01
The system of weakly coupled differential equations describing traveling waves in dispersive media is considered. The Lyapunov — Schmidt construction is used to study the branching of cnoidal-type periodic solutions. The analysis of bifurcation equations uses the group symmetry and cosymmetry of original equations. Sufficient condition for existence of the phase-shifted modes of cnoidal waves is formulated in terms of the Pontryagin's function determined by the nonlinear perturbation terms
NASA Astrophysics Data System (ADS)
Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed
2015-02-01
The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.
NASA Astrophysics Data System (ADS)
Ren, Dandan; Ou, Yaobin
2016-08-01
In this paper, we prove the incompressible limit of all-time strong solutions to the three-dimensional full compressible Navier-Stokes equations. Here the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively. The uniform estimates in both the Mach number {ɛin(0,overline{ɛ}]} and time {tin[0,∞)} are established by deriving a differential inequality with decay property, where {overline{ɛ} in(0,1]} is a constant. Based on these uniform estimates, the global solution of full compressible Navier-Stokes equations with "well-prepared" initial conditions converges to the one of isentropic incompressible Navier-Stokes equations as the Mach number goes to zero.
NASA Technical Reports Server (NTRS)
Shareef, N. H.; Amirouche, F. M. L.
1991-01-01
A computational algorithmic procedure is developed and implemented for the dynamic analysis of a multibody system with rigid/flexible interconnected bodies. The algorithm takes into consideration the large rotation/translation and small elastic deformations associated with the rigid-body degrees of freedom and the flexibility of the bodies in the system respectively. Versatile three-dimensional isoparametric brick elements are employed for the modeling of the geometric configurations of the bodies. The formulation of the recursive dynamical equations of motion is based on the recursive Kane's equations, strain energy concepts, and the techniques of component mode synthesis. In order to minimize CPU-intensive matrix multiplication operations and speed up the execution process, the concepts of indexed arrays is utilized in the formulation of the equations of motion. A spin-up maneuver of a space robot with three flexible links carrying a solar panel is used as an illustrative example.
PLOT3D/AMES, GENERIC UNIX VERSION USING DISSPLA (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, GENERIC UNIX VERSION USING DISSPLA (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
A large active wave trapped in Jupiter's equator
NASA Astrophysics Data System (ADS)
Legarreta, J.; Barrado-Izagirre, N.; García-Melendo, E.; Sánchez-Lavega, A.; Gómez-Forrellad, J. M.
2016-02-01
Context. A peculiar atmospheric feature was observed in the equatorial zone (EZ) of Jupiter between September and December 2012 in ground-based and Hubble Space Telescope (HST) images. This feature consisted of two low albedo Y-shaped cloud structures (Y1 and Y2) oriented along the equator and centred on it (latitude 0.5°-1°N). Aims: We wanted to characterize these features, and also tried to find out their properties and understand their nature. Methods: We tracked these features to obtain their velocity and analyse their cloud morphology and the interaction with their surroundings. We present numerical simulations of the phenomenon based on one- and two-layer shallow water models under a Gaussian pulse excitation. Results: Each Y feature had a characteristic zonal length of ~15° (18 000 km) and a meridional width (distance between the north-south extremes of the Y) of 5° (6000 km), and moved eastward with a speed of around 20-40 m s-1 relative to Jupiter's mean flow. Their lifetime was 90 and 60 days for Y1 and Y2, respectively. In November, both Y1 and Y2 exhibited outbursts of rapidly evolving bright spots emerging from the Y vertex. The Y features were not visible at wavelengths of 255 or 890 nm, which suggests that they were vertically shallow and placed in altitude between the upper equatorial hazes and the main cloud deck. Numerical simulations of the dynamics of the Jovian equatorial region generate Kelvin and Rossby waves, which are similar to those in the Matsuno-Gill model for Earth's equatorial dynamics, and reproduce the observed cloud morphology and the main properties the main properties of the Y features.
3d-3d correspondence revisited
NASA Astrophysics Data System (ADS)
Chung, Hee-Joong; Dimofte, Tudor; Gukov, Sergei; Sułkowski, Piotr
2016-04-01
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d {N}=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.
3d-3d correspondence revisited
Chung, Hee -Joong; Dimofte, Tudor; Gukov, Sergei; Sułkowski, Piotr
2016-04-21
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-15
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
NASA Astrophysics Data System (ADS)
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
Ge, Liang; Sotiropoulos, Fotis
2008-01-01
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 [1]. 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 through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533
NASA Astrophysics Data System (ADS)
Zhang, Zhen-dong; Schuster, Gerard; Liu, Yike; Hanafy, Sherif M.; Li, Jing
2016-10-01
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method.
Nonlinear modulation of periodic waves in the small dispersion limit of the Benjamin-Ono equation
NASA Astrophysics Data System (ADS)
Matsuno, Y.
1998-12-01
The Whitham modulation theory is used to construct large time asymptotic solutions of the Benjamin-Ono (BO) equation in the small dispersion limit. For a wide class of initial data, asymptotic solutions are represented by a single-phase periodic solution of the BO equation with slowly varying amplitude and wave number. The Whitham system of modulation equations for these wave parameters has a very simple structure, and it can be solved exactly under appropriate boundary conditions. It is found that the oscillating zone expands with time, and eventually evolves into a train of solitary waves. In the case of localized initial data, the number density function of solitary waves is derived in a closed form. The resulting expression coincides with the corresponding formula obtained from the asymptotic theory based on the conservation laws of the BO equation. For steplike initial data, the total number of created solitary waves increases without limit in proportion to time.
Linking multiple relaxation, power-law attenuation, and fractional wave equations.
Näsholm, Sven Peter; Holm, Sverre
2011-11-01
The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.
On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations.
Alias, A; Grimshaw, R H J; Khusnutdinova, K R
2013-06-01
In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky equations. These are systematically derived for a density-stratified ocean. Some preliminary numerical simulations are reported which show that, in the generic case, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation. PMID:23822486
On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations.
Alias, A; Grimshaw, R H J; Khusnutdinova, K R
2013-06-01
In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky equations. These are systematically derived for a density-stratified ocean. Some preliminary numerical simulations are reported which show that, in the generic case, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation.
NASA Astrophysics Data System (ADS)
Mohammed, K. Elboree
2015-10-01
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.
PLOT3D/AMES, UNIX SUPERCOMPUTER AND SGI IRIS VERSION (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, UNIX SUPERCOMPUTER AND SGI IRIS VERSION (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
Circularly polarized few-cycle optical rogue waves: rotating reduced Maxwell-Bloch equations.
Xu, Shuwei; Porsezian, K; He, Jingsong; Cheng, Yi
2013-12-01
The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.
Orbital stability of periodic waves in the class of reduced Ostrovsky equations
NASA Astrophysics Data System (ADS)
Johnson, Edward R.; Pelinovsky, Dmitry E.
2016-09-01
Periodic travelling waves are considered in the class of reduced Ostrovsky equations that describe low-frequency internal waves in the presence of rotation. The reduced Ostrovsky equations with either quadratic or cubic nonlinearities can be transformed to integrable equations of the Klein-Gordon type by means of a change of coordinates. By using the conserved momentum and energy as well as an additional conserved quantity due to integrability, we prove that small-amplitude periodic waves are orbitally stable with respect to subharmonic perturbations, with period equal to an integer multiple of the period of the wave. The proof is based on construction of a Lyapunov functional, which is convex at the periodic wave and is conserved in the time evolution. We also show numerically that convexity of the Lyapunov functional holds for periodic waves of arbitrary amplitudes.
NASA Astrophysics Data System (ADS)
Meulien Ohlmann, Odile
2013-02-01
Today the industry offers a chain of 3D products. Learning to "read" and to "create in 3D" becomes an issue of education of primary importance. 25 years professional experience in France, the United States and Germany, Odile Meulien set up a personal method of initiation to 3D creation that entails the spatial/temporal experience of the holographic visual. She will present some different tools and techniques used for this learning, their advantages and disadvantages, programs and issues of educational policies, constraints and expectations related to the development of new techniques for 3D imaging. Although the creation of display holograms is very much reduced compared to the creation of the 90ies, the holographic concept is spreading in all scientific, social, and artistic activities of our present time. She will also raise many questions: What means 3D? Is it communication? Is it perception? How the seeing and none seeing is interferes? What else has to be taken in consideration to communicate in 3D? How to handle the non visible relations of moving objects with subjects? Does this transform our model of exchange with others? What kind of interaction this has with our everyday life? Then come more practical questions: How to learn creating 3D visualization, to learn 3D grammar, 3D language, 3D thinking? What for? At what level? In which matter? for whom?
NASA Astrophysics Data System (ADS)
Lang, Jörg; Winsemann, Jutta; Steinmetz, Dominik; Polom, Ulrich; Pollok, Lukas; Böhner, Utz; Serangeli, Jordi; Brandes, Christian; Hampel, Andrea; Winghart, Stefan
2012-04-01
The Pleistocene deposits of Schöningen represent an outstanding geological and archaeological archive, where an up to 45 m thick Middle to Late Pleistocene succession has been preserved and unique artefacts from the Lower Palaeolithic have been discovered. The preservation of such a thick and complete glacial/interglacial succession is very rare in the geological record and requires a specific depositional setting. We will present a new depositional model for the Pleistocene succession of Schöningen, integrating outcrop data, borehole data and high-resolution shear wave seismics. A total of four outcrop sections and 744 borehole logs were examined to document the complex facies architecture. All collected sedimentological and geophysical data sets were integrated into a high-resolution 3D geological model (GOCAD®) for reconstructing the spatial distribution of facies associations and the large-scale depositional architecture. The spatial distribution of the artefacts will be discussed with respect to the depositional environment. The Elsterian and Holsteinian deposits are restricted to a NNW-SSE trending, elongated trough, which is deeply incised into unconsolidated lignite-bearing Palaeogene deposits. The geometry of this erosional structure points to a tunnel valley origin that was incised below the Elsterian ice sheet. The basal tunnel valley fill consists of cross-stratified pebbly sand and gravel overlain by till. After deglaciation the tunnel valley remained underfilled and acted as a depocentre for interglacial deposition. During the subsequent Holsteinian interglacial (MIS 9) a lake formed within this depocentre and lacustrine sediments accumulated. This interglacial succession consists of peat, organic-rich silt and fine-grained sand interpreted as lake-bottom and deltaic sediments fed by surface run-off shed from the Elm ridge. The lacustrine deposition was controlled by repeated lake-level fluctuations in the range of 1-6 m leading to the formation of
NASA Astrophysics Data System (ADS)
Feng, Lian-Li; Tian, Shou-Fu; Yan, Hui; Wang, Li; Zhang, Tian-Tian
2016-07-01
In this paper, a lucid and systematic approach is proposed to systematically study the periodic-wave solutions and asymptotic behaviors of a (2 + 1) -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. Based on Bell's polynomials, the bilinear formalism and N -soliton solution of the gKDKK equation are derived, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic-wave solutions of the equation are also constructed. Finally, an asymptotic relation between the periodic-wave solutions and soliton solutions are strictly established under a limited procedure.
NASA Astrophysics Data System (ADS)
Santos Júnior, S. I.; Cardoso, J. G.
2016-10-01
The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is reviewed. Subsequently, the entire set of field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are ultimately carried by the wave equations at issue. What results is, in effect, that the only interactions which occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.
Exact Travelling Wave Solutions of the Schamel-Korteweg-de Vries Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy
2011-12-01
The Schamel-Korteweg-de Vries (S-KdV) equation containing a square root nonlinearity is a very attractive model for the study of ion-acoustic waves in plasma and dusty plasma. In this work, we obtain exact travelling wave solutions of the S-KdV equation by employing the exp function method. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution equations. The work emphasizes the power of the method in providing distinct solutions of different physical problems.
Localized modes of the Hirota equation: Nth order rogue wave and a separation of variable technique
NASA Astrophysics Data System (ADS)
Mu, Gui; Qin, Zhenyun; Chow, Kwok Wing; Ee, Bernard K.
2016-10-01
The Hirota equation is a special extension of the intensively studied nonlinear Schrödinger equation, by incorporating third order dispersion and one form of the self-steepening effect. Higher order rogue waves of the Hirota equation can be calculated theoretically through a Darboux-dressing transformation by a separation of variable approach. A Taylor expansion is used and no derivative calculation is invoked. Furthermore, stability of these rogue waves is studied computationally. By tracing the evolution of an exact solution perturbed by random noise, it is found that second order rogue waves are generally less stable than first order ones.
PLOT3D/AMES, SGI IRIS VERSION (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, SGI IRIS VERSION (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
Twisted electrostatic ion-cyclotron waves in dusty plasmas.
Shukla, P K
2013-01-01
We show the existence of a twisted electrostatic ion-cyclotron (ESIC) wave carrying orbital angular momentum (OAM) in a magnetized dusty plasma. For our purposes, we derive a 3D wave equation for the coupled ESIC and dust ion-acoustic (DIA) waves from the hydrodynamic equations that are composed of the continuity and momentum equations, together with Poisson's equation. The 3D wave equation reveals the formation of a braided or twisted ESIC wave structure carrying OAM. The braided or twisted ESIC wave structure can trap and transport plasma particles in magnetoplasmas, such as those in Saturn's F-ring and in the forthcoming magnetized dusty plasma experiments. PMID:23410477
NASA Astrophysics Data System (ADS)
Bruno, Oscar P.; Cubillos, Max
2016-02-01
This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas-Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are "quasi-unconditionally stable" in the following sense: each algorithm is stable for all couples (h , Δt)of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form (0 ,Mh) × (0 ,Mt). In other words, for each fixed value of Δt below a certain threshold, the Navier-Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier-Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier-Stokes solvers for which second-order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions.
A simple and direct method for generating travelling wave solutions for nonlinear equations
Bazeia, D. Das, Ashok; Silva, A.
2008-05-15
We propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method.
Exact Traveling Wave Solutions of a Higher-Dimensional Nonlinear Evolution Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy; Wazzan, Luwai
The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh-coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
Grating formation by a high power radio wave in near-equator ionosphere
Singh, Rohtash; Sharma, A. K.; Tripathi, V. K.
2011-11-15
The formation of a volume grating in the near-equator regions of ionosphere due to a high power radio wave is investigated. The radio wave, launched from a ground based transmitter, forms a standing wave pattern below the critical layer, heating the electrons in a space periodic manner. The thermal conduction along the magnetic lines of force inhibits the rise in electron temperature, limiting the efficacy of heating to within a latitude of few degrees around the equator. The space periodic electron partial pressure leads to ambipolar diffusion creating a space periodic density ripple with wave vector along the vertical. Such a volume grating is effective to cause strong reflection of radio waves at a frequency one order of magnitude higher than the maximum plasma frequency in the ionosphere. Linearly mode converted plasma wave could scatter even higher frequency radio waves.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation
NASA Astrophysics Data System (ADS)
Whitfield, A. J.; Johnson, E. R.
2015-05-01
The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.
Whitfield, A J; Johnson, E R
2015-05-01
The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting. PMID:26066112
Fractal ladder models and power law wave equations
Kelly, James F.; McGough, Robert J.
2009-01-01
The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816
Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2014-09-01
In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts-the linear equation and the nonlinear equation-then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method.
Group classification and conservation laws of anisotropic wave equations with a source
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.; Gandarias, M. L.; Galiakberova, L. R.; Bruzon, M. S.; Avdonina, E. D.
2016-08-01
Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.
NASA Astrophysics Data System (ADS)
Jia, Xuanji; Zhou, Yong
2015-09-01
We prove that a weak solution (u, b) to the MHD equations is smooth on (0, T ] if \\text{M}\\in {{L}α}≤ft(0,T;{{L}γ}≤ft({{{R}}3}\\right)\\right) with 2/α +3/γ =2 , 1≤slant α <∞ and 3/2<γ ≤slant ∞ , where \\text{M} is a 3× 3 mixture matrix (see its definition below). As we will explain later, this kind of regularity criteria is more likely to capture the nature of the coupling effects between the fluid velocity and the magnetic field in the evolution of the MHD flows. Moreover, the condition on \\text{M} is scaling invariant, i.e. it is of Ladyzhenskaya-Prodi-Serrin type.
NASA Astrophysics Data System (ADS)
Seadawy, Aly R.
2015-12-01
The propagation of dust-ion-acoustic waves with high-energy electrons and positrons in three-dimensional is considered. The Zakharov-Kuznetsov-Burgers (ZKB) equations for the dust-ion-acoustic waves in dusty plasmas is obtained. The conservations laws and integrals of motion for the ZKB equation are deduced. In the present study, by applying the modified direct algebraic method, we found the electric field potential, electric field and quantum statistical pressure in form water wave solutions for three-dimensional ZKB equation. The solutions for the ZKB equation are obtained precisely and efficiency of the method can be demonstrated. The stability of the obtained solutions and the movement role of the waves by making the graphs of the exact solutions are discussed and analyzed.
Field verification of Wave Equation tidal dynamics in the English Channel and southern North Sea
NASA Astrophysics Data System (ADS)
Werner, Francisco E.; Lynch, Daniel R.
Finite element results obtained with the implicit Wave Equation algorithm are compared with field data in a blind (uncalibrated) verification exercise. The study area comprises the English Channel and the southern North Sea.
PLOT3D/AMES, UNIX SUPERCOMPUTER AND SGI IRIS VERSION (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, SGI IRIS VERSION (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, SGI IRIS VERSION (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, UNIX SUPERCOMPUTER AND SGI IRIS VERSION (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
Klein-Gordon equation and reflection of Alfven waves in nonuniform media
NASA Technical Reports Server (NTRS)
Musielak, Z. E.; Fontenla, J. M.; Moore, R. L.
1992-01-01
A new analytical approach is presented for assessing the reflection of linear Alfven waves in smoothly nonuniform media. The general one-dimensional case in Cartesian coordinates is treated. It is shown that the wave equations, upon transformation into the form of the Klein-Gordon equation, display a local critical frequency for reflection. At any location in the medium, reflection becomes strong as the wave frequency descends past this characteristic frequency set by the local nonuniformity of the medium. This critical frequecy is given by the transformation as an explicit function of the Alfven velocity and its first and second derivatives, and hence as an explicit spatial function. The transformation thus directly yields, without solution of the wave equations, the location in the medium at which an Alfven wave of any given frequency becomes strongly reflected and has its propagation practically cut off.
ERIC Educational Resources Information Center
Hastings, S. K.
2002-01-01
Discusses 3 D imaging as it relates to digital representations in virtual library collections. Highlights include X-ray computed tomography (X-ray CT); the National Science Foundation (NSF) Digital Library Initiatives; output peripherals; image retrieval systems, including metadata; and applications of 3 D imaging for libraries and museums. (LRW)
Nonlocal Symmetries, Explicit Solutions, and Wave Structures for the Korteweg-de Vries Equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Fei, Jin-Xi
2016-08-01
From the known Lax pair of the Korteweg-de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. PMID:27586629
Simple equations guide high-frequency surface-wave investigation techniques
Xia, J.; Xu, Y.; Chen, C.; Kaufmann, R.D.; Luo, Y.
2006-01-01
We discuss five useful equations related to high-frequency surface-wave techniques and their implications in practice. These equations are theoretical results from published literature regarding source selection, data-acquisition parameters, resolution of a dispersion curve image in the frequency-velocity domain, and the cut-off frequency of high modes. The first equation suggests Rayleigh waves appear in the shortest offset when a source is located on the ground surface, which supports our observations that surface impact sources are the best source for surface-wave techniques. The second and third equations, based on the layered earth model, reveal a relationship between the optimal nearest offset in Rayleigh-wave data acquisition and seismic setting - the observed maximum and minimum phase velocities, and the maximum wavelength. Comparison among data acquired with different offsets at one test site confirms the better data were acquired with the suggested optimal nearest offset. The fourth equation illustrates that resolution of a dispersion curve image at a given frequency is directly proportional to the product of a length of a geophone array and the frequency. We used real-world data to verify the fourth equation. The last equation shows that the cut-off frequency of high modes of Love waves for a two-layer model is determined by shear-wave velocities and the thickness of the top layer. We applied this equation to Rayleigh waves and multi-layer models with the average velocity and obtained encouraging results. This equation not only endows with a criterion to distinguish high modes from numerical artifacts but also provides a straightforward means to resolve the depth to the half space of a layered earth model. ?? 2005 Elsevier Ltd. All rights reserved.
Automating adjoint wave-equation travel-time tomography using scientific workflow
NASA Astrophysics Data System (ADS)
Zhang, Xiaofeng; Chen, Po; Pullammanappallil, Satish
2013-10-01
Recent advances in commodity high-performance computing technology have dramatically reduced the computational cost for solving the seismic wave equation in complex earth structure models. As a consequence, wave-equation-based seismic tomography techniques are being actively developed and gradually adopted in routine subsurface seismic imaging practices. Wave-equation travel-time tomography is a seismic tomography technique that inverts cross-correlation travel-time misfits using full-wave Fréchet kernels computed by solving the wave equation. This technique can be implemented very efficiently using the adjoint method, in which the misfits are back-propagated from the receivers (i.e., seismometers) to produce the adjoint wave-field and the interaction between the adjoint wave-field and the forward wave-field from the seismic source gives the gradient of the objective function. Once the gradient is available, a gradient-based optimization algorithm can then be adopted to produce an optimal earth structure model that minimizes the objective function. This methodology is conceptually straightforward, but its implementation in practical situations is highly complex, error-prone and computationally demanding. In this study, we demonstrate the feasibility of automating wave-equation travel-time tomography based on the adjoint method using Kepler, an open-source software package for designing, managing and executing scientific workflows. The workflow technology allows us to abstract away much of the complexity involved in the implementation in a manner that is both robust and scalable. Our automated adjoint wave-equation travel-time tomography package has been successfully applied on a real active-source seismic dataset.
NASA Astrophysics Data System (ADS)
Fortes, A. Dominic; Suard, Emmanuelle; Lemée-Cailleau, Marie-Hélène; Pickard, Christopher J.; Needs, Richard J.
2009-10-01
We describe the results of a neutron powder diffraction study of perdeuterated ammonia monohydrate (AMH, ND3ṡD2O) carried out in the range 102
equation of state of AMH I has parameters, V0=248.00(2) Å3, K0=7.33(3) GPa with the first pressure derivative of K0 fixed at the value obtained in ab initio calculations, (∂K0/∂P)T=K0'=5.3; the implied value of the second derivative is therefore (∂2K0/∂P2)T=K0″=-0.94(1) GPa-1. At 351 MPa, we observed that the transition from AMH I to AMH II occurred over a period of 90 min, with an associated reduction in molar volume of 4.6% and an increase in the incompressibility of 19.6%.
Zaeytijd, J. de Bogaert, I.; Franchois, A.
2008-07-01
Electromagnetic scattering problems involving inhomogeneous objects can be numerically solved by applying a Method of Moments discretization to the volume integral equation. For electrically large problems, the iterative solution of the resulting linear system is expensive, both computationally and in memory use. In this paper, a hybrid MLFMA-FFT method is presented, which combines the fast Fourier transform (FFT) method and the High Frequency Multilevel Fast Multipole Algorithm (MLFMA) in order to reduce the cost of the matrix-vector multiplications needed in the iterative solver. The method represents the scatterers within a set of possibly disjoint identical cubic subdomains, which are meshed using a uniform cubic grid. This specific mesh allows for the application of FFTs to calculate the near interactions in the MLFMA and reduces the memory cost considerably, since the aggregation and disaggregation matrices of the MLFMA can be reused. Additional improvements to the general MLFMA framework, such as an extention of the FFT interpolation scheme of Sarvas et al. from the scalar to the vectorial case in combination with a more economical representation of the radiation patterns on the lowest level in vector spherical harmonics, are proposed and the choice of the subdomain size is discussed. The hybrid method performs better in terms of speed and memory use on large sparse configurations than both the FFT method and the HF MLFMA separately and it has lower memory requirements on general large problems. This is illustrated on a number of representative numerical test cases.