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## Numerical Tests (numerical + test)
Terms modified by Numerical Tests
## Selected Abstracts## Traveltime computation with the linearized eikonal equation for anisotropic media GEOPHYSICAL PROSPECTING, Issue 4 2002Tariq AlkhalifahA linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter ,. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite-difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter , (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of , from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate , in areas where the traveltime field is independent of ,, such as areas where the wave propagates vertically. Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. [source] ## An accurate hybrid macro-element with linear displacements INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2005Xiao-Ping XieAbstract A hybrid stress quadrilateral macro-element HQM is proposed. Compatible linear displacements are used on its two triangular sub-domains, and a 5-parameter incomplete linear stress mode is suggested. Equivalence to another quadrilateral element HQ4 with compatible isoparametric bilinear displacements is proven. Due to elimination of stress parameters at the element level, the computational cost of HQM/HQ4 is as same as that of Q4. Numerical tests show that the element is accurate, insensitive to mesh distortions, and free from Poisson locking. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Parallel asynchronous variational integrators INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2007Kedar G. KaleAbstract This paper presents a scalable parallel variational time integration algorithm for nonlinear elastodynamics with the distinguishing feature of allowing each element in the mesh to have a possibly different time step. Furthermore, the algorithm is obtained from a discrete variational principle, and hence it is termed parallel asynchronous variational integrator (PAVI). The underlying variational structure grants it outstanding conservation properties. Based on a domain decomposition strategy, PAVI combines a careful scheduling of computations with fully asynchronous communications to provide a very efficient methodology for finite element models with even mild distributions of time step sizes. Numerical tests are shown to illustrate PAVI's performance on both slow and fast networks, showing scalability properties similar to the best parallel explicit synchronous algorithms, with lower execution time. Finally, a numerical example in which PAVI needs ,100 times less computing than an explicit synchronous algorithm is shown. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated plates INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2004Y. X. ZhangAbstract Two simple 4-node 20-DOF and 4-node 24-DOF displacement-based quadrilateral elements named RDKQ-L20 and RDKQ-L24 are developed in this paper based on the first-order shear deformation theory (FSDT) for linear analysis of thin to moderately thick laminates. The deflection and rotation functions of the element sides are obtained from Timoshenko's laminated composite beam functions. Linear displacement interpolation functions of the standard 4-node quadrilateral isoparametric plane element and displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as in-plane displacements of the proposed elements RDKQ-L20 and RDKQ-L24, respectively. Due to the application of Timoshenko's laminated composite beam functions, convergence can be ensured theoretically for very thin laminates. The elements are simple in formulation, and shear-locking free for extremely thin laminates even with full integration. A hybrid-enhanced procedure is employed to improve the accuracy of stress analysis, especially for transverse shear stresses. Numerical tests show that the new elements are convergent, not sensitive to mesh distortion, accurate and efficient for analysis of thin to moderately thick laminates. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## BILU implicit multiblock Euler/Navier,Stokes simulation for rotor tip vortex and wake convection INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2007Bowen ZhongAbstract In this paper, a block incomplete lower,upper (BILU) decomposition method is incorporated with a multiblock three-dimensional Euler/Navier,Stokes solver for simulation of hovering rotor tip vortices and rotor wake convection. Results of both Euler and Navier,Stokes simulations are obtained and compared with experimental observations. The comparisons include surface pressure distributions and tip vortex trajectories. The comparisons suggest that resolution of the boundary layer is important for the accurate evaluation of the blade surface loading, but is less so for the correct prediction of the vortex trajectory. Numerical tests show that, using Courant,Friedrichs,Lewy (CFL) number of 10 or 30 with the developed BILU implicit scheme can be 6,7 times faster than an explicit scheme. The importance of solution acceleration schemes that increase the permitted time-step is illustrated by comparing the evolving wake structures at different stages of the calculation. In contrast to fixed wing simulations, the extent of the wake structures is shown to require resolution of large physical time. This observation explains the poor performance that is obtained when employing convergence acceleration strategies originally intended for solution of equilibrium problems, such as the multigrid methods. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Numerical simulation of the miscible displacement of radionuclides in a heterogeneous porous medium INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005C.-H. BruneauAbstract The aim of this paper is to model and simulate the displacement of radioactive elements in a saturated heterogeneous porous medium. New schemes are proposed to solve accurately the convection,diffusion,reaction equations including nonlinear terms in the time derivative. Numerical tests show the stability and robustness of these schemes through strong heterogeneities of the medium. Finally the COUPLEX 1 benchmark concerning the far field simulation of a polluted flow by a leak of a nuclear waste disposal is performed and compared with the results available in the literature. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Parallel computation of a highly nonlinear Boussinesq equation model through domain decomposition INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Khairil Irfan SitanggangAbstract Implementations of the Boussinesq wave model to calculate free surface wave evolution in large basins are, in general, computationally very expensive, requiring huge amounts of CPU time and memory. For large scale problems, it is either not affordable or practical to run on a single PC. To facilitate such extensive computations, a parallel Boussinesq wave model is developed using the domain decomposition technique in conjunction with the message passing interface (MPI). The published and well-tested numerical scheme used by the serial model, a high-order finite difference method, is identical to that employed in the parallel model. Parallelization of the tridiagonal matrix systems included in the serial scheme is the most challenging aspect of the work, and is accomplished using a parallel matrix solver combined with an efficient data transfer scheme. Numerical tests on a distributed-memory super-computer show that the performance of the current parallel model in simulating wave evolution is very satisfactory. A linear speedup is gained as the number of processors increases. These tests showed that the CPU time efficiency of the model is about 75,90%. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## k,l based hybrid LES/RANS approach and its application to heat transfer simulation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2004Bowen ZhongAbstract To improve the compatibility of a k,l based hybrid LES/RANS approach, a controllable transitional zone is introduced to bridge the RANS and LES zones. This allows blending of the very different modelled turbulence length scales in these regions. To obtain a smooth variation of the length scales and transitional zone parameters different weighting functions are proposed. Results show the ,RANS' region has significant coherent unsteadiness. For Unsteady RANS (URANS) theoretical correctness, a favourable spectral gap between the modelled and resolved scales is required. The use of unsteadiness damping and time step filtering to ensure this is explored. Approaches are tested for a plane channel flow and the flow over a matrix of surface mounted cubes. The capability of the new hybrid LES/RANS method in improving heat transfer prediction in a conjugate heat transfer problem is examined. Numerical tests show that, compared to the RANS simulation, the proposed hybrid LES/RANS scheme performs well for the flow with large scale unsteadiness. It is also effective for improving the prediction of heat transfer. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## An implicit three-dimensional fully non-hydrostatic model for free-surface flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2004Hengliang YuanAbstract An implicit method is developed for solving the complete three-dimensional (3D) Navier,Stokes equations. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. A new top-layer pressure treatment and a partial cell bottom treatment are introduced so that the 3D model is fully non-hydrostatic and is free of any hydrostatic assumption. A domain decomposition method is used to segregate the resulting 3D matrix system into a series of two-dimensional vertical plane problems, for each of which a block tri-diagonal system can be directly solved for the unknown horizontal velocity. Numerical tests including linear standing waves, nonlinear sloshing motions, and progressive wave interactions with uneven bottoms are performed. It is found that the model is capable to simulate accurately a range of free-surface flow problems using a very small number of vertical layers (e.g. two,four layers). The developed model is second-order accuracy in time and space and is unconditionally stable; and it can be effectively used to model 3D surface wave motions. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Development of a convection,diffusion-reaction magnetohydrodynamic solver on non-staggered grids INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2004Tony W. H. SheuAbstract This paper presents a convection,diffusion-reaction (CDR) model for solving magnetic induction equations and incompressible Navier,Stokes equations. For purposes of increasing the prediction accuracy, the general solution to the one-dimensional constant-coefficient CDR equation is employed. For purposes of extending this discrete formulation to two-dimensional analysis, the alternating direction implicit solution algorithm is applied. Numerical tests that are amenable to analytic solutions were performed in order to validate the proposed scheme. Results show good agreement with the analytic solutions and high rate of convergence. Like many magnetohydrodynamic studies, the Hartmann,Poiseuille problem is considered as a benchmark test to validate the code. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2002R. TorrensAbstract The one-dimensional flow field generated by the passage of a shock wave in a rigid, thermoelastic porous foam has been simulated using a two-phase mathematical model. The work presented here makes use of the weighted average flux method to solve the system of six equations that govern the problem. Spurious oscillations are eliminated through the application of total variation diminishing limiting methods. Four different limiters were tested: van Leer, SuperA, MinA and van Albada. Numerical tests were carried out to verify the performance of each flux limiter in terms of accuracy. The results were compared to analytical and previously obtained data to assess the performance of the mathematical model. Excellent agreement was obtained. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Injection/suction boundary conditions for fluid,structure interaction simulations in incompressible flow INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2002G. MedicAbstract This paper presents the analysis of injection/suction boundary conditions in the context of the fluid,structure interactions simulation of the incompressible turbulent flow. First, the equations used in the modelling of the fluid and the structure are presented, as well as the numerical methods used in the corresponding solvers. Injection/suction boundary conditions are then presented with details of different implementation alternatives. Arbitrary Lagrangian,Eulerian (ALE) approach was also implemented in order to test the injection/suction boundary conditions. Numerical tests are performed where injection/suction boundary conditions are compared to ALE simulations. These tests include forced movement of the structure and two-degrees-of-freedom structure model simulations. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Towards a transparent boundary condition for compressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001C. H. BruneauAbstract A new artificial boundary condition for two-dimensional subsonic flows governed by the compressible Navier,Stokes equations is derived. It is based on the hyperbolic part of the equations, according to the way of propagation of the characteristic waves. A reference flow, as well as a convection velocity, is used to properly discretize the terms corresponding to the entering waves. Numerical tests on various classical model problems, whose solutions are known, and comparisons with other boundary conditions (BCs), show the efficiency of the BC. Direct numerical simulations of more complex flows over a dihedral plate are simulated, without creation of acoustic waves going back in the flow. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## A parallel hybrid local search algorithm for the container loading problem INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2004D. MackAbstract In this contribution, a parallel hybrid local search algorithm for the three-dimensional container loading problem (CLP) is proposed. First a simulated annealing method for the CLP is developed, which is then combined with an existing tabu search algorithm to form a hybrid metaheuristic. Finally, parallel versions are introduced for these algorithms. The emphasis is on CLP instances with a weakly heterogeneous load. Numerical tests based on the well-known 700 test instances from Bischoff and Ratcliff are performed, and the outcome is compared with methods from other authors. The results show a high solution quality obtained with reasonable computing time. [source] ## Scan profiles for neutron spectrometers. JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2003Newly developed reflecting neutron collimators promise increased detector count rates in a field where most work is intensity-limited. The effects of such elements on instrument resolution are complicated and appear to be even more subtle than previously imagined. Numerical tests using the McSTAS ray-tracing program (http://neutron.risoe.dk/mcstas) are reported which support and extend the recent analysis of these effects. If reflecting collimators are used in all instrument positions they give unusual scan profiles. Using reflecting collimators only before the monochromator and immediately before the detector has no deleterious resolution effects and increases count rates by a factor of more than two on powder diffractometers. [source] ## PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHOD MATHEMATICAL FINANCE, Issue 1 2010Jin E. ZhangThis paper studies the critical stock price of American options with continuous dividend yield. We solve the integral equation and derive a new analytical formula in a series form for the critical stock price. American options can be priced and hedged analytically with the help of our critical-stock-price formula. Numerical tests show that our formula gives very accurate prices. With the error well controlled, our formula is now ready for traders to use in pricing and hedging the S&P 100 index options and for the Chicago Board Options Exchange to use in computing the VXO volatility index. [source] ## Anisotropic curve shortening flow in higher codimension MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2007Paola PozziAbstract We consider the evolution of parametric curves by anisotropic mean curvature flow in ,n for an arbitrary n,2. After the introduction of a spatial discretization, we prove convergence estimates for the proposed finite-element model. Numerical tests and simulations based on a fully discrete semi-implicit stable algorithm are presented. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Appropriate SCF basis sets for orbital studies of galaxies and a ,quantum-mechanical' method to compute them MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2008Constantinos KalapotharakosABSTRACT We address the question of an appropriate choice of basis functions for the self-consistent field (SCF) method of simulation of the N -body problem. Our criterion is based on a comparison of the orbits found in N -body realizations of analytical potential,density models of triaxial galaxies, in which the potential is fitted by the SCF method using a variety of basis sets, with those of the original models. Our tests refer to maximally triaxial Dehnen ,-models for values of , in the range 0 ,,, 1, i.e. from the harmonic core up to the weak cusp limit. When an N -body realization of a model is fitted by the SCF method, the choice of radial basis functions affects significantly the way the potential, forces or derivatives of the forces are reproduced, especially in the central regions of the system. We find that this results in serious discrepancies in the relative amounts of chaotic versus regular orbits, or in the distributions of the Lyapunov characteristic exponents, as found by different basis sets. Numerical tests include the Clutton-Brock and the Hernquist,Ostriker basis sets, as well as a family of numerical basis sets which are ,close' to the Hernquist,Ostriker basis set (according to a given definition of distance in the space of basis functions). The family of numerical basis sets is parametrized in terms of a quantity , which appears in the kernel functions of the Sturm,Liouville equation defining each basis set. The Hernquist,Ostriker basis set is the ,= 0 member of the family. We demonstrate that grid solutions of the Sturm,Liouville equation yielding numerical basis sets introduce large errors in the variational equations of motion. We propose a quantum-mechanical method of solution of the Sturm,Liouville equation which overcomes these errors. We finally give criteria for a choice of optimal value of , and calculate the latter as a function of the value of ,, i.e. of the power-law exponent of the radial density profile at the central regions of the galaxy. [source] ## Resource allocation with lumpy demand: To speed or not to speed? NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2004Bintong ChenAbstract In the classical EPQ model with continuous and constant demand, holding and setup costs are minimized when the production rate is no larger than the demand rate. However, the situation may change when demand is lumpy. We consider a firm that produces multiple products, each having a unique lumpy demand pattern. The decision involves determining both the lot size for each product and the allocation of resources for production rate improvements among the products. We find that each product's optimal production policy will take on only one of two forms: either continuous production or lot-for-lot production. The problem is then formulated as a nonlinear nonsmooth knapsack problem among products determined to be candidates for resource allocation. A heuristic procedure is developed to determine allocation amounts. The procedure decomposes the problem into a mixed integer program and a nonlinear convex resource allocation problem. Numerical tests suggest that the heuristic performs very well on average compared to the optimal solution. Both the model and the heuristic procedure can be extended to allow the company to simultaneously alter both the production rates and the incoming demand lot sizes through quantity discounts. Extensions can also be made to address the case where a single investment increases the production rate of multiple products. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004. [source] ## Low frequency tangential filtering decomposition NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2007Y. AchdouAbstract For block-tridiagonal systems of linear equations arising from the discretization of partial differential equations, a composite preconditioner is proposed and tested. It combines a classical ILU0 factorization for high frequencies with a tangential filtering preconditioner. The choice of the filtering vector is important: the test-vector is the Ritz eigenvector corresponding to the approximate lowest eigenvalue, obtained after a limited number of iterations of a ILU0 preconditioned Krylov method. Numerical tests are carried out for this method. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equations NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006C. CalgaroAbstract In this article we consider the stationary Navier-Stokes system discretized by finite element methods which do not satisfy the inf-sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen-type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices ("generalized saddle point problems"). We show that if the underlying finite element spaces satisfy a generalized inf-sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1-P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier-Stokes flows confirm our results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] ## Coupling finite difference methods and integral formulas for elliptic problems arising in fluid mechanics NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2004C. AlbuquerqueAbstract This article is devoted to the numerical analysis of two classes of iterative methods that combine integral formulas with finite-difference Poisson solvers for the solution of elliptic problems. The first method is in the spirit of the Schwarz domain decomposition method for exterior domains. The second one is motivated by potential calculations in free boundary problems and can be viewed as a numerical analytic continuation algorithm. Numerical tests are presented that confirm the convergence properties predicted by numerical analysis. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 199,229, 2004 [source] ## The preservation of seismic anisotropy in the Earth's mantle during diffusion creep GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2009J. WheelerSUMMARY Seismic anisotropy in the Earth, particularly in the mantle, is commonly interpreted as the result of solid-state deformation by dislocation creep that induces a lattice preferred orientation (LPO). Diffusion creep operates where stress levels are lower and/or grain sizes smaller. It is often assumed that diffusion creep induces grain rotations that eventually destroy any existing LPO. A new numerical test of this assumption shows that it is not necessarily the case: diffusion creep will create some relative grain rotations, but rotation rates decrease through time. Hence, when microstructural change due to diffusion creep dominates that due to grain growth, defined here as ,type P' behaviour (the converse being ,type O' behaviour), the model indicates that LPO will be weakened but preserved (for a variety of strain paths including both pure and simple shear). One measure of anisotropy is the proportional difference in shear wave velocities for different polarization vectors (AVs). A model olivine microstructure with equant grains and initial maximum AVs of 10.0 percent has this value reduced to 6.7 per cent when ,rotational steady state' is attained. Other models with different initial maximum AVs values exhibit final maximum AVs values more than half the initial values. If the grains are initially elongate by a factor of 2, maximum AVs is reduced just slightly, to 8.5 per cent. Thus, when grain growth plays a subordinate role to the deformation, diffusion creep weakens seismic anisotropy by a factor of less than 2 (using maximum AVs as a measure and olivine as an example). Consequently, the link between seismic anisotropy and deformation mechanism in the mantle requires reappraisal: regions with LPO may comprise material which once deformed by dislocation creep, but is now deforming by diffusion creep in a rotational steady state. [source] ## Moduli stabilisation and applications in IIB string theory FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 3 2007J.P. ConlonString compactifications represent the most promising approach towards unifying general relativity with particle physics. However, naive compactifications give rise to massless particles (moduli) which would mediate unobserved long-range forces, and it is therefore necessary to generate a potential for the moduli. In the introductory chapters I review this problem and recall how in IIB compactifications the dilaton and complex structure moduli can be stabilised by 3-form fluxes. There exist very many possible discrete flux choices which motivates the use of statistical techniques to analyse this discretuum of choices. Such approaches generate formulae predicting the distribution of vacua and I describe numerical tests of these formulae on the Calabi-Yau ,4[1,1,2,2,6]. Stabilising the Kähler moduli requires nonperturbative superpotential effects. I review the KKLT construction and explain why this must in general be supplemented with perturbative Kähler corrections. I show how the incorporation of such corrections generically leads to non-supersymmetric minima at exponentially large volumes, giving a detailed account of the,, expansion and its relation to Kähler corrections. I illustrate this with explicit computations for the Calabi-Yau ,4[1,1,1,6,9]. The next part of the article examines phenomenological applications of this construction. I first describe how the magnitude of the soft supersymmetry parameters may be computed. In the large-volume models the gravitino mass and soft terms are volume-suppressed. As we naturally have ,, ,1, this gives a dynamical solution of the hierarchy problem. I also demonstrate the existence of a fine structure in the soft terms, with gaugino masses naturally lighter than the gravitino mass by a factor ln (MP/m3/2). A second section gives a detailed analysis of the relationship of moduli stabilisation to the QCD axions relevant to the strong CP problem, proving a no-go theorem on the compatibility of a QCD axion with supersymmetric moduli stabilisation. I describe how QCD axions can coexist with nonsupersymmetric perturbative stabilisation and how the large-volume models naturally contain axions with decay constants that are phenomenologically allowed and satisfy the appealing relationship fa2 ,MPMsusy. A further section describe how a simple and predictive inflationary model can be built in the context of the above large-volume construction, using the no-scale Kähler potential to avoid the , problem. I finally conclude, summarising the phenomenological scenario and outlining the prospects for future work. [source] ## A practical grid-based method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2006M. De KoolSUMMARY We present a practical grid-based method in 3-D spherical coordinates for computing multiple phases comprising any number of reflection and transmission branches in heterogeneous layered media. The new scheme is based on a multistage approach which treats each layer that the wave front enters as a separate computational domain. A finite-difference eikonal solver known as the fast-marching method (FMM) is reinitialized at each interface to track the evolving wave front as either a reflection back into the incident layer or a transmission through to the adjacent layer. Unlike the standard FMM, which only finds first arrivals, this multistage approach can track those later arriving phases explicitly caused by the presence of discontinuities. Notably, the method does not require an irregular mesh to be constructed in order to connect interface nodes to neighbouring velocity nodes which lie on a regular grid. To improve accuracy, local grid refinement is used in the neighbourhood of a source point where wave front curvature is high. The method also provides a way to trace reflections from an interface that are not the first arrival (e.g. the global PP phase). These are computed by initializing the multistage FMM from both the source and receiver, propagating the two wave fronts to the reflecting interface, and finding stationary points of the sum of the two traveltime fields on the reflecting interface. A series of examples are presented to test the efficiency, accuracy and robustness of the new scheme. As well as efficiently computing various global phases to an acceptable accuracy through the ak135 model, we also demonstrate the ability of the scheme to track complex crustal phases that may be encountered in coincident reflection, wide-angle reflection/refraction or local earthquake surveys. In one example, a variety of phases are computed in the presence of a realistic subduction zone, which includes several layer pinch-outs and a subducting slab. Our numerical tests show that the new scheme is a practical and robust alternative to conventional ray tracing for finding various phases in layered media at a variety of scales. [source] ## Comparison of waveform inversion, part 3: amplitude approach GEOPHYSICAL PROSPECTING, Issue 4 2007Sukjoon PyunABSTRACT In the second paper of this three part series, we studied the case of conventional and logarithmic phase-only approaches to full-waveform inversion. Here, we concentrate on deriving amplitude-only approaches for both conventional- and logarithmic-based methods. We define two amplitude-only objective functions by simply assuming that the phase of the modelled wavefield is equal to that of the observed wavefield. We do this for both the conventional least-squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse-time propagation algorithm of the full conventional methodology. Although the residuals in this case are not really residual wavefields, they can both be considered and utilized in that sense. In contrast to the case for our phase-only algorithms, we show through numerical tests that the conventional amplitude-only inversion is better than the logarithmic method. [source] ## Effective elastic properties of randomly fractured soils: 3D numerical experiments GEOPHYSICAL PROSPECTING, Issue 3 2004Erik H. SaengerABSTRACT This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so-called rotated staggered finite-difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non-intersecting thin penny-shaped dry cracks, the numerical simulations of P- and S-wave velocities are in good agreement with the predictions of the self-consistent approximation. We observe similar results for fluid-filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non-intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective-medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results. [source] ## Micromechanical modelling of monotonic drained and undrained shear behaviour of granular media using three-dimensional DEM INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2002Thallak.Abstract In this paper, numerical simulation results of isotropic compression and triaxial static shear tests under drained and undrained stress paths on polydisperse assembly of loose and dense spheres are presented. An examination of the micromechanical behaviour of loose and dense assemblies under drained and undrained conditions, considering the particulate nature of granular materials, has been carried out to explain micromechanically the granular material behaviour at the grain scale level. The numerical simulations have been carried out using a discrete element model (DEM) which considers a 1000 sphere particle polydisperse assembly with periodic space representing an infinite three-dimensional space. In this paper, we present how DEM simulations can contribute to developments in constitutive modelling of granular materials through micromechanical approach using information on microstructure evolution. A series of numerical tests are performed using DEM on 3-D assemblages of spheres to study the evolution of the internal variables such as average co-ordination number and induced anisotropy during deformation along with the macroscopic behaviour of the assemblage in drained and undrained shear tests. In a qualitative sense, the macroscopic stress,strain results and stress path evolution in these simulations using 3-D assemblies demonstrate that DEM simulations are capable of reproducing realistic compression and shear behaviour of granular materials. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Microstructural deformation mechanisms of unsaturated granular soils INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2002J. A. GiliAbstract A discrete model for unsaturated granular soils has been developed. Three discrete entities have been defined: particles, water menisci and pores. Local interaction forces and water transfer mechanisms have been integrated into a model through the appropriate equilibrium and balance equations. The results of several numerical tests using this model have been described and discussed. Simulations include wetting and drying under load tests, the application of suction cycles and the effect of a deviatoric stress ratio on wetting-induced collapse. The model reacts just as true granular soil samples behave in laboratory tests. The model provides a new insight into the internal mechanisms leading to large-scale features of behaviour such as wetting-induced collapse or the increase in soil strength provided by suction. The paper also stresses that matric suction changes acting on a granular structure are capable of explaining most of the macroscopic features of stress,strain behaviour. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## A stabilized smoothed finite element method for free vibration analysis of Mindlin,Reissner plates INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2009H. Nguyen-XuanAbstract A free vibration analysis of Mindlin,Reissner plates using the stabilized smoothed finite element method is studied. The bending strains of the MITC4 and STAB elements are incorporated with a cell-wise smoothing operation to give new proposed elements, the mixed interpolation and smoothed curvatures (MISCk) and SMISCk elements. The corresponding bending stiffness matrix is computed along the boundaries of the smoothing elements (smoothing cells). Note that shearing strains and the shearing stiffness matrix of the proposed elements are unchanged from the original elements, the MITC4 and STAB elements. It is confirmed by numerical tests that the present method is free of shear locking and has the marginal improvements compared with the original elements. Copyright © 2008 John Wiley & Sons, Ltd. [source] |