Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation
Swager, Melissa; Gray, Leonard J; Nintcheu Fata, Sylvain
2010-01-01
A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.
NASA Astrophysics Data System (ADS)
Klibanov, Michael V.; Romanov, Vladimir G.
2016-01-01
The 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. Applications are in imaging of nanostructures and biological cells. The main difference with the conventional inverse scattering problems is that only the modulus of the scattering wave field is measured. The phase is not measured. The initializing wave field is the incident plane wave. On the other hand, in the previous recent works of the authors about the ‘phaseless topic’ the case of the point source was considered (Klibanov and Romanov 2015 J. Inverse Ill-Posed Problem 23 415-28 J. Inverse Ill-Posed Problem 23 187-93). Two reconstruction procedures are developed.
Accelerated Schwarz iterations for Helmholtz equation
NASA Astrophysics Data System (ADS)
Nagid, Nabila; Belhadj, Hassan; Amattouch, Mohamed Ridouan
2017-01-01
In this paper, the Restricted additive Schwarz (RAS) method is applied to solve Helmholtz equation. To accelerate the RAS iterations, we propose to apply the vector ɛ-algorithm. Some convergence analysis of the proposed method is presented, and applied succeffully to Helmholtz problem. The obtained results show the efficiency of the proposed approach. Moreover, the algorithm yields much faster convergence than the classical Schwarz iterations.
Preconditioning the Helmholtz Equation for Rigid Ducts
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.; Kreider, Kevin L.
1998-01-01
An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.
Iterative solution of the Helmholtz equation
Larsson, E.; Otto, K.
1996-12-31
We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.
Multigrid and cyclic reduction applied to the Helmholtz equation
NASA Technical Reports Server (NTRS)
Brackenridge, Kenneth
1993-01-01
We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction (CR) is employed to facilitate the design of improved multigrid (MG) components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.
Bistable dark solitons of a cubic-quintic Helmholtz equation
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-05-15
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.
Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation
NASA Technical Reports Server (NTRS)
Fu, L. S.; Mura, T.
1982-01-01
Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.
Precise evaluation of the Helmholtz equation for optical propagation.
Pond, John E; Sutton, George W
2015-01-01
A precise computational integration of the Helmholtz equation was performed for laser propagation of an electromagnetic wave with no approximations or linearization. This computation integration was performed using 64-bit processors. This is illustrated for a uniform monochromatic beam from a circular aperture that has a uniform intensity. It predicts many Arago spots and near-field intensity fluctuations for a large ratio of aperture size to wavelength and converges to the usual Airy pattern in the far field.
Exact nonparaxial beams of the scalar Helmholtz equation.
Rodríguez-Morales, Gustavo; Chávez-Cerda, Sabino
2004-03-01
It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For what is believed to be the first time, their beam behavior is investigated and their corresponding parameters are defined. Using the fact that the beam width of the family of paraxial Gaussian beams is described by a hyperbola, we formally establish the connection between the physical parameters of nonparaxial spheroidal beam solutions and those of paraxial beams. These results are also helpful for investigating exact vector nonparaxial beams.
A double-sweeping preconditioner for the Helmholtz equation
NASA Astrophysics Data System (ADS)
Eslaminia, Mehran; Guddati, Murthy N.
2016-06-01
A new preconditioner is developed to increase the efficiency of iterative solution of the Helmholtz equation. The key idea of the proposed preconditioner is to split the domain of interest into smaller subdomains and sequentially approximate the forward and backward components of the solution. The sequential solution is facilitated by approximate interface conditions that ignore the effect of multiple reflections. The efficiency of the proposed method is tested using various 2-D heterogeneous media. We observe that the proposed preconditioner results in good convergence, with number of iterations growing very slowly with increasing frequency. We also note that the mesh size and number of subdomains do not affect the convergence rate. Finally, we find that the overall computational time is much smaller than that of the sweeping preconditioner.
Inverse obstacle problem for the scalar Helmholtz equation
NASA Astrophysics Data System (ADS)
Crosta, Giovanni F.
1994-07-01
The method presented is aimed at identifying the shape of an axially symmetric, sound soft acoustic scatterer from knowledge of the incident plane wave and of the scattering amplitude. The method relies on the approximate back propagation (ABP) of the estimated far field coefficients to the obstacle boundary and iteratively minimizes a boundary defect, without the addition of any penalty term. The ABP operator owes its structure to the properties of complete families of linearly independent solutions of Helmholtz equation. If the obstacle is known, as it happens in simulations, the theory also provides some independent means of predicting the performance of the ABP method. The ABP algorithm and the related computer code are outlined. Several reconstruction examples are considered, where noise is added to the estimated far field coefficients and other errors are deliberately introduced in the data. Many numerical and graphical results are provided.
Reck, Kasper; Thomsen, Erik V; Hansen, Ole
2011-01-31
The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.
A numerical method for inverse source problems for Poisson and Helmholtz equations
NASA Astrophysics Data System (ADS)
Hamad, A.; Tadi, M.
2016-11-01
This paper is concerned with an iterative algorithm for inverse evaluation of the source function for two elliptic systems. The algorithm starts with an initial guess for the unknown source function, obtains a background field and, obtains the working equations for the error field. The correction to the assumed value appears as a source term for the error field. It formulates two well-posed problems for the error field which makes it possible to obtain the correction term. The algorithm can also recover the source function with partial data at the boundary. We consider 2-D as well as 3-D domains. The method can be applied to both Poisson and Helmholtz operators. Numerical results indicate that the algorithm can recover close estimates of the unknown source functions based on measurements collected at the boundary.
A note on singularities of the 3-D Euler equation
NASA Technical Reports Server (NTRS)
Tanveer, S.
1994-01-01
In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.
An invariant shape representation using the anisotropic Helmholtz equation.
Joshi, A A; Ashrafulla, S; Shattuck, D W; Damasio, H; Leahy, R M
2012-01-01
Analyzing geometry of sulcal curves on the human cortical surface requires a shape representation invariant to Euclidean motion. We present a novel shape representation that characterizes the shape of a curve in terms of a coordinate system based on the eigensystem of the anisotropic Helmholtz equation. This representation has many desirable properties: stability, uniqueness and invariance to scaling and isometric transformation. Under this representation, we can find a point-wise shape distance between curves as well as a bijective smooth point-to-point correspondence. When the curves are sampled irregularly, we also present a fast and accurate computational method for solving the eigensystem using a finite element formulation. This shape representation is used to find symmetries between corresponding sulcal shapes between cortical hemispheres. For this purpose, we automatically generate 26 sulcal curves for 24 subject brains and then compute their invariant shape representation. Left-right sulcal shape symmetry as measured by the shape representation's metric demonstrates the utility of the presented invariant representation for shape analysis of the cortical folding pattern.
NASA Astrophysics Data System (ADS)
Luo, Songting; Qian, Jianliang; Burridge, Robert
2014-08-01
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian computational geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green functions of Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the new method is that the Huygens-Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics associated with the usual geometrical-optics ansatz can be treated automatically. The second novelty is that a butterfly algorithm is adapted to carry out the matrix-vector products induced by the Huygens-Kirchhoff integration in O(Nlog N) operations, where N is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. To reduce the storage of the resulting traveltime and amplitude tables, we compress each table into a linear combination of tensor-product based multivariate Chebyshev polynomials so that the information of each table is encoded into a small number of Chebyshev coefficients. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green functions of the Helmholtz equation for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green function in nearly optimal complexity in terms of the total number of mesh points, where the prefactor of the complexity only depends on the specified accuracy and is independent of the frequency parameter. Both two-dimensional (2-D) and three-dimensional (3
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.
A spectral boundary integral equation method for the 2-D Helmholtz equation
NASA Technical Reports Server (NTRS)
Hu, Fang Q.
1994-01-01
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.
SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.
Wan, Xiaohai; Li, Zhilin
2012-06-01
Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.
Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C
2015-01-01
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.
Li,Jing; Tu, Xuemin
2008-12-10
A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite system of linear equations, which arises from the finite element discretization of the Helmholtz equation of time-harmonic wave propagation in a bounded interior domain. The proposed BDDC algorithm is closely related to the dual-primal finite element tearing and interconnecting algorithm for solving Helmholtz equations (FETI-DPH). Under the condition that the diameters of the subdomains are small enough, the rate of convergence is established which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with the decrease of the subdomain diameters. These results are supported by numerical experiments of solving a Helmholtz equation on a two-dimensional square domain.
Active exterior cloaking for the 2D Laplace and Helmholtz equations.
Vasquez, Fernando Guevara; Milton, Graeme W; Onofrei, Daniel
2009-08-14
A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is close to 1 in a disk and close to 0 in another disk, and such a polynomial is constructed. For the 2D Helmholtz equation it is numerically shown that three exterior cloaking devices placed around the object suffice to hide it.
Wavenumber Explicit Analysis for a DPG Method for the Multidimensional Helmholtz Equation
2011-07-01
Application to the Helmholtz equation. We consider a bounded domain Ω ⊂ Rn (n ≥ 2) with Lipschitz boundary. Let f ∈ L2(Ω) and g ∈ H−1/2(∂Ω). We...Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?, SIAM Rev., 42 (2000), pp. 451–484 ( electronic ...equations, Electron . Trans. Numer. Anal., 6 (1997), pp. 162–181 ( electronic ). Special issue on multilevel methods (Copper Mountain, CO, 1997). [4] O
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
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.
Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region
NASA Technical Reports Server (NTRS)
Fu, L. S.; Mura, T.
1983-01-01
Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.
NASA Astrophysics Data System (ADS)
Bour, M.; Toumanari, A.; Khatib, D.
2007-04-01
This paper presents the application of the Finite Element Method FEM to the resolution of system Helmholtz coupled equations that has been obtained in the coaxial waveguides containing magnetic anisotropic materials with loss. This application is based on variational method which necessitates the construction of functional stationary written in the form of integral equation and dependent on the electromagnetic fields. After being minimized, this functional leads to algebraic equation system to which we can apply many numerical resolution algorithms. The electromagnetic study of the waveguide led us to a system of Helmholtz coupled equations which is difficult to be solved analytically. Our software code allows us to determine the electromagnetic field distribution in all points of the coaxial waveguide. The result has been validated when the coaxial waveguide was entirely loaded with air. This software has later been applied when the waveguide was partially filled with a magnetic anisotropic material with loss (\\varepsilon_r, overline{overline{μ_r}}).
On the solution of the Helmholtz equation on regions with corners.
Serkh, Kirill; Rokhlin, Vladimir
2016-08-16
In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method.
Belai, Oleg V; Frumin, Leonid L; Podivilov, Evgeny V; Shapiro, David A
2008-09-15
The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has Töplitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
NASA Technical Reports Server (NTRS)
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
The arithmetic mean iterative method for solving 2D Helmholtz equation
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Suleiman, Mohamed; Dass, Sarat Chandra; Singh, Narinderjit Singh Sawaran
2014-10-01
In this paper, application of the Arithmetic Mean (AM) iterative method is extended by solving second order finite difference algebraic equations. The performance of AM method in solving second order finite difference algebraic equations is comparatively studied by their application on two-dimensional Helmholtz equation. Numerical results of AM method in solving two test problems are included and compared with the standard Gauss-Seidel (GS) method. Based on the numerical results obtained, the results show that AM method is better than GS method in the sense of number of iterations and CPU time.
Fathi, S. M. Saberi
2010-12-15
In this paper we first show in the framework of quaternion analysis how the fundamental solutions of the Dirac operators with vector potential can be obtained. Then, we use the obtained results to present a derivation of the exact analytic Green function for the Helmholtz equation, i.e., ({Delta}+|a(x)|{sup 2})G{sub 0}(x)={delta}(x), for the case a(x) is a monogenic (analytic) vector potential.
A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media
NASA Astrophysics Data System (ADS)
Osnabrugge, Gerwin; Leedumrongwatthanakun, Saroch; Vellekoop, Ivo M.
2016-10-01
We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1, 2, and 3-dimensional systems.
NASA Astrophysics Data System (ADS)
Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.
2017-02-01
A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.
Wu, Sean F; Zhao, Xiang
2002-07-01
A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.
NASA Astrophysics Data System (ADS)
Wu, Sean F.; Zhao, Xiang
2002-07-01
A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated. copyright 2002 Acoustical Society of America.
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.
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.
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
NASA Technical Reports Server (NTRS)
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.
Xu, Zhengfu; Bao, Gang
2010-11-01
A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.
Vortex lattices generated by the Kelvin-Helmholtz instability in the Gross-Pitaevskii equation
Ohta, A.; Kashiwa, R.; Sakaguchi, H.
2010-11-15
Vortex streets are formed from sheared initial conditions in classical fluids even without viscosity, which is called the Kelvin-Helmholtz instability. We demonstrate that similar vortex streets are generated from sheared initial conditions by the direct numerical simulation of the Gross-Pitaevskii (GP) equation which describes the dynamics of the Bose-Einstein condensates. Furthermore, we show the vortex-lattice formation from sheared initial conditions analogous to the rigid-body rotation in the GP equation under a rotating harmonic potential. The vortex-lattice formation by the dynamical instability in the system without energy dissipation differs from the vortex-lattice formation process by the imaginary time evolution of the GP equation where the lowest energy state is obtained.
NASA Astrophysics Data System (ADS)
Krutitskii, P. A.
2013-10-01
The Dirichlet problem for the dissipative Helmholtz equation is considered in the exterior of non-closed Lipschitz surfaces in R3. Theorems on existence and uniqueness of a weak solution of the problem are proved. The problem is reduced to a uniquely solvable integral equation. The integral representation of a weak solution is obtained.
Gumerov, Nail A; Duraiswami, Ramani
2009-01-01
The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.
Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation
NASA Astrophysics Data System (ADS)
Sheikh, A. H.; Lahaye, D.; Garcia Ramos, L.; Nabben, R.; Vuik, C.
2016-10-01
Many important physical phenomena can be described by the Helmholtz equation. We investigate to what extent the convergence of the shifted Laplacian preconditioner for the Helmholtz equation can be accelerated using deflation with multigrid vectors. We therefore present a unified framework for two published algorithms. The first deflates the preconditioned operator and requires no further preconditioning. The second deflates the original operator and combines deflation and preconditioning in a multiplicative fashion. We pursue two scientific contributions. First we show, using a model problem analysis, that both algorithms cluster the eigenvalues. The new and key insight here is that the near-kernel of the coarse grid operator causes a limited set of eigenvalues to shift away from the center of the cluster with a distance proportional to the wave number. This effect is less pronounced in the first algorithmic variant at the expense of a higher computational cost. In the second contribution we quantify for the first time the large amount of reduction in CPU-time that results from the clustering of eigenvalues and the reduction in iteration count. We report to this end on the findings of an implementation in PETSc on two and three-dimensional problems with constant and variable wave number.
NASA Astrophysics Data System (ADS)
Sheng, Qin; Sun, Hai-wei
2016-11-01
This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman-Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.
NASA Astrophysics Data System (ADS)
Niino, Kazuki; Nishimura, Naoshi
2012-01-01
Solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics, electromagnetics and mechanics. In our previous studies we have developed a periodic fast multipole method (FMM) as a fast solver of wave problems in periodic domains. It has been found, however, that the convergence of the iterative solvers for linear equations slows down when the solutions show anomalies related to the periodicity of the problems. In this paper, we propose preconditioning schemes based on Calderon's formulae to accelerate convergence of iterative solvers in the periodic FMM for Helmholtz' equations. The proposed preconditioners can be implemented more easily than conventional ones. We present several numerical examples to test the performance of the proposed preconditioners. We show that the effectiveness of these preconditioners is definite even near anomalies.
Convergence of the point vortex method for the 3-D Euler equations
NASA Astrophysics Data System (ADS)
Hou, Thomas Y.; Lowengrub, John
1990-11-01
Consistency, stability, and convergence of a point vortex approximation to the 3-D incompressible Euler equations with smooth solutions. The 3-D algorithm considered is similar to the corresponding 3-D vortex are proved blob algorithm introduced by Beale and Majda; The discretization error is second-order accurate. Then the method is stable in l sup p norm for the particle trajectories and in w sup -1,p norm for discrete vorticity. Consequently, the method converges up to any time for which the Euler equations have a smooth solution. One immediate application of the convergence result is that the vortex filament method without smoothing also converges.
On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method
Wu
2000-05-01
This paper presents analyses and implementation of the reconstruction of acoustic pressure fields radiated from a general, three-dimensional complex vibrating structure using the Helmholtz equation least-squares (HELS) method. The structure under consideration emulates a full-size four-cylinder engine. To simulate sound radiation from a vibrating structure, harmonic excitations are assumed to act on arbitrarily selected surfaces. The resulting vibration responses are solved by the commercial FEM (finite element method) software I-DEAS. Once the normal component of the surface velocity distribution is determined, the surface acoustic pressures are calculated using standard boundary element method (BEM) codes. The radiated acoustic pressures over several planar surfaces at certain distances from the source are calculated by the Helmholtz integral formulation. These field pressures are taken as the input to the HELS formulation to reconstruct acoustic pressures on the entire source surface, as well as in the field. The reconstructed acoustic pressures thus obtained are then compared with benchmark values. Numerical results demonstrate that good agreements can be obtained with relatively few expansion functions. The HELS method is shown to be very effective in the low-to-mid frequency regime, and can potentially become a powerful noise diagnostic tool.
NASA Astrophysics Data System (ADS)
Lu, Wangtao; Qian, Jianliang; Burridge, Robert
2016-05-01
In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation can be viewed as an evolution equation in one of the spatial directions. With such applications in mind, starting from Babich's expansion, we develop a new high-order asymptotic method, which we dub the fast Huygens sweeping method, for solving point-source Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of this method is that we develop a new Eulerian approach to compute the asymptotics, i.e. the traveltime function and amplitude coefficients that arise in Babich's expansion, yielding a locally valid solution, which is accurate close enough to the source. The second novelty is that we utilize the Huygens-Kirchhoff integral to integrate many locally valid wavefields to construct globally valid wavefields. This automatically treats caustics and yields uniformly accurate solutions both near the source and remote from it. The third novelty is that the butterfly algorithm is adapted to accelerate the Huygens-Kirchhoff summation, achieving nearly optimal complexity O (Nlog N), where N is the number of mesh points; the complexity prefactor depends on the desired accuracy and is independent of the frequency. To reduce the storage of the resulting tables of asymptotics in Babich's expansion, we use the multivariable Chebyshev series expansion to compress each table by encoding the information into a small number of coefficients. The new method enjoys the following desired features. First, it precomputes the asymptotics in Babich's expansion, such as traveltime and amplitudes. Second, it takes care of caustics automatically. Third, it can compute the point-source Helmholtz solution for many different sources at many frequencies simultaneously. Fourth, for a specified number of points per wavelength, it can construct the wavefield in nearly optimal complexity in terms
An exact solution of the 3-D Navier-Stokes equation
NASA Astrophysics Data System (ADS)
Muriel, A.
2011-01-01
We continue our work (A. Muriel and M. Dresden, Physica D 101, 299, 1997) to calculate the time evolution of the one-particle distribution function. An improved operator formalism, heretofore unused, is applied for spatially uniform initial data. We then choose a Gaussian pair potential between particles. With these two conditions, the velocity fields, energy and pressure are calculated exactly. All stipulations of the Clay Mathematics Institute for proposed solutions of the 3-D Navier-Stokes Equation [ http://www.claymath.org/millennium/Navier-Stokes_Equations/navierstokes.pdf] are satisfied by our time evolution equation. We then substitute our results for the velocity fields into the 3-D Navier-Stokes Equation and calculate the pressure. The results from our time evolution equation and the prescribed pressure from the Navier-Stokes Equation constitute an exact solution to the Navier-Stokes Equation. No turbulence is obtained from the solution.
On the Dynamic Programming Approach for the 3D Navier-Stokes Equations
Manca, Luigi
2008-06-15
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.
Effect of triangular element orientation on finite element solutions of the Helmholtz equation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1986-01-01
The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is examined. Nonsymmetric element patterns are found to give generally poor results in the model problems investigated, particularly for cases where standing waves exist. For a fixed number of vertical elements, the results showed that symmetric element patterns give much better agreement with corresponding exact analytical results. In laminated wave guide application, the symmetric pyramid pattern is convenient to use and is shown to give excellent results.
Ong, Eng Teo; Lee, Heow Pueh; Lim, Kian Meng
2004-09-01
This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.
Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.
April, Alexandre
2011-10-01
The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.
NASA Astrophysics Data System (ADS)
Engquist, Björn; Frederick, Christina; Huynh, Quyen; Zhou, Haomin
2017-06-01
We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial, and military applications. The forward model incorporates multiscale simulations, by coupling Helmholtz equations and geometrical optics for a wide range of spatial scales in the seafloor geometry. This allows for detailed recovery of seafloor parameters including material type. Simulated backscattered data is generated using numerical microlocal analysis techniques. In order to lower the computational cost of the large-scale simulations in the inversion process, we take advantage of a pre-computed library of representative acoustic responses from various seafloor parameterizations.
Wave Gradiometry and Helmholtz Equation Solutions Applied to USArray across the Contiguous U.S.
NASA Astrophysics Data System (ADS)
Liu, Y.; Holt, W. E.
2015-12-01
Wave gradiometry is an array processing technique utilizing the shape of seismic wavefields captured by USArray TA stations to determine fundamental wave propagation characteristics. We first explore a compatibility relation that links spatial gradients of the wavefield with the displacements and the time derivatives of displacements through two unknown coefficients Aand B, which are solved through iterative, damped least-square inversion, to provide estimates of phase velocity, back-azimuth, radiation pattern and geometrical spreading. We show that the A-coefficient corresponds to the gradient of logarithmic amplitude and the B-coefficient corresponds approximately to the local dynamic phase velocity. These vector fields are interpolated to explore a second compatibility relation through solutions to the Helmholtz equation. For most wavefields passing through the eastern U.S., we show that the A-coefficients are generally orthogonal to the B-coefficients. Where they are not completely orthogonal, there is a strong positive correlation between the gradients of B-coefficients and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We then obtain isotropic phase velocity maps across the contiguous United States for 20 - 150 s Rayleigh wave by stacking results from 700 earthquakes. The strong velocity variations in the western U.S. correlate well with known geological features and the am- plitude correction terms from Helmholtz equation solutions generally improve the resolution of small-scale structures for all periods analyzed. We also observe a velocity change along the approximate boundary of the early Paleozoic continental margin in the eastern U.S and two significant low velocity anomalies within the central Appalachians, one centered where Eocene basaltic volcanism has occurred, and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation.
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2016-11-01
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ^{*}, scattering phase function f, and anisotropy factor g. Discarding the operator term in the wave equation is shown to have a significant impact on f and g, yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓ_{c} is smaller than or comparable to the wavelength λ. More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ^{*} whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300% in the low-frequency regime, and still above 30% for ℓ_{c}/λ=10^{3} no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation
NASA Astrophysics Data System (ADS)
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2016-11-01
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r . In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ*, scattering phase function f , and anisotropy factor g . Discarding the operator term in the wave equation is shown to have a significant impact on f and g , yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓc is smaller than or comparable to the wavelength λ . More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ* whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300 % in the low-frequency regime, and still above 30 % for ℓc/λ =103 no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.
Helmholtz and parabolic equation solutions to a benchmark problem in ocean acoustics.
Larsson, Elisabeth; Abrahamsson, Leif
2003-05-01
The Helmholtz equation (HE) describes wave propagation in applications such as acoustics and electromagnetics. For realistic problems, solving the HE is often too expensive. Instead, approximations like the parabolic wave equation (PE) are used. For low-frequency shallow-water environments, one persistent problem is to assess the accuracy of the PE model. In this work, a recently developed HE solver that can handle a smoothly varying bathymetry, variable material properties, and layered materials, is used for an investigation of the errors in PE solutions. In the HE solver, a preconditioned Krylov subspace method is applied to the discretized equations. The preconditioner combines domain decomposition and fast transform techniques. A benchmark problem with upslope-downslope propagation over a penetrable lossy seamount is solved. The numerical experiments show that, for the same bathymetry, a soft and slow bottom gives very similar HE and PE solutions, whereas the PE model is far from accurate for a hard and fast bottom. A first attempt to estimate the error is made by computing the relative deviation from the energy balance for the PE solution. This measure gives an indication of the magnitude of the error, but cannot be used as a strict error bound.
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.
First-order system least-squares for the Helmholtz equation
Lee, B.; Manteuffel, T.; McCormick, S.; Ruge, J.
1996-12-31
We apply the FOSLS methodology to the exterior Helmholtz equation {Delta}p + k{sup 2}p = 0. Several least-squares functionals, some of which include both H{sup -1}({Omega}) and L{sup 2}({Omega}) terms, are examined. We show that in a special subspace of [H(div; {Omega}) {intersection} H(curl; {Omega})] x H{sup 1}({Omega}), each of these functionals are equivalent independent of k to a scaled H{sup 1}({Omega}) norm of p and u = {del}p. This special subspace does not include the oscillatory near-nullspace components ce{sup ik}({sup {alpha}x+{beta}y)}, where c is a complex vector and where {alpha}{sub 2} + {beta}{sup 2} = 1. These components are eliminated by applying a non-standard coarsening scheme. We achieve this scheme by introducing {open_quotes}ray{close_quotes} basis functions which depend on the parameter pair ({alpha}, {beta}), and which approximate ce{sup ik}({sup {alpha}x+{beta}y)} well on the coarser levels where bilinears cannot. We use several pairs of these parameters on each of these coarser levels so that several coarse grid problems are spun off from the finer levels. Some extensions of this theory to the transverse electric wave solution for Maxwell`s equations will also be presented.
NASA Astrophysics Data System (ADS)
Wang, Yanqing; Wu, Gang; Zhou, Daoguo
2016-12-01
By means of blow-up method and the special structure of the 3D viscous magnetohydrodynamics equations, we derive some interior regularity criteria in terms of horizontal part of the velocity with sufficiently small local scaled norm and both the vertical part of the velocity and the magnetic field with bounded local scaled norm for the suitable weak solutions to this system. As an application, this allows us to improve the previous limiting case for the regularity criterion about the MHD equations.
Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver
NASA Technical Reports Server (NTRS)
Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.
2000-01-01
USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.
NASA Astrophysics Data System (ADS)
Wichert, Viktoria; Arkenberg, Mario; Hauschildt, Peter H.
2016-10-01
Highly resolved state-of-the-art 3D atmosphere simulations will remain computationally extremely expensive for years to come. In addition to the need for more computing power, rethinking coding practices is necessary. We take a dual approach by introducing especially adapted, parallel numerical methods and correspondingly parallelizing critical code passages. In the following, we present our respective work on PHOENIX/3D. With new parallel numerical algorithms, there is a big opportunity for improvement when iteratively solving the system of equations emerging from the operator splitting of the radiative transfer equation J = ΛS. The narrow-banded approximate Λ-operator Λ* , which is used in PHOENIX/3D, occurs in each iteration step. By implementing a numerical algorithm which takes advantage of its characteristic traits, the parallel code's efficiency is further increased and a speed-up in computational time can be achieved.
3D linearized stability analysis of various forms of Burnett equations
NASA Astrophysics Data System (ADS)
Zhao, Wenwen; Chen, Weifang; Liu, Hualin; Agarwal, Ramesh K.
2014-12-01
Burnett equations were originally derived in 1935 by Burnett by employing the Chapman-Enskog expansion to Classical Boltzmann equation to second order in Knudsen number Kn. Since then several variants of these equations have been proposed in the literature; these variants have differing physical and numerical properties. In this paper, we consider three such variants which are known in the literature as `the Original Burnett (OB) equations', the Conventional Burnett (CB) equations' and the recently formulated by the authors `the Simplified Conventional (SCB) equations.' One of the most important issues in obtaining numerical solutions of the Burnett equations is their stability under small perturbations. In this paper, we perform the linearized stability (known as the Bobylev Stability) analysis of three-dimensional Burnett equations for all the three variants (OB, CB, and SCB) for the first time in the literature on this subject. By introducing small perturbations in the steady state flow field, the trajectory curve and the variation in attenuation coefficient with wave frequency of the characteristic equation are obtained for all the three variants of Burnett equations to determine their stability. The results show that the Simplified Conventional Burnett (SCB) equations are unconditionally stable under small wavelength perturbations. However, the Original Burnett (OB) and the Conventional Burnett (CB) equations are unstable when the Knudsen number becomes greater than a critical value and the stability condition worsens in 3D when compared to the stability condition for 1-D and 2-D equations. The critical Knudsen number for 3-D OB and CB equations is 0.061 and 0.287 respectively.
3D FEM-BEM-coupling method to solve magnetostatic Maxwell equations
NASA Astrophysics Data System (ADS)
Bruckner, Florian; Vogler, Christoph; Feischl, Michael; Praetorius, Dirk; Bergmair, Bernhard; Huber, Thomas; Fuger, Markus; Suess, Dieter
2012-05-01
3D magnetostatic Maxwell equations are solved using the direct Johnson-Nédélec FEM-BEM coupling method and a reduced scalar potential approach. The occurring BEM matrices are calculated analytically and approximated by H-matrices using the ACA+ algorithm. In addition a proper preconditioning method is suggested that allows to solve large-scale problems using iterative solvers.
On the breakdown of axisymmetric smooth solutions for the 3-D Euler equations
NASA Astrophysics Data System (ADS)
Chae, Dongho; Kim, Namkwon
1996-05-01
We refine the Beale-Kato-Majda criterion for the breakdown of smooth solutions of the 3-D incompressible Euler equations in the case of axisymmetry. In this case the angular component of vorticity in the cylindrical coordinates alone controls blow-up of the higher Sobolev norms of the velocity.
Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods
NASA Astrophysics Data System (ADS)
Ren, Z. X.; Zhang, S. Q.; Meng, J.
2017-02-01
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in a 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single-particle energy are smaller than 10-4 MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial-deformed, nonaxial-deformed, and octupole-deformed potential are provided and discussed.
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.
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
Scattering mean free path in continuous complex media: beyond the Helmholtz equation.
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2015-09-01
We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.
Scattering mean free path in continuous complex media: Beyond the Helmholtz equation
NASA Astrophysics Data System (ADS)
Baydoun, Ibrahim; Baresch, Diego; Pierrat, Romain; Derode, Arnaud
2015-09-01
We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.
The method of polarized traces for the 2D Helmholtz equation
NASA Astrophysics Data System (ADS)
Zepeda-Núñez, Leonardo; Demanet, Laurent
2016-03-01
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O (N/L), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N. The solver decomposes the domain into layers, and uses transmission conditions in boundary integral form to explicitly define "polarized traces", i.e., up- and down-going waves sampled at interfaces. Local direct solvers are used in each layer to precompute traces of local Green's functions in an embarrassingly parallel way (the offline part), and incomplete Green's formulas are used to propagate interface data in a sweeping fashion, as a preconditioner inside a GMRES loop (the online part). Adaptive low-rank partitioning of the integral kernels is used to speed up their application to interface data. The method uses second-order finite differences. The complexity scalings are empirical but motivated by an analysis of ranks of off-diagonal blocks of oscillatory integrals. They continue to hold in the context of standard geophysical community models such as BP and Marmousi 2, where convergence occurs in 5 to 10 GMRES iterations. While the parallelism in this paper stems from decomposing the domain, we do not explore the alternative of parallelizing the systems solves with distributed linear algebra routines.
On the choice of expansion functions in the Helmholtz equation least-squares method.
Semenova, Tatiana; Wu, Sean F
2005-02-01
This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.
Lu, Huancai; Wu, Sean F
2009-03-01
The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.
Numerical modeling of Kelvin-Helmholtz instability by using potential equation
NASA Astrophysics Data System (ADS)
Ahmadi, Somayeh
2012-11-01
This paper presents a potential flow numerical solution for the Kelvin-Helmholtz Instability (KHI) problem of an incompressible two-phase immiscible fluid in a stratified shear flow. As a problem: the two-fluid model becomes illposed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the potential equation method for the time derivatives in conjunction with the two-fluid model is analyzed. The normal stress balance (with the normal viscous stress) at the interface for the two-fluid model is carefully implemented to minimize its effect on numerical stability. Von Neumann stability analysis shows that: stability condition for two-fluid with equal kinematic viscosity ratio and inviscid flow, supply numerical stability. Excellent agreement has obtained according to analytical result that existing of imaginary part in solution which specialized this method. The numerical algorithm presented in this work can easily handle two-phase fluid flow with various density and viscosity ratios in rectangular channel. Simulation of this model has implemented by writing a code in FORTRAN programming.
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.
NASA Astrophysics Data System (ADS)
Zhai, Xiaoping; Yin, Zhaoyang
2017-02-01
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (2012) [2], and (2013) [3] to a lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as L2 in R3. Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations.
3-D zebrafish embryo image filtering by nonlinear partial differential equations.
Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro
2007-01-01
We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.
The Beale-Kato-Majda Criterion for the 3D Magneto-Hydrodynamics Equations
NASA Astrophysics Data System (ADS)
Chen, Qionglei; Miao, Changxing; Zhang, Zhifei
2007-11-01
We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, namely sup_{jinmathbb{Z}}int_0^T\\|Δ_j(nabla× u)\\|_infty dt, where Δ j is the frequency localization operator in the Littlewood-Paley decomposition.
NuSol - Numerical solver for the 3D stationary nuclear Schrödinger equation
NASA Astrophysics Data System (ADS)
Graen, Timo; Grubmüller, Helmut
2016-01-01
The classification of short hydrogen bonds depends on several factors including the shape and energy spacing between the nuclear eigenstates of the hydrogen. Here, we describe the NuSol program in which three classes of algorithms were implemented to solve the 1D, 2D and 3D time independent nuclear Schrödinger equation. The Schrödinger equation was solved using the finite differences based Numerov's method which was extended to higher dimensions, the more accurate pseudo-spectral Chebyshev collocation method and the sinc discrete variable representation by Colbert and Miller. NuSol can be applied to solve the Schrödinger equation for arbitrary analytical or numerical potentials with focus on nuclei bound by the potential of their molecular environment. We validated the methods against literature values for the 2D Henon-Heiles potential, the 3D linearly coupled sextic oscillators and applied them to study hydrogen bonding in the malonaldehyde derivate 4-cyano-2,2,6,6-tetramethyl-3,5-heptanedione. With NuSol, the extent of nuclear delocalization in a given molecular potential can directly be calculated without relying on linear reaction coordinates in 3D molecular space.
Analytical and numerical aspects in solving the controlled 3D Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
Fedele, R.; Jovanović, D.; De Nicola, S.; Eliasson, B.; Shukla, P. K.
2009-11-01
The results of recently developed investigations, that have been carried out within the framework of the controlling potential method (CPM), are reviewed. This method allows one to decompose a three dimensional (3D) Gross-Pitaevskii equation (GPE) into the pair of coupled Schrödinger-type equations. Under suitable mathematical conditions, the solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schrödinger equation (the transverse component of the GPE) coupled with a 1D nonlinear Schrödinger equation (the longitudinal component of the GPE). Such decomposition allows one to cast the solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. It is shown that the CPM can be used to obtain a new class of three-dimensional solitary waves solutions of the GPE, which governs the dynamics of Bose-Einstein condensates. By imposing an external controlling potential, the desired time-dependent shape of the localized BECs is obtained. The stability of the exact solutions was checked with direct simulations of the time -dependent, three-dimensional GPE. Our simulations show that the localized condensates are stable with respect to perturbed initial conditions.
Analytical and numerical aspects in solving the controlled 3D Gross-Pitaevskii equation
Fedele, R.; Jovanovic, D.; De Nicola, S.; Eliasson, B.; Shukla, P. K.
2009-11-10
The results of recently developed investigations, that have been carried out within the framework of the controlling potential method (CPM), are reviewed. This method allows one to decompose a three dimensional (3D) Gross-Pitaevskii equation (GPE) into the pair of coupled Schroedinger-type equations. Under suitable mathematical conditions, the solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schroedinger equation (the transverse component of the GPE) coupled with a 1D nonlinear Schroedinger equation (the longitudinal component of the GPE). Such decomposition allows one to cast the solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. It is shown that the CPM can be used to obtain a new class of three-dimensional solitary waves solutions of the GPE, which governs the dynamics of Bose-Einstein condensates. By imposing an external controlling potential, the desired time-dependent shape of the localized BECs is obtained. The stability of the exact solutions was checked with direct simulations of the time -dependent, three-dimensional GPE. Our simulations show that the localized condensates are stable with respect to perturbed initial conditions.
The regularized 3D Boussinesq equations with fractional Laplacian and no diffusion
NASA Astrophysics Data System (ADS)
Bessaih, H.; Ferrario, B.
2017-02-01
In this paper, we study the 3D regularized Boussinesq equations. The velocity equation is regularized à la Leray through a smoothing kernel of order α in the nonlinear term and a β-fractional Laplacian; we consider the critical case α + β =5/4 and we assume 1/2 < β <5/4. The temperature equation is a pure transport equation, where the transport velocity is regularized through the same smoothing kernel of order α. We prove global well posedness when the initial velocity is in Hr and the initial temperature is in H r - β for r > max (2 β , β + 1). This regularity is enough to prove uniqueness of solutions. We also prove a continuous dependence of solutions on the initial conditions.
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.
NASA Astrophysics Data System (ADS)
Li, Jingzhi; Liu, Hongyu; Rondi, Luca; Uhlmann, Gunther
2015-04-01
We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics. There are four major ingredients in our proposed theory: (1) The non-singular cloaking medium is obtained by the push-forwarding construction through a transformation that blows up a subset in the virtual space, where is an asymptotic regularization parameter. will degenerate to K 0 as , and in our theory K 0 could be any convex compact set in , or any set whose boundary consists of Lipschitz hypersurfaces, or a finite combination of those sets. (2) A general lossy layer with the material parameters satisfying certain compatibility integral conditions is employed right between the cloaked and cloaking regions. (3) The contents being cloaked could also be extremely general, possibly including, at the same time, generic mediums and, sound-soft, sound-hard and impedance-type obstacles, as well as some sources or sinks. (4) In order to achieve a cloaking device of compact size, particularly for the case when is not "uniformly small", an assembly-by-components, the (ABC) geometry is developed for both the virtual and physical spaces and the blow-up construction is based on concatenating different components. Within the proposed framework, we show that the scattered wave field corresponding to a cloaking problem will converge to u 0 as , with u 0 being the scattered wave field corresponding to a sound-hard K 0. The convergence result is used to theoretically justify the approximate full and partial invisibility cloaks, depending on the geometry of K 0. On the other hand, the convergence results are conducted in a much more general setting than what is needed for the invisibility cloaking, so they are of significant mathematical interest for their own sake. As for applications, we construct three types of full and partial cloaks. Some numerical experiments are
ben-Avraham, D; Fokas, A S
2001-07-01
A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.
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.
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.
Chamorro-Posada, P; McDonald, G S
2003-05-15
A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.
Statistical properties of the 3-D poor man's Navier--Stokes equation
NASA Astrophysics Data System (ADS)
McDonough, J. M.
2007-11-01
The poor man's Navier--Stokes (PMNS) equation is an efficiently-evaluated discrete dynamical system (DDS) derived directly from the Navier--Stokes (N.--S.) equations via a Galerkin procedure. The 2-D version of this DDS was introduced by McDonough and Huang, Int. J. Numer. Meth. Fluids (2004), where it was thoroughly analyzed for values of bifurcation parameters that might be associated with isotropic turbulence. Yang et al., AIAA J. (2003), demonstrated that the PMNS equation could be employed to accurately fit experimental data. These results suggest possible use of the PMNS equation as part of a subgrid-scale (SGS) model for LES formulated to capture effects of interactions between turbulence and other physics on unresolved scales. Here, we consider statistical properties of the 3-D PMNS equation to ascertain whether they are sufficiently close to those of physical N.--S. flows to warrant development of such models. In particular, we will present auto and cross correlation of velocity components, probability density functions, flatness and skewness of velocity derivatives, and scaling of longitudinal velocity structure functions of orders two, three, four and six. It will be demonstrated that PMNS equation statistics are generally in accord with those of the full N.--S. equations, and as a consequence this DDS could lead to very efficient LES SGS models able to replicate small-scale turbulence interactions with other physics.
Stability of Blowup for a 1D Model of Axisymmetric 3D Euler Equation
NASA Astrophysics Data System (ADS)
Do, Tam; Kiselev, Alexander; Xu, Xiaoqian
2016-10-01
The question of the global regularity versus finite- time blowup in solutions of the 3D incompressible Euler equation is a major open problem of modern applied analysis. In this paper, we study a class of one-dimensional models of the axisymmetric hyperbolic boundary blow-up scenario for the 3D Euler equation proposed by Hou and Luo (Multiscale Model Simul 12:1722-1776, 2014) based on extensive numerical simulations. These models generalize the 1D Hou-Luo model suggested in Hou and Luo Luo and Hou (2014), for which finite-time blowup has been established in Choi et al. (arXiv preprint. arXiv:1407.4776, 2014). The main new aspects of this work are twofold. First, we establish finite-time blowup for a model that is a closer approximation of the three-dimensional case than the original Hou-Luo model, in the sense that it contains relevant lower-order terms in the Biot-Savart law that have been discarded in Hou and Luo Choi et al. (2014). Secondly, we show that the blow-up mechanism is quite robust, by considering a broader family of models with the same main term as in the Hou-Luo model. Such blow-up stability result may be useful in further work on understanding the 3D hyperbolic blow-up scenario.
NASA Astrophysics Data System (ADS)
Kashirin, A. A.; Smagin, S. I.; Taltykina, M. Yu.
2016-04-01
Interior and exterior three-dimensional Dirichlet problems for the Helmholtz equation are solved numerically. They are formulated as equivalent boundary Fredholm integral equations of the first kind and are approximated by systems of linear algebraic equations, which are then solved numerically by applying an iteration method. The mosaic-skeleton method is used to speed up the solution procedure.
Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways
NASA Astrophysics Data System (ADS)
Ibison, Michael; Puthoff, Harold E.
2001-04-01
It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.
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.
NASA Astrophysics Data System (ADS)
Natarajan, Logesh Kumar
This dissertation presents a structure-borne noise analysis technology that is focused on providing a cost-effective noise reduction strategy. Structure-borne sound is generated or transmitted through structural vibration; however, only a small portion of the vibration can effectively produce sound and radiate it to the far-field. Therefore, cost-effective noise reduction is reliant on identifying and suppressing the critical vibration components that are directly responsible for an undesired sound. However, current technologies cannot successfully identify these critical vibration components from the point of view of direct contribution to sound radiation and hence cannot guarantee the best cost-effective noise reduction. The technology developed here provides a strategy towards identifying the critical vibration components and methodically suppressing them to achieve a cost-effective noise reduction. The core of this technology is Helmholtz equation least squares (HELS) based nearfield acoustic holography method. In this study, the HELS formulations derived in spherical co-ordinates using spherical wave expansion functions utilize the input data of acoustic pressures measured in the nearfield of a vibrating object to reconstruct the vibro-acoustic responses on the source surface and acoustic quantities in the far field. Using these formulations, three steps were taken to achieve the goal. First, hybrid regularization techniques were developed to improve the reconstruction accuracy of normal surface velocity of the original HELS method. Second, correlations between the surface vibro-acoustic responses and acoustic radiation were factorized using singular value decomposition to obtain orthogonal basis known here as the forced vibro-acoustic components (F-VACs). The F-VACs enables one to identify the critical vibration components for sound radiation in a similar manner that modal decomposition identifies the critical natural modes in a structural vibration. Finally
NASA Astrophysics Data System (ADS)
Olsen, Scott Charles
In this dissertation, new inverse scattering algorithms are derived for the Helmholtz equation using the Extended Born field model (eikonal rescattered field), and the angular spectrum (parabolic) layered field model. These two field models performed the 'best' of all the field models evaluated. Algorithms are solved with conjugate gradient methods. An advanced ultrasonic data acquisition system is also designed. Many different field models for use in a reconstruction algorithm are investigated. 'Layered' field models that mathematically partition the field calculation in layers in space possess the advantage that the field in layer n is calculated from the field in layer n - 1. Several of the 'layered' field models are investigated in terms of accuracy and computational complexity. Field model accuracy using field rescattering is also tested. The models investigated are the eikonal field model, the angular spectrum (AS) field model, and the parabolic field models known as the Split-Step Fast-Fourier Transform and the Crank-Nicolson algorithms. All of the 'layered' field models can be referred to as Extended Born field models since the 'layered' field models are more accurate than the Born approximated total field. The Rescattered Extended Born (eikonal rescattered field) Transmission Mode (REBTM) algorithm with the AS field model and the Nonrescattered AS Reconstruction (NASR) algorithm are tested with several types of objects: a single-layer cylinder, double-layer cylinders, two double-layer cylinders and the breast model. Both algorithms, REBTM and NASR work well; however, the NASR algorithm is faster and more accurate than the REBTM algorithm. The NASR algorithm is matched well with the requirements of breast model reconstructions. A major purpose of new scanner development is to collect both transmission and reflection data from multiple ultrasonic transducer arrays to test the next generation of reconstruction algorithms. The data acquisition system advanced
Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations
NASA Astrophysics Data System (ADS)
Kong, Huihui; Li, Hai-Liang
2017-02-01
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with γ -law pressure density function for 6/5 <γ ≤ 4/3. For stress-free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
Baruch, G; Fibich, G; Tsynkov, Semyon
2008-08-18
We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.
Ciraolo, Giulio Gargano, Francesco Sciacca, Vincenzo
2013-08-01
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.
2004-07-02
Helmholtz equation was introduced by Nedelec in 1980 [5]. These functions maintain tangential cell-to-cell continuity and are known as curl...Forghani functions [8], but have been modified to satisfy the Nedelec conditions [5]. Functions have been included up to order 4/5. For source-free...satisfy the Nedelec conditions. In Table 1, functions of degrees 3 and 4 are constructed using polynomial products such as (3L1 – L2) (L1 – L2) (L1
High speed and flexible PEB 3D diffusion simulation based on Sylvester equation
NASA Astrophysics Data System (ADS)
Lin, Pei-Chun; Chen, Charlie Chung-Ping
2013-04-01
Post exposure bake (PEB) Diffusion effect is one of the most difficult issues in modeling chemically amplified resists. These model equations result in a system of nonlinear partial differential equations describing the time rate of change reaction and diffusion. Verifying such models are difficult, so numerical simulations are needed to solve the model equations. In this paper, we propose a high speed 3D resist image simulation algorithm based on a novel method to solve the PEB Diffusion equation. Our major discovery is that the matrix formulation of the diffusion equation under the Crank- Nicolson scheme can be derived into a special form, AX+XB=C, where the X matrix is a 3D resist image after diffusion effect, A and B matrices contain the diffusion coefficients and the space relationship between directions x, y and z. These matrices are sparse, symmetric and diagonal dominant. The C matrix is the last time-step resist image. The Sylvester equation can be reduced to another form as (I⊗A + BT⊗I) X =C, in which the operator ⊗ is the Kronecker product notation. Compared with a traditional convolution method, our method is more useful in a way that boundary conditions can be more flexible. From our experimental results, we see that the error of the convolution method can be as high as 30% at borders of the design pattern. Furthermore, since the PEB temperature may not be uniform at multi-zone PEB, the convolution method might not be directly applicable in this scenario. Our method is about 20 times faster than the convolution method for a single time step (2 seconds) as illustrated in the attached figure. To simulate 50 seconds of the flexible PEB diffusion process, our method only takes 210 seconds with a convolution set up for a 1240×1240 working area. We use the typical 45nm immersion lithography in our work. The exposure wavelength is set to 193nm; the NA is 1.3775; and the diffusion coefficient is 1.455×10-17m2/s at PEB temperature 150°C along with PEB
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
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.
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.
3D early embryogenesis image filtering by nonlinear partial differential equations.
Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O
2010-08-01
We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which
Chen, I L; Chen, J T; Kuo, S R; Liang, M T
2001-03-01
Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.
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.
Ying, Michael; Yung, Dennis M C; Ho, Karen K L
2008-01-01
This study aimed to develop a new two-dimensional (2-D) ultrasound thyroid volume estimation equation using three-dimensional (3-D) ultrasound as the standard of reference, and to compare the thyroid volume estimation accuracy of the new equation with three previously reported equations. 2-D and 3-D ultrasound examinations of the thyroid gland were performed in 150 subjects with normal serum thyrotropin (TSH, thyroid-stimulating hormone) and free thyroxine (fT4) levels (63 men and 87 women, age range: 17 to 71 y). In each subject, the volume of both thyroid lobes was measured by 3-D ultrasound. On 2-D ultrasound, the craniocaudal (CC), lateromedial (LM) and anteroposterior (AP) dimensions of the thyroid lobes were measured. The equation was derived by correlating the volume of the thyroid lobes measured with 3-D ultrasound and the product of the three dimensions measured with 2-D ultrasound using linear regression analysis, in 75 subjects without thyroid nodule. The accuracy of thyroid volume estimation of the new equation and the three previously reported equations was evaluated and compared in another 75 subjects (without thyroid nodule, n = 30; with thyroid nodule, n = 45). It is suggested that volume of thyroid lobe may be estimated as: volume of thyroid lobe = 0.38.(CC.LM.AP) + 1.76. Result showed that the new equation (16.9% to 36.1%) had a significantly smaller thyroid volume estimation error than the previously reported equations (20.8% to 54.9%) (p < 0.05). There was a significantly larger thyroid volume estimation error when thyroid glands with nodules were examined (p < 0.05). With the use of the appropriate thyroid volume equation, 2-D ultrasound can be a useful alternative in thyroid volume measurement when 3-D ultrasound is not available.
NASA Astrophysics Data System (ADS)
Rabinowitch, Alexander S.
2015-09-01
A special class of axially symmetric nonstationary flows of incompressible viscous fluids is examined. For it, the 3D Navier-Stokes equations are reduced to a nonlinear partial differential equation of the third order and a linear partial differential equation of the second order. These equations are studied and their particular analytical solutions are found. The obtained particular solution to the Navier-Stokes equations could be used to describe some types of turbulent flows of viscous fluids in the case of high Reynolds numbers.
Christian, J M; McDonald, G S; Chamorro-Posada, P
2006-12-01
A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2011-06-01
We prove by an explicit construction that solutions to incompressible 3D Euler equations defined in the periodic cube Ω=[0 can be mapped bijectively to a new system of equations whose solutions are globally regular. We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding regular solution of the new system. In the hypothetical case of Euler finite-time singularity, we provide an explicit formula for the blowup time in terms of the regular solution of the new system. The new system is amenable to being integrated numerically using similar methods as in Euler equations. We propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite-time singularity problem of Euler equations, based on the conservation of quantities directly related to energy and circulation. The method of mapping to a regular system can be extended to any fluid equation that admits a Beale-Kato-Majda type of theorem, e.g. 3D Navier-Stokes, 2D and 3D magnetohydrodynamics, and 1D inviscid Burgers. We discuss briefly the case of 2D ideal magnetohydrodynamics. In order to illustrate the usefulness of the mapping, we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1D inviscid Burgers equation.
A 3D staggered-grid finite difference scheme for poroelastic wave equation
NASA Astrophysics Data System (ADS)
Zhang, Yijie; Gao, Jinghuai
2014-10-01
Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.
An integral equation approach to smooth 3D Navier-Stokes solution
NASA Astrophysics Data System (ADS)
Costin, O.; Luo, G.; Tanveer, S.
2008-12-01
We summarize a recently developed integral equation (IE) approach to tackling the long-time existence problem for smooth solution v(x, t) to the 3D Navier-Stokes (NS) equation in the context of a periodic box problem with smooth time independent forcing and initial condition v0. Using an inverse-Laplace transform of {\\skew5\\hat v} (k, t) - {\\skew5\\hat v}_0 in 1/t, we arrive at an IE for {\\skew5\\hat U} (k, p) , where p is inverse-Laplace dual to 1/t and k is the Fourier variable dual to x. The advantage of this formulation is that the solution {\\skew5\\hat U} to the IE is known to exist a priori for p \\in \\mathbb{R}^+ and the solution is integrable and exponentially bounded at ∞. Global existence of NS solution in this formulation is reduced to an asymptotics question. If \\parallel\\!{\\skew5\\hat U} (\\cdot, p)\\!\\parallel_{{l^{1} (\\mathbb{Z}^3)}} has subexponential bounds as p→∞, then global existence to NS follows. Moreover, if f=0, then the converse is also true in the following sense: if NS has global solution, then there exists n>=1 for which the inverse-Laplace transform of {\\skew5\\hat v} (k, t) - {\\skew5\\hat v}_0 in 1/tn necessarily decays as q→∞, where q is the inverse-Laplace dual to 1/tn. We also present refined estimates of the exponential growth when the solution {\\skew5\\hat U} is known on a finite interval [0, p0]. We also show that for analytic v[0] and f, with finitely many nonzero Fourier-coefficients, the series for {\\skew5\\hat U} (k, p) in powers of p has a radius of convergence independent of initial condition and forcing; indeed the radius gets bigger for smaller viscosity. We also show that the IE can be solved numerically with controlled errors. Preliminary numerical calculations for Kida (1985 J. Phys. Soc. Japan 54 2132) initial conditions, though far from being optimized, and performed on a modest interval in the accelerated variable q show decay in q.
A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero magnetic diffusivity
NASA Astrophysics Data System (ADS)
Gala, Sadek; Ragusa, Maria Alessandra
2016-06-01
In this work, we show that a smooth solution of the 3D MHD equations with zero magnetic diffusivity in the whole space ℝ3 breaks down if and only if a certain norm of the magnetic field blows up at the same time.
NASA Astrophysics Data System (ADS)
Shalaev, V. I.
2016-10-01
Singularities appearing in solutions of 3D laminar boundary layer (BL) equations, when two streamline families are collided, are discussed. For conical bodies, equations are investigated using asymptotic methods. Analytical solutions are obtained for the outer BL region; their singularities in the runoff plane are studied. The asymptotic flow structure near the singularity is constructed on the base of Navier-Stokes equations at large Reynolds numbers. For different flow regions analytical solutions are found and are matched with BL equation solutions. Properties of BL equations for the near-wall region in the runoff plane are investigated and a criterion of the solution disappearing is found. It is shown that this criterion separates two different topological flow structures and corresponds to the singularity appearance in this plane in solutions of full equations. Calculations confirmed obtained results are presented.
NASA Astrophysics Data System (ADS)
Fedele, Renato; Jovanović, Dušan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.
2010-01-01
The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schrödinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schrödinger equation coupled with a 1D nonlinear Schrödinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.
Diffuse optical 3D-slice imaging of bounded turbid media using a new integro-differential equation.
Pattanayak, D; Yodh, A
1999-04-12
A new integro-differential equation for diffuse photon density waves (DPDW) is derived within the diffusion approximation. The new equation applies to inhomogeneous bounded turbid media. Interestingly, it does not contain any terms involving gradients of the light diffusion coefficient. The integro-differential equation for diffusive waves is used to develop a 3D-slice imaging algorithm based the on angular spectrum representation in the parallel plate geometry. The algorithm may be useful for near infrared optical imaging of breast tissue, and is applicable to other diagnostics such as ultrasound and microwave imaging.
2016-01-01
We investigate the transmission properties of a metallic layer with narrow slits. We consider (time-harmonic) Maxwell's equations in the H-parallel case with a fixed incident wavelength. We denote η > 0 as the typical size of the complex structure and obtain the effective equations by letting η → 0. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfaces of the slits. For the waves to be in resonance with the height of the metallic layer, the corresponding results can be perfect transmission through the layer. PMID:27738650
Mahato, Hari Shankar
2016-01-01
We investigate the transmission properties of a metallic layer with narrow slits. We consider (time-harmonic) Maxwell's equations in the H-parallel case with a fixed incident wavelength. We denote η > 0 as the typical size of the complex structure and obtain the effective equations by letting η → 0. For metallic permittivities with negative real part, plasmonic waves can be excited on the surfaces of the slits. For the waves to be in resonance with the height of the metallic layer, the corresponding results can be perfect transmission through the layer.
NASA Technical Reports Server (NTRS)
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
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.
PSH3D fast Poisson solver for petascale DNS
NASA Astrophysics Data System (ADS)
Adams, Darren; Dodd, Michael; Ferrante, Antonino
2016-11-01
Direct numerical simulation (DNS) of high Reynolds number, Re >= O (105) , turbulent flows requires computational meshes >= O (1012) grid points, and, thus, the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the solver. We have developed a parallel solver of the Helmholtz equation in 3D, PSH3D. The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform in two spatial directions, and a parallel linear solver in the third direction. For computational meshes up to 81923 grid points, our numerical results show that PSH3D scales up to at least 262k cores of Cray XT5 (Blue Waters). PSH3D has a peak performance 6 × faster than 3D FFT-based methods when used with the 'partial-global' optimization, and for a 81923 mesh solves the Poisson equation in 1 sec using 128k cores. Also, we have verified that the use of PSH3D with the 'partial-global' optimization in our DNS solver does not reduce the accuracy of the numerical solution of the incompressible Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Bakker, Mark; Kuhlman, Kristopher L.
2011-09-01
Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks.
Natarajan, Logesh Kumar; Wu, Sean F
2012-06-01
This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.
NASA Astrophysics Data System (ADS)
Liu, Yuanyuan; Holt, William E.
2015-08-01
Wave gradiometry is an array processing technique utilizing the shape of seismic wavefields captured by USArray TA stations to determine fundamental wave propagation characteristics. We first explore a compatibility relation that links the displacement spatial gradients to seismogram displacements and velocities through two unknown coefficients, A→ and B→. These coefficients are solved for through iterative, damped least squares inversion to provide estimates of phase velocity, back azimuth, radiation pattern, and geometrical spreading. We show that the A→ coefficient corresponds to the gradient of logarithmic amplitude, and the B→ coefficient corresponds approximately to the local wave slowness. A→ and B→ vector fields are interpolated to explore a second compatibility relation through solutions to the Helmholtz equation. For most wavefields passing through the eastern U.S., we show that the A→ coefficients are generally orthogonal to the B→ coefficients. Where they are not completely orthogonal, there is a strong positive correlation between ∇·B→ and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We finally obtain isotropic Rayleigh wave phase velocity maps for 15 periods between 20 and 150 s, by stacking results from 37 earthquakes, which show a velocity change along the approximate boundary of the early Paleozoic continental margin. We also observe two low-velocity anomalies, one centered over the central Appalachians where Eocene basaltic volcanism has occurred and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.
NASA Astrophysics Data System (ADS)
Ozgun, Ozlem; Kuzuoglu, Mustafa
2014-06-01
A computational model is developed for efficient solutions of electromagnetic scattering from obstacles having random surface deformations or irregularities (such as roughness or randomly-positioned bump on the surface), by combining the Monte Carlo method with the principles of transformation electromagnetics in the context of finite element method. In conventional implementation of the Monte Carlo technique in such problems, a set of random rough surfaces is defined from a given probability distribution; a mesh is generated anew for each surface realization; and the problem is solved for each surface. Hence, this repeated mesh generation process places a heavy burden on CPU time. In the proposed approach, a single mesh is created assuming smooth surface, and a transformation medium is designed on the smooth surface of the object. Constitutive parameters of the medium are obtained by the coordinate transformation technique combined with the form-invariance property of Maxwell's equations. At each surface realization, only the material parameters are modified according to the geometry of the deformed surface, thereby avoiding repeated mesh generation process. In this way, a simple, single and uniform mesh is employed; and CPU time is reduced to a great extent. The technique is demonstrated via various finite element simulations for the solution of two-dimensional, Helmholtz-type and transverse magnetic scattering problems.
3-D Acoustic Scattering from 2-D Rough Surfaces Using A Parabolic Equation Model
2013-12-01
acoustic propagation signals, especially at mid- frequencies and higher (e.g., acoustic communications systems). For many years, the effects of rough...of the effect of surface scattering on 3-D propagation , which is critical in evaluating the variability in underwater acoustic propagation . Results...14. SUBJECT TERMS Acoustic Propagation , Acoustic Scattering, Sea Surface Perturbations, Split- Step Fourier Algorithm, Finite Difference Algorithm
NASA Astrophysics Data System (ADS)
Samian, R. S.; Abbassi, A.; Ghazanfarian, J.
2013-09-01
The thermal performance of two-dimensional (2D) field-effect transistors (FET) is investigated frequently by solving the Fourier heat diffusion law and the Boltzmann transport equation (BTE). With the introduction of the new generation of 3D FETs in which their thickness is less than the phonon mean-free-path it is necessary to carefully simulate the thermal performance of such devices. This paper numerically integrates the BTE in common 2D transistors including planar single layer and Silicon-On-Insulator (SOI) transistor, and the new generation of 3D transistors including FinFET and Tri-Gate devices. In order to decrease the directional dependency of results in 3D simulations; the Legendre equal-weight (PN-EW) quadrature set has been employed. It is found that if similar switching time is assumed for 3D and 2D FETs while the new generation of 3D FETs has less net energy consumption, they have higher hot-spot temperature. The results show continuous heat flux distribution normal to the silicon/oxide interface while the temperature jump is seen at the interface in double layer transistors.
Daniell, Nathan; Olds, Timothy; Tomkinson, Grant
2012-05-01
Measurements of whole body surface area (WBSA) have important applications in numerous fields including biological anthropology, clinical medicine, biomechanics, and sports science. Currently, WBSA is most often estimated using predictive equations due to the complex and time consuming methods required for direct measurement. The main aim of this study was to identify whether there were significant and meaningful differences between WBSA measurements taken using a whole body three-dimensional (3D) scanner (criterion measure) and the estimates derived from each WBSA equation identified from a systematic review. The study also aimed to determine whether differences varied according to body mass index (BMI), sex, or athletic status. Fifteen WBSA equations were compared with direct measurements taken on 1,714 young adult subjects, aged 18-30 years, using the Vitus Smart 3D whole body scanner, including 1,452 subjects (753 males, 699 females) from the general Australian population and 262 rowers (148 males, 114 females). Mixed-design analysis of variances determined significant differences and accuracy was quantified using Bland-Altman analysis and effect sizes. Thirteen of the 15 equations overestimated WBSA. With a few exceptions, equations were accurate with a low-systematic error (bias ≤2%) and low-random error (standard deviation of the differences 1.5-3.0%). However, BMI did have a substantial impact with the accuracy of some WBSA equations varying between the four BMI categories. The Shuter and Aslani: Eur J Appl Physiol 82 (2000) 250-254 equation was identified as the most accurate equation and should be used for Western populations 18-30 years of age. Care must be taken when deciding which equation to use when estimating WBSA.
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).
Universal Bounds for the Littlewood-Paley First-Order Moments of the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Otto, Felix; Ramos, Fabio
2010-12-01
We derive upper bounds for the infinite-time and space average of the L 1-norm of the Littlewood-Paley decomposition of weak solutions of the 3 D periodic Navier-Stokes equations. The result suggests that the Kolmogorov characteristic velocity scaling, {mathbf{U}_kappa˜ɛ^{1/3} kappa^{-1/3}} , holds as an upper bound for a region of wavenumbers near the dissipative cutoff.
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.
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.
A full-wave Helmholtz model for continuous-wave ultrasound transmission.
Huttunen, Tomi; Malinen, Matti; Kaipio, Jari P; White, Phillip Jason; Hynynen, Kullervo
2005-03-01
A full-wave Helmholtz model of continuous-wave (CW) ultrasound fields may offer several attractive features over widely used partial-wave approximations. For example, many full-wave techniques can be easily adjusted for complex geometries, and multiple reflections of sound are automatically taken into account in the model. To date, however, the full-wave modeling of CW fields in general 3D geometries has been avoided due to the large computational cost associated with the numerical approximation of the Helmholtz equation. Recent developments in computing capacity together with improvements in finite element type modeling techniques are making possible wave simulations in 3D geometries which reach over tens of wavelengths. The aim of this study is to investigate the feasibility of a full-wave solution of the 3D Helmholtz equation for modeling of continuous-wave ultrasound fields in an inhomogeneous medium. The numerical approximation of the Helmholtz equation is computed using the ultraweak variational formulation (UWVF) method. In addition, an inverse problem technique is utilized to reconstruct the velocity distribution on the transducer which is used to model the sound source in the UWVF scheme. The modeling method is verified by comparing simulated and measured fields in the case of transmission of 531 kHz CW fields through layered plastic plates. The comparison shows a reasonable agreement between simulations and measurements at low angles of incidence but, due to mode conversion, the Helmholtz model becomes insufficient for simulating ultrasound fields in plates at large angles of incidence.
NASA Astrophysics Data System (ADS)
Gusyev, M. A.; Haitjema, H. M.
2011-04-01
We obtained an exact solution in terms of the discharge potential for a constant-strength line-sink that satisfies the modified Helmholtz equation for groundwater flow, for example for semi-confined flow and transient flow. The solution is obtained by integrating the potential for a point sink (well) along a straight line element. The potential for the point-sink is the modified Bessel function of the second kind and zero order K0. Since K0 cannot be integrated directly (in closed form) along a line-element, earlier solutions for a line-sink have been obtained by integrating polynomial approximations to K0. These approximations, however, are only valid up to a certain distance from the well and consequently impose a limit on the length of the line-sink. In this paper we integrate an exact series representation for K0 that is valid at any distance from the well, thus allowing integration along line-elements of any length, at least in theory. Numerical difficulties arise when evaluating our expressions at large distances from the line-sink, but these are shown to be of little consequence in practice. We made use of Wirtinger calculus to facilitate integration and also to allow us to arrive at exact expressions for the integrated flux over a poly-line and the total leakage over a domain. These properties are essential when using the solution in the context of the Analytic Element Method (AEM). We demonstrate our solution for the case of semi-confined flow (with leakage) and for the case of transient flow in the context of the Laplace Transform Analytic Element Method (LT-AEM).
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.
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.
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.
Geometric constraints on potentially singular solutions for the 3-D Euler equations
Constantin, P.; Fefferman, C.; Majda, A.J.
1996-12-31
We discuss necessary and sufficient conditions for the formation of finite time singularities (blow up) in the incompressible three dimensional Euler equations. The well-known result of Beale, Kato and Majda states that these equations have smooth solutions on the time interval (0,t) if, and only if lim/t{r_arrow}T {integral}{sup t}{sub 0} {parallel}{Omega}({center_dot},s){parallel}{sub L}{sup {infinity}} (dx)dx < {infinity} where {Omega} = {triangledown} X u is the vorticity of the fluid and u is its divergence=free velocity. In this paper we prove criteria in which the direction of vorticity {xi} = {Omega}/{vert_bar}{Omega}{vert_bar} plays an important role.
Frequency Localized Regularity Criteria for the 3D Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Bradshaw, Z.; Grujić, Z.
2017-04-01
Two regularity criteria are established to highlight which Littlewood-Paley frequencies play an essential role in possible singularity formation in a Leray-Hopf weak solution to the Navier-Stokes equations in three spatial dimensions. One of these is a frequency localized refinement of known Ladyzhenskaya-Prodi-Serrin-type regularity criteria restricted to a finite window of frequencies, the lower bound of which diverges to {+∞} as t approaches an initial singular time.
Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver
NASA Technical Reports Server (NTRS)
Kim, S.-W.
1991-01-01
A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.
NASA Astrophysics Data System (ADS)
Le Hardy, D.; Favennec, Y.; Rousseau, B.; Hecht, F.
2017-04-01
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
NASA Astrophysics Data System (ADS)
Yu, Haibo; Zhao, Junning
2017-01-01
In this paper, we study the global existence for classical solutions to the 3D isentropic compressible Navier-Stokes equations in a cuboid domain. Compared to the Cauchy problem studied in Hoff (1995 J. Differ. Equ. 120 215-54), Hoff (2005 J. Math. Fluid Mech. 7 315-38), Huang et al (2012 Commun. Pure Appl. Math. 65 549-85), some new thoughts are applied to obtain upper bounds for density. Precisely, through piecewise estimation and some time-depending a priori estimates, we establish time-uniform upper bounds for density under the assumption that the initial energy is small. The initial vacuum is allowed.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
NASA Astrophysics Data System (ADS)
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-02-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
NASA Astrophysics Data System (ADS)
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Statistical shape analysis using 3D Poisson equation--A quantitatively validated approach.
Gao, Yi; Bouix, Sylvain
2016-05-01
Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc. Unfortunately, the proposed methods are rarely quantitatively evaluated, and as shown in recent studies, when they are evaluated, significant discrepancies exist in their outputs. In this work, we concentrate on the problem of finding the consistent location of deformation between two population of shapes. We propose a new shape analysis algorithm along with a framework to perform a quantitative evaluation of its performance. Specifically, the algorithm constructs a Signed Poisson Map (SPoM) by solving two Poisson equations on the volumetric shapes of arbitrary topology, and statistical analysis is then carried out on the SPoMs. The method is quantitatively evaluated on synthetic shapes and applied on real shape data sets in brain structures.
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.
Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
NASA Astrophysics Data System (ADS)
Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu
2011-09-01
Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis.
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.
Further Remarks on the Luo-Hou's Ansatz for a Self-similar Solution to the 3D Euler Equations
NASA Astrophysics Data System (ADS)
Sperone, Gianmarco
2017-01-01
It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a singular solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profiles, to an overdetermined system of partial differential equations that produces two families of solutions: a class of trivial solutions in which the vorticity field is identically zero, and a family of solutions that blow-up immediately, where the vorticity field is governed by a stationary regime. In any case, the analytical properties of these solutions are not consistent with the numerical observations reported by T. Hou and G. Luo. Therefore, this result is a refinement of the previous work published by D. Chae and T.-P. Tsai on this matter, where the authors found the trivial class of solutions under a certain decay condition of the blow-up profiles.
Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Birken, Philipp; Gassner, Gregor; Haas, Mark; Munz, Claus-Dieter
2013-05-01
We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton-Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier-Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low number of elements on the processor. For high order DG discretizations, a particular problem that needs to be addressed is the size of the blocks in the Jacobian. Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks. While the standard preconditioners 'block Jacobi' (no off-blocks) and full symmetric Gauss-Seidel (full off-blocks) are included as special cases, the reduction of the off-block order results in the new scheme ROBO-SGS. This allows us to investigate the impact of the preconditioner's sparsity pattern with respect to the computational performance. Since the number of iterations is not well suited to judge the efficiency of a preconditioner, we additionally consider CPU time for the comparisons. We found that both block Jacobi and ROBO-SGS have good overall performance and good strong parallel scaling behavior.
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
NASA Astrophysics Data System (ADS)
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Ibraheem, S. O.
1993-01-01
The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.
NASA 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)
Chatterjee, Kausik
2016-06-01
The objective of this paper is the extension and application of a newly-developed Green's function Monte Carlo (GFMC) algorithm to the estimation of the derivative of the solution of the one-dimensional (1D) Helmholtz equation subject to Neumann and mixed boundary conditions problems. The traditional GFMC approach for the solution of partial differential equations subject to these boundary conditions involves "reflecting boundaries" resulting in relatively large computational times. My work, inspired by the work of K.K. Sabelfeld is philosophically different in that there is no requirement for reflection at these boundaries. The underlying feature of this algorithm is the elimination of the use of reflecting boundaries through the use of novel Green's functions that mimic the boundary conditions of the problem of interest. My past work has involved the application of this algorithm to the estimation of the solution of the 1D Laplace equation, the Helmholtz equation and the modified Helmholtz equation. In this work, this algorithm has been adapted to the estimation of the derivative of the solution which is a very important development. In the traditional approach involving reflection, to estimate the derivative at a certain number of points, one has to a priori estimate the solution at a larger number of points. In the case of a one-dimensional problem for instance, to obtain the derivative of the solution at a point, one has to obtain the solution at two points, one on each side of the point of interest. These points have to be close enough so that the validity of the first-order approximation for the derivative operator is justified and at the same time, the actual difference between the solutions at these two points has to be at least an order of magnitude higher than the statistical error in the estimation of the solution, thus requiring a significantly larger number of random-walks than that required for the estimation of the solution. In this new approach
NASA Astrophysics Data System (ADS)
Chevalier, Paul; Bouchon, Patrick; Haïdar, Riad; Pardo, Fabrice
2014-08-01
Helmholtz resonators are widely used acoustic components able to select a single frequency. Here, based on an analogy between acoustics and electromagnetism wave equations, we present an electromagnetic 2D Helmholtz resonator made of a metallic slit-box structure. At the resonance, the light is funneled in the λ/800 apertures, and is subsequently absorbed in the cavity. As in acoustics, there is no higher order of resonance, which is an appealing feature for applications such as photodetection or thermal emission. Eventually, we demonstrate that the slit is of capacitive nature while the box behaves inductively. We derive an analytical formula for the resonance wavelength, which does not rely on wave propagation and therefore does not depend on the permittivity of the material filling the box. Besides, in contrast with half-wavelength resonators, the resonance wavelength can be engineered by both the slit aspect ratio and the box area.
NASA Astrophysics Data System (ADS)
Simpson, J. J.; Taflove, A.
2005-12-01
We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A
Gadyl'shin, R R
2000-06-30
In this article the two-dimensional Dirichlet boundary-value problem is considered for the Helmholtz operator with boundary conditions on an almost closed curve {gamma}{sub {epsilon}} where {epsilon}<<1 is the distance between the end-points of the curve. A complete asymptotic expression is constructed for a pole of the analytic continuation of the Green's function of this problem as the pole converges to a simple eigenfrequency of the limiting interior problem in the case when the corresponding eigenfunction of the limiting problem has a second-order zero at the centre of contraction of the gap. The influence of symmetry of the gap on the absolute value of the imaginary parts of the poles is investigated.
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)
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.
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…
1993-11-01
methou, mn: A.K. Aziz (ed.), The mathematical foundations of tile finite element, method with applicai.4ons to partial differential equations , Academic...nonlinear differential equations and problems in linear and nonlinear algebra. "* To help bridge gaps between computational directions in engineering, physics...Life of Contract Equation with High Wave Number Part 1: The h-Version of the FEM 7. Au TNO R(a)COTATO ATgUSAs Frank Ihlenburgi - Ivo Babuska 2 2ONR
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.
Measurement of Helmholtz wave fields
Alonso
2000-07-01
A simple formalism is found for the measurement of wave fields that satisfy the Helmholtz equation in free space. This formalism turns out to be analogous to the well-known theory of measurements for quantum-mechanical wave functions: A measurement corresponds to the squared magnitude of the inner product (in a suitable Hilbert space) of the wave field and a field that is associated with the detector. The measurement can also be expressed as an overlap in phase space of a special form of the Wigner function that is tailored for Helmholtz wave fields.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
NASA Technical Reports Server (NTRS)
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
[Hermann von Helmholtz--a physicist in medicine].
Omerbasić, A
1999-01-01
Helmholtz left an indelible mark in science. He was a predecessor to the multidisciplinary scientific approach, and his contribution to physics (The Law on Energy Sustainability, Helmholtz's Free Energy, Gibs-Helmholtz's Equationes, Helmholtz Theory of Rotational Liquids Flow, Helmholtz's Oscillatory Cycle, Helmholtz's Waves Equation) and to medicine (Ophthalmoscope, Young-Helmholtz's Theory of Colours, Sight Theory, Speed of Impulse Transfer, Speech and Tone of Voice, The Sound Transfer to Nerves) was indispensable. Helmholtz was surrounded by the respect and love of his contemporaries, appreciated and respected by his followers for the results he left. As a respectable professor of anatomy, physiology and physics at the most eminent universities, "he used to give lectures in such a clear and concise way that they could have been, without any changes, published in a form of a textbook" (Ostwald).
Experiments with Helmholtz Resonators.
ERIC Educational Resources Information Center
Greenslade, Thomas B., Jr.
1996-01-01
Presents experiments that use Helmholtz resonators and have been designed for a sophomore-level course in oscillations and waves. Discusses the theory of the Helmholtz resonator and resonance curves. (JRH)
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.
Liu, Gang; Jayathilake, Pahala G; Khoo, Boo Cheong; Han, Feng; Liu, Dian Kui
2012-02-01
The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid.
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 Technical Reports Server (NTRS)
Biyabani, S. R.
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
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)
Wu, Guochun
2017-01-01
In this paper, we investigate the global existence and uniqueness of strong solutions to the initial boundary value problem for the 3D compressible Navier-Stokes equations without heat conductivity in a bounded domain with slip boundary. The global existence and uniqueness of strong solutions are obtained when the initial data is near its equilibrium in H2 (Ω). Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
Dahms, Rainer N
2015-05-01
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. The new model preserves the accuracy of previous temperature
Dahms, Rainer N.
2014-12-31
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phasemore » components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of
Dahms, Rainer N.
2014-12-31
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous
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.
Spong, Donald A
2016-06-20
AE3D solves for the shear Alfven eigenmodes and eigenfrequencies in a torodal magnetic fusion confinement device. The configuration can be either 2D (e.g. tokamak, reversed field pinch) or 3D (e.g. stellarator, helical reversed field pinch, tokamak with ripple). The equations solved are based on a reduced MHD model and sound wave coupling effects are not currently included.
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.
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.
NASA Astrophysics Data System (ADS)
Razafison, Ulrich
We consider the three-dimensional exterior problem for stationary Navier-Stokes equations. We prove, under assumptions of smallness of the data, existence and uniqueness of solutions. By setting the problem in weighted spaces where the weights reflect the anisotropic decay properties of the fundamental solution of Oseen, we show the better decay of the solutions outside the wake region. Moreover, the solutions we obtained have a finite Dirichlet integral and under additional assumptions on the weights they are also PR-solutions in the sense of Finn [R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Ration. Mech. Anal. 19 (1965) 363-406]. The study relies on an L-theory for 1
NASA Astrophysics Data System (ADS)
Pu, Xueke; Guo, Boling
In this paper, we consider the ergodicity of invariant measures for the stochastic Ginzburg-Landau equation with degenerate random forcing. First, we show the existence and pathwise uniqueness of strong solutions with H-initial data, and then the existence of an invariant measure for the Feller semigroup by the Krylov-Bogoliubov method. Then in the case of degenerate additive noise, using the notion of asymptotically strong Feller property, we prove the uniqueness of invariant measures for the transition semigroup.
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.
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.
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.
2016-02-15
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
NASA Astrophysics Data System (ADS)
Berselli, Luigi C.; Spirito, Stefano
2017-03-01
In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier slip boundary conditions. We prove that weak solutions obtained as limits of solutions of the Navier-Stokes-Voigt model satisfy the local energy inequality, and we also prove certain regularity results for the pressure. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions through a Fourier-Galerkin finite-dimensional approximation in the space variables.
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.
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.
NASA Technical Reports Server (NTRS)
Cwik, T.; Jamnejad, V.; Zuffada, C.
1993-01-01
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
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)
Li, Liang; Lanteri, Stéphane; Perrussel, Ronan
2014-01-01
A Schwarz-type domain decomposition method is presented for the solution of the system of 3d time-harmonic Maxwell's equations. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of the problem based on a tetrahedrization of the computational domain. The discrete system of the HDG method on each subdomain is solved by an optimized sparse direct (LU factorization) solver. The solution of the interface system in the domain decomposition framework is accelerated by a Krylov subspace method. The formulation and the implementation of the resulting DD-HDG (Domain Decomposed-Hybridizable Discontinuous Galerkin) method are detailed. Numerical results show that the resulting DD-HDG solution strategy has an optimal convergence rate and can save both CPU time and memory cost compared to a classical upwind flux-based DD-DG (Domain Decomposed-Discontinuous Galerkin) approach.
NASA Astrophysics Data System (ADS)
Cheskidov, A.; Shvydkoy, R.
2014-06-01
Motivated by Kolmogorov's theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wavenumber that separates low modes where the Euler dynamics is predominant from the high modes where the viscous forces take over. Then using an indifferent to the viscosity technique we obtain a new regularity criterion which is weaker than every Ladyzhenskaya-Prodi-Serrin condition in the viscous case, and reduces to the Beale-Kato-Majda criterion in the inviscid case. In the viscous case we prove that Leray-Hopf solutions are regular provided , which improves our previous condition. We also show that for all Leray-Hopf solutions. Finally, we prove that Leray-Hopf solutions are regular when the time-averaged spatial intermittency is small, i.e., close to Kolmogorov's regime.
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.
NASA Astrophysics Data System (ADS)
Martin, R.; Komatitsch, D.
2007-05-01
In geophysical exploration, high computational cost of full waveform inverse problem can be drastically reduced by implementing efficient boundary conditions. In many regions of interest for the oil industry or geophysical exploration, nearly tabular geological structures can be handled and analyzed by setting receivers in wells or/and at large offset. Then, the numerical modelling of waves travelling in thin slices along wells and near surface structures can provide very fast responses if highly accurate absorbing conditions around the slice are introduced in the wave propagation modelling. Here we propose then a Convolutional version of the well known Perfectly Matched layer technique. This optimized version allows the generation of seismic waves travelling close to the boundary layer at almost grazing incidence, which allows the treatment of thin 3D slices. The Perfectly Matched Layer (PML) technique, introduced in 1994 by Bérenger for Maxwell's equations, has become classical in the context of numerical simulations in electromagnetics, in particular for 3D finite difference in the time domain (FDTD) calculations. One of the most attractive properties of a PML model is that no reflection occurs at the interface between the physical domain and the absorbing layer before truncation to a finite-size layer and discretization by a numerical scheme. Therefore, the absorbing layer does not send spurious energy back into the medium. This property holds for any frequency and angle of incidence. However, the layer must be truncated in order to be able to perform numerical simulations, and such truncation creates a reflected wave whose amplitude is amplified by the discretization process. In 2001, Collino and Tsogka introduced a PML model for the elastodynamics equation written as a first-order system in velocity and stress with split unknowns, and discretized it based on the standard 2D staggered-grid finite-difference scheme of Virieux (1986). Then in 2001 and 2004
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.
NASA Astrophysics Data System (ADS)
Wang, F.; Jordan, T. H.
2012-12-01
Seismic hazard models based on empirical ground motion prediction equations (GMPEs) employ a model-based factorization to account for source, propagation, and path effects. An alternative is to simulate these effects directly using earthquake source models combined with three-dimensional (3D) models of Earth structure. We have developed an averaging-based factorization (ABF) scheme that facilitates the geographically explicit comparison of these two types of seismic hazard models. For any fault source k with epicentral position x, slip spatial and temporal distribution f, and moment magnitude m, we calculate the excitation functions G(s, k, x, m, f) for sites s in a geographical region R, such as 5% damped spectral acceleration at a particular period. Through a sequence of weighted-averaging and normalization operations following a certain hierarchy over f, m, x, k, and s, we uniquely factorize G(s, k, x, m, f) into six components: A, B(s), C(s, k), D(s, k, x), E(s, k, x, m), and F(s, k, x, m, f). Factors for a target model can be divided by those of a reference model to obtain six corresponding factor ratios, or residual factors: a, b(s), c(s, k), d(s, k, x), e(s, k, x, m), and f(s, k, x, m, f). We show that these residual factors characterize differences in basin effects primarily through b(s), distance scaling primarily through c(s, k), and source directivity primarily through d(s, k, x). We illustrate the ABF scheme by comparing CyberShake Hazard Model (CSHM) for the Los Angeles region (Graves et. al. 2010) with the Next Generation Attenuation (NGA) GMPEs modified according to the directivity relations of Spudich and Chiou (2008). Relative to CSHM, all NGA models underestimate the directivity and basin effects. In particular, the NGA models do not account for the coupling between source directivity and basin excitation that substantially enhance the low-frequency seismic hazards in the sedimentary basins of the Los Angeles region. Assuming Cyber
The ophthalmoscope: Helmholtz's Augenspiegel.
Pearce, J M S
2009-01-01
The origins of Helmholtz's invention of the ophthalmoscope are found in the ancient observation that the back of the eye appeared black. In 1703, Jean Méry reported that the luminosity of the cat's eye could be seen when the animal was held under water, and Mariotte observed that a dog's eye was luminous but erroneously thought this was because its choroid was white. Prévost made a breakthrough when he deduced it was incident light and not light coming out of the eye. Purkinje and von Brucke used lenses to attempt to see the fundus and almost succeeded. However, it was Helmholtz who created the first useable ophthalmoscope, whose development and clinical application are traced in this paper. One of the greatest physical scientists in many spheres of learning, his biography is briefly sketched.
2015-06-04
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...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...of Spectral Elements, Deep Convection , Kessler Microphysics Preprint J. Comput. Phys. 283 (2015) 360-373 June 4, 2015 1. Introduction In the field of
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)
Frediani, Luca; Fossgaard, Eirik; Flå, Tor; Ruud, Kenneth
2013-07-01
We have developed and implemented a general formalism for fast numerical solution of time-independent linear partial differential equations as well as integral equations through the application of numerically separable integral operators in d ≥ 1 dimensions using the non-standard (NS) form. The proposed formalism is universal, compact and oriented towards the practical implementation into a working code using multiwavelets. The formalism is applied to the case of Poisson and bound-state Helmholtz operators in d = 3. Our algorithms are fully adaptive in the sense that the grid supporting each function is obtained on the fly while the function is being computed. In particular, when the function g = O f is obtained by applying an integral operator O, the corresponding grid is not obtained by transferring the grid from the input function f. This aspect has significant implications that will be discussed in the numerical section. The operator kernels are represented in a separated form with finite but arbitrary precision using Gaussian functions. Such a representation combined with the NS form allows us to build a sparse, banded representation of Green's operator kernel. We have implemented a code for the application of such operators in a separated NS form to a multivariate function in a finite but, in principle, arbitrary number of dimensions. The error of the method is controlled, while the low complexity of the numerical algorithm is kept. The implemented code explicitly computes all the 22d components of the d-dimensional operator. Our algorithms are described in detail in the paper through pseudo-code examples. The final goal of our work is to be able to apply this method to build a fast and accurate Kohn-Sham solver for density functional theory.
NASA Technical Reports Server (NTRS)
Phillips, J. R.
1996-01-01
In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.
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
3d-3d correspondence revisited
Chung, Hee -Joong; Dimofte, Tudor; Gukov, Sergei; ...
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.
Vector Helmholtz-Gauss and vector Laplace-Gauss beams.
Bandres, Miguel A; Gutiérrez-Vega, Julio C
2005-08-15
We demonstrate the existence of vector Helmholtz-Gauss (vHzG) and vector Laplace-Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu-Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.
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.
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)
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)
Wolkov, A. V.
2010-03-01
The Galerkin method with discontinuous basis functions is adapted for solving the Euler and Navier-Stokes equations on unstructured hexahedral grids. A hybrid multigrid algorithm involving the finite element and grid stages is used as an iterative solution method. Numerical results of calculating the sphere inviscid flow, viscous flow in a bent pipe, and turbulent flow past a wing are presented. The numerical results and the computational cost are compared with those obtained using the finite volume method.
NASA Astrophysics Data System (ADS)
Chen, Thomas; Pavlović, Nataša
2012-08-01
We prove a Beale-Kato-Majda type criterion for the loss of regularity for solutions of the incompressible Euler equations in {Hs({R}^3)} , for {s>5/2} . Instead of double exponential estimates of Beale-Kato-Majda type, we obtain a single exponential bound on {|u(t)|_{H^s}} involving the length parameter introduced by Constantin in (SIAM Rev. 36(1):73-98, 1994). In particular, we derive lower bounds on the blowup rate of such solutions.
Optical structure based on the acoustic Helmholtz resonator
NASA Astrophysics Data System (ADS)
Chevalier, Paul; Bouchon, Patrick; Pelouard, Jean-Luc; Pardo, Fabrice; Haidar, Riad
2015-02-01
Here, based on an analogy between acoustics and electromagnetism wave equations, we present an electromagnetic resonator analogous to the Helmholtz resonator in acoustics. This structure is made of a tiny slit above a box and exhibits appealing properties for applications such as thermal emission, bio-sensing or spectroscopy.
NASA Astrophysics Data System (ADS)
Korayem, M. H.; Shafei, A. M.
2013-02-01
The goal of this paper is to describe the application of Gibbs-Appell (G-A) formulation and the assumed modes method to the mathematical modeling of N-viscoelastic link manipulators. The paper's focus is on obtaining accurate and complete equations of motion which encompass the most related structural properties of lightweight elastic manipulators. In this study, two important damping mechanisms, namely, the structural viscoelasticity (Kelvin-Voigt) effect (as internal damping) and the viscous air effect (as external damping) have been considered. To include the effects of shear and rotational inertia, the assumption of Timoshenko beam (TB) theory (TBT) has been applied. Gravity, torsion, and longitudinal elongation effects have also been included in the formulations. To systematically derive the equations of motion and improve the computational efficiency, a recursive algorithm has been used in the modeling of the system. In this algorithm, all the mathematical operations are carried out by only 3×3 and 3×1 matrices. Finally, a computational simulation for a manipulator with two elastic links is performed in order to verify the proposed method.
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)
Kelvin-Helmholtz versus Hall magnetoshear instability in astrophysical flows.
Gómez, Daniel O; Bejarano, Cecilia; Mininni, Pablo D
2014-05-01
We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well-known macroscopic and ideal shear-driven instability. In sufficiently low-density plasmas, also the microscopic Hall magnetoshear instability can take place. We performed three-dimensional simulations of the Hall-magnetohydrodynamic equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magnetoshear instability is not only non-negligible, but it actually displays growth rates larger than those of the Kelvin-Helmholtz instability.
Helmholtz solitons in power-law optical materials
Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.
2007-09-15
A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified.
Bistable Helmholtz solitons in cubic-quintic materials
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2007-09-15
We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations.
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.
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.
Analysis of Kelvin Helmholtz Instabilities of Plasma Jets
NASA Technical Reports Server (NTRS)
Friedman, Mark J.; Hollingsworth, Blane J.
1999-01-01
Ulysses data indicates density fluctuations which axe theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.
Analysis of Kelvin Helmholtz Instabilities of Plasma Jets
NASA Technical Reports Server (NTRS)
Friedman, Mark J.; Hollingsworth, Blane J.
1999-01-01
Ulysses data indicates density fluctuations which are theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.
6D Interpretation of 3D Gravity
NASA Astrophysics Data System (ADS)
Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2017-02-01
We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern–Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets an explanation of why the pure connection formulation of 3D gravity exists. More generally, we interpret 3D gravity as the dimensional reduction of the 6D Hitchin theory. To this end, we show that any \\text{SU}(2) invariant closed 3-form in the total space of the principal \\text{SU}(2) bundle can be parametrised by a connection together with a 2-form field on the base. The dimensional reduction of the 6D Hitchin theory then gives rise to 3D gravity coupled to a topological 2-form field.
The possibility of Kelvin-Helmholtz instability in solar spicules
NASA Astrophysics Data System (ADS)
Ajabshirizadeh, A.; Ebadi, H.; Vekalati, R. E.; Molaverdikhani, K.
2015-05-01
Transversal oscillations of spicules axes may be related to the propagation of magnetohydrodynamic waves along them. These waves may become unstable and the instability can be of the Kelvin-Helmholtz type. We use the dispersion relation of kink mode derived from linearized magnetohydrodynamic equations. The input parameters of the derived dispersion equation, namely, spicules and their ambient medium densities ratios as well as their corresponding magnetic fields ratios, are considered to be within the range 0-1. By solving the dispersion equation numerically, we show that for higher densities and lower magnetic fields ratios within the range mentioned, the KHI onset in type ii spicules conditions is possible. This possibility decreases with an increase in Alfvén velocity inside spicules. A rough criterion for appearing of Kelvin-Helmholtz instability is obtained. We also drive a more reliable and exact criterion for KHI onset of kink waves.
NASA Astrophysics Data System (ADS)
Moore, Gregory F.
2009-05-01
This volume is a brief introduction aimed at those who wish to gain a basic and relatively quick understanding of the interpretation of three-dimensional (3-D) seismic reflection data. The book is well written, clearly illustrated, and easy to follow. Enough elementary mathematics are presented for a basic understanding of seismic methods, but more complex mathematical derivations are avoided. References are listed for readers interested in more advanced explanations. After a brief introduction, the book logically begins with a succinct chapter on modern 3-D seismic data acquisition and processing. Standard 3-D acquisition methods are presented, and an appendix expands on more recent acquisition techniques, such as multiple-azimuth and wide-azimuth acquisition. Although this chapter covers the basics of standard time processing quite well, there is only a single sentence about prestack depth imaging, and anisotropic processing is not mentioned at all, even though both techniques are now becoming standard.
NASA Astrophysics Data System (ADS)
Oldham, Mark
2015-01-01
Radiochromic materials exhibit a colour change when exposed to ionising radiation. Radiochromic film has been used for clinical dosimetry for many years and increasingly so recently, as films of higher sensitivities have become available. The two principle advantages of radiochromic dosimetry include greater tissue equivalence (radiologically) and the lack of requirement for development of the colour change. In a radiochromic material, the colour change arises direct from ionising interactions affecting dye molecules, without requiring any latent chemical, optical or thermal development, with important implications for increased accuracy and convenience. It is only relatively recently however, that 3D radiochromic dosimetry has become possible. In this article we review recent developments and the current state-of-the-art of 3D radiochromic dosimetry, and the potential for a more comprehensive solution for the verification of complex radiation therapy treatments, and 3D dose measurement in general.
Improvement Of The Helmholtz Absorber
NASA Technical Reports Server (NTRS)
Morrow, Duane L.
1992-01-01
Helmholtz-resonator system improved to enable it to absorb sound at more than one frequency without appreciable loss of effectiveness at primary frequency. Addition of annular cavities enables absorption of sound at harmonic frequencies in addition to primary frequency. Improved absorber designed for use on structures of high transmission loss. Applied to such machines as fixed-speed engines and fans.
Iliesiu, Luca; Kos, Filip; Poland, David; ...
2016-03-17
We study the conformal bootstrap for a 4-point function of fermions <ψψψψ> in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge CT. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N. Finally, we also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran
2016-03-17
We study the conformal bootstrap for a 4-point function of fermions <ψψψψ> in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C_{T}. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N. Finally, we also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Clement, T.P.; Jones, N.L.
1998-02-01
RT3D (Reactive Transport in 3-Dimensions) is a computer code that solves coupled partial differential equations that describe reactive-flow and transport of multiple mobile and/or immobile species in a three dimensional saturated porous media. RT3D was developed from the single-species transport code, MT3D (DoD-1.5, 1997 version). As with MT3D, RT3D also uses the USGS groundwater flow model MODFLOW for computing spatial and temporal variations in groundwater head distribution. This report presents a set of tutorial problems that are designed to illustrate how RT3D simulations can be performed within the Department of Defense Groundwater Modeling System (GMS). GMS serves as a pre- and post-processing interface for RT3D. GMS can be used to define all the input files needed by RT3D code, and later the code can be launched from within GMS and run as a separate application. Once the RT3D simulation is completed, the solution can be imported to GMS for graphical post-processing. RT3D v1.0 supports several reaction packages that can be used for simulating different types of reactive contaminants. Each of the tutorials, described below, provides training on a different RT3D reaction package. Each reaction package has different input requirements, and the tutorials are designed to describe these differences. Furthermore, the tutorials illustrate the various options available in GMS for graphical post-processing of RT3D results. Users are strongly encouraged to complete the tutorials before attempting to use RT3D and GMS on a routine basis.
NASA Technical Reports Server (NTRS)
Plaut, Jeffrey J.
1993-01-01
Stereographic images of the surface of Venus which enable geologists to reconstruct the details of the planet's evolution are discussed. The 120-meter resolution of these 3D images make it possible to construct digital topographic maps from which precise measurements can be made of the heights, depths, slopes, and volumes of geologic structures.
NASA Astrophysics Data System (ADS)
Carson, Jeffrey J. L.; Roumeliotis, Michael; Chaudhary, Govind; Stodilka, Robert Z.; Anastasio, Mark A.
2010-06-01
Our group has concentrated on development of a 3D photoacoustic imaging system for biomedical imaging research. The technology employs a sparse parallel detection scheme and specialized reconstruction software to obtain 3D optical images using a single laser pulse. With the technology we have been able to capture 3D movies of translating point targets and rotating line targets. The current limitation of our 3D photoacoustic imaging approach is its inability ability to reconstruct complex objects in the field of view. This is primarily due to the relatively small number of projections used to reconstruct objects. However, in many photoacoustic imaging situations, only a few objects may be present in the field of view and these objects may have very high contrast compared to background. That is, the objects have sparse properties. Therefore, our work had two objectives: (i) to utilize mathematical tools to evaluate 3D photoacoustic imaging performance, and (ii) to test image reconstruction algorithms that prefer sparseness in the reconstructed images. Our approach was to utilize singular value decomposition techniques to study the imaging operator of the system and evaluate the complexity of objects that could potentially be reconstructed. We also compared the performance of two image reconstruction algorithms (algebraic reconstruction and l1-norm techniques) at reconstructing objects of increasing sparseness. We observed that for a 15-element detection scheme, the number of measureable singular vectors representative of the imaging operator was consistent with the demonstrated ability to reconstruct point and line targets in the field of view. We also observed that the l1-norm reconstruction technique, which is known to prefer sparseness in reconstructed images, was superior to the algebraic reconstruction technique. Based on these findings, we concluded (i) that singular value decomposition of the imaging operator provides valuable insight into the capabilities of
3D structured illumination microscopy
NASA Astrophysics Data System (ADS)
Dougherty, William M.; Goodwin, Paul C.
2011-03-01
Three-dimensional structured illumination microscopy achieves double the lateral and axial resolution of wide-field microscopy, using conventional fluorescent dyes, proteins and sample preparation techniques. A three-dimensional interference-fringe pattern excites the fluorescence, filling in the "missing cone" of the wide field optical transfer function, thereby enabling axial (z) discrimination. The pattern acts as a spatial carrier frequency that mixes with the higher spatial frequency components of the image, which usually succumb to the diffraction limit. The fluorescence image encodes the high frequency content as a down-mixed, moiré-like pattern. A series of images is required, wherein the 3D pattern is shifted and rotated, providing down-mixed data for a system of linear equations. Super-resolution is obtained by solving these equations. The speed with which the image series can be obtained can be a problem for the microscopy of living cells. Challenges include pattern-switching speeds, optical efficiency, wavefront quality and fringe contrast, fringe pitch optimization, and polarization issues. We will review some recent developments in 3D-SIM hardware with the goal of super-resolved z-stacks of motile cells.
Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows.
Park, H M; Lee, W M
2008-01-15
Many biofluids such as blood and DNA solutions are viscoelastic and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. However, the governing equations for viscoelastic flows are not easily solvable, especially for electroosmotic flows where the streamwise velocity varies rapidly from zero at the wall to a nearly uniform velocity at the outside of the very thin electric double layer. In the present investigation, we have devised a simple method to find the volumetric flow rate of viscoelastic electroosmotic flows through microchannels. It is based on the concept of the Helmholtz-Smoluchowski velocity which is widely adopted in the electroosmotic flows of Newtonian fluids. It is shown that the Helmholtz-Smoluchowski velocity for viscoelastic fluids can be found by solving a simple cubic algebraic equation. The volumetric flow rate obtained using this Helmholtz-Smoluchowski velocity is found to be almost the same as that obtained by solving the governing partial differential equations for various viscoelastic fluids.
Hong, X; Gao, H
2014-06-15
Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.
NASA Technical Reports Server (NTRS)
1997-01-01
The two hills in the distance, approximately one to two kilometers away, have been dubbed the 'Twin Peaks' and are of great interest to Pathfinder scientists as objects of future study. 3D glasses are necessary to identify surface detail. The white areas on the left hill, called the 'Ski Run' by scientists, may have been formed by hydrologic processes.
The IMP is a stereo imaging system with color capability provided by 24 selectable filters -- twelve filters per 'eye.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
NASA Astrophysics Data System (ADS)
Fung, Y. C.
1995-05-01
This conference on physiology and function covers a wide range of subjects, including the vasculature and blood flow, the flow of gas, water, and blood in the lung, the neurological structure and function, the modeling, and the motion and mechanics of organs. Many technologies are discussed. I believe that the list would include a robotic photographer, to hold the optical equipment in a precisely controlled way to obtain the images for the user. Why are 3D images needed? They are to achieve certain objectives through measurements of some objects. For example, in order to improve performance in sports or beauty of a person, we measure the form, dimensions, appearance, and movements.
NASA Technical Reports Server (NTRS)
1992-01-01
Ames Research Center research into virtual reality led to the development of the Convolvotron, a high speed digital audio processing system that delivers three-dimensional sound over headphones. It consists of a two-card set designed for use with a personal computer. The Convolvotron's primary application is presentation of 3D audio signals over headphones. Four independent sound sources are filtered with large time-varying filters that compensate for motion. The perceived location of the sound remains constant. Possible applications are in air traffic control towers or airplane cockpits, hearing and perception research and virtual reality development.
The Poisson-Helmholtz-Boltzmann model.
Bohinc, K; Shrestha, A; May, S
2011-10-01
We present a mean-field model of a one-component electrolyte solution where the mobile ions interact not only via Coulomb interactions but also through a repulsive non-electrostatic Yukawa potential. Our choice of the Yukawa potential represents a simple model for solvent-mediated interactions between ions. We employ a local formulation of the mean-field free energy through the use of two auxiliary potentials, an electrostatic and a non-electrostatic potential. Functional minimization of the mean-field free energy leads to two coupled local differential equations, the Poisson-Boltzmann equation and the Helmholtz-Boltzmann equation. Their boundary conditions account for the sources of both the electrostatic and non-electrostatic interactions on the surface of all macroions that reside in the solution. We analyze a specific example, two like-charged planar surfaces with their mobile counterions forming the electrolyte solution. For this system we calculate the pressure between the two surfaces, and we analyze its dependence on the strength of the Yukawa potential and on the non-electrostatic interactions of the mobile ions with the planar macroion surfaces. In addition, we demonstrate that our mean-field model is consistent with the contact theorem, and we outline its generalization to arbitrary interaction potentials through the use of a Laplace transformation.
Cevidanes, Lucia; Tucker, Scott; Styner, Martin; Kim, Hyungmin; Chapuis, Jonas; Reyes, Mauricio; Proffit, William; Turvey, Timothy; Jaskolka, Michael
2009-01-01
This paper discusses the development of methods for computer-aided jaw surgery. Computer-aided jaw surgery allows us to incorporate the high level of precision necessary for transferring virtual plans into the operating room. We also present a complete computer-aided surgery (CAS) system developed in close collaboration with surgeons. Surgery planning and simulation include construction of 3D surface models from Cone-beam CT (CBCT), dynamic cephalometry, semi-automatic mirroring, interactive cutting of bone and bony segment repositioning. A virtual setup can be used to manufacture positioning splints for intra-operative guidance. The system provides further intra-operative assistance with the help of a computer display showing jaw positions and 3D positioning guides updated in real-time during the surgical procedure. The CAS system aids in dealing with complex cases with benefits for the patient, with surgical practice, and for orthodontic finishing. Advanced software tools for diagnosis and treatment planning allow preparation of detailed operative plans, osteotomy repositioning, bone reconstructions, surgical resident training and assessing the difficulties of the surgical procedures prior to the surgery. CAS has the potential to make the elaboration of the surgical plan a more flexible process, increase the level of detail and accuracy of the plan, yield higher operative precision and control, and enhance documentation of cases. Supported by NIDCR DE017727, and DE018962 PMID:20816308
NASA Technical Reports Server (NTRS)
1997-01-01
An area of rocky terrain near the landing site of the Sagan Memorial Station can be seen in this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. This image is part of a 3D 'monster' panorama of the area surrounding the landing site.
Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is an operating division of the California Institute of Technology (Caltech). The Imager for Mars Pathfinder (IMP) was developed by the University of Arizona Lunar and Planetary Laboratory under contract to JPL. Peter Smith is the Principal Investigator.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
MAP3D: a media processor approach for high-end 3D graphics
NASA Astrophysics Data System (ADS)
Darsa, Lucia; Stadnicki, Steven; Basoglu, Chris
1999-12-01
Equator Technologies, Inc. has used a software-first approach to produce several programmable and advanced VLIW processor architectures that have the flexibility to run both traditional systems tasks and an array of media-rich applications. For example, Equator's MAP1000A is the world's fastest single-chip programmable signal and image processor targeted for digital consumer and office automation markets. The Equator MAP3D is a proposal for the architecture of the next generation of the Equator MAP family. The MAP3D is designed to achieve high-end 3D performance and a variety of customizable special effects by combining special graphics features with high performance floating-point and media processor architecture. As a programmable media processor, it offers the advantages of a completely configurable 3D pipeline--allowing developers to experiment with different algorithms and to tailor their pipeline to achieve the highest performance for a particular application. With the support of Equator's advanced C compiler and toolkit, MAP3D programs can be written in a high-level language. This allows the compiler to successfully find and exploit any parallelism in a programmer's code, thus decreasing the time to market of a given applications. The ability to run an operating system makes it possible to run concurrent applications in the MAP3D chip, such as video decoding while executing the 3D pipelines, so that integration of applications is easily achieved--using real-time decoded imagery for texturing 3D objects, for instance. This novel architecture enables an affordable, integrated solution for high performance 3D graphics.
Dust Dynamics in Kelvin-Helmholtz Instabilities
NASA Astrophysics Data System (ADS)
Hendrix, Tom; Keppens, Rony
2013-04-01
The Kelvin-Helmholtz instability (KHI) is a fluid instability which arises when two contacting flows have different tangential velocities. As shearing flows are very common in all sorts of (astro)physical fluid setups, the KHI is frequently encountered. In many astrophysical fluids the gas fluid in loaded with additional dust particles. Here we study the influence of these dust particles on the initiation of the KHI, as well as the effect the KHI has on the density distribution of dust species in a range of different particle sizes. This redistribution by the instability is of importance in the formation of dust structures in astrophysical fluids. To study the effect of dust on the linear and nonlinear phase of the KHI, we use the multi-fluid dust + gas module of the MPI-AMRVAC [1] code to perform 2D and 3D simulations of KHI in setups with physical quantities relevant to astrophysical fluids. A clear dependency on dust sizes is seen, with larger dust particles displaying significantly more clumping than smaller ones.
Finite Element Based Anisotropic 3D Inversion of Marine CSEM Data
NASA Astrophysics Data System (ADS)
Chung, Y.; Byun, J.
2015-12-01
In order to interpret three-dimensional (3D) marine controlled-source electromagnetic (MCSEM) data, it is critical to accurately determine electrical anisotropy because ignoring anisotropy can produce misleading artifacts. In this study, we present an inversion method for 3D subsurface imaging in media with an inhomogeneous and anisotropic conductivity distribution. Direct solvers are incorporated both in the forward and inverse problems, For the forward problem, the vector Helmholtz equation for the secondary electric field is discretized on a hexahedral mesh using edge finite elements, then a direct sparse-matrix solver is chosen to effectively reuse its factorization both in the survey simulation and Jacobian computation. The inversion method is formulated as a functional optimization with an objective functional containing terms measuring data misfit and model structure by means of smoothness and anisotropy. These measures are efficiently incorporated through the use of an iteratively reweighted least-squares scheme. The objective functional is minimized by a Gauss-Newton approach using a direct dense-matrix solver. We demonstrate the accuracy and applicability of the algorithm by testing it on synthetic data sets.
3D Global Two-Fluid Simulations of Turbulence in LAPD
NASA Astrophysics Data System (ADS)
Fisher, Dustin; Rogers, Barrett; Ricci, Paolo
2012-10-01
3D global two-fluid simulations are presented in an ongoing effort to identify and understand the physics of instabilities that arise in the Large Plasma Device (LAPD) at UCLA's Basic Science Facility. The LAPD, with its wide range of tunable parameters and device configurations, is ideally suited for studying space and laboratory plasmas. Moreover, the highly detailed and reproducible measurements of the LAPD lend themselves amicably to comparisons with simulations. Ongoing modeling is done using a modified version of the Global Braginskii Solver (GBS) [1] that models the plasma from source to edge region in a fully 3D two-fluid code. The reduced Braginskii equations are solved on a field-aligned grid using a finite difference method and 4th order Runge-Kutta time stepping and are parallelized on Dartmouth's Discovery cluster. Recent progress has been made to account for the thermionic cathode emission of fast electrons at the source, the axial dependence of the plasma source, and it is now possible to vary the potential on the front and side walls. Preliminary results, seen from the density and temperature profiles, show that the low frequency Kelvin Helmholtz instability still dominates the turbulence in the device.[4pt] [1] B. Rogers and P. Ricci. Phys. Rev. Lett. 104:225002, 2010
Caspi, S.; Helm, M.; Laslett, L.J.
1991-03-30
We have developed an harmonic representation for the three dimensional field components within the windings of accelerator magnets. The form by which the field is presented is suitable for interfacing with other codes that make use of the 3D field components (particle tracking and stability). The field components can be calculated with high precision and reduced cup time at any location (r,{theta},z) inside the magnet bore. The same conductor geometry which is used to simulate line currents is also used in CAD with modifications more readily available. It is our hope that the format used here for magnetic fields can be used not only as a means of delivering fields but also as a way by which beam dynamics can suggest correction to the conductor geometry. 5 refs., 70 figs.
Spiking neuron network Helmholtz machine
Sountsov, Pavel; Miller, Paul
2015-01-01
An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule. PMID:25954191
Spiking neuron network Helmholtz machine.
Sountsov, Pavel; Miller, Paul
2015-01-01
An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule.
Nonlinear behavior of Helmholtz resonators
NASA Astrophysics Data System (ADS)
Hersh, A. S.
1990-10-01
A semi-empirical fluid mechanical model has been derived to predict the nonlinear acoustic behavior of thin-walled, single-orifice Helmholtz resonators. The model assumed that the sound particle velocity field approaches the resonator in a spherically symmetric manner. The incident and cavity sound pressure fields are connected in terms of an orifice discharge coefficient and an end correction parameter whose values are determined empirically. The accuracy of the model was verified by comparing predicted with measured impedance over a wide range of sound amplitudes and frequencies for two different resonator geometries and with measurements conducted by Ingard and Ising.
Monolithically integrated Helmholtz coils by 3-dimensional printing
NASA Astrophysics Data System (ADS)
Li, Longguang; Abedini-Nassab, Roozbeh; Yellen, Benjamin B.
2014-06-01
3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.
Monolithically integrated Helmholtz coils by 3-dimensional printing
Li, Longguang; Abedini-Nassab, Roozbeh; Yellen, Benjamin B.
2014-06-23
3D printing technology is of great interest for the monolithic fabrication of integrated systems; however, it is a challenge to introduce metallic components into 3D printed molds to enable broader device functionality. Here, we develop a technique for constructing a multi-axial Helmholtz coil by injecting a eutectic liquid metal Gallium Indium alloy (EGaIn) into helically shaped orthogonal cavities constructed in a 3D printed block. The tri-axial solenoids each carry up to 3.6 A of electrical current and produce magnetic field up to 70 G. Within the central section of the coil, the field variation is less than 1% and is in agreement with theory. The flow rates and critical pressures required to fill the 3D cavities with liquid metal also agree with theoretical predictions and provide scaling trends for filling the 3D printed parts. These monolithically integrated solenoids may find future applications in electronic cell culture platforms, atomic traps, and miniaturized chemical analysis systems based on nuclear magnetic resonance.
NASA Astrophysics Data System (ADS)
Kühmstedt, Peter; Bräuer-Burchardt, Christian; Munkelt, Christoph; Heinze, Matthias; Palme, Martin; Schmidt, Ingo; Hintersehr, Josef; Notni, Gunther
2007-09-01
Here a new set-up of a 3D-scanning system for CAD/CAM in dental industry is proposed. The system is designed for direct scanning of the dental preparations within the mouth. The measuring process is based on phase correlation technique in combination with fast fringe projection in a stereo arrangement. The novelty in the approach is characterized by the following features: A phase correlation between the phase values of the images of two cameras is used for the co-ordinate calculation. This works contrary to the usage of only phase values (phasogrammetry) or classical triangulation (phase values and camera image co-ordinate values) for the determination of the co-ordinates. The main advantage of the method is that the absolute value of the phase at each point does not directly determine the coordinate. Thus errors in the determination of the co-ordinates are prevented. Furthermore, using the epipolar geometry of the stereo-like arrangement the phase unwrapping problem of fringe analysis can be solved. The endoscope like measurement system contains one projection and two camera channels for illumination and observation of the object, respectively. The new system has a measurement field of nearly 25mm × 15mm. The user can measure two or three teeth at one time. So the system can by used for scanning of single tooth up to bridges preparations. In the paper the first realization of the intraoral scanner is described.
NASA Technical Reports Server (NTRS)
2004-01-01
This 3-D, microscopic imager mosaic of a target area on a rock called 'Diamond Jenness' was taken after NASA's Mars Exploration Rover Opportunity ground into the surface with its rock abrasion tool for a second time.
Opportunity has bored nearly a dozen holes into the inner walls of 'Endurance Crater.' On sols 177 and 178 (July 23 and July 24, 2004), the rover worked double-duty on Diamond Jenness. Surface debris and the bumpy shape of the rock resulted in a shallow and irregular hole, only about 2 millimeters (0.08 inch) deep. The final depth was not enough to remove all the bumps and leave a neat hole with a smooth floor. This extremely shallow depression was then examined by the rover's alpha particle X-ray spectrometer.
On Sol 178, Opportunity's 'robotic rodent' dined on Diamond Jenness once again, grinding almost an additional 5 millimeters (about 0.2 inch). The rover then applied its Moessbauer spectrometer to the deepened hole. This double dose of Diamond Jenness enabled the science team to examine the rock at varying layers. Results from those grindings are currently being analyzed.
The image mosaic is about 6 centimeters (2.4 inches) across.
NASA Technical Reports Server (NTRS)
1997-01-01
Many prominent rocks near the Sagan Memorial Station are featured in this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. Wedge is at lower left; Shark, Half-Dome, and Pumpkin are at center. Flat Top, about four inches high, is at lower right. The horizon in the distance is one to two kilometers away.
Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is an operating division of the California Institute of Technology (Caltech). The Imager for Mars Pathfinder (IMP) was developed by the University of Arizona Lunar and Planetary Laboratory under contract to JPL. Peter Smith is the Principal Investigator.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
SB3D User Manual, Santa Barbara 3D Radiative Transfer Model
O'Hirok, William
1999-01-01
SB3D is a three-dimensional atmospheric and oceanic radiative transfer model for the Solar spectrum. The microphysics employed in the model are the same as used in the model SBDART. It is assumed that the user of SB3D is familiar with SBDART and IDL. SB3D differs from SBDART in that computations are conducted on media in three-dimensions rather than a single column (i.e. plane-parallel), and a stochastic method (Monte Carlo) is employed instead of a numerical approach (Discrete Ordinates) for estimating a solution to the radiative transfer equation. Because of these two differences between SB3D and SBDART, the input and running of SB3D is more unwieldy and requires compromises between model performance and computational expense. Hence, there is no one correct method for running the model and the user must develop a sense to the proper input and configuration of the model.
Fluid mechanical model of the Helmholtz resonator
NASA Technical Reports Server (NTRS)
Hersh, A. S.; Walker, B.
1977-01-01
A semi-empirical fluid mechanical model of the acoustic behavior of Helmholtz resonators is presented which predicts impedance as a function of the amplitude and frequency of the incident sound pressure field and resonator geometry. The model assumes that the particle velocity approaches the orifice in a spherical manner. The incident and cavity sound fields are connected by solving the governing oscillating mass and momentum conservation equations. The model is in agreement with the Rayleigh slug-mass model at low values of incident sound pressure level. At high values, resistance is predicted to be independent of frequency, proportional to the square root of the amplitude of the incident sound pressure field, and virtually independent of resonator geometry. Reactance is predicted to depend in a very complicated way upon resonator geometry, incident sound pressure level, and frequency. Nondimensional parameters are defined that divide resonator impedance into three categories corresponding to low, moderately low, and intense incident sound pressure amplitudes. The two-microphone method was used to measure the impedance of a variety of resonators. The data were used to refine and verify the model.
Recent EFIT Developments and 3D Extension
NASA Astrophysics Data System (ADS)
Lao, L. L.; Chu, M. S.; St. John, H. E.; Strait, E. J.; Montgomery, A. L.; Perkins, F. W.
2006-10-01
Recent developments of the equilibrium reconstruction code EFIT and its 3D extension to model toroidally asymmetric effects due to error and externally applied perturbation magnetic fields are presented. These include a new more complete uncertainty matrix for magnetic diagnostics based on detailed knowledge about their fabrication, installation, calibration, and operation. A new algorithm to efficiently compute high bootstrap-fraction equilibria that explicitly separates out the Pfirsch-Schluter and bootstrap contributions to the poloidal current stream function is also being developed. Other on-going and planned developments include a new computational structure based on Fortran 90/95 with a unified interface that can conveniently accommodate different tokamak devices and grid sizes, as well as a computational link that allows easy integration with transport and stability physics modules for integrated modeling. EFIT reconstruction capability is also being extended to 3D based on perturbation solutions to the 3D Grad-Shafranov equilibrium equation.
3-D Mesh Generation Nonlinear Systems
Christon, M. A.; Dovey, D.; Stillman, D. W.; Hallquist, J. O.; Rainsberger, R. B
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surface equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.
NASA Astrophysics Data System (ADS)
Mediavilla, Evencio; Arribas, Santiago; Roth, Martin; Cepa-Nogué, Jordi; Sánchez, Francisco
2011-09-01
Preface; Acknowledgements; 1. Introductory review and technical approaches Martin M. Roth; 2. Observational procedures and data reduction James E. H. Turner; 3. 3D Spectroscopy instrumentation M. A. Bershady; 4. Analysis of 3D data Pierre Ferruit; 5. Science motivation for IFS and galactic studies F. Eisenhauer; 6. Extragalactic studies and future IFS science Luis Colina; 7. Tutorials: how to handle 3D spectroscopy data Sebastian F. Sánchez, Begona García-Lorenzo and Arlette Pécontal-Rousset.
Spherical 3D isotropic wavelets
NASA Astrophysics Data System (ADS)
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
De Kock, Liesbet
2016-04-01
In this analysis, the classical problem of Hermann von Helmholtz's (1821-1894) Kantianism is explored from a particular vantage point, that to my knowledge, has not received the attention it deserves notwithstanding its possible key role in disentangling Helmholtz's relation to Kant's critical project. More particularly, we will focus on Helmholtz's critical engagement with Kant's concept of intuition [Anschauung] and (the related issue of) his dissatisfaction with Kant's doctrinal dualism. In doing so, it soon becomes clear that both (i) crucially mediated Helmholtz's idiosyncratic appropriation and criticism of (certain aspects of) Kant's critical project, and (ii) can be considered as a common denominator in a variety of issues that are usually addressed separately under the general header of (the problem of) Helmholtz's Kantianism. The perspective offered in this analysis can not only shed interesting new light on some interpretive issues that have become commonplace in discussions on Helmholtz's Kantianism, but also offers a particular way of connecting seemingly unrelated dimensions of Helmholtz's engagement with Kant's critical project (e.g. Helmholtz's views on causality and space). Furthermore, it amounts to the rather surprising conclusion that Helmholtz's most drastic revision of Kant's project pertains to his assumption of free will as a formal condition of experience and knowledge.
3D Elevation Program—Virtual USA in 3D
Lukas, Vicki; Stoker, J.M.
2016-04-14
The U.S. Geological Survey (USGS) 3D Elevation Program (3DEP) uses a laser system called ‘lidar’ (light detection and ranging) to create a virtual reality map of the Nation that is very accurate. 3D maps have many uses with new uses being discovered all the time.
Parametric design of tri-axial nested Helmholtz coils
Abbott, Jake J.
2015-05-15
This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.
Parametric design of tri-axial nested Helmholtz coils.
Abbott, Jake J
2015-05-01
This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.
Drift Kelvin-Helmholtz instabilities in space plasmas
NASA Technical Reports Server (NTRS)
Sharma, Avadhesh C.; Srivastava, Krishna M.
1992-01-01
Drift Kelvin-Helmholtz instabilities of a finite-beta plasma in equilibrium electric and magnetic fields which are perpendicular to each other are studied using two fluid equations. Three types of these instabilities are considered including the magnetosonic instability of a finite beta-homogeneous plasma, the electrostatic drift instability of an inhomogeneous low-beta plasma, and the magneto-acoustic instability of a high-beta inhomogeneous isothermal plasma. It is shown that the electric field has either stabilizing or destabilizing effect depending on conditions under consideration.
Fully vectorial accelerating diffraction-free Helmholtz beams.
Aleahmad, Parinaz; Miri, Mohammad-Ali; Mills, Matthew S; Kaminer, Ido; Segev, Mordechai; Christodoulides, Demetrios N
2012-11-16
We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.
A transverse Kelvin-Helmholtz instability in a magnetized plasma
NASA Technical Reports Server (NTRS)
Kintner, P.; Dangelo, N.
1977-01-01
An analysis is conducted of the transverse Kelvin-Helmholtz instability in a magnetized plasma for unstable flute modes. The analysis makes use of a two-fluid model. Details regarding the instability calculation are discussed, taking into account the ion continuity and momentum equations, the solution of a zero-order and a first-order component, and the properties of the solution. It is expected that the linear calculation conducted will apply to situations in which the plasma has experienced no more than a few growth periods.
The Magnetic Field of Helmholtz Coils
ERIC Educational Resources Information Center
Berridge, H. J. J.
1975-01-01
Describes the magnetic field of Helmholtz coils qualitatively and then provides the basis for a quantitative expression. Since the mathematical calculations are very involved, a computer program for solving the mathematical expression is presented and explained. (GS)
None
2016-07-12
This video provides an overview of the Sandia National Laboratories developed 3-D World Model Building capability that provides users with an immersive, texture rich 3-D model of their environment in minutes using a laptop and color and depth camera.
NASA Astrophysics Data System (ADS)
van Hecke, Martin; de Reus, Koen; Florijn, Bastiaan; Coulais, Corentin
2014-03-01
We present a class of elastic structures which exhibit collective buckling in 3D, and create these by a 3D printing/moulding technique. Our structures consist of cubic lattice of anisotropic unit cells, and we show that their mechanical properties are programmable via the orientation of these unit cells.
2013-10-30
This video provides an overview of the Sandia National Laboratories developed 3-D World Model Building capability that provides users with an immersive, texture rich 3-D model of their environment in minutes using a laptop and color and depth camera.
2013-10-01
Earth3D is a computer code designed to allow fast calculation of seismic rays and travel times through a 3D model of the Earth. LLNL is using this for earthquake location and global tomography efforts and such codes are of great interest to the Earth Science community.
NASA Technical Reports Server (NTRS)
1977-01-01
A market study of a proposed version of a 3-D eyetracker for initial use at NASA's Ames Research Center was made. The commercialization potential of a simplified, less expensive 3-D eyetracker was ascertained. Primary focus on present and potential users of eyetrackers, as well as present and potential manufacturers has provided an effective means of analyzing the prospects for commercialization.
Development and Testing of EFIT 3D Equilibrium Reconstruction Capability
NASA Astrophysics Data System (ADS)
Lao, L. L.; Ferraro, N. M.; Strait, E. J.; Turnbull, A. D.; King, J. D.
2014-10-01
Recent development and testing of EFIT capability to reconstruct tokamak 3D perturbed equilibrium are described. The 3D extension is based on an expansion of the MHD equations to account for the 3D effects. EFIT uses the cylindrical coordinate system and can include magnetic island and stochastic effects. Several linearization schemes are being explored to improve the EFIT 3D perturbed solutions. Algorithms are also being developed to allow EFIT to reconstruct 3D perturbed equilibria directly making use of plasma response to 3D perturbations from the MARS or M3D-C1 MHD codes. Other efforts include testing of the new EFIT 3D capability using simulated magnetic data based on response calculations from MARS and M3D-C1, and performing detailed benchmarking calculations against other 3D codes such as VMEC/V3FIT. Reconstruction examples using EFIT and the new DIII-D 3D magnetic measurements to reconstruct 3D perturbed experimental equilibria using well-diagnosed discharges from DIII-D error field, RWM, and RMP experiments will be presented. Work supported by the US DOE under DE-FC02-04ER54698 and DE-FG02-95ER54309.
Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.
Kiselev, Aleksei P; Plachenov, Alexandr B
2016-04-01
The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.
NASA Astrophysics Data System (ADS)
Walsh, J. R.
2004-02-01
The Euro3D RTN is an EU funded Research Training Network to foster the exploitation of 3D spectroscopy in Europe. 3D spectroscopy is a general term for spectroscopy of an area of the sky and derives its name from its two spatial + one spectral dimensions. There are an increasing number of instruments which use integral field devices to achieve spectroscopy of an area of the sky, either using lens arrays, optical fibres or image slicers, to pack spectra of multiple pixels on the sky (``spaxels'') onto a 2D detector. On account of the large volume of data and the special methods required to reduce and analyse 3D data, there are only a few centres of expertise and these are mostly involved with instrument developments. There is a perceived lack of expertise in 3D spectroscopy spread though the astronomical community and its use in the armoury of the observational astronomer is viewed as being highly specialised. For precisely this reason the Euro3D RTN was proposed to train young researchers in this area and develop user tools to widen the experience with this particular type of data in Europe. The Euro3D RTN is coordinated by Martin M. Roth (Astrophysikalisches Institut Potsdam) and has been running since July 2002. The first Euro3D science conference was held in Cambridge, UK from 22 to 23 May 2003. The main emphasis of the conference was, in keeping with the RTN, to expose the work of the young post-docs who are funded by the RTN. In addition the team members from the eleven European institutes involved in Euro3D also presented instrumental and observational developments. The conference was organized by Andy Bunker and held at the Institute of Astronomy. There were over thirty participants and 26 talks covered the whole range of application of 3D techniques. The science ranged from Galactic planetary nebulae and globular clusters to kinematics of nearby galaxies out to objects at high redshift. Several talks were devoted to reporting recent observations with newly
NASA Astrophysics Data System (ADS)
Pezzaniti, J. Larry; Edmondson, Richard; Vaden, Justin; Hyatt, Bryan; Chenault, David B.; Kingston, David; Geulen, Vanilynmae; Newell, Scott; Pettijohn, Brad
2009-02-01
In this paper, we report on the development of a 3D vision system consisting of a flat panel stereoscopic display and auto-converging stereo camera and an assessment of the system's use for robotic driving, manipulation, and surveillance operations. The 3D vision system was integrated onto a Talon Robot and Operator Control Unit (OCU) such that direct comparisons of the performance of a number of test subjects using 2D and 3D vision systems were possible. A number of representative scenarios were developed to determine which tasks benefited most from the added depth perception and to understand when the 3D vision system hindered understanding of the scene. Two tests were conducted at Fort Leonard Wood, MO with noncommissioned officers ranked Staff Sergeant and Sergeant First Class. The scenarios; the test planning, approach and protocols; the data analysis; and the resulting performance assessment of the 3D vision system are reported.
Dawood, A; Marti Marti, B; Sauret-Jackson, V; Darwood, A
2015-12-01
3D printing has been hailed as a disruptive technology which will change manufacturing. Used in aerospace, defence, art and design, 3D printing is becoming a subject of great interest in surgery. The technology has a particular resonance with dentistry, and with advances in 3D imaging and modelling technologies such as cone beam computed tomography and intraoral scanning, and with the relatively long history of the use of CAD CAM technologies in dentistry, it will become of increasing importance. Uses of 3D printing include the production of drill guides for dental implants, the production of physical models for prosthodontics, orthodontics and surgery, the manufacture of dental, craniomaxillofacial and orthopaedic implants, and the fabrication of copings and frameworks for implant and dental restorations. This paper reviews the types of 3D printing technologies available and their various applications in dentistry and in maxillofacial surgery.
NASA Technical Reports Server (NTRS)
Walatka, Pamela P.; Buning, Pieter G.; Pierce, Larry; Elson, Patricia A.
1990-01-01
PLOT3D is a computer graphics program designed to visualize the grids and solutions of computational fluid dynamics. Seventy-four functions are available. Versions are available for many systems. PLOT3D can handle multiple grids with a million or more grid points, and can produce varieties of model renderings, such as wireframe or flat shaded. Output from PLOT3D can be used in animation programs. The first part of this manual is a tutorial that takes the reader, keystroke by keystroke, through a PLOT3D session. The second part of the manual contains reference chapters, including the helpfile, data file formats, advice on changing PLOT3D, and sample command files.
Parallel CARLOS-3D code development
Putnam, J.M.; Kotulski, J.D.
1996-02-01
CARLOS-3D is a three-dimensional scattering code which was developed under the sponsorship of the Electromagnetic Code Consortium, and is currently used by over 80 aerospace companies and government agencies. The code has been extensively validated and runs on both serial workstations and parallel super computers such as the Intel Paragon. CARLOS-3D is a three-dimensional surface integral equation scattering code based on a Galerkin method of moments formulation employing Rao- Wilton-Glisson roof-top basis for triangular faceted surfaces. Fully arbitrary 3D geometries composed of multiple conducting and homogeneous bulk dielectric materials can be modeled. This presentation describes some of the extensions to the CARLOS-3D code, and how the operator structure of the code facilitated these improvements. Body of revolution (BOR) and two-dimensional geometries were incorporated by simply including new input routines, and the appropriate Galerkin matrix operator routines. Some additional modifications were required in the combined field integral equation matrix generation routine due to the symmetric nature of the BOR and 2D operators. Quadrilateral patched surfaces with linear roof-top basis functions were also implemented in the same manner. Quadrilateral facets and triangular facets can be used in combination to more efficiently model geometries with both large smooth surfaces and surfaces with fine detail such as gaps and cracks. Since the parallel implementation in CARLOS-3D is at high level, these changes were independent of the computer platform being used. This approach minimizes code maintenance, while providing capabilities with little additional effort. Results are presented showing the performance and accuracy of the code for some large scattering problems. Comparisons between triangular faceted and quadrilateral faceted geometry representations will be shown for some complex scatterers.
Unassisted 3D camera calibration
NASA Astrophysics Data System (ADS)
Atanassov, Kalin; Ramachandra, Vikas; Nash, James; Goma, Sergio R.
2012-03-01
With the rapid growth of 3D technology, 3D image capture has become a critical part of the 3D feature set on mobile phones. 3D image quality is affected by the scene geometry as well as on-the-device processing. An automatic 3D system usually assumes known camera poses accomplished by factory calibration using a special chart. In real life settings, pose parameters estimated by factory calibration can be negatively impacted by movements of the lens barrel due to shaking, focusing, or camera drop. If any of these factors displaces the optical axes of either or both cameras, vertical disparity might exceed the maximum tolerable margin and the 3D user may experience eye strain or headaches. To make 3D capture more practical, one needs to consider unassisted (on arbitrary scenes) calibration. In this paper, we propose an algorithm that relies on detection and matching of keypoints between left and right images. Frames containing erroneous matches, along with frames with insufficiently rich keypoint constellations, are detected and discarded. Roll, pitch yaw , and scale differences between left and right frames are then estimated. The algorithm performance is evaluated in terms of the remaining vertical disparity as compared to the maximum tolerable vertical disparity.
2007-11-02
AGENCY USE ONLY (Leave Blank) 2. REPORT DATE 5 Feb 98 4. TITLE AND SUBTITLE 3D Scan Systems Integration REPORT TYPE AND DATES COVERED...2-89) Prescribed by ANSI Std. Z39-1 298-102 [ EDO QUALITY W3PECTEDI DLA-ARN Final Report for US Defense Logistics Agency on DDFG-T2/P3: 3D...SCAN SYSTEMS INTEGRATION Contract Number SPO100-95-D-1014 Contractor Ohio University Delivery Order # 0001 Delivery Order Title 3D Scan Systems
Simon, Carl G; Yang, Yanyin; Dorsey, Shauna M; Ramalingam, Murugan; Chatterjee, Kaushik
2011-01-01
We have developed a combinatorial platform for fabricating tissue scaffold arrays that can be used for screening cell-material interactions. Traditional research involves preparing samples one at a time for characterization and testing. Combinatorial and high-throughput (CHT) methods lower the cost of research by reducing the amount of time and material required for experiments by combining many samples into miniaturized specimens. In order to help accelerate biomaterials research, many new CHT methods have been developed for screening cell-material interactions where materials are presented to cells as a 2D film or surface. However, biomaterials are frequently used to fabricate 3D scaffolds, cells exist in vivo in a 3D environment and cells cultured in a 3D environment in vitro typically behave more physiologically than those cultured on a 2D surface. Thus, we have developed a platform for fabricating tissue scaffold libraries where biomaterials can be presented to cells in a 3D format.
NASA Astrophysics Data System (ADS)
Lee-Elkin, Forest
2008-04-01
Three dimensional (3D) autofocus remains a significant challenge for the development of practical 3D multipass radar imaging. The current 2D radar autofocus methods are not readily extendable across sensor passes. We propose a general framework that allows a class of data adaptive solutions for 3D auto-focus across passes with minimal constraints on the scene contents. The key enabling assumption is that portions of the scene are sparse in elevation which reduces the number of free variables and results in a system that is simultaneously solved for scatterer heights and autofocus parameters. The proposed method extends 2-pass interferometric synthetic aperture radar (IFSAR) methods to an arbitrary number of passes allowing the consideration of scattering from multiple height locations. A specific case from the proposed autofocus framework is solved and demonstrates autofocus and coherent multipass 3D estimation across the 8 passes of the "Gotcha Volumetric SAR Data Set" X-Band radar data.
Extraordinary acoustic transmission mediated by Helmholtz resonators
NASA Astrophysics Data System (ADS)
Koju, Vijay; Rowe, Ebony; Robertson, William M.
2014-07-01
We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.
Extraordinary acoustic transmission mediated by Helmholtz resonators
Koju, Vijay; Rowe, Ebony; Robertson, William M.
2014-07-15
We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics.
Combinatorial 3D Mechanical Metamaterials
NASA Astrophysics Data System (ADS)
Coulais, Corentin; Teomy, Eial; de Reus, Koen; Shokef, Yair; van Hecke, Martin
2015-03-01
We present a class of elastic structures which exhibit 3D-folding motion. Our structures consist of cubic lattices of anisotropic unit cells that can be tiled in a complex combinatorial fashion. We design and 3d-print this complex ordered mechanism, in which we combine elastic hinges and defects to tailor the mechanics of the material. Finally, we use this large design space to encode smart functionalities such as surface patterning and multistability.
EFIT 3D Reconstruction and Recent Developments
NASA Astrophysics Data System (ADS)
Lao, L. L.; Chu, M. S.; St. John, H. E.; Strait, E. J.; Turnbull, A. D.; Ren, Q.; Jeon, Y. M.; Flannagan, D.
2007-11-01
Recent 3D extension of the EFIT equilibrium reconstruction code to model toroidally asymmetric effects due to error and externally applied perturbation magnetic fields and other developments are presented. The 3D extension is based on an expansion of the MHD equations. Other developments include a new computational structure based on Fortran 90/95 with a unified interface that can conveniently accommodate different tokamak devices and grid sizes, as well as a Python-based GUI. New computational links that allow easy integration with transport and stability physics modules to facilitate kinetic reconstruction and stability analysis are also being developed. A new more complete uncertainty matrix for magnetic diagnostics based on knowledge about their fabrication, installation, calibration, and operation has also been implemented into EFIT and tested. Reconstructions with the new magnetic uncertainty matrix yield results similar to those using the existing one but with more realistic fitting merit figures.
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
Helmholtz and the psychophysiology of time.
Debru, C
2001-09-01
After having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves (as well as with aspects of perception) were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz's conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background.
3-D Force-balanced Magnetospheric Configurations
Sorin Zaharia; C.Z. Cheng; K. Maezawa
2003-02-10
The knowledge of plasma pressure is essential for many physics applications in the magnetosphere, such as computing magnetospheric currents and deriving magnetosphere-ionosphere coupling. A thorough knowledge of the 3-D pressure distribution has however eluded the community, as most in-situ pressure observations are either in the ionosphere or the equatorial region of the magnetosphere. With the assumption of pressure isotropy there have been attempts to obtain the pressure at different locations by either (a) mapping observed data (e.g., in the ionosphere) along the field lines of an empirical magnetospheric field model or (b) computing a pressure profile in the equatorial plane (in 2-D) or along the Sun-Earth axis (in 1-D) that is in force balance with the magnetic stresses of an empirical model. However, the pressure distributions obtained through these methods are not in force balance with the empirical magnetic field at all locations. In order to find a global 3-D plasma pressure distribution in force balance with the magnetospheric magnetic field, we have developed the MAG-3D code, that solves the 3-D force balance equation J x B = (upside-down delta) P computationally. Our calculation is performed in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials as B = (upside-down delta) psi x (upside-down delta) alpha. The pressure distribution, P = P(psi,alpha), is prescribed in the equatorial plane and is based on satellite measurements. In addition, computational boundary conditions for y surfaces are imposed using empirical field models. Our results provide 3-D distributions of magnetic field and plasma pressure as well as parallel and transverse currents for both quiet-time and disturbed magnetospheric conditions.
NASA Astrophysics Data System (ADS)
Dima, M.; Farisato, G.; Bergomi, M.; Viotto, V.; Magrin, D.; Greggio, D.; Farinato, J.; Marafatto, L.; Ragazzoni, R.; Piazza, D.
2014-08-01
In the last few years 3D printing is getting more and more popular and used in many fields going from manufacturing to industrial design, architecture, medical support and aerospace. 3D printing is an evolution of bi-dimensional printing, which allows to obtain a solid object from a 3D model, realized with a 3D modelling software. The final product is obtained using an additive process, in which successive layers of material are laid down one over the other. A 3D printer allows to realize, in a simple way, very complex shapes, which would be quite difficult to be produced with dedicated conventional facilities. Thanks to the fact that the 3D printing is obtained superposing one layer to the others, it doesn't need any particular work flow and it is sufficient to simply draw the model and send it to print. Many different kinds of 3D printers exist based on the technology and material used for layer deposition. A common material used by the toner is ABS plastics, which is a light and rigid thermoplastic polymer, whose peculiar mechanical properties make it diffusely used in several fields, like pipes production and cars interiors manufacturing. I used this technology to create a 1:1 scale model of the telescope which is the hardware core of the space small mission CHEOPS (CHaracterising ExOPlanets Satellite) by ESA, which aims to characterize EXOplanets via transits observations. The telescope has a Ritchey-Chrétien configuration with a 30cm aperture and the launch is foreseen in 2017. In this paper, I present the different phases for the realization of such a model, focusing onto pros and cons of this kind of technology. For example, because of the finite printable volume (10×10×12 inches in the x, y and z directions respectively), it has been necessary to split the largest parts of the instrument in smaller components to be then reassembled and post-processed. A further issue is the resolution of the printed material, which is expressed in terms of layers
NASA Astrophysics Data System (ADS)
Keefe, Laurence
2016-11-01
Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.
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
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
YouDash3D: exploring stereoscopic 3D gaming for 3D movie theaters
NASA Astrophysics Data System (ADS)
Schild, Jonas; Seele, Sven; Masuch, Maic
2012-03-01
Along with the success of the digitally revived stereoscopic cinema, events beyond 3D movies become attractive for movie theater operators, i.e. interactive 3D games. In this paper, we present a case that explores possible challenges and solutions for interactive 3D games to be played by a movie theater audience. We analyze the setting and showcase current issues related to lighting and interaction. Our second focus is to provide gameplay mechanics that make special use of stereoscopy, especially depth-based game design. Based on these results, we present YouDash3D, a game prototype that explores public stereoscopic gameplay in a reduced kiosk setup. It features live 3D HD video stream of a professional stereo camera rig rendered in a real-time game scene. We use the effect to place the stereoscopic effigies of players into the digital game. The game showcases how stereoscopic vision can provide for a novel depth-based game mechanic. Projected trigger zones and distributed clusters of the audience video allow for easy adaptation to larger audiences and 3D movie theater gaming.
NASA Technical Reports Server (NTRS)
2002-01-01
In 1999, Genex submitted a proposal to Stennis Space Center for a volumetric 3-D display technique that would provide multiple users with a 360-degree perspective to simultaneously view and analyze 3-D data. The futuristic capabilities of the VolumeViewer(R) have offered tremendous benefits to commercial users in the fields of medicine and surgery, air traffic control, pilot training and education, computer-aided design/computer-aided manufacturing, and military/battlefield management. The technology has also helped NASA to better analyze and assess the various data collected by its satellite and spacecraft sensors. Genex capitalized on its success with Stennis by introducing two separate products to the commercial market that incorporate key elements of the 3-D display technology designed under an SBIR contract. The company Rainbow 3D(R) imaging camera is a novel, three-dimensional surface profile measurement system that can obtain a full-frame 3-D image in less than 1 second. The third product is the 360-degree OmniEye(R) video system. Ideal for intrusion detection, surveillance, and situation management, this unique camera system offers a continuous, panoramic view of a scene in real time.
A 3-D chimera grid embedding technique
NASA Technical Reports Server (NTRS)
Benek, J. A.; Buning, P. G.; Steger, J. L.
1985-01-01
A three-dimensional (3-D) chimera grid-embedding technique is described. The technique simplifies the construction of computational grids about complex geometries. The method subdivides the physical domain into regions which can accommodate easily generated grids. Communication among the grids is accomplished by interpolation of the dependent variables at grid boundaries. The procedures for constructing the composite mesh and the associated data structures are described. The method is demonstrated by solution of the Euler equations for the transonic flow about a wing/body, wing/body/tail, and a configuration of three ellipsoidal bodies.
Van Goethem, Emeline; Guiet, Romain; Balor, Stéphanie; Charrière, Guillaume M; Poincloux, Renaud; Labrousse, Arnaud; Maridonneau-Parini, Isabelle; Le Cabec, Véronique
2011-01-01
Macrophage tissue infiltration is a critical step in the immune response against microorganisms and is also associated with disease progression in chronic inflammation and cancer. Macrophages are constitutively equipped with specialized structures called podosomes dedicated to extracellular matrix (ECM) degradation. We recently reported that these structures play a critical role in trans-matrix mesenchymal migration mode, a protease-dependent mechanism. Podosome molecular components and their ECM-degrading activity have been extensively studied in two dimensions (2D), but yet very little is known about their fate in three-dimensional (3D) environments. Therefore, localization of podosome markers and proteolytic activity were carefully examined in human macrophages performing mesenchymal migration. Using our gelled collagen I 3D matrix model to obligate human macrophages to perform mesenchymal migration, classical podosome markers including talin, paxillin, vinculin, gelsolin, cortactin were found to accumulate at the tip of F-actin-rich cell protrusions together with β1 integrin and CD44 but not β2 integrin. Macrophage proteolytic activity was observed at podosome-like protrusion sites using confocal fluorescence microscopy and electron microscopy. The formation of migration tunnels by macrophages inside the matrix was accomplished by degradation, engulfment and mechanic compaction of the matrix. In addition, videomicroscopy revealed that 3D F-actin-rich protrusions of migrating macrophages were as dynamic as their 2D counterparts. Overall, the specifications of 3D podosomes resembled those of 2D podosome rosettes rather than those of individual podosomes. This observation was further supported by the aspect of 3D podosomes in fibroblasts expressing Hck, a master regulator of podosome rosettes in macrophages. In conclusion, human macrophage podosomes go 3D and take the shape of spherical podosome rosettes when the cells perform mesenchymal migration. This work
3D Printed Bionic Nanodevices.
Kong, Yong Lin; Gupta, Maneesh K; Johnson, Blake N; McAlpine, Michael C
2016-06-01
The ability to three-dimensionally interweave biological and functional materials could enable the creation of bionic devices possessing unique and compelling geometries, properties, and functionalities. Indeed, interfacing high performance active devices with biology could impact a variety of fields, including regenerative bioelectronic medicines, smart prosthetics, medical robotics, and human-machine interfaces. Biology, from the molecular scale of DNA and proteins, to the macroscopic scale of tissues and organs, is three-dimensional, often soft and stretchable, and temperature sensitive. This renders most biological platforms incompatible with the fabrication and materials processing methods that have been developed and optimized for functional electronics, which are typically planar, rigid and brittle. A number of strategies have been developed to overcome these dichotomies. One particularly novel approach is the use of extrusion-based multi-material 3D printing, which is an additive manufacturing technology that offers a freeform fabrication strategy. This approach addresses the dichotomies presented above by (1) using 3D printing and imaging for customized, hierarchical, and interwoven device architectures; (2) employing nanotechnology as an enabling route for introducing high performance materials, with the potential for exhibiting properties not found in the bulk; and (3) 3D printing a range of soft and nanoscale materials to enable the integration of a diverse palette of high quality functional nanomaterials with biology. Further, 3D printing is a multi-scale platform, allowing for the incorporation of functional nanoscale inks, the printing of microscale features, and ultimately the creation of macroscale devices. This blending of 3D printing, novel nanomaterial properties, and 'living' platforms may enable next-generation bionic systems. In this review, we highlight this synergistic integration of the unique properties of nanomaterials with the
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
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
NASA Technical Reports Server (NTRS)
1997-01-01
Portions of the lander's deflated airbags and a petal are at the lower area of this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. The metallic object at lower right is part of the lander's low-gain antenna. This image is part of a 3D 'monster
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
3D Computations and Experiments
Couch, R; Faux, D; Goto, D; Nikkel, D
2004-04-05
This project consists of two activities. Task A, Simulations and Measurements, combines all the material model development and associated numerical work with the materials-oriented experimental activities. The goal of this effort is to provide an improved understanding of dynamic material properties and to provide accurate numerical representations of those properties for use in analysis codes. Task B, ALE3D Development, involves general development activities in the ALE3D code with the focus of improving simulation capabilities for problems of mutual interest to DoD and DOE. Emphasis is on problems involving multi-phase flow, blast loading of structures and system safety/vulnerability studies.
Elastic wave modelling in 3D heterogeneous media: 3D grid method
NASA Astrophysics Data System (ADS)
Jianfeng, Zhang; Tielin, Liu
2002-09-01
We present a new numerical technique for elastic wave modelling in 3D heterogeneous media with surface topography, which is called the 3D grid method in this paper. This work is an extension of the 2D grid method that models P-SV wave propagation in 2D heterogeneous media. Similar to the finite-element method in the discretization of a numerical mesh, the proposed scheme is flexible in incorporating surface topography and curved interfaces; moreover it satisfies the free-surface boundary conditions of 3D topography naturally. The algorithm, developed from a parsimonious staggered-grid scheme, solves the problem using integral equilibrium around each node, instead of satisfying elastodynamic differential equations at each node as in the conventional finite-difference method. The computational cost and memory requirements for the proposed scheme are approximately the same as those used by the same order finite-difference method. In this paper, a mixed tetrahedral and parallelepiped grid method is presented; and the numerical dispersion and stability criteria on the tetrahedral grid method and parallelepiped grid method are discussed in detail. The proposed scheme is successfully tested against an analytical solution for the 3D Lamb problem and a solution of the boundary method for the diffraction of a hemispherical crater. Moreover, examples of surface-wave propagation in an elastic half-space with a semi-cylindrical trench on the surface and 3D plane-layered model are presented.
Park, H M; Kim, T W
2009-01-21
Electrokinetic flows through hydrophobic microchannels experience velocity slip at the microchannel wall, which affects volumetric flow rate and solute retention time. The usual method of predicting the volumetric flow rate and velocity profile for hydrophobic microchannels is to solve the Navier-Stokes equation and the Poisson-Boltzmann equation for the electric potential with the boundary condition of velocity slip expressed by the Navier slip coefficient, which is computationally demanding and defies analytic solutions. In the present investigation, we have devised a simple method of predicting the velocity profiles and volumetric flow rates of electrokinetic flows by extending the concept of the Helmholtz-Smoluchowski velocity to microchannels with Navier slip. The extended Helmholtz-Smoluchowski velocity is simple to use and yields accurate results as compared to the exact solutions. Employing the extended Helmholtz-Smoluchowski velocity, the analytical expressions for volumetric flow rate and velocity profile for electrokinetic flows through rectangular microchannels with Navier slip have been obtained at high values of zeta potential. The range of validity of the extended Helmholtz-Smoluchowski velocity is also investigated.
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, 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
Tilted planes in 3D image analysis
NASA Astrophysics Data System (ADS)
Pargas, Roy P.; Staples, Nancy J.; Malloy, Brian F.; Cantrell, Ken; Chhatriwala, Murtuza
1998-03-01
Reliable 3D wholebody scanners which output digitized 3D images of a complete human body are now commercially available. This paper describes a software package, called 3DM, being developed by researchers at Clemson University and which manipulates and extracts measurements from such images. The focus of this paper is on tilted planes, a 3DM tool which allows a user to define a plane through a scanned image, tilt it in any direction, and effectively define three disjoint regions on the image: the points on the plane and the points on either side of the plane. With tilted planes, the user can accurately take measurements required in applications such as apparel manufacturing. The user can manually segment the body rather precisely. Tilted planes assist the user in analyzing the form of the body and classifying the body in terms of body shape. Finally, titled planes allow the user to eliminate extraneous and unwanted points often generated by a 3D scanner. This paper describes the user interface for tilted planes, the equations defining the plane as the user moves it through the scanned image, an overview of the algorithms, and the interaction of the tilted plane feature with other tools in 3DM.
Helmholtz Hodge decomposition of scalar optical fields.
Bahl, Monika; Senthilkumaran, P
2012-11-01
It is shown that the vector field decomposition method, namely, the Helmholtz Hodge decomposition, can also be applied to analyze scalar optical fields that are ubiquitously present in interference and diffraction optics. A phase gradient field that depicts the propagation and Poynting vector directions can hence be separated into solenoidal and irrotational components.
ERIC Educational Resources Information Center
Mayshark, Robin K.
1991-01-01
Students explore three-dimensional properties by creating red and green wall decorations related to Christmas. Students examine why images seem to vibrate when red and green pieces are small and close together. Instructions to conduct the activity and construct 3-D glasses are given. (MDH)
3D Printing: Exploring Capabilities
ERIC Educational Resources Information Center
Samuels, Kyle; Flowers, Jim
2015-01-01
As 3D printers become more affordable, schools are using them in increasing numbers. They fit well with the emphasis on product design in technology and engineering education, allowing students to create high-fidelity physical models to see and test different iterations in their product designs. They may also help students to "think in three…
Russ, Trina; Koch, Mark; Koudelka, Melissa; Peters, Ralph; Little, Charles; Boehnen, Chris; Peters, Tanya
2007-07-20
This software distribution contains MATLAB and C++ code to enable identity verification using 3D images that may or may not contain a texture component. The code is organized to support system performance testing and system capability demonstration through the proper configuration of the available user interface. Using specific algorithm parameters the face recognition system has been demonstrated to achieve a 96.6% verification rate (Pd) at 0.001 false alarm rate. The system computes robust facial features of a 3D normalized face using Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (FLDA). A 3D normalized face is obtained by alighning each face, represented by a set of XYZ coordinated, to a scaled reference face using the Iterative Closest Point (ICP) algorithm. The scaled reference face is then deformed to the input face using an iterative framework with parameters that control the deformed surface regulation an rate of deformation. A variety of options are available to control the information that is encoded by the PCA. Such options include the XYZ coordinates, the difference of each XYZ coordinates from the reference, the Z coordinate, the intensity/texture values, etc. In addition to PCA/FLDA feature projection this software supports feature matching to obtain similarity matrices for performance analysis. In addition, this software supports visualization of the STL, MRD, 2D normalized, and PCA synthetic representations in a 3D environment.
ERIC Educational Resources Information Center
Manos, Harry
2016-01-01
Visual aids are important to student learning, and they help make the teacher's job easier. Keeping with the "TPT" theme of "The Art, Craft, and Science of Physics Teaching," the purpose of this article is to show how teachers, lacking equipment and funds, can construct a durable 3-D model reference frame and a model gravity…
De Kock, Liesbet
2014-12-01
This paper aims at contributing to the ongoing efforts to get a firmer grasp of the systematic significance of the entanglement of idealism and empiricism in Helmholtz's work. Contrary to existing analyses, however, the focal point of the present exposition is Helmholtz's attempt to articulate a psychological account of objectification. Helmholtz's motive, as well as his solution to the problem of the object are outlined, and interpreted against the background of his scientific practice on the one hand, and that of empiricist and (transcendental) idealist analyses of experience on the other. The specifically psychological angle taken, not only prompts us to consider figures who have hitherto been treated as having only minor import for Helmholtz interpretation (most importantly J.S. Mill and J.G. Fichte), it furthermore sheds new light on some central tenets of the latter's psychological stance that have hitherto remained underappreciated. For one thing, this analysis reveals an explicit voluntarist tendency in Helmholtz's psychological theory. In conclusion, it is argued that the systematic significance of Helmholtz's empirico-transcendentalism with respect to questions of the mind is best understood as an attempt to found his empirical theory of perception in a second order, normative account of epistemic subjectivity.
[Kelvin-Helmholtz instability in protostellar jets
NASA Technical Reports Server (NTRS)
Stone, James; Hardee, Philip
1996-01-01
NASA grant NAG 5 2866, funded by the Astrophysics Theory Program, enabled the study the Kelvin-Helmholtz instability in protostellar jets. In collaboration with co-investigator Philip Hardee, the PI derived the analytic dispersion relation for the instability in including a cooling term in the energy equation which was modeled as one of two different power laws. Numerical solutions to this dispersion relation over a wide range of perturbation frequencies, and for a variety of parameter values characterizing the jet (such as Mach number, and density ratio) were found It was found that the growth rates and wavelengths associated with unstable roots of the dispersion relation in cooling jets are significantly different than those associated with adiabatic jets, which have been studied previously. In collaboration with graduate student Jianjun Xu (funded as a research associate under this grant), hydrodynamical simulations were used to follow the growth of the instability into the nonlinear regime. It was found that asymmetric surface waves lead to large amplitude, sinusoidal distortions of the jet, and ultimately to disruption Asymmetric body waves, on the other hand, result in the formation of shocks in the jet beam in the nonlinear regime. In cooling jets, these shocks lead to the formation of dense knots and filaments of gas within the jet. For sufficiently high perturbation frequencies, however, the jet cannot respond and it remains symmetric. Applying these results to observed systems, such as the Herbig-Haro jets HH34, HH111 and HH47 which have been observed with the Hubble Space Telescope, we predicted that some of the asymmetric structures observed in these systems could be attributed to the K-H modes, but that perturbations on timescales associated with the inner disk (about 1 year) would be too rapid to cause disruption. Moreover, it was discovered that weak shock 'spurs' in the ambient gas produced by ripples in the jet surface due to nonlinear, modes of
TACO3D. 3-D Finite Element Heat Transfer Code
Mason, W.E.
1992-03-04
TACO3D is a three-dimensional, finite-element program for heat transfer analysis. An extension of the two-dimensional TACO program, it can perform linear and nonlinear analyses and can be used to solve either transient or steady-state problems. The program accepts time-dependent or temperature-dependent material properties, and materials may be isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions and loadings are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additional specialized features treat enclosure radiation, bulk nodes, and master/slave internal surface conditions (e.g., contact resistance). Data input via a free-field format is provided. A user subprogram feature allows for any type of functional representation of any independent variable. A profile (bandwidth) minimization option is available. The code is limited to implicit time integration for transient solutions. TACO3D has no general mesh generation capability. Rows of evenly-spaced nodes and rows of sequential elements may be generated, but the program relies on separate mesh generators for complex zoning. TACO3D does not have the ability to calculate view factors internally. Graphical representation of data in the form of time history and spatial plots is provided through links to the POSTACO and GRAPE postprocessor codes.
3D simulation for solitons used in optical fibers
NASA Astrophysics Data System (ADS)
Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.
2016-12-01
In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.
3D Equilibrium Reconstructions in DIII-D
NASA Astrophysics Data System (ADS)
Lao, L. L.; Ferraro, N. W.; Strait, E. J.; Turnbull, A. D.; King, J. D.; Hirshman, H. P.; Lazarus, E. A.; Sontag, A. C.; Hanson, J.; Trevisan, G.
2013-10-01
Accurate and efficient 3D equilibrium reconstruction is needed in tokamaks for study of 3D magnetic field effects on experimentally reconstructed equilibrium and for analysis of MHD stability experiments with externally imposed magnetic perturbations. A large number of new magnetic probes have been recently installed in DIII-D to improve 3D equilibrium measurements and to facilitate 3D reconstructions. The V3FIT code has been in use in DIII-D to support 3D reconstruction and the new magnetic diagnostic design. V3FIT is based on the 3D equilibrium code VMEC that assumes nested magnetic surfaces. V3FIT uses a pseudo-Newton least-square algorithm to search for the solution vector. In parallel, the EFIT equilibrium reconstruction code is being extended to allow for 3D effects using a perturbation approach based on an expansion of the MHD equations. EFIT uses the cylindrical coordinate system and can include the magnetic island and stochastic effects. Algorithms are being developed to allow EFIT to reconstruct 3D perturbed equilibria directly making use of plasma response to 3D perturbations from the GATO, MARS-F, or M3D-C1 MHD codes. DIII-D 3D reconstruction examples using EFIT and V3FIT and the new 3D magnetic data will be presented. Work supported in part by US DOE under DE-FC02-04ER54698, DE-FG02-95ER54309 and DE-AC05-06OR23100.
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.
Forensic 3D scene reconstruction
NASA Astrophysics Data System (ADS)
Little, Charles Q.; Small, Daniel E.; Peters, Ralph R.; Rigdon, J. B.
2000-05-01
Traditionally law enforcement agencies have relied on basic measurement and imaging tools, such as tape measures and cameras, in recording a crime scene. A disadvantage of these methods is that they are slow and cumbersome. The development of a portable system that can rapidly record a crime scene with current camera imaging, 3D geometric surface maps, and contribute quantitative measurements such as accurate relative positioning of crime scene objects, would be an asset to law enforcement agents in collecting and recording significant forensic data. The purpose of this project is to develop a fieldable prototype of a fast, accurate, 3D measurement and imaging system that would support law enforcement agents to quickly document and accurately record a crime scene.
NASA Technical Reports Server (NTRS)
Pizarro, Yaritzmar Rosario; Schuler, Jason M.; Lippitt, Thomas C.
2013-01-01
Dexterous robotic hands are changing the way robots and humans interact and use common tools. Unfortunately, the complexity of the joints and actuations drive up the manufacturing cost. Some cutting edge and commercially available rapid prototyping machines now have the ability to print multiple materials and even combine these materials in the same job. A 3D model of a robotic hand was designed using Creo Parametric 2.0. Combining "hard" and "soft" materials, the model was printed on the Object Connex350 3D printer with the purpose of resembling as much as possible the human appearance and mobility of a real hand while needing no assembly. After printing the prototype, strings where installed as actuators to test mobility. Based on printing materials, the manufacturing cost of the hand was $167, significantly lower than other robotic hands without the actuators since they have more complex assembly processes.
van Geer, Erik; Molenbroek, Johan; Schreven, Sander; deVoogd-Claessen, Lenneke; Toussaint, Huib
2012-01-01
In competitive swimming, suits have become more important. These suits influence friction, pressure and wave drag. Friction drag is related to the surface properties whereas both pressure and wave drag are greatly influenced by body shape. To find a relationship between the body shape and the drag, the anthropometry of several world class female swimmers wearing different suits was accurately defined using a 3D scanner and traditional measuring methods. The 3D scans delivered more detailed information about the body shape. On the same day the swimmers did performance tests in the water with the tested suits. Afterwards the result of the performance tests and the differences found in body shape was analyzed to determine the deformation caused by a swimsuit and its effect on the swimming performance. Although the amount of data is limited because of the few test subjects, there is an indication that the deformation of the body influences the swimming performance.
Forensic 3D Scene Reconstruction
LITTLE,CHARLES Q.; PETERS,RALPH R.; RIGDON,J. BRIAN; SMALL,DANIEL E.
1999-10-12
Traditionally law enforcement agencies have relied on basic measurement and imaging tools, such as tape measures and cameras, in recording a crime scene. A disadvantage of these methods is that they are slow and cumbersome. The development of a portable system that can rapidly record a crime scene with current camera imaging, 3D geometric surface maps, and contribute quantitative measurements such as accurate relative positioning of crime scene objects, would be an asset to law enforcement agents in collecting and recording significant forensic data. The purpose of this project is to develop a feasible prototype of a fast, accurate, 3D measurement and imaging system that would support law enforcement agents to quickly document and accurately record a crime scene.
Belenkov, E. A. Ali-Pasha, V. A.
2011-01-15
The structure of clusters of some new carbon 3D-graphite phases have been calculated using the molecular-mechanics methods. It is established that 3D-graphite polytypes {alpha}{sub 1,1}, {alpha}{sub 1,3}, {alpha}{sub 1,5}, {alpha}{sub 2,1}, {alpha}{sub 2,3}, {alpha}{sub 3,1}, {beta}{sub 1,2}, {beta}{sub 1,4}, {beta}{sub 1,6}, {beta}{sub 2,1}, and {beta}{sub 3,2} consist of sp{sup 2}-hybridized atoms, have hexagonal unit cells, and differ in regards to the structure of layers and order of their alternation. A possible way to experimentally synthesize new carbon phases is proposed: the polymerization and carbonization of hydrocarbon molecules.
CFL3D User's Manual (Version 5.0)
NASA Technical Reports Server (NTRS)
Krist, Sherrie L.; Biedron, Robert T.; Rumsey, Christopher L.
1998-01-01
This document is the User's Manual for the CFL3D computer code, a thin-layer Reynolds-averaged Navier-Stokes flow solver for structured multiple-zone grids. Descriptions of the code's input parameters, non-dimensionalizations, file formats, boundary conditions, and equations are included. Sample 2-D and 3-D test cases are also described, and many helpful hints for using the code are provided.
[Real time 3D echocardiography
NASA Technical Reports Server (NTRS)
Bauer, F.; Shiota, T.; Thomas, J. D.
2001-01-01
Three-dimensional representation of the heart is an old concern. Usually, 3D reconstruction of the cardiac mass is made by successive acquisition of 2D sections, the spatial localisation and orientation of which require complex guiding systems. More recently, the concept of volumetric acquisition has been introduced. A matricial emitter-receiver probe complex with parallel data processing provides instantaneous of a pyramidal 64 degrees x 64 degrees volume. The image is restituted in real time and is composed of 3 planes (planes B and C) which can be displaced in all spatial directions at any time during acquisition. The flexibility of this system of acquisition allows volume and mass measurement with greater accuracy and reproducibility, limiting inter-observer variability. Free navigation of the planes of investigation allows reconstruction for qualitative and quantitative analysis of valvular heart disease and other pathologies. Although real time 3D echocardiography is ready for clinical usage, some improvements are still necessary to improve its conviviality. Then real time 3D echocardiography could be the essential tool for understanding, diagnosis and management of patients.
Analogues of the Helmholtz resonator in homogenization theory
Gadyl'shin, R R
2002-12-31
Perturbed two-dimensional boundary-value problems are considered for Helmholtz's equation with Dirichlet and Neumann boundary conditions on a family of arcs obtained from the boundary of a bounded domain {omega} by cutting out a large number of small holes distributed almost periodically and close to one another. Relations between the sizes of the openings and of the boundary ensuring that the solution of the perturbed problem converges to the solutions of the Dirichlet or the Neumann problem in {omega} and outside {omega}-bar are established. In the case when {omega} is a disc, the holes are periodically distributed and the homogenized problems are Dirichlet problems, asymptotic formulae with respect to a small parameter {epsilon} (characterizing the sizes of the openings and the distance between them) are constructed for the poles with small imaginary parts of the analytic continuation of the solution of the perturbed problem and their resonance behaviour is demonstrated.
GPU-Accelerated Denoising in 3D (GD3D)
2013-10-01
The raw computational power GPU Accelerators enables fast denoising of 3D MR images using bilateral filtering, anisotropic diffusion, and non-local means. This software addresses two facets of this promising application: what tuning is necessary to achieve optimal performance on a modern GPU? And what parameters yield the best denoising results in practice? To answer the first question, the software performs an autotuning step to empirically determine optimal memory blocking on the GPU. To answer the second, it performs a sweep of algorithm parameters to determine the combination that best reduces the mean squared error relative to a noiseless reference image.
NASA Astrophysics Data System (ADS)
Kent, G. M.; Harding, A. J.; Babcock, J. M.; Orcutt, J. A.; Bazin, S.; Singh, S.; Detrick, R. S.; Canales, J. P.; Carbotte, S. M.; Diebold, J.
2002-12-01
Multichannel seismic (MCS) images of crustal magma chambers are ideal targets for advanced visualization techniques. In the mid-ocean ridge environment, reflections originating at the melt-lens are well separated from other reflection boundaries, such as the seafloor, layer 2A and Moho, which enables the effective use of transparency filters. 3-D visualization of seismic reflectivity falls into two broad categories: volume and surface rendering. Volumetric-based visualization is an extremely powerful approach for the rapid exploration of very dense 3-D datasets. These 3-D datasets are divided into volume elements or voxels, which are individually color coded depending on the assigned datum value; the user can define an opacity filter to reject plotting certain voxels. This transparency allows the user to peer into the data volume, enabling an easy identification of patterns or relationships that might have geologic merit. Multiple image volumes can be co-registered to look at correlations between two different data types (e.g., amplitude variation with offsets studies), in a manner analogous to draping attributes onto a surface. In contrast, surface visualization of seismic reflectivity usually involves producing "fence" diagrams of 2-D seismic profiles that are complemented with seafloor topography, along with point class data, draped lines and vectors (e.g. fault scarps, earthquake locations and plate-motions). The overlying seafloor can be made partially transparent or see-through, enabling 3-D correlations between seafloor structure and seismic reflectivity. Exploration of 3-D datasets requires additional thought when constructing and manipulating these complex objects. As numbers of visual objects grow in a particular scene, there is a tendency to mask overlapping objects; this clutter can be managed through the effective use of total or partial transparency (i.e., alpha-channel). In this way, the co-variation between different datasets can be investigated
Adapting 3D Equilibrium Reconstruction to Reconstruct Weakly 3D H-mode Tokamaks
NASA Astrophysics Data System (ADS)
Cianciosa, M. R.; Hirshman, S. P.; Seal, S. K.; Unterberg, E. A.; Wilcox, R. S.; Wingen, A.; Hanson, J. D.
2015-11-01
The application of resonant magnetic perturbations for edge localized mode (ELM) mitigation breaks the toroidal symmetry of tokamaks. In these scenarios, the axisymmetric assumptions of the Grad-Shafranov equation no longer apply. By extension, equilibrium reconstruction tools, built around these axisymmetric assumptions, are insufficient to fully reconstruct a 3D perturbed equilibrium. 3D reconstruction tools typically work on systems where the 3D components of signals are a significant component of the input signals. In nominally axisymmetric systems, applied field perturbations can be on the order of 1% of the main field or less. To reconstruct these equilibria, the 3D component of signals must be isolated from the axisymmetric portions to provide the necessary information for reconstruction. This presentation will report on the adaptation to V3FIT for application on DIII-D H-mode discharges with applied resonant magnetic perturbations (RMPs). Newly implemented motional stark effect signals and modeling of electric field effects will also be discussed. Work supported under U.S. DOE Cooperative Agreement DE-AC05-00OR22725.
Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption.
Griffiths, Stéphane; Nennig, Benoit; Job, Stéphane
2017-01-01
A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.
The Kelvin–Helmholtz instability at Venus: What is the unstable boundary?
Möstl, Ute V.; Erkaev, Nikolay V.; Zellinger, Michael; Lammer, Helmut; Gröller, Hannes; Biernat, Helfried K.; Korovinskiy, Daniil
2011-01-01
The Kelvin–Helmholtz instability gained scientific attention after observations at Venus by the spacecraft Pioneer Venus Orbiter gave rise to speculations that the instability contributes to the loss of planetary ions through the formation of plasma clouds. Since then, a handful of studies were devoted to the Kelvin–Helmholtz instability at the ionopause and its implications for Venus. The aim of this study is to investigate the stability of the two instability-relevant boundary layers around Venus: the induced magnetopause and the ionopause. We solve the 2D magnetohydrodynamic equations with the total variation diminishing Lax–Friedrichs algorithm and perform simulation runs with different initial conditions representing the situation at the boundary layers around Venus. Our results show that the Kelvin–Helmholtz instability does not seem to be able to reach its nonlinear vortex phase at the ionopause due to the very effective stabilizing effect of a large density jump across this boundary layer. This seems also to be true for the induced magnetopause for low solar activity. During high solar activity, however, there could occur conditions at the induced magnetopause which are in favour of the nonlinear evolution of the instability. For this situation, we estimated roughly a growth rate for planetary oxygen ions of about 7.6 × 1025 s−1, which should be regarded as an upper limit for loss due to the Kelvin–Helmholtz instability. PMID:22347723
The PRISM3D paleoenvironmental reconstruction
Dowsett, H.; Robinson, M.; Haywood, A.M.; Salzmann, U.; Hill, Daniel; Sohl, L.E.; Chandler, M.; Williams, Mark; Foley, K.; Stoll, D.K.
2010-01-01
The Pliocene Research, Interpretation and Synoptic Mapping (PRISM) paleoenvironmental reconstruction is an internally consistent and comprehensive global synthesis of a past interval of relatively warm and stable climate. It is regularly used in model studies that aim to better understand Pliocene climate, to improve model performance in future climate scenarios, and to distinguish model-dependent climate effects. The PRISM reconstruction is constantly evolving in order to incorporate additional geographic sites and environmental parameters, and is continuously refined by independent research findings. The new PRISM three dimensional (3D) reconstruction differs from previous PRISM reconstructions in that it includes a subsurface ocean temperature reconstruction, integrates geochemical sea surface temperature proxies to supplement the faunal-based temperature estimates, and uses numerical models for the first time to augment fossil data. Here we describe the components of PRISM3D and describe new findings specific to the new reconstruction. Highlights of the new PRISM3D reconstruction include removal of Hudson Bay and the Great Lakes and creation of open waterways in locations where the current bedrock elevation is less than 25m above modern sea level, due to the removal of the West Antarctic Ice Sheet and the reduction of the East Antarctic Ice Sheet. The mid-Piacenzian oceans were characterized by a reduced east-west temperature gradient in the equatorial Pacific, but PRISM3D data do not imply permanent El Niño conditions. The reduced equator-to-pole temperature gradient that characterized previous PRISM reconstructions is supported by significant displacement of vegetation belts toward the poles, is extended into the Arctic Ocean, and is confirmed by multiple proxies in PRISM3D. Arctic warmth coupled with increased dryness suggests the formation of warm and salty paleo North Atlantic Deep Water (NADW) and a more vigorous thermohaline circulation system that may
Hermann von Helmholtz and his students
NASA Astrophysics Data System (ADS)
Mulligan, Joseph F.
1989-01-01
During the years 1871-1888, when Hermann von Helmholtz was professor of physics at the University of Berlin, physicists from all over the world flocked to Berlin to study and do research with him. Among these were the German physicists Max Planck, Heinrich Kayser, Eugen Goldstein, Wilhelm Wien, and Heinrich Hertz, and Americans Henry Rowland, A. A. Michelson, and Michael Pupin. Examples of Helmholtz's scientific and personal interactions with these students and research associates show why he is justly considered the outstanding physics mentor of the 19th century. Both his ideas and his students played a major role in the development of physics in the late 19th and early 20th centuries.
Lattice Boltzmann Method for 3-D Flows with Curved Boundary
NASA Technical Reports Server (NTRS)
Mei, Renwei; Shyy, Wei; Yu, Dazhi; Luo, Li-Shi
2002-01-01
In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.
Subcritical Kelvin-Helmholtz instability in a Hele-Shaw cell.
Meignin, L; Gondret, P; Ruyer-Quil, C; Rabaud, M
2003-06-13
We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.
Interactive 3D Mars Visualization
NASA Technical Reports Server (NTRS)
Powell, Mark W.
2012-01-01
The Interactive 3D Mars Visualization system provides high-performance, immersive visualization of satellite and surface vehicle imagery of Mars. The software can be used in mission operations to provide the most accurate position information for the Mars rovers to date. When integrated into the mission data pipeline, this system allows mission planners to view the location of the rover on Mars to 0.01-meter accuracy with respect to satellite imagery, with dynamic updates to incorporate the latest position information. Given this information so early in the planning process, rover drivers are able to plan more accurate drive activities for the rover than ever before, increasing the execution of science activities significantly. Scientifically, this 3D mapping information puts all of the science analyses to date into geologic context on a daily basis instead of weeks or months, as was the norm prior to this contribution. This allows the science planners to judge the efficacy of their previously executed science observations much more efficiently, and achieve greater science return as a result. The Interactive 3D Mars surface view is a Mars terrain browsing software interface that encompasses the entire region of exploration for a Mars surface exploration mission. The view is interactive, allowing the user to pan in any direction by clicking and dragging, or to zoom in or out by scrolling the mouse or touchpad. This set currently includes tools for selecting a point of interest, and a ruler tool for displaying the distance between and positions of two points of interest. The mapping information can be harvested and shared through ubiquitous online mapping tools like Google Mars, NASA WorldWind, and Worldwide Telescope.
3D Nanostructuring of Semiconductors
NASA Astrophysics Data System (ADS)
Blick, Robert
2000-03-01
Modern semiconductor technology allows to machine devices on the nanometer scale. I will discuss the current limits of the fabrication processes, which enable the definition of single electron transistors with dimensions down to 8 nm. In addition to the conventional 2D patterning and structuring of semiconductors, I will demonstrate how to apply 3D nanostructuring techniques to build freely suspended single-crystal beams with lateral dimension down to 20 nm. In transport measurements in the temperature range from 30 mK up to 100 K these nano-crystals are characterized regarding their electronic as well as their mechanical properties. Moreover, I will present possible applications of these devices.
NASA Technical Reports Server (NTRS)
2004-01-01
This 3-D cylindrical-perspective mosaic taken by the navigation camera on the Mars Exploration Rover Spirit on sol 82 shows the view south of the large crater dubbed 'Bonneville.' The rover will travel toward the Columbia Hills, seen here at the upper left. The rock dubbed 'Mazatzal' and the hole the rover drilled in to it can be seen at the lower left. The rover's position is referred to as 'Site 22, Position 32.' This image was geometrically corrected to make the horizon appear flat.
NASA Astrophysics Data System (ADS)
Manos, Harry
2016-03-01
Visual aids are important to student learning, and they help make the teacher's job easier. Keeping with the TPT theme of "The Art, Craft, and Science of Physics Teaching," the purpose of this article is to show how teachers, lacking equipment and funds, can construct a durable 3-D model reference frame and a model gravity well tailored to specific class lessons. Most of the supplies are readily available in the home or at school: rubbing alcohol, a rag, two colors of spray paint, art brushes, and masking tape. The cost of these supplies, if you don't have them, is less than 20.
NASA Technical Reports Server (NTRS)
2004-01-01
This is a 3-D anaglyph showing a microscopic image taken of an area measuring 3 centimeters (1.2 inches) across on the rock called Adirondack. The image was taken at Gusev Crater on the 33rd day of the Mars Exploration Rover Spirit's journey (Feb. 5, 2004), after the rover used its rock abrasion tool brush to clean the surface of the rock. Dust, which was pushed off to the side during cleaning, can still be seen to the left and in low areas of the rock.
Love, Lonnie
2015-01-09
ORNL's newly printed 3D Shelby Cobra was showcased at the 2015 NAIAS in Detroit. This "laboratory on wheels" uses the Shelby Cobra design, celebrating the 50th anniversary of this model and honoring the first vehicle to be voted a national monument. The Shelby was printed at the Department of Energy’s Manufacturing Demonstration Facility at ORNL using the BAAM (Big Area Additive Manufacturing) machine and is intended as a “plug-n-play” laboratory on wheels. The Shelby will allow research and development of integrated components to be tested and enhanced in real time, improving the use of sustainable, digital manufacturing solutions in the automotive industry.
Multigrid calculations of 3-D turbulent viscous flows
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1989-01-01
Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.
Positional Awareness Map 3D (PAM3D)
NASA Technical Reports Server (NTRS)
Hoffman, Monica; Allen, Earl L.; Yount, John W.; Norcross, April Louise
2012-01-01
The Western Aeronautical Test Range of the National Aeronautics and Space Administration s Dryden Flight Research Center needed to address the aging software and hardware of its current situational awareness display application, the Global Real-Time Interactive Map (GRIM). GRIM was initially developed in the late 1980s and executes on older PC architectures using a Linux operating system that is no longer supported. Additionally, the software is difficult to maintain due to its complexity and loss of developer knowledge. It was decided that a replacement application must be developed or acquired in the near future. The replacement must provide the functionality of the original system, the ability to monitor test flight vehicles in real-time, and add improvements such as high resolution imagery and true 3-dimensional capability. This paper will discuss the process of determining the best approach to replace GRIM, and the functionality and capabilities of the first release of the Positional Awareness Map 3D.
Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints
NASA Technical Reports Server (NTRS)
Kangro, Urve; Nicolaides, Roy
1997-01-01
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Mannoor, Manu S; Jiang, Ziwen; James, Teena; Kong, Yong Lin; Malatesta, Karen A; Soboyejo, Winston O; Verma, Naveen; Gracias, David H; McAlpine, Michael C
2013-06-12
The ability to three-dimensionally interweave biological tissue with functional electronics could enable the creation of bionic organs possessing enhanced functionalities over their human counterparts. Conventional electronic devices are inherently two-dimensional, preventing seamless multidimensional integration with synthetic biology, as the processes and materials are very different. Here, we present a novel strategy for overcoming these difficulties via additive manufacturing of biological cells with structural and nanoparticle derived electronic elements. As a proof of concept, we generated a bionic ear via 3D printing of a cell-seeded hydrogel matrix in the anatomic geometry of a human ear, along with an intertwined conducting polymer consisting of infused silver nanoparticles. This allowed for in vitro culturing of cartilage tissue around an inductive coil antenna in the ear, which subsequently enables readout of inductively-coupled signals from cochlea-shaped electrodes. The printed ear exhibits enhanced auditory sensing for radio frequency reception, and complementary left and right ears can listen to stereo audio music. Overall, our approach suggests a means to intricately merge biologic and nanoelectronic functionalities via 3D printing.
3D Printable Graphene Composite
Wei, Xiaojun; Li, Dong; Jiang, Wei; Gu, Zheming; Wang, Xiaojuan; Zhang, Zengxing; Sun, Zhengzong
2015-01-01
In human being’s history, both the Iron Age and Silicon Age thrived after a matured massive processing technology was developed. Graphene is the most recent superior material which could potentially initialize another new material Age. However, while being exploited to its full extent, conventional processing methods fail to provide a link to today’s personalization tide. New technology should be ushered in. Three-dimensional (3D) printing fills the missing linkage between graphene materials and the digital mainstream. Their alliance could generate additional stream to push the graphene revolution into a new phase. Here we demonstrate for the first time, a graphene composite, with a graphene loading up to 5.6 wt%, can be 3D printable into computer-designed models. The composite’s linear thermal coefficient is below 75 ppm·°C−1 from room temperature to its glass transition temperature (Tg), which is crucial to build minute thermal stress during the printing process. PMID:26153673
Mannoor, Manu S.; Jiang, Ziwen; James, Teena; Kong, Yong Lin; Malatesta, Karen A.; Soboyejo, Winston O.; Verma, Naveen; Gracias, David H.; McAlpine, Michael C.
2013-01-01
The ability to three-dimensionally interweave biological tissue with functional electronics could enable the creation of bionic organs possessing enhanced functionalities over their human counterparts. Conventional electronic devices are inherently two-dimensional, preventing seamless multidimensional integration with synthetic biology, as the processes and materials are very different. Here, we present a novel strategy for overcoming these difficulties via additive manufacturing of biological cells with structural and nanoparticle derived electronic elements. As a proof of concept, we generated a bionic ear via 3D printing of a cell-seeded hydrogel matrix in the precise anatomic geometry of a human ear, along with an intertwined conducting polymer consisting of infused silver nanoparticles. This allowed for in vitro culturing of cartilage tissue around an inductive coil antenna in the ear, which subsequently enables readout of inductively-coupled signals from cochlea-shaped electrodes. The printed ear exhibits enhanced auditory sensing for radio frequency reception, and complementary left and right ears can listen to stereo audio music. Overall, our approach suggests a means to intricately merge biologic and nanoelectronic functionalities via 3D printing. PMID:23635097
Martian terrain & airbags - 3D
NASA Technical Reports Server (NTRS)
1997-01-01
Portions of the lander's deflated airbags and a petal are at lower left in this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. This image is part of a 3D 'monster' panorama of the area surrounding the landing site.
Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is an operating division of the California Institute of Technology (Caltech). The Imager for Mars Pathfinder (IMP) was developed by the University of Arizona Lunar and Planetary Laboratory under contract to JPL. Peter Smith is the Principal Investigator.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
Martian terrain & airbags - 3D
NASA Technical Reports Server (NTRS)
1997-01-01
Portions of the lander's deflated airbags and a petal are at the lower area of this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. This image is part of a 3D 'monster' panorama of the area surrounding the landing site.
Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is an operating division of the California Institute of Technology (Caltech). The Imager for Mars Pathfinder (IMP) was developed by the University of Arizona Lunar and Planetary Laboratory under contract to JPL. Peter Smith is the Principal Investigator.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
NASA Astrophysics Data System (ADS)
Huber, C.; Abert, C.; Bruckner, F.; Groenefeld, M.; Muthsam, O.; Schuschnigg, S.; Sirak, K.; Thanhoffer, R.; Teliban, I.; Vogler, C.; Windl, R.; Suess, D.
2016-10-01
3D print is a recently developed technique, for single-unit production, and for structures that have been impossible to build previously. The current work presents a method to 3D print polymer bonded isotropic hard magnets with a low-cost, end-user 3D printer. Commercially available isotropic NdFeB powder inside a PA11 matrix is characterized, and prepared for the printing process. An example of a printed magnet with a complex shape that was designed to generate a specific stray field is presented, and compared with finite element simulation solving the macroscopic Maxwell equations. For magnetic characterization, and comparing 3D printed structures with injection molded parts, hysteresis measurements are performed. To measure the stray field outside the magnet, the printer is upgraded to a 3D magnetic flux density measurement system. To skip an elaborate adjusting of the sensor, a simulation is used to calibrate the angles, sensitivity, and the offset of the sensor. With this setup, a measurement resolution of 0.05 mm along the z-axes is achievable. The effectiveness of our calibration method is shown. With our setup, we are able to print polymer bonded magnetic systems with the freedom of having a specific complex shape with locally tailored magnetic properties. The 3D scanning setup is easy to mount, and with our calibration method we are able to get accurate measuring results of the stray field.
3D Printing of Graphene Aerogels.
Zhang, Qiangqiang; Zhang, Feng; Medarametla, Sai Pradeep; Li, Hui; Zhou, Chi; Lin, Dong
2016-04-06
3D printing of a graphene aerogel with true 3D overhang structures is highlighted. The aerogel is fabricated by combining drop-on-demand 3D printing and freeze casting. The water-based GO ink is ejected and freeze-cast into designed 3D structures. The lightweight (<10 mg cm(-3) ) 3D printed graphene aerogel presents superelastic and high electrical conduction.
Quasi 3D dispersion experiment
NASA Astrophysics Data System (ADS)
Bakucz, P.
2003-04-01
This paper studies the problem of tracer dispersion in a coloured fluid flowing through a two-phase 3D rough channel-system in a 40 cm*40 cm plexi-container filled by homogen glass fractions and colourless fluid. The unstable interface between the driving coloured fluid and the colourless fluid develops viscous fingers with a fractal structure at high capillary number. Five two-dimensional fractal fronts have been observed at the same time using four cameras along the vertical side-walls and using one camera located above the plexi-container. In possession of five fronts the spatial concentration contours are determined using statistical models. The concentration contours are self-affine fractal curves with a fractal dimension D=2.19. This result is valid for disperison at high Péclet numbers.
Sinclair, Michael B
2012-01-05
ShowMe3D is a data visualization graphical user interface specifically designed for use with hyperspectral image obtained from the Hyperspectral Confocal Microscope. The program allows the user to select and display any single image from a three dimensional hyperspectral image stack. By moving a slider control, the user can easily move between images of the stack. The user can zoom into any region of the image. The user can select any pixel or region from the displayed image and display the fluorescence spectrum associated with that pixel or region. The user can define up to 3 spectral filters to apply to the hyperspectral image and view the image as it would appear from a filter-based confocal microscope. The user can also obtain statistics such as intensity average and variance from selected regions.
Love, Lonnie
2016-11-02
ORNL's newly printed 3D Shelby Cobra was showcased at the 2015 NAIAS in Detroit. This "laboratory on wheels" uses the Shelby Cobra design, celebrating the 50th anniversary of this model and honoring the first vehicle to be voted a national monument. The Shelby was printed at the Department of Energyâs Manufacturing Demonstration Facility at ORNL using the BAAM (Big Area Additive Manufacturing) machine and is intended as a âplug-n-playâ laboratory on wheels. The Shelby will allow research and development of integrated components to be tested and enhanced in real time, improving the use of sustainable, digital manufacturing solutions in the automotive industry.
NASA Technical Reports Server (NTRS)
2009-01-01
wavelengths. Since the amount of the wavelength shift is related to the speed of motion, one can determine how fast the debris are moving in either direction. Because Cas A is the result of an explosion, the stellar debris is expanding radially outwards from the explosion center. Using simple geometry, the scientists were able to construct a 3-D model using all of this information. A program called 3-D Slicer modified for astronomical use by the Astronomical Medicine Project at Harvard University in Cambridge, Mass. was used to display and manipulate the 3-D model. Commercial software was then used to create the 3-D fly-through.
The blue filaments defining the blast wave were not mapped using the Doppler effect because they emit a different kind of light synchrotron radiation that does not emit light at discrete wavelengths, but rather in a broad continuum. The blue filaments are only a representation of the actual filaments observed at the blast wave.
This visualization shows that there are two main components to this supernova remnant: a spherical component in the outer parts of the remnant and a flattened (disk-like) component in the inner region. The spherical component consists of the outer layer of the star that exploded, probably made of helium and carbon. These layers drove a spherical blast wave into the diffuse gas surrounding the star. The flattened component that astronomers were unable to map into 3-D prior to these Spitzer observations consists of the inner layers of the star. It is made from various heavier elements, not all shown in the visualization, such as oxygen, neon, silicon, sulphur, argon and iron.
High-velocity plumes, or jets, of this material are shooting out from the explosion in the plane of the disk-like component mentioned above. Plumes of silicon appear in the northeast and southwest, while those of iron are seen in the southeast and north. These jets were already known and Doppler velocity measurements have been made for these
Helmholtz's early empiricism and the Erhaltung der Kraft.
Jurkowitz, Edward
2010-01-01
Hermann Helmholtz has often been understood to have started research under the influence of Kant, and then to have made a transition to a later mature empiricist phase. Without claiming that in 1847 Helmholtz held the same positions that he later espoused, I suggest that already in his 1847 'Uber die Erhaltung der Kraft' one may find important aspects of his later empiricism. I highlight the ways in which, from early on, Helmholtz turned Kant to use in developing an empirical program of inquiry into possible basic natural causes. To that end, I indicate how, throughout his arguments, Helmholtz employed, sometimes explicitly, but often tacitly, an empiricist logic, one that ran contrary to any form of transcendental deduction, and even to all a priori knowledge. Instead of deriving aspects about the ultimate constituents of nature, Helmholtz aimed to define the proper project for physical natural science. The first part of the paper describes the context of discussion in which Helmholtz entered. The bulk of the paper then analyzes Helmholtz's arguments in order to make space between (1) Kantian, and other, deductions of characteristics that must be true of nature and (2) Helmholtz's delineation of empirically determinable characteristics of presumed ultimate elements of nature, ones that he meant to be specified and delimited through future experimental research. The paper highlights that throughout his discussion Helmholtz meant to define the proper project for physical natural science, a project rife with empiricist aspects.
ERIC Educational Resources Information Center
Snyder, Jennifer
2012-01-01
Students often have a hard time equating time spent on art history as time well spent in the art room. Likewise, art teachers struggle with how to keep interest in their classrooms high when the subject turns to history. Some teachers show endless videos, with the students nodding sleepily along to the narrator. Others try to incorporate small…
Bohinc, Klemen; Shrestha, Ahis; Brumen, Milan; May, Sylvio
2012-03-01
In the classical mean-field description of the electric double layer, known as the Poisson-Boltzmann model, ions interact exclusively through their Coulomb potential. Ion specificity can arise through solvent-mediated, nonelectrostatic interactions between ions. We employ the Yukawa pair potential to model the presence of nonelectrostatic interactions. The combination of Yukawa and Coulomb potential on the mean-field level leads to the Poisson-Helmholtz-Boltzmann model, which employs two auxiliary potentials: one electrostatic and the other nonelectrostatic. In the present work we apply the Poisson-Helmholtz-Boltzmann model to ionic mixtures, consisting of monovalent cations and anions that exhibit different Yukawa interaction strengths. As a specific example we consider a single charged surface in contact with a symmetric monovalent electrolyte. From the minimization of the mean-field free energy we derive the Poisson-Boltzmann and Helmholtz-Boltzmann equations. These nonlinear equations can be solved analytically in the weak perturbation limit. This together with numerical solutions in the nonlinear regime suggests an intricate interplay between electrostatic and nonelectrostatic interactions. The structure and free energy of the electric double layer depends sensitively on the Yukawa interaction strengths between the different ion types and on the nonelectrostatic interactions of the mobile ions with the surface.
Formation and destabilization of Kelvin-Helmholtz billows in stably stratified turbulence
NASA Astrophysics Data System (ADS)
Kimura, Yoshifumi; Herring, Jackson
2013-11-01
We investigate the formation and destabilization of Kelvin-Helmholtz billows in stably stratified turbulence using the pseudo-spectral DNS of the Navier-Stokes equations under the Boussinesq approximation with 20483 grid points. Our method is to integrate the equations from the zero total energy initial condition with horizontal forcing imposed in a narrow wave number band. In the course of developments, the horizontal spectra first show a single steep power-law (k ? 4 , 5, where k is the horizontal wavenumber), and then the tail part of the spectrum begins to rise to show the Kolmogorov-type slope (k ? 5 / 3). From the viewpoint of vortex formation, we first observe that many wedge vortices are produced which move horizontally (like dipoles) in random directions. As time goes on, the wings of the wedges become thinner and thinner while translating, and finally detach to be almost independent vortex layers. This thinning mechanism makes the vertical shear stronger and eventually the local Richardson number small enough to produce Kelvin-Helmholtz billows. We will demonstrate that the transition in the horizontal energy spectra has a close relation with the destabilizing process of the Kelvin-Helmholtz billows.
Non-isothermal 3D SDPD Simulations
NASA Astrophysics Data System (ADS)
Yang, Jun; Potami, Raffaele; Gatsonis, Nikolaos
2012-11-01
The study of fluids at micro and nanoscale requires new modeling and computational approaches. Smooth Particle Dissipative Dynamics (SDPD) is a mesh-free method that provides a bridge between the continuum equations of hydrodynamics embedded in the Smooth Particle Hydrodynamics approach and the molecular nature embedded in the DPD approach. SDPD is thermodynamically consistent, does not rely on arbitrary coefficients for its thermostat, involves realistic transport coefficients, and includes fluctuation terms. SDPD is implemented in our work for arbitrary 3D geometries with a methodology to model solid wall boundary conditions. We present simulations for isothermal flows for verification of our approach. The entropy equation is implemented with a velocity-entropy Verlet integration algorithm Flows with heat transfer are simulated for verification of the SDPD. We present also the self-diffusion coefficient derived from SDPD simulations for gases and liquids. Results show the scale dependence of self-diffusion coefficient on SDPD particle size. Computational Mathematics Program of the Air Force Office of Scientific Research under grant/contract number FA9550-06-1-0236.
An acoustic double fishnet using Helmholtz resonators.
Murray, A R J; Summers, I R; Sambles, J R; Hibbins, A P
2014-09-01
The acoustic transmission of a closely spaced pair of patterned and perforated rigid plates is explored in air. The structure resembles an acoustic double fishnet design, with each plate modified such that the gap between them acts as an array of Helmholtz resonators. This allows the center frequency of the stop band to be reduced by a factor greater than 2 from the value obtained for the conventional acoustic double fishnet design. Experimental results accord well with the predictions of a finite element model.
Extraordinary transmission in optical Helmholtz resonators.
Chevalier, Paul; Bouchon, Patrick; Sakat, Emilie; Pelouard, Jean-Luc; Pardo, Fabrice; Haïdar, Riad
2015-06-15
Optical Helmholtz resonators (OHRs) have been adapted from acoustics designs for light absorbing structures, exhibiting extreme light confinement. Here, extraordinary transmission of light is theoretically demonstrated through symmetric OHRs, comprising a cavity with two λ/500 narrow slits on either side. This device has appealing features to act as a spectral bandpass filter in the context of multispectral imaging, in particular its high angular tolerance because of the localized nature of the resonance. Besides, the cavity can be modeled as an inductor and the two slits can be modeled as capacitors, the whole design acting as a LC circuit thus preventing any harmonic features.
Measuring the acoustic response of Helmholtz resonators
NASA Astrophysics Data System (ADS)
Monteiro, Martín; Marti, Arturo C.; Vogt, Patrik; Kasper, Lutz; Quarthal, Dominik
2015-04-01
Many experiments have been proposed to investigate acoustic phenomena in college and early undergraduate levels, in particular the speed of sound,1-9 by means of different methods, such as time of flight, transit time, or resonance in tubes. In this paper we propose to measure the acoustic response curves of a glass beaker filled with different gases, used as an acoustic resonator. We show that these curves expose many interesting peaks and features, one of which matches the resonance peak predicted for a Helmholtz resonator fairly well, and gives a decent estimate for the speed of sound in some cases. The measures are obtained thanks to the capabilities of smartphones.
Giant field enhancement in electromagnetic Helmholtz nanoantenna
NASA Astrophysics Data System (ADS)
Chevalier, Paul; Bouchon, Patrick; Greffet, Jean-Jacques; Pelouard, Jean-Luc; Haïdar, Riad; Pardo, Fabrice
2014-11-01
Inspired by the acoustic Helmholtz resonator, we propose a slit-box electromagnetic nanoantenna able to concentrate the energy of an incident beam into surfaces a thousand times smaller than with a classical lens. This design produces a giant electric field enhancement throughout the slit. The intensity enhancement reaches 104 in the visible range up to 108 in the THz range even with focused beams, thanks to an omnidirectional reception. These properties could target applications requiring extreme light concentration, such as surface-enhanced infrared absorption, nonlinear optics, and biophotonics.
NASA Astrophysics Data System (ADS)
Hermanns, Maria
The Kitaev honeycomb model has become one of the archetypal spin models exhibiting topological phases of matter, where the magnetic moments fractionalize into Majorana fermions interacting with a Z2 gauge field. In this talk, we discuss generalizations of this model to three-dimensional lattice structures. Our main focus is the metallic state that the emergent Majorana fermions form. In particular, we discuss the relation of the nature of this Majorana metal to the details of the underlying lattice structure. Besides (almost) conventional metals with a Majorana Fermi surface, one also finds various realizations of Dirac semi-metals, where the gapless modes form Fermi lines or even Weyl nodes. We introduce a general classification of these gapless quantum spin liquids using projective symmetry analysis. Furthermore, we briefly outline why these Majorana metals in 3D Kitaev systems provide an even richer variety of Dirac and Weyl phases than possible for electronic matter and comment on possible experimental signatures. Work done in collaboration with Kevin O'Brien and Simon Trebst.
3D multiplexed immunoplasmonics microscopy
NASA Astrophysics Data System (ADS)
Bergeron, Éric; Patskovsky, Sergiy; Rioux, David; Meunier, Michel
2016-07-01
Selective labelling, identification and spatial distribution of cell surface biomarkers can provide important clinical information, such as distinction between healthy and diseased cells, evolution of a disease and selection of the optimal patient-specific treatment. Immunofluorescence is the gold standard for efficient detection of biomarkers expressed by cells. However, antibodies (Abs) conjugated to fluorescent dyes remain limited by their photobleaching, high sensitivity to the environment, low light intensity, and wide absorption and emission spectra. Immunoplasmonics is a novel microscopy method based on the visualization of Abs-functionalized plasmonic nanoparticles (fNPs) targeting cell surface biomarkers. Tunable fNPs should provide higher multiplexing capacity than immunofluorescence since NPs are photostable over time, strongly scatter light at their plasmon peak wavelengths and can be easily functionalized. In this article, we experimentally demonstrate accurate multiplexed detection based on the immunoplasmonics approach. First, we achieve the selective labelling of three targeted cell surface biomarkers (cluster of differentiation 44 (CD44), epidermal growth factor receptor (EGFR) and voltage-gated K+ channel subunit KV1.1) on human cancer CD44+ EGFR+ KV1.1+ MDA-MB-231 cells and reference CD44- EGFR- KV1.1+ 661W cells. The labelling efficiency with three stable specific immunoplasmonics labels (functionalized silver nanospheres (CD44-AgNSs), gold (Au) NSs (EGFR-AuNSs) and Au nanorods (KV1.1-AuNRs)) detected by reflected light microscopy (RLM) is similar to the one with immunofluorescence. Second, we introduce an improved method for 3D localization and spectral identification of fNPs based on fast z-scanning by RLM with three spectral filters corresponding to the plasmon peak wavelengths of the immunoplasmonics labels in the cellular environment (500 nm for 80 nm AgNSs, 580 nm for 100 nm AuNSs and 700 nm for 40 nm × 92 nm AuNRs). Third, the developed
Crowdsourcing Based 3d Modeling
NASA Astrophysics Data System (ADS)
Somogyi, A.; Barsi, A.; Molnar, B.; Lovas, T.
2016-06-01
Web-based photo albums that support organizing and viewing the users' images are widely used. These services provide a convenient solution for storing, editing and sharing images. In many cases, the users attach geotags to the images in order to enable using them e.g. in location based applications on social networks. Our paper discusses a procedure that collects open access images from a site frequently visited by tourists. Geotagged pictures showing the image of a sight or tourist attraction are selected and processed in photogrammetric processing software that produces the 3D model of the captured object. For the particular investigation we selected three attractions in Budapest. To assess the geometrical accuracy, we used laser scanner and DSLR as well as smart phone photography to derive reference values to enable verifying the spatial model obtained from the web-album images. The investigation shows how detailed and accurate models could be derived applying photogrammetric processing software, simply by using images of the community, without visiting the site.
A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels.
Parkkinen, Pauli; Losilla, Sergio A; Solala, Eelis; Toivanen, Elias A; Xu, Wen-Hua; Sundholm, Dage
2017-02-14
A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid. The integration of the bubbles part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H2, H2O, and CO. Our calculations show that an accuracy of 10(-4) to 10(-7) Eh can be reached in HF-SCF calculations on general molecules.
[3D emulation of epicardium dynamic mapping].
Lu, Jun; Yang, Cui-Wei; Fang, Zu-Xiang
2005-03-01
In order to realize epicardium dynamic mapping of the whole atria, 3-D graphics are drawn with OpenGL. Some source codes are introduced in the paper to explain how to produce, read, and manipulate 3-D model data.
An interactive multiview 3D display system
NASA Astrophysics Data System (ADS)
Zhang, Zhaoxing; Geng, Zheng; Zhang, Mei; Dong, Hui
2013-03-01
The progresses in 3D display systems and user interaction technologies will help more effective 3D visualization of 3D information. They yield a realistic representation of 3D objects and simplifies our understanding to the complexity of 3D objects and spatial relationship among them. In this paper, we describe an autostereoscopic multiview 3D display system with capability of real-time user interaction. Design principle of this autostereoscopic multiview 3D display system is presented, together with the details of its hardware/software architecture. A prototype is built and tested based upon multi-projectors and horizontal optical anisotropic display structure. Experimental results illustrate the effectiveness of this novel 3D display and user interaction system.
Laser Based 3D Volumetric Display System
1993-03-01
Literature, Costa Mesa, CA July 1983. 3. "A Real Time Autostereoscopic Multiplanar 3D Display System", Rodney Don Williams, Felix Garcia, Jr., Texas...8217 .- NUMBERS LASER BASED 3D VOLUMETRIC DISPLAY SYSTEM PR: CD13 0. AUTHOR(S) PE: N/AWIU: DN303151 P. Soltan, J. Trias, W. Robinson, W. Dahlke 7...laser generated 3D volumetric images on a rotating double helix, (where the 3D displays are computer controlled for group viewing with the naked eye
True 3d Images and Their Applications
NASA Astrophysics Data System (ADS)
Wang, Z.; wang@hzgeospace., zheng.
2012-07-01
A true 3D image is a geo-referenced image. Besides having its radiometric information, it also has true 3Dground coordinates XYZ for every pixels of it. For a true 3D image, especially a true 3D oblique image, it has true 3D coordinates not only for building roofs and/or open grounds, but also for all other visible objects on the ground, such as visible building walls/windows and even trees. The true 3D image breaks the 2D barrier of the traditional orthophotos by introducing the third dimension (elevation) into the image. From a true 3D image, for example, people will not only be able to read a building's location (XY), but also its height (Z). true 3D images will fundamentally change, if not revolutionize, the way people display, look, extract, use, and represent the geospatial information from imagery. In many areas, true 3D images can make profound impacts on the ways of how geospatial information is represented, how true 3D ground modeling is performed, and how the real world scenes are presented. This paper first gives a definition and description of a true 3D image and followed by a brief review of what key advancements of geospatial technologies have made the creation of true 3D images possible. Next, the paper introduces what a true 3D image is made of. Then, the paper discusses some possible contributions and impacts the true 3D images can make to geospatial information fields. At the end, the paper presents a list of the benefits of having and using true 3D images and the applications of true 3D images in a couple of 3D city modeling projects.
SALE3D. ICEd-ALE Treatment of 3-D Fluid Flow
Amsden, A.A.; Ruppel, H.M.
1992-01-14
SALE3D calculates three-dimensional fluid flow at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program.
3D Printing and Its Urologic Applications
Soliman, Youssef; Feibus, Allison H; Baum, Neil
2015-01-01
3D printing is the development of 3D objects via an additive process in which successive layers of material are applied under computer control. This article discusses 3D printing, with an emphasis on its historical context and its potential use in the field of urology. PMID:26028997
Teaching Geography with 3-D Visualization Technology
ERIC Educational Resources Information Center
Anthamatten, Peter; Ziegler, Susy S.
2006-01-01
Technology that helps students view images in three dimensions (3-D) can support a broad range of learning styles. "Geo-Wall systems" are visualization tools that allow scientists, teachers, and students to project stereographic images and view them in 3-D. We developed and presented 3-D visualization exercises in several undergraduate courses.…
Expanding Geometry Understanding with 3D Printing
ERIC Educational Resources Information Center
Cochran, Jill A.; Cochran, Zane; Laney, Kendra; Dean, Mandi
2016-01-01
With the rise of personal desktop 3D printing, a wide spectrum of educational opportunities has become available for educators to leverage this technology in their classrooms. Until recently, the ability to create physical 3D models was well beyond the scope, skill, and budget of many schools. However, since desktop 3D printers have become readily…
NASA Astrophysics Data System (ADS)
Engle, Rob
2008-02-01
This paper discusses the creative and technical challenges encountered during the production of "Beowulf 3D," director Robert Zemeckis' adaptation of the Old English epic poem and the first film to be simultaneously released in IMAX 3D and digital 3D formats.
3D Flow Visualization Using Texture Advection
NASA Technical Reports Server (NTRS)
Kao, David; Zhang, Bing; Kim, Kwansik; Pang, Alex; Moran, Pat (Technical Monitor)
2001-01-01
Texture advection is an effective tool for animating and investigating 2D flows. In this paper, we discuss how this technique can be extended to 3D flows. In particular, we examine the use of 3D and 4D textures on 3D synthetic and computational fluid dynamics flow fields.
Quasi-3D Algorithm in Multi-scale Modeling Framework
NASA Astrophysics Data System (ADS)
Jung, J.; Arakawa, A.
2008-12-01
As discussed in the companion paper by Arakawa and Jung, the Quasi-3D (Q3D) Multi-scale Modeling Framework (MMF) is a 4D estimation/prediction framework that combines a GCM with a 3D anelastic vector vorticity equation model (VVM) applied to a Q3D network of horizontal grid points. This paper presents an outline of the recently revised Q3D algorithm and a highlight of the results obtained by application of the algorithm to an idealized model setting. The Q3D network of grid points consists of two sets of grid-point arrays perpendicular to each other. For a scalar variable, for example, each set consists of three parallel rows of grid points. Principal and supplementary predictions are made on the central and the two adjacent rows, respectively. The supplementary prediction is to allow the principal prediction be three-dimensional at least to the second-order accuracy. To accommodate a higher-order accuracy and to make the supplementary predictions formally three-dimensional, a few rows of ghost points are added at each side of the array. Values at these ghost points are diagnostically determined by a combination of statistical estimation and extrapolation. The basic structure of the estimation algorithm is determined in view of the global stability of Q3D advection. The algorithm is calibrated using the statistics of past data at and near the intersections of the two sets of grid- point arrays. Since the CRM in the Q3D MMF extends beyond individual GCM boxes, the CRM can be a GCM by itself. However, it is better to couple the CRM with the GCM because (1) the CRM is a Q3D CRM based on a highly anisotropic network of grid points and (2) coupling with a GCM makes it more straightforward to inherit our experience with the conventional GCMs. In the coupled system we have selected, prediction of thermdynamic variables is almost entirely done by the Q3D CRM with no direct forcing by the GCM. The coupling of the dynamics between the two components is through mutual
3-D Perspective Pasadena, California
NASA Technical Reports Server (NTRS)
2000-01-01
This perspective view shows the western part of the city of Pasadena, California, looking north towards the San Gabriel Mountains. Portions of the cities of Altadena and La Canada, Flintridge are also shown. The image was created from three datasets: the Shuttle Radar Topography Mission (SRTM) supplied the elevation data; Landsat data from November 11, 1986 provided the land surface color (not the sky) and U.S. Geological Survey digital aerial photography provides the image detail. The Rose Bowl, surrounded by a golf course, is the circular feature at the bottom center of the image. The Jet Propulsion Laboratory is the cluster of large buildings north of the Rose Bowl at the base of the mountains. A large landfill, Scholl Canyon, is the smooth area in the lower left corner of the scene. This image shows the power of combining data from different sources to create planning tools to study problems that affect large urban areas. In addition to the well-known earthquake hazards, Southern California is affected by a natural cycle of fire and mudflows. Wildfires strip the mountains of vegetation, increasing the hazards from flooding and mudflows for several years afterwards. Data such as shown on this image can be used to predict both how wildfires will spread over the terrain and also how mudflows will be channeled down the canyons. The Shuttle Radar Topography Mission (SRTM), launched on February 11, 2000, uses the same radar instrument that comprised the Spaceborne Imaging Radar-C/X-Band Synthetic Aperture Radar (SIR-C/X-SAR) that flew twice on the Space Shuttle Endeavour in 1994. The mission was designed to collect three dimensional measurements of the Earth's surface. To collect the 3-D data, engineers added a 60-meter-long (200-foot) mast, an additional C-band imaging antenna and improved tracking and navigation devices. The mission is a cooperative project between the National Aeronautics and Space Administration (NASA), the National Imagery and Mapping Agency
Multitasking the code ARC3D. [for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Barton, John T.; Hsiung, Christopher C.
1986-01-01
The CRAY multitasking system was developed in order to utilize all four processors and sharply reduce the wall clock run time. This paper describes the techniques used to modify the computational fluid dynamics code ARC3D for this run and analyzes the achieved speedup. The ARC3D code solves either the Euler or thin-layer N-S equations using an implicit approximate factorization scheme. Results indicate that multitask processing can be used to achieve wall clock speedup factors of over three times, depending on the nature of the program code being used. Multitasking appears to be particularly advantageous for large-memory problems running on multiple CPU computers.
Case study: Beauty and the Beast 3D: benefits of 3D viewing for 2D to 3D conversion
NASA Astrophysics Data System (ADS)
Handy Turner, Tara
2010-02-01
From the earliest stages of the Beauty and the Beast 3D conversion project, the advantages of accurate desk-side 3D viewing was evident. While designing and testing the 2D to 3D conversion process, the engineering team at Walt Disney Animation Studios proposed a 3D viewing configuration that not only allowed artists to "compose" stereoscopic 3D but also improved efficiency by allowing artists to instantly detect which image features were essential to the stereoscopic appeal of a shot and which features had minimal or even negative impact. At a time when few commercial 3D monitors were available and few software packages provided 3D desk-side output, the team designed their own prototype devices and collaborated with vendors to create a "3D composing" workstation. This paper outlines the display technologies explored, final choices made for Beauty and the Beast 3D, wish-lists for future development and a few rules of thumb for composing compelling 2D to 3D conversions.
Mini 3D for shallow gas reconnaissance
Vallieres, T. des; Enns, D.; Kuehn, H.; Parron, D.; Lafet, Y.; Van Hulle, D.
1996-12-31
The Mini 3D project was undertaken by TOTAL and ELF with the support of CEPM (Comite d`Etudes Petrolieres et Marines) to define an economical method of obtaining 3D seismic HR data for shallow gas assessment. An experimental 3D survey was carried out with classical site survey techniques in the North Sea. From these data 19 simulations, were produced to compare different acquisition geometries ranging from dual, 600 m long cables to a single receiver. Results show that short offset, low fold and very simple streamer positioning are sufficient to give a reliable 3D image of gas charged bodies. The 3D data allow a much more accurate risk delineation than 2D HR data. Moreover on financial grounds Mini-3D is comparable in cost to a classical HR 2D survey. In view of these results, such HR 3D should now be the standard for shallow gas surveying.
NASA Astrophysics Data System (ADS)
Bogena, H. R.; Sciuto, G.; Rosenbaum, U.; Herbst, M.; Huisman, J. A.; Vereecken, H.; Diekkrueger, B.
2010-12-01
Hydrological analysis is often limited by the number of data available. Usually, discharge data and only little point information concerning soil moisture status are available. This might give a good representation of the temporal variability of runoff, but it does not provide insights into the spatial dynamics of soil moisture and water fluxes within the catchment. The small forested Wüstebach catchment (~27 ha) has been instrumented with a wireless sensor network consisting of 150 nodes and more than 1200 soil moisture sensors in the framework of the Transregio32 and the Helmholtz initiative TERENO (Terrestrial Environmental Observatories) [1]. This unique data set provides a consistent picture of the hydrological status of the catchment in a high spatial and temporal resolution. We present first results of a geostatistical analysis of the data and an application of the integrated surface/subsurface 3D finite element model HydroGeoSphere model to investigate the scale dependency of the temporal dynamics of soil moisture patterns. A variogram analysis showed that the sum of the sub-scale variability and the measurement error is close to time-invariant. Wet situations showed smaller spatial variability, which is attributed to saturated soil moisture, which poses an upper limit and is typically not strongly variable in headwater catchments with relatively homogeneous soil. The spatiotemporal variability in soil moisture at 50 cm depth was significantly lower than at 5 and 20 cm. This finding indicates that the considerable variability of the top soil is buffered deeper in the soil due to root water uptake, lateral and vertical water fluxes. Topographic features showed the strongest correlation with soil moisture during dry periods, indicating that the control of topography on the soil moisture pattern depends on the soil water status. The temporal patterns of runoff discharge were reproduced by the HydroGeoSphere model in a satisfying way. The observed soil
Unstructured grid solutions to a wing/pylon/store configuration using VGRID3D/USM3D
NASA Technical Reports Server (NTRS)
Parikh, Paresh; Pirzadeh, Shahyar; Frink, Neal T.
1992-01-01
The purpose of this paper is to validate an inviscid flow solution package based on a new unstructured grid methodology using experimental data on a wing/pylon/store configuration. The solution package consists of an advancing front unstructured grid generator, VGRID3D, and an efficient Euler equation solver, USM3D. Comparisons of computed data versus experimental data are made for two free-stream Mach numbers at five store locations relative to the wing. Both rigid body aerodynamics and mutual interference effects are explored. A very good agreement is observed between computed and wind tunnel data.
POISs3: A 3D poisson smoother of structured grids
NASA Astrophysics Data System (ADS)
Lehtimaeki, R.
Flow solvers based on solving Navier-Stokes or Euler equations generally need a computational grid to represent the domain of the flow. A structured computational grid can be efficiently produced by algebraic methods like transfinite interpolation. Unfortunately, algebraic methods propagate all kinds of unsmoothness of the boundary into the field. Unsmoothness of the grid, in turn, can result in inaccuracy in the flow solver. In the present work a 3D elliptic grid smoother was developed. The smoother is based on solving three Poisson equations, one for each curvilinear direction. The Poisson equations formed in the physical region are first transformed to the computational (rectilinear) region. The resulting equations form a system of three coupled elliptic quasi-linear partial differential equations in the computational domain. A short review of the Poisson method is presented. The regularity of a grid cell is studied and a skewness value is developed.
NASA Astrophysics Data System (ADS)
Hejazialhosseini, Babak; Rossinelli, Diego; Koumoutsakos, Petros
2013-09-01
We present a simulation for the interactions of shockwaves with light spherical density inhomogeneities. Euler equations for two-phase compressible flows are solved in a 3D uniform resolution finite volume based solver using 5th order WENO reconstructions of the primitive quantities, HLL-type numerical fluxes and 3rd order TVD time stepping scheme. In this study, a normal Mach 3 shockwave in air is directed at a helium bubble with an interface Atwood number of -0.76. We employ 4 billion cells on a supercomputing cluster and demonstrate the development of this flow until relatively late times. Shock passage compresses the bubble and deposits baroclinic vorticity on the interface. Initial distribution of the vorticity and compressions lead to the formation of an air jet, interface roll-ups and the formation of a long lasting vortical core, the white core. Compressed upstream of the bubble turns into a mixing zone and as the vortex ring distances from this mixing zone, a plume-shaped region is formed and sustained. Close observations have been reported in previous experimental works. The visualization is presented in a fluid dynamics video.
3D RISM theory with fast reciprocal-space electrostatics
Heil, Jochen; Kast, Stefan M.
2015-03-21
The calculation of electrostatic solute-solvent interactions in 3D RISM (“three-dimensional reference interaction site model”) integral equation theory is recast in a form that allows for a computational treatment analogous to the “particle-mesh Ewald” formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.
VISRAD, 3-D Target Design and Radiation Simulation Code
NASA Astrophysics Data System (ADS)
Golovkin, Igor; Macfarlane, Joseph; Golovkina, Viktoriya
2016-10-01
The 3-D view factor code VISRAD is widely used in designing HEDP experiments at major laser and pulsed-power facilities, including NIF, OMEGA, OMEGA-EP, ORION, LMJ, Z, and PLX. It simulates target designs by generating a 3-D grid of surface elements, utilizing a variety of 3-D primitives and surface removal algorithms, and can be used to compute the radiation flux throughout the surface element grid by computing element-to-element view factors and solving power balance equations. Target set-up and beam pointing are facilitated by allowing users to specify positions and angular orientations using a variety of coordinates systems (e.g., that of any laser beam, target component, or diagnostic port). Analytic modeling for laser beam spatial profiles for OMEGA DPPs and NIF CPPs is used to compute laser intensity profiles throughout the grid of surface elements. We will discuss recent improvements to the software package and plans for future developments.
3-D Technology Approaches for Biological Ecologies
NASA Astrophysics Data System (ADS)
Liu, Liyu; Austin, Robert; U. S-China Physical-Oncology Sciences Alliance (PS-OA) Team
Constructing three dimensional (3-D) landscapes is an inevitable issue in deep study of biological ecologies, because in whatever scales in nature, all of the ecosystems are composed by complex 3-D environments and biological behaviors. Just imagine if a 3-D technology could help complex ecosystems be built easily and mimic in vivo microenvironment realistically with flexible environmental controls, it will be a fantastic and powerful thrust to assist researchers for explorations. For years, we have been utilizing and developing different technologies for constructing 3-D micro landscapes for biophysics studies in in vitro. Here, I will review our past efforts, including probing cancer cell invasiveness with 3-D silicon based Tepuis, constructing 3-D microenvironment for cell invasion and metastasis through polydimethylsiloxane (PDMS) soft lithography, as well as explorations of optimized stenting positions for coronary bifurcation disease with 3-D wax printing and the latest home designed 3-D bio-printer. Although 3-D technologies is currently considered not mature enough for arbitrary 3-D micro-ecological models with easy design and fabrication, I hope through my talk, the audiences will be able to sense its significance and predictable breakthroughs in the near future. This work was supported by the State Key Development Program for Basic Research of China (Grant No. 2013CB837200), the National Natural Science Foundation of China (Grant No. 11474345) and the Beijing Natural Science Foundation (Grant No. 7154221).
3D change detection - Approaches and applications
NASA Astrophysics Data System (ADS)
Qin, Rongjun; Tian, Jiaojiao; Reinartz, Peter
2016-12-01
Due to the unprecedented technology development of sensors, platforms and algorithms for 3D data acquisition and generation, 3D spaceborne, airborne and close-range data, in the form of image based, Light Detection and Ranging (LiDAR) based point clouds, Digital Elevation Models (DEM) and 3D city models, become more accessible than ever before. Change detection (CD) or time-series data analysis in 3D has gained great attention due to its capability of providing volumetric dynamics to facilitate more applications and provide more accurate results. The state-of-the-art CD reviews aim to provide a comprehensive synthesis and to simplify the taxonomy of the traditional remote sensing CD techniques, which mainly sit within the boundary of 2D image/spectrum analysis, largely ignoring the particularities of 3D aspects of the data. The inclusion of 3D data for change detection (termed 3D CD), not only provides a source with different modality for analysis, but also transcends the border of traditional top-view 2D pixel/object-based analysis to highly detailed, oblique view or voxel-based geometric analysis. This paper reviews the recent developments and applications of 3D CD using remote sensing and close-range data, in support of both academia and industry researchers who seek for solutions in detecting and analyzing 3D dynamics of various objects of interest. We first describe the general considerations of 3D CD problems in different processing stages and identify CD types based on the information used, being the geometric comparison and geometric-spectral analysis. We then summarize relevant works and practices in urban, environment, ecology and civil applications, etc. Given the broad spectrum of applications and different types of 3D data, we discuss important issues in 3D CD methods. Finally, we present concluding remarks in algorithmic aspects of 3D CD.
Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators
NASA Astrophysics Data System (ADS)
Lombard, Bruno; Mercier, Jean-François
2014-02-01
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a nonlinear PDE describing nonlinear acoustic waves, and a linear ODE describing the oscillations in the Helmholtz resonators. The thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives. A diffusive representation is followed: the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly. Various strategies are examined to compute the coefficients of the diffusive representation; finally, an optimization method is preferred to the usual quadrature rules. The numerical model is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, the existence of acoustic solitary waves is confirmed.
Helmholtz decomposition coupling rotational to irrotational flow of a viscous fluid
Joseph, Daniel D.
2006-01-01
In this work, I present the form of the Navier–Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the irrotational flow compatible with the flow boundaries and other prescribed conditions. The rotational component of velocity is then the difference between the solution of the Navier–Stokes equations and the selected irrotational flow. To satisfy the boundary conditions, the irrotational field is required, and it depends on the viscosity. Five unknown fields are determined by the decomposed form of the Navier–Stokes equations for an incompressible fluid: the rotational component of velocity, the pressure, and the harmonic potential. These five fields may be readily identified in analytic solutions available in the literature. It is clear from these exact solutions that potential flow of a viscous fluid is required to satisfy prescribed conditions, like the no-slip condition at the boundary of a solid or continuity conditions across a two-fluid boundary. It can be said that equations governing the Helmholtz decomposition describe the modification of irrotational flow due to vorticity, but the analysis shows the two fields are coupled and cannot be completely determined independently. PMID:16983077
Cardiac video analysis using Hodge-Helmholtz field decomposition.
Guo, Qinghong; Mandal, Mrinal K; Liu, Gang; Kavanagh, Katherine M
2006-01-01
The critical points (also known as phase singularities) in the heart reflect the pathological change of the heart tissue, and hence can be used to describe and analyze the dynamics of the cardiac electrical activity. As a result, the detection of these critical points can lead to correct understanding and effective therapy of the tachycardia. In this paper, we propose a novel approach to address this problem. The proposed approach includes four stages: image smoothing, motion estimation, motion decomposition, and detection of the critical points. In the image smoothing stage, the noisy cardiac optical data are smoothed using anisotropic diffusion equation. The conduction velocity fields of the cardiac electrical patterns can then be estimated from two consecutive smoothed images. Using the recently developed discrete Hodge-Helmholtz motion decomposition technique, the curl-free and divergence-free potential surfaces of an estimated velocity field are extracted. Finally, hierarchically searching the minima and maxima on the potential surfaces, the sources, sinks, and rotational centers are located with high accuracy. Experimental results with four real cardiac videos show that the proposed approach performs satisfactorily, especially for the cardiac electrical patterns with simple propagations.
Modelling discontinuities and Kelvin Helmholtz instabilities in SPH
NASA Astrophysics Data System (ADS)
Price, Daniel J.
2008-12-01
In this paper we discuss the treatment of discontinuities in smoothed particle hydrodynamics (SPH) simulations. In particular we discuss the difference between integral and differential representations of the fluid equations in an SPH context and how this relates to the formulation of dissipative terms for the capture of shocks and other discontinuities. This has important implications for many problems, in particular related to recently highlighted problems in treating Kelvin Helmholtz instabilities across entropy gradients in SPH. The specific problems pointed out by Agertz et al. [O. Agertz, B. Moore, J. Stadel, D. Potter, F. Miniati, J. Read, L. Mayer, A. Gawryszczak, A. Kravtsov, Å. Nordlund, F. Pearce, V. Quilis, D. Rudd, V. Springel, J. Stone, E. Tasker, R. Teyssier, J. Wadsley, R. Walder, Fundamental differences between SPH and grid methods, MNRAS 380 (2007) 963 978] are shown to be related in particular to the (lack of) treatment of contact discontinuities in standard SPH formulations which can be cured by the simple application of an artificial thermal conductivity term. We propose a new formulation of artificial thermal conductivity in SPH which minimises dissipation away from discontinuities and can therefore be applied quite generally in SPH calculations.
The Goos-Hanchen shift in Helmholtz-Gauss beams
NASA Astrophysics Data System (ADS)
Jezzini, Moises A.; Gutierrez-Vega, Julio C.
2006-08-01
We present a study of the total internal reflection of a Helmholtz-Gauss beam at a plane interface between two dielectric media. The derivation is based on the decomposition of the Helmholtz-Gauss beams in terms of its constituent plane waves components. We determine the shift predicted by the classical theory of the Goos- Hänchen shift and analyze the transverse intensity patterns of the reflected waves for a variety of Helmholtz-Gauss beam including Bessel-Gauss and Cosine-Gauss beams.
3D measurement for rapid prototyping
NASA Astrophysics Data System (ADS)
Albrecht, Peter; Lilienblum, Tilo; Sommerkorn, Gerd; Michaelis, Bernd
1996-08-01
Optical 3-D measurement is an interesting approach for rapid prototyping. On one hand it's necessary to get the 3-D data of an object and on the other hand it's necessary to check the manufactured object (quality checking). Optical 3-D measurement can realize both. Classical 3-D measurement procedures based on photogrammetry cause systematic errors at strongly curved surfaces or steps in surfaces. One possibility to reduce these errors is to calculate the 3-D coordinates from several successively taken images. Thus it's possible to get higher spatial resolution and to reduce the systematic errors at 'problem surfaces.' Another possibility is to process the measurement values by neural networks. A modified associative memory smoothes and corrects the calculated 3-D coordinates using a-priori knowledge about the measurement object.
Coronal roots of solar wind streams: 3-D MHD modeling
NASA Technical Reports Server (NTRS)
Pisanko, Yu. V.
1995-01-01
Weak (discontinuous) solutions of the 3-D MHD equations look like a promising tool to model the transonic solar wind with structural elements: current sheets, coronal plumes etc. Using the observational information about various coronal emissions one can include these structural elements into the 3-D MHD solar wind model by embedding the discontinuities of given type. Such 3-D MHD structured solar wind is calculated self-consistently: variants are examined via numerical experiments. In particular, the behavior of coronal plumes in the transonic solar wind flow, is modeled. The input information for numerical modeling (for example, the magnetic field map at the very base of the solar corona) can be adjusted so that fast stream arises over the center of the coronal hole, over the coronal hole boundaries and, even, over the region with closed magnetic topology. 3-D MHD equations have the analytical solution which can serve as a model of supersonic trans-alfvenic solar wind in the (5-20) solar radii heliocentric distance interval. The transverse, nonradial total (gas + magnetic field) pressure balance in the flow is the corner-stone of this solution. The solution describes the filamentation (ray-like structure of the solar corona) and streaming (formation of high-speed streams with velocities up to 800 km/sec) as a consequence of the magnetic field spatial inhomogeneous structure and trans-alfvenic character of the flow. The magnetic field works in the model as a 'controller' for the solar wind streaming and filamentation.
Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU.
Xia, Yong; Wang, Kuanquan; Zhang, Henggui
2015-01-01
Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations.
Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU
Xia, Yong; Wang, Kuanquan; Zhang, Henggui
2015-01-01
Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations. PMID:26581957
Photorefractive Polymers for Updateable 3D Displays
2010-02-24
Final Performance Report 3. DATES COVERED (From - To) 01-01-2007 to 11-30-2009 4. TITLE AND SUBTITLE Photorefractive Polymers for Updateable 3D ...ABSTRACT During the tenure of this project a large area updateable 3D color display has been developed for the first time using a new co-polymer...photorefractive polymers have been demonstrated. Moreover, a 6 inch × 6 inch sample was fabricated demonstrating the feasibility of making large area 3D
3D Microperfusion Model of ADPKD
2015-10-01
Stratasys 3D printer . PDMS was cast in the negative molds in order to create permanent biocompatible plastic masters (SmoothCast 310). All goals of task...1 AWARD NUMBER: W81XWH-14-1-0304 TITLE: 3D Microperfusion Model of ADPKD PRINCIPAL INVESTIGATOR: David L. Kaplan CONTRACTING ORGANIZATION...ADDRESS. 1. REPORT DATE October 2015 2. REPORT TYPE Annual Report 3. DATES COVERED 15 Sep 2014 - 14 Sep 2015 4. TITLE AND SUBTITLE 3D
Parker, Dennis L.
2015-01-01
SYNOPSIS There has been significant progress made in 3D carotid plaque magnetic resonance imaging techniques in recent years. 3D plaque imaging clearly represents the future in clinical use. With effective flow suppression techniques, choices of different contrast weighting acquisitions, and time-efficient imaging approaches, 3D plaque imaging offers flexible imaging plane and view angle analysis, large coverage, multi-vascular beds capability, and even can be used in fast screening. PMID:26610656
3-D Extensions for Trustworthy Systems
2011-01-01
3- D Extensions for Trustworthy Systems (Invited Paper) Ted Huffmire∗, Timothy Levin∗, Cynthia Irvine∗, Ryan Kastner† and Timothy Sherwood...address these problems, we propose an approach to trustworthy system development based on 3- D integration, an emerging chip fabrication technique in...which two or more integrated circuit dies are fabricated individually and then combined into a single stack using vertical conductive posts. With 3- D
Hardware Trust Implications of 3-D Integration
2010-12-01
enhancing a commod- ity processor with a variety of security functions. This paper examines the 3-D design approach and provides an analysis concluding...of key components. The question addressed by this paper is, “Can a 3-D control plane provide useful secure services when it is conjoined with an...untrust- worthy computation plane?” Design-level investigation of this question yields a definite yes. This paper explores 3- D applications and their
Digital holography and 3-D imaging.
Banerjee, Partha; Barbastathis, George; Kim, Myung; Kukhtarev, Nickolai
2011-03-01
This feature issue on Digital Holography and 3-D Imaging comprises 15 papers on digital holographic techniques and applications, computer-generated holography and encryption techniques, and 3-D display. It is hoped that future work in the area leads to innovative applications of digital holography and 3-D imaging to biology and sensing, and to the development of novel nonlinear dynamic digital holographic techniques.
3D seismic image processing for interpretation
NASA Astrophysics Data System (ADS)
Wu, Xinming
Extracting fault, unconformity, and horizon surfaces from a seismic image is useful for interpretation of geologic structures and stratigraphic features. Although interpretation of these surfaces has been automated to some extent by others, significant manual effort is still required for extracting each type of these geologic surfaces. I propose methods to automatically extract all the fault, unconformity, and horizon surfaces from a 3D seismic image. To a large degree, these methods just involve image processing or array processing which is achieved by efficiently solving partial differential equations. For fault interpretation, I propose a linked data structure, which is simpler than triangle or quad meshes, to represent a fault surface. In this simple data structure, each sample of a fault corresponds to exactly one image sample. Using this linked data structure, I extract complete and intersecting fault surfaces without holes from 3D seismic images. I use the same structure in subsequent processing to estimate fault slip vectors. I further propose two methods, using precomputed fault surfaces and slips, to undo faulting in seismic images by simultaneously moving fault blocks and faults themselves. For unconformity interpretation, I first propose a new method to compute a unconformity likelihood image that highlights both the termination areas and the corresponding parallel unconformities and correlative conformities. I then extract unconformity surfaces from the likelihood image and use these surfaces as constraints to more accurately estimate seismic normal vectors that are discontinuous near the unconformities. Finally, I use the estimated normal vectors and use the unconformities as constraints to compute a flattened image, in which seismic reflectors are all flat and vertical gaps correspond to the unconformities. Horizon extraction is straightforward after computing a map of image flattening; we can first extract horizontal slices in the flattened space
A Nonlinear Modal Aeroelastic Solver for FUN3D
NASA Technical Reports Server (NTRS)
Goldman, Benjamin D.; Bartels, Robert E.; Biedron, Robert T.; Scott, Robert C.
2016-01-01
A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.
Dimensional accuracy of 3D printed vertebra
NASA Astrophysics Data System (ADS)
Ogden, Kent; Ordway, Nathaniel; Diallo, Dalanda; Tillapaugh-Fay, Gwen; Aslan, Can
2014-03-01
3D printer applications in the biomedical sciences and medical imaging are expanding and will have an increasing impact on the practice of medicine. Orthopedic and reconstructive surgery has been an obvious area for development of 3D printer applications as the segmentation of bony anatomy to generate printable models is relatively straightforward. There are important issues that should be addressed when using 3D printed models for applications that may affect patient care; in particular the dimensional accuracy of the printed parts needs to be high to avoid poor decisions being made prior to surgery or therapeutic procedures. In this work, the dimensional accuracy of 3D printed vertebral bodies derived from CT data for a cadaver spine is compared with direct measurements on the ex-vivo vertebra and with measurements made on the 3D rendered vertebra using commercial 3D image processing software. The vertebra was printed on a consumer grade 3D printer using an additive print process using PLA (polylactic acid) filament. Measurements were made for 15 different anatomic features of the vertebral body, including vertebral body height, endplate width and depth, pedicle height and width, and spinal canal width and depth, among others. It is shown that for the segmentation and printing process used, the results of measurements made on the 3D printed vertebral body are substantially the same as those produced by direct measurement on the vertebra and measurements made on the 3D rendered vertebra.
Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes
NASA Technical Reports Server (NTRS)
Abdol-Hamid, Khaled S.; Carlson, Jan-Renee; Rumsey, Christopher L.
2015-01-01
The implementation of the k-kL turbulence model using multiple computational uid dy- namics (CFD) codes is reported herein. The k-kL model is a two-equation turbulence model based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's equation is well suited for term-by-term mod- eling and displays useful features compared to other two-equation models. An important di erence is that this formulation leads to the inclusion of higher-order velocity derivatives in the source terms of the scale equations. This can enhance the ability of the Reynolds- averaged Navier-Stokes (RANS) solvers to simulate unsteady ows. The present report documents the formulation of the model as implemented in the CFD codes Fun3D and CFL3D. Methodology, veri cation and validation examples are shown. Attached and sepa- rated ow cases are documented and compared with experimental data. The results show generally very good comparisons with canonical and experimental data, as well as matching results code-to-code. The results from this formulation are similar or better than results using the SST turbulence model.
FastScript3D - A Companion to Java 3D
NASA Technical Reports Server (NTRS)
Koenig, Patti
2005-01-01
FastScript3D is a computer program, written in the Java 3D(TM) programming language, that establishes an alternative language that helps users who lack expertise in Java 3D to use Java 3D for constructing three-dimensional (3D)-appearing graphics. The FastScript3D language provides a set of simple, intuitive, one-line text-string commands for creating, controlling, and animating 3D models. The first word in a string is the name of a command; the rest of the string contains the data arguments for the command. The commands can also be used as an aid to learning Java 3D. Developers can extend the language by adding custom text-string commands. The commands can define new 3D objects or load representations of 3D objects from files in formats compatible with such other software systems as X3D. The text strings can be easily integrated into other languages. FastScript3D facilitates communication between scripting languages [which enable programming of hyper-text markup language (HTML) documents to interact with users] and Java 3D. The FastScript3D language can be extended and customized on both the scripting side and the Java 3D side.
3D ultrafast ultrasound imaging in vivo.
Provost, Jean; Papadacci, Clement; Arango, Juan Esteban; Imbault, Marion; Fink, Mathias; Gennisson, Jean-Luc; Tanter, Mickael; Pernot, Mathieu
2014-10-07
Very high frame rate ultrasound imaging has recently allowed for the extension of the applications of echography to new fields of study such as the functional imaging of the brain, cardiac electrophysiology, and the quantitative imaging of the intrinsic mechanical properties of tumors, to name a few, non-invasively and in real time. In this study, we present the first implementation of Ultrafast Ultrasound Imaging in 3D based on the use of either diverging or plane waves emanating from a sparse virtual array located behind the probe. It achieves high contrast and resolution while maintaining imaging rates of thousands of volumes per second. A customized portable ultrasound system was developed to sample 1024 independent channels and to drive a 32 × 32 matrix-array probe. Its ability to track in 3D transient phenomena occurring in the millisecond range within a single ultrafast acquisition was demonstrated for 3D Shear-Wave Imaging, 3D Ultrafast Doppler Imaging, and, finally, 3D Ultrafast combined Tissue and Flow Doppler Imaging. The propagation of shear waves was tracked in a phantom and used to characterize its stiffness. 3D Ultrafast Doppler was used to obtain 3D maps of Pulsed Doppler, Color Doppler, and Power Doppler quantities in a single acquisition and revealed, at thousands of volumes per second, the complex 3D flow patterns occurring in the ventricles of the human heart during an entire cardiac cycle, as well as the 3D in vivo interaction of blood flow and wall motion during the pulse wave in the carotid at the bifurcation. This study demonstrates the potential of 3D Ultrafast Ultrasound Imaging for the 3D mapping of stiffness, tissue motion, and flow in humans in vivo and promises new clinical applications of ultrasound with reduced intra--and inter-observer variability.
3D ultrafast ultrasound imaging in vivo
NASA Astrophysics Data System (ADS)
Provost, Jean; Papadacci, Clement; Esteban Arango, Juan; Imbault, Marion; Fink, Mathias; Gennisson, Jean-Luc; Tanter, Mickael; Pernot, Mathieu
2014-10-01
Very high frame rate ultrasound imaging has recently allowed for the extension of the applications of echography to new fields of study such as the functional imaging of the brain, cardiac electrophysiology, and the quantitative imaging of the intrinsic mechanical properties of tumors, to name a few, non-invasively and in real time. In this study, we present the first implementation of Ultrafast Ultrasound Imaging in 3D based on the use of either diverging or plane waves emanating from a sparse virtual array located behind the probe. It achieves high contrast and resolution while maintaining imaging rates of thousands of volumes per second. A customized portable ultrasound system was developed to sample 1024 independent channels and to drive a 32 × 32 matrix-array probe. Its ability to track in 3D transient phenomena occurring in the millisecond range within a single ultrafast acquisition was demonstrated for 3D Shear-Wave Imaging, 3D Ultrafast Doppler Imaging, and, finally, 3D Ultrafast combined Tissue and Flow Doppler Imaging. The propagation of shear waves was tracked in a phantom and used to characterize its stiffness. 3D Ultrafast Doppler was used to obtain 3D maps of Pulsed Doppler, Color Doppler, and Power Doppler quantities in a single acquisition and revealed, at thousands of volumes per second, the complex 3D flow patterns occurring in the ventricles of the human heart during an entire cardiac cycle, as well as the 3D in vivo interaction of blood flow and wall motion during the pulse wave in the carotid at the bifurcation. This study demonstrates the potential of 3D Ultrafast Ultrasound Imaging for the 3D mapping of stiffness, tissue motion, and flow in humans in vivo and promises new clinical applications of ultrasound with reduced intra—and inter-observer variability.
An aerial 3D printing test mission
NASA Astrophysics Data System (ADS)
Hirsch, Michael; McGuire, Thomas; Parsons, Michael; Leake, Skye; Straub, Jeremy
2016-05-01
This paper provides an overview of an aerial 3D printing technology, its development and its testing. This technology is potentially useful in its own right. In addition, this work advances the development of a related in-space 3D printing technology. A series of aerial 3D printing test missions, used to test the aerial printing technology, are discussed. Through completing these test missions, the design for an in-space 3D printer may be advanced. The current design for the in-space 3D printer involves focusing thermal energy to heat an extrusion head and allow for the extrusion of molten print material. Plastics can be used as well as composites including metal, allowing for the extrusion of conductive material. A variety of experiments will be used to test this initial 3D printer design. High altitude balloons will be used to test the effects of microgravity on 3D printing, as well as parabolic flight tests. Zero pressure balloons can be used to test the effect of long 3D printing missions subjected to low temperatures. Vacuum chambers will be used to test 3D printing in a vacuum environment. The results will be used to adapt a current prototype of an in-space 3D printer. Then, a small scale prototype can be sent into low-Earth orbit as a 3-U cube satellite. With the ability to 3D print in space demonstrated, future missions can launch production hardware through which the sustainability and durability of structures in space will be greatly improved.
Intersecting D 3 -D3 ' -brane system at finite temperature
NASA Astrophysics Data System (ADS)
Cottrell, William; Hanson, James; Hashimoto, Akikazu; Loveridge, Andrew; Pettengill, Duncan
2017-02-01
We analyze the dynamics of the intersecting D 3 -D3 ' -brane system overlapping in 1 +1 dimensions, in a holographic treatment where N D3 branes are manifested as anti-de Sitter Schwartzschild geometry, and the D3 ' brane is treated as a probe. We extract the thermodynamic equation of state from the set of embedding solutions, and analyze the stability at the perturbative and the nonperturbative level. We review a systematic procedure to resolve local instabilities and multivaluedness in the equations of state based on classic ideas of convexity in the microcanonical ensemble. We then identify a runaway behavior which was not noticed previously for this system.
A non-conforming 3D spherical harmonic transport solver
Van Criekingen, S.
2006-07-01
A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)
Kelvin-Helmholtz instability in an Alfven resonant layer of a solar coronal loop
NASA Technical Reports Server (NTRS)
Uchimoto, E.; Strauss, H. R.; Lawson, W. S.
1991-01-01
A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfven resonant layer in an axially bounded, straight cylindrical coronal loop. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfven driving amplitude and inversely proportional to the width of the Alfven resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfven resonant layer width, and decreases at higher azimuthal mode number.
Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function
Linton, C. M.
2015-01-15
A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.
Loss-improved electroacoustical modeling of small Helmholtz resonators.
Starecki, Tomasz
2007-10-01
Modeling of small Helmholtz resonators based on electroacoustical analogies often results in significant disagreement with measurements, as existing models do not take into account some losses that are observed in practical implementations of such acoustical circuits, e.g., in photoacoustic Helmholtz cells. The paper presents a method which introduces loss corrections to the transmission line model, resulting in substantial improvement of simulations. Values of the loss corrections obtained from comparison of frequency responses of practically implemented resonators with computer simulations are presented in tabular and graphical form. A simple analytical function that can be used for interpolation or extrapolation of the loss corrections for other dimensions of the Helmholtz resonators is also given. Verification of such a modeling method against an open two-cavity Helmholtz structure shows very good agreement between measurements and simulations.
Integration of real-time 3D image acquisition and multiview 3D display
NASA Astrophysics Data System (ADS)
Zhang, Zhaoxing; Geng, Zheng; Li, Tuotuo; Li, Wei; Wang, Jingyi; Liu, Yongchun
2014-03-01
Seamless integration of 3D acquisition and 3D display systems offers enhanced experience in 3D visualization of the real world objects or scenes. The vivid representation of captured 3D objects displayed on a glasses-free 3D display screen could bring the realistic viewing experience to viewers as if they are viewing real-world scene. Although the technologies in 3D acquisition and 3D display have advanced rapidly in recent years, effort is lacking in studying the seamless integration of these two different aspects of 3D technologies. In this paper, we describe our recent progress on integrating a light-field 3D acquisition system and an autostereoscopic multiview 3D display for real-time light field capture and display. This paper focuses on both the architecture design and the implementation of the hardware and the software of this integrated 3D system. A prototype of the integrated 3D system is built to demonstrate the real-time 3D acquisition and 3D display capability of our proposed system.
Immersive 3D Geovisualization in Higher Education
ERIC Educational Resources Information Center
Philips, Andrea; Walz, Ariane; Bergner, Andreas; Graeff, Thomas; Heistermann, Maik; Kienzler, Sarah; Korup, Oliver; Lipp, Torsten; Schwanghart, Wolfgang; Zeilinger, Gerold
2015-01-01
In this study, we investigate how immersive 3D geovisualization can be used in higher education. Based on MacEachren and Kraak's geovisualization cube, we examine the usage of immersive 3D geovisualization and its usefulness in a research-based learning module on flood risk, called GEOSimulator. Results of a survey among participating students…
A 3D Geostatistical Mapping Tool
Weiss, W. W.; Stevenson, Graig; Patel, Ketan; Wang, Jun
1999-02-09
This software provides accurate 3D reservoir modeling tools and high quality 3D graphics for PC platforms enabling engineers and geologists to better comprehend reservoirs and consequently improve their decisions. The mapping algorithms are fractals, kriging, sequential guassian simulation, and three nearest neighbor methods.
ERIC Educational Resources Information Center
Love, Tyler S.; Roy, Ken
2016-01-01
Health concerns from 3D printing were first documented by Stephens, Azimi, Orch, and Ramos (2013), who found that commercially available 3D printers were producing hazardous levels of ultrafine particles (UFPs) and volatile organic compounds (VOCs) when plastic materials were melted through the extruder. UFPs are particles less than 100 nanometers…
Topology dictionary for 3D video understanding.
Tung, Tony; Matsuyama, Takashi
2012-08-01
This paper presents a novel approach that achieves 3D video understanding. 3D video consists of a stream of 3D models of subjects in motion. The acquisition of long sequences requires large storage space (2 GB for 1 min). Moreover, it is tedious to browse data sets and extract meaningful information. We propose the topology dictionary to encode and describe 3D video content. The model consists of a topology-based shape descriptor dictionary which can be generated from either extracted patterns or training sequences. The model relies on 1) topology description and classification using Reeb graphs, and 2) a Markov motion graph to represent topology change states. We show that the use of Reeb graphs as the high-level topology descriptor is relevant. It allows the dictionary to automatically model complex sequences, whereas other strategies would require prior knowledge on the shape and topology of the captured subjects. Our approach serves to encode 3D video sequences, and can be applied for content-based description and summarization of 3D video sequences. Furthermore, topology class labeling during a learning process enables the system to perform content-based event recognition. Experiments were carried out on various 3D videos. We showcase an application for 3D video progressive summarization using the topology dictionary.
3D elastic control for mobile devices.
Hachet, Martin; Pouderoux, Joachim; Guitton, Pascal
2008-01-01
To increase the input space of mobile devices, the authors developed a proof-of-concept 3D elastic controller that easily adapts to mobile devices. This embedded device improves the completion of high-level interaction tasks such as visualization of large documents and navigation in 3D environments. It also opens new directions for tomorrow's mobile applications.
3D Printing of Molecular Models
ERIC Educational Resources Information Center
Gardner, Adam; Olson, Arthur
2016-01-01
Physical molecular models have played a valuable role in our understanding of the invisible nano-scale world. We discuss 3D printing and its use in producing models of the molecules of life. Complex biomolecular models, produced from 3D printed parts, can demonstrate characteristics of molecular structure and function, such as viral self-assembly,…
3D Printed Block Copolymer Nanostructures
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Turner, C. Heath; Rupar, Paul A.; Jenkins, Alexander H.; Bara, Jason E.
2015-01-01
The emergence of 3D printing has dramatically advanced the availability of tangible molecular and extended solid models. Interestingly, there are few nanostructure models available both commercially and through other do-it-yourself approaches such as 3D printing. This is unfortunate given the importance of nanotechnology in science today. In this…
Infrastructure for 3D Imaging Test Bed
2007-05-11
analysis. (c.) Real time detection & analysis of human gait: using a video camera we capture walking human silhouette for pattern modeling and gait ... analysis . Fig. 5 shows the scanning result result that is fed into a Geo-magic software tool for 3D meshing. Fig. 5: 3D scanning result In
Wow! 3D Content Awakens the Classroom
ERIC Educational Resources Information Center
Gordon, Dan
2010-01-01
From her first encounter with stereoscopic 3D technology designed for classroom instruction, Megan Timme, principal at Hamilton Park Pacesetter Magnet School in Dallas, sensed it could be transformative. Last spring, when she began pilot-testing 3D content in her third-, fourth- and fifth-grade classrooms, Timme wasn't disappointed. Students…
Stereo 3-D Vision in Teaching Physics
ERIC Educational Resources Information Center
Zabunov, Svetoslav
2012-01-01
Stereo 3-D vision is a technology used to present images on a flat surface (screen, paper, etc.) and at the same time to create the notion of three-dimensional spatial perception of the viewed scene. A great number of physical processes are much better understood when viewed in stereo 3-D vision compared to standard flat 2-D presentation. The…
Pathways for Learning from 3D Technology
ERIC Educational Resources Information Center
Carrier, L. Mark; Rab, Saira S.; Rosen, Larry D.; Vasquez, Ludivina; Cheever, Nancy A.
2012-01-01
The purpose of this study was to find out if 3D stereoscopic presentation of information in a movie format changes a viewer's experience of the movie content. Four possible pathways from 3D presentation to memory and learning were considered: a direct connection based on cognitive neuroscience research; a connection through "immersion"…
ERIC Educational Resources Information Center
Norbury, Keith
2012-01-01
It may be too soon for students to be showing up for class with popcorn and gummy bears, but technology similar to that behind the 3D blockbuster movie "Avatar" is slowly finding its way into college classrooms. 3D classroom projectors are taking students on fantastic voyages inside the human body, to the ruins of ancient Greece--even to faraway…
Static & Dynamic Response of 3D Solids
Lin, Jerry
1996-07-15
NIKE3D is a large deformations 3D finite element code used to obtain the resulting displacements and stresses from multi-body static and dynamic structural thermo-mechanics problems with sliding interfaces. Many nonlinear and temperature dependent constitutive models are available.
Kingfish striations and the Kelvin-Helmholtz instability. Part 1
Hunter, J.H. Jr.
1985-10-01
The role of the Kelvin-Helmholtz instability in initiating the formation of the density striations observed in the Kingfish fireball is examined. Two idealized models are proposed for the velocity shear layer on the sides of the fireball, each of which includes essential characteristics of the Kingfish event insofar as the development of Kelvin-Helmholtz instabilities is concerned. A complete linear analysis is presented for each model.
BEAMS3D Neutral Beam Injection Model
Lazerson, Samuel
2014-04-14
With the advent of applied 3D fi elds in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous velocity reduction, and pitch angle scattering are modeled with the ADAS atomic physics database [1]. Benchmark calculations are presented to validate the collisionless particle orbits, neutral beam injection model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields.
Fabrication of 3D Silicon Sensors
Kok, A.; Hansen, T.E.; Hansen, T.A.; Lietaer, N.; Summanwar, A.; Kenney, C.; Hasi, J.; Da Via, C.; Parker, S.I.; /Hawaii U.
2012-06-06
Silicon sensors with a three-dimensional (3-D) architecture, in which the n and p electrodes penetrate through the entire substrate, have many advantages over planar silicon sensors including radiation hardness, fast time response, active edge and dual readout capabilities. The fabrication of 3D sensors is however rather complex. In recent years, there have been worldwide activities on 3D fabrication. SINTEF in collaboration with Stanford Nanofabrication Facility have successfully fabricated the original (single sided double column type) 3D detectors in two prototype runs and the third run is now on-going. This paper reports the status of this fabrication work and the resulted yield. The work of other groups such as the development of double sided 3D detectors is also briefly reported.
NASA Astrophysics Data System (ADS)
Dekker, T.; de Zwart, S. T.; Willemsen, O. H.; Hiddink, M. G. H.; IJzerman, W. L.
2006-02-01
A prerequisite for a wide market acceptance of 3D displays is the ability to switch between 3D and full resolution 2D. In this paper we present a robust and cost effective concept for an auto-stereoscopic switchable 2D/3D display. The display is based on an LCD panel, equipped with switchable LC-filled lenticular lenses. We will discuss 3D image quality, with the focus on display uniformity. We show that slanting the lenticulars in combination with a good lens design can minimize non-uniformities in our 20" 2D/3D monitors. Furthermore, we introduce fractional viewing systems as a very robust concept to further improve uniformity in the case slanting the lenticulars and optimizing the lens design are not sufficient. We will discuss measurements and numerical simulations of the key optical characteristics of this display. Finally, we discuss 2D image quality, the switching characteristics and the residual lens effect.
Biocompatible 3D Matrix with Antimicrobial Properties.
Ion, Alberto; Andronescu, Ecaterina; Rădulescu, Dragoș; Rădulescu, Marius; Iordache, Florin; Vasile, Bogdan Ștefan; Surdu, Adrian Vasile; Albu, Madalina Georgiana; Maniu, Horia; Chifiriuc, Mariana Carmen; Grumezescu, Alexandru Mihai; Holban, Alina Maria
2016-01-20
The aim of this study was to develop, characterize and assess the biological activity of a new regenerative 3D matrix with antimicrobial properties, based on collagen (COLL), hydroxyapatite (HAp), β-cyclodextrin (β-CD) and usnic acid (UA). The prepared 3D matrix was characterized by Scanning Electron Microscopy (SEM), Fourier Transform Infrared Microscopy (FT-IRM), Transmission Electron Microscopy (TEM), and X-ray Diffraction (XRD). In vitro qualitative and quantitative analyses performed on cultured diploid cells demonstrated that the 3D matrix is biocompatible, allowing the normal development and growth of MG-63 osteoblast-like cells and exhibited an antimicrobial effect, especially on the Staphylococcus aureus strain, explained by the particular higher inhibitory activity of usnic acid (UA) against Gram positive bacterial strains. Our data strongly recommend the obtained 3D matrix to be used as a successful alternative for the fabrication of three dimensional (3D) anti-infective regeneration matrix for bone tissue engineering.
Quon 3D language for quantum information
Liu, Zhengwei; Wozniakowski, Alex; Jaffe, Arthur M.
2017-01-01
We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string–genus “joint relation,” involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the C∗-Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation. PMID:28167790
Tuned passive control of combustion instabilities using multiple Helmholtz resonators
NASA Astrophysics Data System (ADS)
Zhao, Dan; Morgans, A. S.
2009-03-01
In this work, tuned passive control is used to damp unstable combustion systems, with particular emphasis on systems which exhibit multiple unstable modes. Helmholtz resonators are used as passive dampers. The frequency at which they offer maximum damping is varied by altering their geometry; in this work, geometry changes are achieved by varying the area of the Helmholtz resonator neck. For each unstable mode exhibited by the combustion system, a separate Helmholtz resonator has its neck area tuned. Two algorithms are developed, one for identifying the characteristics of all modes present in real time, and another for tuning the neck areas of the Helmholtz resonators. These algorithms are successfully implemented in numerical simulations of a longitudinal combustor exhibiting two unstable modes. The algorithms result in both modes being stabilised as long as two Helmholtz resonators are used. Experiments are then conducted on a Rijke tube with its upper part split into two branches of differing lengths, shaped like a 'Y'. The differing lengths give rise to two unstable modes at different frequencies. A Helmholtz resonator is attached to each branch; the neck area of both can be varied by means of an 'iris' valve, which opens and closes like a camera lens. On implementing the procedure for tuning the neck areas, both unstable modes are stabilised, and stability is maintained for large changes in operating condition. This confirms that the procedure developed is sufficiently robust for use in real combustion systems exhibiting multiple unstable modes.
Experimental realization of extraordinary acoustic transmission using Helmholtz resonators
NASA Astrophysics Data System (ADS)
Crow, Brian C.; Cullen, Jordan M.; McKenzie, William W.; Koju, Vijay; Robertson, William M.
2015-02-01
The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR) is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted sound as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.
Experimental realization of extraordinary acoustic transmission using Helmholtz resonators
Crow, Brian C.; Cullen, Jordan M.; McKenzie, William W.; Koju, Vijay; Robertson, William M.
2015-02-15
The phenomenon of extraordinary acoustic transmission through a solid barrier with an embedded Helmholtz resonator (HR) is demonstrated. The Helmholtz resonator consists of an embedded cavity and two necks that protrude, one on each side of the barrier. Extraordinary transmission occurs for a narrow spectral range encompassing the resonant frequency of the Helmholtz resonator. We show that an amplitude transmission of 97.5% is achieved through a resonator whose neck creates an open area of 6.25% of the total barrier area. In addition to the enhanced transmission, we show that there is a smooth, continuous phase transition in the transmitted sound as a function of frequency. The frequency dependent phase transition is used to experimentally realize slow wave propagation for a narrow-band Gaussian wave packet centered at the maximum transmission frequency. The use of parallel pairs of Helmholtz resonators tuned to different resonant frequencies is experimentally explored as a means of increasing the transmission bandwidth. These experiments show that because of the phase transition, there is always a frequency between the two Helmholtz resonant frequencies at which destructive interference occurs whether the resonances are close or far apart. Finally, we explain how the phase transition associated with Helmholtz-resonator-mediated extraordinary acoustic transmission can be exploited to produce diffractive acoustic components including sub-wavelength thickness acoustic lenses.
3D Ultrafast Ultrasound Imaging In Vivo
Provost, Jean; Papadacci, Clement; Arango, Juan Esteban; Imbault, Marion; Gennisson, Jean-Luc; Tanter, Mickael; Pernot, Mathieu
2014-01-01
Very high frame rate ultrasound imaging has recently allowed for the extension of the applications of echography to new fields of study such as the functional imaging of the brain, cardiac electrophysiology, and the quantitative real-time imaging of the intrinsic mechanical properties of tumors, to name a few, non-invasively and in real time. In this study, we present the first implementation of Ultrafast Ultrasound Imaging in three dimensions based on the use of either diverging or plane waves emanating from a sparse virtual array located behind the probe. It achieves high contrast and resolution while maintaining imaging rates of thousands of volumes per second. A customized portable ultrasound system was developed to sample 1024 independent channels and to drive a 32×32 matrix-array probe. Its capability to track in 3D transient phenomena occurring in the millisecond range within a single ultrafast acquisition was demonstrated for 3-D Shear-Wave Imaging, 3-D Ultrafast Doppler Imaging and finally 3D Ultrafast combined Tissue and Flow Doppler. The propagation of shear waves was tracked in a phantom and used to characterize its stiffness. 3-D Ultrafast Doppler was used to obtain 3-D maps of Pulsed Doppler, Color Doppler, and Power Doppler quantities in a single acquisition and revealed, for the first time, the complex 3-D flow patterns occurring in the ventricles of the human heart during an entire cardiac cycle, and the 3-D in vivo interaction of blood flow and wall motion during the pulse wave in the carotid at the bifurcation. This study demonstrates the potential of 3-D Ultrafast Ultrasound Imaging for the 3-D real-time mapping of stiffness, tissue motion, and flow in humans in vivo and promises new clinical applications of ultrasound with reduced intra- and inter-observer variability. PMID:25207828
3D Visualization Development of SIUE Campus
NASA Astrophysics Data System (ADS)
Nellutla, Shravya
Geographic Information Systems (GIS) has progressed from the traditional map-making to the modern technology where the information can be created, edited, managed and analyzed. Like any other models, maps are simplified representations of real world. Hence visualization plays an essential role in the applications of GIS. The use of sophisticated visualization tools and methods, especially three dimensional (3D) modeling, has been rising considerably due to the advancement of technology. There are currently many off-the-shelf technologies available in the market to build 3D GIS models. One of the objectives of this research was to examine the available ArcGIS and its extensions for 3D modeling and visualization and use them to depict a real world scenario. Furthermore, with the advent of the web, a platform for accessing and sharing spatial information on the Internet, it is possible to generate interactive online maps. Integrating Internet capacity with GIS functionality redefines the process of sharing and processing the spatial information. Enabling a 3D map online requires off-the-shelf GIS software, 3D model builders, web server, web applications and client server technologies. Such environments are either complicated or expensive because of the amount of hardware and software involved. Therefore, the second objective of this research was to investigate and develop simpler yet cost-effective 3D modeling approach that uses available ArcGIS suite products and the free 3D computer graphics software for designing 3D world scenes. Both ArcGIS Explorer and ArcGIS Online will be used to demonstrate the way of sharing and distributing 3D geographic information on the Internet. A case study of the development of 3D campus for the Southern Illinois University Edwardsville is demonstrated.
Pathways for Learning from 3D Technology
Carrier, L. Mark; Rab, Saira S.; Rosen, Larry D.; Vasquez, Ludivina; Cheever, Nancy A.
2016-01-01
The purpose of this study was to find out if 3D stereoscopic presentation of information in a movie format changes a viewer's experience of the movie content. Four possible pathways from 3D presentation to memory and learning were considered: a direct connection based on cognitive neuroscience research; a connection through "immersion" in that 3D presentations could provide additional sensorial cues (e.g., depth cues) that lead to a higher sense of being surrounded by the stimulus; a connection through general interest such that 3D presentation increases a viewer’s interest that leads to greater attention paid to the stimulus (e.g., "involvement"); and a connection through discomfort, with the 3D goggles causing discomfort that interferes with involvement and thus with memory. The memories of 396 participants who viewed two-dimensional (2D) or 3D movies at movie theaters in Southern California were tested. Within three days of viewing a movie, participants filled out an online anonymous questionnaire that queried them about their movie content memories, subjective movie-going experiences (including emotional reactions and "presence") and demographic backgrounds. The responses to the questionnaire were subjected to path analyses in which several different links between 3D presentation to memory (and other variables) were explored. The results showed there were no effects of 3D presentation, either directly or indirectly, upon memory. However, the largest effects of 3D presentation were on emotions and immersion, with 3D presentation leading to reduced positive emotions, increased negative emotions and lowered immersion, compared to 2D presentations. PMID:28078331
The psychology of the 3D experience
NASA Astrophysics Data System (ADS)
Janicke, Sophie H.; Ellis, Andrew
2013-03-01
With 3D televisions expected to reach 50% home saturation as early as 2016, understanding the psychological mechanisms underlying the user response to 3D technology is critical for content providers, educators and academics. Unfortunately, research examining the effects of 3D technology has not kept pace with the technology's rapid adoption, resulting in large-scale use of a technology about which very little is actually known. Recognizing this need for new research, we conducted a series of studies measuring and comparing many of the variables and processes underlying both 2D and 3D media experiences. In our first study, we found narratives within primetime dramas had the power to shift viewer attitudes in both 2D and 3D settings. However, we found no difference in persuasive power between 2D and 3D content. We contend this lack of effect was the result of poor conversion quality and the unique demands of 3D production. In our second study, we found 3D technology significantly increased enjoyment when viewing sports content, yet offered no added enjoyment when viewing a movie trailer. The enhanced enjoyment of the sports content was shown to be the result of heightened emotional arousal and attention in the 3D condition. We believe the lack of effect found for the movie trailer may be genre-related. In our final study, we found 3D technology significantly enhanced enjoyment of two video games from different genres. The added enjoyment was found to be the result of an increased sense of presence.
Applying the Helmholtz illusion to fashion: horizontal stripes won't make you look fatter.
Thompson, Peter; Mikellidou, Kyriaki
2011-01-01
A square composed of horizontal lines appears taller and narrower than an identical square made up of vertical lines. Reporting this illusion, Hermann von Helmholtz noted that such illusions, in which filled space seems to be larger than unfilled space, were common in everyday life, adding the observation that ladies' frocks with horizontal stripes make the figure look taller. As this assertion runs counter to modern popular belief, we have investigated whether vertical or horizontal stripes on clothing should make the wearer appear taller or fatter. We find that a rectangle of vertical stripes needs to be extended by 7.1% vertically to match the height of a square of horizontal stripes and that a rectangle of horizontal stripes must be made 4.5% wider than a square of vertical stripes to match its perceived width. This illusion holds when the horizontal or vertical lines are on the dress of a line drawing of a woman. We have examined the claim that these effects apply only for 2-dimensional figures in an experiment with 3-D cylinders and find no support for the notion that horizontal lines would be 'fattening' on clothes. Significantly, the illusion persists when the horizontal or vertical lines are on pictures of a real half-body mannequin viewed stereoscopically. All the evidence supports Helmholtz's original assertion.
Applying the Helmholtz illusion to fashion: horizontal stripes won't make you look fatter
Thompson, Peter; Mikellidou, Kyriaki
2011-01-01
A square composed of horizontal lines appears taller and narrower than an identical square made up of vertical lines. Reporting this illusion, Hermann von Helmholtz noted that such illusions, in which filled space seems to be larger than unfilled space, were common in everyday life, adding the observation that ladies' frocks with horizontal stripes make the figure look taller. As this assertion runs counter to modern popular belief, we have investigated whether vertical or horizontal stripes on clothing should make the wearer appear taller or fatter. We find that a rectangle of vertical stripes needs to be extended by 7.1% vertically to match the height of a square of horizontal stripes and that a rectangle of horizontal stripes must be made 4.5% wider than a square of vertical stripes to match its perceived width. This illusion holds when the horizontal or vertical lines are on the dress of a line drawing of a woman. We have examined the claim that these effects apply only for 2-dimensional figures in an experiment with 3-D cylinders and find no support for the notion that horizontal lines would be ‘fattening’ on clothes. Significantly, the illusion persists when the horizontal or vertical lines are on pictures of a real half-body mannequin viewed stereoscopically. All the evidence supports Helmholtz's original assertion. PMID:23145226
Kelvin-Helmholtz instabilities and Bénard Von-Karman Streets under lateral confinement
NASA Astrophysics Data System (ADS)
Lebon, Luc; Boniface, Paul; Receveur, Mathieu; Limat, Laurent; Bouillet, Fabien
2013-11-01
We have investigated Kelvin-Helmholtz instabilities in a confined geometry. We used a large tank of water with a belt moving at high speed on the central part of its free surface. The water below the belt is dragged by this one, while the excess is recirculating along the lateral walls. Using displaceable walls, belts of different widths, and modifying the water height, it is possible to tune at will the geometry. Depending on the involved ratios, two different behaviors are observed: (1) recirculation by the bottom of the tank, (2) recirculation along the walls with the growth of two coupled Kelvin-Helmholtz instabilities on each side of the belt. At long time scale, and depending again on the involved geometry, the flow evolves to a 3D turbulence or to a well organized Bénard-Von-Karman street, with a 2D spatial organization of the flow. The wave-length in each vortex row is in agreement with a stability calculations of point vortices developed in the 30's by Rosenhead.
Cloud-resolving component in the quasi-3D multi-scale modeling framework
NASA Astrophysics Data System (ADS)
Jung, Joon-Hee; Arakawa, Akio
2010-05-01
A quasi-3D multi-scale modeling framework (Q3D MMF), which combines a GCM with a Q3D CRM, is an attempt to include three dimensional cloud effects in a GCM without necessarily using a global cloud-resolving model. The horizontal domain of the Q3D CRM consists of two perpendicular sets of channels crossing at the center of a GCM grid box, each of which includes two grid-point arrays. Through coupling this structure with a GCM, the whole system of the Q3D MMF can converge to a fully 3D global CRM as the GCM's resolution is refined. Consequently, the horizontal resolution of the GCM can be freely chosen depending on the objective of application. However, due to the use of very narrow channels for the cloud-resolving component, its prediction algorithm must be specially designed. As a step in developing a Q3D MMF, we have first constructed a prediction algorithm for the Q3D CRM applying a 3D anelastic vector vorticity equation model to the Q3D network of grid points. Preliminary tests of the Q3D CRM have been performed for an idealized small domain. Comparing the results with those of the straightforward application of a 3D CRM, it is concluded that the Q3D CRM can reproduce most of the important statistics of the 3D solutions and the MMF based on the Q3D CRM will be a useful framework for climate modeling. This paper presents an outline of the Q3D algorithm and highlights of the results.
MOM3D/EM-ANIMATE - MOM3D WITH ANIMATION CODE
NASA Technical Reports Server (NTRS)
Shaeffer, J. F.
1994-01-01
MOM3D (LAR-15074) is a FORTRAN method-of-moments electromagnetic analysis algorithm for open or closed 3-D perfectly conducting or resistive surfaces. Radar cross section with plane wave illumination is the prime analysis emphasis; however, provision is also included for local port excitation for computing antenna gain patterns and input impedances. The Electric Field Integral Equation form of Maxwell's equations is solved using local triangle couple basis and testing functions with a resultant system impedance matrix. The analysis emphasis is not only for routine RCS pattern predictions, but also for phenomenological diagnostics: bistatic imaging, currents, and near scattered/total electric fields. The images, currents, and near fields are output in form suitable for animation. MOM3D computes the full backscatter and bistatic radar cross section polarization scattering matrix (amplitude and phase), body currents and near scattered and total fields for plane wave illumination. MOM3D also incorporates a new bistatic k space imaging algorithm for computing down range and down/cross range diagnostic images using only one matrix inversion. MOM3D has been made memory and cpu time efficient by using symmetric matrices, symmetric geometry, and partitioned fixed and variable geometries suitable for design iteration studies. MOM3D may be run interactively or in batch mode on 486 IBM PCs and compatibles, UNIX workstations or larger computers. A 486 PC with 16 megabytes of memory has the potential to solve a 30 square wavelength (containing 3000 unknowns) symmetric configuration. Geometries are described using a triangular mesh input in the form of a list of spatial vertex points and a triangle join connection list. The EM-ANIMATE (LAR-15075) program is a specialized visualization program that displays and animates the near-field and surface-current solutions obtained from an electromagnetics program, in particular, that from MOM3D. The EM-ANIMATE program is windows based and
The Helmholtz Total Artificial Heart Labtype.
Kaufmann, R; Reul, H; Rau, G
1994-07-01
To perform the first experimental tests for validation of a new gear unit concept, the pump chamber, diaphragm, and pusher plate design of an orthotopic electromechanical total artificial heart (TAH) (Helmholtz Labtype) was manufactured. In its early stage of development, it provides some of the most important features of the conceptual final artificial heart. The new gear unit transforms a uniform unidirectional rotational motor movement into translatory pusher plate movements, with resting phase in the end-diastolic position, and the angled pump chamber orientation determines the available space for the motor and gear unit. Furthermore, this labtype provides flexibility with regard to use of different types of structural parts for experimental investigations. The first in vitro test results, obtained with specially designed circulatory mockloops that simulate physiological preload and afterload conditions, are presented. They comprise pressure and flow generation, motor performance, efficiency, and energy consumption. The results prove the feasibility of the new gear unit concept for an electromechanical artificial heart and allow a reliable determination of the necessary performance of the future brushless DC motor for the first in vivo TAH model.
Potential of 3D City Models to assess flood vulnerability
NASA Astrophysics Data System (ADS)
Schröter, Kai; Bochow, Mathias; Schüttig, Martin; Nagel, Claus; Ross, Lutz; Kreibich, Heidi
2016-04-01
Vulnerability, as the product of exposure and susceptibility, is a key factor of the flood risk equation. Furthermore, the estimation of flood loss is very sensitive to the choice of the vulnerability model. Still, in contrast to elaborate hazard simulations, vulnerability is often considered in a simplified manner concerning the spatial resolution and geo-location of exposed objects as well as the susceptibility of these objects at risk. Usually, area specific potential flood loss is quantified on the level of aggregated land-use classes, and both hazard intensity and resistance characteristics of affected objects are represented in highly simplified terms. We investigate the potential of 3D City Models and spatial features derived from remote sensing data to improve the differentiation of vulnerability in flood risk assessment. 3D City Models are based on CityGML, an application scheme of the Geography Markup Language (GML), which represents the 3D geometry, 3D topology, semantics and appearance of objects on different levels of detail. As such, 3D City Models offer detailed spatial information which is useful to describe the exposure and to characterize the susceptibility of residential buildings at risk. This information is further consolidated with spatial features of the building stock derived from remote sensing data. Using this database a spatially detailed flood vulnerability model is developed by means of data-mining. Empirical flood damage data are used to derive and to validate flood susceptibility models for individual objects. We present first results from a prototype application in the city of Dresden, Germany. The vulnerability modeling based on 3D City Models and remote sensing data is compared i) to the generally accepted good engineering practice based on area specific loss potential and ii) to a highly detailed representation of flood vulnerability based on a building typology using urban structure types. Comparisons are drawn in terms of
3-D transient eddy current calculations for the FELIX cylinder experiments
Davey, K.R.; Turner, L.R.
1986-12-01
The three-dimensional eddy current transient field problem is formulated first using the U-V method. This method breaks the vector Helmholtz equation into two scalar Helmholtz equations. Null field integral equations and the appropriate boundary conditions are used to set up an identification matrix which is independent of null field point locations. Embedded in the identification matrix are the unknown eigenvalues of the problem representing its impulse response in time. These eigenvalues are found by equating the determinant of the identification matrix to zero. When this initial forcing function is Fourier decomposed into its spatial harmonics, each Fourier component can be associated with a unique eigenvalue by this technique. The true transient solution comes through a convolution of the impulse response so obtained with the particular external field decay governing the problem at hand. The technique is applied to the FELIX cylinder experiments; computed results are compared to data. A pseudoanalytic confirmation of the eigenvalues so obtained is formulated to validate the procedure.
3D bioprinting of tissues and organs.
Murphy, Sean V; Atala, Anthony
2014-08-01
Additive manufacturing, otherwise known as three-dimensional (3D) printing, is driving major innovations in many areas, such as engineering, manufacturing, art, education and medicine. Recent advances have enabled 3D printing of biocompatible materials, cells and supporting components into complex 3D functional living tissues. 3D bioprinting is being applied to regenerative medicine to address the need for tissues and organs suitable for transplantation. Compared with non-biological printing, 3D bioprinting involves additional complexities, such as the choice of materials, cell types, growth and differentiation factors, and technical challenges related to the sensitivities of living cells and the construction of tissues. Addressing these complexities requires the integration of technologies from the fields of engineering, biomaterials science, cell biology, physics and medicine. 3D bioprinting has already been used for the generation and transplantation of several tissues, including multilayered skin, bone, vascular grafts, tracheal splints, heart tissue and cartilaginous structures. Other applications include developing high-throughput 3D-bioprinted tissue models for research, drug discovery and toxicology.
Medical 3D Printing for the Radiologist.
Mitsouras, Dimitris; Liacouras, Peter; Imanzadeh, Amir; Giannopoulos, Andreas A; Cai, Tianrun; Kumamaru, Kanako K; George, Elizabeth; Wake, Nicole; Caterson, Edward J; Pomahac, Bohdan; Ho, Vincent B; Grant, Gerald T; Rybicki, Frank J
2015-01-01
While use of advanced visualization in radiology is instrumental in diagnosis and communication with referring clinicians, there is an unmet need to render Digital Imaging and Communications in Medicine (DICOM) images as three-dimensional (3D) printed models capable of providing both tactile feedback and tangible depth information about anatomic and pathologic states. Three-dimensional printed models, already entrenched in the nonmedical sciences, are rapidly being embraced in medicine as well as in the lay community. Incorporating 3D printing from images generated and interpreted by radiologists presents particular challenges, including training, materials and equipment, and guidelines. The overall costs of a 3D printing laboratory must be balanced by the clinical benefits. It is expected that the number of 3D-printed models generated from DICOM images for planning interventions and fabricating implants will grow exponentially. Radiologists should at a minimum be familiar with 3D printing as it relates to their field, including types of 3D printing technologies and materials used to create 3D-printed anatomic models, published applications of models to date, and clinical benefits in radiology. Online supplemental material is available for this article.
Medical 3D Printing for the Radiologist
Mitsouras, Dimitris; Liacouras, Peter; Imanzadeh, Amir; Giannopoulos, Andreas A.; Cai, Tianrun; Kumamaru, Kanako K.; George, Elizabeth; Wake, Nicole; Caterson, Edward J.; Pomahac, Bohdan; Ho, Vincent B.; Grant, Gerald T.
2015-01-01
While use of advanced visualization in radiology is instrumental in diagnosis and communication with referring clinicians, there is an unmet need to render Digital Imaging and Communications in Medicine (DICOM) images as three-dimensional (3D) printed models capable of providing both tactile feedback and tangible depth information about anatomic and pathologic states. Three-dimensional printed models, already entrenched in the nonmedical sciences, are rapidly being embraced in medicine as well as in the lay community. Incorporating 3D printing from images generated and interpreted by radiologists presents particular challenges, including training, materials and equipment, and guidelines. The overall costs of a 3D printing laboratory must be balanced by the clinical benefits. It is expected that the number of 3D-printed models generated from DICOM images for planning interventions and fabricating implants will grow exponentially. Radiologists should at a minimum be familiar with 3D printing as it relates to their field, including types of 3D printing technologies and materials used to create 3D-printed anatomic models, published applications of models to date, and clinical benefits in radiology. Online supplemental material is available for this article. ©RSNA, 2015 PMID:26562233
3D imaging in forensic odontology.
Evans, Sam; Jones, Carl; Plassmann, Peter
2010-06-16
This paper describes the investigation of a new 3D capture method for acquiring and subsequent forensic analysis of bite mark injuries on human skin. When documenting bite marks with standard 2D cameras errors in photographic technique can occur if best practice is not followed. Subsequent forensic analysis of the mark is problematic when a 3D structure is recorded into a 2D space. Although strict guidelines (BAFO) exist, these are time-consuming to follow and, due to their complexity, may produce errors. A 3D image capture and processing system might avoid the problems resulting from the 2D reduction process, simplifying the guidelines and reducing errors. Proposed Solution: a series of experiments are described in this paper to demonstrate that the potential of a 3D system might produce suitable results. The experiments tested precision and accuracy of the traditional 2D and 3D methods. A 3D image capture device minimises the amount of angular distortion, therefore such a system has the potential to create more robust forensic evidence for use in courts. A first set of experiments tested and demonstrated which method of forensic analysis creates the least amount of intra-operator error. A second set tested and demonstrated which method of image capture creates the least amount of inter-operator error and visual distortion. In a third set the effects of angular distortion on 2D and 3D methods of image capture were evaluated.
NUBEAM developments and 3d halo modeling
NASA Astrophysics Data System (ADS)
Gorelenkova, M. V.; Medley, S. S.; Kaye, S. M.
2012-10-01
Recent developments related to the 3D halo model in NUBEAM code are described. To have a reliable halo neutral source for diagnostic simulation, the TRANSP/NUBEAM code has been enhanced with full implementation of ADAS atomic physic ground state and excited state data for hydrogenic beams and mixed species plasma targets. The ADAS codes and database provide the density and temperature dependence of the atomic data, and the collective nature of the state excitation process. To be able to populate 3D halo output with sufficient statistical resolution, the capability to control the statistics of fast ion CX modeling and for thermal halo launch has been added to NUBEAM. The 3D halo neutral model is based on modification and extension of the ``beam in box'' aligned 3d Cartesian grid that includes the neutral beam itself, 3D fast neutral densities due to CX of partially slowed down fast ions in the beam halo region, 3D thermal neutral densities due to CX deposition and fast neutral recapture source. More details on the 3D halo simulation design will be presented.
Optically rewritable 3D liquid crystal displays.
Sun, J; Srivastava, A K; Zhang, W; Wang, L; Chigrinov, V G; Kwok, H S
2014-11-01
Optically rewritable liquid crystal display (ORWLCD) is a concept based on the optically addressed bi-stable display that does not need any power to hold the image after being uploaded. Recently, the demand for the 3D image display has increased enormously. Several attempts have been made to achieve 3D image on the ORWLCD, but all of them involve high complexity for image processing on both hardware and software levels. In this Letter, we disclose a concept for the 3D-ORWLCD by dividing the given image in three parts with different optic axis. A quarter-wave plate is placed on the top of the ORWLCD to modify the emerging light from different domains of the image in different manner. Thereafter, Polaroid glasses can be used to visualize the 3D image. The 3D image can be refreshed, on the 3D-ORWLCD, in one-step with proper ORWLCD printer and image processing, and therefore, with easy image refreshing and good image quality, such displays can be applied for many applications viz. 3D bi-stable display, security elements, etc.
Three-dimensional modeling and analysis of a high energy density Kelvin-Helmholtz experiment
Raman, K. S.; Hurricane, O. A.; Park, H.-S.; Remington, B. A.; Robey, H.; Smalyuk, V. A.; Drake, R. P.; Krauland, C. M.; Kuranz, C. C.; Hansen, J. F.; Harding, E. C.
2012-09-15
A recent series of experiments on the OMEGA laser provided the first controlled demonstration of the Kelvin-Helmholtz (KH) instability in a high-energy-density physics context [E. C. Harding et al., Phys. Rev. Lett. 103, 045005, (2009); O. A. Hurricane et al., Phys. Plasmas 16, 056305, (2009)]. We present 3D simulations which resolve previously reported discrepancies between those experiments and the 2D simulation used to design them. Our new simulations reveal a three-dimensional mechanism behind the low density 'bubble' structures which appeared in the experimental x-ray radiographs at late times but were completely absent in the 2D simulations. We also demonstrate that the three-dimensional expansion of the walls of the target is sufficient to explain the 20% overprediction by 2D simulation of the late-time growth of the KH rollups. The implications of these results for the design of future experiments are discussed.
Nonlocal description of sound propagation through an array of Helmholtz resonators
NASA Astrophysics Data System (ADS)
Nemati, Navid; Kumar, Anshuman; Lafarge, Denis; Fang, Nicholas X.
2015-12-01
A generalized macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid has been recently proposed, which takes into account both temporal and spatial dispersion. Here, we consider applying this theory, which enables the description of resonance effects, to the case of sound propagation through an array of Helmholtz resonators whose unusual metamaterial properties, such as negative bulk moduli, have been experimentally demonstrated. Three different calculations are performed, validating the results of the nonlocal theory, related to the frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode, for 1D propagation in 2D or 3D periodic structures. xml:lang="fr"
3D packaging for integrated circuit systems
Chu, D.; Palmer, D.W.
1996-11-01
A goal was set for high density, high performance microelectronics pursued through a dense 3D packing of integrated circuits. A {open_quotes}tool set{close_quotes} of assembly processes have been developed that enable 3D system designs: 3D thermal analysis, silicon electrical through vias, IC thinning, mounting wells in silicon, adhesives for silicon stacking, pretesting of IC chips before commitment to stacks, and bond pad bumping. Validation of these process developments occurred through both Sandia prototypes and subsequent commercial examples.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, William L.; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2014-01-01
This manual describes the installation and execution of FUN3D version 12.5, including optional dependent packages. FUN3D is a suite of computational uid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables ecient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2014-01-01
This manual describes the installation and execution of FUN3D version 12.4, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixedelement unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
3D Immersive Visualization with Astrophysical Data
NASA Astrophysics Data System (ADS)
Kent, Brian R.
2017-01-01
We present the refinement of a new 3D immersion technique for astrophysical data visualization.Methodology to create 360 degree spherical panoramas is reviewed. The 3D software package Blender coupled with Python and the Google Spatial Media module are used together to create the final data products. Data can be viewed interactively with a mobile phone or tablet or in a web browser. The technique can apply to different kinds of astronomical data including 3D stellar and galaxy catalogs, images, and planetary maps.
A high capacity 3D steganography algorithm.
Chao, Min-Wen; Lin, Chao-hung; Yu, Cheng-Wei; Lee, Tong-Yee
2009-01-01
In this paper, we present a very high-capacity and low-distortion 3D steganography scheme. Our steganography approach is based on a novel multilayered embedding scheme to hide secret messages in the vertices of 3D polygon models. Experimental results show that the cover model distortion is very small as the number of hiding layers ranges from 7 to 13 layers. To the best of our knowledge, this novel approach can provide much higher hiding capacity than other state-of-the-art approaches, while obeying the low distortion and security basic requirements for steganography on 3D models.
2015-04-23
A new type of graphene aerogel will make for better energy storage, sensors, nanoelectronics, catalysis and separations. Lawrence Livermore National Laboratory researchers have made graphene aerogel microlattices with an engineered architecture via a 3D printing technique known as direct ink writing. The research appears in the April 22 edition of the journal, Nature Communications. The 3D printed graphene aerogels have high surface area, excellent electrical conductivity, are lightweight, have mechanical stiffness and exhibit supercompressibility (up to 90 percent compressive strain). In addition, the 3D printed graphene aerogel microlattices show an order of magnitude improvement over bulk graphene materials and much better mass transport.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, William L.; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2015-01-01
This manual describes the installation and execution of FUN3D version 12.6, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2016-01-01
This manual describes the installation and execution of FUN3D version 12.9, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2017-01-01
This manual describes the installation and execution of FUN3D version 13.1, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2015-01-01
This manual describes the installation and execution of FUN3D version 12.7, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bill; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2016-01-01
This manual describes the installation and execution of FUN3D version 13.0, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
NASA Technical Reports Server (NTRS)
Biedron, Robert T.; Carlson, Jan-Renee; Derlaga, Joseph M.; Gnoffo, Peter A.; Hammond, Dana P.; Jones, William T.; Kleb, Bil; Lee-Rausch, Elizabeth M.; Nielsen, Eric J.; Park, Michael A.; Rumsey, Christopher L.; Thomas, James L.; Wood, William A.
2015-01-01
This manual describes the installation and execution of FUN3D version 12.8, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
An Improved Version of TOPAZ 3D
Krasnykh, Anatoly
2003-07-29
An improved version of the TOPAZ 3D gun code is presented as a powerful tool for beam optics simulation. In contrast to the previous version of TOPAZ 3D, the geometry of the device under test is introduced into TOPAZ 3D directly from a CAD program, such as Solid Edge or AutoCAD. In order to have this new feature, an interface was developed, using the GiD software package as a meshing code. The article describes this method with two models to illustrate the results.
RHOCUBE: 3D density distributions modeling code
NASA Astrophysics Data System (ADS)
Nikutta, Robert; Agliozzo, Claudia
2016-11-01
RHOCUBE models 3D density distributions on a discrete Cartesian grid and their integrated 2D maps. It can be used for a range of applications, including modeling the electron number density in LBV shells and computing the emission measure. The RHOCUBE Python package provides several 3D density distributions, including a powerlaw shell, truncated Gaussian shell, constant-density torus, dual cones, and spiralling helical tubes, and can accept additional distributions. RHOCUBE provides convenient methods for shifts and rotations in 3D, and if necessary, an arbitrary number of density distributions can be combined into the same model cube and the integration ∫ dz performed through the joint density field.
Explicit 3-D Hydrodynamic FEM Program
2000-11-07
DYNA3D is a nonlinear explicit finite element code for analyzing 3-D structures and solid continuum. The code is vectorized and available on several computer platforms. The element library includes continuum, shell, beam, truss and spring/damper elements to allow maximum flexibility in modeling physical problems. Many materials are available to represent a wide range of material behavior, including elasticity, plasticity, composites, thermal effects and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, including frictional sliding, single surface contact and automatic contact generation.
3D-HIM: A 3D High-density Interleaved Memory for Bipolar RRAM Design
2013-05-01
JOURNAL ARTICLE (Post Print ) 3. DATES COVERED (From - To) DEC 2010 – NOV 2012 4. TITLE AND SUBTITLE 3D -HIM: A 3D HIGH-DENSITY INTERLEAVED MEMORY...emerged as one of the promising candidates for large data storage in computing systems. Moreover, building up RRAM in a three dimensional ( 3D ) stacking...brings in the potential reliability issue. To alleviate the situation, we introduce two novel 3D stacking structures built upon bipolar RRAM
MOM3D/EM-ANIMATE - MOM3D WITH ANIMATION CODE
NASA Technical Reports Server (NTRS)
Shaeffer, J. F.
1994-01-01
MOM3D (LAR-15074) is a FORTRAN method-of-moments electromagnetic analysis algorithm for open or closed 3-D perfectly conducting or resistive surfaces. Radar cross section with plane wave illumination is the prime analysis emphasis; however, provision is also included for local port excitation for computing antenna gain patterns and input impedances. The Electric Field Integral Equation form of Maxwell's equations is solved using local triangle couple basis and testing functions with a resultant system impedance matrix. The analysis emphasis is not only for routine RCS pattern predictions, but also for phenomenological diagnostics: bistatic imaging, currents, and near scattered/total electric fields. The images, currents, and near fields are output in form suitable for animation. MOM3D computes the full backscatter and bistatic radar cross section polarization scattering matrix (amplitude and phase), body currents and near scattered and total fields for plane wave illumination. MOM3D also incorporates a new bistatic k space imaging algorithm for computing down range and down/cross range diagnostic images using only one matrix inversion. MOM3D has been made memory and cpu time efficient by using symmetric matrices, symmetric geometry, and partitioned fixed and variable geometries suitable for design iteration studies. MOM3D may be run interactively or in batch mode on 486 IBM PCs and compatibles, UNIX workstations or larger computers. A 486 PC with 16 megabytes of memory has the potential to solve a 30 square wavelength (containing 3000 unknowns) symmetric configuration. Geometries are described using a triangular mesh input in the form of a list of spatial vertex points and a triangle join connection list. The EM-ANIMATE (LAR-15075) program is a specialized visualization program that displays and animates the near-field and surface-current solutions obtained from an electromagnetics program, in particular, that from MOM3D. The EM-ANIMATE program is windows based and
Do-It-Yourself: 3D Models of Hydrogenic Orbitals through 3D Printing
ERIC Educational Resources Information Center
Griffith, Kaitlyn M.; de Cataldo, Riccardo; Fogarty, Keir H.
2016-01-01
Introductory chemistry students often have difficulty visualizing the 3-dimensional shapes of the hydrogenic electron orbitals without the aid of physical 3D models. Unfortunately, commercially available models can be quite expensive. 3D printing offers a solution for producing models of hydrogenic orbitals. 3D printing technology is widely…
Optical 3D surface digitizing in forensic medicine: 3D documentation of skin and bone injuries.
Thali, Michael J; Braun, Marcel; Dirnhofer, Richard
2003-11-26
Photography process reduces a three-dimensional (3D) wound to a two-dimensional level. If there is a need for a high-resolution 3D dataset of an object, it needs to be three-dimensionally scanned. No-contact optical 3D digitizing surface scanners can be used as a powerful tool for wound and injury-causing instrument analysis in trauma cases. The 3D skin wound and a bone injury documentation using the optical scanner Advanced TOpometric Sensor (ATOS II, GOM International, Switzerland) will be demonstrated using two illustrative cases. Using this 3D optical digitizing method the wounds (the virtual 3D computer model of the skin and the bone injuries) and the virtual 3D model of the injury-causing tool are graphically documented in 3D in real-life size and shape and can be rotated in the CAD program on the computer screen. In addition, the virtual 3D models of the bone injuries and tool can now be compared in a 3D CAD program against one another in virtual space, to see if there are matching areas. Further steps in forensic medicine will be a full 3D surface documentation of the human body and all the forensic relevant injuries using optical 3D scanners.
XML3D and Xflow: combining declarative 3D for the Web with generic data flows.
Klein, Felix; Sons, Kristian; Rubinstein, Dmitri; Slusallek, Philipp
2013-01-01
Researchers have combined XML3D, which provides declarative, interactive 3D scene descriptions based on HTML5, with Xflow, a language for declarative, high-performance data processing. The result lets Web developers combine a 3D scene graph with data flows for dynamic meshes, animations, image processing, and postprocessing.
3D critical layers in fully-developed turbulent flows
NASA Astrophysics Data System (ADS)
Saxton-Fox, Theresa; McKeon, Beverley
2016-11-01
Recent work has shown that 3D critical layers drive self-sustaining behavior of exact coherent solutions of the Navier-Stokes equations (Wang et al. 2007; Hall and Sherwin 2010; Park and Graham 2015). This study investigates the role of 3D critical layers in fully-developed turbulent flows. 3D critical layer effects are identified in instantaneous snapshots of turbulent boundary layers in both experimental and DNS data (Wu et al. 2014). Additionally, a 3D critical layer effect is demonstrated to appear using only a few resolvent response modes from the resolvent analysis of McKeon and Sharma 2010, with phase relationships appropriately chosen. Connections are sought to the thin shear layers observed in turbulent boundary layers (Klewicki and Hirschi 2004; Eisma et al. 2015) and to amplitude modulation observations (Mathis et al. 2009; Duvvuri and McKeon 2014). This research is made possible by the Department of Defense through the National Defense & Engineering Graduate Fellowship (NDSEG) Program and by the Air Force Office of Scientific Research Grant # FA9550-12-1-0060. The support of the Center for Turbulence Research (CTR) summer program at Stanford is gratefully acknowledged.
Frozen Gaussian approximation for 3-D seismic wave propagation
NASA Astrophysics Data System (ADS)
Chai, Lihui; Tong, Ping; Yang, Xu
2017-01-01
We present a systematic introduction on applying frozen Gaussian approximation (FGA) to compute synthetic seismograms in 3-D earth models. In this method, seismic wavefield is decomposed into frozen (fixed-width) Gaussian functions, which propagate along ray paths. Rather than the coherent state solution to the wave equation, this method is rigorously derived by asymptotic expansion on phase plane, with analysis of its accuracy determined by the ratio of short wavelength over large domain size. Similar to other ray-based beam methods (e.g. Gaussian beam methods), one can use relatively small number of Gaussians to get accurate approximations of high-frequency wavefield. The algorithm is embarrassingly parallel, which can drastically speed up the computation with a multicore-processor computer station. We illustrate the accuracy and efficiency of the method by comparing it to the spectral element method for a 3-D seismic wave propagation in homogeneous media, where one has the analytical solution as a benchmark. As another proof of methodology, simulations of high-frequency seismic wave propagation in heterogeneous media are performed for 3-D waveguide model and smoothed Marmousi model, respectively. The second contribution of this paper is that, we incorporate the Snell's law into the FGA formulation, and asymptotically derive reflection, transmission and free surface conditions for FGA to compute high-frequency seismic wave propagation in high contrast media. We numerically test these conditions by computing traveltime kernels of different phases in the 3-D crust-over-mantle model.
Extremely accurate sequential verification of RELAP5-3D
Mesina, George L.; Aumiller, David L.; Buschman, Francis X.
2015-11-19
Large computer programs like RELAP5-3D solve complex systems of governing, closure and special process equations to model the underlying physics of nuclear power plants. Further, these programs incorporate many other features for physics, input, output, data management, user-interaction, and post-processing. For software quality assurance, the code must be verified and validated before being released to users. For RELAP5-3D, verification and validation are restricted to nuclear power plant applications. Verification means ensuring that the program is built right by checking that it meets its design specifications, comparing coding to algorithms and equations and comparing calculations against analytical solutions and method of manufactured solutions. Sequential verification performs these comparisons initially, but thereafter only compares code calculations between consecutive code versions to demonstrate that no unintended changes have been introduced. Recently, an automated, highly accurate sequential verification method has been developed for RELAP5-3D. The method also provides to test that no unintended consequences result from code development in the following code capabilities: repeating a timestep advancement, continuing a run from a restart file, multiple cases in a single code execution, and modes of coupled/uncoupled operation. In conclusion, mathematical analyses of the adequacy of the checks used in the comparisons are provided.
Extremely accurate sequential verification of RELAP5-3D
Mesina, George L.; Aumiller, David L.; Buschman, Francis X.
2015-11-19
Large computer programs like RELAP5-3D solve complex systems of governing, closure and special process equations to model the underlying physics of nuclear power plants. Further, these programs incorporate many other features for physics, input, output, data management, user-interaction, and post-processing. For software quality assurance, the code must be verified and validated before being released to users. For RELAP5-3D, verification and validation are restricted to nuclear power plant applications. Verification means ensuring that the program is built right by checking that it meets its design specifications, comparing coding to algorithms and equations and comparing calculations against analytical solutions and method ofmore » manufactured solutions. Sequential verification performs these comparisons initially, but thereafter only compares code calculations between consecutive code versions to demonstrate that no unintended changes have been introduced. Recently, an automated, highly accurate sequential verification method has been developed for RELAP5-3D. The method also provides to test that no unintended consequences result from code development in the following code capabilities: repeating a timestep advancement, continuing a run from a restart file, multiple cases in a single code execution, and modes of coupled/uncoupled operation. In conclusion, mathematical analyses of the adequacy of the checks used in the comparisons are provided.« less
Quantifying modes of 3D cell migration
Driscoll, Meghan K.; Danuser, Gaudenz
2015-01-01
Although it is widely appreciated that cells migrate in a variety of diverse environments in vivo, we are only now beginning to use experimental workflows that yield images with sufficient spatiotemporal resolution to study the molecular processes governing cell migration in 3D environments. Since cell migration is a dynamic process, it is usually studied via microscopy, but 3D movies of 3D processes are difficult to interpret by visual inspection. In this review, we discuss the technologies required to study the diversity of 3D cell migration modes with a focus on the visualization and computational analysis tools needed to study cell migration quantitatively at a level comparable to the analyses performed today on cells crawling on flat substrates. PMID:26603943
Modeling cellular processes in 3D.
Mogilner, Alex; Odde, David
2011-12-01
Recent advances in photonic imaging and fluorescent protein technology offer unprecedented views of molecular space-time dynamics in living cells. At the same time, advances in computing hardware and software enable modeling of ever more complex systems, from global climate to cell division. As modeling and experiment become more closely integrated we must address the issue of modeling cellular processes in 3D. Here, we highlight recent advances related to 3D modeling in cell biology. While some processes require full 3D analysis, we suggest that others are more naturally described in 2D or 1D. Keeping the dimensionality as low as possible reduces computational time and makes models more intuitively comprehensible; however, the ability to test full 3D models will build greater confidence in models generally and remains an important emerging area of cell biological modeling.
Cyclone Rusty's Landfall in 3-D
This 3-D image derived from NASA's TRMM satellite Precipitation Radar data on February 26, 2013 at 0654 UTC showed that the tops of some towering thunderstorms in Rusty's eye wall were reaching hei...
Tropical Cyclone Jack in Satellite 3-D
This 3-D flyby from NASA's TRMM satellite of Tropical Cyclone Jack on April 21 shows that some of the thunderstorms were shown by TRMM PR were still reaching height of at least 17 km (10.5 miles). ...
Future Engineers 3-D Print Timelapse
NASA Challenges K-12 students to create a model of a container for space using 3-D modeling software. Astronauts need containers of all kinds - from advanced containers that can study fruit flies t...
3-D Animation of Typhoon Bopha
This 3-D animation of NASA's TRMM satellite data showed Typhoon Bopha tracking over the Philippines on Dec. 3 and moving into the Sulu Sea on Dec. 4, 2012. TRMM saw heavy rain (red) was falling at ...
DNA biosensing with 3D printing technology.
Loo, Adeline Huiling; Chua, Chun Kiang; Pumera, Martin
2017-01-16
3D printing, an upcoming technology, has vast potential to transform conventional fabrication processes due to the numerous improvements it can offer to the current methods. To date, the employment of 3D printing technology has been examined for applications in the fields of engineering, manufacturing and biological sciences. In this study, we examined the potential of adopting 3D printing technology for a novel application, electrochemical DNA biosensing. Metal 3D printing was utilized to construct helical-shaped stainless steel electrodes which functioned as a transducing platform for the detection of DNA hybridization. The ability of electroactive methylene blue to intercalate into the double helix structure of double-stranded DNA was then exploited to monitor the DNA hybridization process, with its inherent reduction peak serving as an analytical signal. The designed biosensing approach was found to demonstrate superior selectivity against a non-complementary DNA target, with a detection range of 1-1000 nM.
Designing Biomaterials for 3D Printing.
Guvendiren, Murat; Molde, Joseph; Soares, Rosane M D; Kohn, Joachim
2016-10-10
Three-dimensional (3D) printing is becoming an increasingly common technique to fabricate scaffolds and devices for tissue engineering applications. This is due to the potential of 3D printing to provide patient-specific designs, high structural complexity, rapid on-demand fabrication at a low-cost. One of the major bottlenecks that limits the widespread acceptance of 3D printing in biomanufacturing is the lack of diversity in "biomaterial inks". Printability of a biomaterial is determined by the printing technique. Although a wide range of biomaterial inks including polymers, ceramics, hydrogels and composites have been developed, the field is still struggling with processing of these materials into self-supporting devices with tunable mechanics, degradation, and bioactivity. This review aims to highlight the past and recent advances in biomaterial ink development and design considerations moving forward. A brief overview of 3D printing technologies focusing on ink design parameters is also included.