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Sample records for anisotropic hexahedra finite

  1. EEG source analysis of epileptiform activity using a 1mm anisotropic hexahedra finite element head model

    PubMed Central

    Rullmann, M.; Anwander, A.; Dannhauer, M.; Warfield, S.K.; Duffy, F.H.; Wolters, C.H.

    2009-01-01

    The major goal of the evaluation in presurgical epilepsy diagnosis for medically intractable patients is the precise reconstruction of the epileptogenic foci, preferably with non-invasive methods. This paper evaluates whether surface electroencephalography (EEG) source analysis based on a 1mm anisotropic finite element (FE) head model can provide additional guidance for presurgical epilepsy diagnosis and whether it is practically feasible in daily routine. A 1mm hexahedra FE volume conductor model of the patient’s head with special focus on accurately modeling the compartments skull, cerebrospinal fluid (CSF) and the anisotropic conducting brain tissues was constructed using non-linearly co-registered T1-, T2- and diffusion-tensor- magnetic resonance imaging data. The electrodes of intra-cranial EEG (iEEG) measurements were extracted from a co-registered computed tomography image. Goal function scan (GFS), minimum norm least squares (MNLS), standardized low resolution electromagnetic tomography (sLORETA) and spatio-temporal current dipole modeling inverse methods were then applied to the peak of the averaged ictal discharges EEG data. MNLS and sLORETA pointed to a single center of activity. Moving and rotating single dipole fits resulted in an explained variance of more than 97%. The non-invasive EEG source analysis methods localized at the border of the lesion and at the border of the iEEG electrodes which mainly received ictal discharges. Source orientation was towards the epileptogenic tissue. For the reconstructed superficial source, brain conductivity anisotropy and the lesion conductivity had only a minor influence, whereas a correct modeling of the highly conducting CSF compartment and the anisotropic skull was found to be important. The proposed FE forward modeling approach strongly simplifies meshing and reduces run-time (37 Milliseconds for one forward computation in the model with 3.1 Million unknowns), corroborating the practical feasibility of the

  2. Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra

    SciTech Connect

    Wheeler, M. F.; Xue, G.; Yotov, I.

    2012-01-01

    The authors formulated in a multipoint flux mixed finite element method that reduces to a cell-centered pressure system on general quadrilaterals and hexahedra for elliptic equations arising in subsurface flow problems. In addition they showed that a special quadrature rule yields O(h) convergence for face fluxes on distorted hexahedra. Here a first order local velocity postprocessing procedure using these face fluxes is developed and analyzed. The algorithm involves solving a 3 × 3 system on each element and utilizes an enhanced mixed finite element space introduced by Falk, Gatto, and Monk. Computational results verifying the theory are demonstrated.

  3. Finite-volume scheme for anisotropic diffusion

    SciTech Connect

    Es, Bram van; Koren, Barry; Blank, Hugo J. de

    2016-02-01

    In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

  4. Evaluation of a hybrid, anisotropic, multilayered, quadrilateral finite element

    NASA Technical Reports Server (NTRS)

    Robinson, J. C.; Blackburn, C. L.

    1978-01-01

    A multilayered finite element with bending-extensional coupling is evaluated for: (1) buckling of general laminated plates; (2) thermal stresses of laminated plates cured at elevated temperatures; (3) displacements of a bimetallic beam; and (4) displacement and stresses of a single-cell box beam with warped cover panels. Also, displacements and stresses for flat and spherical orthotropic and anisotropic segments are compared with results from higher order plate and shell finite-element analyses.

  5. Finite-difference schemes for anisotropic diffusion

    SciTech Connect

    Es, Bram van; Koren, Barry; Blank, Hugo J. de

    2014-09-01

    In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.

  6. High-order optimal edge elements for pyramids, prisms and hexahedra

    NASA Astrophysics Data System (ADS)

    Bergot, Morgane; Duruflé, Marc

    2013-01-01

    Edge elements are a popular method to solve Maxwell's equations especially in time-harmonic domain. However, when non-affine elements are considered, elements of the Nédélec's first family [19] are not providing an optimal rate of the convergence of the numerical solution toward the solution of the exact problem in H(curl)-norm. We propose new finite element spaces for pyramids, prisms, and hexahedra in order to recover the optimal convergence. In the particular case of pyramids, a comparison with other existing elements found in the literature is performed. Numerical results show the good behavior of these new finite elements.

  7. A hybrid-stress finite element for linear anisotropic elasticity

    NASA Technical Reports Server (NTRS)

    Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.

    1988-01-01

    Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.

  8. Anisotropic adaptive finite element method for modelling blood flow.

    PubMed

    Müller, J; Sahni, O; Li, X; Jansen, K E; Shephard, M S; Taylor, C A

    2005-10-01

    In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.

  9. Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements

    PubMed Central

    Cuccuru, Gianmauro; Fotia, Giorgio; Maggio, Fabio; Southern, James

    2015-01-01

    We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model. PMID:26583112

  10. Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements.

    PubMed

    Cuccuru, Gianmauro; Fotia, Giorgio; Maggio, Fabio; Southern, James

    2015-01-01

    We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.

  11. Finite-element modeling of layered, anisotropic composite plates and shells: A review of recent research

    NASA Technical Reports Server (NTRS)

    Reddy, J. N.

    1981-01-01

    Finite element papers published in the open literature on the static bending and free vibration of layered, anisotropic, and composite plates and shells are reviewed. A literature review of large-deflection bending and large-amplitude free oscillations of layered composite plates and shells is also presented. Non-finite element literature is cited for continuity of the discussion.

  12. Finite-element modeling of layered, anisotropic composite plates and shells: A review of recent research

    NASA Technical Reports Server (NTRS)

    Reddy, J. N.

    1981-01-01

    Finite element papers published in the open literature on the static bending and free vibration of layered, anisotropic, and composite plates and shells are reviewed. A literature review of large-deflection bending and large-amplitude free oscillations of layered composite plates and shells is also presented. Non-finite element literature is cited for continuity of the discussion.

  13. A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

    NASA Technical Reports Server (NTRS)

    Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.

    1987-01-01

    A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

  14. Modeling anisotropic flow and heat transport by using mimetic finite differences

    NASA Astrophysics Data System (ADS)

    Chen, Tao; Clauser, Christoph; Marquart, Gabriele; Willbrand, Karen; Büsing, Henrik

    2016-08-01

    Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.

  15. Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera

    PubMed Central

    Zheng, Wanqiu; Zou, Beiji

    2017-01-01

    Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies. PMID:28271067

  16. Dynamic finite element implementation of nonlinear, anisotropic hyperelastic biological membranes.

    PubMed

    Einstein, D R; Reinhall, P; Nicosia, M; Cochran, R P; Kunzelman, K

    2003-02-01

    We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function.

  17. Finite-Temperature Entanglement Dynamics in an Anisotropic Two-Qubit Heisenberg Spin Chain

    NASA Astrophysics Data System (ADS)

    Chen, Tao; Shan, Chuanjia; Li, Jinxing; Liu, Tangkun; Huang, Yanxia; Li, Hong

    2010-07-01

    This paper investigates the entanglement dynamics of an anisotropic two-qubit Heisenberg spin chain in the presence of decoherence at finite temperature. The time evolution of the concurrence is studied for different initial Werner states. The influences of initial purity, finite temperature, spontaneous decay and Hamiltonian on the entanglement evolution are analyzed in detail. Our calculations show that the finite temperature restricts the evolution of the entanglement all the time when the Hamiltonian improves it and the spontaneous decay to the reservoirs can produce quantum entanglement with the anisotropy of spin-spin interaction. Finally, the steady-state concurrence which may remain non-zero for low temperature is also given.

  18. Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.

    PubMed

    Oskooi, Ardavan F; Kottke, Chris; Johnson, Steven G

    2009-09-15

    Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.

  19. Modeling Optical Properties of Mineral Aerosol Particles by Using Nonsymmetric Hexahedra

    NASA Technical Reports Server (NTRS)

    Bi, Lei; Yang, Ping; Kattawar, George W.; Kahn, Ralph

    2010-01-01

    We explore the use of nonsymmetric geometries to simulate the single-scattering properties of airborne dust particles with complicated morphologies. Specifically, the shapes of irregular dust particles are assumed to be nonsymmetric hexahedra defined by using the Monte Carlo method. A combination of the discrete dipole approximation method and an improved geometric optics method is employed to compute the single-scattering properties of dust particles for size parameters ranging from 0.5 to 3000. The primary optical effect of eliminating the geometric symmetry of regular hexahedra is to smooth the scattering features in the phase function and to decrease the backscatter. The optical properties of the nonsymmetric hexahedra are used to mimic the laboratory measurements. It is demonstrated that a relatively close agreement can be achieved by using only one shape of nonsymmetric hexahedra. The agreement between the theoretical results and their measurement counterparts can be further improved by using a mixture of nonsymmetric hexahedra. It is also shown that the hexahedron model is much more appropriate than the "equivalent sphere" model for simulating the optical properties of dust particles, particularly, in the case of the elements of the phase matrix that associated with the polarization state of scattered light.

  20. Modeling Optical Properties of Mineral Aerosol Particles by Using Nonsymmetric Hexahedra

    NASA Technical Reports Server (NTRS)

    Bi, Lei; Yang, Ping; Kattawar, George W.; Kahn, Ralph

    2010-01-01

    We explore the use of nonsymmetric geometries to simulate the single-scattering properties of airborne dust particles with complicated morphologies. Specifically, the shapes of irregular dust particles are assumed to be nonsymmetric hexahedra defined by using the Monte Carlo method. A combination of the discrete dipole approximation method and an improved geometric optics method is employed to compute the single-scattering properties of dust particles for size parameters ranging from 0.5 to 3000. The primary optical effect of eliminating the geometric symmetry of regular hexahedra is to smooth the scattering features in the phase function and to decrease the backscatter. The optical properties of the nonsymmetric hexahedra are used to mimic the laboratory measurements. It is demonstrated that a relatively close agreement can be achieved by using only one shape of nonsymmetric hexahedra. The agreement between the theoretical results and their measurement counterparts can be further improved by using a mixture of nonsymmetric hexahedra. It is also shown that the hexahedron model is much more appropriate than the "equivalent sphere" model for simulating the optical properties of dust particles, particularly, in the case of the elements of the phase matrix that associated with the polarization state of scattered light.

  1. Finite Element Analysis of Ultrasonic Phased Array Inspections on Anisotropic Welds

    NASA Astrophysics Data System (ADS)

    Harvey, G.; Tweedie, A.; Carpentier, C.; Reynolds, P.

    2011-06-01

    This paper describes a theoretical investigation into the behaviour of anisotropic welds under phased array inspection procedures using a 128 element linear array. Two advanced inspection techniques are simulated, and their suitability compared. A finite element (FE) model, configured in PZFlex, is used to represent both the variations in crystal orientation found in a typical anisotropic weld, and also the linear array configuration. Firstly, through transmission spectra of the weld are used to determine the optimum operating frequency and configuration of the array in order to detect a 3 mm SDH in the weld. Next, the Full Matrix Capture (FMC) technique is simulated, and an image of the weld constructed using the Total Focussing Method (TFM). This is accomplished by transmitting on each element sequentially, while receiving on the remaining 127 elements. This approach provides spatial averaging over the weld area, reducing the distortion caused by the anisotropic media. Finally, Time Reversal Acoustic (TRA) methods were employed to coherently focus the array at the defect and compensate for the elemental timing variations caused by the complex medium. Results illustrate the potential for inspecting anisotropic welds when using correctly designed arrays and implementing novel inspection procedures.

  2. An inverse finite element method for determining the anisotropic properties of the cornea.

    PubMed

    Nguyen, T D; Boyce, B L

    2011-06-01

    An inverse finite element method was developed to determine the anisotropic properties of bovine cornea from an in vitro inflation experiment. The experiment used digital image correlation (DIC) to measure the three-dimensional surface geometry and displacement field of the cornea at multiple pressures. A finite element model of a bovine cornea was developed using the DIC measured surface geometry of the undeformed specimen. The model was applied to determine five parameters of an anisotropic hyperelastic model that minimized the error between the measured and computed surface displacement field and to investigate the sensitivity of the measured bovine inflation response to variations in the anisotropic properties of the cornea. The results of the parameter optimization revealed that the collagen structure of bovine cornea exhibited a high degree of anisotropy in the limbus region, which agreed with recent histological findings, and a transversely isotropic central region. The parameter study showed that the bovine corneal response to the inflation experiment was sensitive to the shear modulus of the matrix at pressures below the intraocular pressure, the properties of the collagen lamella at higher pressures, and the degree of anisotropy in the limbus region. It was not sensitive to a weak collagen anisotropy in the central region.

  3. A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

    NASA Astrophysics Data System (ADS)

    Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

    2015-12-01

    Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties

  4. Development of the Finite Difference Time Domain Method on a Lebedev Grid for Anisotropic Materials

    NASA Astrophysics Data System (ADS)

    Nauta, Marcel D.

    The finite-difference time-domain (FDTD) method is derived on a Lebedev grid, instead of the standard Yee grid, to better represent the constitutive relations in anisotropic materials. The Lebedev grid extends the Yee grid by approximating Maxwell's equations with tensor constitutive relations using only central differences. A dispersion relation with stability criteria is derived and it is proven that the Lebedev grid has a consistent calculus. An integral derivation of the update equations illustrates how to appropriately excite the grid. This approach is also used to derive the update equations at planar material interfaces and domain edge PEC. Lebedev grid results are compared with analytical and Yee grid solutions using an equal memory comparison. Numerical results show that the Lebedev grid suffers greater dispersion error but better represents material interfaces. Focus is given to generalizing the concepts that make the Yee grid robust for isotropic materials. Keywords: FDTD, anisotropic materials, Lebedev grid, collocated grids.

  5. A parametric finite element method for solid-state dewetting problems with anisotropic surface energies

    NASA Astrophysics Data System (ADS)

    Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan

    2017-02-01

    We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the sharp-interface models belong to a new type of high-order (4th- or 6th-order) geometric evolution partial differential equations about open curve/surface interface tracking problems which include anisotropic surface diffusion flow and contact line migration. Compared to the traditional methods (e.g., marker-particle methods), the proposed PFEM not only has very good accuracy, but also poses very mild restrictions on the numerical stability, and thus it has significant advantages for solving this type of open curve evolution problems with applications in the simulation of solid-state dewetting. Extensive numerical results are reported to demonstrate the accuracy and high efficiency of the proposed PFEM.

  6. A study of symmetry restoration at finite temperature in the O(4) model using anisotropic lattices

    NASA Astrophysics Data System (ADS)

    Gavai, R. V.; Heller, U. M.; Karsch, F.; Plache, B.; Neuhaus, T.

    Results of investigations of the O(4) spin model at finite temperature using anisotropic lattices are presented. In both the large N approximation and the numerical simulations using the Wolff cluster algorithm we find that the ratio of the symmetry restoration temperature TSR to the Higgs mass mH is independent of the anisotropy. We obtain a lower bound of 0.59 ± 0.04 for the ratio, T SR/m H, at m H ⋍ 0.5 , which is lowered furhter by about 10% at m Ha ⋍ 1 .

  7. Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM).

    PubMed

    Feerick, Emer M; Liu, Xiangyi Cheryl; McGarry, Patrick

    2013-04-01

    Anisotropic damage initiation criteria were developed for extended finite element method (XFEM) prediction of crack initiation and propagation in cortical bone. This anisotropic damage model was shown to accurately predict the dependence of crack propagation patterns and fracture toughness on mode mixity and on osteon orientations, as observed experimentally. Four initiation criteria were developed to define crack trajectories relative to osteon orientations and max principal stress for single and mixed mode fracture. Alternate failure strengths for tensile and compressive loading were defined to simulate the asymmetric failure of cortical bone. The dependence of cortical bone elasticity and failure properties on osteon orientation is analogous to the dependence of composite properties on fibre orientation. Hence, three of the criteria developed in the present study were based upon the Hashin damage criteria. The fourth criterion developed was defined in terms of the max principal stress. This criterion initiated off axis crack growth perpendicular to the direction of the max principal stress. The unique set of parameters calibrated accurately predicted; (i) the relationship between fracture energy and osteon alignment, (ii) the alternate crack patterns for both varying osteon orientations and loading angle. Application of the developed anisotropic damage models to cortical bone screw pullout highlights the potential application for orthopaedic device design evaluation.

  8. Anisotropic Resistivity Forward Modelling Using Automatic Generated Higher-order Finite Element Codes

    NASA Astrophysics Data System (ADS)

    Wang, W.; Liu, J.

    2016-12-01

    Forward modelling is the general way to obtain responses of geoelectrical structures. Field investigators might find it useful for planning surveys and choosing optimal electrode configurations with respect to their targets. During the past few decades much effort has been put into the development of numerical forward codes, such as integral equation method, finite difference method and finite element method. Nowadays, most researchers prefer the finite element method (FEM) for its flexible meshing scheme, which can handle models with complex geometry. Resistivity Modelling with commercial sofewares such as ANSYS and COMSOL is convenient, but like working with a black box. Modifying the existed codes or developing new codes is somehow a long period. We present a new way to obtain resistivity forward modelling codes quickly, which is based on the commercial sofeware FEPG (Finite element Program Generator). Just with several demanding scripts, FEPG could generate FORTRAN program framework which can easily be altered to adjust our targets. By supposing the electric potential is quadratic in each element of a two-layer model, we obtain quite accurate results with errors less than 1%, while more than 5% errors could appear by linear FE codes. The anisotropic half-space model is supposed to concern vertical distributed fractures. The measured apparent resistivities along the fractures are bigger than results from its orthogonal direction, which are opposite of the true resistivities. Interpretation could be misunderstood if this anisotropic paradox is ignored. The technique we used can obtain scientific codes in a short time. The generated powerful FORTRAN codes could reach accurate results by higher-order assumption and can handle anisotropy to make better interpretations. The method we used could be expand easily to other domain where FE codes are needed.

  9. Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

    NASA Technical Reports Server (NTRS)

    Dame, L. T.; Stouffer, D. C.

    1986-01-01

    A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

  10. Finite deformation analysis of continuum structures with time dependent anisotropic elastic plastic material behavior (LWBR/AWBA Development Program)

    SciTech Connect

    Hutula, D.N.

    1980-03-01

    A finite element procedure is presented for finite deformation analysis of continuum structures with time-dependent anisotropic elastic-plastic material behavior. An updated Lagrangian formulation is used to describe the kinematics of deformation. Anisotropic constitutive relations are referred, at each material point, to a set of three mutually orthogonal axes which rotate as a unit with an angular velocity equal to the spin at the point. The time-history of the solution is generated by using a linear incremental procedure with residual force correction, along with an automatic time step control algorithm which chooses time step sizes to control the accuracy and numerical stability of the solution.

  11. Bending and stretching finite element analysis of anisotropic viscoelastic composite plates

    NASA Technical Reports Server (NTRS)

    Hilton, Harry H.; Yi, Sung

    1990-01-01

    Finite element algorithms have been developed to analyze linear anisotropic viscoelastic plates, with or without holes, subjected to mechanical (bending, tension), temperature, and hygrothermal loadings. The analysis is based on Laplace transforms rather than direct time integrations in order to improve the accuracy of the results and save on extensive computational time and storage. The time dependent displacement fields in the transverse direction for the cross ply and angle ply laminates are calculated and the stacking sequence effects of the laminates are discussed in detail. Creep responses for the plates with or without a circular hole are also studied. The numerical results compare favorably with analytical solutions, i.e. within 1.8 percent for bending and 10(exp -3) 3 percent for tension. The tension results of the present method are compared with those using the direct time integration scheme.

  12. Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

    SciTech Connect

    Maliassov, S.Y.

    1996-12-31

    An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

  13. Anisotropic Turbulent Advection of a Passive Vector Field: Effects of the Finite Correlation Time

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Gulitskiy, N. M.

    2016-02-01

    The turbulent passive advection under the environment (velocity) field with finite correlation time is studied. Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is investigated by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and prescribed pair correlation function. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to nontrivial fixed points of the RG equations and depend on the relation between the exponents in the energy energy spectrum ɛ ∝ k⊥1-ξ and the dispersion law ω ∝ k⊥2-η . The corresponding anomalous exponents are associated with the critical dimensions of tensor composite operators built solely of the passive vector field itself. In contrast to the well-known isotropic Kraichnan model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of power-like corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L. Due to the presence of the anisotropy in the model, all multiloop diagrams are equal to zero, thus this result is exact.

  14. The discrete maximum principle for finite element approximations of anisotropic diffusion problems on arbitrary meshes

    SciTech Connect

    Svyatskiy, Daniil; Shashkov, Mikhail; Kuzmin, D

    2008-01-01

    A new approach to the design of constrained finite element approximations to second-order elliptic problems is introduced. This approach guarantees that the finite element solution satisfies the discrete maximum principle (DMP). To enforce these monotonicity constrains the sufficient conditions for elements of the stiffness matrix are formulated. An algebraic splitting of the stiffness matrix is employed to separate the contributions of diffusive and antidiffusive numerical fluxes, respectively. In order to prevent the formation of spurious undershoots and overshoots, a symmetric slope limiter is designed for the antidiffusive part. The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes. The recovery of nodal gradients is performed by means of a lumped-mass L{sub 2} projection. The proposed slope limiting strategy preserves the consistency of the underlying discrete problem and the structure of the stiffness matrix (symmetry, zero row and column sums). A positivity-preserving defect correction scheme is devised for the nonlinear algebraic system to be solved. Numerical results and a grid convergence study are presented for a number of anisotropic diffusion problems in two space dimensions.

  15. A computer program for anisotropic shallow-shell finite elements using symbolic integration

    NASA Technical Reports Server (NTRS)

    Andersen, C. M.; Bowen, J. T.

    1976-01-01

    A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

  16. Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling

    NASA Astrophysics Data System (ADS)

    Alastrué, V.; Martínez, M. A.; Doblaré, M.; Menzel, A.

    2009-01-01

    A fully three-dimensional anisotropic elastic model for vascular tissue modelling is presented here. The underlying strain energy density function is assumed to additively decouple into volumetric and deviatoric contributions. A straightforward isotropic neo-Hooke-type law is used to model the deviatoric response of the ground substance, whereas a micro-structurally or rather micro-sphere-based approach will be employed to model the contribution and distribution of fibres within the biological tissue of interest. Anisotropy was introduced by means of the use of von Mises orientation distribution functions. Two different micro-mechanical approaches—a, say phenomenological, exponential ansatz, and a worm-like-chain-based formulation—are applied to the micro-fibres and illustratively compared. The passage from micro-structural contributions to the macroscopic response is obtained by a computational homogenisation scheme, namely numerical integration over the surface of the individual micro-spheres. The algorithmic treatment of this integration is discussed in detail for the anisotropic problem at hand, so that several cubatures of the micro-sphere are tested in order to optimise the accuracy at reasonable computational cost. Moreover, the introduced material parameters are identified from simple tension tests on human coronary arterial tissue for the two micro-mechanical models investigated. Both approaches are able to recapture the experimental data. Based on the identified sets of parameters, we first discuss a homogeneous deformation in simple shear to evaluate the models' response at the micro-structural level. Later on, an artery-like two-layered tube subjected to internal pressure is simulated by making use of a non-linear finite element setting. This enables to obtain the micro- and macroscopic responses in an inhomogeneous deformation problem, namely a blood vessel representative boundary value problem. The effect of residual stresses is additionally

  17. Finite-size effects for anisotropic 2D Ising model with various boundary conditions

    NASA Astrophysics Data System (ADS)

    Izmailian, N. Sh

    2012-12-01

    We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

  18. A novel finite element model of the ovine lumbar intervertebral disc with anisotropic hyperelastic material properties

    PubMed Central

    Galbusera, Fabio; Jonas, René; Schlager, Benedikt; Wilke, Hans-Joachim; Villa, Tomaso

    2017-01-01

    The Ovine spine is an accepted model to investigate the biomechanical behaviour of the human lumbar one. Indeed, the use of animal models for in vitro studies is necessary to investigate the mechanical behaviour of biological tissue, but needs to be reduced for ethical and social reasons. The aim of this study was to create a finite element model of the lumbar intervertebral disc of the sheep that may help to refine the understanding of parallel in vitro experiments and that can be used to predict when mechanical failure occurs. Anisotropic hyperelastic material properties were assigned to the annulus fibrosus and factorial optimization analyses were performed to find out the optimal parameters of the ground substance and of the collagen fibers. For the ground substance of the annulus fibrosus the investigation was based on experimental data taken from the literature, while for the collagen fibers tensile tests on annulus specimens were conducted. Flexibility analysis in flexion-extension, lateral bending and axial rotation were conducted. Different material properties for the anterior, lateral and posterior regions of the annulus were found. The posterior part resulted the stiffest region in compression whereas the anterior one the stiffest region in tension. Since the flexibility outcomes were in a good agreement with the literature data, we considered this model suitable to be used in conjunction with in vitro and in vivo tests to investigate the mechanical behaviour of the ovine lumbar disc. PMID:28472100

  19. Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem

    NASA Astrophysics Data System (ADS)

    Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.

    2017-02-01

    We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.

  20. 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.

  1. Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

    DOE PAGES

    Petersson, N. Anders; Sjogreen, Bjorn

    2015-07-20

    We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

  2. Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

    SciTech Connect

    Petersson, N. Anders; Sjogreen, Bjorn

    2015-07-20

    We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.

  3. Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

    DOE PAGES

    Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...

    2015-04-14

    It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

  4. Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

    SciTech Connect

    Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin

    2015-04-14

    It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

  5. Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

    SciTech Connect

    Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin

    2015-08-15

    It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

  6. Anisotropic poroelasticity and wave-induced fluid flow: harmonic finite-element simulations

    NASA Astrophysics Data System (ADS)

    Carcione, J. M.; Santos, J. E.; Picotti, S.

    2011-09-01

    A dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is due to wave-induced fluid flow (mesoscopic loss). The P-wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength), generating fluid flow and slow (diffusion) Biot waves. The theory has been developed in the 1970s for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a finely layered medium, and has recently been generalized to all propagation angles. The new theory states that the fluid-flow direction is perpendicular to the layering plane and it is independent of the loading direction. As a consequence, the relaxation behaviour can be described by a single relaxation function, since the medium consists of plane homogeneous layers. Besides P-wave losses, the coupling between the qP and qSV waves generates shear-wave anisotropic velocity dispersion and attenuation. In this work, we introduce a set of quasi-static numerical experiments to determine the equivalent viscoelastic TI medium to a finely layered poroelastic medium, which is validated using a recently developed analytical solution. The modelling technique is the finite-element (FE) method, where the equations of motion are solved in the space-frequency domain. Numerical rock physics may, in many circumstances, offer an alternative to laboratory measurements. Numerical experiments are inexpensive and informative since the physical process of wave propagation can be inspected during the experiment. Moreover, they are repeatable, essentially free from experimental errors, and may easily be run using alternative models of the rock and fluid properties. We apply the methodology to the Utsira aquifer of the North Sea, where carbon dioxide (CO2) has been injected during the last 15 years. The tests consider alternating layers of the same rock saturated with gas and brine and a sequence of gas-saturated sandstone and

  7. A two-step finite volume method to discretize heterogeneous and anisotropic pressure equation on general grids

    NASA Astrophysics Data System (ADS)

    Zhang, Wenjuan; Al Kobaisi, Mohammed

    2017-10-01

    A novel Two-Step cell-centered Finite Volume Method (TSFVM) is developed in this work to discretize the heterogeneous and anisotropic pressure equation on triangular and quadrilateral grids in 2D and hexahedral and tetrahedral grids in 3D. Physical properties such as permeability and porosity are piece-wise constant on each grid cell. In the first step, the Galerkin Finite Element Method (FEM) is utilized to compute pressure solutions at all cell vertices. In the second step, pressure values at cell vertices are used to derive continuous two-point flux stencils for cell faces. Mass conservation equations are then written for each cell to obtain a system of linear equations that can be solved for pressure at cell centers. Extensive numerical experiments are carried out to test the performance of our TSFVM. In particular, we compare TSFVM with the classical Multipoint Flux Approximation (MPFA-O) method as well as a more recently developed MPFA method with full pressure support called enhanced MPFA (eMPFA). The results show that the TSFVM compares well with eMPFA for challenging test cases for which MPFA-O breaks down. Specifically, and as a significant step forward, our TSFVM is quite robust for challenging problems involving heterogeneous and highly anisotropic permeability tensors when both MPFA-O and eMPFA suffer from unphysical oscillations. Finally, the numerical convergence study demonstrates that TSFVM has comparable convergence behavior to MPFA-O method for both homogeneous and discontinuous permeability fields.

  8. Investigation of the ultrasonic attenuation in anisotropic weld materials with finite element modeling and grain-scale material description.

    PubMed

    Lhuillier, P E; Chassignole, B; Oudaa, M; Kerhervé, S O; Rupin, F; Fouquet, T

    2017-03-08

    A finite element modeling approach of ultrasonic propagation combined with a description of the microstructure at the scale of the grains has been implemented. The simulations seek to determine the contribution of scattering to the ultrasonic attenuation in polycrystalline materials. The approach is applied to anisotropic microstructures exhibiting both elongated grains and transversely isotropic crystallographic texture which can be found in multipass welds. The ultrasonic propagation is computed with the 2D finite element code ATHENA 2D. The description of the propagation media accounts for the geometric, elastic and crystallographic properties of anisotropic welds. The study is focused on two types of welds made of austenitic 316L stainless steel and Ni-based alloy (182). The attenuation was computed from the decay of multiple backwall echoes. The contribution of the microstructure scattering was isolated by a correction of the attenuation data with the attenuation obtained in an equivalent homogenized material. The simulation investigates the attenuation as a function of several parameters: grain orientation and size, ultrasonic frequency, or anisotropy level. The attenuation level of elastic pressure waves was specifically examined as a function of the angle between the propagation direction and the grain orientation. The evolution of the attenuation is consistent with the theoretical models. Moreover the simulation results were compared to experimental data available from the literature in 316L stainless steel welds. The simulated and experimental values are in very good agreement.

  9. Analysis of stresses in finite anisotropic panels with centrally located cutouts

    NASA Technical Reports Server (NTRS)

    Britt, Vicki O.

    1992-01-01

    A method for analyzing biaxial- and shear-loaded anisotropic rectangular panels with centrally located circular and elliptical cutouts is presented in the present paper. The method is based on Lekhnitskii's complex variable equations of plane elastostatics combined with a boundary collocation method and a Laurent series approximation. Results are presented for anisotropic panels with elliptical cutouts and subjected to combined shear and compression loading. The effects on the stress field of panel aspect ratio, anisotropy, cutout size, and cutout orientation are addressed. Angle-ply laminates, unidirectional off-axis laminates, and ((+ or - 45/0/90)(sub 3))s, ((+ or - 45/0(sub 2))(sub 3))s, and ((+ or - 45/90(sub 2))(sub 3))s laminates are examined.

  10. On the modelling of complex kinematic hardening and nonquadratic anisotropic yield criteria at finite strains: application to sheet metal forming

    NASA Astrophysics Data System (ADS)

    Grilo, Tiago J.; Vladimirov, Ivaylo N.; Valente, Robertt A. F.; Reese, Stefanie

    2016-06-01

    In the present paper, a finite strain model for complex combined isotropic-kinematic hardening is presented. It accounts for finite elastic and finite plastic strains and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data.

  11. Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Binder, Kurt; Wang, Jian-Sheng

    1989-04-01

    Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponents v ‖, v ⊥: uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimension L ‖ in the special direction and linear dimensions L ⊥ in all other directions. The related shape effects for L ‖≠ L ⊥ but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relation v ‖+( d-1) v ⊥=γ+2 β does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.

  12. Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

    DOE PAGES

    Juan, Pierre -Alexandre; Dingreville, Remi

    2016-10-31

    Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

  13. Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

    NASA Astrophysics Data System (ADS)

    Juan, Pierre-Alexandre; Dingreville, Rémi

    2017-02-01

    Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive "interferences" are directly affected by the interface structure and its elastic response. This general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.

  14. Finite Element Simulation of Sheet Metal Forming Using Anisotropic Strain-Rate Potentials

    SciTech Connect

    Rabahallah, Meziane; Balan, Tudor; Bouvier, Salima; Bacroix, Brigitte; Teodosiu, Cristian

    2007-05-17

    In continuum mechanics, plastic anisotropy is described using anisotropic stress potentials or, alternatively, strain-rate potentials. In this work, a stress update algorithm is developed for this later case. The implicit, backward Euler method is adopted. A specific numerical treatment is required to deal with the plasticity criterion, which is not defined explicitly. Also, a sub-stepping procedure is adopted in order to deal with the strong nonlinearity of the yield surfaces when applied to FCC materials. The resulting algorithm is implemented in the static implicit version of the Abaqus FE code. Several recent plastic potentials have been implemented in this framework and their parameters identified for a number of BCC and FCC materials. Numerical simulations of a cup drawing process are performed in order to address the robustness of the implementation and the ability of these potentials to predict e.g. earing for materials with different anisotropy.

  15. Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

    SciTech Connect

    Juan, Pierre -Alexandre; Dingreville, Remi

    2016-10-31

    Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” are directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.

  16. Continuum Multiscale Modeling of Finite Deformation Plasticity and Anisotropic Damage in Polycrystals

    DTIC Science & Technology

    2006-09-01

    neighboring grains cannot be spa- tially resolved. 3.5. Homogenization of damage Effects from mechanisms modeled individually— elastoplasticity within each...crystal plasticity routines are available, as the damage computations are effectively uncoupled from the constitutive update of the elastoplastic response... elastoplasticity and damage : multiscale kinematics, Int. J. Solids Struct. 40 (2003) 5669–5688. [17] C. Teodosiu, F. Sidoroff, A finite theory of

  17. A finite-difference program for stresses in anisotropic, layered plates in bending

    NASA Technical Reports Server (NTRS)

    Salamon, N. J.

    1975-01-01

    The interlaminar stresses induced in a layered laminate that is bent into a cylindrical surface are studied. The laminate is modeled as a continuum, and the resulting elasticity equations are solved using the finite difference method. The report sets forth the mathematical framework, presents some preliminary results, and provides a listing and explanation of the computer program. Significant among the results are apparent symmetry relationships that will reduce the numerical size of certain problems and an interlaminar stress behavior having a sharp rise at the free edges.

  18. Diffusion in bulk liquids: finite-size effects in anisotropic systems

    NASA Astrophysics Data System (ADS)

    Botan, Alexandru; Marry, Virginie; Rotenberg, Benjamin

    2015-09-01

    We investigate systematically the effect of the cell size and shape on the diffusion properties in molecular dynamics simulations. Specifically, we consider a bulk Lennard-Jones fluid in orthorhombic cells with one length differing from the other two. The components of the diffusion tensor display complex variations as a function of the two independent lengths and may even become in some cases larger than the macroscopic limit for a cubic cell. These results can be perfectly explained by a purely hydrodynamic theory, which extends results obtained previously for the isotropic case. We provide the explicit expression of the diffusion tensor, including the effect of the finite size of the diffusing particle. The simulation results follow a simple scaling as a function of box size and aspect ratio and the corresponding scaling functions are determined numerically. These findings should have implications for the practically more relevant case of confined fluids.

  19. A combined dislocation fan-finite element (DF-FE) method for stress field simulation of dislocations emerging at the free surfaces of 3D elastically anisotropic crystals

    NASA Astrophysics Data System (ADS)

    Balusu, K.; Huang, H.

    2017-04-01

    A combined dislocation fan-finite element (DF-FE) method is presented for efficient and accurate simulation of dislocation nodal forces in 3D elastically anisotropic crystals with dislocations intersecting the free surfaces. The finite domain problem is decomposed into half-spaces with singular traction stresses, an infinite domain, and a finite domain with non-singular traction stresses. As such, the singular and non-singular parts of the traction stresses are addressed separately; the dislocation fan (DF) method is introduced to balance the singular traction stresses in the half-spaces while the finite element method (FEM) is employed to enforce the non-singular boundary conditions. The accuracy and efficiency of the DF method is demonstrated using a simple isotropic test case, by comparing it with the analytical solution as well as the FEM solution. The DF-FE method is subsequently used for calculating the dislocation nodal forces in a finite elastically anisotropic crystal, which produces dislocation nodal forces that converge rapidly with increasing mesh resolutions. In comparison, the FEM solution fails to converge, especially for nodes closer to the surfaces.

  20. Effect of specimen-specific anisotropic material properties in quantitative computed tomography-based finite element analysis of the vertebra.

    PubMed

    Unnikrishnan, Ginu U; Barest, Glenn D; Berry, David B; Hussein, Amira I; Morgan, Elise F

    2013-10-01

    Intra- and inter-specimen variations in trabecular anisotropy are often ignored in quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra. The material properties are typically estimated solely from local variations in bone mineral density (BMD), and a fixed representation of elastic anisotropy ("generic anisotropy") is assumed. This study evaluated the effect of incorporating specimen-specific, trabecular anisotropy on QCT-based FE predictions of vertebral stiffness and deformation patterns. Orthotropic material properties estimated from microcomputed tomography data ("specimen-specific anisotropy"), were assigned to a large, columnar region of the L1 centrum (n = 12), and generic-anisotropic material properties were assigned to the remainder of the vertebral body. Results were compared to FE analyses in which generic-anisotropic properties were used throughout. FE analyses were also performed on only the columnar regions. For the columnar regions, the axial stiffnesses obtained from the two categories of material properties were uncorrelated with each other (p = 0.604), and the distributions of minimum principal strain were distinctly different (p ≤ 0.022). In contrast, for the whole vertebral bodies in both axial and flexural loading, the stiffnesses obtained using the two categories of material properties were highly correlated (R2 > 0.82, p < 0.001) with, and were no different (p > 0.359) from, each other. Only moderate variations in strain distributions were observed between the two categories of material properties. The contrasting results for the columns versus vertebrae indicate a large contribution of the peripheral regions of the vertebral body to the mechanical behavior of this bone. In companion analyses on the effect of the degree of anisotropy (DA), the axial stiffnesses of the trabecular column (p < 0.001) and vertebra (p = 0.007) increased with increasing DA. These findings

  1. Understanding anisotropic mechanical properties of shales at different length scales: In situ micropillar compression combined with finite element calculations

    NASA Astrophysics Data System (ADS)

    Keller, Lukas M.; Schwiedrzik, Jakob J.; Gasser, Philippe; Michler, Johann

    2017-08-01

    From microstructural observations and experimental work it is known that shales consist of a mechanically weak porous fine-grained clay matrix with embedded and mechanically strong silt/sand grains. Thereby, the respective contents of weak and strong constituents control bulk mechanical properties. In addition, the clay matrix is characterized by a preferred orientation of clay platelets, which are a major control on the bulk anisotropy of shales. To date, little is known about the micromechanical properties of the fine-grained porous clay matrix, which is particularly true in case of its micromechanical anisotropy. Such information can, however, only be assessed on the microscale. Therefore, the drained micromechanical properties parallel and perpendicular to bedding were investigated by means of compressing micropillars with a flat punch indenter in a scanning electron microscope. Microscopic failure mechanism was found to be anisotropic: (i) in case loading was parallel to bedding it occurred by a combination of localized shearing, kinking/buckling of elongated clay aggregates, and bedding parallel splitting and (ii) for loading perpendicular to bedding failure occurred mainly by localized shearing. The measured stiffness of the drained porous clay matrix perpendicular (Ev) and parallel (Eh) to bedding was about 8 GPa and 30 GPa, respectively. Using these stiffness values as input in voxel-based finite element modeling and in combination with realistic microstructures, which are characterized with different contents of "soft" and "hard" constituents, revealed that the measured high microscale anisotropy Eh/Ev = 3.75 is crucial in understanding the bulk anisotropy of clay rocks.

  2. Regional electric field induced by electroconvulsive therapy in a realistic finite element head model: Influence of white matter anisotropic conductivity

    PubMed Central

    Lee, Won Hee; Deng, Zhi-De; Kim, Tae-Seong; Laine, Andrew F.; Lisanby, Sarah H.; Peterchev, Angel V.

    2012-01-01

    We present the first computational study investigating the electric field (E-field) strength generated by various electroconvulsive therapy (ECT) electrode configurations in specific brain regions of interest (ROIs) that have putative roles in the therapeutic action and/or adverse side effects of ECT. This study also characterizes the impact of the white matter (WM) conductivity anisotropy on the E-field distribution. A finite element head model incorporating tissue heterogeneity and WM anisotropic conductivity was constructed based on structural magnetic resonance imaging (MRI) and diffusion tensor MRI data. We computed the spatial E-field distributions generated by three standard ECT electrode placements including bilateral (BL), bifrontal (BF), and right unilateral (RUL) and an investigational electrode configuration for focal electrically administered seizure therapy (FEAST). The key results are that (1) the median E-field strength over the whole brain is 3.9, 1.5, 2.3, and 2.6 V/cm for the BL, BF, RUL, and FEAST electrode configurations, respectively, which coupled with the broad spread of the BL E-field suggests a biophysical basis for observations of superior efficacy of BL ECT compared to BF and RUL ECT; (2) in the hippocampi, BL ECT produces a median E-field of 4.8 V/cm that is 1.5–2.8 times stronger than that for the other electrode configurations, consistent with the more pronounced amnestic effects of BL ECT; and (3) neglecting the WM conductivity anisotropy results in E-field strength error up to 18% overall and up to 39% in specific ROIs, motivating the inclusion of the WM conductivity anisotropy in accurate head models. This computational study demonstrates how the realistic finite element head model incorporating tissue conductivity anisotropy provides quantitative insight into the biophysics of ECT, which may shed light on the differential clinical outcomes seen with various forms of ECT, and may guide the development of novel stimulation

  3. Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation.

    PubMed

    Lee, Won Hee; Kim, Tae-Seong

    2012-01-01

    This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions

  4. An improved rotated staggered-grid finite-difference method with fourth-order temporal accuracy for elastic-wave modeling in anisotropic media

    DOE PAGES

    Gao, Kai; Huang, Lianjie

    2017-08-31

    The rotated staggered-grid (RSG) finite-difference method is a powerful tool for elastic-wave modeling in 2D anisotropic media where the symmetry axes of anisotropy are not aligned with the coordinate axes. We develop an improved RSG scheme with fourth-order temporal accuracy to reduce the numerical dispersion associated with prolonged wave propagation or a large temporal step size. The high-order temporal accuracy is achieved by including high-order temporal derivatives, which can be converted to high-order spatial derivatives to reduce computational cost. Dispersion analysis and numerical tests show that our method exhibits very low temporal dispersion even with a large temporal step sizemore » for elastic-wave modeling in complex anisotropic media. Using the same temporal step size, our method is more accurate than the conventional RSG scheme. In conclusion, our improved RSG scheme is therefore suitable for prolonged modeling of elastic-wave propagation in 2D anisotropic media.« less

  5. Three-dimensional modeling of a thermal dendrite using the phase field method with automatic anisotropic and unstructured adaptive finite element meshing

    NASA Astrophysics Data System (ADS)

    Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.

    2016-03-01

    Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.

  6. Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

    PubMed

    Balzani, Daniel; Deparis, Simone; Fausten, Simon; Forti, Davide; Heinlein, Alexander; Klawonn, Axel; Quarteroni, Alfio; Rheinbach, Oliver; Schröder, Joerg

    2016-10-01

    The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to

  7. A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behavior of the tissue.

    PubMed

    Carnelli, D; Gastaldi, D; Sassi, V; Contro, R; Ortiz, C; Vena, P

    2010-08-01

    A finite element model was developed for numerical simulations of nanoindentation tests on cortical bone. The model allows for anisotropic elastic and post-yield behavior of the tissue. The material model for the post-yield behavior was obtained through a suitable linear transformation of the stress tensor components to define the properties of the real anisotropic material in terms of a fictitious isotropic solid. A tension-compression yield stress mismatch and a direction-dependent yield stress are allowed for. The constitutive parameters are determined on the basis of literature experimental data. Indentation experiments along the axial (the longitudinal direction of long bones) and transverse directions have been simulated with the purpose to calculate the indentation moduli and the tissue hardness in both the indentation directions. The results have shown that the transverse to axial mismatch of indentation moduli was correctly simulated regardless of the constitutive parameters used to describe the post-yield behavior. The axial to transverse hardness mismatch observed in experimental studies (see, for example, Rho et al. [1999, "Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation," J. Biomed. Mater. Res., 45, pp. 48-54] for results on human tibial cortical bone) can be correctly simulated through an anisotropic yield constitutive model. Furthermore, previous experimental results have shown that cortical bone tissue subject to nanoindentation does not exhibit piling-up. The numerical model presented in this paper shows that the probe tip-tissue friction and the post-yield deformation modes play a relevant role in this respect; in particular, a small dilatation angle, ruling the volumetric inelastic strain, is required to approach the experimental findings.

  8. A 3D finite element-based model order reduction method for parametric resonance and whirling analysis of anisotropic rotor-bearing systems

    NASA Astrophysics Data System (ADS)

    Wang, Shuai; Wang, Yu; Zi, Yanyang; He, Zhengjia

    2015-12-01

    A generalized and efficient model for rotating anisotropic rotor-bearing systems is presented in this paper with full considerations of the system's anisotropy in stiffness, inertia and damping. Based on the 3D finite element model and the model order reduction method, the effects of anisotropy in shaft and bearings on the forced response and whirling of anisotropic rotor-bearing systems are systematically investigated. First, the coefficients of journal bearings are transformed from the fixed frame to the rotating one. Due to the anisotropy in shaft and bearings, the motion is governed by differential equations with periodically time-variant coefficients. Then, a free-interface complex component mode synthesis (CMS) method is employed to generate efficient reduced-order models (ROM) for the periodically time-variant systems. In order to solve the obtained equations, a variant of Hill's method for systems with multiple harmonic excitations is developed. Four dimensionless parameters are defined to quantify the types and levels of anisotropy of bearings. Finally, the effects of the four types of anisotropy on the forced response and whirl orbits are studied. Numerical results show that the anisotropy of bearings in stiffness splits the sole resonant peak into two isolated ones, but the anisotropy of bearings in damping coefficients mainly affect the response amplitudes. Moreover, the whirl orbits become much more complex when the shaft and bearings are both anisotropic. In addition, the cross-coupling stiffness coefficients of bearings significantly affect the dynamic behaviors of the systems and cannot be neglected, though they are often much smaller than the principle stiffness terms.

  9. Shape dependence and anisotropic finite-size scaling of the phase coherence of three-dimensional Bose-Einstein-condensed gases

    NASA Astrophysics Data System (ADS)

    Ceccarelli, Giacomo; Delfino, Francesco; Mesiti, Michele; Vicari, Ettore

    2016-11-01

    We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L ×L ×La boxes, below the Bose-Einstein-condensate (BEC) transition temperature Tc. We show that the phase correlations develop peculiar anisotropic FSS for any T

  10. Anisotropic 2.5D Inversion of Towed Streamer EM Data from Three North Sea Fields Using Parallel Adaptive Finite Elements

    NASA Astrophysics Data System (ADS)

    Key, K.; Du, Z.

    2014-12-01

    We present anisotropic inversion results from towed streamer electromagnetic (EM) surveys of the Bressay, Bentley and Kraken (BBK) heavy oil fields in the North Sea. The BBK discoveries pose several challenges to conventional controlled-source EM surveying since the relatively shallow water dampens the anomaly magnitudes due to airwave coupling, and the reservoirs are in close proximity to other resistive features. The 160 m spacing of the 44 receiver bipoles on the towed streamer offers much higher data density than is typically achieved with conventional seafloor receiver surveys. We tested the resolving capabilities of the towed-streamer by inverting the survey data using a new code based on a 2.5D parallel goal-oriented adaptive finite element method and a modified implementation of the Occam inversion algorithm. The inversion successfully images the 1-2 km wide Bressay and ~5 km wide Bentley reservoirs, illustrating that the high data density of the towed streamer offers improved resolution over sparsely sampled nodal seafloor receiver data. The results also demonstrate the importance of allowing for anisotropy when inverting data from this region. Whereas anisotropic inversion clearly recovers the lateral edges of the known reservoirs, isotropic inversion results in inter-bedding of resistive and conductive layers that conceal the reservoirs.

  11. Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability.

    PubMed

    Giordano, Chiara; Zappalà, Stefano; Kleiven, Svein

    2017-02-23

    Computational models incorporating anisotropic features of brain tissue have become a valuable tool for studying the occurrence of traumatic brain injury. The tissue deformation in the direction of white matter tracts (axonal strain) was repeatedly shown to be an appropriate mechanical parameter to predict injury. However, when assessing the reliability of axonal strain to predict injury in a population, it is important to consider the predictor sensitivity to the biological inter-subject variability of the human brain. The present study investigated the axonal strain response of 485 white matter subject-specific anisotropic finite element models of the head subjected to the same loading conditions. It was observed that the biological variability affected the orientation of the preferential directions (coefficient of variation of 39.41% for the elevation angle-coefficient of variation of 29.31% for the azimuth angle) and the determination of the mechanical fiber alignment parameter in the model (gray matter volume 55.55-70.75%). The magnitude of the maximum axonal strain showed coefficients of variation of 11.91%. On the contrary, the localization of the maximum axonal strain was consistent: the peak of strain was typically located in a 2 cm(3) volume of the brain. For a sport concussive event, the predictor was capable of discerning between non-injurious and concussed populations in several areas of the brain. It was concluded that, despite its sensitivity to biological variability, axonal strain is an appropriate mechanical parameter to predict traumatic brain injury.

  12. A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

    PubMed

    Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

    2014-01-01

    The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

  13. A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem

    PubMed Central

    Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D.

    2014-01-01

    The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique. PMID:24527060

  14. Wave steering effects in anisotropic composite structures: Direct calculation of the energy skew angle through a finite element scheme.

    PubMed

    Chronopoulos, D

    2017-01-01

    A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors. Copyright © 2016 Elsevier B.V. All rights reserved.

  15. An efficient model to predict guided wave radiation by finite-sized sources in multilayered anisotropic plates with account of caustics

    NASA Astrophysics Data System (ADS)

    Stévenin, M.; Lhémery, A.; Grondel, S.

    2016-01-01

    Elastic guided waves (GW) are used in various non-destructive testing (NDT) methods to inspect plate-like structures, generated by finite-sized transducers. Thanks to GW long range propagation, using a few transducers at permanent positions can provide a full coverage of the plate. Transducer diffraction effects take place, leading to complex radiated fields. Optimizing transducers positioning makes it necessary to accurately predict the GW field radiated by a transducer. Fraunhofer-like approximations applied to GW in isotropic homogeneous plates lead to fast and accurate field computation but can fail when applied to multi-layered anisotropic composite plates, as shown by some examples given. Here, a model is proposed for composite plates, based on the computation of the approximate Green's tensor describing modal propagation from a source point, with account of caustics typically seen when strong anisotropy is concerned. Modal solutions are otherwise obtained by the Semi-Analytic Finite Element method. Transducer diffraction effects are accounted for by means of an angular integration over the transducer surface as seen from the calculation point, that is, over energy paths involved, which are mode-dependent. The model is validated by comparing its predictions with those computed by means of a full convolution integration of the Green's tensor with the source over transducer surface. Examples given concern disk and rectangular shaped transducers commonly used in NDT.

  16. A smoothed finite element method for analysis of anisotropic large deformation of passive rabbit ventricles in diastole.

    PubMed

    Jiang, Chen; Liu, Gui-Rong; Han, Xu; Zhang, Zhi-Qian; Zeng, Wei

    2015-01-01

    The smoothed FEM (S-FEM) is firstly extended to explore the behavior of 3D anisotropic large deformation of rabbit ventricles during the passive filling process in diastole. Because of the incompressibility of myocardium, a special method called selective face-based/node-based S-FEM using four-node tetrahedral elements (FS/NS-FEM-TET4) is adopted in order to avoid volumetric locking. To validate the proposed algorithms of FS/NS-FEM-TET4, the 3D Lame problem is implemented. The performance contest results show that our FS/NS-FEM-TET4 is accurate, volumetric locking-free and insensitive to mesh distortion than standard linear FEM because of absence of isoparametric mapping. Actually, the efficiency of FS/NS-FEM-TET4 is comparable with higher-order FEM, such as 10-node tetrahedral elements. The proposed method for Holzapfel myocardium hyperelastic strain energy is also validated by simple shear tests through the comparison outcomes reported in available references. Finally, the FS/NS-FEM-TET4 is applied in the example of the passive filling of MRI-based rabbit ventricles with fiber architecture derived from rule-based algorithm to demonstrate its efficiency. Hence, we conclude that FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics.

  17. Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing

    NASA Astrophysics Data System (ADS)

    Francés, Jorge; Bleda, Sergio; Álvarez, Mariela Lázara; Martínez, Francisco Javier; Márquez, Andres; Neipp, Cristian; Beléndez, Augusto

    2014-01-01

    The implementation of split-field finite difference time domain (SF-FDTD) applied to light-wave propagation through periodic media with arbitrary anisotropy method in graphics processing units (GPUs) is described. The SF-FDTD technique and the periodic boundary condition allow the consideration of a single period of the structure reducing the simulation grid. Nevertheless, the analysis of the anisotropic media implies considering all the electromagnetic field components and the use of complex notation. These aspects reduce the computational efficiency of the numerical method compared with the isotropic and nonperiodic implementation. Specifically, the implementation of the SF-FDTD in the Kepler family of GPUs of NVIDIA is presented. An analysis of the performance of this implementation is done, and several applications have been considered in order to estimate the possibilities provided by both the formalism and the implementation into GPU: binary phase gratings and twisted-nematic liquid crystal cells. Regarding the analysis of binary phase gratings, the validity of the scalar diffraction theory is evaluated by the comparison of the diffraction efficiencies predicted by SF-FDTD. The analysis for the second order of diffraction is extended, which is considered as a reference for the transmittance obtained by the SF-FDTD scheme for periodic media.

  18. A weighted reverse Cuthill-McKee procedure for finite element method algorithms to solve strongly anisotropic electrodynamic problems

    SciTech Connect

    Cristofolini, Andrea; Latini, Chiara; Borghi, Carlo A.

    2011-02-01

    This paper presents a technique for improving the convergence rate of a generalized minimum residual (GMRES) algorithm applied for the solution of a algebraic system produced by the discretization of an electrodynamic problem with a tensorial electrical conductivity. The electrodynamic solver considered in this work is a part of a magnetohydrodynamic (MHD) code in the low magnetic Reynolds number approximation. The code has been developed for the analysis of MHD interaction during the re-entry phase of a space vehicle. This application is a promising technique intensively investigated for the shock mitigation and the vehicle control in the higher layers of a planetary atmosphere. The medium in the considered application is a low density plasma, characterized by a tensorial conductivity. This is a result of the behavior of the free electric charges, which tend to drift in a direction perpendicular both to the electric field and to the magnetic field. In the given approximation, the electrodynamics is described by an elliptical partial differential equation, which is solved by means of a finite element approach. The linear system obtained by discretizing the problem is solved by means of a GMRES iterative method with an incomplete LU factorization threshold preconditioning. The convergence of the solver appears to be strongly affected by the tensorial characteristic of the conductivity. In order to deal with this feature, the bandwidth reduction in the coefficient matrix is considered and a novel technique is proposed and discussed. First, the standard reverse Cuthill-McKee (RCM) procedure has been applied to the problem. Then a modification of the RCM procedure (the weighted RCM procedure, WRCM) has been developed. In the last approach, the reordering is performed taking into account the relation between the mesh geometry and the magnetic field direction. In order to investigate the effectiveness of the methods, two cases are considered. The RCM and WRCM procedures

  19. Anisotropic universe with anisotropic sources

    SciTech Connect

    Aluri, Pavan K.; Panda, Sukanta; Sharma, Manabendra; Thakur, Snigdha E-mail: sukanta@iiserb.ac.in E-mail: snigdha@iiserb.ac.in

    2013-12-01

    We analyze the state space of a Bianchi-I universe with anisotropic sources. Here we consider an extended state space which includes null geodesics in this background. The evolution equations for all the state observables are derived. Dynamical systems approach is used to study the evolution of these equations. The asymptotic stable fixed points for all the evolution equations are found. We also check our analytic results with numerical analysis of these dynamical equations. The evolution of the state observables are studied both in cosmic time and using a dimensionless time variable. Then we repeat the same analysis with a more realistic scenario, adding the isotropic (dust like dark) matter and a cosmological constant (dark energy) to our anisotropic sources, to study their co-evolution. The universe now approaches a de Sitter space asymptotically dominated by the cosmological constant. The cosmic microwave background anisotropy maps due to shear are also generated in this scenario, assuming that the universe contains anisotropic matter along with the usual (dark) matter and vacuum (dark) energy since decoupling. We find that they contribute dominantly to the CMB quadrupole. We also constrain the current level of anisotropy and also search for any cosmic preferred axis present in the data. We use the Union 2 Supernovae data to this extent. An anisotropy axis close to the mirror symmetry axis seen in the cosmic microwave background data from Planck probe is found.

  20. Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent.

    PubMed

    Jacobs, Nathan T; Cortes, Daniel H; Peloquin, John M; Vresilovic, Edward J; Elliott, Dawn M

    2014-08-22

    Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.

  1. Finite element simulation of the generation and detection by air-coupled transducers of guided waves in viscoelastic and anisotropic materials.

    PubMed

    Hosten, Bernard; Biateau, Christine

    2008-04-01

    The measured characteristics (efficiency and sensitivity) of two air-coupled transducers allow for the prediction of the absolute values of the pressure of the bulk waves generated in air and for the measurement of the pressure of the field radiated in air by guided waves propagating in a structure. With finite element software, the pressure field generated by an air-coupled transducer is simulated by introducing a right-hand side member in the Helmholtz equation, which is used for computing the propagation from the transducer to a plate. The simulated source is rotated in order to impose an angle of incidence with respect to the normal of the plate and generate the corresponding guided mode. Inside the plate, the propagation is simulated with the dynamic equations of equilibrium and a complex stiffness tensor to take into account the viscoelastic anisotropy of the material. For modeling the three-dimensional fields of the guided modes propagating in a two-dimensional non-symmetry plane, a 2.5 dimensional model is introduced. The model computes the value of the pressure field radiated in air by the plates for any guided modes and can predict the detectability of the system for a known defect in a structure. A test bed incorporating two air-coupled transducers is used to generate and receive various guided modes. Two plates made of Perspex and carbon-epoxy composite are tested. The pressure measured by the receiver at various positions is compared to the results of the model to validate it.

  2. Shaped beam scattering by an anisotropic particle

    NASA Astrophysics Data System (ADS)

    Chen, Zhenzhen; Zhang, Huayong; Huang, Zhixiang; Wu, Xianliang

    2017-03-01

    An exact semi-analytical solution to the electromagnetic scattering from an optically anisotropic particle illuminated by an arbitrarily shaped beam is proposed. The scattered fields and fields within the anisotropic particle are expanded in terms of spherical vector wave functions. The unknown expansion coefficients are determined by using the boundary conditions and the method of moments scheme. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are given to a uniaxial, gyrotropic anisotropic spheroid and circular cylinder of finite length. The scattering properties are analyzed concisely.

  3. 3D unstructured mesh discontinuous finite element hydro

    SciTech Connect

    Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.

    1995-07-01

    The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D.

  4. Viscoacoustic anisotropic full waveform inversion

    NASA Astrophysics Data System (ADS)

    Qu, Yingming; Li, Zhenchun; Huang, Jianping; Li, Jinli

    2017-01-01

    A viscoacoustic vertical transverse isotropic (VTI) quasi-differential wave equation, which takes account for both the viscosity and anisotropy of media, is proposed for wavefield simulation in this study. The finite difference method is used to solve the equations, for which the attenuation terms are solved in the wavenumber domain, and all remaining terms in the time-space domain. To stabilize the adjoint wavefield, robust regularization operators are applied to the wave equation to eliminate the high-frequency component of the numerical noise produced during the backward propagation of the viscoacoustic wavefield. Based on these strategies, we derive the corresponding gradient formula and implement a viscoacoustic VTI full waveform inversion (FWI). Numerical tests verify that our proposed viscoacoustic VTI FWI can produce accurate and stable inversion results for viscoacoustic VTI data sets. In addition, we test our method's sensitivity to velocity, Q, and anisotropic parameters. Our results show that the sensitivity to velocity is much higher than that to Q and anisotropic parameters. As such, our proposed method can produce acceptable inversion results as long as the Q and anisotropic parameters are within predefined thresholds.

  5. Anisotropic Failure Modeling for HY-100 Steel

    NASA Astrophysics Data System (ADS)

    Harstad, E. N.; Maudlin, P. J.; McKirgan, J. B.

    2004-07-01

    HY-100 steel is a material that behaves isotropically in the elastic and plastic region and acts anisotropically in failure. Since HY-100 is a ductile metal, a more gradual failure process is observed as opposed to the nearly instantaneous failure in brittle materials. We extend our elasto-plastic-damage constitutive model by including of a decohesion model to describe material behavior between the onset of failure and fracture. We also develop an anisotropic failure surface to account for directionality in material failure. Both the anisotropic failure and decohesion models have been implemented into a finite element code, where the effects of these models are studied in a uniaxial stress simulations, a plate impact simulations, and a quasistatic notched round bar tensile test simulations.

  6. Quasiparticle anisotropic hydrodynamics for central collisions

    NASA Astrophysics Data System (ADS)

    Alqahtani, Mubarak; Nopoush, Mohammad; Strickland, Michael

    2017-03-01

    We use quasiparticle anisotropic hydrodynamics to study an azimuthally symmetric boost-invariant quark-gluon plasma including the effects of both shear and bulk viscosities. In quasiparticle anisotropic hydrodynamics, a single finite-temperature quasiparticle mass is introduced and fit to the lattice data in order to implement a realistic equation of state (EoS). We compare results obtained by using the quasiparticle method with the standard method of imposing the EoS in anisotropic hydrodynamics and viscous hydrodynamics. Using these three methods, we extract the primordial particle spectra, total number of charged particles, and average transverse momentum for various values of the shear viscosity to entropy density ratio η /s . We find that the three methods agree well for small shear viscosity to entropy density ratio η /s , but differ at large η /s , with the standard anisotropic EoS method showing suppressed production at low transverse-momentum compared with the other two methods considered. Finally, we demonstrate explicitly that, when using standard viscous hydrodynamics, the bulk-viscous correction can drive the primordial particle spectra negative at large pT. Such behavior is not seen in either anisotropic hydrodynamics approach, irrespective of the value of η /s .

  7. Cosmic anisotropic doomsday in Bianchi type I universes

    NASA Astrophysics Data System (ADS)

    Cataldo, Mauricio; Cid, Antonella; Labraña, Pedro; Mella, Patricio

    2016-11-01

    In this paper we study finite time future singularities in anisotropic Bianchi type I models. It is shown that there exist future singularities similar to Big Rip ones (which appear in the framework of phantom Friedmann-Robertson-Walker cosmologies). Specifically, in an ellipsoidal anisotropic scenario or in a fully anisotropic scenario, the three directional and average scale factors may diverge at a finite future time, together with energy densities and anisotropic pressures. We call these singularities "Anisotropic Big Rip Singularities." We show that there also exist Bianchi type I models filled with matter, where one or two directional scale factors may diverge. Another type of future anisotropic singularities is shown to be present in vacuum cosmologies, i.e., Kasner spacetimes. These singularities are induced by the shear scalar, which also blows up at a finite time. We call such a singularity "Vacuum Rip." In this case one directional scale factor blows up, while the other two and average scale factors tend to zero.

  8. Anisotropic non-Fermi liquids

    NASA Astrophysics Data System (ADS)

    Sur, Shouvik; Lee, Sung-Sik

    2016-11-01

    We study non-Fermi-liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in (3 -ɛ ) -dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points: the speed of the collective mode along the ordering wave vector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi-liquid state is realized for small ɛ , where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction antiscreens the coupling at the SDW critical point whereas it screens at the CDW critical point.

  9. Postbuckling of laminated anisotropic panels

    NASA Technical Reports Server (NTRS)

    Jeffrey, Glenda L.

    1987-01-01

    A two-part study of the buckling and postbuckling of laminated anisotropic plates with bending-extensional coupling is presented. The first part involves the development and application of a modified Rayleigh-Ritz analysis technique. Modifications made to the classical technique can be grouped into three areas. First, known symmetries of anisotropic panels are exploited in the selection of approximation functions. Second, a reduced basis technique based on these same symmetries is applied in the linear range. Finally, geometric boundary conditions are enforced via an exterior penalty function approach, rather than relying on choice of approximation functions to satisfy these boundary conditions. Numerical results are presented for both the linear and nonlinear range, with additional studies made to determine the effect of variation in penalty parameter and number of basis vectors. In the second part, six panels possessing anisotropy and bending-extensional coupling are tested. Detailed comparisons are made between experiment and finite element results in order to gain insight into the postbuckling and failure characteristics of such panels. The panels are constructed using two different lamination sequences, and panels with three different aspect ratios were constructed for each lamination sequence.

  10. Modeling Geodynamic Mobility of Anisotropic Lithosphere

    NASA Astrophysics Data System (ADS)

    Perry-Houts, J.; Karlstrom, L.

    2016-12-01

    The lithosphere is often idealized as a linear, or plastic layer overlying a Newtonian half-space. This approach has led to many insights into lithospheric foundering that include Rayligh-Taylor drips, slab-style delaminations, and small scale convection in the asthenosphere. More recent work has begun to quantify the effect of anisotropic lithosphere viscosity on these same phenomena. Anisotropic viscosity may come about due to stratigraphic deposition in the upper crust, dike/sill emplacement in the mid crust, or volcanic underplating at the Moho related to arcs or plumes. Anisotropic viscosity is also observed in the mantle, due to preferential orientation of olivine grains during flow. Here we extend the work of Lev & Hager (2008) on modeling anisotropic lithospheric foundering to investigate the effects of anisotropic regions which vary in size, magnitude, and orientation. We have extended Aspect, a modern geodynamic finite element code with a large developer and user base, to model exotic constitutive laws with an arbitrary fourth order tensor in place of the viscosity term. We further implement a material model to represent a transverse isotropic medium, such as is expected in a layered, or fractured lithosphere. We have validated our implementation against previous results, and analytic solutions, reproducing the result that horizontally oriented anisotropy tends to inhibit drips, and produce longer-wavelength instabilities. We expect that increased lateral extent of anisotropic regions will exaggerate this effect, to a limit at which the effect will plateau. Varying lithosphere thickness, and mantle anisotropy anisotropy may produce similar behavior. The implications of this effect are significant to lithospheric foundering beneath arcs and hotspots, possibly influencing the recycling of eclogite, production of silicic magmas, and dynamic topography.

  11. Anisotropic Artificial Impedance Surfaces

    NASA Astrophysics Data System (ADS)

    Quarfoth, Ryan Gordon

    Anisotropic artificial impedance surfaces are a group of planar materials that can be modeled by the tensor impedance boundary condition. This boundary condition relates the electric and magnetic field components on a surface using a 2x2 tensor. The advantage of using the tensor impedance boundary condition, and by extension anisotropic artificial impedance surfaces, is that the method allows large and complex structures to be modeled quickly and accurately using a planar boundary condition. This thesis presents the theory of anisotropic impedance surfaces and multiple applications. Anisotropic impedance surfaces are a generalization of scalar impedance surfaces. Unlike the scalar version, anisotropic impedance surfaces have material properties that are dependent on the polarization and wave vector of electromagnetic radiation that interacts with the surface. This allows anisotropic impedance surfaces to be used for applications that scalar surfaces cannot achieve. Three of these applications are presented in this thesis. The first is an anisotropic surface wave waveguide which allows propagation in one direction, but passes radiation in the orthogonal direction without reflection. The second application is a surface wave beam shifter which splits a surface wave beam in two directions and reduces the scattering from an object placed on the surface. The third application is a patterned surface which can alter the scattered radiation pattern of a rectangular shape. For each application, anisotropic impedance surfaces are constructed using periodic unit cells. These unit cells are designed to give the desired surface impedance characteristics by modifying a patterned metallic patch on a grounded dielectric substrate. Multiple unit cell geometries are analyzed in order to find the setup with the best performance in terms of impedance characteristics and frequency bandwidth.

  12. Anisotropic Nanoparticles and Anisotropic Surface Chemistry.

    PubMed

    Burrows, Nathan D; Vartanian, Ariane M; Abadeer, Nardine S; Grzincic, Elissa M; Jacob, Lisa M; Lin, Wayne; Li, Ji; Dennison, Jordan M; Hinman, Joshua G; Murphy, Catherine J

    2016-02-18

    Anisotropic nanoparticles are powerful building blocks for materials engineering. Unusual properties emerge with added anisotropy-often to an extraordinary degree-enabling countless new applications. For bottom-up assembly, anisotropy is crucial for programmability; isotropic particles lack directional interactions and can self-assemble only by basic packing rules. Anisotropic particles have long fascinated scientists, and their properties and assembly behavior have been the subjects of many theoretical studies over the years. However, only recently has experiment caught up with theory. We have begun to witness tremendous diversity in the synthesis of nanoparticles with controlled anisotropy. In this Perspective, we highlight the synthetic achievements that have galvanized the field, presenting a comprehensive discussion of the mechanisms and products of both seed-mediated and alternative growth methods. We also address recent breakthroughs and challenges in regiospecific functionalization, which is the next frontier in exploiting nanoparticle anisotropy.

  13. Second order tensor finite element

    NASA Technical Reports Server (NTRS)

    Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

    1990-01-01

    The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

  14. Anisotropic ray trace

    NASA Astrophysics Data System (ADS)

    Lam, Wai Sze Tiffany

    Optical components made of anisotropic materials, such as crystal polarizers and crystal waveplates, are widely used in many complex optical system, such as display systems, microlithography, biomedical imaging and many other optical systems, and induce more complex aberrations than optical components made of isotropic materials. The goal of this dissertation is to accurately simulate the performance of optical systems with anisotropic materials using polarization ray trace. This work extends the polarization ray tracing calculus to incorporate ray tracing through anisotropic materials, including uniaxial, biaxial and optically active materials. The 3D polarization ray tracing calculus is an invaluable tool for analyzing polarization properties of an optical system. The 3x3 polarization ray tracing P matrix developed for anisotropic ray trace assists tracking the 3D polarization transformations along a ray path with series of surfaces in an optical system. To better represent the anisotropic light-matter interactions, the definition of the P matrix is generalized to incorporate not only the polarization change at a refraction/reflection interface, but also the induced optical phase accumulation as light propagates through the anisotropic medium. This enables realistic modeling of crystalline polarization elements, such as crystal waveplates and crystal polarizers. The wavefront and polarization aberrations of these anisotropic components are more complex than those of isotropic optical components and can be evaluated from the resultant P matrix for each eigen-wavefront as well as for the overall image. One incident ray refracting or reflecting into an anisotropic medium produces two eigenpolarizations or eigenmodes propagating in different directions. The associated ray parameters of these modes necessary for the anisotropic ray trace are described in Chapter 2. The algorithms to calculate the P matrix from these ray parameters are described in Chapter 3 for

  15. Monotonic solution of heterogeneous anisotropic diffusion problems

    NASA Astrophysics Data System (ADS)

    Aricò, Costanza; Tucciarelli, Tullio

    2013-11-01

    Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of each side with the “anisotropic” circumcentre of each final triangle. A structure of the flux across the control volume sides similar to the standard Galerkin Finite Element scheme is derived. A special treatment of the flux computation, mainly based on edge swaps of the initial mesh triangles, is proposed in order to obtain a stiffness M-matrix system that guarantees the monotonicity of the solution. The proposed scheme is tested using several literature tests and the results are compared with analytical solutions, as well as with the results of other algorithms, in terms of convergence order. Computational costs are also investigated.

  16. Magnetospheric equilibrium with anisotropic pressure

    SciTech Connect

    Cheng, C.Z.

    1991-07-01

    Self-consistent magnetospheric equilibrium with anisotropic pressure is obtained by employing an iterative metric method for solving the inverse equilibrium equation in an optimal flux coordinate system. A method of determining plasma parallel and perpendicular pressures from either analytic particle distribution or particle distribution measured along the satellite's path is presented. The numerical results of axisymmetric magnetospheric equilibrium including the effects of finite beta, pressure anisotropy, and boundary conditions are presented for a bi-Maxwellian particle distribution. For the isotropic pressure cases, the finite beta effect produces an outward expansion of the constant magnetic flux surfaces in relation to the dipole field lines, and along the magnetic field the toroidal ring current is maximum at the magnetic equator. The effect of pressure anisotropy is found to further expand the flux surfaces outward. Along the magnetic field lines the westward ring current can be peak away from the equator due to an eastward current contribution resulting from pressure anisotropy. As pressure anisotropy increases, the peak westward current can become more singular. The outer boundary flux surface has significant effect on the magnetospheric equilibrium. For the outer flux boundary resembling dayside compressed flux surface due to solar wind pressure, the deformation of the magnetic field can be quite different from that for the outer flux boundary resembling the tail-like surface. 23 refs., 17 figs.

  17. A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

    DTIC Science & Technology

    2014-02-01

    Polycrystals. International Journal of Plasticity 2003, 19, 1401–1444. 26. Clayton, J. D.; McDowell, D. L. Homogenized Finite Elastoplasticity and Damage ...Materials and Technology 2002, 124, 302– 313. 25. Clayton, J. D.; McDowell, D. L. A Multiscale Multiplicative Decomposition for Elastoplasticity of...29. Clayton, J. D. Continuum Multiscale Modeling of Finite Deformation Plasticity and Anisotropic Damage in Polycrystals. Theoretical and Applied

  18. Anisotropic properties of tracheal smooth muscle tissue.

    PubMed

    Sarma, P A; Pidaparti, R M; Meiss, R A

    2003-04-01

    The anisotropic (directional-dependent) properties of contracting tracheal smooth muscle tissue are estimated from a computational model based on the experimental data of length-dependent stiffness. The area changes are obtained at different muscle lengths from experiments in which stimulated muscle undergoes unrestricted shortening. Then, through an interative process, the anisotropic properties are estimated by matching the area changes obtained from the finite element analysis to those derived from the experiments. The results obtained indicate that the anisotropy ratio (longitudinal stiffness to transverse stiffness) is about 4 when the smooth muscle undergoes 70% strain shortening, indicating that the transverse stiffness reduces as the longitudinal stiffness increases. It was found through a sensitivity analysis from the simulation model that the longitudinal stiffness and the in-plane shear modulus are not very sensitive as compared to major Poisson's ratio to the area changes of the muscle tissue. Copyright 2003 Wiley Periodicals, Inc.

  19. Enhancement of non-resonant dielectric cloaks using anisotropic composites

    SciTech Connect

    Takezawa, Akihiro Kitamura, Mitsuru

    2014-01-15

    Cloaking techniques conceal objects by controlling the flow of electromagnetic waves to minimize scattering. Herein, the effectiveness of homogenized anisotropic materials in non-resonant dielectric multilayer cloaking is studied. Because existing multilayer cloaking by isotropic materials can be regarded as homogenous anisotropic cloaking from a macroscopic view, anisotropic materials can be efficiently designed through optimization of their physical properties. Anisotropic properties can be realized in two-phase composites if the physical properties of the material are within appropriate bounds. The optimized anisotropic physical properties are identified by a numerical optimization technique based on a full-wave simulation using the finite element method. The cloaking performance measured by the total scattering width is improved by about 2.8% and 25% in eight- and three-layer cylindrical cloaking materials, respectively, compared with multilayer cloaking by isotropic materials. In all cloaking examples, the optimized microstructures of the two-phase composites are identified as the simple lamination of two materials, which maximizes the anisotropy. The same performance as published for eight-layer cloaking by isotropic materials is achieved by three-layer cloaking using the anisotropic material. Cloaking with an approximately 50% reduction of total scattering width is achieved even in an octagonal object. Since the cloaking effect can be realized using just a few layers of the laminated anisotropic dielectric composite, this may have an advantage in the mass production of cloaking devices.

  20. Scattering and Radiation from Anisotropic, Lossy Bodies of Revolution

    NASA Technical Reports Server (NTRS)

    Epp, L.; Hoppe, D.; Chinn, G.; Lee, J.

    1994-01-01

    The scattered fields from axisymmetric problems containing lossy dielectrics and an anisotropic media characterized by a lossless permeability tensor are found by the Hybrid Symmetric Finite Element (HSFEM) method. This method, recently applied to lossless ferrite objects, is applied to a lossy dielectric sphere. Extension of this method to scattering from cylindrical horns is discussed.

  1. Anisotropic contrast optical microscope

    NASA Astrophysics Data System (ADS)

    Peev, D.; Hofmann, T.; Kananizadeh, N.; Beeram, S.; Rodriguez, E.; Wimer, S.; Rodenhausen, K. B.; Herzinger, C. M.; Kasputis, T.; Pfaunmiller, E.; Nguyen, A.; Korlacki, R.; Pannier, A.; Li, Y.; Schubert, E.; Hage, D.; Schubert, M.

    2016-11-01

    An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent, or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. These images are obtained from sets of multiple images obtained under various polarizer, analyzer, and compensator settings. Up to 16 independent Mueller matrix images can be obtained, while our current setup is limited to 11 images normalized by the unpolarized intensity. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. Comparison with an isotropic glass slide demonstrates the image enhancement obtained by our method over microscopy without the use of an anisotropic filter. In our current instrument, we estimate the limit of detection for organic volumetric mass within the object plane of ≈49 fg within ≈7 × 7 μm2 object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of ≈500 pg for detection, the instrumentation demonstrated here improves

  2. Molecular anisotropic magnetoresistance

    NASA Astrophysics Data System (ADS)

    Otte, Fabian; Heinze, Stefan; Mokrousov, Yuriy

    2015-12-01

    Using density functional theory calculations, we demonstrate that the effect of anisotropic magnetoresistance (AMR) can be enhanced by orders of magnitude with respect to conventional bulk ferromagnets in junctions containing molecules sandwiched between ferromagnetic leads. We study ballistic transport in metal-benzene complexes contacted by 3 d transition-metal wires. We show that a gigantic AMR can arise from spin-orbit coupling effects in the leads, drastically enhanced by orbital-symmetry filtering properties of the molecules. We further discuss how this molecular anisotropic magnetoresistance (MAMR) can be tuned by the proper choice of materials and their electronic properties.

  3. Anisotropic contrast optical microscope.

    PubMed

    Peev, D; Hofmann, T; Kananizadeh, N; Beeram, S; Rodriguez, E; Wimer, S; Rodenhausen, K B; Herzinger, C M; Kasputis, T; Pfaunmiller, E; Nguyen, A; Korlacki, R; Pannier, A; Li, Y; Schubert, E; Hage, D; Schubert, M

    2016-11-01

    An optical microscope is described that reveals contrast in the Mueller matrix images of a thin, transparent, or semi-transparent specimen located within an anisotropic object plane (anisotropic filter). The specimen changes the anisotropy of the filter and thereby produces contrast within the Mueller matrix images. Here we use an anisotropic filter composed of a semi-transparent, nanostructured thin film with sub-wavelength thickness placed within the object plane. The sample is illuminated as in common optical microscopy but the light is modulated in its polarization using combinations of linear polarizers and phase plate (compensator) to control and analyze the state of polarization. Direct generalized ellipsometry data analysis approaches permit extraction of fundamental Mueller matrix object plane images dispensing with the need of Fourier expansion methods. Generalized ellipsometry model approaches are used for quantitative image analyses. These images are obtained from sets of multiple images obtained under various polarizer, analyzer, and compensator settings. Up to 16 independent Mueller matrix images can be obtained, while our current setup is limited to 11 images normalized by the unpolarized intensity. We demonstrate the anisotropic contrast optical microscope by measuring lithographically defined micro-patterned anisotropic filters, and we quantify the adsorption of an organic self-assembled monolayer film onto the anisotropic filter. Comparison with an isotropic glass slide demonstrates the image enhancement obtained by our method over microscopy without the use of an anisotropic filter. In our current instrument, we estimate the limit of detection for organic volumetric mass within the object plane of ≈49 fg within ≈7 × 7 μm(2) object surface area. Compared to a quartz crystal microbalance with dissipation instrumentation, where contemporary limits require a total load of ≈500 pg for detection, the instrumentation demonstrated here improves

  4. A robust anisotropic hyperelastic formulation for the modelling of soft tissue.

    PubMed

    Nolan, D R; Gower, A L; Destrade, M; Ogden, R W; McGarry, J P

    2014-11-01

    The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψ of the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψ is decoupled into volumetric and isochoric parts and the anisotropic part of Ψ is expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformations. To look at more practical applications, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model).

  5. Multidimensional Gravitational Model with Anisotropic Pressure

    NASA Astrophysics Data System (ADS)

    Grigorieva, O. A.; Sharov, G. S.

    2013-08-01

    We consider the gravitational model with additional spatial dimensions and anisotropic pressure which is nonzero only in these dimensions. Cosmological solutions of the Einstein equations in this model include accelerated expansion of the universe at late stage of its evolution and dynamical compactification of extra dimensions. This model describes observational data for Type Ia supernovae on the level or better than the ΛCDM model. We analyze two equations of state resulting in different predictions for further evolution, but in both variants the acceleration epoch is finite.

  6. Staggered Fermion Thermodynamics using Anisotropic Lattices

    NASA Astrophysics Data System (ADS)

    Levkova, L.

    2003-05-01

    Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with 2-flavors of dynamical fermions where all bare parameters and hence the physics scales are kept constant while the temperature is changed in small steps by varying only the number of the time slices. The results from a series of zero-temperature scale setting simulations are used to determine the Karsch coefficients and the equation of state at finite temperatures.

  7. Anisotropic eddy viscosity models

    NASA Technical Reports Server (NTRS)

    Carati, D.; Cabot, W.

    1996-01-01

    A general discussion on the structure of the eddy viscosity tensor in anisotropic flows is presented. The systematic use of tensor symmetries and flow symmetries is shown to reduce drastically the number of independent parameters needed to describe the rank 4 eddy viscosity tensor. The possibility of using Onsager symmetries for simplifying further the eddy viscosity is discussed explicitly for the axisymmetric geometry.

  8. Generalized anisotropic turbulence spectra and applications in the optical waves' propagation through anisotropic turbulence.

    PubMed

    Cui, Linyan; Xue, Bindang; Zhou, Fugen

    2015-11-16

    Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this work, two theoretical atmosphere refractive-index fluctuations spectral models are derived for optical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence. They consider simultaneously the finite turbulence inner and outer scales and the asymmetric property of turbulence eddies in the orthogonal xy-plane throughout the path. Two anisotropy factors which parameterize the asymmetry of turbulence eddies in both horizontal and vertical directions are introduced in the orthogonal xy-plane, so that the circular symmetry assumption of turbulence eddies in the xy-plane is no longer required. Deviations from the classic 11/3 power law behavior in the spectrum model are also allowed by assuming power law value variations between 3 and 4. Based on the derived anisotropic spectral model and the Rytov approximation theory, expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov turbulence. Calculations are performed to analyze the derived spectral models and the variance of AOA fluctuations.

  9. Constitutive modeling of inelastic anisotropic material response

    NASA Technical Reports Server (NTRS)

    Stouffer, D. C.

    1984-01-01

    A constitutive equation was developed to predict the inelastic thermomechanical response of single crystal turbine blades. These equations are essential for developing accurate finite element models of hot section components and contribute significantly to the understanding and prediction of crack initiation and propagation. The method used was limited to unified state variable constitutive equations. Two approaches to developing an anisotropic constitutive equation were reviewed. One approach was to apply the Stouffer-Bodner representation for deformation induced anisotropy to materials with an initial anisotropy such as single crystals. The second approach was to determine the global inelastic strain rate from the contribution of the slip in each of the possible crystallographic slip systems. A three dimensional finite element is being developed with a variable constitutive equation link that can be used for constitutive equation development and to predict the response of an experiment using the actual specimen geometry and loading conditions.

  10. Anisotropic hydrodynamics for conformal Gubser flow

    NASA Astrophysics Data System (ADS)

    Strickland, Michael; Nopoush, Mohammad; Ryblewski, Radoslaw

    2016-12-01

    In this proceedings contribution, we review the exact solution of the anisotropic hydrodynamics equations for a system subject to Gubser flow. For this purpose, we use the leading-order anisotropic hydrodynamics equations which assume that the distribution function is ellipsoidally symmetric in local-rest-frame momentum. We then prove that the SO(3)q symmetry in de Sitter space constrains the anisotropy tensor to be of spheroidal form with only one independent anisotropy parameter remaining. As a consequence, the exact solution reduces to the problem of solving two coupled non-linear differential equations. We show that, in the limit that the relaxation time goes to zero, one obtains Gubser's ideal hydrodynamic solution and, in the limit that the relaxation time goes to infinity, one obtains the exact free streaming solution obtained originally by Denicol et al. For finite relaxation time, we solve the equations numerically and compare to the exact solution of the relaxation-time-approximation Boltzmann equation subject to Gubser flow. Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.

  11. Longitudinal fluctuations and decorrelation of anisotropic flow

    NASA Astrophysics Data System (ADS)

    Pang, Long-Gang; Petersen, Hannah; Qin, Guang-You; Roy, Victor; Wang, Xin-Nian

    2016-12-01

    We investigate the decorrelation of 2nd and 3rd order anisotropic flow for charged particles in two different pseudo rapidity (η) windows by varying the pseudo rapidity gap, in an event-by-event (3+1)D ideal hydrodynamic model, with fluctuating initial conditions from A Multi-Phase Transport (AMPT) model. We visualize the parton distribution at initial state for Pb+Pb collisions at LHC and Au+Au collisions at RHIC, and demonstrate the longitudinal fluctuations originating from the asymmetry between forward and backward going participants, the fluctuations of the string length and the fluctuations due to finite number of partons at different beam energies. The decorrelation of anisotropic flow of final hadrons with large η gaps is found to originate from the spatial decorrelation along the longitudinal direction in the AMPT initial conditions through hydrodynamic evolution. The agreement between our results and recent CMS data in most centralities suggests that the string-like mechanism of initial parton production in AMPT model captures the initial longitudinal fluctuation that is responsible for the measured decorrelation of anisotropic flow in Pb+Pb collisions at LHC. Our predictions for Au+Au collisions at the highest RHIC energy show stronger longitudinal decorrelation than at LHC, indicating larger longitudinal fluctuations at lower beam energies.

  12. Anisotropic subvoxel-smooth conduction model for bioelectromagnetism analysis

    NASA Astrophysics Data System (ADS)

    He, Zhi Zhu; Liu, Jing

    2016-01-01

    The bioelectric conduction model plays a key role in bioelectromagnetism analysis, such as solving electromagnetic forward and inverse problems. This paper is aimed to develop an anisotropic subvoxel-smooth conduction model (ASCM) to characterize the electrical conductivity tensor jump across the tissue interface, which is derived based on the interfacial continuity condition with asymptotic analysis method. This conduction model is furthermore combined with finite volume method to improve the numerical accuracy for solving electromagnetic forward problem. The performance of ASCM for electrical potential analysis is verified by comparison with analytic solution. The method is also applied to investigate the effect of anisotropic conduction on EEG analysis in a realistic human head model.

  13. Tunable waveguide bends with graphene-based anisotropic metamaterials

    NASA Astrophysics Data System (ADS)

    Chen, Zhao-xian; Chen, Ze-guo; Ming, Yang; Wu, Ying; Lu, Yan-qing

    2016-02-01

    We design tunable waveguide bends filled with graphene-based anisotropic metamaterials to achieve a nearly perfect bending effect. The anisotropic properties of the metamaterials can be described by the effective medium theory. The nearly perfect bending effect is demonstrated by finite element simulations of various structures with different bending curvatures and shapes. This effect is attributed to zero effective permittivity along the direction of propagation and matched effective impedance at the interfaces between the bending part and the dielectric waveguides. We envisage that the design will be applicable in the far-infrared and terahertz frequency ranges owing to the tunable dielectric responses of graphene.

  14. Fractures in anisotropic media

    NASA Astrophysics Data System (ADS)

    Shao, Siyi

    Rocks may be composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties of a rock to be anisotropic. Coexisting fractures and layers in rock give rise to competing mechanisms of anisotropy. For example: (1) at low fracture stiffness, apparent shear-wave anisotropy induced by matrix layering can be masked or enhanced by the presence of a fracture, depending on the fracture orientation with respect to layering, and (2) compressional-wave guided modes generated by parallel fractures can also mask the presence of matrix layerings for particular fracture orientations and fracture specific stiffness. This report focuses on two anisotropic sources that are widely encountered in rock engineering: fractures (mechanical discontinuity) and matrix layering (impedance discontinuity), by investigating: (1) matrix property characterization, i.e., to determine elastic constants in anisotropic solids, (2) interface wave behavior in single-fractured anisotropic media, (3) compressional wave guided modes in parallel-fractured anisotropic media (single fracture orientation) and (4) the elastic response of orthogonal fracture networks. Elastic constants of a medium are required to understand and quantify wave propagation in anisotropic media but are affected by fractures and matrix properties. Experimental observations and analytical analysis demonstrate that behaviors of both fracture interface waves and compressional-wave guided modes for fractures in anisotropic media, are affected by fracture specific stiffness (controlled by external stresses), signal frequency and relative orientation between layerings in the matrix and fractures. A fractured layered medium exhibits: (1) fracture-dominated anisotropy when the fractures are weakly coupled; (2) isotropic behavior when fractures delay waves that are usually fast in a layered medium; and (3) matrix-dominated anisotropy when the fractures are closed and no longer delay the signal. The

  15. Parallel Anisotropic Tetrahedral Adaptation

    NASA Technical Reports Server (NTRS)

    Park, Michael A.; Darmofal, David L.

    2008-01-01

    An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

  16. Anisotropic Total Variation Filtering

    SciTech Connect

    Grasmair, Markus; Lenzen, Frank

    2010-12-15

    Total variation regularization and anisotropic filtering have been established as standard methods for image denoising because of their ability to detect and keep prominent edges in the data. Both methods, however, introduce artifacts: In the case of anisotropic filtering, the preservation of edges comes at the cost of the creation of additional structures out of noise; total variation regularization, on the other hand, suffers from the stair-casing effect, which leads to gradual contrast changes in homogeneous objects, especially near curved edges and corners. In order to circumvent these drawbacks, we propose to combine the two regularization techniques. To that end we replace the isotropic TV semi-norm by an anisotropic term that mirrors the directional structure of either the noisy original data or the smoothed image. We provide a detailed existence theory for our regularization method by using the concept of relaxation. The numerical examples concluding the paper show that the proposed introduction of an anisotropy to TV regularization indeed leads to improved denoising: the stair-casing effect is reduced while at the same time the creation of artifacts is suppressed.

  17. Anisotropic Weyl symmetry and cosmology

    SciTech Connect

    Moon, Taeyoon; Oh, Phillial; Sohn, Jongsu E-mail: ploh@skku.edu

    2010-11-01

    We construct an anisotropic Weyl invariant theory in the ADM formalism and discuss its cosmological consequences. It extends the original anisotropic Weyl invariance of Hořava-Lifshitz gravity using an extra scalar field. The action is invariant under the anisotropic transformations of the space and time metric components with an arbitrary value of the critical exponent z. One of the interesting features is that the cosmological constant term maintains the anisotropic symmetry for z = −3. We also include the cosmological fluid and show that it can preserve the anisotropic Weyl invariance if the equation of state satisfies P = zρ/3. Then, we study cosmology of the Einstein-Hilbert-anisotropic Weyl (EHaW) action including the cosmological fluid, both with or without anisotropic Weyl invariance. The correlation of the critical exponent z and the equation of state parameter ω-bar provides a new perspective of the cosmology. It is also shown that the EHaW action admits a late time accelerating universe for an arbitrary value of z when the anisotropic conformal invariance is broken, and the anisotropic conformal scalar field is interpreted as a possible source of dark energy.

  18. On the relativistic anisotropic configurations

    NASA Astrophysics Data System (ADS)

    Shojai, F.; Kohandel, M.; Stepanian, A.

    2016-06-01

    In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.

  19. Anisotropic multiple bounce models

    NASA Astrophysics Data System (ADS)

    Bacalhau, Anna Paula; Peter, Patrick; Vitenti, Sandro D. P.

    2017-07-01

    We analyze the Galileon ghost condensate implementation of a bouncing cosmological model in the presence of a non-negligible anisotropic stress. We exhibit its structure, which we find to be far richer than previously thought. In particular, even restricting attention to a single set of underlying microscopic parameters, we obtain, numerically, many qualitatively different regimes: depending on the initial conditions on the scalar field leading the dynamics of the Universe, the contraction phase can evolve directly towards a singularity, avoid it by bouncing once, or even bounce many times before settling into an ever-expanding phase. We clarify the behavior of the anisotropies in these various situations.

  20. High anisotropic pitch

    SciTech Connect

    Dickakian, G. B.

    1985-11-05

    An improved process for preparing an optically anisotropic pitch which comprises heating a pitch feed material at a temperature within the range of about 350/sup 0/ C. to 450/sup 0/ C. while passing an inert gas therethrough at a rate of at least 2.5 SCFH/lb of pitch feed material and agitating said pitch feed material at a stirrer rate of from about 500 to 600 rpm to obtain an essentially 100% mesophase pitch product suitable for carbon production.

  1. Anisotropic spinfoam cosmology

    NASA Astrophysics Data System (ADS)

    Rennert, Julian; Sloan, David

    2014-01-01

    The dynamics of a homogeneous, anisotropic universe are investigated within the context of spinfoam cosmology. Transition amplitudes are calculated for a graph consisting of a single node and three links—the ‘Daisy graph’—probing the behaviour a classical Bianchi I spacetime. It is shown further how the use of such single node graphs gives rise to a simplification of states such that all orders in the spin expansion can be calculated, indicating that it is the vertex expansion that contains information about quantum dynamics.

  2. A lowest-order composite finite element exact sequence on pyramids

    NASA Astrophysics Data System (ADS)

    Ainsworth, Mark; Fu, Guosheng

    2017-09-01

    Composite basis functions for pyramidal elements on the spaces $H^1(\\Omega)$, $H(\\mathrm{curl},\\Omega)$, $H(\\mathrm{div},\\Omega)$ and $L^2(\\Omega)$ are presented. In particular, we construct the lowest-order composite pyramidal elements and show that they respect the de Rham diagram, i.e. we have an exact sequence and satisfy the commuting property. Moreover, the finite elements are fully compatible with the standard finite elements for the lowest-order Raviart-Thomas-N\\'ed\\'elec sequence on tetrahedral and hexahedral elements. That is to say, the new elements have the same degrees of freedom on the shared interface with the neighbouring hexahedral or tetrahedra elements, and the basis functions are conforming in the sense that they maintain the required level of continuity (full, tangential component, normal component, ...) across the interface. Furthermore, we study the approximation properties of the spaces as an initial partition consisting of tetrahedra, hexahedra and pyramid elements is successively subdivided and show that the spaces result in the same (optimal) order of approximation in terms of the mesh size $h$ as one would obtain using purely hexahedral or purely tetrahedral partitions.

  3. Seismic Gradiometry using Ambient Seismic Noise in an Anisotropic Earth

    NASA Astrophysics Data System (ADS)

    de Ridder, S. A. L.; Curtis, A.

    2017-02-01

    We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results where obtained using only a few minutes of ambient seismic noise.

  4. Seismic gradiometry using ambient seismic noise in an anisotropic Earth

    NASA Astrophysics Data System (ADS)

    de Ridder, S. A. L.; Curtis, A.

    2017-05-01

    We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

  5. Inhomogeneous anisotropic cosmology

    NASA Astrophysics Data System (ADS)

    Kleban, Matthew; Senatore, Leonardo

    2016-10-01

    In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with ``flat'' (including toroidal) and ``open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are ``flat'' or ``open''. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with ``flat'' or ``open'' topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.

  6. Inhomogeneous anisotropic cosmology

    SciTech Connect

    Kleban, Matthew; Senatore, Leonardo

    2016-10-12

    In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with “flat” (including toroidal) and “open” (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are “flat” or “open”. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with “flat” or “open” topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.

  7. Inhomogeneous anisotropic cosmology

    DOE PAGES

    Kleban, Matthew; Senatore, Leonardo

    2016-10-12

    In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarilymore » large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.« less

  8. Inhomogeneous anisotropic cosmology

    SciTech Connect

    Kleban, Matthew; Senatore, Leonardo

    2016-10-12

    In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here in this paper, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with "flat'' (including toroidal) and "open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are "flat" or "open". Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with "flat'' or "open" topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.

  9. Anisotropic Particles in Turbulence

    NASA Astrophysics Data System (ADS)

    Voth, Greg A.; Soldati, Alfredo

    2017-01-01

    Anisotropic particles are common in many industrial and natural turbulent flows. When these particles are small and neutrally buoyant, they follow Lagrangian trajectories while exhibiting rich orientational dynamics from the coupling of their rotation to the velocity gradients of the turbulence field. This system has proven to be a fascinating application of the fundamental properties of velocity gradients in turbulence. When particles are not neutrally buoyant, they experience preferential concentration and very different preferential alignment than neutrally buoyant tracer particles. A vast proportion of the parameter range of anisotropic particles in turbulence is still unexplored, with most existing research focusing on the simple foundational cases of axisymmetric ellipsoids at low concentrations in homogeneous isotropic turbulence and in turbulent channel flow. Numerical simulations and experiments have recently developed a fairly comprehensive picture of alignment and rotation in these cases, and they provide an essential foundation for addressing more complex problems of practical importance. Macroscopic effects of nonspherical particle dynamics include preferential concentration in coherent structures and drag reduction by fiber suspensions. We review the models used to describe nonspherical particle motion, along with numerical and experimental methods for measuring particle dynamics.

  10. Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Hopkins, Philip F.

    2017-04-01

    We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

  11. Analytical Yield Criterion for an Anisotropic Material Containing Spherical Voids and Exhibiting Tension-Compression Asymmetry

    DTIC Science & Technology

    2011-11-01

    an overview of experimental evidence for anisotropic ductile fracture in steels ). Liao et al. (1997) extended Gurson’s (1977) cylindrical criterion to...validate these anisotropic Gurson-like criteria (e.g., Chien et al., 2001; Wang and Pan, 2004). Generally, finite-element analyses of a cube containing...in the absence of voids, some materials with cubic crystal structure (see Benzerga et al., 2004a, for experimental data on high strength steels ) are

  12. Time-independent Anisotropic Plastic Behavior by Mechanical Subelement Models

    NASA Technical Reports Server (NTRS)

    Pian, T. H. H.

    1983-01-01

    The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the iscoplasticity-theory.

  13. Stopping light by an air waveguide with anisotropic metamaterial cladding.

    PubMed

    Jiang, Tian; Zhao, Junming; Feng, Yijun

    2009-01-05

    We present a detailed study of oscillating modes in a slab waveguide with air core and anisotropic metamaterial cladding. It is shown that, under specific dielectric configurations, slow and even stopped electromagnetic wave can be supported by such an air waveguide. We propose a linearly tapped waveguide structure that could lead the propagating light to a complete standstill. Both the theoretical analysis and the proposed waveguide have been validated by full-wave simulation based on finite-difference time-domain method.

  14. Anisotropic power-law inflation

    SciTech Connect

    Kanno, Sugumi; Soda, Jiro; Watanabe, Masa-aki E-mail: jiro@tap.scphys.kyoto-u.ac.jp

    2010-12-01

    We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.

  15. Mixed-hybrid and vertex-discontinuous-Galerkin finite element modeling of multiphase compositional flow on 3D unstructured grids

    NASA Astrophysics Data System (ADS)

    Moortgat, Joachim; Firoozabadi, Abbas

    2016-06-01

    Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element methods accurately describe flow on unstructured meshes with complex geometries, and their flexible formulation allows implementation on different grid types. In this work, we consider for the first time the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by any combination of tetrahedra, prisms, and hexahedra. We employ a mass conserving mixed hybrid finite element (MHFE) method to solve for the pressure and flux fields. The transport equations are approximated with a higher-order vertex-based discontinuous Galerkin (DG) discretization. We show that this approach outperforms a face-based implementation of the same polynomial order. These methods are well suited for heterogeneous and fractured reservoirs, because they provide globally continuous pressure and flux fields, while allowing for sharp discontinuities in compositions and saturations. The higher-order accuracy improves the modeling of strongly non-linear flow, such as gravitational and viscous fingering. We review the literature on unstructured reservoir simulation models, and present many examples that consider gravity depletion, water flooding, and gas injection in oil saturated reservoirs. We study convergence rates, mesh sensitivity, and demonstrate the wide applicability of our chosen finite element methods for challenging multiphase flow problems in geometrically complex subsurface media.

  16. Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy

    NASA Astrophysics Data System (ADS)

    Cervera, M.; Barbat, G. B.; Chiumenti, M.

    2017-07-01

    This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force-displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson's ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem.

  17. Improved finite-element methods for rotorcraft structures

    NASA Technical Reports Server (NTRS)

    Hinnant, Howard E.

    1991-01-01

    An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.

  18. Anisotropic Kepler and anisotropic two fixed centres problems

    NASA Astrophysics Data System (ADS)

    Maciejewski, Andrzej J.; Przybylska, Maria; Szumiński, Wojciech

    2017-02-01

    In this paper we show that the anisotropic Kepler problem is dynamically equivalent to a system of two point masses which move in perpendicular lines (or planes) and interact according to Newton's law of universal gravitation. Moreover, we prove that generalised version of anisotropic Kepler problem as well as anisotropic two centres problem are non-integrable. This was achieved thanks to investigation of differential Galois groups of variational equations along certain particular solutions. Properties of these groups yield very strong necessary integrability conditions.

  19. Thermodynamics of anisotropic branes

    NASA Astrophysics Data System (ADS)

    Ávila, Daniel; Fernández, Daniel; Patiño, Leonardo; Trancanelli, Diego

    2016-11-01

    We study the thermodynamics of flavor D7-branes embedded in an anisotropic black brane solution of type IIB supergravity. The flavor branes undergo a phase transition between a `Minkowski embedding', in which they lie outside of the horizon, and a `black hole embedding', in which they fall into the horizon. This transition depends on the black hole temperature, its degree of anisotropy, and the mass of the flavor degrees of freedom. It happens either at a critical temperature or at a critical anisotropy. A general lesson we learn from this analysis is that the anisotropy, in this particular realization, induces similar effects as the temperature. In particular, increasing the anisotropy bends the branes more and more into the horizon. Moreover, we observe that the transition becomes smoother for higher anisotropies.

  20. Anisotropic Elastic-Waveform Modeling for Fracture Characterization in EGS Reservoirs

    SciTech Connect

    Gao, Kai; Huang, Lianjie

    2015-01-28

    Enhanced geothermal systems (EGS) contain newly created fractures in addition to possible existing fractures. Accurate characterization and monitoring of EGS reservoirs are crucial for optimal placement of new wells and effective extraction of geothermal heat. The fractured reservoirs behave as anisotropic media where seismic waves propagate with different velocities along different directions. In addition, the anisotropic properties of fluid-filled fracture zones could be different from those of dry fracture zones. We develop an optimized rotated staggered-grid elastic-wave finite-difference method for simulating seismic-wave propagation in heterogeneous, anisotropic media. Our new method uses a few extra grid points and optimized finite-difference coefficients based on the space-time dispersion relation, and reduce numerical dispersion of the conventional rotated staggered-grid finite-difference scheme. We validate our new method using synthetic vertical-seismic-profiling (VSP) data for an anisotropic geophysical model built with geologic features found at the Raft River EGS reservoir. This improved and optimized rotated staggered-grid finite-difference method provides an essential tool for analyzing VSP data, reverse-time migration, and elastic-waveform inversion in anisotropic, fractured reservoirs.

  1. Shear waves in acoustic anisotropic media

    SciTech Connect

    Grechka, Vladimir; Zhang, Linbin; Rector, James W.

    2003-01-02

    Acoustic transversely isotropic (TI) media are defined by artificially setting the shear-wave velocity in the direction of symmetry axis, VS0, to zero. Contrary to conventional wisdom that equating VS0 = 0 eliminates shear waves, we demonstrate their presence and examine their properties. Specifically, we show that SV-waves generally have finite nonzero phase and group velocities in acoustic TI media. In fact, these waves have been observed in full waveform modeling, but apparently they were not understood and labeled as numerical artifacts. Acoustic TI media are characterized by extreme, in some sense infinite strength of anisotropy. It makes the following unusual wave phenomena possible: (1) there are propagation directions, where the SV-ray is orthogonal to the corresponding wavefront normal, (2) the SV-wave whose ray propagates along the symmetry axis is polarized parallel to the P-wave propagating in the same direction, (3) P-wave singularities, that is, directions where P- and SV -wave phase velocities coincide might exist in acoustic TI media. We also briefly discuss some aspects of wave propagation in low-symmetry acoustic anisotropic models. Extreme anisotropy in those media creates bizarre phase- and group-velocity surfaces that might bring intellectual delight to an anisotropic guru.

  2. Anisotropic hydraulic permeability in compressed articular cartilage.

    PubMed

    Reynaud, Boris; Quinn, Thomas M

    2006-01-01

    The extent to which articular cartilage hydraulic permeability is anisotropic is largely unknown, despite its importance for understanding mechanisms of joint lubrication, load bearing, transport phenomena, and mechanotransduction. We developed and applied new techniques for the direct measurement of hydraulic permeability within statically compressed adult bovine cartilage explant disks, dissected such that disk axes were perpendicular to the articular surface. Applied pressure gradients were kept small to minimize flow-induced matrix compaction, and fluid outflows were measured by observation of a meniscus in a glass capillary under a microscope. Explant disk geometry under radially unconfined axial compression was measured by direct microscopic observation. Pressure, flow, and geometry data were input to a finite element model where hydraulic permeabilities in the disk axial and radial directions were determined. At less than 10% static compression, near free-swelling conditions, hydraulic permeability was nearly isotropic, with values corresponding to those of previous studies. With increasing static compression, hydraulic permeability decreased, but the radially directed permeability decreased more dramatically than the axially directed permeability such that strong anisotropy (a 10-fold difference between axial and radial directions) in the hydraulic permeability tensor was evident for static compression of 20-40%. Results correspond well with predictions of a previous microstructurally-based model for effects of tissue mechanical deformations on glycosaminoglycan architecture and cartilage hydraulic permeability. Findings inform understanding of structure-function relationships in cartilage matrix, and suggest several biomechanical roles for compression-induced anisotropic hydraulic permeability in articular cartilage.

  3. A FDM anisotropic formulation for EEG simulation.

    PubMed

    Bruno, P; Hyttinen, J; Inchingolo, P; Magrofuoco, A; Mininel, S; Vatta, F

    2006-01-01

    Accurate head modeling is required to properly simulate bioelectric phenomena in 3-D as well as to estimate the 3-D bioelectric activity starting from superficial bioelectric measurements and 3-D imaging. Aiming to build an accurate and realistic representation of the volume conductor of the head, also the anisotropy of head tissues should be taken into account. In this paper we describe a new finite-difference method (FDM) formulation which accounts for anisotropy of the various head tissues. Our proposal, being based on FDM, derives the head model directly from patient's specific clinical images. We present here the details of the numerical formulation and the method validation by comparing our numerical proposal and known analytical results using a multi-shell anisotropic head model with skull anisotropy. Furthermore, we analyzed also different numerical grid refinement and EEG source characteristics. The comparison with previously developed FDM methods shows a good performance of the proposed method.

  4. Optical trapping of anisotropic nanocylinder

    NASA Astrophysics Data System (ADS)

    Bareil, Paul B.; Sheng, Yunlong

    2013-09-01

    The T-matrix method with the Vector Spherical Wave Function (VSWF) expansions represents some difficulties for computing optical scattering of anisotropic particles. As the divergence of the electric field is nonzero in the anisotropic medium and the VSWFs do not satisfy the anisotropic wave equations one questioned whether the VSWFs are still a suitable basis in the anisotropic medium. We made a systematic and careful review on the vector basis functions and the VSWFs. We found that a field vector in Euclidean space can be decomposed to triplet vectors {L, M, N}, which as non-coplanar. Especially, the vector L is designed to represent non-zero divergence component of the vector solution, so that the VSWF basis is sufficiently general to represent the solutions of the anisotropic wave equation. The mathematical proof can be that when the anisotropic wave equations is solved in the Fourier space, the solution is expanded in the basis of the plan waves with angular spectrum amplitude distributions. The plane waves constitute an orthogonal and complete set for the anisotropic solutions. Furthermore, the plane waves are expanded into the VSWF basis. These two-step expansions are equivalent to the one-step direct expansion of the anisotropic solution to the VSWF basis. We used direct VSWF expansion, along with the point-matching method in the T-matrix, and applied the boundary condition to the normal components displacement field in order to compute the stress and the related forces and torques and to show the mechanism of the optical trap of the anisotropic nano-cylinders.

  5. Standing shear waves in anisotropic viscoelastic media

    NASA Astrophysics Data System (ADS)

    Krit, T.; Golubkova, I.; Andreev, V.

    2015-10-01

    We studied standing shear waves in anisotropic resonator represented by a rectangular parallelepiped (layer) fixed without slipping between two wooden plates of finite mass. The viscoelastic layer with edges of 70 mm × 40 mm × 15 mm was made of a rubber-like polymer plastisol with rubber bands inside. The bands were placed vertical between the top and the bottom plate. Mechanical properties of the plastisol itself were carefully measured previously. It was found that plastisol shows a cubic nonlinear behavior, i.e. the stress-strain curve could be represented as: σ = μɛ + βμɛ3, where ɛ stands for shear strain and σ is an applied shear stress. The value of shear modulus μ depends on frequency and was found to be several kilopascals which is common for such soft solids. Nonlinear parameter β is frequency dependent too and varies in range from tenths to unity at 1-100 Hz frequency range, decreasing with frequency growth. Stretching the rubber bands inside the layer leads to change of elastic properties in resonator. Such effect could be noticed due to frequency response of the resonator. The numerical model of the resonator was based on finite elements method (FEM) and performed in MatLab. The resonator was cut in hundreds of right triangular prisms. Each prism was provided with viscoelastic properties of the layer except for the top prisms provided with the wooden plate properties and the prisms at the site of the rubber bands provided with the rubber properties. The boundary conditions on each prism satisfied the requirements that resonator is inseparable and all its boundaries but bottom are free. The bottom boundary was set to move horizontally with constant acceleration amplitude. It was shown numerically that the resonator shows anisotropic behavior expressed in different frequency response to oscillations applied to a bottom boundary in different directions.

  6. Vortex dynamics in anisotropic traps

    SciTech Connect

    McEndoo, S.; Busch, Th.

    2010-07-15

    We investigate the dynamics of linear vortex lattices in anisotropic traps in two dimensions and show that the interplay between the rotation and the anisotropy leads to a rich but highly regular dynamics.

  7. Cracking on anisotropic neutron stars

    NASA Astrophysics Data System (ADS)

    Setiawan, A. M.; Sulaksono, A.

    2017-07-01

    We study the effect of cracking of a local anisotropic neutron star (NS) due to small density fluctuations. It is assumed that the neutron star core consists of leptons, nucleons and hyperons. The relativistic mean field model is used to describe the core of equation of state (EOS). For the crust, we use the EOS introduced by Miyatsu et al. [1]. Furthermore, two models are used to describe pressure anisotropic in neutron star matter. One is proposed by Doneva-Yazadjiev (DY) [2] and the other is proposed by Herrera-Barreto (HB) [3]. The anisotropic parameter of DY and HB models are adjusted in order the predicted maximum mass compatible to the mass of PSR J1614-2230 [4] and PSR J0348+0432 [5]. We have found that cracking can potentially present in the region close to the neutron star surface. The instability due cracking is quite sensitive to the NS mass and anisotropic parameter used.

  8. Actuation performances of anisotropic gels

    NASA Astrophysics Data System (ADS)

    Nardinocchi, P.; Teresi, L.

    2016-12-01

    We investigated the actuation performances of anisotropic gels driven by mechanical and chemical stimuli, in terms of both deformation processes and stroke-curves, and distinguished between the fast response of gels before diffusion starts and the asymptotic response attained at the steady state. We also showed as the range of forces that an anisotropic hydrogel can exert when constrained is especially wide; indeed, changing fiber orientation allows us to induce shear as well as transversely isotropic extensions.

  9. Anisotropic assembly and pattern formation

    NASA Astrophysics Data System (ADS)

    von Brecht, James H.; Uminsky, David T.

    2017-01-01

    We investigate the role of anisotropy in two classes of individual-based models for self-organization, collective behavior and self-assembly. We accomplish this via first-order dynamical systems of pairwise interacting particles that incorporate anisotropic interactions. At a continuum level, these models represent the natural anisotropic variants of the well-known aggregation equation. We leverage this framework to analyze the impact of anisotropic effects upon the self-assembly of co-dimension one equilibrium structures, such as micelles and vesicles. Our analytical results reveal the regularizing effect of anisotropy, and isolate the contexts in which anisotropic effects are necessary to achieve dynamical stability of co-dimension one structures. Our results therefore place theoretical limits on when anisotropic effects can be safely neglected. We also explore whether anisotropic effects suffice to induce pattern formation in such particle systems. We conclude with brief numerical studies that highlight various aspects of the models we introduce, elucidate their phase structure and partially validate the analysis we provide.

  10. Finite Earth

    NASA Astrophysics Data System (ADS)

    2015-10-01

    The world has agreed on 17 Sustainable Development Goals, to be adopted this week. This is great progress towards acknowledging that the planet's finite resources need to be managed carefully in the face of humanity's unlimited aspirations.

  11. Anisotropic Mesh Adaptivity for FE-simulation of cardiovascular flow

    NASA Astrophysics Data System (ADS)

    Mueller, Jens; Sahni, Onkar; Jansen, Kenneth E.; Shephard, Mark S.; Taylor, Charles A.

    2004-11-01

    In this study we present an adaptive anisotropic finite element method and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the weak SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretized by linear finite elements, both for the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptavity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical pipe and then to a pig artery with a stenosis bypassed by a graft. The efficiency of the method is measured in terms of computational savings when we compute the wall shear stresses, a quantity identified to be important to understanding arterial disease.

  12. Anisotropic Alfven-ballooning modes in the Earth's magnetosphere

    SciTech Connect

    Chan, A.A. . Dept. of Physics and Astronomy); Xia, Mengfen . Dept. of Physics); Chen, Liu . Plasma Physics Lab.)

    1993-05-01

    We have carried out a theoretical analysis of the stability and parallel structure of coupled shear-Alfven and slow-magnetosonic waves in the Earth's inner magnetosphere including effects of finite anisotropic plasma pressure. Multiscale perturbation analysis of the anisotropic Grad-Shafranov equation yields an approximate self-consistent magnetohydrodynamic (MHD) equilibrium. This MHD equilibrium is used in the numerical solution of a set of eigenmode equations which describe the field line eigenfrequency, linear stability, and parallel eigenmode structure. We call these modes anisotropic Alfven-ballooning modes. The main results are: The field line eigenfrequency can be significantly lowered by finite pressure effects. The parallel mode structure of the transverse wave components is fairly insensitive to changes in the plasma pressure but the compressional magnetic component can become highly peaked near the magnetic equator due to increased pressure, especially when P[perpendicular] > P[parallel]. For the isotropic case ballooning instability can occur when the ratio of the plasma pressure to the magnetic pressure, exceeds a critical value [beta][sub o][sup B] [approx] 3.5 at the equator. Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field-line-bending stabilization when P[parallel] > P[perpendicular], or due to increased ballooning-mirror destabilization when P[perpendicular] > P[parallel]. We use a [beta]-6 stability diagram'' to display the regions of instability with respect to the equatorial values of the parameters [bar [beta

  13. Light propagation through anisotropic turbulence.

    PubMed

    Toselli, Italo; Agrawal, Brij; Restaino, Sergio

    2011-03-01

    A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς(2-α).

  14. Deep Tunnel in Transversely Anisotropic Rock with Groundwater Flow

    NASA Astrophysics Data System (ADS)

    Bobet, Antonio

    2016-12-01

    Closed-form solutions for the stresses and deformations induced in the ground and tunnel liner are provided for a deep tunnel in a transversely anisotropic elastic rock, with anisotropic permeability, when subjected to groundwater seepage. Complex variable theory and conformal mapping are used to obtain the solutions; additional complex functions, necessary to prevent multiple solutions of the displacements, are included. The analytical solutions are verified by comparing their results from those of a finite element method. Simplified formulations are presented for tunnels with a perfectly flexible and completely incompressible liner. A spreadsheet is included that can be used to obtain stresses and displacements of the liner due to groundwater flow and far-field geostatic stresses.

  15. Dynamic pressure-shear loading of materials using anisotropic crystals

    NASA Astrophysics Data System (ADS)

    Chhabildas, L. C.; Swegle, J. W.

    1980-09-01

    An experimental technique is described which uses anisotropic crystals to generate dynamic pressure-shear loading in materials. The coupled longitudinal and shear motion generated upon planar impact of the anisotropic crystal can be transmitted into a specimen bonded to the rear surface of the crystal, and monitored using velocity interferometer techniques. Test results using y-cut quartz generators and x-cut quartz and y-cut quartz samples indicate that shear stresses up to 0.35 GPa can be transmitted across epoxy-bonded interfaces. The technique has been successfully used to detect a 0.2 GPa shear wave in 6061-T6 aluminum at 0.7 GPa longitudinal stress. The shear wave velocity profiles have an accuracy of ±12%. The use of longer delay legs in the interferometer is suggested to improve the accuracy. Results obtained in this investigation are compared with numerical solutions obtained using the finite-difference wave propagation code TOODY.

  16. Time-independent one-speed neutron transport equation with anisotropic scattering in absorbing media

    SciTech Connect

    Hangelbroek, R. J.

    1980-06-01

    This report treats the time-independent, one-speed neutron transport equation with anisotropic scattering in absorbing media. For nuclear gain operators existence and uniqueness of solutions to the half-space and finite-slab problems are proved in L/sub 2/-space. The formulas needed for explicit calculations are derived by the use of perturbation theory techniques.

  17. Anisotropic lattice models of electrolytes

    NASA Astrophysics Data System (ADS)

    Kobelev, Vladimir; Kolomeisky, Anatoly B.

    2002-11-01

    Systems of charged particles on anisotropic three-dimensional lattices are investigated theoretically using Debye-Huckel theory. It is found that the thermodynamics of these systems strongly depends on the degree of anisotropy. For weakly anisotropic simple cubic lattices, the results indicate the existence of order-disorder phase transitions and a tricritical point, while the possibility of low-density gas-liquid coexistence is suppressed. For strongly anisotropic lattices this picture changes dramatically: The low-density gas-liquid phase separation reappears and the phase diagram exhibits critical, tricritical, and triple points. For body-centered lattices, the low-density gas-liquid phase coexistence is suppressed for all degrees of anisotropy. These results show that the effect of anisotropy in lattice models of electrolytes amounts to reduction of spatial dimensionality.

  18. Fluctuation relations for anisotropic systems

    NASA Astrophysics Data System (ADS)

    Villavicencio-Sanchez, R.; Harris, R. J.; Touchette, H.

    2014-02-01

    Currents of particles or energy in driven non-equilibrium steady states are known to satisfy certain symmetries, referred to as fluctuation relations, determining the ratio of the probabilities of positive fluctuations to negative ones. A generalization of these fluctuation relations has been proposed recently for extended non-equilibrium systems of dimension greater than one, assuming, crucially, that they are isotropic (Hurtado P. I., Pérez-Espigares C., del Pozo J. J. and Garrido P. L., Proc. Natl. Acad. Sci. U.S.A., 108 (2011) 7704). Here we relax this assumption and derive a fluctuation relation for d-dimensional systems having anisotropic bulk driving rates. We test the validity of this anisotropic fluctuation relation by calculating the particle current fluctuations in the 2d anisotropic zero-range process, using both exact and fluctuating hydrodynamic approaches.

  19. Anisotropic superfluidity in a dipolar Bose gas

    SciTech Connect

    Ticknor, Christopher; Wilson, Ryan M; Bohn, John L

    2010-11-04

    A quintessential feature of superfluidity is the ability to support dissipationless flow, for example, when an object moves through a superfluid and experiences no drag. This, however, only occurs when the object is moving below a certain critical velocity; when it exceeds this critical velocity it dissipates energy into excitations of the superfluid, resulting in a net drag force on the object and the breakdown of superfluid flow. In many superfluids, such as dilute Bose-Einstein condensates (BECs) of atoms with contact interactions, this critical velocity is simply the speed of sound in the system, where the speed of sound is set by the density and the s-wave scattering length of the atoms. However, for other superfluids, such as liquid {sup 4}He, this is not the case. In {sup 4}He, the critical velocity is set by a roton mode, corresponding to a peak in the static structure factor of the system at some finite, non-zero momentum, with a characteristic velocity that is considerably less than the speed of sound in the liquid. This feature has been verified experimentally via measurements of ion-drift velocity in the fluid, thereby providing insight into the detailed structure of the system. Interestingly, a roton-like feature was predicted to exist in the dispersion relation of a quasi-two-dimensional (q2D) dipolar BEC (DBEC) [16], or a BEC with dipole-dipole interactions. However, unlike the dispersion of {sup 4}He, the disperSion of a DBEC is highly tunable as a function of the condensate density or dipole-dipole interaction (ddi) strength. Additionally, the DBEC is set apart from liquid {sup 4}He in that its interactions depend on how the dipoles are oriented in space. Thus, the DBEC provides an ideal system to study the effects that anisotropies have on the bulk properties of a superfluid, such as the critical velocity. Here we consider a DBEC in a quasi-two-dimensional (q2D) geometry and allow for the dipoles to be polarized at a nonzero angle into the plane

  20. Anisotropically structured magnetic aerogel monoliths

    NASA Astrophysics Data System (ADS)

    Heiligtag, Florian J.; Airaghi Leccardi, Marta J. I.; Erdem, Derya; Süess, Martin J.; Niederberger, Markus

    2014-10-01

    Texturing of magnetic ceramics and composites by aligning and fixing of colloidal particles in a magnetic field is a powerful strategy to induce anisotropic chemical, physical and especially mechanical properties into bulk materials. If porosity could be introduced, anisotropically structured magnetic materials would be the perfect supports for magnetic separations in biotechnology or for magnetic field-assisted chemical reactions. Aerogels, combining high porosity with nanoscale structural features, offer an exceptionally large surface area, but they are difficult to magnetically texture. Here we present the preparation of anatase-magnetite aerogel monoliths via the assembly of preformed nanocrystallites. Different approaches are proposed to produce macroscopic bodies with gradient-like magnetic segmentation or with strongly anisotropic magnetic texture.Texturing of magnetic ceramics and composites by aligning and fixing of colloidal particles in a magnetic field is a powerful strategy to induce anisotropic chemical, physical and especially mechanical properties into bulk materials. If porosity could be introduced, anisotropically structured magnetic materials would be the perfect supports for magnetic separations in biotechnology or for magnetic field-assisted chemical reactions. Aerogels, combining high porosity with nanoscale structural features, offer an exceptionally large surface area, but they are difficult to magnetically texture. Here we present the preparation of anatase-magnetite aerogel monoliths via the assembly of preformed nanocrystallites. Different approaches are proposed to produce macroscopic bodies with gradient-like magnetic segmentation or with strongly anisotropic magnetic texture. Electronic supplementary information (ESI) available: Digital photographs of dispersions and gels with different water-to-ethanol ratios; magnetic measurements of an anatase aerogel containing 0.25 mol% Fe3O4 nanoparticles; XRD patterns of the iron oxide and

  1. Barkhausen avalanches in anisotropic ferromagnets with 180 degrees domain walls

    PubMed

    Tadic; Nowak

    2000-04-01

    We show that Barkhausen noise in two-dimensional disordered ferromagnets with extended domain walls is characterized by the avalanche size exponent tau(s)=1.54 at low disorder. With increasing disorder the characteristic domain size is reduced relative to the system size due to nucleation of new domains and a dynamic phase transition occurs to the scaling behavior with tau(s)=1.30. The exponents decrease at finite driving rate. The results agree with recently observed behavior in amorphous Metglas and Fe-Co-B ribbons when the applied anisotropic stress is varied.

  2. Two-flavor QCD thermodynamics using anisotropic lattices

    NASA Astrophysics Data System (ADS)

    Levkova, Ludmila; Manke, Thomas; Mawhinney, Robert

    2006-04-01

    Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale-setting simulations, which determine the Karsch coefficients, allows for the calculation of the equation of state at finite temperatures.

  3. Anisotropic linear elastic properties of fractal-like composites.

    PubMed

    Carpinteri, Alberto; Cornetti, Pietro; Pugno, Nicola; Sapora, Alberto

    2010-11-01

    In this work, the anisotropic linear elastic properties of two-phase composite materials, made up of square inclusions embedded in a matrix, are investigated. The inclusions present a fractal hierarchical distribution and are supposed to have the same Poisson's ratio as the matrix but a different Young's modulus. The effective elastic moduli of the medium are computed at each fractal iteration by coupling a position-space renormalization-group technique with a finite element analysis. The study allows to obtain and generalize some fundamental properties of fractal composite materials.

  4. Anisotropic linear elastic properties of fractal-like composites

    NASA Astrophysics Data System (ADS)

    Carpinteri, Alberto; Cornetti, Pietro; Pugno, Nicola; Sapora, Alberto

    2010-11-01

    In this work, the anisotropic linear elastic properties of two-phase composite materials, made up of square inclusions embedded in a matrix, are investigated. The inclusions present a fractal hierarchical distribution and are supposed to have the same Poisson’s ratio as the matrix but a different Young’s modulus. The effective elastic moduli of the medium are computed at each fractal iteration by coupling a position-space renormalization-group technique with a finite element analysis. The study allows to obtain and generalize some fundamental properties of fractal composite materials.

  5. Geometric multigrid to accelerate the solution of the quasi-static electric field problem by tetrahedral finite elements.

    PubMed

    Hollaus, K; Weiss, B; Magele, Ch; Hutten, H

    2004-02-01

    The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.

  6. Arbitrarily laminated, anisotropic cylindrical shell under internal pressure

    NASA Technical Reports Server (NTRS)

    Chaudhuri, Reaz Z.; Balaraman, K.; Kunukkasseril, Vincent X.

    1986-01-01

    An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

  7. Arbitrarily laminated, anisotropic cylindrical shell under internal pressure

    NASA Technical Reports Server (NTRS)

    Chaudhuri, Reaz Z.; Balaraman, K.; Kunukkasseril, Vincent X.

    1986-01-01

    An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

  8. Identifying heterogeneous anisotropic properties in cerebral aneurysms: a pointwise approach.

    PubMed

    Zhao, Xuefeng; Raghavan, Madhavan L; Lu, Jia

    2011-04-01

    The traditional approaches of estimating heterogeneous properties in a soft tissue structure using optimization-based inverse methods often face difficulties because of the large number of unknowns to be simultaneously determined. This article proposes a new method for identifying the heterogeneous anisotropic nonlinear elastic properties in cerebral aneurysms. In this method, the local properties are determined directly from the pointwise stress-strain data, thus avoiding the need for simultaneously optimizing for the property values at all points/regions in the aneurysm. The stress distributions needed for a pointwise identification are computed using an inverse elastostatic method without invoking the material properties in question. This paradigm is tested numerically through simulated inflation tests on an image-based cerebral aneurysm sac. The wall tissue is modeled as an eight-ply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain energy function containing four parameters. The parameters are assumed to vary continuously in the sac. Deformed configurations generated from forward finite element analysis are taken as input to inversely establish the parameter distributions. The delineated and the assigned distributions are in excellent agreement. A forward verification is conducted by comparing the displacement solutions obtained from the delineated and the assigned material parameters at a different pressure. The deviations in nodal displacements are found to be within 0.2% in most part of the sac. The study highlights some distinct features of the proposed method, and demonstrates the feasibility of organ level identification of the distributive anisotropic nonlinear properties in cerebral aneurysms.

  9. Numerical simulation and rational design of optically anisotropic columnar films

    NASA Astrophysics Data System (ADS)

    Leontyev, Viktor A.; Hawkeye, Matthew M.; Wakefield, Nicholas G.; Tabunshchyk, Kyrylo; Sit, Jeremy C.; Kovalenko, Andriy; Brett, Michael J.

    2011-03-01

    Optical anisotropy is an inherent property of columnar dielectric films, such as those fabricated by the glancing angle deposition (GLAD) technique. This process utilizes physical vapor deposition combined with computer-controlled substrate motion to finely tune the direction of column growth and vital morphological parameters such as column cross-section and inter-columnar spacing. Control over the anisotropic properties of the porous film provides an opportunity to design polarization-selective photonic devices and films with improved band gap properties. Anisotropic defects in multilayer films also result in a polarization-sensitive position of resonant transmission modes. We employed the finite-difference time-domain and frequency-domain methods to theoretically analyze and design columnar films with unique band-gap properties. The following morphologies were considered: (i) S-shaped columnar films with polarization-dependent band-gap position and width. Using numerical simulations we have shown that the competitive effect of different sources of anisotropy can be used to engineer photonic band gaps with strong selectivity to linearly-polarized light; (ii) Rugate thin films with an anisotropic defect, which exhibit resonant mode splitting. Optical devices were fabricated using titanium dioxide because it has good transparency in the visible range of the optical spectrum and a large bulk refractive index. Experimental results were compared to simulations to verify the designs and understand the limitations of the fabrication process.

  10. Anisotropic constitutive model and FE simulation of the sintering process of slip cast traditional porcelain

    NASA Astrophysics Data System (ADS)

    Sarbandi, B.; Besson, J.; Boussuge, M.; Ryckelynck, D.

    2010-06-01

    Slip cast ceramic components undergo both sintering shrinkage and creep deformation caused by gravity during the firing cycle. In addition sintering may be anisotropic due to the development of preferential directions during slip casting. Both phenomena induce complex deformations of parts which make the design of casting molds difficult. To help solving this problem, anisotropic constitutive equations are proposed to represent the behavior of the ceramic compacts during sintering. The model parameters are identified using tests allowing to characterize both sintering and creep. The model was implemented in a finite element software and used to simulate the deformation of a traditional ceramic object during sintering.

  11. Anisotropic constitutive model and FE simulation of the sintering process of slip cast traditional porcelain

    SciTech Connect

    Sarbandi, B.; Besson, J.; Boussuge, M.; Ryckelynck, D.

    2010-06-15

    Slip cast ceramic components undergo both sintering shrinkage and creep deformation caused by gravity during the firing cycle. In addition sintering may be anisotropic due to the development of preferential directions during slip casting. Both phenomena induce complex deformations of parts which make the design of casting molds difficult. To help solving this problem, anisotropic constitutive equations are proposed to represent the behavior of the ceramic compacts during sintering. The model parameters are identified using tests allowing to characterize both sintering and creep. The model was implemented in a finite element software and used to simulate the deformation of a traditional ceramic object during sintering.

  12. Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus.

    PubMed

    Fei, Ruixiang; Yang, Li

    2014-05-14

    Newly fabricated few-layer black phosphorus and its monolayer structure, phosphorene, are expected to be promising for electronic and optical applications because of their finite direct band gaps and sizable but anisotropic electronic mobility. By first-principles simulations, we show that this unique anisotropic free-carrier mobility can be controlled by using simple strain conditions. With the appropriate biaxial or uniaxial strain (4-6%), we can rotate the preferred conducting direction by 90°. This will be useful for exploring unusual quantum Hall effects and exotic electronic and mechanical applications based on phosphorene.

  13. Strain-Engineering the Anisotropic Electrical Conductance of Few-Layer Black Phosphorus

    NASA Astrophysics Data System (ADS)

    Fei, Ruixiang; Yang, Li

    2014-05-01

    Newly fabricated monolayer phosphorene and its few-layer structures are expected to be promising for electronic and optical applications because of their finite direct band gaps and sizable but anisotropic electronic mobility. By first-principles simulations, we show that this unique anisotropic conductance can be controlled by using simple strain conditions. With the appropriate biaxial or uniaxial strain, we can rotate the preferred conducting direction by 90 degrees. This will be of useful for exploring quantum Hall effects, and exotic electronic and mechanical applications based on phosphorene.

  14. Shear-flexible finite-element models of laminated composite plates and shells

    NASA Technical Reports Server (NTRS)

    Noor, A. K.; Mathers, M. D.

    1975-01-01

    Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.

  15. Anisotropic ripple deformation in phosphorene

    SciTech Connect

    Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; Chen, Changfeng

    2015-04-07

    Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.

  16. Anisotropic ripple deformation in phosphorene

    DOE PAGES

    Kou, Liangzhi; Ma, Yandong; Smith, Sean C.; ...

    2015-04-07

    Here, two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticitymore » theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.« less

  17. Yield surfaces for anisotropic plates

    NASA Astrophysics Data System (ADS)

    Walker, J. D.; Thacker, B. H.

    2000-04-01

    Aerospace systems are incorporating composite materials into their structures. The composite materials are often anisotropic in mechanical response due to their geometric layout. For many years, the failure surfaces of anisotropic materials were thought to be characterizable by a quadratic function in the stress, referred to as a Tsai-Wu yield surface, or, in a more restrictive form, a Tsai-Hill yield surface. Such a representation does not work for materials that are strong in two directions and weak in one direction, which is the case of most interest since it represents fiber/epoxy composite plates. This paper demonstrates the impossibility of modeling the failure surface with either the Tsai-Wu or Tsai-Hill failure surfaces. A yield surface is presented based on the lemniscate, which is quartic in the stress. This new yield surface addresses the case of strong in two directions and weak in one.

  18. Conductivity in an anisotropic background

    SciTech Connect

    Lee, Bum-Hoon; Nam, Siyoung; Pang, Da-Wei; Park, Chanyong

    2011-03-15

    By using the gauge/gravity duality, we investigate the dual field theories of the anisotropic backgrounds, which are exact solutions of Einstein-Maxwell-dilaton theory with a Liouville potential. When we turn on the bulk gauge field fluctuation A{sub x} with a nontrivial dilaton coupling, the AC conductivity of this dual field theory is proportional to the frequency with an exponent depending on parameters of the anisotropic background. In some parameter regions, we find that this conductivity can have the negative exponent like the strange metal. In addition, we also investigate another U(1) gauge field fluctuation, which is not coupled with a dilaton field. We classify all possible conductivities of this system and find that the exponent of the conductivity is always positive.

  19. Anisotropic Ripple Deformation in Phosphorene.

    PubMed

    Kou, Liangzhi; Ma, Yandong; Smith, Sean C; Chen, Changfeng

    2015-05-07

    Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.

  20. Cracking in charged anisotropic cylinder

    NASA Astrophysics Data System (ADS)

    Sharif, M.; Sadiq, Sobia

    2017-06-01

    In this paper, we study the stability of static charged anisotropic cylindrically symmetric compact object through cracking. The Einstein-Maxwell field equations and conservation equation are formulated. We then apply local density perturbation and study the behavior of force distribution function. Finally, the cracking is explored for two models satisfying specific form of Chaplygin equation of state. It is found that these models exhibit cracking and the instability increases as the value of charge parameter is increased.

  1. Spin noise in the anisotropic central spin model

    NASA Astrophysics Data System (ADS)

    Hackmann, Johannes; Anders, Frithjof B.

    2014-01-01

    Spin-noise measurements can serve as a direct probe for the microscopic decoherence mechanism of an electronic spin in semiconductor quantum dots (QDs). We have calculated the spin-noise spectrum in the anisotropic central spin model using a Chebyshev expansion technique which exactly accounts for the dynamics up to an arbitrary long but fixed time in a finite-size system. In the isotropic case, describing QD charge with a single electron, the short-time dynamics is in good agreement with quasistatic approximations for the thermodynamic limit. The spin-noise spectrum, however, shows strong deviations at low frequencies with a power-law behavior of ω-3/4 corresponding to a t-1/4 decay at intermediate and long times. In the Ising limit, applicable to QDs with heavy-hole spins, the spin-noise spectrum exhibits a threshold behavior of (ω-ωL)-1/2 above the Larmor frequency ωL=gμBB. In the generic anisotropic central spin model we have found a crossover from a Gaussian type of spin-noise spectrum to a more Ising-type spectrum with increasing anisotropy in a finite magnetic field. In order to make contact with experiments, we present ensemble averaged spin-noise spectra for QD ensembles charged with single electrons or holes. The Gaussian-type noise spectrum evolves to a more Lorentzian shape spectrum with increasing spread of characteristic time scales and g factors of the individual QDs.

  2. Anisotropic effects on ultrasonic guided waves propagation in composite bends.

    PubMed

    Yu, Xudong; Ratassepp, Madis; Rajagopal, Prabhu; Fan, Zheng

    2016-12-01

    Ultrasonic guided waves have proven to be attractive to the long-range testing of composite laminates. As complex-shaped composite components are increasingly incorporated in high-performance structures, understanding of both anisotropic and geometric effects on guided waves propagation is needed to evaluate their suitability for the non-destructive testing (NDT) of such complex structures. This paper reports the Semi-Analytical Finite Element (SAFE) simulations revealing the capability of energy confinement carried by two types of guided modes in 90° carbon fiber/epoxy (CF/EP) bends. Existence of the phenomenon is cross-validated by both 3D Finite Element (FE) modeling and experimental measurements. The physics of such energy trapping effect is explained in view of geometric variation and anisotropic properties, and the frequency effect on the extent of energy concentration is discussed. Finally, the feasibility of using such confined guided waves for rapid inspection of bent composite plate structures is also discussed. Copyright © 2016 Elsevier B.V. All rights reserved.

  3. Stress and vibraton analyses of anisotropic shells of revolution

    NASA Technical Reports Server (NTRS)

    Noor, Ahmed K.; Peters, Jeanne M.

    1988-01-01

    An efficient computational strategy is presented for reducing the cost of the stress and free vibration analyses of laminated anisotropic shells of revolution. The analytical formulation is based on a form of the Sanders-Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight strain components, the eight stress resultants and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions (Fourier series) in the circumferential co-ordinate, and a three-field mixed finite element model is used for the discretization in the meridional direction. The shell response associated with a range of Fourier harmonics is approximated by a linear combination of a few global approximation vectors, which are generated at a particular value of the Fourier harmonic, within that range. The full equations of the finite element model are solved for only a single Fourier harmonic, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.

  4. Stress and vibraton analyses of anisotropic shells of revolution

    NASA Technical Reports Server (NTRS)

    Noor, Ahmed K.; Peters, Jeanne M.

    1988-01-01

    An efficient computational strategy is presented for reducing the cost of the stress and free vibration analyses of laminated anisotropic shells of revolution. The analytical formulation is based on a form of the Sanders-Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight strain components, the eight stress resultants and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions (Fourier series) in the circumferential co-ordinate, and a three-field mixed finite element model is used for the discretization in the meridional direction. The shell response associated with a range of Fourier harmonics is approximated by a linear combination of a few global approximation vectors, which are generated at a particular value of the Fourier harmonic, within that range. The full equations of the finite element model are solved for only a single Fourier harmonic, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.

  5. Yield Surfaces for Anisotropic Plates

    NASA Astrophysics Data System (ADS)

    Walker, J. D.; Thacker, B. H.

    1999-06-01

    Modern aerospace systems are incorporating composite materials into their structures. Often, the composite materials are anisotropic in their mechanical response due to the geometric layout of fibers. For many years, the failure surfaces of anisotropic materials were thought to be characterizable by a quadratic function in the stress, often referred to as a Tsai-Wu yield surface, or, in a more restrictive form, a Tsai-Hill yield surface. Such a representation does not work for materials that are strong in two directions and weak in one direction, which, unfortunately, is the case of most interest since it represents most composite plates. This paper demonstrates the impossibility of modeling the failure surface with both the Tsai-Wu and Tsai-Hill failure surfaces. We then present a yield surface based on the lemniscate, which is quartic in the stress. This new yield surface addresses the case of strong in two directions and weak in one. Calculations with a fragment impacting a composite plate modeled with the new yield surface are presented. Modifications of the yield surface are presented to allow, in a limited way, materials that are both anisotropic and have differing strengths in tension and compression.

  6. Anisotropic characterization of magnetorheological materials

    NASA Astrophysics Data System (ADS)

    Dohmen, E.; Modler, N.; Gude, M.

    2017-06-01

    For the development of energy efficient lightweight parts novel function integrating materials are needed. Concerning this field of application magnetorheological (MR) fluids, MR elastomers and MR composites are promising materials allowing the adjustment of mechanical properties by an external magnetic field. A key issue for operating such structures in praxis is the magneto-mechanical description. Most rheological properties are gathered at laboratory conditions for high magnetic flux densities and a single field direction, which does not correspond to real praxis conditions. Although anisotropic formation of superstructures can be observed in MR suspensions (Fig. 1) or experimenters intentionally polymerize MR elastomers with anisotropic superstructures these MR materials are usually described in an external magnetic field as uniform, isotropic materials. This is due to missing possibilities for experimentally measuring field angle dependent properties and ways of distinguishing between material properties and frictional effects. Just a few scientific works experimentally investigated the influence of different field angles (Ambacher et al., 1992; Grants et al., 1990; Kuzhir et al., 2003) [1-3] or the influence of surface roughness on the shear behaviour of magnetic fluids (Tang and Conrad, 1996) [4]. The aim of this work is the introduction of a novel field angle cell allowing the determination of anisotropic mechanical properties for various MR materials depending on the applied magnetic field angle.

  7. Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

    NASA Technical Reports Server (NTRS)

    Arakere, Nagaraj K.; Knudsen, Erik; Swanson, Gregory R.; Duke, Gregory; Ham-Battista, Gilda

    2004-01-01

    Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves

  8. Application of Mass Lumped Higher Order Finite Elements

    SciTech Connect

    Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.

    2005-11-01

    There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.

  9. Modeling Three-Phase Compositional Flow on Complex 3D Unstructured Grids with Higher-Order Finite Element Methods

    NASA Astrophysics Data System (ADS)

    Moortgat, J.; Firoozabadi, A.

    2013-12-01

    Most problems of interest in hydrogeology and subsurface energy resources involve complex heterogeneous geological formations. Such domains are most naturally represented in numerical reservoir simulations by unstructured computational grids. Finite element methods are a natural choice to describe fluid flow on unstructured meshes, because the governing equations can be readily discretized for any grid-element geometry. In this work, we consider the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by tetrahedra, prisms, or hexahedra, and compare to simulations on 3D structured grids. We employ a combination of mixed hybrid finite element methods to solve for the pressure and flux fields in a fractional flow formulation, and higher-order discontinuous Galerkin methods for the mass transport equations. These methods are well suited to simulate flow in heterogeneous and fractured reservoirs, because they provide a globally continuous pressure and flux field, while allowing for sharp discontinuities in the phase properties, such as compositions and saturations. The increased accuracy from using higher-order methods improves the modeling of highly non-linear flow, such as gravitational and viscous fingering. We present several numerical examples to study convergence rates and the (lack of) sensitivity to gridding/mesh orientation, and mesh quality. These examples consider gravity depletion, water and gas injection in oil saturated subsurface reservoirs with species exchange between up to three fluid phases. The examples demonstrate the wide applicability of our chosen finite element methods in the study of challenging multiphase flow problems in porous, geometrically complex, subsurface media.

  10. PyLith: A Finite-Element Code for Modeling Quasi-Static and Dynamic Crustal Deformation

    NASA Astrophysics Data System (ADS)

    Aagaard, B.; Williams, C. A.; Knepley, M. G.

    2011-12-01

    We have developed open-source finite-element software for 2-D and 3-D dynamic and quasi-static modeling of crustal deformation. This software, PyLith (current release is version 1.6) can be used for quasi-static viscoelastic modeling, dynamic spontaneous rupture and/or ground-motion modeling. Unstructured and structured finite-element discretizations allow for spatial scales ranging from tens of meters to hundreds of kilometers with temporal scales in dynamic problems ranging from milliseconds to minutes and temporal scales in quasi-static problems ranging from minutes to thousands of years. PyLith development is part of the NSF funded Computational Infrastructure for Geodynamics (CIG) and the software runs on a wide variety of platforms (laptops, workstations, and Beowulf clusters). Binaries (Linux, Darwin, and Windows systems) and source code are available from geodynamics.org. PyLith uses a suite of general, parallel, graph data structures called Sieve for storing and manipulating finite-element meshes. This permits use of a variety of 2-D and 3-D cell types including triangles, quadrilaterals, hexahedra, and tetrahedra. Current PyLith features include prescribed fault ruptures with multiple earthquakes and aseismic creep, spontaneous fault ruptures with a variety of fault constitutive models, time-dependent Dirichlet and Neumann boundary conditions, absorbing boundary conditions, time-dependent point forces, and gravitational body forces. PyLith supports infinitesimal and small strain formulations for linear elastic rheologies, linear and generalized Maxwell viscoelastic rheologies, power-law viscoelastic rheologies, and Drucker-Prager elastoplastic rheologies. Current software development focuses on coupling quasi-static and dynamic simulations to resolve multi-scale deformation across the entire seismic cycle and the coupling of elasticity to heat and/or fluid flow.

  11. Borehole Deformation and Failure in Anisotropic Media

    NASA Astrophysics Data System (ADS)

    Gaede, Oliver; Regenauer-Lieb, Klaus; Lumley, David

    2010-05-01

    Borehole breakouts develop due to compressive shear failure along the borehole wall and subsequent spalling of near wellbore rock. These compressive shear failures can occur during drilling and lead to a borehole enlargement in the direction of the minimum horizontal stress. In order to investigate the initiation of borehole breakouts in anisotropic media a numerical analysis of the borehole deformation has been performed. The numerical model is based on an extensive geophysical and geomechanical dataset, provided by BHP Billiton Petroleum. This dataset was established during the development and production phase of an oil reservoir on the North West Shelf, Western Australia. The aim of this study is to estimate the severity of the influence of anisotropy on the breakout process. It is proposed that there is a hierarchy among the possible influences on the breakout process: 1. The regional stress field has a first order effect on the borehole breakout direction. 2. This is followed by a preferential fracture direction or anisotropic failure criterion of the medium. 3. And finally the elastic anisotropy of the medium affecting the local stress field around the borehole. A clear separation of these influences through methods of observation is not always trivial. Firstly, the preferential fracture direction and the elastic anisotropy, at least to some degree, are functions of the regional stress field. Secondly, most of the knowledge we have about the regional stress field in relatively aseismic regions is inferred from borehole breakout data. Therefore a numerical simulation is chosen as a method of study. Material properties like elastic anisotropy or failure criterion and even their dependency on the stress field can easily be manipulated. This geophysical and geomechanical data is used to populate the numerical model. The regional stress field is implemented as a boundary condition. The commercial Finite Element package ABAQUS is used to obtain the stress / strain

  12. A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

    NASA Astrophysics Data System (ADS)

    Huang, Weizhang; Kamenski, Lennard; Lang, Jens

    2010-03-01

    A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

  13. Constitutive Equation for Anisotropic Rock

    NASA Astrophysics Data System (ADS)

    Cazacu, O.

    2006-12-01

    In many rocks, due to the existence of well-defined fabric elements such as bedding, layering, foliation or lamination planes, or due to the existence of linear structures, anisotropy can be important. The symmetries most frequently encountered are: transverse isotropy and orthotropy. By adopting both theoretical and experimental approaches, many authors have investigated the effect of the presence within the rock of pronounced anisotropic feature on the mechanical behavior in the elastic regime and on strength properties. Fewer attempts however have been made to capture the anisotropy of rocks in the plastic range. In this paper an elastic/viscoplastic non-associated constitutive equation for an initially transversely isotropic material is presented. The model captures the observed dependency of the elastic moduli on the stress state. The limit of the elastic domain is given by an yield function whose expression is a priori unknown and is determined from data. The basic assumption adopted is that the type of anisotropy of the rock does not change during the deformation process. The anisotropy is thus described by a fourth order tensor invariant with respect to any transformation belonging to the symmetry group of the material. This tensor is assumed to be constant: it does not depend on time nor on deformation; A is involved in the expression of the flow rule, of the yield function, and of the failure criterion in the form of a transformed stress tensor. The components of the anisotropic tensor A are determined from the compressive strengths in conjunction with an anisotropic short- term failure The irreversibility is supposed to be due to transient creep, the irreversible stress work per unit volume being considered as hardening parameter. The adequacy of the model is demonstrated by applying it to a stratified sedimentary rock, Tournemire shale.

  14. Anisotropic inflation from vector impurity

    SciTech Connect

    Kanno, Sugumi; Kimura, Masashi; Soda, Jiro; Yokoyama, Shuichiro E-mail: mkimura@sci.osaka-cu.ac.jp E-mail: shu@a.phys.nagoya-u.ac.jp

    2008-08-15

    We study an inflationary scenario with a vector impurity. We show that the universe undergoes anisotropic inflationary expansion due to a preferred direction determined by the vector. Using the slow roll approximation, we find a formula for determining the anisotropy of the inflationary universe. We discuss possible observable predictions of this scenario. In particular, it is stressed that primordial gravitational waves can be induced from curvature perturbations. Hence, even in low scale inflation, a sizable amount of primordial gravitational waves may be produced during inflation.

  15. Anisotropic Geometrodynamics in Cosmological Problems

    NASA Astrophysics Data System (ADS)

    Siparov, Sergey

    2010-10-01

    Anisotropic geometrodynamics (AGD) is the GRT modification that takes into account the dependence of metric on the velocities of the sources which follows from the equivalence principle and from the inseparability of the field equations and geodesics equations. The AGD provides the explanation for the flat character of the rotation curves of spiral galaxies, for Tully-Fisher law, for some specific features of globular clusters behavior and for the essential excess of the observable gravitational lens effect over the predicted one. Neither dark matter nor arbitrary change of dynamics equations as in known approaches appears to be needed. Important cosmological consequences are discussed.

  16. Light Propagation through Anisotropic Turbulence

    DTIC Science & Technology

    2011-03-01

    Kolmogorov stratospheric turbulence on star image motion,” Proc. SPIE 3126, 113–123 (1997). 5. B. E . Stribling, B. M . Welsh, and M . C. Roggemann...746407 (2009). 10. M . Chang, C. O. Font, F. Santiago, Y. Luna, E . Roura, and S. Restaino, “Marine environment optical propagation measure- ments,” Proc...Anisotropic factor as a function of alpha for several zeta values. Toselli et al. Vol. 28, No. 3 / March 2011 / J. Opt. Soc. Am. A 487 14. M . S

  17. Granular Segregation with Anisotropic Particles

    NASA Astrophysics Data System (ADS)

    Sykes, Tim

    2005-11-01

    The results from experimental investigations of horizontally vibrated mixtures of anisotropic poppy seeds and long chains of linked spheres will be presented. A critical packing fraction was observed to be required to initiate a transition to segregation. The average size of the resulting patterns was measured and the concentration ratio of the mixtures was varied by changing the number of chains present in the mixtures. A change in the order of the transition, from second to first order with associated hysteresis, was observed as the chain number was reduced. This gave rise to three distinct regions of behaviour: segregated, mixed and a bi-stable state.

  18. Signature of anisotropic bubble collisions

    SciTech Connect

    Salem, Michael P.

    2010-09-15

    Our universe may have formed via bubble nucleation in an eternally inflating background. Furthermore, the background may have a compact dimension--the modulus of which tunnels out of a metastable minimum during bubble nucleation--which subsequently grows to become one of our three large spatial dimensions. When in this scenario our bubble universe collides with other ones like it, the collision geometry is constrained by the reduced symmetry of the tunneling instanton. While the regions affected by such bubble collisions still appear (to leading order) as disks in an observer's sky, the centers of these disks all lie on a single great circle, providing a distinct signature of anisotropic bubble nucleation.

  19. Fluid-structure interaction simulations of cerebral arteries modeled by isotropic and anisotropic constitutive laws

    NASA Astrophysics Data System (ADS)

    Tricerri, Paolo; Dedè, Luca; Deparis, Simone; Quarteroni, Alfio; Robertson, Anne M.; Sequeira, Adélia

    2015-03-01

    This paper considers numerical simulations of fluid-structure interaction (FSI) problems in hemodynamics for idealized geometries of healthy cerebral arteries modeled by both nonlinear isotropic and anisotropic material constitutive laws. In particular, it focuses on an anisotropic model initially proposed for cerebral arteries to characterize the activation of collagen fibers at finite strains. In the current work, this constitutive model is implemented for the first time in the context of an FSI formulation. In this framework, we investigate the influence of the material model on the numerical results and, in the case of the anisotropic laws, the importance of the collagen fibers on the overall mechanical behavior of the tissue. With this aim, we compare our numerical results by analyzing fluid dynamic indicators, vessel wall displacement, Von Mises stress, and deformations of the collagen fibers. Specifically, for an anisotropic model with collagen fiber recruitment at finite strains, we highlight the progressive activation and deactivation processes of the fibrous component of the tissue throughout the wall thickness during the cardiac cycle. The inclusion of collagen recruitment is found to have a substantial impact on the intramural stress, which will in turn impact the biological response of the intramural cells. Hence, the methodology presented here will be particularly useful for studies of mechanobiological processes in the healthy and diseased vascular wall.

  20. Anisotropic N=4 Super-Yang-Mills Plasma and Its Instabilities

    SciTech Connect

    Mateos, David; Trancanelli, Diego

    2011-09-02

    We present a type-IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super-Yang-Mills plasma. The solution is static and completely regular. The full geometry can be viewed as a renormalization group flow from an ultraviolet anti-de Sitter geometry to an infrared Lifshitz-like geometry. The anisotropy can be equivalently understood as resulting from a position-dependent {theta} term or from a nonzero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e., mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.

  1. Anisotropic water reorientation around ions.

    PubMed

    Tielrooij, K J; van der Post, S T; Hunger, J; Bonn, M; Bakker, H J

    2011-11-03

    We study the reorientation dynamics of water molecules around ions using terahertz dielectric relaxation spectroscopy and polarization-resolved femtosecond infrared pump-probe spectroscopy. The results are discussed in relation to the ion-specific Hofmeister series and the concomitant "structure-making" and "structure-breaking" effects of ions on water. We show that when a dissolved salt consists of a strongly hydrated ion with a weakly hydrated counterion the reorientation of water molecules around the strongly hydrated ion is anisotropic, in the sense that differently charged ions affect reorientation along different molecular axes: cations mainly slow the reorientation dynamics of the water dipole vectors, and anions mainly slow down the reorientation dynamics of the hydroxyl group that points toward the anion. In both cases, motion along only one molecular axis is impeded, so that the hydration shell is best described as semirigid. In this semirigid hydration picture, water molecules in the first hydration shell show anisotropic reorientation, whereas water molecules outside the first hydration shell remain unaffected. The inferred anisotropy in molecular motion explains why terahertz dielectric relaxation spectroscopy, which probes dipolar relaxation, is more sensitive to cation hydration effects while femtosecond infrared pump-probe spectroscopy, which is sensitive to reorientation of hydroxyl groups, is more sensitive to anion hydration effects. We also show that dissolution of CsI-a salt for which both cation and anion are weakly hydrated-has little effect on water reorientation dynamics, with hydration water displaying dynamics that are similar to those in bulk water.

  2. Anisotropic Plasticity of BN Nanotubes

    NASA Technical Reports Server (NTRS)

    Madhu, Menon; Srivastava, Deepak; Woo, Alex (Technical Monitor)

    1999-01-01

    Plastic collapse of compressed BN nanotubes are investigated and compared with carbon nanotubes of similar nature. Using a generalized tight-binding molecular dynamics (GTBMD) method for system containing B, N and C atoms we compute stiffness and plastic collapse of BN and C nanotubes under axial compression. For small compressional strain, BN nanotubes are found to be about 92% as stiff as similar C nanotubes. Due to BN bond buckling effect, however, the elastic limit of BN nanotubes is found to be more than C nanotubes. A route to plasticity is explored in which we find that at elastic limit the accumulated strain is released by a local plastic deformation of the nanotube. The mechanism of strain release and the resulting plastic deformation, however. are anisotropic in nature. The strain is released preferentially towards N as leading edge of a buckled BN bond and the tube, compressed at both ends, plastically collapses preferentially towards one end. Details of the anisotropic plasticity and prospective applications will be discussed in this presentation.

  3. Recent progress in anisotropic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Strickland, Michael

    2017-03-01

    The quark-gluon plasma created in a relativistic heavy-ion collisions possesses a sizable pressure anisotropy in the local rest frame at very early times after the initial nuclear impact and this anisotropy only slowly relaxes as the system evolves. In a kinetic theory picture, this translates into the existence of sizable momentum-space anisotropies in the underlying partonic distribution functions, < pL2> ≪ < pT2>. In such cases, it is better to reorganize the hydrodynamical expansion by taking into account momentum-space anisotropies at leading-order in the expansion instead of as a perturbative correction to an isotropic distribution. The resulting anisotropic hydrodynamics framework has been shown to more accurately describe the dynamics of rapidly expanding systems such as the quark-gluon plasma. In this proceedings contribution, I review the basic ideas of anisotropic hydrodynamics, recent progress, and present a few preliminary phenomenological predictions for identified particle spectra and elliptic flow.

  4. Effects of inner and outer scale on the modulation transfer function for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

    NASA Astrophysics Data System (ADS)

    Gao, Chao; Li, Xiaofeng

    2017-03-01

    Both experimental results and empirical research have shown that the atmospheric turbulence can present the anisotropic property not only at a few meters above the ground but also at high altitudes of up to several kilometers. This paper investigates the modulation transfer function of a Gaussian beam propagating along a horizontal path in weak anisotropic non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized exponential spectrum for anisotropic turbulence, which includes the spectral power law value, the finite inner and outer scales of turbulence, the anisotropic factor, and other essential optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the anisotropic factor.

  5. Characterization of anisotropic acoustic metamaterial slabs

    NASA Astrophysics Data System (ADS)

    Park, Jun Hyeong; Lee, Hyung Jin; Kim, Yoon Young

    2016-01-01

    In an anisotropic acoustic metamaterial, the off-diagonal components of its effective mass density tensor should be considered in order to describe the anisotropic behavior produced by arbitrarily shaped inclusions. However, few studies have been carried out to characterize anisotropic acoustic metamaterials. In this paper, we propose a method that uses the non-diagonal effective mass density tensor to determine the behavior of anisotropic acoustic metamaterials. Our method accurately evaluates the effective properties of anisotropic acoustic metamaterials by separately dealing with slabs made of single and multiple unit cells along the thickness direction. To determine the effective properties, the reflection and transmission coefficients of an acoustic metamaterial slab are calculated, and then the wave vectors inside of the slab are determined using these coefficients. The effective material properties are finally determined by utilizing the spatial dispersion relation of the anisotropic acoustic metamaterial. Since the dispersion relation of an anisotropic acoustic metamaterial is explicitly used, its effective properties can be easily determined by only using a limited number of normal and oblique plane wave incidences into a metamaterial slab, unlike existing approaches requiring a large number of wave incidences. The validity of the proposed method is verified by conducting wave simulations for anisotropic acoustic metamaterial slabs with Z-shaped elastic inclusions of tilted principal material axes.

  6. Linearized holographic isotropization at finite coupling

    NASA Astrophysics Data System (ADS)

    Atashi, Mahdi; Fadafan, Kazem Bitaghsir; Jafari, Ghadir

    2017-06-01

    We study holographic isotropization of an anisotropic homogeneous non-Abelian strongly coupled plasma in the presence of Gauss-Bonnet corrections. It was verified before that one can linearize Einstein's equations around the final black hole background and simplify the complicated setup. Using this approach, we study the expectation value of the boundary stress tensor. Although we consider small values of the Gauss-Bonnet coupling constant, it is found that finite coupling leads to significant increasing of the thermalization time. By including higher order corrections in linearization, we extend the results to study the effect of the Gauss-Bonnet coupling on the entropy production on the event horizon.

  7. Finite difference neuroelectric modeling software.

    PubMed

    Dang, Hung V; Ng, Kwong T

    2011-06-15

    This paper describes a finite difference neuroelectric modeling software (FNS), written in C and MATLAB, which can be executed as a standalone program or integrated with other packages for electroencephalography (EEG) analysis. The package from the Oxford Center for Functional MRI of the Brain (FMRIB), FMRIB Software Library (FSL), is used to segment the anatomical magnetic resonance (MR) image for realistic head modeling. The EEG electrode array is fitted to the realistic head model using the Bioelectromagnetism MATLAB toolbox. The finite difference formulation for a general inhomogeneous anisotropic body is used to obtain the system matrix equation, which is then solved using the conjugate gradient algorithm. The reciprocity theorem is utilized to limit the number of required forward solutions to N-1, where N is the number of electrodes. Results show that the forward solver only requires 500 MB of random-access memory (RAM) for a realistic 256×256×256 head model and that the software can be conveniently combined with inverse algorithms such as beamformers and MUSIC. The software is freely available under the GNU Public License.

  8. The effect of anisotropic heat transport on magnetic islands in 3-D configurations

    SciTech Connect

    Schlutt, M. G.; Hegna, C. C.

    2012-08-15

    An analytic theory of nonlinear pressure-induced magnetic island formation using a boundary layer analysis is presented. This theory extends previous work by including the effects of finite parallel heat transport and is applicable to general three dimensional magnetic configurations. In this work, particular attention is paid to the role of finite parallel heat conduction in the context of pressure-induced island physics. It is found that localized currents that require self-consistent deformation of the pressure profile, such as resistive interchange and bootstrap currents, are attenuated by finite parallel heat conduction when the magnetic islands are sufficiently small. However, these anisotropic effects do not change saturated island widths caused by Pfirsch-Schlueter current effects. Implications for finite pressure-induced island healing are discussed.

  9. Anisotropic Charge Distribution and Anisotropic van der Waals Radius Leading to Intriguing Anisotropic Noncovalent Interactions

    PubMed Central

    Kim, Hahn; Van Dung Doan; Cho, Woo Jong; Madhav, Miriyala Vijay; Kim, Kwang S.

    2014-01-01

    Although group (IV–VII) nonmetallic elements do not favor interacting with anionic species, there are counterexamples including the halogen bond. Such binding is known to be related to the charge deficiency because of the adjacent atom's electron withdrawing effect, which creates σ/π-holes at the bond-ends. However, a completely opposite behavior is exhibited by N2 and O2, which have electrostatically positive/negative character around cylindrical-bond-surface/bond-ends. Inspired by this, here we elucidate the unusual features and origin of the anisotropic noncovalent interactions in the ground and excited states of the 2nd and 3rd row elements belonging to groups IV–VII. The anisotropy in charge distributions and van der Waals radii of atoms in such molecular systems are scrutinized. This provides an understanding of their unusual molecular configuration, binding and recognition modes involved in new types of molecular assembling and engineering. This work would lead to the design of intriguing molecular systems exploiting anisotropic noncovalent interactions. PMID:25059645

  10. Higher Order Lagrange Finite Elements In M3D

    SciTech Connect

    J. Chen; H.R. Strauss; S.C. Jardin; W. Park; L.E. Sugiyama; G. Fu; J. Breslau

    2004-12-17

    The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.

  11. PyLith: A Finite-Element Code for Modeling Quasi-Static and Dynamic Crustal Deformation

    NASA Astrophysics Data System (ADS)

    Aagaard, B.; Williams, C.; Knepley, M.

    2008-12-01

    We have developed open-source finite-element software for 2-D and 3-D dynamic and quasi-static modeling of crustal deformation. This software, PyLith (current release is version 1.3), combines the quasi-static viscoelastic modeling functionality of PyLith 0.8 and its predecessors (LithoMop and Tecton) and the wave propagation modeling functionality of EqSim. The target applications contain spatial scales ranging from tens of meters to hundreds of kilometers with temporal scales for dynamic modeling ranging from milliseconds to minutes and temporal scales for quasi-static modeling ranging from minutes to hundreds of years. PyLith is part of the NSF funded Computational Infrastructure for Geodynamics (CIG) and runs on a wide variety of platforms (laptops, workstations, and Beowulf clusters). It uses a suite of general, parallel, graph data structures called Sieve for storing and manipulating finite-element meshes. This permits use of a variety of 2-D and 3-D cell types including triangles, quadrilaterals, hexahedra, and tetrahedra. Current features include kinematic fault ruptures, Dirichlet (displacement or velocity), Neumann (traction), and absorbing boundary conditions, linear elastic, generalized Maxwell, and Maxwell linear viscoelastic materials, gravitational body forces, and automatic time step selection for quasi-static problems. Future releases will add dynamic fault interface conditions (employing fault constitutive models), additional viscoelastic and viscoplastic materials, and automated calculation of suites of Green's functions. We also plan to extend PyLith to allow coupling multiple simultaneous simulations. For example, this could include (1) coupling an interseismic deformation simulation to a spontaneous earthquake rupture simulation (each using subsets of the software), (2) coupling a spontaneous earthquake rupture simulation to a global wave propagation simulation, or (3) coupling a short-term crustal deformation simulation to a mantle convection

  12. PyLith: A Finite-Element Code for Modeling Quasi-Static and Dynamic Crustal Deformation

    NASA Astrophysics Data System (ADS)

    Aagaard, B.; Williams, C.; Knepley, M.

    2007-12-01

    We have developed open-source finite-element software for 2-D and 3-D dynamic and quasi-static modeling of crustal deformation. This software, PyLith version 1.1, combines the quasi-static viscoelastic modeling functionality of PyLith 0.8 and its predecessors (LithoMop and Tecton) and the wave propagation and spontaneous rupture modeling functionality of EqSim. The target applications contain spatial scales ranging from tens of meters to hundreds of kilometers with temporal scales for dynamic modeling ranging from milliseconds to minutes and temporal scales for quasi-static modeling ranging from minutes to hundreds of years. PyLith is part of the NSF funded Computational Infrastructure for Geodynamics (CIG) and runs on a wide variety of platforms, from laptops to Beowulf clusters. It uses a suite of general, parallel, graph data structures called Sieve for storing and manipulating finite-element meshes. This permits use of a variety of 2-D and 3-D cell types including triangles, quadrilaterals, hexahedra, and tetrahedra. Current features include kinematic fault interface conditions, Dirichlet (displacement or velocity), Neumann (traction), and absorbing boundary conditions, linear elastic, generalized Maxwell, and Maxwell linear viscoelastic materials, and quasi-static and dynamic time-stepping. Future releases will add dynamic fault interface conditions (employing fault constitutive models), additional viscoelastic and viscoplastic materials, and automated calculation of suites of Green's functions. We also plan to extend PyLith to allow coupling multiple simultaneous simulations. For example, this could include (1) coupling an interseismic deformation simulation to a spontaneous earthquake rupture simulation (each using subsets of the software), (2) coupling a spontaneous earthquake rupture simulation to a global wave propagation simulation, or (3) coupling a short-term crustal deformation simulation to a mantle convection simulation and an orogenesis and basin

  13. Anisotropic invariance in minisuperspace models

    NASA Astrophysics Data System (ADS)

    Chagoya, Javier; Sabido, Miguel

    2016-06-01

    In this paper we introduce invariance under anisotropic transformations to cosmology. This invariance is one of the key ingredients of the theory of quantum gravity at a Lifshitz point put forward by Hořava. We find that this new symmetry in the minisuperspace introduces characteristics to the model that can be relevant in the ultraviolet regime. For example, by canonical quantization we find a Schrödinger-type equation which avoids the problem of frozen time in quantum cosmology. For simple cases we obtain solutions to this quantum equation in a Kantowski-Sachs (KS) minisuperspace. At the classical level, we study KS and Friedmann-Robertson-Walker cosmologies, obtaining modifications to the solutions of general relativity that can be relevant in the early Universe.

  14. Anisotropic Decomposition of Energetic Materials

    SciTech Connect

    Pravica, Michael; Quine, Zachary; Romano, Edward; Bajar, Sean; Yulga, Brian; Yang, Wenge; Hooks, Daniel

    2008-01-17

    Using a white x-ray synchrotron beam, we have dynamically studied radiation-induced decomposition in single crystalline PETN and TATB. By monitoring the integrated intensity of selected diffraction spots via a CCD x-ray camera as a function of time, we have found that the decomposition rate varies dramatically depending upon the orientation of the crystalline axes relative to polarized x-ray beam and for differing diffracting conditions (spots) within the same crystalline orientation. We suggest that this effect is due to Compton scattering of the polarized x-rays with electron clouds that is dependent upon their relative orientation. This novel effect may yield valuable insight regarding anisotropic detonation sensitivity in energetic materials such as PETN.

  15. Anisotropic decomposition of energetic materials

    SciTech Connect

    Pravica, Michael; Quine, Zachary; Romano, Edward; Bajar, Sean; Yulga, Brian; Yang Wenge; Hooks, Daniel

    2007-12-12

    Using a white x-ray synchrotron beam, we have dynamically studied radiation-induced decomposition in single crystalline PETN and TATB. By monitoring the integrated intensity of selected diffraction spots via a CCD x-ray camera as a function of time, we have found that the decomposition rate varies dramatically depending upon the orientation of the crystalline axes relative to polarized x-ray beam and for differing diffracting conditions (spots) within the same crystalline orientation. We suggest that this effect is due to Compton scattering of the polarized x-rays with electron clouds that is dependent upon their relative orientation. This novel effect may yield valuable insight regarding anisotropic detonation sensitivity in energetic materials such as PETN.

  16. Anisotropic grid adaptation in LES

    NASA Astrophysics Data System (ADS)

    Toosi, Siavash; Larsson, Johan

    2016-11-01

    The modeling errors depend directly on the grid (or filter) spacing in turbulence-resolving simulations (LES, DNS, DES, etc), and are typically at least as significant as the numerical errors. This makes adaptive grid-refinement complicated, since it prevents the estimation of the local error sources through numerical analysis. The present work attempts to address this difficulty with a physics-based error-source indicator that accounts for the anisotropy in the smallest resolved scales, which can thus be used to drive an anisotropic grid-adaptation process. The proposed error indicator is assessed on a sequence of problems, including turbulent channel flow and flows in more complex geometries. The formulation is geometrically general and applicable to complex geometries.

  17. Mechanics of anisotropic spring networks

    NASA Astrophysics Data System (ADS)

    Zhang, T.; Schwarz, J. M.; Das, Moumita

    2014-12-01

    We construct and analyze a model for a disordered linear spring network with anisotropy. The modeling is motivated by, for example, granular systems, nematic elastomers, and ultimately cytoskeletal networks exhibiting some underlying anisotropy. The model consists of a triangular lattice with two different bond occupation probabilities, px and py, for the linear springs. We develop an effective medium theory (EMT) to describe the network elasticity as a function of px and py. We find that the onset of rigidity in the EMT agrees with Maxwell constraint counting. We also find beyond linear behavior in the shear and bulk modulus as a function of occupation probability in the rigid phase for small strains, which differs from the isotropic case. We compare our EMT with numerical simulations to find rather good agreement. Finally, we discuss the implications of extending the reach of effective medium theory as well as draw connections with prior work on both anisotropic and isotropic spring networks.

  18. Modeling of Anisotropic Inelastic Behavior

    SciTech Connect

    Nikkel, D.J.; Nath, D.S.; Brown, A.A.; Casey, J.

    2000-02-25

    An experimental capability, developed at Lawrence Livermore National Laboratory (LLNL), is being used to study the yield behavior of elastic-plastic materials. The objective of our research is to develop better constitutive equations for polycrystalline metals. We are experimentally determining the multidimensional yield surface of the material, both in its initial state and as it evolves during large inelastic deformations. These experiments provide a more complete picture of material behavior than can be obtained from traditional uniaxial tests. Experimental results show that actual material response can differ significantly from that predicted by simple idealized models. These results are being used to develop improved constitutive models of anisotropic plasticity for use in continuum computer codes.

  19. Thermodynamics of soft anisotropic interfaces.

    PubMed

    Rey, Alejandro D

    2004-01-22

    The Gibbs-Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs-Duhem equations is established. Consistency between the surface Gibbs-Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs-Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space.

  20. Anisotropic microstructure near the sun

    NASA Astrophysics Data System (ADS)

    Coles, W. A.; Grall, R. R.; Spangler, S. R.; Sakurai, T.; Harmon, J. K.

    1996-07-01

    Radio scattering observations provide a means of measuring a two-dimensional projection of the three-dimensional spatial spectrum of electron density, i.e., in the plane perpendicular to the line of sight. Earlier observations have shown that the microstructure at scales of the order of 10 km becomes highly field-aligned inside of 10 Rsolar [Armstrong et al., 1990]. Earlier work has also shown that density fluctuations at scales larger than 1000 km have a Kolmogorov spectrum, whereas the smaller scale structure has a flatter spectrum and is considerably enhanced above the Kolmogorov ``background'' [Coles et al., 1991]. Here we present new observations made during 1990 and 1992. These confirm the earlier work, which was restricted to one source on a few days, but they suggest that the anisotropy changes abruptly near 6 Rsolar which was not clear in the earlier data. The axial ratio measurements are shown on Figure 1 below. The new observations were made with a more uniform sampling of the spatial plane. They show that contours of constant correlation are elliptical. This is apparently inconsistent with the spatial correlation of the ISEE-3 magnetic field which shows a ``Maltese Cross'' shape [Matthaeus et al., 1990]. However this inconsistency may be only apparent: the magnetic field and density correlations need not have the same shape; the scale of the magnetic field correlations is at least 4 orders of magnitude larger; they are much further from the sun; and they are point measurements whereas ours are path-integrated. We also made two simultaneous measurements, at 10 Rsolar, of the anisotropy on scales of 200 to 4000 km. Significant anisotropy was seen on the smaller scales, but the larger scale structure was essentially isotropic. This suggests that the process responsible for the anisotropic microstructure is independent of the larger scale isotropic turbulence. It is then tempting to speculate that the damping of this anisotropic process inside of 6 Rsolar

  1. Ultrasonic field profile evaluation in acoustically inhomogeneous anisotropic materials using 2D ray tracing model: Numerical and experimental comparison.

    PubMed

    Kolkoori, S R; Rahman, M-U; Chinta, P K; Ktreutzbruck, M; Rethmeier, M; Prager, J

    2013-02-01

    Ultrasound propagation in inhomogeneous anisotropic materials is difficult to examine because of the directional dependency of elastic properties. Simulation tools play an important role in developing advanced reliable ultrasonic non destructive testing techniques for the inspection of anisotropic materials particularly austenitic cladded materials, austenitic welds and dissimilar welds. In this contribution we present an adapted 2D ray tracing model for evaluating ultrasonic wave fields quantitatively in inhomogeneous anisotropic materials. Inhomogeneity in the anisotropic material is represented by discretizing into several homogeneous layers. According to ray tracing model, ultrasonic ray paths are traced during its energy propagation through various discretized layers of the material and at each interface the problem of reflection and transmission is solved. The presented algorithm evaluates the transducer excited ultrasonic fields accurately by taking into account the directivity of the transducer, divergence of the ray bundle, density of rays and phase relations as well as transmission coefficients. The ray tracing model is able to calculate the ultrasonic wave fields generated by a point source as well as a finite dimension transducer. The ray tracing model results are validated quantitatively with the results obtained from 2D Elastodynamic Finite Integration Technique (EFIT) on several configurations generally occurring in the ultrasonic non destructive testing of anisotropic materials. Finally, the quantitative comparison of ray tracing model results with experiments on 32mm thick austenitic weld material and 62mm thick austenitic cladded material is discussed. Copyright © 2012 Elsevier B.V. All rights reserved.

  2. An optimal nonorthogonal separation of the anisotropic Gaussian convolution filter.

    PubMed

    Lampert, Christoph H; Wirjadi, Oliver

    2006-11-01

    We give an analytical and geometrical treatment of what it means to separate a Gaussian kernel along arbitrary axes in R(n), and we present a separation scheme that allows us to efficiently implement anisotropic Gaussian convolution filters for data of arbitrary dimensionality. Based on our previous analysis we show that this scheme is optimal with regard to the number of memory accesses and interpolation operations needed. The proposed method relies on nonorthogonal convolution axes and works completely in image space. Thus, it avoids the need for a fast Fourier transform (FFT)-subroutine. Depending on the accuracy and speed requirements, different interpolation schemes and methods to implement the one-dimensional Gaussian (finite impulse response and infinite impulse response) can be integrated. Special emphasis is put on analyzing the performance and accuracy of the new method. In particular, we show that without any special optimization of the source code, it can perform anisotropic Gaussian filtering faster than methods relying on the FFT.

  3. Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law

    NASA Technical Reports Server (NTRS)

    Yueh, Simon H.; Kwok, R.

    1993-01-01

    In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.

  4. Subsurface Stress Fields In Single Crystal (Anisotropic) Contacts

    NASA Technical Reports Server (NTRS)

    Arakere, Nagaraj K.; Knudsen, Erik C.; Duke, Greg; Battista, Gilda; Swanson, Greg

    2004-01-01

    Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent HCF failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and noncrystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is , presented, for evaluating the subsurface stresses in the elastic half-space, using a complex potential method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis. Effects of crystal orientation on stress response and fatigue life are examined.

  5. DNA-mediated anisotropic mechanical reinforcement of a virus

    PubMed Central

    Carrasco, C.; Carreira, A.; Schaap, I. A. T.; Serena, P. A.; Gómez-Herrero, J.; Mateu, M. G.; de Pablo, P. J.

    2006-01-01

    In this work, we provide evidence of a mechanism to reinforce the strength of an icosahedral virus by using its genomic DNA as a structural element. The mechanical properties of individual empty capsids and DNA-containing virions of the minute virus of mice are investigated by using atomic force microscopy. The stiffness of the empty capsid is found to be isotropic. Remarkably, the presence of the DNA inside the virion leads to an anisotropic reinforcement of the virus stiffness by ≈3%, 40%, and 140% along the fivefold, threefold, and twofold symmetry axes, respectively. A finite element model of the virus indicates that this anisotropic mechanical reinforcement is due to DNA stretches bound to 60 concavities of the capsid. These results, together with evidence of biologically relevant conformational rearrangements of the capsid around pores located at the fivefold symmetry axes, suggest that the bound DNA may reinforce the overall stiffness of the viral particle without canceling the conformational changes needed for its infectivity. PMID:16945903

  6. Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law

    NASA Technical Reports Server (NTRS)

    Yueh, Simon H.; Kwok, R.

    1993-01-01

    In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.

  7. Entropic contributions in Langevin equations for anisotropic driven systems

    NASA Astrophysics Data System (ADS)

    de los Santos, Francisco; Garrido, Pedro L.; Muñoz, Miguel A.

    2001-07-01

    We report on analytical results for a series of anisotropic driven systems in the context of a recently proposed Langevin equation approach. In a recent paper (P.L. Garrido et al., Phys. Rev. E 61 (2000) R4683) we have pointed out that entropic contributions, over-looked in previous works, are crucial in order to obtain suitable Langevin descriptions of driven lattice gases. Here, we present a more detailed derivation and justification of the entropic term for the standard driven lattice gas, and also we extend the improved approach to other anisotropic driven systems, namely: (i) the randomly driven lattice gas, (ii) the two-temperature model and, (iii) the bi-layer lattice gas. It is shown that the two-temperature model and the lattice gas driven either by a random field or by an uniform infinite one are members of the same universality class. When the drive is uniform and finite the ‘standard’ theory is recovered. A Langevin equation describing the phenomenology of the bi-layer lattice gas is also presented.

  8. Ferrimagnetism in delta chain with anisotropic ferromagnetic and antiferromagnetic interactions

    NASA Astrophysics Data System (ADS)

    Dmitriev, D. V.; Krivnov, V. Ya

    2016-12-01

    We consider analytically and numerically an anisotropic spin-\\frac{1}{2} delta-chain (sawtooth chain) in which exchange interactions between apical and basal spins are ferromagnetic and those between basal spins are antiferromagnetic. In the limit of strong anisotropy of exchange interactions this model can be considered as the Ising delta chain with macroscopic degenerate ground state perturbed by transverse quantum fluctuations. These perturbations lift the ground state degeneracy and the model reduces to the basal XXZ spin chain in the magnetic field induced by static apical spins. We show that the ground state of such a model is ferrimagnetic. The excitations of the model are formed by ferrimagnetic domains separated by domain walls with a finite energy. At low temperatures the system is effectively divided into two independent subsystems, the apical subsystem described by the Ising spin-\\frac{1}{2} chain and the basal subsystem described by the XXZ chain with infinite zz interactions.

  9. Anisotropic diffusion of spherical particles in closely confining microchannels.

    PubMed

    Dettmer, Simon L; Pagliara, Stefano; Misiunas, Karolis; Keyser, Ulrich F

    2014-06-01

    We present here the measurement of the diffusivity of spherical particles closely confined by narrow microchannels. Our experiments yield a two-dimensional map of the position-dependent diffusion coefficients parallel and perpendicular to the channel axis with a resolution down to 129 nm. The diffusivity was measured simultaneously in the channel interior, the bulk reservoirs, as well as the channel entrance region. In the channel interior we found strongly anisotropic diffusion. While the perpendicular diffusion coefficient close to the confining walls decreased down to approximately 25% of the value on the channel axis, the parallel diffusion coefficient remained constant throughout the entire channel width. In addition to the experiment, we performed finite element simulations for the diffusivity in the channel interior and found good agreement with the measurements. Our results reveal the distinctive influence of strong confinement on Brownian motion, which is of significance to microfluidics as well as quantitative models of facilitated membrane transport.

  10. Ferrimagnetism in delta chain with anisotropic ferromagnetic and antiferromagnetic interactions.

    PubMed

    Dmitriev, D V; Ya Krivnov, V

    2016-12-21

    We consider analytically and numerically an anisotropic spin-[Formula: see text] delta-chain (sawtooth chain) in which exchange interactions between apical and basal spins are ferromagnetic and those between basal spins are antiferromagnetic. In the limit of strong anisotropy of exchange interactions this model can be considered as the Ising delta chain with macroscopic degenerate ground state perturbed by transverse quantum fluctuations. These perturbations lift the ground state degeneracy and the model reduces to the basal XXZ spin chain in the magnetic field induced by static apical spins. We show that the ground state of such a model is ferrimagnetic. The excitations of the model are formed by ferrimagnetic domains separated by domain walls with a finite energy. At low temperatures the system is effectively divided into two independent subsystems, the apical subsystem described by the Ising spin-[Formula: see text] chain and the basal subsystem described by the XXZ chain with infinite zz interactions.

  11. Anisotropic inflation in Gauss-Bonnet gravity

    SciTech Connect

    Lahiri, Sayantani

    2016-09-19

    We study anisotropic inflation with Gauss-Bonnet correction in presence of a massless vector field. In this scenario, exact anisotropic power-law inflation is realized when the inflaton potential, gauge coupling function and the Gauss-Bonnet coupling are exponential functions. We show that anisotropy becomes proportional to two slow-roll parameters of the theory and hence gets enhanced in presence of quadratic curvature corrections. The stability analysis reveals that anisotropic power-law solutions remain stable over a substantially large parameter region.

  12. Anisotropic superfluidity in a dipolar Bose gas.

    PubMed

    Ticknor, Christopher; Wilson, Ryan M; Bohn, John L

    2011-02-11

    We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional geometry. We consider the dipole polarization to have some nonzero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion relation. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the probe's motion. This anisotropy emerges because of the anisotropic manifestation of a rotonlike mode in the system.

  13. Anisotropic Superfluidity in a Dipolar Bose Gas

    SciTech Connect

    Ticknor, Christopher; Wilson, Ryan M.; Bohn, John L.

    2011-02-11

    We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional geometry. We consider the dipole polarization to have some nonzero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion relation. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the probe's motion. This anisotropy emerges because of the anisotropic manifestation of a rotonlike mode in the system.

  14. Better Finite-Element Analysis of Composite Shell Structures

    NASA Technical Reports Server (NTRS)

    Clarke, Gregory

    2007-01-01

    A computer program implements a finite-element-based method of predicting the deformations of thin aerospace structures made of isotropic materials or anisotropic fiber-reinforced composite materials. The technique and corresponding software are applicable to thin shell structures in general and are particularly useful for analysis of thin beamlike members having open cross-sections (e.g. I-beams and C-channels) in which significant warping can occur.

  15. Negative refraction in anisotropic composites

    NASA Astrophysics Data System (ADS)

    Chui, S. T.

    2004-03-01

    Left-handed materials (LHM) are materials in which the direction of wave propagation S is opposite to the wave vector k . S <0 .[1,2,3] LHM exhibit nagative refraction. Experiments have been carried out on a medium consisting of arrays of metallic rings and wrires.[3] An example of a different class of anisotropic left-handed materials are metallic magnetic granular composites. Based on the effective medium approximation, we show that by incorporating metallic magnetic nanoparticles into an appropriate insulating matrix, it may be possible to prepare a composite medium of low eddy current loss which is left-handed for electromagnetic waves propagating in some special direction and polarization in a frequency region near the ferromagnetic resonance frequency.[4,5] This composite may be easier to make on an industrial scale. In addition, its physical properties may be easily tuned by rotating the magnetization locally. The physics involved seems to be different from the original argument.[1,2] In our argument[5], the imaginary part of the dielectric constant of the metal is much larger than the real part, opposite to the original argument. In anisotropic materials so that some of the susceptibilities are negative, the criterion for LHM may not be the same as that for negative refraction.[6] Ansiotropic materials exhibit a richer manifold of anomlous behaviour[6,7,8] and offers more flexibility in apllications.[8] More recently it was found that negative refraction can occur in anisotropic materials where all the susceptibilities are positive.[9] We found that the range of applicability of this effect is much larger than originally thought.[10] S. T. Chui was supported in part by the Office of Naval Research, by the Army Research Laboratory through the Center of Composite Materials at the University of Delaware, by DARPA and by the NSF. [1] J.B.Pendry, A.J.Holden, W.J.Stewart, and I.Youngs, Phys. Rev. Lett 76, 4773 (1996). [2] V.G.Veselago, Sov. Phys. Usp. 10, 509

  16. Generalized similarity in finite range solar wind magnetohydrodynamic turbulence.

    PubMed

    Chapman, S C; Nicol, R M

    2009-12-11

    Extended or generalized similarity is a ubiquitous but not well understood feature of turbulence that is realized over a finite range of scales. The ULYSSES spacecraft solar polar passes at solar minimum provide in situ observations of evolving anisotropic magnetohydrodynamic turbulence in the solar wind under ideal conditions of fast quiet flow. We find a single generalized scaling function characterizes this finite range turbulence and is insensitive to plasma conditions. The recent unusually inactive solar minimum--with turbulent fluctuations down by a factor of approximately 2 in power--provides a test of this invariance.

  17. Generalized Similarity in Finite Range Solar Wind Magnetohydrodynamic Turbulence

    SciTech Connect

    Chapman, S. C.; Nicol, R. M.

    2009-12-11

    Extended or generalized similarity is a ubiquitous but not well understood feature of turbulence that is realized over a finite range of scales. The ULYSSES spacecraft solar polar passes at solar minimum provide in situ observations of evolving anisotropic magnetohydrodynamic turbulence in the solar wind under ideal conditions of fast quiet flow. We find a single generalized scaling function characterizes this finite range turbulence and is insensitive to plasma conditions. The recent unusually inactive solar minimum - with turbulent fluctuations down by a factor of approx2 in power - provides a test of this invariance.

  18. Anisotropic wettability on imprinted hierarchical structures.

    PubMed

    Zhang, Fengxiang; Low, Hong Yee

    2007-07-03

    A series of two-level hierarchical structures on polystyrene (PS) and poly(methyl methacrylate) (PMMA) were fabricated using sequential nanoimprinting lithography (NIL). The hierarchical structures consist of micrometer and sub-micrometer scale grating imprinted with varying orientations. Through water contact angle measurements, these surface hierarchical structures showed a wide range of anisotropic wettabilities on PMMA and PS, with PMMA having an anisotropic wettability from 6 degrees to 54 degrees and PS having an anisotropic wettability from 8 degrees to 32 degrees. At the same time, the water contact angle of PMMA and PS can be tuned to nearly 120 degrees without modifying the surface chemistry. A tunable anisotropic wettability is beneficial for applications where controlling the direction of liquid flow is important, such as in microfluidic devices.

  19. Nonlinear inversion for arbitrarily-oriented anisotropic models: Synthetic testing

    NASA Astrophysics Data System (ADS)

    Bremner, P. M.; Panning, M. P.

    2010-12-01

    We present an implementation of new 3-D finite-frequency kernels, based on the Born approximation, for inversion of a synthetic surface wave dataset. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests are performed to achieve a robust inversion scheme. Nonlinear inversion schemes are examined for adequate recovery of three input models to include: isotropic, anisotropic, and both anisotropic and isotropic input models. Output models from inversions of calculated synthetic data are compared against these input models to test for accurate reproduction of input model features, and the resolution of those features. The focus of this study is on inverting for structure beneath western North America. The synthetic dataset consists of collected seismic waveforms of 128 earthquake mechanisms, of magnitude 6-7 from Dec 2006 to Feb 2009, from the IRIS database. Events were selected to correlate with USArray deployments, and to have as complete an azimuthal coverage as possible. The events occurred within a circular region of radius 150° centered about 44° lat, -110° lon (an arbitrary location within USArray coverage). The seismograms have been calculated within a simplified version of PREM in which the crust and 220 km discontinuity have been removed, dubbed PREM LIGHT, utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 400 km depth, coupled to a spherically symmetric inner sphere. The SEM solves the weak formulation of the seismic wave equation in the outer shell, and uses normal mode summation methods for the inner sphere. To validate the results of the SEM, seismograms are benchmarked against seismograms calculated with a 1-D normal mode summation. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π spheroidal wave function

  20. Inflation in anisotropic scalar-tensor theories

    NASA Technical Reports Server (NTRS)

    Pimentel, Luis O.; Stein-Schabes, Jaime

    1988-01-01

    The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.

  1. Anisotropic Interactions between Cold Rydberg Atoms

    DTIC Science & Technology

    2015-09-28

    AFRL-AFOSR-CL-TR-2015-0002 Anisotropic interactions between cold Rydberg atoms Luis Marcassa INSTITUTO DE FISICA DE SAO CARLOS Final Report 09/28...34Anisotropic Interactions Between Cold Rydberg Atoms " 5a. CONTRACT NUMBER FA9550-12-1-0434 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6...processes in an atomic sample trapped in a CO2 optical dipole trap. The process was investigated as a function of: i) atomic density; ii) dc electric

  2. Phase space analysis in anisotropic optical systems

    NASA Technical Reports Server (NTRS)

    Rivera, Ana Leonor; Chumakov, Sergey M.; Wolf, Kurt Bernardo

    1995-01-01

    From the minimal action principle follows the Hamilton equations of evolution for geometric optical rays in anisotropic media. As in classical mechanics of velocity-dependent potentials, the velocity and the canonical momentum are not parallel, but differ by an anisotropy vector potential, similar to that of linear electromagnetism. Descartes' well known diagram for refraction is generalized and a factorization theorem holds for interfaces between two anisotropic media.

  3. On the anisotropic elastic properties of hydroxyapatite.

    NASA Technical Reports Server (NTRS)

    Katz, J. L.; Ukraincik, K.

    1971-01-01

    Experimental measurements of the isotropic elastic moduli on polycrystalline specimens of hydroxyapatite and fluorapatite are compared with elastic constants measured directly from single crystals of fluorapatite in order to derive a set of pseudo single crystal elastic constants for hydroxyapatite. The stiffness coefficients thus derived are given. The anisotropic and isotropic elastic properties are then computed and compared with similar properties derived from experimental observations of the anisotropic behavior of bone.

  4. SAR Segmentation using Anisotropic Diffusion

    NASA Astrophysics Data System (ADS)

    Intajag, Sathit; Tipsuwanporn, Vittaya; Cheevasuwit, Fusak

    Speckle effects are commonly observed in synthetic aperture radar (SAR) images. The human eye is capable of deriving meaningful information from SAR images; however, an automatic or semi-automatic processing algorithm has difficulty in distinguishing objects in the images because of noise effects present in those images. This paper presents a segmentation method for SAR images, which employs an anisotropic diffusion algorithm. In the proposed scheme, a SAR image is transformed into a logarithmic domain where the diffusion process is used to grow homogeneous regions in the noise environment until the regions reach some criteria for homogeneity; consequently, the segmented image in the logarithm domain is converted to the intensity domain by an exponential function. To grow homogeneous regions the adaptive diffusion method is introduced with a tensor technique in which tensor data are varied with the neighboring pixels. The diffusion algorithm will stop itself by a standard deviation divided by the mean, which is provided according to the homogeneity criteria. Results are shown on both synthetic and satellite SAR images. The evaluation of the proposed method employs the theoretical gain of equivalent numbers of looks (ENL).

  5. Spin precession in anisotropic media

    NASA Astrophysics Data System (ADS)

    Raes, B.; Cummings, A. W.; Bonell, F.; Costache, M. V.; Sierra, J. F.; Roche, S.; Valenzuela, S. O.

    2017-02-01

    We generalize the diffusive model for spin injection and detection in nonlocal spin structures to account for spin precession under an applied magnetic field in an anisotropic medium, for which the spin lifetime is not unique and depends on the spin orientation. We demonstrate that the spin precession (Hanle) line shape is strongly dependent on the degree of anisotropy and on the orientation of the magnetic field. In particular, we show that the anisotropy of the spin lifetime can be extracted from the measured spin signal, after dephasing in an oblique magnetic field, by using an analytical formula with a single fitting parameter. Alternatively, after identifying the fingerprints associated with the anisotropy, we propose a simple scaling of the Hanle line shapes at specific magnetic field orientations that results in a universal curve only in the isotropic case. The deviation from the universal curve can be used as a complementary means of quantifying the anisotropy by direct comparison with the solution of our generalized model. Finally, we applied our model to graphene devices and find that the spin relaxation for graphene on silicon oxide is isotropic within our experimental resolution.

  6. SAW imaging in anisotropic media

    NASA Astrophysics Data System (ADS)

    Clark, M.; Sharples, S. D.; Somekh, M. G.

    2000-05-01

    We have developed a non-contact laser ultrasound SAW microscope operating at 82 MHz and harmonics thereof, which is capable of rapid image acquisition. Conventional acoustic microscopy is largely immune to the effects of aberration because of the very short acoustic path length that is imposed by the presence of the couplant. The couplant also limits the sensitivity of contacting acoustic microscopy. In laser ultrasound systems the absence of couplant means that longer path lengths are possible but the anisotropy and grain structure of the material can aberrate the passage of the acoustic wave limiting the performance of the system and producing acoustic speckle. We show that even weakly aberrating materials (e.g. aluminum) can produce significant speckle effects. We present experimental non-contacting imaging results on isotropic and textured anisotropic samples; together with simulated images. The results demonstrate that the speckle statistics of the experimental and simulated results agree well; thus demonstrating the cause of the speckle in the experimental images. We demonstrate how a wavefront sensor and adaptation of the optical excitation profile offers a solution to the problem of texture in non-contacting SAW imaging. Finally, we discuss how some material properties may be inferred from the speckle.

  7. Influence of heterogeneous and anisotropic tissue conductivity on electric field distribution in deep brain stimulation.

    PubMed

    Aström, Mattias; Lemaire, Jean-Jacques; Wårdell, Karin

    2012-01-01

    The aim was to quantify the influence of heterogeneous isotropic and heterogeneous anisotropic tissue on the spatial distribution of the electric field during deep brain stimulation (DBS). Three finite element tissue models were created of one patient treated with DBS. Tissue conductivity was modelled as (I) homogeneous isotropic, (II) heterogeneous isotropic based on MRI, and (III) heterogeneous anisotropic based on diffusion tensor MRI. Modelled DBS electrodes were positioned in the subthalamic area, the pallidum, and the internal capsule in each tissue model. Electric fields generated during DBS were simulated for each model and target-combination and visualized with isolevels at 0.20 (inner), and 0.05 V mm(-1) (outer). Statistical and vector analysis was used for evaluation of the distribution of the electric field. Heterogeneous isotropic tissue altered the spatial distribution of the electric field by up to 4% at inner, and up to 10% at outer isolevel. Heterogeneous anisotropic tissue influenced the distribution of the electric field by up to 18 and 15% at each isolevel, respectively. The influence of heterogeneous and anisotropic tissue on the electric field may be clinically relevant in anatomic regions that are functionally subdivided and surrounded by multiple fibres of passage.

  8. Instabilities of collisionless current sheets revisited: The role of anisotropic heating

    SciTech Connect

    Muñoz, P. A. Kilian, P. Büchner, J.

    2014-11-15

    In this work, we investigate the influence of the anisotropic heating on the spontaneous instability and evolution of thin Harris-type collisionless current sheets, embedded in antiparallel magnetic fields. In particular, we explore the influence of the macroparticle shape-function using a 2D version of the PIC code ACRONYM. We also investigate the role of the numerical collisionality due to the finite number of macroparticles in PIC codes. It is shown that it is appropriate to choose higher order shape functions of the macroparticles compared to a larger number of macroparticles per cell. This allows to estimate better the anisotropic electron heating due to the collisions of macroparticles in a PIC code. Temperature anisotropies can stabilize the tearing mode instability and trigger additional current sheet instabilities. We found a good agreement between the analytically derived threshold for the stabilization of the anisotropic tearing mode and other instabilities, either spontaneously developing or initially triggered ones. Numerical effects causing anisotropic heating at electron time scales become especially important for higher mass ratios (above m{sub i}/m{sub e}=180). If numerical effects are carefully taken into account, one can recover the theoretical estimated linear growth rates of the tearing instability of thin isotropic collisionless current sheets, also for higher mass ratios.

  9. Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators

    PubMed Central

    Li, Baode; Yang, Dachun; Yuan, Wen

    2014-01-01

    Let φ : ℝn × [0, ∞)→[0, ∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, H A φ(ℝn), via the grand maximal function. The authors then obtain some real-variable characterizations of H A φ(ℝn) in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space H A p(ℝn) with p ∈ (0,1] and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization of H A φ(ℝn), and, as an application, the authors prove that, for a given admissible triplet (φ, q, s), if T is a sublinear operator and maps all (φ, q, s)-atoms with q < ∞ (or all continuous (φ, q, s)-atoms with q = ∞) into uniformly bounded elements of some quasi-Banach spaces ℬ, then T uniquely extends to a bounded sublinear operator from H A φ(ℝn) to ℬ. These results are new even for anisotropic Orlicz-Hardy spaces on ℝn. PMID:24757418

  10. Stress distribution in a premolar 3D model with anisotropic and isotropic enamel.

    PubMed

    Munari, Laís S; Cornacchia, Tulimar P M; Moreira, Allyson N; Gonçalves, Jason B; De Las Casas, Estevam B; Magalhães, Cláudia S

    2015-08-01

    The aim of this study was to compare the areas of stress concentration in a three-dimensional (3D) premolar tooth model with anisotropic or isotropic enamel using the finite element method. A computed tomography was imported to an image processing program to create the tooth model which was exported to a 3D modeling program. The mechanical properties and loading conditions were prescribed in Abaqus. In order to evaluate stresses, axial and oblique loads were applied simulating realistic conditions. Compression stress was observed on the side of load application, and tensile stress was observed on the opposite side. Tensile stress was concentrated mainly in the cervical region and in the alveolar insertion bone. Although stress concentration analyses of the isotropic 3D models produced similar stress distribution results when compared to the anisotropic models, tensile stress values shown by anisotropic models were smaller than the isotropic models. Oblique loads resulted in higher values of tensile stresses, which concentrate mainly in the cervical area of the tooth and in the alveolar bone insertion. Anisotropic properties must be utilized in enamel stress evaluation in non-carious cervical lesions.

  11. Dispersive Alfvén waves in a plasma with anisotropic superthermal particles

    SciTech Connect

    Liu, Y. Wang, Y. F.; Hu, T. P.

    2016-04-15

    The dispersion of dispersive Alfvén wave in a low β plasma with anisotropic superthermal particles modeled by a bi-nonextensive distribution is derived from a kinetic way. The effect of anisotropic temperature on inertial Alfvén wave is so small that it is negligible. However, it will play an important role on the property of kinetic Alfvén wave (KAW). The numerical results reveal that the presence of superthermal electrons in the small wavenumber limit will lead the damping rate of the KAW bigger than the one with Maxwellian distribution. Whereas, the damping rate of KAW in the large wavenumber limit will decrease with the presence of superthermal electrons. When the effect of electron anisotropic temperature overwhelms the effect of finite ion gyroradius in the small wavenumber regime, the damping rate of KAW grows with the presence of electron temperature anisotropy. On the other hand, when the effects of finite ion gyroradius play a dominant role in the large wavenumber regime, the damping rate of KAW increases with the effective perpendicular and parallel electron temperatures.

  12. Field dependent spin transport of anisotropic Heisenberg chain

    NASA Astrophysics Data System (ADS)

    Rezania, H.

    2016-04-01

    We have addressed the static spin conductivity and spin Drude weight of one-dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg chain in the finite magnetic field. We have investigated the behavior of transport properties by means of excitation spectrum in terms of a hard core bosonic representation. The effect of in-plane anisotropy on the spin transport properties has also been studied via the bosonic model by Green's function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the spin conductivity and spin Drude weight in the gapped field induced spin-polarized phase for various magnetic field and anisotropy parameters. Furthermore we have studied the magnetic field dependence of static spin conductivity and Drude weight for various anisotropy parameters. Our results show the regular part of spin conductivity vanishes in isotropic case however Drude weight has a finite non-zero value and the system exhibits ballistic transport properties. We also find the peak in the static spin conductivity factor moves to higher temperature upon increasing the magnetic field at fixed anisotropy. The static spin conductivity is found to be monotonically decreasing with magnetic field due to increase of energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of spin Drude weight for different magnetic field and various anisotropy parameters.

  13. Application of Perona Malik anisotropic diffusion on digital radiographic image

    NASA Astrophysics Data System (ADS)

    Halim, Suhaila Abd; Razak, Rohayu Abdul; Ibrahim, Arsmah; Manurung, Yupiter HP

    2014-07-01

    Perona Malik Anisotropic Diffusion (PMAD) is a very useful and efficient denoising technique if the parameters are properly selected. Overestimating the parameters may cause oversmoothed and underestimating it may leave unfiltered noise. This makes the selection of parameters a crucial process. In this paper the PMAD model is solved using a finite difference scheme The discretized model is evaluated using different diffusion coefficient of exponential and quadratic on defective radiographic images in terms of quality and efficiency. In the application of the PMAD model on image data, a set of defective radiographic images of welding is used as input data. Peak Signal to Noise Ratio (PSNR), Structural Similarity Measure (SSIM) and temporal time are used to evaluate the performance of the model. The implementation of the experiment has been carried out using MATLAB R2009a. In terms of quality, results show that the Quadratic Diffusion Coefficient Function (QDCF) provides better results compared with the Exponential Diffusion Coefficient Function (EDCF). In conclusion, the denoising effect using PMAD model based on finite difference scheme shows able to improve image quality by removing noise in the defective radiographic image.

  14. Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture

    NASA Astrophysics Data System (ADS)

    Shanthraj, P.; Svendsen, B.; Sharma, L.; Roters, F.; Raabe, D.

    2017-02-01

    A finite-strain anisotropic phase field method is developed to model the localisation of damage on a defined family of crystallographic planes, characteristic of cleavage fracture in metals. The approach is based on the introduction of an undamaged configuration, and the inelastic deformation gradient mapping this configuration to a damaged configuration is microstructurally represented by the opening of a set of cleavage planes in the three fracture modes. Crack opening is modelled as a dissipative process, and its evolution is thermodynamically derived. To couple this approach with a physically-based phase field method for brittle fracture, a scalar measure of the overall local damage is introduced, whose evolution is determined by the crack opening rates, and weakly coupled with the non-local phase field energy representing the crack opening resistance in the classical sense of Griffith. A finite-element implementation of the proposed model is employed to simulate the crack propagation path in a laminate and a polycrystalline microstructure. As shown in this work, it is able to predict the localisation of damage on the set of pre-defined cleavage planes, as well as the kinking and branching of the crack resulting from the crystallographic misorientation across the laminate boundary and the grain boundaries respectively.

  15. Application of Perona Malik anisotropic diffusion on digital radiographic image

    SciTech Connect

    Halim, Suhaila Abd; Razak, Rohayu Abdul; Ibrahim, Arsmah; Manurung, Yupiter HP

    2014-07-10

    Perona Malik Anisotropic Diffusion (PMAD) is a very useful and efficient denoising technique if the parameters are properly selected. Overestimating the parameters may cause oversmoothed and underestimating it may leave unfiltered noise. This makes the selection of parameters a crucial process. In this paper the PMAD model is solved using a finite difference scheme The discretized model is evaluated using different diffusion coefficient of exponential and quadratic on defective radiographic images in terms of quality and efficiency. In the application of the PMAD model on image data, a set of defective radiographic images of welding is used as input data. Peak Signal to Noise Ratio (PSNR), Structural Similarity Measure (SSIM) and temporal time are used to evaluate the performance of the model. The implementation of the experiment has been carried out using MATLAB R2009a. In terms of quality, results show that the Quadratic Diffusion Coefficient Function (QDCF) provides better results compared with the Exponential Diffusion Coefficient Function (EDCF). In conclusion, the denoising effect using PMAD model based on finite difference scheme shows able to improve image quality by removing noise in the defective radiographic image.

  16. S-wave superconductivity in anisotropic holographic insulators

    NASA Astrophysics Data System (ADS)

    Erdmenger, Johanna; Herwerth, Benedikt; Klug, Steffen; Meyer, René; Schalm, Koenraad

    2015-05-01

    Within gauge/gravity duality, we consider finite density systems in a helical lattice dual to asymptotically anti-de Sitter space-times with Bianchi VII symmetry. These systems can become an anisotropic insulator in one direction while retaining metallic be- havior in others. To this model, we add a U(1) charged scalar and show that below a critical temperature, it forms a spatially homogeneous condensate that restores isotropy in a new superconducting ground state. We determine the phase diagram in terms of the helix parameters and perform a stability analysis on its IR fixed point corresponding to a finite density condensed phase at zero temperature. Moreover, by analyzing fluctuations about the gravity background, we study the optical conductivity. Due to the lattice, this model provides an example for a holographic insulator-superfluid transition in which there is no unrealistic delta-function peak in the normal phase DC conductivity. Our results suggest that in the zero temperature limit, all degrees of freedom present in the normal phase condense. This, together with the breaking of translation invariance, has implications for Homes' and Uemuras's relations. This is of relevance for applications to real world condensed matter systems. We find a range of parameters in this system where Homes' relation holds.

  17. Stability of grain boundary texture during isothermal grain growth in UO2 considering anisotropic grain boundary properties

    NASA Astrophysics Data System (ADS)

    Hallberg, Håkan; Zhu, Yaochan

    2015-10-01

    In the present study, mesoscale simulations of grain growth in UO2 are performed using a 2D level set representation of the polycrystal grain boundary network, employed in a finite element setting. Anisotropic grain boundary properties are considered by evaluating how grain boundary energy and mobility varies with local grain boundary character. This is achieved by considering different formulations of the anisotropy of grain boundary properties, for example in terms of coincidence site lattice (CSL) correspondence. Such modeling approaches allow tracing of the stability of a number of characteristic low-Σ boundaries in the material during grain growth. The present simulations indicate that anisotropic grain boundary properties have negligible influence on the grain growth rate. However, considering the evolution of grain boundary character distribution and the grain size distribution, it is found that neglecting anisotropic boundary properties will strongly bias predictions obtained from numerical simulations.

  18. Finite-element model for three-dimensional optical scattering problems.

    PubMed

    Wei, Xiuhong; Wachters, Arthur J; Urbach, H Paul

    2007-03-01

    We present a three-dimensional model based on the finite-element method for solving the time-harmonic Maxwell equation in optics. It applies to isotropic or anisotropic dielectrics and metals and to many configurations such as an isolated scatterer in a multilayer, bi-gratings, and crystals. We discuss the application of the model to near-field optical recording.

  19. Finite Deformation by Elasticity, Slip, and Twinning: Atomistic Considerations, Continuum Modeling, and Application to Ceramic Crystals

    DTIC Science & Technology

    2009-03-01

    finite shear strains associated with slip and deformation twinning and improper lattice rotations across twin boundaries . Nonlinear anisotropic...of (2) results from gradients in twin fractions, e.g. interface dislocations at tapered twin boundaries . Disclination models of twins (Clayton et

  20. Finite-element model for three-dimensional optical scattering problems

    NASA Astrophysics Data System (ADS)

    Wei, Xiuhong; Wachters, Arthur J.; Urbach, H. Paul

    2007-03-01

    We present a three-dimensional model based on the finite-element method for solving the time-harmonic Maxwell equation in optics. It applies to isotropic or anisotropic dielectrics and metals and to many configurations such as an isolated scatterer in a multilayer, bi-gratings, and crystals. We discuss the application of the model to near-field optical recording.

  1. Anisotropic nanomaterials: structure, growth, assembly, and functions

    PubMed Central

    Sajanlal, Panikkanvalappil R.; Sreeprasad, Theruvakkattil S.; Samal, Akshaya K.; Pradeep, Thalappil

    2011-01-01

    Comprehensive knowledge over the shape of nanomaterials is a critical factor in designing devices with desired functions. Due to this reason, systematic efforts have been made to synthesize materials of diverse shape in the nanoscale regime. Anisotropic nanomaterials are a class of materials in which their properties are direction-dependent and more than one structural parameter is needed to describe them. Their unique and fine-tuned physical and chemical properties make them ideal candidates for devising new applications. In addition, the assembly of ordered one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) arrays of anisotropic nanoparticles brings novel properties into the resulting system, which would be entirely different from the properties of individual nanoparticles. This review presents an overview of current research in the area of anisotropic nanomaterials in general and noble metal nanoparticles in particular. We begin with an introduction to the advancements in this area followed by general aspects of the growth of anisotropic nanoparticles. Then we describe several important synthetic protocols for making anisotropic nanomaterials, followed by a summary of their assemblies, and conclude with major applications. PMID:22110867

  2. Anisotropic nanomaterials: structure, growth, assembly, and functions.

    PubMed

    Sajanlal, Panikkanvalappil R; Sreeprasad, Theruvakkattil S; Samal, Akshaya K; Pradeep, Thalappil

    2011-01-01

    Comprehensive knowledge over the shape of nanomaterials is a critical factor in designing devices with desired functions. Due to this reason, systematic efforts have been made to synthesize materials of diverse shape in the nanoscale regime. Anisotropic nanomaterials are a class of materials in which their properties are direction-dependent and more than one structural parameter is needed to describe them. Their unique and fine-tuned physical and chemical properties make them ideal candidates for devising new applications. In addition, the assembly of ordered one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) arrays of anisotropic nanoparticles brings novel properties into the resulting system, which would be entirely different from the properties of individual nanoparticles. This review presents an overview of current research in the area of anisotropic nanomaterials in general and noble metal nanoparticles in particular. We begin with an introduction to the advancements in this area followed by general aspects of the growth of anisotropic nanoparticles. Then we describe several important synthetic protocols for making anisotropic nanomaterials, followed by a summary of their assemblies, and conclude with major applications.

  3. Matter sourced anisotropic stress for dark energy

    NASA Astrophysics Data System (ADS)

    Chang, Baorong; Lu, Jianbo; Xu, Lixin

    2014-11-01

    Usually a dark energy as a perfect fluid is characterized by the ratio of pressure to energy density (w =p /ρ ) and the ratio of their perturbations in its rest frame (cs2=δ p /δ ρ ). However, a dark energy would have other characteristics beyond its equation of state and the effective speed of sound. Here the extra property is the anisotropic stress sourced by matter as a simple extension to the perfect fluid model. At the background level, this anisotropic stress is zero with respect to the cosmological principle, but not at the first-order perturbation. We tested the viability of the existence of this kind of anisotropic stress by using the currently available cosmic observations through the geometrical and dynamical measurements. Using the Markov-chain Monte Carlo method, we found that the upper bounds on the anisotropic stress which enters into the summation of the Newtonian potentials should be of the order O (1 0-3)Δm . We did not find any strong evidence for the existence of this matter-sourced anisotropic stress, even in the 1 σ region.

  4. Spin-anisotropic magnetic impurity in a Fermi gas: Integration of poor man's scaling equations

    NASA Astrophysics Data System (ADS)

    Kogan, Eugene; Noda, Kazuto; Yunoki, Seiji

    2017-04-01

    We consider a single magnetic impurity described by the spin-anisotropic s -d (f ) exchange (Kondo) model and formulate a scaling equation for the spin-anisotropic model when the density of states (DOS) of electrons is a power-law function of energy (measured relative to the Fermi energy). We solve this equation containing terms up to the second order in coupling constants in terms of elliptic functions. From the obtained solution we find the phases corresponding to the infinite isotropic antiferromagnetic Heisenberg exchange, to the impurity spin decoupled from the electron environment (only for the pseudogap DOS), and to the infinite Ising exchange (only for the diverging DOS). We analyze the critical surfaces, corresponding to the finite isotropic antiferromagnetic Heisenberg exchange for the pseudogap DOS.

  5. The effect of beam directivity on the inspection of anisotropic materials using ultrasonic arrays

    NASA Astrophysics Data System (ADS)

    Lane, C. J. L.; Wilcox, P. D.

    2012-05-01

    The beam directivity from an ultrasonic transducer in isotropic materials is well documented. However, beam directivities in elastically anisotropic materials and their effect on ultrasonic NDE inspection has been investigated far less extensively. In this paper, analytical and numerical finite element models are developed to predict the beam directivity in a single crystal nickel-based superalloy. This material is highly anisotropic and is used widely in the gas-turbine industry. The developed models are used to investigate the effect of the crystallographic orientation on the beam directivity. In turn, the effect of beam directivity on defect detection sensitivity and characterization capability using an ultrasonic array is demonstrated. It is shown that the effect is particularly important for the accurate sizing of small defects.

  6. Calculations of Diffuser Flows with an Anisotropic K-Epsilon Model

    NASA Technical Reports Server (NTRS)

    Zhu, J.; Shih, T.-H.

    1995-01-01

    A newly developed anisotropic K-epsilon model is applied to calculate three axisymmetric diffuser flows with or without separation. The new model uses a quadratic stress-strain relation and satisfies the realizability conditions, i.e., it ensures both the positivity of the turbulent normal stresses and the Schwarz' inequality between any fluctuating velocities. Calculations are carried out with a finite-element method. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to ensure numerical credibility of the solutions. The standard K-epsilon model is also used in order to highlight the performance of the new model. Comparison with the experimental data shows that the anisotropic K-epsilon model performs consistently better than does the standard K-epsilon model in all of the three test cases.

  7. Five-layer realistic head model based on inhomogeneous and anisotropic conductivity distribution of different tissues

    NASA Astrophysics Data System (ADS)

    Yan, Dandan; Zhang, Jianwei; Wu, Weijuan; Ying, Xiaoyan; Wu, Xiangping

    2009-10-01

    This paper is focused on the sophisticated realistic head modeling based on inhomogeneous and anisotropic conductivity distribution of the head tissues. The finite element method (FEM) was used to model the five-layer head volume conductor models with hexahedral elements from segmentation and mapping of DT-MRI data. Then the inhomogeneous conductivities of the scalp, CSF and gray matter tissue were distributed according a normal distribution based on the mean value of respective tissues. The electric conductivity of the brain tissues dictates different inhomogeneous and anisotropic at some different microscopic levels. Including the inhomogeneous and anisotropy of the tissue would improve the accuracy of the MREIT, EEG and MEG problems in the simulation research.

  8. Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media

    SciTech Connect

    Oskooi, Ardavan; Johnson, Steven G.

    2011-04-01

    We show that some previous proposals for perfectly matched layer (PML) absorbers in anisotropic media or for waveguides at oblique incidence are not, in fact true PMLs; in previous work we similarly showed a failure of several PML proposals for periodic media (photonic crystals). We therefore argue that a more careful validation scheme is required for PML proposals, in contrast to past authors who have typically checked only that reflections are small for a fixed resolution, and suggest a simple validation scheme that can be readily applied to any PML proposal regardless of derivation or implementation. We demonstrate this test for a corrected, unsplit-field PML valid for anisotropic, dispersive media, implemented in both planewave-expansion and finite-difference time-domain (FDTD) methods.

  9. Nanoindentation study of electrodeposited Ag thin coating: An inverse calculation of anisotropic elastic-plastic properties

    SciTech Connect

    Cheng, Guang; Sun, Xin; Wang, Yuxin; Tay, See Leng; Gao, Wei

    2017-01-01

    A new inverse method was proposed to calculate the anisotropic elastic-plastic properties (flow stress) of thin electrodeposited Ag coating utilizing nanoindentation tests, previously reported inverse method for isotropic materials and three-dimensional (3-D) finite element analyses (FEA). Indentation depth was ~4% of coating thickness (~10 μm) to avoid substrate effect and different indentation responses were observed in the longitudinal (L) and the transverse (T) directions. The estimated elastic-plastic properties were obtained in the newly developed inverse method by matching the predicted indentation responses in the L and T directions with experimental measurements considering indentation size effect (ISE). The results were validated with tensile flow curves measured from free-standing (FS) Ag film. The current method can be utilized to characterize the anisotropic elastic-plastic properties of coatings and to provide the constitutive properties for coating performance evaluations.

  10. Evaluation of Springback for DP980 S Rail Using Anisotropic Hardening Models

    NASA Astrophysics Data System (ADS)

    Choi, Jisik; Lee, Jinwoo; Bae, Gihyun; Barlat, Frederic; Lee, Myoung-Gyu

    2016-07-01

    The effect of anisotropic hardening models on springback of an S-rail part was investigated. Two advanced constitutive models based on distortional and kinematic hardening, which captured the Bauschinger effect, transient hardening, and permanent softening during strain path change, were implemented in a finite element (FE) code. In-plane compression-tension tests were performed to identify the model parameters. The springback of the S-rail after forming a 980 MPa dual-phase steel sheet sample was measured and analyzed using different hardening models. The comparison between experimental and FE results demonstrated that the advanced anisotropic hardening models, which are particularly suitable for non-proportional loading, significantly improved the springback prediction capability of an advanced high strength steel.

  11. Transversely anisotropic optical fiber: Variatioonal analysis of a nonstandard eigen problem

    NASA Astrophysics Data System (ADS)

    Lindell, I. V.; Oksanen, M. I.

    1982-12-01

    The variational principle for nonstandard eigenvalue problems is applied to guided wave propagation in an anisotropic dielectric waveguide. A stationary functional is derived for the general dielectric waveguide with transverse anisotropy. The functional is tested for an isotropic step index single mode fiber. For simple trial functions with only two parameters, good accuracy is obtained. For two types of transversely anisotropic step index fibers, relations between the propagation factor, anisotropy parameter, dielectric parameter and frequency are calculated. The functional does not assume weak guidance condition nor perturbational anisotropy and, hence, is also applicable for other dielectric waveguides. A small computer or a programmable calculator is adequate. The spurious modes causing confusion in the finite element method of calculation do not appear with the method.

  12. Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

    NASA Astrophysics Data System (ADS)

    Zhang, Xue-Feng; Hu, Shijie; Pelster, Axel; Eggert, Sebastian

    2016-11-01

    We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both hopping and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase.

  13. Sheet resistance characterization of locally anisotropic transparent conductive films made of aligned metal-enriched single-walled carbon nanotubes.

    PubMed

    Kang, Hosung; Kim, Duckjong; Baik, Seunghyun

    2014-09-21

    One-dimensional conductive fillers such as single-walled carbon nanotubes (SWNTs) can be aggregated and aligned during transparent conductive film (TCF) formation by the vacuum filtration method. The potential error of analysing the average sheet resistance of these anisotropic films, using the four-point probe in-line method and the conversion formula developed assuming uniform isotropic material properties, was systematically investigated by finite element analysis and experiments. The finite element analysis of anisotropic stripe-patterned TCFs with alternating low (ρ1) and high (ρ2) resistivities revealed that the estimated average sheet resistance approached ρ1/t when the probes were parallel to the aligned nanotubes. The thickness of the film is t. It was more close to ρ2/t when the probes were perpendicular to the aligned tubes. Indeed, TCFs fabricated by the vacuum filtration method using metal-enriched SWNTs exhibited highly anisotropic local regions where tubes were aggregated and aligned. The local sheet resistances of randomly oriented, aligned, and perpendicular tube regions of the TCF at a transmittance of 89.9% were 5000, 2.4, and 12 300 Ω □(-1), respectively. Resistivities of the aggregated and aligned tube region (ρ1 = 1.2 × 10(-5) Ω cm) and the region between tubes (ρ2 = 6.2 × 10(-2) Ω cm) could be approximated with the aid of finite element analysis. This work demonstrates the potential error of characterizing the average sheet resistance of anisotropic TCFs using the four-point probe in-line method since surprisingly high or low values could be obtained depending on the measurement angle. On the other hand, a better control of aggregation and alignment of nanotubes would realize TCFs with a very small anisotropic resistivity and a high transparency.

  14. A kinematically driven anisotropic viscoelastic constitutive model applied to tires

    NASA Astrophysics Data System (ADS)

    Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

    1995-08-01

    Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

  15. A kinematically driven anisotropic viscoelastic constitutive model applied to tires

    NASA Technical Reports Server (NTRS)

    Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

    1995-01-01

    Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

  16. A kinematically driven anisotropic viscoelastic constitutive model applied to tires

    NASA Technical Reports Server (NTRS)

    Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

    1995-01-01

    Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

  17. New methodology for mechanical characterization of human superficial facial tissue anisotropic behaviour in vivo.

    PubMed

    Then, C; Stassen, B; Depta, K; Silber, G

    2017-02-21

    Mechanical characterization of human superficial facial tissue has important applications in biomedical science, computer assisted forensics, graphics, and consumer goods development. Specifically, the latter may include facial hair removal devices. Predictive accuracy of numerical models and their ability to elucidate biomechanically relevant questions depends on the acquisition of experimental data and mechanical tissue behavior representation. Anisotropic viscoelastic behavioral characterization of human facial tissue, deformed in vivo with finite strain, however, is sparse. Employing an experimental-numerical approach, a procedure is presented to evaluate multidirectional tensile properties of superficial tissue layers of the face in vivo. Specifically, in addition to stress relaxation, displacement-controlled multi-step ramp-and-hold protocols were performed to separate elastic from inelastic properties. For numerical representation, an anisotropic hyperelastic material model in conjunction with a time domain linear viscoelasticity formulation with Prony series was employed. Model parameters were inversely derived, employing finite element models, using multi-criteria optimization. The methodology provides insight into mechanical superficial facial tissue properties. Experimental data shows pronounced anisotropy, especially with large strain. The stress relaxation rate does not depend on the loading direction, but is strain-dependent. Preconditioning eliminates equilibrium hysteresis effects and leads to stress-strain repeatability. In the preconditioned state tissue stiffness and hysteresis insensitivity to strain rate in the applied range is evident. The employed material model fits the nonlinear anisotropic elastic results and the viscoelasticity model reasonably reproduces time-dependent results. Inversely deduced maximum anisotropic long-term shear modulus of linear elasticity is G∞,max(aniso)=2.43kPa and instantaneous initial shear modulus at an

  18. Temperature-dependent anisotropic charge-carrier mobility limited by ionized impurity scattering in thin-layer black phosphorus

    NASA Astrophysics Data System (ADS)

    Liu, Yue; Ruden, P. Paul

    2017-04-01

    Anisotropic charge-carrier transport in black phosphorus limited by ionized impurity scattering at finite temperature is explored theoretically. The anisotropic electronic structure enters the calculation for the polarizability (screening), the momentum relaxation time, and the mobility. For finite temperature, elastic scattering is not limited to the Fermi surface and the polarizability is temperature dependent. The impact of screening is investigated in detail with its dependence on carrier density and temperature. Competing with the thermal excitation effects, the temperature dependence of the polarizability is found to dominate for T <100 K. As a result, the charge-carrier mobility slowly decreases with increasing temperature. The weak temperature dependence of the mobility and its anisotropy ratio of 1.9-3.2 agree with published experimental data.

  19. Leith diffusion model for homogeneous anisotropic turbulence

    NASA Astrophysics Data System (ADS)

    Rubinstein, Robert; Clark, Timothy; Kurien, Susan

    2016-11-01

    A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.

  20. Leith diffusion model for homogeneous anisotropic turbulence

    DOE PAGES

    Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan

    2017-06-01

    Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numericalmore » simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.« less

  1. Elliptical-anisotropic eikonal phase velocity tomography

    NASA Astrophysics Data System (ADS)

    de Ridder, S. A. L.; Biondi, B. L.; Nichols, D.

    2015-02-01

    We formulated an anisotropic eikonal tomography approach for phase velocities based on a two-dimensional elliptical-anisotropic wave equation. We can fit the parameters of the ellipse directly from measured first-order traveltime surface gradients and constrain these parameters to vary smoothly over space. The method is applied to Scholte waves in virtual seismic sources from stations in the Life of Field Seismic Ocean Bottom Cable array installed over the Ekofisk field. The fast directions of the azimuthally anisotropic Scholte wave velocities form a large circular pattern over the Ekofisk field. This pattern dominates the Scholte wave phase velocities at Ekofisk between 0.7 and 1.1 Hz. It results from the overburden stress state and from seafloor subsidence induced by decades of hydrocarbon extraction.

  2. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

    PubMed Central

    Hilton, Harry H.

    2012-01-01

    Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated. PMID:28817038

  3. Azimuthally Anisotropic 3D Velocity Continuation

    DOE PAGES

    Burnett, William; Fomel, Sergey

    2011-01-01

    We extend time-domain velocity continuation to the zero-offset 3D azimuthally anisotropic case. Velocity continuation describes how a seismic image changes given a change in migration velocity. This description turns out to be of a wave propagation process, in which images change along a velocity axis. In the anisotropic case, the velocity model is multiparameter. Therefore, anisotropic image propagation is multidimensional. We use a three-parameter slowness model, which is related to azimuthal variations in velocity, as well as their principal directions. This information is useful for fracture and reservoir characterization from seismic data. We provide synthetic diffraction imaging examples to illustratemore » the concept and potential applications of azimuthal velocity continuation and to analyze the impulse response of the 3D velocity continuation operator.« less

  4. Elastic properties of spherically anisotropic piezoelectric composites

    NASA Astrophysics Data System (ADS)

    Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming

    2010-09-01

    Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.

  5. Gravitational stresses in anisotropic rock masses

    USGS Publications Warehouse

    Amadei, B.; Savage, W.Z.; Swolfs, H.S.

    1987-01-01

    This paper presents closed-form solutions for the stress field induced by gravity in anisotropic rock masses. These rocks are assumed to be laterally restrained and are modelled as a homogeneous, orthotropic or transversely isotropic, linearly elastic material. The analysis, constrained by the thermodynamic requirement that strain energy be positive definite, gives the following important result: inclusion of anisotropy broadens the range of permissible values of gravity-induced horizontal stresses. In fact, for some ranges of anisotropic rock properties, it is thermodynamically admissible for gravity-induced horizontal stresses to exceed the vertical stress component; this is not possible for the classical isotropic solution. Specific examples are presented to explore the nature of the gravity-induced stress field in anisotropic rocks and its dependence on the type, degree and orientation of anisotropy with respect to the horizontal ground surface. ?? 1987.

  6. Magnetization of anisotropic Type II superconductors

    SciTech Connect

    Mints, R.G.

    1989-04-10

    Peculiarities of magnetization of anisotropic type II superconductors are of considerable interest in view of the discovery of high-T/sub c/ superconductors characterized by strongly asymmetric layered structure. Specifics of the penetration of magnetic flux into an anisotropic type II superconductor were discussed in the literature. This analysis gave the distribution of induction in an isolated vortex, its energy, and critical magnetic field H/sub c1/. However, the magnetization curve of anisotropic superconductors was not considered. This paper deals with the magnetic moment of uniaxial London superconductor in the interval H/sub c1/ /le/ H/sub 0/ << H/sub c2/, where H/sub 0/ is the external magnetic field strength.

  7. Infrared properties of an anisotropically stirred fluid

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Barton, J. Michael

    1987-01-01

    A renormalization group is developed for the Navier-Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen, so that the fixed point of renormalization group has a k exp -5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. when the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of two-dimensional turbulence is discussed.

  8. Leith diffusion model for homogeneous anisotropic turbulence

    SciTech Connect

    Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan

    2016-07-19

    Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.

  9. Isotropic versus anisotropic modeling of photorefractive solitons.

    PubMed

    Belić, M R; Vujić, D; Stepken, A; Kaiser, F; Calvo, G F; Agulló-López, F; Carrascosa, M

    2002-06-01

    The question of the isotropic versus anisotropic modeling of incoherent spatial screening solitons in photorefractive crystals is addressed by a careful theoretical and numerical analysis. Isotropic, or local, models allow for an extended spiraling of two interacting scalar solitons, and for a prolonged propagation of vortex vector solitons, whereas anisotropic, nonlocal, models prevent such phenomena. In the context of Kukhtarev's material equations, the difference in behavior is traced to the continuity equation for the current density. We further show that neither an indefinite spiraling of two solitons nor stable propagation of vortex vector solitons is generally possible in both isotropic and anisotropic models. Such systems do not conserve angular momentum, even in the case of an isotropic change in the index of refraction.

  10. Forming Limits for Anisotropic Sheet Metals

    NASA Astrophysics Data System (ADS)

    Kim, Youngsuk; Kim, Chul; Lee, Sangryong; Won, Sungyeun; Hwang, Sangmoo

    Most failures of ductile materials in metal forming processes occurred due to material damage evolution-void nucleation, growth and coalescence. In this paper, modified version of Gurson-Tvergaard's yield function in conjunction with the Hosford's non-quadratic anisotropic yield criterion is studied to clarify the plastic deformation characteristic of voided anisotropic sheet metals. The void growth of an anisotropic sheet under biaxial tensile loading and damage effect of void growth on forming limits of sheet metals are investigated. Also the characteristic length defining the neck geometry is introduced in M-K model to incorporate the effect of triaxial stress in necked region on forming limits. The forming limits theoretically predicted are compared with some experimental data. Satisfactory agreement was obtained between the predictions and experimental data.

  11. Anisotropic Hanle line shape via magnetothermoelectric phenomena

    NASA Astrophysics Data System (ADS)

    Das, K. S.; Dejene, F. K.; van Wees, B. J.; Vera-Marun, I. J.

    2016-11-01

    We observe anisotropic Hanle line shape with unequal in-plane and out-of-plane nonlocal signals for spin precession measurements carried out on lateral metallic spin valves with transparent interfaces. The conventional interpretation for this anisotropy corresponds to unequal spin relaxation times for in-plane and out-of-plane spin orientations as for the case of two-dimensional materials like graphene, but it is unexpected in a polycrystalline metallic channel. Systematic measurements as a function of temperature and channel length, combined with both analytical and numerical thermoelectric transport models, demonstrate that the anisotropy in the Hanle line shape is magnetothermal in origin, caused by the anisotropic modulation of the Peltier and Seebeck coefficients of the ferromagnetic electrodes. Our results call for the consideration of such magnetothermoelectric effects in the study of anisotropic spin relaxation.

  12. Foam front propagation in anisotropic oil reservoirs.

    PubMed

    Grassia, P; Torres-Ulloa, C; Berres, S; Mas-Hernández, E; Shokri, N

    2016-04-01

    The pressure-driven growth model is considered, describing the motion of a foam front through an oil reservoir during foam improved oil recovery, foam being formed as gas advances into an initially liquid-filled reservoir. In the model, the foam front is represented by a set of so-called "material points" that track the advance of gas into the liquid-filled region. According to the model, the shape of the foam front is prone to develop concave sharply curved concavities, where the orientation of the front changes rapidly over a small spatial distance: these are referred to as "concave corners". These concave corners need to be propagated differently from the material points on the foam front itself. Typically the corner must move faster than those material points, otherwise spurious numerical artifacts develop in the computed shape of the front. A propagation rule or "speed up" rule is derived for the concave corners, which is shown to be sensitive to the level of anisotropy in the permeability of the reservoir and also sensitive to the orientation of the corners themselves. In particular if a corner in an anisotropic reservoir were to be propagated according to an isotropic speed up rule, this might not be sufficient to suppress spurious numerical artifacts, at least for certain orientations of the corner. On the other hand, systems that are both heterogeneous and anisotropic tend to be well behaved numerically, regardless of whether one uses the isotropic or anisotropic speed up rule for corners. This comes about because, in the heterogeneous and anisotropic case, the orientation of the corner is such that the "correct" anisotropic speed is just very slightly less than the "incorrect" isotropic one. The anisotropic rule does however manage to keep the corner very slightly sharper than the isotropic rule does.

  13. The family of anisotropically scaled equatorial waves

    NASA Astrophysics Data System (ADS)

    RamíRez GutiéRrez, Enver; da Silva Dias, Pedro Leite; Raupp, Carlos; Bonatti, Jose Paulo

    2011-04-01

    In the present work we introduce the family of anisotropic equatorial waves. This family corresponds to equatorial waves at intermediate states between the shallow water and the long wave approximation model. The new family is obtained by using anisotropic time/space scalings on the linearized, unforced and inviscid shallow water model. It is shown that the anisotropic equatorial waves tend to the solutions of the long wave model in one extreme and to the shallow water model solutions in the other extreme of the parameter dependency. Thus, the problem associated with the completeness of the long wave model solutions can be asymptotically addressed. The anisotropic dispersion relation is computed and, in addition to the typical dependency on the equivalent depth, meridional quantum number and zonal wavenumber, it also depends on the anisotropy between both zonal to meridional space and velocity scales as well as the fast to slow time scales ratio. For magnitudes of the scales compatible with those of the tropical region, both mixed Rossby-gravity and inertio-gravity waves are shifted to a moderately higher frequency and, consequently, not filtered out. This draws attention to the fact that, for completeness of the long wave like solutions, it is necessary to include both the anisotropic mixed Rossby-gravity and inertio-gravity waves. Furthermore, the connection of slow and fast manifolds (distinguishing feature of equatorial dynamics) is preserved, though modified for the equatorial anisotropy parameters used δ ∈ < 1]. New possibilities of horizontal and vertical scale nonlinear interactions are allowed. Thus, the anisotropic shallow water model is of fundamental importance for understanding multiscale atmosphere and ocean dynamics in the tropics.

  14. Quantifying the Nonlinear, Anisotropic Material Response of Spinal Ligaments

    NASA Astrophysics Data System (ADS)

    Robertson, Daniel J.

    Spinal ligaments may be a significant source of chronic back pain, yet they are often disregarded by the clinical community due to a lack of information with regards to their material response, and innervation characteristics. The purpose of this dissertation was to characterize the material response of spinal ligaments and to review their innervation characteristics. Review of relevant literature revealed that all of the major spinal ligaments are innervated. They cause painful sensations when irritated and provide reflexive control of the deep spinal musculature. As such, including the neurologic implications of iatrogenic ligament damage in the evaluation of surgical procedures aimed at relieving back pain will likely result in more effective long-term solutions. The material response of spinal ligaments has not previously been fully quantified due to limitations associated with standard soft tissue testing techniques. The present work presents and validates a novel testing methodology capable of overcoming these limitations. In particular, the anisotropic, inhomogeneous material constitutive properties of the human supraspinous ligament are quantified and methods for determining the response of the other spinal ligaments are presented. In addition, a method for determining the anisotropic, inhomogeneous pre-strain distribution of the spinal ligaments is presented. The multi-axial pre-strain distributions of the human anterior longitudinal ligament, ligamentum flavum and supraspinous ligament were determined using this methodology. Results from this work clearly demonstrate that spinal ligaments are not uniaxial structures, and that finite element models which account for pre-strain and incorporate ligament's complex material properties may provide increased fidelity to the in vivo condition.

  15. Charged anisotropic matter with linear or nonlinear equation of state

    SciTech Connect

    Varela, Victor; Rahaman, Farook; Ray, Saibal; Chakraborty, Koushik; Kalam, Mehedi

    2010-08-15

    Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplifications achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or nonlinear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge (10{sup 19}C) and maximum electric field intensities are very large (10{sup 23}-10{sup 24} statvolt/cm) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.

  16. A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

    SciTech Connect

    Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin

    2015-06-05

    The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

  17. A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

    DOE PAGES

    Gao, Kai; Chung, Eric T.; Gibson, Richard L.; ...

    2015-06-05

    The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elasticmore » wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.« less

  18. An Anisotropic Multiphysics Model for Intervertebral Disk

    PubMed Central

    Gao, Xin; Zhu, Qiaoqiao; Gu, Weiyong

    2016-01-01

    Intervertebral disk (IVD) is the largest avascular structure in human body, consisting of three types of charged hydrated soft tissues. Its mechanical behavior is nonlinear and anisotropic, due mainly to nonlinear interactions among different constituents within tissues. In this study, a more realistic anisotropic multiphysics model was developed based on the continuum mixture theory and employed to characterize the couplings of multiple physical fields in the IVD. Numerical simulations demonstrate that this model is capable of systematically predicting the mechanical and electrochemical signals within the disk under various loading conditions, which is essential in understanding the mechanobiology of IVD. PMID:27099402

  19. Evolution of multidimensional flat anisotropic cosmological models

    SciTech Connect

    Beloborodov, A. ); Demianski, M. Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw International Center for Relativistic Astrophysics , Universita di Roma I, La Sapienza, Rome ); Ivanov, P.; Polnarev, A.G. )

    1993-07-15

    We study the dynamics of a flat multidimensional anisotropic cosmological model filled with an anisotropic fluidlike medium. By an appropriate choice of variables, the dynamical equations reduce to a two-dimensional dynamical system. We present a detailed analysis of the time evolution of this system and the conditions of the existence of spacetime singularities. We investigate the conditions under which violent, exponential, and power-law inflation is possible. We show that dimensional reduction cannot proceed by anti-inflation (rapid contraction of internal space). Our model indicates that it is very difficult to achieve dimensional reduction by classical means.

  20. Inverse moments equilibria for helical anisotropic systems

    NASA Astrophysics Data System (ADS)

    Cooper, W. A.; Hirshman, S. P.; Depassier, M. C.

    1987-11-01

    An energy functional is devised for magnetic confinement schemes that have anisotropic plasma pressure. The minimization of this energy functional is demonstrated to reproduce components of the magnetohydrodynamic (MHD) force balance relation in systems with helical symmetry. An iterative steepest descent procedure is applied to the Fourier moments of the inverse magnetic flux coordinates to minimize the total energy and thus generate anisotropic pressure MHD equilibria. Applications to straight ELMO Snaky Torus (NTIS Document No. DE-84002406) configurations that have a magnetic well on the outermost flux surfaces have been obtained.

  1. On cracking of charged anisotropic polytropes

    NASA Astrophysics Data System (ADS)

    Azam, M.; Mardan, S. A.

    2017-01-01

    Recently in [1], the role of electromagnetic field on the cracking of spherical polytropes has been investigated without perturbing charge parameter explicitly. In this study, we have examined the occurrence of cracking of anisotropic spherical polytropes through perturbing parameters like anisotropic pressure, energy density and charge. We consider two different types of polytropes in this study. We discuss the occurrence of cracking in two different ways (i) by perturbing polytropic constant, anisotropy and charge parameter (ii) by perturbing polytropic index, anisotropy and charge parameter for each case. We conclude that cracking appears for a wide range of parameters in both cases. Also, our results are reduced to [2] in the absence of charge.

  2. Raman Tensor Formalism for Optically Anisotropic Crystals.

    PubMed

    Kranert, Christian; Sturm, Chris; Schmidt-Grund, Rüdiger; Grundmann, Marius

    2016-03-25

    We present a formalism for calculating the Raman scattering intensity dependent on the polarization configuration for optically anisotropic crystals. It can be applied to crystals of arbitrary orientation and crystal symmetry measured in normal incidence backscattering geometry. The classical Raman tensor formalism cannot be used for optically anisotropic materials due to birefringence causing the polarization within the crystal to be depth dependent. We show that in the limit of averaging over a sufficiently large scattering depth, the observed Raman intensities converge and can be described by an effective Raman tensor given here. Full agreement with experimental results for uniaxial and biaxial crystals is demonstrated.

  3. Optical Activity of Anisotropic Achiral Surfaces

    SciTech Connect

    Verbiest, T.; Kauranen, M.; Van Rompaey, Y.; Persoons, A. |

    1996-08-01

    Anisotropic achiral surfaces respond differently to left- and right-hand circularly polarized light. This occurs when the orientation of the surface with respect to an otherwise achiral experimental setup makes the total geometry chiral. Such optical activity is demonstrated in second-harmonic generation from an anisotropic thin molecular film. The circular-difference response reverses sign as the handedness of the geometry is reversed and vanishes when the setup possesses a mirror plane. The results are explained within the electric-dipole-allowed second-order surface nonlinearity. {copyright} {ital 1996 The American Physical Society.}

  4. Directional wetting in anisotropic inverse opals.

    PubMed

    Phillips, Katherine R; Vogel, Nicolas; Burgess, Ian B; Perry, Carole C; Aizenberg, Joanna

    2014-07-01

    Porous materials display interesting transport phenomena due to restricted motion of fluids within the nano- to microscale voids. Here, we investigate how liquid wetting in highly ordered inverse opals is affected by anisotropy in pore geometry. We compare samples with different degrees of pore asphericity and find different wetting patterns depending on the pore shape. Highly anisotropic structures are infiltrated more easily than their isotropic counterparts. Further, the wetting of anisotropic inverse opals is directional, with liquids filling from the side more easily. This effect is supported by percolation simulations as well as direct observations of wetting using time-resolved optical microscopy.

  5. Anisotropic superconductors in tilted magnetic fields

    SciTech Connect

    Vlasko-Vlasov, V. K.; Glatz, A.; Koshelev, A. E.; Welp, U.; Kwok, W. K.

    2015-06-01

    We present images of magnetic flux structures in a single crystal of YBa2Cu3O7-d during remagnetization by fields tilted from the basal plane of the crystal. Depending on the magnitude and angle of the applied field we observe anisotropic flux penetration along and across the in-plane field component and emergence of vortex instabilities resulting in modulated flux distributions. We associate the observed patterns with flux cutting effects and with tilted vortex structures intrinsic for layered superconductors. Time dependent Ginzburg-Landau simulations show preferential vortex motion across the c-axis and reveal the flux structure evolution in anisotropic superconductors under tilted magnetic fields.

  6. Differential matrix formalism for depolarizing anisotropic media.

    PubMed

    Ossikovski, Razvigor

    2011-06-15

    Azzam's differential matrix formalism [J. Opt. Soc. Am. 68, 1756 (1978)], originally developed for longitudinally inhomogeneous anisotropic nondepolarizing media, is extended to include depolarizing media. The generalization is physically interpreted in terms of means and uncertainties of the elementary optical properties of the medium, as well as of three anisotropy absorption parameters introduced to describe the depolarization. The formalism results in a particularly simple mathematical procedure for the retrieval of the elementary properties of a generally depolarizing anisotropic medium, assumed to be globally homogeneous, from its experimental Mueller matrix. The approach is illustrated on literature data and the conditions of its validity are identified and discussed.

  7. Development of the subroutine library ‘UMMDp’ for anisotropic yield functions commonly applicable to commercial FEM codes

    NASA Astrophysics Data System (ADS)

    Takizawa, Hideo; Kuwabara, Toshihiko; Oide, Kai; Yoshida, Junji

    2016-08-01

    Numerous types of yield functions have been proposed to describe the shape of a realistic yield surface. Major commercial finite element codes include few anisotropic functions. Alternatively, the codes allow users to implement material models through user- subroutines. We develop the Unified Material Model Driver for Plasticity (UMMDp) subroutine library, which enables users to implement an arbitrary yield function easily. In this paper, the framework of the UMMDp is presented and its availabilities is shown through examples of sheet metal forming analyses.

  8. An Engineered Anisotropic Nanofilm with Unidirectional Wetting Properties

    DTIC Science & Technology

    2010-01-01

    ARTICLES PUBLISHED ONLINE: 10 OCTOBER 2010 | DOI: 10.1038/NMAT2864 An engineered anisotropic nanofilm with unidirectional wetting properties Niranjan...body3. Engineering synthetic materials with such anisotropic adhesive properties has led to advances in digitalmicrofluidic devices5,6 andmedicine7,8...The anisotropic wetting properties of existing engineered surfaces are derived either from spatial gradients (for example, temperature, surface

  9. Simple Finite Jordan Pseudoalgebras

    NASA Astrophysics Data System (ADS)

    Kolesnikov, Pavel

    2009-01-01

    We consider the structure of Jordan H-pseudoalgebras which are linearly finitely generated over a Hopf algebra H. There are two cases under consideration: H = U(h) and H = U(h) # C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits-Kantor-Koecher construction for finite Jordan pseudoalgebras and describe all simple ones.

  10. Simulation of Anisotropic Rock Damage for Geologic Fracturing

    NASA Astrophysics Data System (ADS)

    Busetti, S.; Xu, H.; Arson, C. F.

    2014-12-01

    A continuum damage model for differential stress-induced anisotropic crack formation and stiffness degradation is used to study geologic fracturing in rocks. The finite element-based model solves for deformation in the quasi-linear elastic domain and determines the six component damage tensor at each deformation increment. The model permits an isotropic or anisotropic intact or pre-damaged reference state, and the elasticity tensor evolves depending on the stress path. The damage variable, similar to Oda's fabric tensor, grows when the surface energy dissipated by three-dimensional opened cracks exceeds a threshold defined at the appropriate scale of the representative elementary volume (REV). At the laboratory or wellbore scale (<1m) brittle continuum damage reflects microcracking, grain boundary separation, grain crushing, or fine delamination, such as in shale. At outcrop (1m-100m), seismic (10m-1000m), and tectonic (>1000m) scales the damaged REV reflects early natural fracturing (background or tectonic fracturing) or shear strain localization (fault process zone, fault-tip damage, etc.). The numerical model was recently benchmarked against triaxial stress-strain data from laboratory rock mechanics tests. However, the utility of the model to predict geologic fabric such as natural fracturing in hydrocarbon reservoirs was not fully explored. To test the ability of the model to predict geological fracturing, finite element simulations (Abaqus) of common geologic scenarios with known fracture patterns (borehole pressurization, folding, faulting) are simulated and the modeled damage tensor is compared against physical fracture observations. Simulated damage anisotropy is similar to that derived using fractured rock-mass upscaling techniques for pre-determined fracture patterns. This suggests that if model parameters are constrained with local data (e.g., lab, wellbore, or reservoir domain), forward modeling could be used to predict mechanical fabric at the relevant

  11. Wellbore stability analysis in carbonate reservoir considering anisotropic behaviour

    NASA Astrophysics Data System (ADS)

    Alves, José; Guevara, Nestor; Coelho, Lucia; Baud, Patrick

    2010-05-01

    Carbonate reservoirs represent a major part of the world oil and gas reserves. In particular, recent discoveries in the pre-salt offshore Brazil place big challenges to exploration and production under high temperatures and pressures (HTHP). During production, the extraction of hydrocarbons reduces pore pressure and thus causes an increase in the effective stress and mechanical compaction in the reservoir. The compactive deformation and failure may be spatially extensive or localized to the vicinity of the wellbore, but in either case the consequences can be economically severe involving surface subsidence, well failure and various production problems. The analysis of wellbore stability and more generally of deformation and failure in carbonate environments hinges upon a relevant constitutive modeling of carbonate rocks over a wide range of porosities, in particular, observed microstructure of samples suggests anisotropic behaviour. In this study, we performed a wellbore stability analysis for a lateral wellbore junction in three dimensions. The complex geometry for the wellbore junction was modeled with tetrahedral finite elements considering a rate independent elastic-plastic isotropic material that presented linear behavior during elastic strain and associated flow rule. A finite element model simulating drilling and production phases were done for field conditions from a deep water reservoir in Campos basin, offshore Brazil. In this context, several scenarios were studied considering true 3D orientation for both in situ stresses and geometry of the wellbore junction itself. We discussed the impact of constitutive modeling, considering anisotropic ductile damage and pressure sensitiveness on the wellbore stability. Parameter values for the analysis were based based on experimental data on two micritic porous carbonates. Series of conventional triaxial experiments were performed at room temperature in dry and wet conditions on samples of Comiso and Tavel

  12. Buckling Analysis of Anisotropic Curved Panels and Shells with Variable Curvature

    NASA Technical Reports Server (NTRS)

    Jaunky, Navin; Knight, Norman F., Jr.; Ambur, Damodar R.

    1998-01-01

    A buckling formulation for anisotropic curved panels with variable curvature is presented in this paper. The variable curvature panel is assumed to consists of two or more panels of constant but different curvatures. Bezier functions are used as Ritz functions Displacement (C(sup 0)), and slope (C(sup 1)) continuities between segments are imposed by manipulation of the Bezier control points. A first-order shear-deformation theory is used in the buckling formulation. Results obtained from the present formulation are compared with those from finite element simulations and are found to be in good agreement.

  13. Theory of anisotropic thin-walled closed-cross-section beams

    NASA Technical Reports Server (NTRS)

    Berdichevsky, Victor; Armanios, Erian; Badir, Ashraf

    1992-01-01

    A variationally and asymptotically consistent theory is developed in order to derive the governing equations of anisotropic thin-walled beams with closed sections. The theory is based on an asymptotic analysis of two-dimensional shell theory. Closed-form expressions for the beam-stiffness coefficients, stress and displacement fields are provided. The influence of material anisotropy on the displacement field is identified. A comparison with the displacement fields obtained by other analytical developments is performed. The stiffness coefficients and static response are also compared with finite element predictions, closed-form solutions and test data.

  14. Research on dynamic model of printed circuit board based on finite element method

    NASA Astrophysics Data System (ADS)

    Wei, Hui; Xu, Liangjun

    2017-08-01

    The vibration characteristics of printed circuit boards are related to the reliability of electronic components installed on their surface. Finite element software is a powerful tool to analyze the vibration characteristics of printed circuit boards, and the correct establishment of finite element model is very important. In this paper, the dynamic model of anisotropic printed circuit board is established by analyzing the material properties of printed circuit board. The influence of boundary condition and lumped mass on the vibration characteristics of printed circuit board is analyzed. In order to establish a more realistic printed circuit The finite element model of the plate provides the necessary basis.

  15. Data-driven imaging in anisotropic media

    SciTech Connect

    Volker, Arno; Hunter, Alan

    2012-05-17

    Anisotropic materials are being used increasingly in high performance industrial applications, particularly in the aeronautical and nuclear industries. Some important examples of these materials are composites, single-crystal and heavy-grained metals. Ultrasonic array imaging in these materials requires exact knowledge of the anisotropic material properties. Without this information, the images can be adversely affected, causing a reduction in defect detection and characterization performance. The imaging operation can be formulated in two consecutive and reciprocal focusing steps, i.e., focusing the sources and then focusing the receivers. Applying just one of these focusing steps yields an interesting intermediate domain. The resulting common focus point gather (CFP-gather) can be interpreted to determine the propagation operator. After focusing the sources, the observed travel-time in the CFP-gather describes the propagation from the focus point to the receivers. If the correct propagation operator is used, the measured travel-times should be the same as the time-reversed focusing operator due to reciprocity. This makes it possible to iteratively update the focusing operator using the data only and allows the material to be imaged without explicit knowledge of the anisotropic material parameters. Furthermore, the determined propagation operator can also be used to invert for the anisotropic medium parameters. This paper details the proposed technique and demonstrates its use on simulated array data from a specimen of Inconel single-crystal alloy commonly used in the aeronautical and nuclear industries.

  16. Thermal D mesons from anisotropic lattice QCD

    NASA Astrophysics Data System (ADS)

    Kelly, Aoife; Skullerud, Jon-Ivar

    2017-03-01

    We present results for correlators and spectral functions of open charm mesons using 2+1 flavours of clover fermions on anisotropic lattices. The D mesons are found to dissociate close to the deconfinement crossover temperature Tc. Our preliminary results suggest a shift in the thermal D meson mass below Tc. Mesons containing strange quarks exhibit smaller thermal modifications than those containing light quarks.

  17. Casimir interactions for anisotropic magnetodielectric metamaterials

    SciTech Connect

    Da Rosa, Felipe S; Dalvit, Diego A; Milonni, Peter W

    2008-01-01

    We extend our previous work on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces.

  18. Purpose-Built Anisotropic Metal Oxide Nanomaterials

    DTIC Science & Technology

    2001-01-01

    Proceedings Volume 635. Anisotropic Nanoparticles - Synthesis , Characterization and Applications To order the complete compilation report, use...for instance, to the oxidation of sedimentary organic matter [11]. In its various allotropic forms, iron oxides and oxyhydroxides represent important...16-18] and photocatalysts [19], for magnetic storage devices, cathodes for primary and secondary batteries [20], chemical flame suppressant [21] and

  19. Wave propagation in anisotropic layered composites

    NASA Astrophysics Data System (ADS)

    Braga, Arthur Martins Barbosa

    1990-08-01

    The propagation of harmonic waves in laminated anisotropic composites is investigated. The analysis is carried out within the framework of the linear theory of elasticity. Two basic geometries are considered, namely, layered half-spaces and infinite laminated plates. The method employed in the description of the wave motion in the anisotropic composites is based on Stroh's sextic matrix formalism for anisotropic elasticity. An extension of this formalism to periodic media, in conjunction with Floquet's theorem, is applied when the layers are disposed periodically. The 'in vacuo' free motions of laminated composites are investigated. Particular attention is paid to Rayleigh and Rayleigh-Lamb wave propagation in layered media. The dynamic interaction of laminated composites with a surrounding acoustic fluid is also investigated. The concept of surface impedance tensor is introduced. It is shown that, for harmonic motions, this rank-two tensor completely characterizes the solid surface in contact with the fluid. An algorithm for the numerical computation of the surface impedance tensor of anisotropic layered composites is presented. This algorithm is numerically stable for a wide range of frequencies. Special attention is paid to the subsonic Sholte-Gogoladze-like wave, which propagates unattenuated along the planar fluid/solid interface.

  20. Vibrations and stresses in layered anisotropic cylinders

    NASA Technical Reports Server (NTRS)

    Mulholland, G. P.; Gupta, B. P.

    1976-01-01

    An equation describing the radial displacement in a k layered anisotropic cylinder was obtained. The cylinders are initially unstressed but are subjected to either a time dependent normal stress or a displacement at the external boundaries of the laminate. The solution is obtained by utilizing the Vodicka orthogonalization technique. Numerical examples are given to illustrate the procedure.

  1. THEORY OF COMPTON SCATTERING BY ANISOTROPIC ELECTRONS

    SciTech Connect

    Poutanen, Juri; Vurm, Indrek E-mail: indrek.vurm@oulu.f

    2010-08-15

    Compton scattering plays an important role in various astrophysical objects such as accreting black holes and neutron stars, pulsars, relativistic jets, and clusters of galaxies, as well as the early universe. In most of the calculations, it is assumed that the electrons have isotropic angular distribution in some frame. However, there are situations where the anisotropy may be significant due to the bulk motions, or where there is anisotropic cooling by synchrotron radiation or an anisotropic source of seed soft photons. Here we develop an analytical theory of Compton scattering by anisotropic distribution of electrons that can significantly simplify the calculations. Assuming that the electron angular distribution can be represented by a second-order polynomial over the cosine of some angle (dipole and quadrupole anisotropies), we integrate the exact Klein-Nishina cross section over the angles. Exact analytical and approximate formulae valid for any photon and electron energies are derived for the redistribution functions describing Compton scattering of photons with arbitrary angular distribution by anisotropic electrons. The analytical expressions for the corresponding photon scattering cross section on such electrons, as well as the mean energy of scattered photons, its dispersion, and radiation pressure force are also derived. We apply the developed formalism to the accurate calculations of the thermal and kinematic Sunyaev-Zeldovich effects for arbitrary electron distributions.

  2. Anisotropic MHD model and some solutions

    SciTech Connect

    Kuznetsov, V. D.; Dzhalilov, N. S.

    2010-09-15

    MHD waves and instabilities in a collisionless anisotropic-pressure plasma are analyzed in an anisotropic MHD model based on the 16-moment approximation, and the results are found to agree well with those obtained in the low-frequency limit of the kinetic model. It is shown that accounting for heat fluxes leads to an asymmetry in the phase velocities of the wave modes with respect to the heat flux direction and also to a strong interaction between the modes, especially between the backward ones (those that propagate in a direction opposite to that of the heat flux). A correct description of the mirror instability is given. The resonant interaction of three backward modes-fast acoustic, fast magnetosonic, and slow acoustic-under the conditions for the onset of the classical firehose instability triggers a new type of instability the growth rate of which is faster than the maximum growth rate of the conventional firehose instability. The results prove that, in contrast to the familiar Chew-Goldberger-Low approximate model, the anisotropic MHD approach provides a correct description of the large-scale dynamics of collisionless anisotropic plasmas (such as solar corona, solar wind, and ionospheric and magnetospheric plasmas).

  3. Static phantom wormholes of finite size

    NASA Astrophysics Data System (ADS)

    Cataldo, Mauricio; Orellana, Fabian

    2017-09-01

    In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate r . We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state pr/ρ <-1 , dubbed "phantom matter." Among phantom wormhole spacetimes extending to infinity, we show that a quadratic shape function allows us to construct static spacetimes of finite size, composed of a phantom wormhole connected to an anisotropic spherically symmetric distribution of dark energy. The wormhole part of the full spacetime does not fulfill the dominant energy condition, while the dark energy part does.

  4. Vortex Dynamics in Anisotropic Superconductors

    NASA Astrophysics Data System (ADS)

    Steel, David Gordon

    Measurements of the ac screening response and resistance of superconducting Bi_2Sr _2CaCu_2O _8 (BSCCO) crystals have been used to probe the dynamics of the magnetic flux lines within the mixed state as a function of frequency, temperature, and applied dc field. For the particular range of temperature and magnetic field in which measurements were made, the systematic behavior of the observed dissipation peak in the screening response is consistent with electromagnetic skin size effects rather than a phase transition. According to microscopic theories of the interaction between the flux lines and a driving ac field, such a skin size effect is expected for the case when the vortex motion is diffusive in nature. However, diffusive motion is inconsistent with simple activation models that use a single value for the pinning energy (derived from direct measurement of the dc resistance). This contradiction suggests a distribution of pinning energies within the sample. Interlayer vortex decoupling has been directly observed as a function of temperature and applied magnetic field using electronic transport perpendicular to the layers in synthetic amorphous MoGe/Ge multilayer samples. Perpendicular transport has been shown to be a far more sensitive measure of the phase coupling between layers than in-plane properties. Below the decoupling temperature T_{D} the resistivity anisotropy collapses and striking nonlinearities appear in the perpendicular current-voltage behavior, which are not observed in parallel transport. A crossover in behavior is also observed at a field H _{x}, in accordance with theory. The data suggest the presence of a phase transition into a state with finite in-plane resistivity. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

  5. Unconstrained paving and plastering method for generating finite element meshes

    DOEpatents

    Staten, Matthew L.; Owen, Steven J.; Blacker, Teddy D.; Kerr, Robert

    2010-03-02

    Computer software for and a method of generating a conformal all quadrilateral or hexahedral mesh comprising selecting an object with unmeshed boundaries and performing the following while unmeshed voids are larger than twice a desired element size and unrecognizable as either a midpoint subdividable or pave-and-sweepable polyhedra: selecting a front to advance; based on sizes of fronts and angles with adjacent fronts, determining which adjacent fronts should be advanced with the selected front; advancing the fronts; detecting proximities with other nearby fronts; resolving any found proximities; forming quadrilaterals or unconstrained columns of hexahedra where two layers cross; and establishing hexahedral elements where three layers cross.

  6. Finite Control in Korean

    ERIC Educational Resources Information Center

    Lee, Kum Young

    2009-01-01

    This thesis explores finite control in Korean. An overview of the previous studies of control shows that the mainstream literature on control has consistently argued that referential dependence between an overt matrix argument and an embedded null subject is characteristic of non-finite clauses which contain a PRO subject. Moreover, although some…

  7. QUARKONIUM AT FINITE TEMPERATURE.

    SciTech Connect

    UMEDA, T.

    2006-06-09

    Lattice QCD studies on charmonium at finite temperature are presented After a discussion about problems for the Maximum Entropy Method applied to finite temperature lattice QCD, I show several results on charmonium spectral functions. The 'wave function' of charmonium is also discussed to study the spatial correlation between quark and anti-quark in deconfinement phase.

  8. On constitutive relations at finite strain - Hypo-elasticity and elasto-plasticity with isotropic or kinematic hardening

    NASA Technical Reports Server (NTRS)

    Atluri, S. N.

    1984-01-01

    Nagtegaal and de Jong (1982) have studied stresses generated by simple finite shear in the case of elastic-plastic and rigid-plastic materials which exhibit anisotropic hardening. They reported that the shear stress is oscillatory in time. It was found that the occurrence of such an 'anomaly' is not restricted to anisotropic plasticity. Similar behavior in finite shear may result even in the case of hypoelasticity and classical isotropic hardening plasticity theory. The present investigation is concerned with the central problem of 'generalizing' with respect to the finite strain case, taking into account the constitutive relations of infinitesimal strain theories of classical plasticity with isotropic or kinematic hardening. The problem of hypoelasticity is also considered. It is shown that current controversies surrounding the choice of stress rate in the finite-strain generalizations of the constitutive relations and the anomalies surrounding kinematic hardening plasticity theory are easily resolvable.

  9. Finite deformation analysis of geomaterials

    NASA Astrophysics Data System (ADS)

    Jeremi, Boris; Runesson, Kenneth; Sture, Stein

    2001-07-01

    The mathematical structure and numerical analysis of classical small deformation elasto-plasticity is generally well established. However, development of large deformation elastic-plastic numerical formulation for dilatant, pressure sensitive material models is still a research area.In this paper we present development of the finite element formulation and implementation for large deformation, elastic-plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process.The algorithm is tested in conjunction with the novel hyperelasto-plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto-plastic problems in geomechanics.We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS-89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching.

  10. Elliptical silicon arrays with anisotropic optical and wetting properties.

    PubMed

    Wang, Tieqiang; Li, Xiao; Zhang, Junhu; Wang, Xianzhe; Zhang, Xuemin; Zhang, Xun; Zhu, Difu; Hao, Yudong; Ren, Zhiyu; Yang, Bai

    2010-08-17

    We demonstrate a facile etching method to fabricate silicon elliptical pillar arrays (Si-EPAs) with unique anisotropic optical and wetting characters using polystyrene elliptical hemisphere arrays (EHAs) as mask. The EHAs were fabricated via a modified micromolding method. By varying the experimental conditions in the fabrication process, the morphology of the resulting microstructures can be controlled exactly. Because of the anisotropic morphology of the elliptical pillar, the Si-EPA shows unique anisotropic properties, such as anisotropic surface reflection and anisotropic wetting property. Additionally, through oblique evaporation deposition of Au and selective chemical modification to turn the elliptical pillars into "Janus" elliptical pillars, the "Janus" Si-EPA shows more peculiar anisotropic properties owing to the further increased asymmetry. We believe that the Si-EPAs will have potential applications in anisotropic optical and electronic devices.

  11. An Anisotropic Model for Magnetostriction and Magnetization Computing for Noise Generation in Electric Devices

    PubMed Central

    Mbengue, Serigne Saliou; Buiron, Nicolas; Lanfranchi, Vincent

    2016-01-01

    During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material’s behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST) and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI) method. Measurements on the test bench and Finite Elements results are presented. PMID:27092513

  12. Synthetic magnetic field effects on neutral bosonic condensates in quasi-three-dimensional anisotropic layered structures

    SciTech Connect

    Zaleski, T. A.; Polak, T. P.

    2011-02-15

    We discuss a system of dilute Bose gas confined in a layered structure of stacked square lattices (slab geometry). A derived phase diagram reveals a nonmonotonic dependence of the ratio of tunneling to on-site repulsion on the artificial magnetic field applied to the system. The effect is reduced when more layers are added, which mimics a two- to quasi-three-dimensional geometry crossover. Furthermore, we establish a correspondence between anisotropic infinite (quasi-three-dimensional) and isotropic finite (slab geometry) systems that share exactly the same critical values, which can be an important clue for choosing experimental setups that are less demanding, but still leading to the identical results. Finally, we show that the properties of the ideal Bose gas in a three-dimensional optical lattice can be closely mimicked by finite (slab) systems when the number of two-dimensional layers is larger than 10 for isotropic interactions, or even less when the layers are weakly coupled.

  13. An Anisotropic Model for Magnetostriction and Magnetization Computing for Noise Generation in Electric Devices.

    PubMed

    Mbengue, Serigne Saliou; Buiron, Nicolas; Lanfranchi, Vincent

    2016-04-16

    During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material's behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST) and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI) method. Measurements on the test bench and Finite Elements results are presented.

  14. Capillarity-induced ordering of spherical colloids on an interface with anisotropic curvature

    PubMed Central

    Ershov, Dmitry; Sprakel, Joris; Appel, Jeroen; Cohen Stuart, Martien A.; van der Gucht, Jasper

    2013-01-01

    Objects floating at a liquid interface, such as breakfast cereals floating in a bowl of milk or bubbles at the surface of a soft drink, clump together as a result of capillary attraction. This attraction arises from deformation of the liquid interface due to gravitational forces; these deformations cause excess surface area that can be reduced if the particles move closer together. For micrometer-sized colloids, however, the gravitational force is too small to produce significant interfacial deformations, so capillary forces between spherical colloids at a flat interface are negligible. Here, we show that this is different when the confining liquid interface has a finite curvature that is also anisotropic. In that case, the condition of constant contact angle along the three-phase contact line can only be satisfied when the interface is deformed. We present experiments and numerical calculations that demonstrate how this leads to quadrupolar capillary interactions between the particles, giving rise to organization into regular square lattices. We demonstrate that the strength of the governing anisotropic interactions can be rescaled with the deviatoric curvature alone, irrespective of the exact shape of the liquid interface. Our results suggest that anisotropic interactions can easily be induced between isotropic colloids through tailoring of the interfacial curvature. PMID:23690591

  15. Capillarity-induced ordering of spherical colloids on an interface with anisotropic curvature.

    PubMed

    Ershov, Dmitry; Sprakel, Joris; Appel, Jeroen; Cohen Stuart, Martien A; van der Gucht, Jasper

    2013-06-04

    Objects floating at a liquid interface, such as breakfast cereals floating in a bowl of milk or bubbles at the surface of a soft drink, clump together as a result of capillary attraction. This attraction arises from deformation of the liquid interface due to gravitational forces; these deformations cause excess surface area that can be reduced if the particles move closer together. For micrometer-sized colloids, however, the gravitational force is too small to produce significant interfacial deformations, so capillary forces between spherical colloids at a flat interface are negligible. Here, we show that this is different when the confining liquid interface has a finite curvature that is also anisotropic. In that case, the condition of constant contact angle along the three-phase contact line can only be satisfied when the interface is deformed. We present experiments and numerical calculations that demonstrate how this leads to quadrupolar capillary interactions between the particles, giving rise to organization into regular square lattices. We demonstrate that the strength of the governing anisotropic interactions can be rescaled with the deviatoric curvature alone, irrespective of the exact shape of the liquid interface. Our results suggest that anisotropic interactions can easily be induced between isotropic colloids through tailoring of the interfacial curvature.

  16. Guided waves in anisotropic and quasi-isotropic aerospace composites: three-dimensional simulation and experiment.

    PubMed

    Leckey, Cara A C; Rogge, Matthew D; Raymond Parker, F

    2014-01-01

    Three-dimensional (3D) elastic wave simulations can be used to investigate and optimize nondestructive evaluation (NDE) and structural health monitoring (SHM) ultrasonic damage detection techniques for aerospace materials. 3D anisotropic elastodynamic finite integration technique (EFIT) has been implemented for ultrasonic waves in carbon fiber reinforced polymer (CFRP) composite laminates. This paper describes 3D EFIT simulations of guided wave propagation in undamaged and damaged anisotropic and quasi-isotropic composite plates. Comparisons are made between simulations of guided waves in undamaged anisotropic composite plates and both experimental laser Doppler vibrometer (LDV) wavefield data and dispersion curves. Time domain and wavenumber domain comparisons are described. Wave interaction with complex geometry delamination damage is then simulated to investigate how simulation tools incorporating realistic damage geometries can aid in the understanding of wave interaction with CFRP damage. In order to move beyond simplistic assumptions of damage geometry, volumetric delamination data acquired via X-ray microfocus computed tomography is directly incorporated into the simulation. Simulated guided wave interaction with the complex geometry delamination is compared to experimental LDV time domain data and 3D wave interaction with the volumetric damage is discussed. Published by Elsevier B.V.

  17. Superfluid State of 4He on Graphane and Graphene-Fluoride: Anisotropic Roton States

    NASA Astrophysics Data System (ADS)

    Nava, M.; Galli, D. E.; Cole, M. W.; Reatto, L.

    2013-06-01

    We explore the phase behavior of Helium films on two variants of graphene: graphane (graphene coated with H, denoted GH) and graphene-fluoride (GF). A semiempirical interaction with these substrates is used in T=0 K Path Integral Ground State and finite temperature Path Integral Monte Carlo simulations. We predict that 4He forms anisotropic fluid states at low coverage. This behavior differs qualitatively from that on graphite because of the different surface composition, symmetry and spacing of the adsorption sites. The 4He ground state on both substrates is thus a self-bound anisotropic superfluid with a superfluid fraction ρ s / ρ lower than 1 due to the corrugation of the adsorption potential. In the case of GF such corrugation is so large that ρ s / ρ=0.6 at T=0 K and the superfluid is essentially restricted to move in a multiconnected space, along the bonds of a honeycomb lattice. We predict a superfluid transition temperature T≃ 0.25 (1.1) K for 4He on GF (GH). We have studied the elementary excitation spectrum of 4He on GF at equilibrium density finding a phonon-maxon-roton dispersion relation that is strongly anisotropic in the roton region. We conclude that these new platforms for adsorption studies offer the possibility of studying novel superfluid phases of quantum condensed matter.

  18. Full-wave analysis of superconducting microstrip lines on anisotropic substrates using equivalent surface impedance approach

    SciTech Connect

    Lee, L.H.; Lyons, W.G.; Orlando, T.P.; Ali, S.M. . Dept. of Electrical Engineering and Computer Science); Lyons, W.G. . Lincoln Lab.); Withers, R.S. )

    1993-12-01

    A computationally efficient full-wave technique is developed to analyze single and coupled superconducting microstrip lines on anisotropic substrates. The optic axis of the dielectric is in the plane of the substrate at an arbitrary angle with respect to the propagation direction. A dyadic Green's function for layered, anisotropic media is used to formulate an integral equation for the current in the strips. To increase the efficiency of the method, the superconducting strips are replaced by equivalent surface impedances which account for the loss and kinetic inductance of the superconductors. The validity of this equivalent surface impedance (ESI) approach is verified by comparing the calculated complex propagation constant and characteristic impedance for superconducting microstrip lines on an isotropic substrate to measured results, and to numerical results by the more rigorous volume-integral equation method. The results calculated using the ESI approach for perfectly conducting coupled lines on an anisotropic substrate agree with the results by the finite-difference time-domain method. This efficient ESI technique is then used to study the effects of the optic axis orientation and the strip width on the characteristics of single and coupled superconducting microstrip lines on M-plane sapphire. The effects of the line separation and operating temperature on the coupled lines are also investigated.

  19. Theoretical determination of anisotropic thermal conductivity for initially defect-free and defective TATB single crystals

    NASA Astrophysics Data System (ADS)

    Kroonblawd, Matthew P.; Sewell, Thomas D.

    2014-11-01

    The anisotropic thermal conductivity was determined for initially defect-free and defective crystals of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a material that exhibits a graphitic-like packing structure with stacked single-molecule-thick layers, using the reverse non-equilibrium molecular dynamics method and an established TATB molecular dynamics force field. Thermal conduction in TATB is predicted to be substantially higher and more anisotropic than in other related organic molecular explosives, with conduction along directions nominally in the plane of the molecular layers at least 68% greater than conduction along the direction exactly perpendicular to the layers. Finite-size effects along the conduction directions were assessed. The conductivity along directions nominally in the plane of the molecular layers was found to be insensitive to the supercell length along the conduction direction—a result commensurate with the estimated phonon mean free path, ˜6 Å. A small decrease in the conductivity normal to the layers was found for longer supercells and is likely due to increased phonon scattering as a result of dynamic structural transitions in the crystal. The thermal conductivity of TATB crystals containing vacancy defects was also determined and the variation of conductivity with crystal density was found to be both linear and anisotropic, with the introduction of vacancy defects leading to a greater percentage reduction in conduction for the direction perpendicular to the molecular layers.

  20. Theoretical determination of anisotropic thermal conductivity for initially defect-free and defective TATB single crystals.

    PubMed

    Kroonblawd, Matthew P; Sewell, Thomas D

    2014-11-14

    The anisotropic thermal conductivity was determined for initially defect-free and defective crystals of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a material that exhibits a graphitic-like packing structure with stacked single-molecule-thick layers, using the reverse non-equilibrium molecular dynamics method and an established TATB molecular dynamics force field. Thermal conduction in TATB is predicted to be substantially higher and more anisotropic than in other related organic molecular explosives, with conduction along directions nominally in the plane of the molecular layers at least 68% greater than conduction along the direction exactly perpendicular to the layers. Finite-size effects along the conduction directions were assessed. The conductivity along directions nominally in the plane of the molecular layers was found to be insensitive to the supercell length along the conduction direction-a result commensurate with the estimated phonon mean free path, ∼6 Å. A small decrease in the conductivity normal to the layers was found for longer supercells and is likely due to increased phonon scattering as a result of dynamic structural transitions in the crystal. The thermal conductivity of TATB crystals containing vacancy defects was also determined and the variation of conductivity with crystal density was found to be both linear and anisotropic, with the introduction of vacancy defects leading to a greater percentage reduction in conduction for the direction perpendicular to the molecular layers.

  1. Graphics processing unit (GPU)-based computation of heat conduction in thermally anisotropic solids

    NASA Astrophysics Data System (ADS)

    Nahas, C. A.; Balasubramaniam, Krishnan; Rajagopal, Prabhu

    2013-01-01

    Numerical modeling of anisotropic media is a computationally intensive task since it brings additional complexity to the field problem in such a way that the physical properties are different in different directions. Largely used in the aerospace industry because of their lightweight nature, composite materials are a very good example of thermally anisotropic media. With advancements in video gaming technology, parallel processors are much cheaper today and accessibility to higher-end graphical processing devices has increased dramatically over the past couple of years. Since these massively parallel GPUs are very good in handling floating point arithmetic, they provide a new platform for engineers and scientists to accelerate their numerical models using commodity hardware. In this paper we implement a parallel finite difference model of thermal diffusion through anisotropic media using the NVIDIA CUDA (Compute Unified device Architecture). We use the NVIDIA GeForce GTX 560 Ti as our primary computing device which consists of 384 CUDA cores clocked at 1645 MHz with a standard desktop pc as the host platform. We compare the results from standard CPU implementation for its accuracy and speed and draw implications for simulation using the GPU paradigm.

  2. Oligonucleotide-Functionalized Anisotropic Gold Nanoparticles

    NASA Astrophysics Data System (ADS)

    Jones, Matthew Robert

    In this thesis, we describe the properties of oligonucleotide-functionalized gold colloids under the unique set of conditions where the particles are geometrically anisotropic and have nanometer-scale dimensions. While nearly two decades of previous work elucidated numerous unexpected and emergent phenomena arising from the combination of inorganic nanoparticles with surface-bound DNA strands, virtually nothing was known about how these properties are altered when the shape of the nanoparticle core is chosen to be non-spherical. In particular, we are interested in understanding, and ultimately controlling, the ways in which these DNA-conjugated anisotropic nanostructures interact when their attraction is governed by programmable DNA hybridization events. Chapter 1 introduces the field of DNA-based materials assembly by discussing how nanoscale building blocks which present rigid, directional interactions can be thought of as possessing artificial versions of the familiar chemical principles of "bonds" and "valency". In chapter 2 we explore the fundamental interparticle binding thermodynamics of DNA-functionalized spherical and anisotropic nanoparticles, which reveals enormous preferences for collective ligand interactions occurring between flat surfaces over those that occur between curved surfaces. Using these insights, chapter 3 demonstrates that when syntheses produce mixtures of different nanoparticle shapes, the tailorable nature of DNA-mediated interparticle association can be used to selectively crystallize and purify the desired anisotropic nanostructure products, leaving spherical impurity particles behind. Chapter 4 leverages the principle that the flat facets of anisotropic particles generate directional DNA-based hybridization interactions to assemble a variety of tailorable nanoparticle superlattices whose symmetry and dimensionality are a direct consequence of the shape of the nanoparticle building block used in their construction. Chapter 5 explores

  3. Anisotropic electronic states in the fractional quantum Hall regime

    NASA Astrophysics Data System (ADS)

    Ciftja, Orion

    2017-05-01

    Recent experiments indicate the presence of new anisotropic fractional quantum Hall states at regimes not anticipated before. These experiments raise many fundamental questions regarding the inner nature of the electronic system that leads to such anisotropic states. Interplay between electron mass anisotropy and electron-electron correlation effects in a magnetic field can create a rich variety of possibilities. Several anisotropic electronic states ranging from anisotropic quantum Hall liquids to anisotropic Wigner solids may stabilize due to such effects. The electron mass anisotropy in a two-dimensional electron gas effectively leads to an anisotropic Coulomb interaction potential between electrons. An anisotropic interaction potential may strongly influence the stability of various quantum phases that are close in energy since the overall stability of an electronic system is very sensitive to local order. As a result there is a possibility that various anisotropic electronic phases may emerge even in the lowest Landau level in regimes where one would not expect them. In this work we study the state with filling factor 1/6 in the lowest Landau level, a state which is very close to the critical filling factor where the liquid-solid transition takes place. We investigate whether an anisotropic Coulomb interaction potential is able to stabilize an anisotropic electronic liquid state at this filling factor. We describe such an anisotropic state by means of a liquid crystalline wave function with broken rotational symmetry which can be adiabatically connected to the actual wave function for the corresponding isotropic phase. We perform quantum Monte Carlo simulations in a disk geometry to study the properties of the anisotropic electronic liquid state under consideration. The findings indicate stability of liquid crystalline order in presence of an anisotropic Coulomb interaction potential. The results are consistent with the existence of an anisotropic electronic

  4. Analysis Method for Inelastic, Adhesively Bonded Joints with Anisotropic Adherends

    NASA Technical Reports Server (NTRS)

    Smeltzer, Stanley S., III; Klang, Eric C.

    2003-01-01

    A one-dimensional analysis method for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives with nonlinear material behavior is presented in the proposed paper. The strain and resulting stress field in a general, bonded joint overlap are determined by using a variable-step, finite-difference solution algorithm to iteratively solve a system of first-order differential equations. Applied loading is given by a system of combined extensional, bending, and shear forces that are applied to the edge of the joint overlap. Adherends are assumed to behave as linear, cylindrically bent plates using classical laminated plate theory that includes the effects of first-order transverse shear deformation. Using the deformation theory of plasticity and a modified von-Mises yield criterion, inelastic material behavior is modeled in the adhesive layer. Results for the proposed method are verified against previous results from the literature and shown to be in excellent agreement. An additional case that highlights the effects of transverse shear deformation between similar adherends is also presented.

  5. Charge-dependent anisotropic flow in Cu + Au collisions

    NASA Astrophysics Data System (ADS)

    Niida, Takafumi

    2016-12-01

    We present the first measurements of charge-dependent directed flow in Cu+Au collisions at √{sNN} = 200 GeV. The directed flow has been measured as functions of the transverse momentum and pseudorapidity with the STAR detector. The results show a small but finite difference between positively and negatively charged particles. The difference is qualitatively explained by the patron-hadron-string-dynamics (PHSD) model including the effect of the electric field, but much smaller than the model calculation, which indicates only a small fraction of all final state quarks are created within the lifetime of the initial electric field. Higher-order azimuthal anisotropic flow is also presented up to the fourth-order for unidentified charged particles and up to the third-order for identified charged particles (π, K, and p). For unidentified particles, the results are reasonably described by the event-by-event viscous hydrodynamic model with η / s = 0.08 - 0.16. The trends observed for identified particles in Cu+Au collisions are similar to those observed in symmetric (Au+Au) collisions.

  6. An invariant shape representation using the anisotropic Helmholtz equation.

    PubMed

    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.

  7. Global sound modes in mirror traps with anisotropic pressure

    SciTech Connect

    Skovorodin, D. I.; Zaytsev, K. V.; Beklemishev, A. D.

    2013-10-15

    Global oscillations of inhomogeneous plasma with frequencies close to the bounce frequency of ions in mirror traps have been studied. It has been shown that, in some cases, the sound can be reflected from the axial plasma inhomogeneity. The ideal magnetohydrodynamic (MHD) model with Chew-Goldberger-Low approximation has been utilized to determine conditions of existence of the standing waves in the mirror-confined plasma. Linearized wave equation for the longitudinal plasma oscillations in thin anisotropic inhomogeneous plasma with finite β has been derived. The wave equation has been treated numerically. The oscillations are studied for the case of the trap with partially filled loss-cone and the trap with sloshing ions. It has been shown that in cells of the multiple-mirror trap standing waves can exist. The frequency of the wave is of the order of the mean bounce-frequency of ions. In the trap with sloshing ions, the mode supported by the pressure of fast ions could exist. The results of oscillations observation in the experiment on the Gas Dynamic Trap have been presented.

  8. FDTD modeling of anisotropic nonlinear optical phenomena in silicon waveguides.

    PubMed

    Dissanayake, Chethiya M; Premaratne, Malin; Rukhlenko, Ivan D; Agrawal, Govind P

    2010-09-27

    A deep insight into the inherent anisotropic optical properties of silicon is required to improve the performance of silicon-waveguide-based photonic devices. It may also lead to novel device concepts and substantially extend the capabilities of silicon photonics in the future. In this paper, for the first time to the best of our knowledge, we present a three-dimensional finite-difference time-domain (FDTD) method for modeling optical phenomena in silicon waveguides, which takes into account fully the anisotropy of the third-order electronic and Raman susceptibilities. We show that, under certain realistic conditions that prevent generation of the longitudinal optical field inside the waveguide, this model is considerably simplified and can be represented by a computationally efficient algorithm, suitable for numerical analysis of complex polarization effects. To demonstrate the versatility of our model, we study polarization dependence for several nonlinear effects, including self-phase modulation, cross-phase modulation, and stimulated Raman scattering. Our FDTD model provides a basis for a full-blown numerical simulator that is restricted neither by the single-mode assumption nor by the slowly varying envelope approximation.

  9. Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model.

    PubMed

    He, Yin-Chen; Sheng, D N; Chen, Yan

    2014-04-04

    Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.

  10. Anisotropic Andreev reflection in ferromagnet/s-wave superconductors (FS)

    NASA Astrophysics Data System (ADS)

    Hoegl, Petra; Matos Abiague, Alex; Zutic, Igor; Fabian, Jaroslav

    2015-03-01

    Andreev reflection in FS junctions is a sensitive probe of the junction interface as well as of the spin polarization of the F region. By performing analytical and numerical calculations on widely accepted model systems, with interfacial Rashba and Dresselhaus spin-orbit fields, we show that Andreev reflection spectroscopy is also a sensitive tool of the interfacial spin-orbit coupling. In particular, we find a finite subgap conductance even in half-metallic systems due to the spin-flip Andreev reflection, imposing a triplet proximity effect. Furthermore, we predict a giant magnetic anisotropy of the Andreev reflection--anisotropic Andreev reflection (AAR)--with respect to the orientation of the F magnetization. We analyze the effects of the tunnel barrier strength, the F spin polarization, and the effective mass and Fermi wave vector mismatch. Our results should also have implications for designing Majorana states in semiconductor junctions with superconductors. This work has been supported by DFG SFB 689 and the International Doctorate Program Topological Insulators of the Elite Network of Bavaria.

  11. Anisotropic singularities in modified gravity models

    NASA Astrophysics Data System (ADS)

    Figueiró, Michele Ferraz; Saa, Alberto

    2009-09-01

    We show that the common singularities present in generic modified gravity models governed by actions of the type S=∫d4x-gf(R,ϕ,X), with X=-(1)/(2)gab∂aϕ∂bϕ, are essentially the same anisotropic instabilities associated to the hypersurface F(ϕ)=0 in the case of a nonminimal coupling of the type F(ϕ)R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface (∂f)/(∂R)=0 is attained. Some examples are explicitly discussed.

  12. Birefringent light propagation on anisotropic cosmological backgrounds

    NASA Astrophysics Data System (ADS)

    Asenjo, Felipe A.; Hojman, Sergio A.

    2017-08-01

    Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated with linear polarization) and dispersion. The particular case of a vacuum-dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times)—while, for earlier times, it matches a Kasner Universe—is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is then dependent on light polarization, its dispersion, and its non-null geodesic behavior. New results presented here may help to tackle some issues related to the "horizon" problem.

  13. Rainbow metric from quantum gravity: Anisotropic cosmology

    NASA Astrophysics Data System (ADS)

    Assanioussi, Mehdi; Dapor, Andrea

    2017-03-01

    In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter β in the modified dispersion relation of the modes, hence, inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015), 10.1016/j.physletb.2015.10.043], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.

  14. Method of caustics for anisotropic materials

    NASA Astrophysics Data System (ADS)

    Rossmanith, H. P.

    1991-12-01

    During the past 25 years the optical method of caustics has matured to a very powerful tool for application in fracture mechanics for the determination of stress intensity factors or the J- integral, in contact mechanics for the determination of contact forces, etc. The technique is applicable to two-dimensional static or dynamic problems and works for any kind of stress- strain relationship. The method displays its full power when employed in conjunction with interactive numerical data reduction and evaluation procedures. Recently, the industrial application of high strength-low weight composite materials has boomed. Application of the method of caustics to anisotropic materials requires the development of the theoretical background. This contribution focuses on the theoretical development of the method of caustics and its applicability to anisotropic materials.

  15. Nonorthogonal polarisation eigenstates in anisotropic cavities

    SciTech Connect

    Mamaev, Yu A; Khandokhin, Pavel A

    2011-06-30

    The Jones matrix method is used to analyse the polarisation eigenmodes of a solid-state laser with an anisotropic Fabry - Perot cavity containing amplitude and phase anisotropic elements. The results demonstrate that, when the axes of these elements do not coincide, the eigenpolarisations become elliptical and nonorthogonal. The ellipticities and azimuths of the polarisation modes and the magnitude and phase of the nonorthogonality parameter are determined as functions of polariser angle at different relationships between the amplitude and phase anisotropies, and the effect is shown to be strongest at a polariser angle of 45{sup 0}. There is critical phase anisotropy, dependent on amplitude anisotropy, at which the magnitude of the nonorthogonality parameter and ellipticity of the polarisation modes approach unity. (resonators)

  16. Fluctuations in a Primordial Anisotropic ERA

    NASA Astrophysics Data System (ADS)

    Novello, Mário; de Freitas, Luciane R.

    The primordial Universe is treated in terms of a nonperfect fluid configuration endowed with an anisotropic expansion. The deGennes-Landau mechanism of phase transition acts as a very efficient process to provide the elimination of the previous anisotropy and to set the universe in the current isotropic FRW stage. The entropy produced, as a consequence of the phase transition, depends on the strength of the previous shear. We suggest the hypothesis that the germinal perturbations that will grow into the observed system of galaxies occurring in the anisotropic era. We present a model to deal with this idea that provides a power spectrum of fluctuations of the form δ 2k ˜ 1/(a +bk2). We compare this prediction of our model to the current knowledge on the galaxy formation process.

  17. Anisotropic stellar models admitting conformal motion

    NASA Astrophysics Data System (ADS)

    Banerjee, Ayan; Banerjee, Sumita; Hansraj, Sudan; Ovgun, Ali

    2017-04-01

    We address the problem of finding static and spherically symmetric anisotropic compact stars in general relativity that admit conformal motions. The study is framed in the language of f( R) gravity theory in order to expose opportunity for further study in the more general theory. Exact solutions of compact stars are found under the assumption that spherically symmetric spacetimes admit conformal motion with anisotropic matter distribution in nature. In this work, two cases have been studied for the existence of such solutions: first, we consider the model given by f(R)=R and then f(R)=aR+b . Finally, specific characteristics and physical properties have been explored analytically along with graphical representations for conformally symmetric compact stars in f( R) gravity.

  18. Optical sharper focusing in an anisotropic crystal.

    PubMed

    Wang, Sicong; Xie, Xiangsheng; Gu, Min; Zhou, Jianying

    2015-06-01

    Optical super-resolution technique through tight focusing is a widely used technique to image material samples with anisotropic optical properties. The knowledge of the field distribution of a tightly focused beam in anisotropic media is both scientifically interesting and technologically important. In this paper, the optical properties of a uniaxial crystal with the optic axis perpendicular to the interface under a tight focusing configuration are studied with rigorous theoretical and numerical analysis. The significant effect of the Poynting vector on the focal position introduces an obvious displacement of the focal spot formed by the extraordinary waves (e-ray). Moreover, a sharper focus with a lateral size of 0.22λ is obtained as a result of the effective separation of the ordinary waves (o-ray) and the e-ray. It provides a new tool to fabricate optical structures with higher resolutions than that in an isotropic medium through the far-field method.

  19. Performance comparison of fundamental anisotropic diffusion algorithms

    NASA Astrophysics Data System (ADS)

    Bayraktar, Bulent; Analoui, Mostafa

    2004-05-01

    Anisotropic diffusion (AD), first introduced by Perona and Malik (PM), provides image enhancement a strong benefit as it favors intra-region over inter-region smoothing. Early updates on the original PM algorithm focused on the cures for its drawbacks. Later some authors provided their own versions of AD techniques with a wide variety of applications. We surveyed the pros and cons of many fundamental AD techniques. To put our purpose into perspective, we compared the performances of fundamental AD algorithms to simple traditional filters and to more sophisticated tools such as wavelets. Visual inspection and two mathematical criteria are used for performance comparison: Signal-to-noise ratio (SNR) and universal image quality index (UIQI). We believe that a good overview of its simplicity and power will show the rightful reason of so much interest in anisotropic diffusion since its introduction.

  20. Nonminimal coupling in anisotropic teleparallel inflation

    NASA Astrophysics Data System (ADS)

    Abedi, Habib; Wright, Matthew; Abbassi, Amir M.

    2017-03-01

    We study an anisotropic inflationary scenario in teleparallel gravity. We consider a model where the inflaton is nonminimally coupled both to torsion and a vector field, which can lead to anisotropic inflation. In the weak-coupling limit, our results coincide with the results obtained in the general relativistic framework. However, in the strong-coupling regime of the Jordan frame, we show that the anisotropy shear to expansion ratio is a constant, and can be much larger than the slow-roll parameter. Applying a conformal transformation we then work in the Einstein frame, which in teleparallel gravity introduces a different form of coupling between the inflaton and torsion. In this frame we show that in the strong coupling regime the anisotropy shear to expansion ratio is a different constant, that can be made suitably small.

  1. Anisotropic hydrodynamic function of dense confined colloids

    NASA Astrophysics Data System (ADS)

    Nygârd, Kim; Buitenhuis, Johan; Kagias, Matias; Jefimovs, Konstantins; Zontone, Federico; Chushkin, Yuriy

    2017-06-01

    Dense colloidal dispersions exhibit complex wave-vector-dependent diffusion, which is controlled by both direct particle interactions and indirect nonadditive hydrodynamic interactions mediated by the solvent. In bulk the hydrodynamic interactions are probed routinely, but in confined geometries their studies have been hitherto hindered by additional complications due to confining walls. Here we solve this issue by combining high-energy x-ray photon correlation spectroscopy and small-angle x-ray-scattering experiments on colloid-filled microfluidic channels to yield the confined fluid's hydrodynamic function in the short-time limit. Most importantly, we find the confined fluid to exhibit a strongly anisotropic hydrodynamic function, similar to its anisotropic structure factor. This observation is important in order to guide future theoretical research.

  2. Formation of Anisotropic Block Copolymer Gels

    NASA Astrophysics Data System (ADS)

    Liaw, Chya Yan; Shull, Kenneth; Henderson, Kevin; Joester, Derk

    2011-03-01

    Anisotropic, fibrillar gels are important in a variety of processes. Biomineralization is one example, where the mineralization process often occurs within a matrix of collagen or chitin fibers that trap the mineral precursors and direct the mineralization process. We wish to replicate this type of behavior within block copolymer gels. Particularly, we are interested in employing gels composed of cylindrical micelles, which are anisotropic and closely mimic biological fibers. Micelle geometry is controlled in our system by manipulating the ratio of molecular weights of the two blocks and by controlling the detailed thermal processing history of the copolymer solutions. Small-Angle X-ray Scattering and Dynamic Light Scattering are used to determine the temperature dependence of the gel formation process. Initial experiments are based on a thermally-reversible alcohol-soluble system, that can be subsequently converted to a water soluble system by hydrolysis of a poly(t-butyl methacrylate) block to a poly (methacrylic acid) block. MRSEC.

  3. Wireless energy transfer between anisotropic metamaterials shells

    SciTech Connect

    Díaz-Rubio, Ana; Carbonell, Jorge; Sánchez-Dehesa, José

    2014-06-15

    The behavior of strongly coupled Radial Photonic Crystals shells is investigated as a potential alternative to transfer electromagnetic energy wirelessly. These sub-wavelength resonant microstructures, which are based on anisotropic metamaterials, can produce efficient coupling phenomena due to their high quality factor. A configuration of selected constitutive parameters (permittivity and permeability) is analyzed in terms of its resonant characteristics. The coupling to loss ratio between two coupled resonators is calculated as a function of distance, the maximum (in excess of 300) is obtained when the shells are separated by three times their radius. Under practical conditions an 83% of maximum power transfer has been also estimated. -- Highlights: •Anisotropic metamaterial shells exhibit high quality factors and sub-wavelength size. •Exchange of electromagnetic energy between shells with high efficiency is analyzed. •Strong coupling is supported with high wireless transfer efficiency. •End-to-end energy transfer efficiencies higher than 83% can be predicted.

  4. The Impact of Anisotropic Error Correlation Modelling

    NASA Technical Reports Server (NTRS)

    Swinbank, R.; Riishojgaard, L. P.; Menard, R.

    1999-01-01

    Most data assimilation systems assume isotropic forecast error correlations, but results from two dimensional Kalman Filter experiments indicate that the correlations can be far from isotropic. In this paper we use a simple two-dimensional data assimilation system, which analyses trace chemical species such as ozone, to assess different approaches to modelling the error correlations. We compare assimilation results using isotropic correlations with results obtained using different approaches to modelling anisotropic correlations: first, using correlations based on the concentrations of the trace chemicals, and secondly using an advective correlation model. We show that these relatively cheap ways of modelling anisotropic correlations give objectively better results than using isotropic correlations. We discuss the possible extension of these approaches to a full 3-D meteorological data assimilation system.

  5. Modeling anisotropic magnetoresistance in layered antiferromagnets

    NASA Astrophysics Data System (ADS)

    Santos, D. L. R.; Pinheiro, F. A.; Velev, J.; Chshiev, M.; Castro, J. d.'Albuquerque e.; Lacroix, C.

    2017-06-01

    We have investigated the electronic transport and the anisotropic magnetoresistance in systems consisting of pairs of antiferromagnetically aligned layers separated by a non-magnetic layer, across which an antiferromagnetic coupling between the double layers is established. Calculations have been performed within the framework of the tight-binding model, taking into account the exchange coupling within the ferromagnetic layers and the Rashba spin-orbit interaction. Conductivities have been evaluated in the ballistic regime, based on Kubo formula. We have systematically studied the dependence of the conductivity and of the anisotropic magnetoresistance on several material and structural parameters, such as the orientation of the magnetic moments relative to the crystalline axis, band filling, out-of-plane hopping and spin-orbit parameter.

  6. Cosmological signatures of anisotropic spatial curvature

    SciTech Connect

    Pereira, Thiago S.; Marugán, Guillermo A. Mena; Carneiro, Saulo E-mail: mena@iem.cfmac.csic.es

    2015-07-01

    If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free models in which the anisotropy emerges at the level of the curvature of the homogeneous spatial sections, whereas the expansion is dictated by a single scale factor. We show that such models represent viable alternatives to describe the large-scale structure of the inflationary universe, leading to a kinematically equivalent Sachs-Wolfe effect. Through the definition of a complete set of spatial eigenfunctions we compute the two-point correlation function of scalar perturbations in these models. In addition, we show how such scenarios would modify the spectrum of the CMB assuming that the observations take place in a small patch of a universe with anisotropic curvature.

  7. Thermodynamics of soft anisotropic contact lines.

    PubMed

    Rey, Alejandro D

    2004-08-01

    Contact lines arising from the intersection of interfaces between liquids and nematic liquid crystals are representative models of soft anisotropic contact lines. This paper presents the thermodynamics of soft anisotropic contact lines and the derivation of the one dimensional (1D) Gibbs-Duhem adsorption equation. Consistency between the 1D Gibbs-Duhem equation and the classical equations of lineal nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic line Gibbs-Duhem equation reveals the presence of couplings between curvature, torsion, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for contact line shape and orientation selection. The ability of an adsorbed solute to orient the director and to bend and twist the contact line is predicted. The thermodynamic origin of preferred orientation at a straight contact line is established.

  8. Observation of an Anisotropic Wigner Crystal

    NASA Astrophysics Data System (ADS)

    Liu, Yang; Hasdemir, S.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.

    2016-09-01

    We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears in a large range of low Landau level fillings 1 /3 ≲ν ≲2 /3 in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component (B∥) leads to a crossing of the lowest two Landau levels, and an elongated hole wave function in the direction of B∥. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along B∥ about 10 times smaller than the resistance perpendicular to B∥. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal.

  9. Symmetry analysis for anisotropic field theories

    SciTech Connect

    Parra, Lorena; Vergara, J. David

    2012-08-24

    The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.

  10. Continuous Observability for the Anisotropic Maxwell System

    SciTech Connect

    Eller, Matthias M.

    2007-03-15

    A boundary observability inequality for the homogeneous Maxwell system with variable, anisotropic coefficients is proved. The result implies uniqueness for an ill-posed Cauchy problem for Maxwell's system. Both results are so far known only in the special case of isotropic coefficients, i.e., when Maxwell's system reduces to a vector wave equation. Here the analysis has been carried out for the first-order system directly without references to the wave equation.

  11. Slotted Antenna with Anisotropic Magnetic Loading

    DTIC Science & Technology

    2016-07-26

    10 SLOTTED ANTENNA WITH ANISOTROPIC MAGNETIC LOADING STATEMENT OF GOVERNMENT INTEREST [0001] The invention described herein may be manufactured...therefor. CROSS REFERENCE TO OTHER PATENT APPLICATIONS [0002] None. BACKGROUND OF THE INVENTION (1) Field of the Invention [0003] The present invention ...of the VSWR curve, and modest bandwidth in each passband. SUMMARY OF THE INVENTION [0006] It is a first object of the present invention to provide

  12. Anisotropic cosmological solutions in massive vector theories

    NASA Astrophysics Data System (ADS)

    Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

    2016-11-01

    In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/H decreases with the decrease of v. As long as the conditions |Σ| ll H and v2 ll phi2 are satisfied around the onset of late-time cosmic acceleration, where phi is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state wDE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value wDE(iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

  13. Probabilistic Anisotropic Failure Criteria for Composite Materials.

    DTIC Science & Technology

    1987-12-01

    worksheets were based on Microsoft Excel software. 55 55 ’. 2.’ 𔃼..’. -.. ’-,’€’.’’.’ :2.,2..’..’.2.’.’.,’.." .𔃼.. .2...analytically described the failure cri - terion and probabilistic failure states of a anisotropic composite in a combined stress state. Strength...APPENDIX F RELIABILITY/FAILURE FUNCTION WORKSHEET ........... 76 APPENDIX G PERCENTILE STRENGTH WORKSHEET ....................... 80 LIST OF

  14. Anisotropic Thermal Conductivity of Exfoliated Black Phosphorus.

    PubMed

    Jang, Hyejin; Wood, Joshua D; Ryder, Christopher R; Hersam, Mark C; Cahill, David G

    2015-12-22

    The anisotropic thermal conductivity of passivated black phosphorus (BP), a reactive two-dimensional material with strong in-plane anisotropy, is ascertained. The room-temperature thermal conductivity for three crystalline axes of exfoliated BP is measured by time-domain thermo-reflectance. The thermal conductivity along the zigzag direction is ≈2.5 times higher than that of the armchair direction.

  15. Observational signatures of anisotropic inflationary models

    SciTech Connect

    Ohashi, Junko; Tsujikawa, Shinji; Soda, Jiro E-mail: jiro@phys.sci.kobe-u.ac.jp

    2013-12-01

    We study observational signatures of two classes of anisotropic inflationary models in which an inflaton field couples to (i) a vector kinetic term F{sub μν}F{sup μν} and (ii) a two-form kinetic term H{sub μνλ}H{sup μνλ}. We compute the corrections from the anisotropic sources to the power spectrum of gravitational waves as well as the two-point cross correlation between scalar and tensor perturbations. The signs of the anisotropic parameter g{sub *} are different depending on the vector and the two-form models, but the statistical anisotropies generally lead to a suppressed tensor-to-scalar ratio r and a smaller scalar spectral index n{sub s} in both models. In the light of the recent Planck bounds of n{sub s} and r, we place observational constraints on several different inflaton potentials such as those in chaotic and natural inflation in the presence of anisotropic interactions. In the two-form model we also find that there is no cross correlation between scalar and tensor perturbations, while in the vector model the cross correlation does not vanish. The non-linear estimator f{sub NL} of scalar non-Gaussianities in the two-form model is generally smaller than that in the vector model for the same orders of |g{sub *}|, so that the former is easier to be compatible with observational bounds of non-Gaussianities than the latter.

  16. Anisotropic conducting films for electromagnetic radiation applications

    SciTech Connect

    Cavallo, Francesca; Lagally, Max G.; Rojas-Delgado, Richard

    2015-06-16

    Electronic devices for the generation of electromagnetic radiation are provided. Also provided are methods for using the devices to generate electromagnetic radiation. The radiation sources include an anisotropic electrically conducting thin film that is characterized by a periodically varying charge carrier mobility in the plane of the film. The periodic variation in carrier mobility gives rise to a spatially varying electric field, which produces electromagnetic radiation as charged particles pass through the film.

  17. A viscoplastic theory for anisotropic materials

    NASA Technical Reports Server (NTRS)

    Nouailhas, D.; Freed, A. D.

    1992-01-01

    The purpose of this work is the development of a unified, cyclic, viscoplastic model for anisotropic materials. The first part of the paper presents the foundations of the model in the framework of thermodynamics with internal variables. The second part considers the particular case of cubic symmetry, and addresses the cyclic behavior of a nickel-base single-crystal superalloy, CMSX-2, at high temperature (950 C).

  18. Multidimensional reaction rate theory with anisotropic diffusion.

    PubMed

    Berezhkovskii, Alexander M; Szabo, Attila; Greives, Nicholas; Zhou, Huan-Xiang

    2014-11-28

    An analytical expression is derived for the rate constant that describes diffusive transitions between two deep wells of a multidimensional potential. The expression, in contrast to the Kramers-Langer formula for the rate constant, is valid even when the diffusion is highly anisotropic. Our approach is based on a variational principle for the reactive flux and uses a trial function for the splitting probability or commitor. The theoretical result is validated by Brownian dynamics simulations.

  19. Perspectives of anisotropic flow measurements at NICA

    NASA Astrophysics Data System (ADS)

    Korotkikh, V. L.; Lokhtin, I. P.; Malinina, L. V.; Petrushanko, S. V.; Snigirev, A. M.

    2016-08-01

    High-accuracy and high-luminosity measurements of anisotropic flow for various hadron types over full NICA energy range will provide important constraints on the early dynamics of heavy-ion reactions under the conditions where a first-order quark-hadron phase transition may occur. The statistical reach for elliptic flow measurements at NICA is estimated with HYDJET++ heavy-ion event generator.

  20. Effect of inflation on anisotropic cosmologies

    SciTech Connect

    Jensen, L.G.; Stein-Schabes, J.A.

    1986-03-01

    The effects of anisotropic cosmologies on inflation are studied. By properly formulating the field equations it is possible to show that any model that undergoes sufficient inflation will become isotropic on scales greater than the horizon today. Furthermore, we shall show that it takes a very long time for anisotropies to become visible in the observable part of the Universe. It is interesting to note that the time scale will be independent of the Bianchi Model and of the initial anisotropy. 6 refs.

  1. An efficient Matlab script to calculate heterogeneous anisotropically elastic wave propagation in three dimensions

    USGS Publications Warehouse

    Boyd, O.S.

    2006-01-01

    We have created a second-order finite-difference solution to the anisotropic elastic wave equation in three dimensions and implemented the solution as an efficient Matlab script. This program allows the user to generate synthetic seismograms for three-dimensional anisotropic earth structure. The code was written for teleseismic wave propagation in the 1-0.1 Hz frequency range but is of general utility and can be used at all scales of space and time. This program was created to help distinguish among various types of lithospheric structure given the uneven distribution of sources and receivers commonly utilized in passive source seismology. Several successful implementations have resulted in a better appreciation for subduction zone structure, the fate of a transform fault with depth, lithospheric delamination, and the effects of wavefield focusing and defocusing on attenuation. Companion scripts are provided which help the user prepare input to the finite-difference solution. Boundary conditions including specification of the initial wavefield, absorption and two types of reflection are available. ?? 2005 Elsevier Ltd. All rights reserved.

  2. Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field

    NASA Astrophysics Data System (ADS)

    Li, Lei; Yang, Guo-Hui

    2014-07-01

    Quantum correlations in an anisotropic Heisenberg XYZ chain is investigated by use of concurrence C and measurement-induced disturbance (MID). We show that the behaviors of the MID are remarkably different from the concurrence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures, we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant Jz, while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter γ, whereas an opposite effect for MID behaviors is presented.

  3. ARTc: Anisotropic reflectivity and transmissivity calculator

    NASA Astrophysics Data System (ADS)

    Malehmir, Reza; Schmitt, Douglas R.

    2016-08-01

    While seismic anisotropy is known to exist within the Earth's crust and even deeper, isotropic or even highly symmetric elastic anisotropic assumptions for seismic imaging is an over-simplification which may create artifacts in the image, target mis-positioning and hence flawed interpretation. In this paper, we have developed the ARTc algorithm to solve reflectivity, transmissivity as well as velocity and particle polarization in the most general case of elastic anisotropy. This algorithm is able to provide reflectivity solution from the boundary between two anisotropic slabs with arbitrary symmetry and orientation up to triclinic. To achieve this, the algorithm solves full elastic wave equation to find polarization, slowness and amplitude of all six wave-modes generated from the incident plane-wave and welded interface. In the first step to calculate the reflectivity, the algorithm solves properties of the incident wave such as particle polarization and slowness. After calculation of the direction of generated waves, the algorithm solves their respective slowness and particle polarization. With this information, the algorithm then solves a system of equations incorporating the imposed boundary conditions to arrive at the scattered wave amplitudes, and thus reflectivity and transmissivity. Reflectivity results as well as slowness and polarization are then tested in complex computational anisotropic models to ensure their accuracy and reliability. ARTc is coded in MATLAB ® and bundled with an interactive GUI and bash script to run on single or multi-processor computers.

  4. Active Damping Using Distributed Anisotropic Actuators

    NASA Technical Reports Server (NTRS)

    Schiller, Noah H.; Cabell, Randolph H.; Quinones, Juan D.; Wier, Nathan C.

    2010-01-01

    A helicopter structure experiences substantial high-frequency mechanical excitation from powertrain components such as gearboxes and drive shafts. The resulting structure-borne vibration excites the windows which then radiate sound into the passenger cabin. In many cases the radiated sound power can be reduced by adding damping. This can be accomplished using passive or active approaches. Passive treatments such as constrained layer damping tend to reduce window transparency. Therefore this paper focuses on an active approach utilizing compact decentralized control units distributed around the perimeter of the window. Each control unit consists of a triangularly shaped piezoelectric actuator, a miniature accelerometer, and analog electronics. Earlier work has shown that this type of system can increase damping up to approximately 1 kHz. However at higher frequencies the mismatch between the distributed actuator and the point sensor caused control spillover. This paper describes new anisotropic actuators that can be used to improve the bandwidth of the control system. The anisotropic actuators are composed of piezoelectric material sandwiched between interdigitated electrodes, which enables the application of the electric field in a preferred in-plane direction. When shaped correctly the anisotropic actuators outperform traditional isotropic actuators by reducing the mismatch between the distributed actuator and point sensor at high frequencies. Testing performed on a Plexiglas panel, representative of a helicopter window, shows that the control units can increase damping at low frequencies. However high frequency performance was still limited due to the flexible boundary conditions present on the test structure.

  5. Anisotropic impedance surfaces for enhanced antenna isolation

    NASA Astrophysics Data System (ADS)

    Miragliotta, Joseph A.; Shrekenhamer, David; Sievenpiper, Daniel F.

    2015-09-01

    Anisotropic impedance surfaces, which include metasurfaces and high impedance surfaces (HIS), can be designed to control the amplitude and propagation direction of surface electromagnetic waves and are an effective means to enhance the isolation between antennas that share a common ground plane. To date, the majority of metastructures that have been designed for antenna isolation have relied on an isotropic distribution of unit cells that possess a stop band that inhibits the propagation of surface waves between neighboring antennas. A less common approach to isolation has been through the design of a metasurface that enables the re-direction of surface waves away from the location of the antenna structure, which effectively limits the coupling. In this paper, we discuss results from our computational investigation associated with improving antenna isolation through the use of an anisotropic metastructure. Simulated results associated with the isolation performance of two simple, but similar, anisotropic structures are compared to the corresponding results from a broadband magnetic radar absorbing materials (magRAM).

  6. Shock capturing by anisotropic diffusion oscillation reduction

    NASA Astrophysics Data System (ADS)

    Wei, G. W.

    2002-04-01

    This paper introduces an anisotropic diffusion oscillation reduction (ADOR) scheme for shock wave computations. The connection is made between digital image processing, in particular, image edge detection, and numerical shock capturing. Indeed, numerical shock capturing can be formulated on the lines of iterative digital edge detection. Various anisotropic diffusion and super diffusion operators originated from image edge detection are proposed for the treatment of hyperbolic conservation laws and near-hyperbolic hydrodynamic equations of change. The similarity between anisotropic diffusion and artificial viscosity is discussed. Physical origins and mathematical properties of the artificial viscosity are analyzed from the point of view of kinetic theory. A form of pressure tensor is derived from the first principles of the quantum mechanics. Quantum kinetic theory is utilized to arrive at macroscopic transport equations from the microscopic theory. Macroscopic symmetry is used to simplify pressure tensor expressions. The latter provides a basis for the design of artificial viscosity. The ADOR approach is validated by using (inviscid) Burgers' equation, the gas tube problems, the incompressible Navier-Stokes equation and the Euler equation. Both standard central difference schemes and a discrete singular convolution algorithm are utilized to illustrate the approach. Results are compared with those of third-order upwind scheme and essentially non-oscillatory (ENO) scheme.

  7. Anisotropic representations for superresolution of hyperspectral data

    NASA Astrophysics Data System (ADS)

    Bosch, Edward H.; Czaja, Wojciech; Murphy, James M.; Weinberg, Daniel

    2015-05-01

    We develop a method for superresolution based on anisotropic harmonic analysis. Our ambition is to efficiently increase the resolution of an image without blurring or introducing artifacts, and without integrating additional information, such as sub-pixel shifts of the same image at lower resolutions or multimodal images of the same scene. The approach developed in this article is based on analysis of the directional features present in the image that is to be superesolved. The harmonic analytic technique of shearlets is implemented in order to efficiently capture the directional information present in the image, which is then used to provide smooth, accurate images at higher resolutions. Our algorithm is compared to both a recent anisotropic technique based on frame theory and circulant matrices,1 as well as to the standard superresolution method of bicubic interpolation. We evaluate our algorithm on synthetic test images, as well as a hyperspectral image. Our results indicate the superior performance of anisotropic methods, when compared to standard bicubic interpolation.

  8. Waveguide structures in anisotropic nonlinear crystals

    NASA Astrophysics Data System (ADS)

    Li, Da; Hong, Pengda; Meissner, Helmuth E.

    2017-02-01

    We report on the design and manufacturing parameters of waveguiding structures of anisotropic nonlinear crystals that are employed for harmonic conversions, using Adhesive-Free Bonding (AFB®). This technology enables a full range of predetermined refractive index differences that are essential for the design of single mode or low-mode propagation with high efficiency in anisotropic nonlinear crystals which in turn results in compact frequency conversion systems. Examples of nonlinear optical waveguides include periodically bonded walk-off corrected nonlinear optical waveguides and periodically poled waveguide components, such as lithium triborate (LBO), beta barium borate (β-BBO), lithium niobate (LN), potassium titanyl phosphate (KTP), zinc germanium phosphide (ZGP) and silver selenogallate (AGSE). Simulation of planar LN waveguide shows that when the electric field vector E lies in the k-c plane, the power flow is directed precisely along the propagation direction, demonstrating waveguiding effect in the planar waveguide. Employment of anisotropic nonlinear optical waveguides, for example in combination with AFB® crystalline fiber waveguides (CFW), provides access to the design of a number of novel high power and high efficiency light sources spanning the range of wavelengths from deep ultraviolet (as short as 200 nm) to mid-infrared (as long as about 18 μm). To our knowledge, the technique is the only generally applicable one because most often there are no compatible cladding crystals available to nonlinear optical cores, especially not with an engineer-able refractive index difference and large mode area.

  9. Anisotropic and Hierarchical Porosity in Multifunctional Ceramics

    NASA Astrophysics Data System (ADS)

    Lichtner, Aaron Zev

    The performance of multifunctional porous ceramics is often hindered by the seemingly contradictory effects of porosity on both mechanical and non-structural properties and yet a sufficient body of knowledge linking microstructure to these properties does not exist. Using a combination of tailored anisotropic and hierarchical materials, these disparate effects may be reconciled. In this project, a systematic investigation of the processing, characterization and properties of anisotropic and isotropic hierarchically porous ceramics was conducted. The system chosen was a composite ceramic intended as the cathode for a solid oxide fuel cell (SOFC). Comprehensive processing investigations led to the development of approaches to make hierarchical, anisotropic porous microstructures using directional freeze-casting of well dispersed slurries. The effect of all the important processing parameters was investigated. This resulted in an ability to tailor and control the important microstructural features including the scale of the microstructure, the macropore size and total porosity. Comparable isotropic porous ceramics were also processed using fugitive pore formers. A suite of characterization techniques including x-ray tomography and 3-D sectional scanning electron micrographs (FIB-SEM) was used to characterize and quantify the green and partially sintered microstructures. The effect of sintering temperature on the microstructure was quantified and discrete element simulations (DEM) were used to explain the experimental observations. Finally, the comprehensive mechanical properties, at room temperature, were investigated, experimentally and using DEM, for the different microstructures.

  10. Anisotropic halo model: implementation and numerical results

    NASA Astrophysics Data System (ADS)

    Sgró, Mario A.; Paz, Dante J.; Merchán, Manuel

    2013-07-01

    In the present work, we extend the classic halo model for the large-scale matter distribution including a triaxial model for the halo profiles and their alignments. In particular, we derive general expressions for the halo-matter cross-correlation function. In addition, by numerical integration, we obtain instances of the cross-correlation function depending on the directions given by halo shape axes. These functions are called anisotropic cross-correlations. With the aim of comparing our theoretical results with the simulations, we compute averaged anisotropic correlations in cones with their symmetry axis along each shape direction of the centre halo. From these comparisons we characterize and quantify the alignment of dark matter haloes on the Λcold dark matter context by means of the presented anisotropic halo model. Since our model requires multidimensional integral computation we implement a Monte Carlo method on GPU hardware which allows us to increase the precision of the results and it improves the performance of the computation.

  11. Anisotropic Self-Assembly of Nanoparticle Amphiphiles

    NASA Astrophysics Data System (ADS)

    Kumar, Sanat

    2009-03-01

    It is easy to understand the self-assembly of particles having anisotropic shapes or interactions, such as Co nanoparticles or proteins, into highly extended structures. However, there is no experimentally established strategy for creating anisotropic structures from common spherical nanoparticles. We demonstrate that spherical nanoparticles, uniformly grafted with macromolecules, robustly self-assemble into a range of anisotropic superstructures when they are dispersed in the corresponding homopolymer matrix. This phenomenon is driven by the microphase separation between the inorganic nanoparticles and the (organic) polymeric chains grafted to their surfaces in a fashion similar to block copolymers. This microphase separation driven particle self-assembly provides a unique means of controlling the global nanoparticle dispersion state in polymer nanocomposites. The relationship between the state of particle dispersion and nanocomposite properties can thus be critically examined, and in particular we focus on the mechanical reinforcement afforded when particles are added to polymers. Grafted nanoparticles are thus versatile building blocks for creating tunable and functional particle superstructures with significant practical applications. With Pinar Akcora, Hongjun Liu, Yu Li, Brian Benicewicz, Linda Schadler, Thanos Panagiotopoulos, Jack Douglas, P. Thiyagarajan and Ralph Colby.

  12. Anisotropic materials appearance analysis using ellipsoidal mirror

    NASA Astrophysics Data System (ADS)

    Filip, Jiří; Vávra, Radomír.

    2015-03-01

    Many real-world materials exhibit significant changes in appearance when rotated along a surface normal. The presence of this behavior is often referred to as visual anisotropy. Anisotropic appearance of spatially homogeneous materials is commonly characterized by a four-dimensional BRDF. Unfortunately, due to simplicity most past research has been devoted to three dimensional isotropic BRDFs. In this paper, we introduce an innovative, fast, and inexpensive image-based approach to detect the extent of anisotropy, its main axes and width of corresponding anisotropic highlights. The method does not rely on any moving parts and uses only an off-the-shelf ellipsoidal reflector with a compact camera. We analyze our findings with a material microgeometry scan, and present how results correspond to the microstructure of individual threads in a particular fabric. We show that knowledge of a material's anisotropic behavior can be effectively used in order to design a material-dependent sampling pattern so as the material's BRDF could be measured much more precisely in the same amount of time using a common gonioreflectometer.

  13. Efficient Anisotropic Filtering of Diffusion Tensor Images

    PubMed Central

    Xu, Qing; Anderson, Adam W.; Gore, John C.; Ding, Zhaohua

    2009-01-01

    To improve the accuracy of structural and architectural characterization of living tissue with diffusion tensor imaging, an efficient smoothing algorithm is presented for reducing noise in diffusion tensor images. The algorithm is based on anisotropic diffusion filtering, which allows both image detail preservation and noise reduction. However, traditional numerical schemes for anisotropic filtering have the drawback of inefficiency and inaccuracy due to their poor stability and first order time accuracy. To address this, an unconditionally stable and second order time accuracy semi-implicit Craig-Sneyd scheme is adapted in our anisotropic filtering. By using large step size, unconditional stability allows this scheme to take much fewer iterations and thus less computation time than the explicit scheme to achieve a certain degree of smoothing. Second order time accuracy makes the algorithm reduce noise more effectively than a first order scheme with the same total iteration time. Both the efficiency and effectiveness are quantitatively evaluated based on synthetic and in vivo human brain diffusion tensor images, and these tests demonstrate that our algorithm is an efficient and effective tool for denoising diffusion tensor images. PMID:20061113

  14. Accelerating numerical modeling of wave propagation through 2-D anisotropic materials using OpenCL.

    PubMed

    Molero, Miguel; Iturrarán-Viveros, Ursula

    2013-03-01

    We present an implementation of the numerical modeling of elastic waves propagation, in 2D anisotropic materials, using the new parallel computing devices (PCDs). Our study is aimed both to model laboratory experiments and explore the capabilities of the emerging PCDs by discussing performance issues. In the experiments a sample plate of an anisotropic material placed inside a water tank is rotated and, for every angle of rotation it is subjected to an ultrasonic wave (produced by a large source transducer) that propagates in the water and through the material producing some reflection and transmission signals that are recording by a "point-like" receiver. This experiment is numerically modeled by running a finite difference code covering a set of angles θ∈[-50°, 50°], and recorded the signals for the transmission and reflection results. Transversely anisotropic and weakly orthorhombic materials are considered. We accelerated the computation using an open-source toolkit called PyOpenCL, which lets one to easily access the OpenCL parallel computation API's from the high-level programming environment of Python. A speedup factor over 19 using the GPU is obtained when compared with the execution of the same program in parallel using a CPU multi-core (in this case we use the 4-cores that has the CPU). The performance for different graphic cards and operating systems is included together with the full 2-D finite difference code with PyOpenCL. Copyright © 2012 Elsevier B.V. All rights reserved.

  15. Anisotropic Alfven-ballooning modes in the Earth`s magnetosphere

    SciTech Connect

    Chan, A.A.; Xia, Mengfen; Chen, Liu

    1993-05-01

    We have carried out a theoretical analysis of the stability and parallel structure of coupled shear-Alfven and slow-magnetosonic waves in the Earth`s inner magnetosphere including effects of finite anisotropic plasma pressure. Multiscale perturbation analysis of the anisotropic Grad-Shafranov equation yields an approximate self-consistent magnetohydrodynamic (MHD) equilibrium. This MHD equilibrium is used in the numerical solution of a set of eigenmode equations which describe the field line eigenfrequency, linear stability, and parallel eigenmode structure. We call these modes anisotropic Alfven-ballooning modes. The main results are: The field line eigenfrequency can be significantly lowered by finite pressure effects. The parallel mode structure of the transverse wave components is fairly insensitive to changes in the plasma pressure but the compressional magnetic component can become highly peaked near the magnetic equator due to increased pressure, especially when P{perpendicular} > P{parallel}. For the isotropic case ballooning instability can occur when the ratio of the plasma pressure to the magnetic pressure, exceeds a critical value {beta}{sub o}{sup B} {approx} 3.5 at the equator. Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field-line-bending stabilization when P{parallel} > P{perpendicular}, or due to increased ballooning-mirror destabilization when P{perpendicular} > P{parallel}. We use a ``{beta}-6 stability diagram`` to display the regions of instability with respect to the equatorial values of the parameters {bar {beta}} and {delta}, where {bar {beta}} = (1/3)({beta}{sub {parallel}} + 2 {beta}{perpendicular}) is an average beta value and {delta} = 1 - P{parallel}/P{perpendicular} is a measure of the plasma anisotropy.

  16. Textured silicon nitride: processing and anisotropic properties

    PubMed Central

    Zhu, Xinwen; Sakka, Yoshio

    2008-01-01

    Textured silicon nitride (Si3N4) has been intensively studied over the past 15 years because of its use for achieving its superthermal and mechanical properties. In this review we present the fundamental aspects of the processing and anisotropic properties of textured Si3N4, with emphasis on the anisotropic and abnormal grain growth of β-Si3N4, texture structure and texture analysis, processing methods and anisotropic properties. On the basis of the texturing mechanisms, the processing methods described in this article have been classified into two types: hot-working (HW) and templated grain growth (TGG). The HW method includes the hot-pressing, hot-forging and sinter-forging techniques, and the TGG method includes the cold-pressing, extrusion, tape-casting and strong magnetic field alignment techniques for β-Si3N4 seed crystals. Each processing technique is thoroughly discussed in terms of theoretical models and experimental data, including the texturing mechanisms and the factors affecting texture development. Also, methods of synthesizing the rodlike β-Si3N4 single crystals are presented. Various anisotropic properties of textured Si3N4 and their origins are thoroughly described and discussed, such as hardness, elastic modulus, bending strength, fracture toughness, fracture energy, creep behavior, tribological and wear behavior, erosion behavior, contact damage behavior and thermal conductivity. Models are analyzed to determine the thermal anisotropy by considering the intrinsic thermal anisotropy, degree of orientation and various microstructure factors. Textured porous Si3N4 with a unique microstructure composed of oriented elongated β-Si3N4 and anisotropic pores is also described for the first time, with emphasis on its unique mechanical and thermal-mechanical properties. Moreover, as an important related material, textured α-Sialon is also reviewed, because the presence of elongated α-Sialon grains allows the production of textured α-Sialon using the

  17. Textured silicon nitride: processing and anisotropic properties.

    PubMed

    Zhu, Xinwen; Sakka, Yoshio

    2008-07-01

    Textured silicon nitride (Si3N4) has been intensively studied over the past 15 years because of its use for achieving its superthermal and mechanical properties. In this review we present the fundamental aspects of the processing and anisotropic properties of textured Si3N4, with emphasis on the anisotropic and abnormal grain growth of β-Si3N4, texture structure and texture analysis, processing methods and anisotropic properties. On the basis of the texturing mechanisms, the processing methods described in this article have been classified into two types: hot-working (HW) and templated grain growth (TGG). The HW method includes the hot-pressing, hot-forging and sinter-forging techniques, and the TGG method includes the cold-pressing, extrusion, tape-casting and strong magnetic field alignment techniques for β-Si3N4 seed crystals. Each processing technique is thoroughly discussed in terms of theoretical models and experimental data, including the texturing mechanisms and the factors affecting texture development. Also, methods of synthesizing the rodlike β-Si3N4 single crystals are presented. Various anisotropic properties of textured Si3N4 and their origins are thoroughly described and discussed, such as hardness, elastic modulus, bending strength, fracture toughness, fracture energy, creep behavior, tribological and wear behavior, erosion behavior, contact damage behavior and thermal conductivity. Models are analyzed to determine the thermal anisotropy by considering the intrinsic thermal anisotropy, degree of orientation and various microstructure factors. Textured porous Si3N4 with a unique microstructure composed of oriented elongated β-Si3N4 and anisotropic pores is also described for the first time, with emphasis on its unique mechanical and thermal-mechanical properties. Moreover, as an important related material, textured α-Sialon is also reviewed, because the presence of elongated α-Sialon grains allows the production of textured α-Sialon using the

  18. Competition for finite resources

    NASA Astrophysics Data System (ADS)

    Cook, L. Jonathan; Zia, R. K. P.

    2012-05-01

    The resources in a cell are finite, which implies that the various components of the cell must compete for resources. One such resource is the ribosomes used during translation to create proteins. Motivated by this example, we explore this competition by connecting two totally asymmetric simple exclusion processes (TASEPs) to a finite pool of particles. Expanding on our previous work, we focus on the effects on the density and current of having different entry and exit rates.

  19. Influence of the anisotropic mechanical properties of the skull in low-intensity focused ultrasound towards neuromodulation of the brain.

    PubMed

    Metwally, Mohamed K; Han, Hee-Sok; Jeon, Hyun Jae; Khang, Gon; Kim, Tae-Seong

    2013-01-01

    Lately, neuromodulation of the brain is considered one of the promising applications of ultrasound technology in which low-intensity focused ultrasound (LIFU) is used noninvasively to excite or inhibit neuronal activity. In LIFU, one of critical barriers in the propagation of ultrasound wave is the skull, which is known to be highly anisotropic mechanically: this affects the ultrasound focusing, thereby neuromodulation effects. This study aims to investigate the influence of the anisotropic properties of the skull on the LIFU via finite element head models incorporating the anisotropic properties of the skull. We have examined the pressure and stress distributions within the head in LIFU. Our results show that though most of the pressure that reaches to the brain is due to the longitudinal wave propagation through the skull, the normal stress in the transverse direction of the wave propagation has the main role to control the pressure profile inside the brain more than the shear stress. The results also show that the anisotropic properties of skull contribute in broadening the focal zone in comparison to that of the isotropic skull.

  20. Anisotropic macroturbulence and diffusion associated with a westward zonal jet: From laboratory to planetary atmospheres and oceans

    NASA Astrophysics Data System (ADS)

    Galperin, Boris; Hoemann, Jesse; Espa, Stefania; Di Nitto, Gabriella; Lacorata, Guglielmo

    2016-12-01

    Turbulence with inverse energy cascade and its transport properties are investigated experimentally in a flow associated with a westward propagating jet. Turbulence and the jet were produced by an electromagnetic force in a rotating tank filled with an electrolytic saline solution. The parabolic free surface emulated the topographic β effect which evoked the zonation. The spectral and transport flow characteristics were highly anisotropic. Turbulence is diagnosed by exploring the analogy between vertical and horizontal turbulent overturns in, respectively, stably stratified and quasigeostrophic flows which gives rise to a method of potential vorticity (PV) monotonizing. The anisotropization of transport properties of the flow is investigated using the finite scale Lyapunov exponent technique. After initial exponential particle separation, radial (meridional in geophysical and planetary applications) diffusion attains a short-ranged Richardson regime which transitions to the Taylor (scale-independent diffusivity) one. The azimuthal (zonal) diffusion exhibits a double-plateau structure which attains a superdiffusive regime on large scales. The transition to the Taylor regime for the radial diffusion takes place at a scale of turbulence anisotropization. The radial eddy diffusivity in both regimes as well as the transition scale are all determined by the rate of the inverse energy cascade, ɛ , that can be diagnosed by the PV monotonizing. Conversely, ɛ can be deduced from the scale of the Richardson-Taylor regime transition in the radial eddy diffusivity which, thus, provides an additional tool of diagnosing anisotropic macroturbulence with inverse energy cascade.

  1. A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model for Pressure Insensitive and Sensitive Materials

    SciTech Connect

    Choi, Kyoo Sil; Pan, Jwo

    2009-07-27

    In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.

  2. Anisotropic macroturbulence and diffusion associated with a westward zonal jet: From laboratory to planetary atmospheres and oceans.

    PubMed

    Galperin, Boris; Hoemann, Jesse; Espa, Stefania; Di Nitto, Gabriella; Lacorata, Guglielmo

    2016-12-01

    Turbulence with inverse energy cascade and its transport properties are investigated experimentally in a flow associated with a westward propagating jet. Turbulence and the jet were produced by an electromagnetic force in a rotating tank filled with an electrolytic saline solution. The parabolic free surface emulated the topographic β effect which evoked the zonation. The spectral and transport flow characteristics were highly anisotropic. Turbulence is diagnosed by exploring the analogy between vertical and horizontal turbulent overturns in, respectively, stably stratified and quasigeostrophic flows which gives rise to a method of potential vorticity (PV) monotonizing. The anisotropization of transport properties of the flow is investigated using the finite scale Lyapunov exponent technique. After initial exponential particle separation, radial (meridional in geophysical and planetary applications) diffusion attains a short-ranged Richardson regime which transitions to the Taylor (scale-independent diffusivity) one. The azimuthal (zonal) diffusion exhibits a double-plateau structure which attains a superdiffusive regime on large scales. The transition to the Taylor regime for the radial diffusion takes place at a scale of turbulence anisotropization. The radial eddy diffusivity in both regimes as well as the transition scale are all determined by the rate of the inverse energy cascade, ε, that can be diagnosed by the PV monotonizing. Conversely, ε can be deduced from the scale of the Richardson-Taylor regime transition in the radial eddy diffusivity which, thus, provides an additional tool of diagnosing anisotropic macroturbulence with inverse energy cascade.

  3. Ultrasonic guided wave nondestructive evaluation using generalized anisotropic interface waves

    NASA Astrophysics Data System (ADS)

    Gardner, Michael D.

    The motivation for this work is a goal to inspect interfaces between thick layers of materials that can be anisotropic. The specific application is a thick composite bonded to a metal substrate. The interface is inspected for disbonds between the metal and composite. The large thickness allows the problem to be modeled as a half space. The theory behind guided waves in plates is presented. This theory includes the calculation and analysis of dispersion curves and the resulting wave structure. It is noted that for high frequency-thickness values, certain modes will converge to the half-space waves, e.g. the Rayleigh wave and the Stoneley wave. Points of high energy, especially shear energy, at the interface are desirable for interfacial inspection. Therefore, the wave structure for all modes and frequencies is searched for ideal inspection points. Interface waves are inherently good modes to use for interface inspection. Results from the dispersion curves and wave structures are verified in the finite element model software package called Abaqus. It is confirmed that the group speeds and wave structures of the modes match the predicted values. A theoretical development of interface waves is given wherein Rayleigh, Stoneley, and generalized interface waves are discussed. This is applied to both isotropic and anisotropic materials. It is shown that the Stoneley wave only exists for a certain range of material parameters. Because the Stoneley wave is the interface wave between two solid half spaces, it might appear that only certain pairs of solids would allow for inspection via interface wave. However, it is shown that for perturbations of the Stoneley-wave-valid material properties, interface waves which leak energy away from the interface can still propagate. They can also be used for inspection. Certain choices of materials will leak less energy and will therefore allow for longer inspection distances. The solutions to the isotropic leaky wave problem exist on

  4. PyLith: A Finite-Element Code for Modeling Quasi-Static and Dynamic Crustal Deformation

    NASA Astrophysics Data System (ADS)

    Williams, C. A.; Aagaard, B.; Knepley, M. G.

    2009-12-01

    We have developed open-source finite-element software for 2-D and 3-D dynamic and quasi-static modeling of crustal deformation. This software, PyLith (current release is version 1.4), combines the quasi-static viscoelastic modeling functionality of PyLith 0.8 and its predecessors (LithoMop and Tecton) and the wave propagation modeling functionality of EqSim. The target applications contain spatial scales ranging from tens of meters to hundreds of kilometers with temporal scales for dynamic modeling ranging from milliseconds to minutes and temporal scales for quasi-static modeling ranging from minutes to thousands of years. PyLith development is part of the NSF funded Computational Infrastructure for Geodynamics (CIG) and the software runs on a wide variety of platforms (laptops, workstations, and Beowulf clusters). Binaries and source code are available from geodynamics.org. It uses a suite of general, parallel, graph data structures called Sieve for storing and manipulating finite-element meshes. This permits use of a variety of 2-D and 3-D cell types including triangles, quadrilaterals, hexahedra, and tetrahedra. Current features include kinematic fault ruptures with multiple sequential earthquakes and aseismic creep, time-dependent Dirichlet and Neumann boundary conditions, absorbing boundary conditions, time-dependent point forces, linear elastic rheologies, generalized Maxwell and Maxwell linear viscoelastic rheologies, power-law rheologies, and gravitational body forces. Current development focuses on implementing dynamic fault interface conditions (employing fault constitutive models) and additional viscoelastic and viscoplastic materials. Future development plans include support for large deformation and automated calculation of suites of Green's functions. We also plan to extend PyLith to allow coupling multiple simultaneous simulations. For example, this could include (1) coupling an interseismic deformation simulation to a spontaneous earthquake rupture

  5. Investigation of anisotropic thermal transport in cross-linked polymers

    NASA Astrophysics Data System (ADS)

    Simavilla, David Nieto

    Thermal transport in lightly cross-linked polyisoprene and polybutadine subjected to uniaxial elongation is investigated experimentally. We employ two experimental techniques to assess the effect that deformation has on this class of materials. The first technique, which is based on Forced Rayleigh Scattering (FRS), allows us to measure the two independent components of the thermal diffusivity tensor as a function of deformation. These measurements along with independent measurements of the tensile stress and birefringence are used to evaluate the stress-thermal and stress-optic rules. The stress-thermal rule is found to be valid for the entire range of elongations applied. In contrast, the stress-optic rule fails for moderate to large stretch ratios. This suggests that the degree of anisotropy in thermal conductivity depends on both orientation and tension in polymer chain segments. The second technique, which is based on infrared thermography (IRT), allows us to measure anisotropy in thermal conductivity and strain induced changes in heat capacity. We validate this method measurements of anisotropic thermal conductivity by comparing them with those obtained using FRS. We find excellent agreement between the two techniques. Uncertainty in the infrared thermography method measurements is estimated to be about 2-5 %. The accuracy of the method and its potential application to non-transparent materials makes it a good alternative to extend current research on anisotropic thermal transport in polymeric materials. A second IRT application allows us to investigate the dependence of heat capacity on deformation. We find that heat capacity increases with stretch ratio in polyisoprene specimens under uniaxial extension. The deviation from the equilibrium value of heat capacity is consistent with an independent set of experiments comparing anisotropy in thermal diffusivity and conductivity employing FRS and IRT techniques. We identify finite extensibility and strain

  6. Large scale anisotropic bias from primordial non-Gaussianity

    SciTech Connect

    Baghram, Shant; Firouzjahi, Hassan; Namjoo, Mohammad Hossein E-mail: mh.namjoo@ipm.ir

    2013-08-01

    In this work we study the large scale structure bias in models of anisotropic inflation. We use the Peak Background Splitting method in Excursion Set Theory to find the scale-dependent bias. We show that the amplitude of the bias is modified by a direction-dependent factor. In the specific anisotropic inflation model which we study, the scale-dependent bias vanishes at leading order when the long wavelength mode in squeezed limit is aligned with the anisotropic direction in the sky. We also extend the scale-dependent bias formulation to the general situations with primordial anisotropy. We find some selection rules indicating that some specific parts of a generic anisotropic bispectrum is picked up by the bias parameter. We argue that the anisotropic bias is mainly sourced by the angle between the anisotropic direction and the long wavelength mode in the squeezed limit.

  7. Influence of anisotropic white matter modeling on EEG source localization.

    PubMed

    Cuartas-Morales, E; Cardenas-Pena, D; Castellanos-Dominguez, G

    2014-01-01

    We study the influence of the anisotropic white matter within the ElectroEncephaloGraphy source localization problem. To this end, we consider three cases of the anisotropic white matter modeled in two concrete cases: by fixed or variable ratio. We extract information about highly anisotropic areas of the white matter from real Diffusion Weighted Imaging data. To validate the compared anisotropic models, we introduce the localization dipole and orientation errors. Obtained results show that the white matter model with a fixed anisotropic ratio leads to values of dipole localization error close to 1cm and may be enough in those cases avoiding localized analysis of neural brain activity. In contrast, modeling based on the anisotropic variable rate assumption becomes important in tasks regarding analysis and localization of deep sources neighboring the white matter tissue.

  8. Grooved organogel surfaces towards anisotropic sliding of water droplets.

    PubMed

    Zhang, Pengchao; Liu, Hongliang; Meng, Jingxin; Yang, Gao; Liu, Xueli; Wang, Shutao; Jiang, Lei

    2014-05-21

    Periodic micro-grooved organogel surfaces can easily realize the anisotropic sliding of water droplets attributing to the formed slippery water/oil/solid interface. Different from the existing anisotropic surfaces, this novel surface provides a versatile candidate for the anisotropic sliding of water droplets and might present a promising way for the easy manipulation of liquid droplets for water collection, liquid-directional transportation, and microfluidics.

  9. The Relation of Finite Element and Finite Difference Methods

    NASA Technical Reports Server (NTRS)

    Vinokur, M.

    1976-01-01

    Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

  10. Anisotropic viscoelastic shell modeling technique of copper patterns/photoimageable solder resist composite for warpage simulation of multi-layer printed circuit boards

    NASA Astrophysics Data System (ADS)

    Kim, Do-Hyoung; Joo, Sung-Jun; Kwak, Dong-Ok; Kim, Hak-Sung

    2015-10-01

    In this study, the warpage simulation of a multi-layer printed circuit board (PCB) was performed as a function of various copper (Cu) patterns/photoimageable solder resist (PSR) composite patterns and their anisotropic viscoelastic properties. The thermo-mechanical properties of Cu/PSR patterns were obtained from finite element analysis (virtual test) and homogenized with anisotropic composite shell models that considered the viscoelastic properties. The multi-layer PCB model was simplified based on the unit Cu/PSR patterns and the warpage simulation during the reflow process was performed by using ABAQUS combined with a user-defined subroutine. From these results, it was demonstrated that the proposed anisotropic viscoelastic composite shell simulation technique can be successfully used to predict warpage of multi-layer PCBs during the reflow process.

  11. Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres.

    PubMed

    Zhang, Lin; Shi, Yan; Liang, Chang-Hong

    2016-10-03

    In this paper, full-wave electromagnetic scattering theory is employed to investigate illusion and invisibility of inhomogeneous anisotropic cylinders and spheres. With the use of a shell designed according to Mie series theory for multiple piecewise anisotropic layers, radar cross section (RCS) of the coated inhomogeneous anisotropic object can be dramatically reduced or disguised as another object in the long-wavelength limit. With the suitable adjustment of the anisotropy parameters of the shell, optimal illusion and invisibility characteristics of the coated inhomogeneous anisotropic object can be achieved. Details of theoretical analysis and numerical examples are presented to validate the proposed methodology.

  12. Retrieval procedure of effective conductivity for plasmonic resonant anisotropic metasurface

    NASA Astrophysics Data System (ADS)

    Yermakov, O. Y.; Porubaev, F.; Bogdanov, A. A.; Samusev, A. K.; Iorsh, I. V.

    2017-09-01

    In this work we introduce the effective surface conductivity retrieval procedure in order to describe the properties of plasmonic resonant anisotropic metasurface consisting of plasmonic elliptical nanodisks.

  13. Stability conditions for the Bianchi type II anisotropically inflating universes

    SciTech Connect

    Kao, W.F.; Lin, Ing-Chen E-mail: g9522528@oz.nthu.edu.tw

    2009-01-15

    Stability conditions for a class of anisotropically inflating solutions in the Bianchi type II background space are shown explicitly in this paper. These inflating solutions were known to break the cosmic no-hair theorem such that they do not approach the de Sitter universe at large times. It can be shown that unstable modes of the anisotropic perturbations always exist for this class of expanding solutions. As a result, we show that these set of anisotropically expanding solutions are unstable against anisotropic perturbations in the Bianchi type II space.

  14. Finite-element-analysis of fields radiated from ICRF antenna

    NASA Astrophysics Data System (ADS)

    Yamanaka, K.; Sugihara, R.

    1984-04-01

    In several simple geometries, electromagnetic fields radiated from a loop antennas, on which a current oscillately flows across the static magnetic field are calculated by the finite element method (FEM) as well as by analytic methods in a cross section of a plasma cylinder. A finite wave number along the static magnetic field is assumed. Good agreement between FEM and the analytic solutions is obtained, which indicates the accuracy of FEM solutions. The method is applied to calculations of fields from a half turn antenna and reasonable results are obtained. It is found that a straightforward application of FEM to problems in an anisotropic medium may bring about erroneous results and that an appropriate coordinate transformation is needed for FEM become applicable.

  15. Computation of Large Anisotropic Seismic Heterogeneities (CLASH)

    NASA Astrophysics Data System (ADS)

    Beucler, Éric; Montagner, Jean-Paul

    2006-05-01

    A general tomographic technique is designed in order (i) to operate in anisotropic media; (ii) to account for the uneven seismic sampling and (iii) to handle massive data sets in a reasonable computing time. One modus operandi to compute a 3-D body wave velocity model relies on surface wave phase velocity measurements. An intermediate step, shared by other approaches, consists in translating, for each period of a given mode branch, the phase velocities integrated along ray paths into local velocity perturbations. To this end, we develop a method, which accounts for the azimuthal anisotropy in its comprehensive form. The weakly non-linear forward problem allows to use a conjugate gradient optimization. The Earth's surface is regularly discretized and the partial derivatives are assigned to the individual grid points. Possible lack of lateral resolution, due to the inescapable uneven ray path coverage, is taken into account through the a priori covariances on parameters with laterally variable correlation lengths. This method allows to efficiently separate the 2ψ and the 4ψ anisotropic effects from the isotropic perturbations. Fundamental mode and overtone phase velocity maps, derived with real Rayleigh wave data sets, are presented and compared with previous maps. The isotropic models concur well with the results of Trampert & Woodhouse. Large 4ψ heterogeneities are located in the tectonically active regions and over the continental lithospheres such as North America, Antarctica or Australia. At various periods, a significant 4ψ signature is correlated with the Hawaii hotspot track. Finally, concurring with the conclusions of Trampert & Woodhouse, our phase velocity maps show that Rayleigh wave data sets do need both 2ψ and 4ψ anisotropic terms.

  16. The Numerical Solution of the Nonlinear Poisson-Boltzmann Equation Under the Anisotropic Boundary Condition for Colloidal Plasmas

    NASA Astrophysics Data System (ADS)

    Cai, Huanqing; Ye, Qizheng

    2010-04-01

    Based on the model of the Wigner-Seitz cell, the surface potential of the spherical macroparticle (radius a) expands in terms of the monopole (q). A dipole (p) model is assumed for an anisotropic boundary condition of the nonlinear Poisson-Boltzmann equation. Using the finite element method implemented by the FlexPDE software, the potential distribution around the macroparticle is obtained for different ratios p/qa. The calculated results for the potential show that there is an attractive region in the vicinity of the macroparticle when |p/qa|>1.1, and noticeably there is a potential well behind the macroparticle when |p/qa| = 1.1, i.e., there exists both an attractive region and a repulsive region simultaneously. This means that the attractive interaction between macroparticles may arise from the anisotropic distribution of the surrounding plasmas, which well explains some experimental observations.

  17. Investigation on broadband propagation characteristic of terahertz electromagnetic wave in anisotropic magnetized plasma in frequency and time domain

    SciTech Connect

    Tian, Yuan; Han, Yiping; Ai, Xia; Liu, Xiuxiang

    2014-12-15

    In this paper, we investigate the propagation of terahertz (THz) electromagnetic wave in an anisotropic magnetized plasma by JE convolution-finite difference time domain method. The anisotropic characteristic of the plasma, which leads to right-hand circularly polarized (RCP) and right-hand circularly polarized (LCP) waves, has been taken into account. The interaction between electromagnetic waves and magnetized plasma is illustrated by reflection and transmission coefficients for both RCP and LCP THz waves. The effects of both the magnetized plasma thickness and the external magnetized field are analyzed and numerical results demonstrate that the two factors could influence the THz wave greatly. It is worthy to note that besides the reflection and transmission coefficients in the frequency domain, the waveform of the electric field in the time domain varying with thicknesses and external magnetic fields for different polarized direction has been studied.

  18. Fingerprints of the anisotropic spin-split hole dispersion in resonant inelastic light scattering in two-dimensional hole systems.

    PubMed

    Hirmer, M; Hirmer, M; Schuh, D; Wegscheider, W; Korn, T; Winkler, R; Schüller, C

    2011-11-18

    In resonant inelastic light scattering experiments on two-dimensional hole systems in GaAs-Al(x)Ga(1-x)As single quantum wells we find evidence for the strongly anisotropic spin-split hole dispersion at finite in-plane momenta. In all our samples we detect a low-energy spin-density excitation of a few meV, stemming from excitation of holes of the spin-split ground state. The detailed spectral shape of the excitation depends sensitively on the orientations of the linear light polarizations with respect to the in-plane crystal axes. In particular, we observe a doublet structure, which is most pronounced if the polarization of the incident light is parallel to the [110] in-plane direction. Theoretical calculations of the Raman spectra based on a multiband k · p approach confirm that the observed doublet structure is due to the anisotropic spin-split hole dispersion.

  19. Investigation on broadband propagation characteristic of terahertz electromagnetic wave in anisotropic magnetized plasma in frequency and time domain

    NASA Astrophysics Data System (ADS)

    Tian, Yuan; Ai, Xia; Han, Yiping; Liu, Xiuxiang

    2014-12-01

    In this paper, we investigate the propagation of terahertz (THz) electromagnetic wave in an anisotropic magnetized plasma by JE convolution-finite difference time domain method. The anisotropic characteristic of the plasma, which leads to right-hand circularly polarized (RCP) and right-hand circularly polarized (LCP) waves, has been taken into account. The interaction between electromagnetic waves and magnetized plasma is illustrated by reflection and transmission coefficients for both RCP and LCP THz waves. The effects of both the magnetized plasma thickness and the external magnetized field are analyzed and numerical results demonstrate that the two factors could influence the THz wave greatly. It is worthy to note that besides the reflection and transmission coefficients in the frequency domain, the waveform of the electric field in the time domain varying with thicknesses and external magnetic fields for different polarized direction has been studied.

  20. Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

    NASA Technical Reports Server (NTRS)

    Prosser, W. H.; Hamstad, M. A.; Gary, J.; OGallagher, A.

    1998-01-01

    A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

  1. Generalised model for anisotropic compact stars

    NASA Astrophysics Data System (ADS)

    Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Deb, Debabrata

    2016-12-01

    In the present investigation an exact generalised model for anisotropic compact stars of embedding class 1 is sought with a general relativistic background. The generic solutions are verified by exploring different physical aspects, viz. energy conditions, mass-radius relation, stability of the models, in connection to their validity. It is observed that the model presented here for compact stars is compatible with all these physical tests and thus physically acceptable as far as the compact star candidates RXJ 1856-37, SAX J 1808.4-3658 ( SS1) and SAX J 1808.4-3658 ( SS2) are concerned.

  2. Chromo-natural model in anisotropic background

    SciTech Connect

    Maleknejad, Azadeh; Erfani, Encieh E-mail: eerfani@ipm.ir

    2014-03-01

    In this work we study the chromo-natural inflation model in the anisotropic setup. Initiating inflation from Bianchi type-I cosmology, we analyze the system thoroughly during the slow-roll inflation, from both analytical and numerical points of view. We show that the isotropic FRW inflation is an attractor of the system. In other words, anisotropies are damped within few e-folds and the chromo-natural model respects the cosmic no-hair conjecture. Furthermore, we demonstrate that in the slow-roll limit, the anisotropies in both chromo-natural and gauge-flation models share the same dynamics.

  3. Local thermodynamics of a magnetized, anisotropic plasma

    SciTech Connect

    Hazeltine, R. D.; Mahajan, S. M.; Morrison, P. J.

    2013-02-15

    An expression for the internal energy of a fluid element in a weakly coupled, magnetized, anisotropic plasma is derived from first principles. The result is a function of entropy, particle density and magnetic field, and as such plays the role of a thermodynamic potential: it determines in principle all thermodynamic properties of the fluid element. In particular it provides equations of state for the magnetized plasma. The derivation uses familiar fluid equations, a few elements of kinetic theory, the MHD version of Faraday's law, and certain familiar stability and regularity conditions.

  4. Anisotropic thermal expansion of strontium barium niobate

    NASA Astrophysics Data System (ADS)

    Qadri, Syed B.; Bellotti, Jeffrey A.; Garzarella, Anthony; Wu, Dong Ho

    2005-06-01

    Strontium barium niobate is a tungsten-bronze ferroelectric crystal having a tetragonal unit cell. Low-temperature x-ray diffraction studies were performed on a single crystal of Sr0.75Ba0.25Nb2O6 to determine the thermal expansivity along the a- and c-axes. Negative thermal expansion was observed along the c direction while a positive thermal expansion was measured along the a axis. The anisotropic thermal expansion behavior is explained as arising due to the geometry of the crystal structure.

  5. Superscattering pattern shaping for radially anisotropic nanowires

    NASA Astrophysics Data System (ADS)

    Liu, Wei

    2017-08-01

    We achieve efficient shaping of superscattering by radially anisotropic nanowires relying on resonant multipolar interferences. It is shown that the radial anisotropy of refractive index can be employed to resonantly overlap electric and magnetic multipoles of various orders, and as a result, effective superscattering with different engineered angular patterns can be obtained. We further demonstrate that such superscattering shaping relying on unusual radial anisotropy parameters can be directly realized with isotropic multilayered nanowires, which may shed new light on much fundamental research and various applications related to scattering particles.

  6. Capillary interactions between anisotropic colloidal particles.

    PubMed

    Loudet, J C; Alsayed, A M; Zhang, J; Yodh, A G

    2005-01-14

    We report on the behavior of micron-sized prolate ellipsoids trapped at an oil-water interface. The particles experience strong, anisotropic, and long-ranged attractive capillary interactions which greatly exceed the thermal energy k(B)T. Depending on surface chemistry, the particles aggregate into open structures or chains. Using video microscopy, we extract the pair interaction potential between ellipsoids and show it exhibits a power law behavior over the length scales probed. Our observations can be explained using recent calculations, if we describe the interfacial ellipsoids as capillary quadrupoles.

  7. Anisotropic Tribological Properties of Silicon Carbide

    NASA Technical Reports Server (NTRS)

    Miyoshi, K.; Buckley, D. H.

    1980-01-01

    The anisotropic friction, deformation and fracture behavior of single crystal silicon carbide surfaces were investigated in two categories. The categories were called adhesive and abrasive wear processes, respectively. In the adhesive wear process, the adhesion, friction and wear of silicon carbide were markedly dependent on crystallographic orientation. The force to reestablish the shearing fracture of adhesive bond at the interface between silicon carbide and metal was the lowest in the preferred orientation of silicon carbide slip system. The fracturing of silicon carbide occurred near the adhesive bond to metal and it was due to primary cleavages of both prismatic (10(-1)0) and basal (0001) planes.

  8. Creating an anisotropic plasma resistivity with waves

    SciTech Connect

    Fisch, N.J.; Boozer, A.H.

    1980-05-01

    An anisotropic plasma resistivity may be created by preferential heating of electrons traveling in one direction. This can result in a steady-state toroidal current in a tokamak even in the absence of net wave momentum. In fact, at high wave phase velocities, the current associated with the change in resistivity is greater than that associated with net momentum input. An immediate implication is that other waves, such as electron cyclotron waves, may be competitive with lower-hybrid waves as a means for generating current. An analytical expression is derived for the current generated per power dissipated which agrees remarkably well with numerical calculations.

  9. Watertight Anisotropic Surface Meshing Using Quadrilateral Patches

    NASA Technical Reports Server (NTRS)

    Haimes, Robert; Aftosmis, Michael J.

    2004-01-01

    This paper presents a simple technique for generating anisotropic surface triangulations using unstructured quadrilaterals when the CAD entity can be mapped to a logical rectangle. Watertightness and geometric quality measures are maintained and are consistent with the CAPRI default tessellator. These triangulations can match user specified criteria for chord-height tolerance, neighbor triangle dihedral angle, and maximum triangle side length. This discrete representation has hooks back to the owning geometry and therefore can be used in conjunction with these entities to allow for easy enhancement or modification of the tessellation suitable for grid generation or other downstream applications.

  10. Laminated anisotropic reinforced plastic plates and shells

    NASA Technical Reports Server (NTRS)

    Korolev, V. I.

    1981-01-01

    Basic technical theories and engineering calculation equations for anisotropic plates and shells made of rigid reinforced plastics, mainly laminated fiberglass, are presented and discussed. Solutions are given for many problems of design of structural plates and shells, including curved sections and tanks, as well as two chapters on selection of the optimum materials, are given. Accounting for interlayer shearing and transverse separation, which are new engineering properties, are discussed. Application of the results obtained to thin three ply plates and shells wth a light elastic filler is presented and discussed.

  11. Multichannel image regularization using anisotropic geodesic filtering

    SciTech Connect

    Grazzini, Jacopo A

    2010-01-01

    This paper extends a recent image-dependent regularization approach introduced in aiming at edge-preserving smoothing. For that purpose, geodesic distances equipped with a Riemannian metric need to be estimated in local neighbourhoods. By deriving an appropriate metric from the gradient structure tensor, the associated geodesic paths are constrained to follow salient features in images. Following, we design a generalized anisotropic geodesic filter; incorporating not only a measure of the edge strength, like in the original method, but also further directional information about the image structures. The proposed filter is particularly efficient at smoothing heterogeneous areas while preserving relevant structures in multichannel images.

  12. Tunable anisotropic thermal conduction in graphane nanoribbons

    NASA Astrophysics Data System (ADS)

    Li, Dengfeng; Xu, Yong; Chen, Xiaobin; Li, Bolin; Duan, Wenhui

    2014-04-01

    Graphane and graphene are both two-dimensional materials but of different bonding configurations, which can result in distinct thermal conduction properties. We simulate thermal conduction in graphane nanoribbons (GANRs) using the nonequilibrium Green's function method. We find anisotropic thermal conduction in GANRs, with zigzag GANRs giving higher thermal conductance than armchair ones. Compared to the graphene counterparts, GANRs show lower ballistic thermal conductance and stronger thermal conductance anisotropy. Furthermore, hydrogen vacancies of GANRs considerably suppress thermal conduction, accompanied by enhanced thermal conductance anisotropy. The tunable thermal conduction, realized by controlling the ribbon width, edge shape, and hydrogen vacancy concentration of GANRs, could be useful for thermal management and thermoelectric applications.

  13. Anisotropic fiber alignment in composite structures

    DOEpatents

    Graham, Alan L.; Mondy, Lisa A.; Guell, David C.

    1993-01-01

    High strength material composite structures are formed with oriented fibers to provide controlled anisotropic fibers. Fibers suspended in non-dilute concentrations (e.g., up to 20 volume percent for fibers having an aspect ratio of 20) in a selected medium are oriented by moving an axially spaced array of elements in the direction of desired fiber alignment. The array elements are generally perpendicular to the desired orientation. The suspension medium may also include sphere-like particles where the resulting material is a ceramic.

  14. Anisotropic bond percolation in two dimensions

    NASA Astrophysics Data System (ADS)

    Arovas, D.; Bhatt, R. N.; Shapiro, B.

    1983-08-01

    A new single-parameter renormalization-group equation is formulated for anisotropic bond percolation in two dimensions using a position-space renormalization approach. The new equation yields the exact critical line px+py=1 within both the Migdal-Kadanoff decimation and cell renormalization schemes. For large anisotropy, however, an additional critical line appears leading to a spurious divergence in the correlation-length critical exponent. An alternative scheme, which does not preserve the exact critical surface, but yields a correlation-length exponent relatively independent of anisotropy, is also examined.

  15. Temperature and polarization patterns in anisotropic cosmologies

    SciTech Connect

    Sung, Rockhee; Coles, Peter E-mail: Peter.Coles@astro.cf.ac.uk

    2011-06-01

    We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII{sub 0}, VII{sub h} and IX) to illustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters I, Q and U.

  16. Anisotropic elasticity of experimental colloidal Wigner crystals.

    PubMed

    Russell, Emily R; Spaepen, Frans; Weitz, David A

    2015-03-01

    Colloidal particles interacting via a long-range repulsion can, in contrast to hard-sphere systems, exhibit crystalline ordering at low volume fraction. Here we experimentally investigate the structure and properties of such "colloidal Wigner crystals." We find a body-centered-cubic crystalline phase at volume fractions of ϕ≳15%, which exhibits large fluctuations of individual particles from their average positions. We determine the three independent crystalline elastic constants and find that these crystals are very compliant and highly anisotropic.

  17. Finite element modeling of mitral leaflet tissue using a layered shell approximation

    PubMed Central

    Ratcliffe, Mark B.; Guccione, Julius M.

    2012-01-01

    The current study presents a finite element model of mitral leaflet tissue, which incorporates the anisotropic material response and approximates the layered structure. First, continuum mechanics and the theory of layered composites are used to develop an analytical representation of membrane stress in the leaflet material. This is done with an existing anisotropic constitutive law from literature. Then, the concept is implemented in a finite element (FE) model by overlapping and merging two layers of transversely isotropic membrane elements in LS-DYNA, which homogenizes the response. The FE model is then used to simulate various biaxial extension tests and out-of-plane pressure loading. Both the analytical and FE model show good agreement with experimental biaxial extension data, and show good mutual agreement. This confirms that the layered composite approximation presented in the current study is able to capture the exponential stiffening seen in both the circumferential and radial directions of mitral leaflets. PMID:22971896

  18. A Finite Element Projection Method for the Solution of Particle Transport Problems with Anisotropic Scattering.

    DTIC Science & Technology

    1984-07-01

    1975. Przybylski, K. and Ligou, Jr., "Numerical Analysis of the Boltzmann Equation Including Fokker - Planck Terms," Nuclear Science and Engineering, 81...Numerical Method to Solve the Linear Fokker - Planck Equation Charac- terizing Charge Particle Transport in Spherical Plasmas," Nuclear Science and Engineering...investigated. This would entail the inclusion of the Fokker - Planck collision terms into the mathematical and numerical models. 170 APPENDIX A VARIATIONS OF A

  19. Finite-difference grid for a doublet well in an anisotropic aquifer

    USGS Publications Warehouse

    Miller, R.T.; Voss, C.I.

    1986-01-01

    The validity of the flux values at the model boundaries for the isothermal case was tested by simulation of an eight-day injection test of ambient-temperature water. Model-computed pressures compared very favorably with field-observed pressures. The validity of boundary-flux values also was tested for nonisothermal conditions by simulation of injection of 300o F water at 300 gallons per minute for eight days.

  20. Anisotropic mesh adaptation for solution of finite element problems using hierarchical edge-based error estimates

    SciTech Connect

    Lipnikov, Konstantin; Agouzal, Abdellatif; Vassilevski, Yuri

    2009-01-01

    We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.

  1. Finite element analyses of two dimensional, anisotropic heat transfer in wood

    Treesearch

    John F. Hunt; Hongmei Gu

    2004-01-01

    The anisotropy of wood creates a complex problem for solving heat and mass transfer problems that require analyses be based on fundamental material properties of the wood structure. Inputting basic orthogonal properties of the wood material alone are not sufficient for accurate modeling because wood is a combination of porous fiber cells that are aligned and mis-...

  2. Finite-dimensional calculus

    NASA Astrophysics Data System (ADS)

    Feinsilver, Philip; Schott, René

    2009-09-01

    We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.

  3. Finite-Temperature Micromagnetism

    SciTech Connect

    Skomski, R; Kumar, P; Hadjipanayis, GC; Sellmyer, DJ

    2013-07-01

    It is investigated how magnetic hysteresis is affected by finite-temperature excitations, using soft regions in hard-magnetic matrices as model systems. In lowest order, magnetization processes are described by the traditional approach of using finite-temperature materials constants such as K-1(T). Nanoscale excitations are usually small perturbations. For example, a Bloch summation over all magnon wave vectors shows that remanence is slightly enhanced, because long-wavelength excitations are suppressed. However, a reverse magnetic field enhances the effect of thermal excitations and causes a small reduction of the coercivity. To describe such effects, we advocate micromagnetic calculations where finite-temperature fluctuations are treated as small corrections to the traditional approach, as contrasted to full-scale Monte Carlo simulations.

  4. Nonlinear inversion for arbitrarily-oriented anisotropic models II: Inversion techniques

    NASA Astrophysics Data System (ADS)

    Bremner, P. M.; Panning, M. P.

    2011-12-01

    We present output models from inversion of a synthetic surface wave dataset. We implement new 3-D finite-frequency kernels, based on the Born approximation, to invert for upper mantle structure beneath western North America. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests were performed to achieve a robust inversion scheme. Four synthetic input models were created, to include: isotropic, constant strength anisotropic, variable strength anisotropic, and both anisotropic and isotropic together. The reference model was a simplified version of PREM (dubbed PREM LIGHT) in which the crust and 220 km discontinuity have been removed. Output models from inversions of calculated synthetic data are compared against these input models to test for accurate reproduction of input model features, and the resolution of those features. The object of this phase of the study was to determine appropriate nonlinear inversion schemes that adequately recover the input models. The synthetic dataset consists of collected seismic waveforms of 126 earthquake mechanisms, of magnitude 6-7 from Dec 2006 to Feb 2009, from the IRIS database. Events were selected to correlate with USArray deployments, and to have as complete an azimuthal coverage as possible. The events occurred within a circular region of radius 150o centered about 44o lat, -110o lon (an arbitrary location within USArray coverage). Synthetic data were calculated utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 450 km depth, coupled to a spherically symmetric inner sphere. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π -prolate spheroidal wave function eigentapers (Slepian tapers) reduce noise biasing, and can provide error estimates in phase delay measurements. This study is a

  5. Modeling the anisotropic shock response of single-crystal RDX

    NASA Astrophysics Data System (ADS)

    Luscher, Darby

    Explosives initiate under impacts whose energy, if distributed homogeneously throughout the material, translates to temperature increases that are insufficient to drive the rapid chemistry observed. Heterogeneous thermomechanical interactions at the meso-scale (i.e. between single-crystal and macroscale) leads to the formation of localized hot spots. Direct numerical simulations of mesoscale response can contribute to our understanding of hot spots if they include the relevant deformation mechanisms that are essential to the nonlinear thermomechanical response of explosive molecular crystals. We have developed a single-crystal model for the finite deformation thermomechanical response of cyclotrimethylene trinitramine (RDX). Because of the low symmetry of RDX, a complete description of nonlinear thermoelasticity requires a careful decomposition of free energy into components that represent the pressure-volume-temperature (PVT) response and the coupling between isochoric deformation and both deviatoric and hydrostatic stresses. An equation-of-state (EOS) based on Debye theory that defines the PVT response was constructed using experimental data and density functional theory calculations. This EOS replicates the equilibrium states of phase transformation from alpha to gamma polymorphs observed in static high-pressure experiments. Lattice thermoelastic parameters defining the coupled isochoric free energy were obtained from molecular dynamics calculations and previous experimental data. Anisotropic crystal plasticity is modeled using Orowan's expression relating slip rate to dislocation density and velocity. Details of the theory will be presented followed by discussion of simulations of flyer plate impact experiments, including recent experiments diagnosed with in situ X-ray diffraction at the Advanced Photon Source. Impact conditions explored within the experimental effort have spanned shock pressures ranging from 1-10 GPa for several crystallographic orientations

  6. Full-surface deformation measurement of anisotropic tissues under indentation.

    PubMed

    Genovese, Katia; Montes, Areli; Martínez, Amalia; Evans, Sam L

    2015-05-01

    Inverse finite element-based analysis of soft biological tissues is an important tool to investigate their complex mechanical behavior and to develop physical models for medical simulations. Although there have recently been advances in dealing with the computational complexities of modeling biological materials, the collection of a sufficiently dense set of experimental data to properly capture their typically regionally varying properties still remains a critical issue. The aim of this work was to develop and test an optical system that combines 2D-Digital Image Correlation (DIC) and a novel Fringe Projection method with radial sensitivity (RFP) to test soft biological tissues under in vitro indentation. This system has the distinctive capability of using a single camera to retrieve the shape and 3D deformation of the whole upper surface of the indented sample without any blind measurement areas (with exception of the area under the indenter), with nominal depth and in-plane resolution of 0.05 mm and 0.004 mm, respectively. To test and illustrate the capabilities of the developed DIC/RFP system, the in vitro response to indentation of a homogeneous and isotropic latex foam is presented against the response of a slab of porcine ventricular myocardium, a highly in-homogeneous and anisotropic tissue. Our results illustrate the enhanced capabilities of the developed method to capture asymmetry in deformation with respect to standard indentation tests. This feature, together with the possibility of miniaturizing the system into a hand-held probe, makes this method potentially extendable to in vivo settings, alone or in combination with ultrasound measurements.

  7. Two Spin Liquid phases in the anisotropic triangular Heisenberg model

    NASA Astrophysics Data System (ADS)

    Sorella, Sandro

    2005-03-01

    Recently there have been rather clean experimental realizations of the quantum spin 1/2 Heisenberg Hamiltonian on a 2D triangular lattice geometry in systems like Cs2Cu Cl4 and organic compounds like k-(ET)2Cu2(CN)3. These materials are nearly two dimensional and are characterized by an anisotropic antiferromagnetic superexchange. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to non conventional spin liquid phases. In order to understand these interesting phenomena we have studied, by Quantum Monte Carlo methods, the triangular lattice Heisenberg model as a function of the strength of this anisotropy, represented by the ratio r between the intra-chain nearest neighbor coupling J' and the inter-chain one J. We have found evidence of two spin liquid regions, well represented by projected BCS wave functions[1,2] of the type proposed by P. W. Anderson at the early stages of High temperature superconductivity [3]. The first spin liquid phase is stable for small values of the coupling r 0.6 and appears gapless and fractionalized, whereas the second one is a more conventional spin liquid, very similar to the one realized in the quantum dimer model in the triangular lattice[4]. It is characterized by a spin gap and a finite correlation length, and appears energetically favored in the region 0.6 r 0.9. The various phases are in good agreement with the experimental findings and supports the existence of spin liquid phases in 2D quantum spin-half systems. %%%%%%%%%%%%%%%%%% 1cm *[1] L. Capriotti F. Becca A. Parola and S. Sorella , Phys. Rev. Letters 87, 097201 (2001). *[2] S. Yunoki and S. Sorella Phys. Rev. Letters 92, 15003 (2004). *[3] P. W. Anderson, Science 235, 1186 (1987). *[4] P. Fendley, R. Moessner, and S. L. Sondhi Phys. Rev. B 66, 214513 (2002).

  8. Building an anisotropic meniscus with zonal variations.

    PubMed

    Higashioka, Michael M; Chen, Justin A; Hu, Jerry C; Athanasiou, Kyriacos A

    2014-01-01

    Toward addressing the difficult problems of knee meniscus regeneration, a self-assembling process has been used to re-create the native morphology and matrix properties. A significant problem in such attempts is the recapitulation of the distinct zones of the meniscus, the inner, more cartilaginous and the outer, more fibrocartilaginous zones. In this study, an anisotropic and zonally variant meniscus was produced by self-assembly of the inner meniscus (100% chondrocytes) followed by cell seeding the outer meniscus (coculture of chondrocytes and meniscus cells). After 4 weeks in culture, the engineered, inner meniscus exhibited a 42% increase in both instantaneous and relaxation moduli and a 62% increase in GAG/DW, as compared to the outer meniscus. In contrast, the circumferential tensile modulus and collagen/DW of the outer zone was 101% and 129% higher, respectively, than the values measured for the inner zone. Furthermore, there was no difference in the radial tensile modulus between the control and zonal engineered menisci, suggesting that the inner and outer zones of the engineered zonal menisci successfully integrated. These data demonstrate that not only can biomechanical and biochemical properties be engineered to differ by the zone, but they can also recapitulate the anisotropic behavior of the knee meniscus.

  9. Dynamic Smagorinsky model on anisotropic grids

    NASA Technical Reports Server (NTRS)

    Scotti, A.; Meneveau, C.; Fatica, M.

    1996-01-01

    Large Eddy Simulation (LES) of complex-geometry flows often involves highly anisotropic meshes. To examine the performance of the dynamic Smagorinsky model in a controlled fashion on such grids, simulations of forced isotropic turbulence are performed using highly anisotropic discretizations. The resulting model coefficients are compared with a theoretical prediction (Scotti et al., 1993). Two extreme cases are considered: pancake-like grids, for which two directions are poorly resolved compared to the third, and pencil-like grids, where one direction is poorly resolved when compared to the other two. For pancake-like grids the dynamic model yields the results expected from the theory (increasing coefficient with increasing aspect ratio), whereas for pencil-like grids the dynamic model does not agree with the theoretical prediction (with detrimental effects only on smallest resolved scales). A possible explanation of the departure is attempted, and it is shown that the problem may be circumvented by using an isotropic test-filter at larger scales. Overall, all models considered give good large-scale results, confirming the general robustness of the dynamic and eddy-viscosity models. But in all cases, the predictions were poor for scales smaller than that of the worst resolved direction.

  10. New formulation of leading order anisotropic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Tinti, Leonardo

    2015-05-01

    Anisotropic hydrodynamics is a reorganization of the relativistic hydrodynamics expansion, with the leading order already containing substantial momentum-space anisotropies. The latter are a cause of concern in the traditional viscous hydrodynamics, since large momentum anisotropies generated in ultrarelativistic heavy-ion collisions are not consistent with the hypothesis of small deviations from an isotropic background, i.e., from the local equilibrium distribution. We discuss the leading order of the expansion, presenting a new formulation for the (1+1)- dimensional case, namely, for the longitudinally boost invariant and cylindrically symmetric flow. This new approach is consistent with the well established framework of Israel and Stewart in the close to equilibrium limit (where we expect viscous hydrodynamics to work well). If we consider the (0+1)-dimensional case, that is, transversally homogeneous and longitudinally boost invariant flow, the new form of anisotropic hydrodynamics leads to better agreement with known solutions of the Boltzmann equation than the previous formulations, especially when we consider massive particles.

  11. Radial stability of anisotropic strange quark stars

    NASA Astrophysics Data System (ADS)

    Arbañil, José D. V.; Malheiro, M.

    2016-11-01

    The influence of the anisotropy in the equilibrium and stability of strange stars is investigated through the numerical solution of the hydrostatic equilibrium equation and the radial oscillation equation, both modified from their original version to include this effect. The strange matter inside the quark stars is described by the MIT bag model equation of state. For the anisotropy two different kinds of local anisotropic σ = pt-pr are considered, where pt and pr are respectively the tangential and the radial pressure: one that is null at the star's surface defined by pr(R) = 0, and one that is nonnull at the surface, namely, σs = 0 and σs ≠ 0. In the case σs = 0, the maximum mass value and the zero frequency of oscillation are found at the same central energy density, indicating that the maximum mass marks the onset of the instability. For the case σs ≠ 0, we show that the maximum mass point and the zero frequency of oscillation coincide in the same central energy density value only in a sequence of equilibrium configurations with the same value of σs. Thus, the stability star regions are determined always by the condition dM/dρc > 0 only when the tangential pressure is maintained fixed at the star surface's pt(R). These results are also quite important to analyze the stability of other anisotropic compact objects such as neutron stars, boson stars and gravastars.

  12. Gravothermal catastrophe in anisotropic spherical systems

    NASA Astrophysics Data System (ADS)

    Magliocchetti, Manuela; Pucacco, Giuseppe; Vesperini, Enrico

    1998-11-01

    In this paper we investigate the gravothermal instability of spherical stellar systems endowed with a radially anisotropic velocity distribution. We focus our attention on the effects of anisotropy on the conditions for the onset of instability and in particular we study the dependence of the spatial structure of critical models on the amount of anisotropy present in a system. The investigation has been carried out by the method of linear series which has already been used in the past to study the gravothermal instability of isotropic systems._ We consider models described by King, Wilson and Woolley-Dickens distribution functions. In the case of King and Woolley-Dickens models, our results show that, for quite a wide range of the amount of anisotropy in the system, the critical value of the concentration of the system (defined as the ratio of the tidal to the King core radius of the system) is approximately constant and equal to the corresponding value for isotropic systems. Only for very anisotropic systems does the critical value of the concentration start to change and it decreases significantly as the anisotropy increases and penetrates the inner parts of the system. For Wilson models the decrease of the concentration of critical models is preceded by an intermediate regime in which critical concentration increases, reaches a maximum and then starts to decrease. The critical value of the central potential always decreases as the anisotropy increases.

  13. Anisotropic polyvinyl alcohol hydrogel for cardiovascular applications.

    PubMed

    Millon, L E; Mohammadi, H; Wan, W K

    2006-11-01

    Polyvinyl alcohol (PVA) is a hydrophilic polymer with various characteristics desired for biomedical applications and can be transformed into a solid hydrogel by physical crosslinking, using a low-temperature thermal cycling process. As with most polymeric materials, the mechanical properties of the resultant PVA are isotropic, as oppose to most soft tissues, which are anisotropic. The objective of this research is to develop a PVA-based hydrogel that not only mimics the nonlinear mechanical properties displayed by cardiovascular tissues, but also their anisotropic behavior. By applying a controlled strain to the PVA samples, while undergoing low-temperature thermal cycling, we were able to create oriented mechanical properties in PVA hydrogels. The oriented stress-strain properties of porcine aorta were matched simultaneously by a PVA hydrogel prepared (10% PVA, cycle 3, 75% initial strain). This novel technique allows the controlled introduction of anisotropy to PVA hydrogel, and gives a broad range of control of its mechanical properties, for specific medical device applications. (c) 2006 Wiley Periodicals, Inc.

  14. Sheet Metal Formability Analysis for Anisotropic Materials

    NASA Astrophysics Data System (ADS)

    Stoughton, Thomas B.; Yoon, Jeong Whan

    2004-06-01

    Sheet metal formability is conventionally assessed in a two dimensional plot of principal strains or stresses in comparison to a forming limit curve. This method implicitly assumes that the forming limit is isotropic in the plane of the sheet, an assumption that is intrinsically inconsistent with the use of material models that are anisotropic. Since the trend today is to utilize models with full anisotropy in order to more accurately capture the physics of material behavior, the issue of anisotropy of forming limits must also be addressed. The challenge is that the forming limit is no longer defined by a curve but requires the definition of a surface in strain or stress space, and therefore it is no longer appropriate to view these limits with the convenience of the conventional two dimensional diagrams. Furthermore, recent developments in the characterization of sheet forming limits under nonproportional loading suggest that is advantageous to view forming limit behavior in terms of stresses rather than strains, a view that is adopted in this paper. A solution to the challenge of assessing formability for an anisotropic material is proposed and illustrated using an analysis of the 2-Stage Forming Benchmark highlighted in the Numisheet '99 Conference.

  15. Anisotropic swelling behavior of the cornea.

    PubMed

    Matsuura, Toyoaki; Ikeda, Hitoe; Idota, Naokazu; Motokawa, Ryuhei; Hara, Yoshiaki; Annaka, Masahiko

    2009-12-24

    The phase equilibrium property and structural and dynamical properties of pig cornea were studied by macroscopic observation of swelling behavior, dynamic light scattering (DLS), and small-angle X-ray scattering (SAXS) under various conditions. It was found that the corneal gel collapses into a compact state isotropically or anisotropically depending on the external conditions. The corneal gel collapses uniformly into a compact state at a temperature above 55 degrees C because of the denaturation of collagen, whereas it collapses along an axis parallel to the optic axis with increasing NaCl concentration. Anisotropic deswelling was also observed during desiccation. SAXS measurements revealed that the periodicity of the collagen fiber of the cornea does not change even at higher NaCl concentration, which indicates that hydration and dehydration resulting from changes in salt concentration simply cause swelling and deswelling of the glycosaminoglycan (GAG), which is located between the regular two-dimensional lattices of collagen fibers, which obliges the change in thickness. From observations of the dynamics of light scattered by the corneal gel, intensity autocorrelation functions that revealed two independent diffusion coefficients were obtained. Divergent behavior in the measured total scattered light intensities and diffusion coefficients with varying temperature was observed. That is, a slowing of the dynamic modes accompanied by increased "static" scattered intensities was observed. This is indicative of the occurrence of a phase transition as a function of temperature.

  16. Anisotropic diffusion phantoms based on microcapillaries

    NASA Astrophysics Data System (ADS)

    Vellmer, Sebastian; Edelhoff, Daniel; Suter, Dieter; Maximov, Ivan I.

    2017-06-01

    Diffusion MRI is an efficient and widely used technique for the investigation of tissue structure and organisation in vivo. Multiple phenomenological and biophysical diffusion models are intensively exploited for the analysis of the diffusion experiments. However, the verification of the applied diffusion models remains challenging. In order to provide a ;gold standard; and to assess the accuracy of the derived parameters and the limitations of the diffusion models, anisotropic diffusion phantoms with well known architecture are demanded. In the present work we built four anisotropic diffusion phantoms consisting of hollow microcapillaries with very small inner diameters of 5, 10 and 20 μ m and outer diameters of 90 and 150 μ m. For testing the suitability of these phantoms, we performed diffusion measurements on all of them and evaluated the resulting data with a set of popular diffusion models, such as diffusion tensor and diffusion kurtosis imaging, a two compartment model with intra- and extra-capillary water spaces using bi-exponential fitting, and time-dependent diffusion coefficients in Mitra's limit. The perspectives and limitations of these diffusion phantoms are presented and discussed.

  17. Isobaric expansion coefficient and isothermal compressibility for a finite-size ideal Fermi gas system

    NASA Astrophysics Data System (ADS)

    Su, Guozhen; Chen, Liwei; Chen, Jincan

    2014-06-01

    Due to quantum size effects (QSEs), the isobaric thermal expansion coefficient and isothermal compressibility well defined for macroscopic systems are invalid for finite-size systems. The two parameters are redefined and calculated for a finite-size ideal Fermi gas confined in a rectangular container. It is found that the isobaric thermal expansion coefficient and isothermal compressibility are generally anisotropic, i.e., they are generally different in different directions. Moreover, it is found the thermal expansion coefficient may be negative in some directions under the condition that the pressures in all directions are kept constant.

  18. Finite element large-amplitude free and forced vibrations of rectangular thin composite plates

    NASA Technical Reports Server (NTRS)

    Chiang, C. K.; Mei, C.; Gray, C. E., Jr.

    1989-01-01

    A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.

  19. Asymptotic modelling of a thermopiezoelastic anisotropic smart plate

    NASA Astrophysics Data System (ADS)

    Long, Yufei

    Motivated by the requirement of modelling for space flexible reflectors as well as other applications of plate structures in engineering, a general anisotropic laminated thin plate model and a monoclinic Reissner-Mindlin plate model with thermal deformation, two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structure helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. For the zeroth-order approximation, the asymptotically correct expression of energy is derived into the form of energetic equation in classical laminated plate theory, which will be enough to predict the behavior of plate structures as thin as a space flexible reflector. A through-the-thickness strain field can be expressed in terms of material constants and two-dimensional membrane and bending strains, while the transverse normal and shear stresses are not predictable yet. In the first-order approximation, the warping functions are further disturbed into a high order and an asymptotically correct energy expression with derivatives of the two-dimensional strains is acquired. For the convenience of practical use, the expression is transformed into a Reissner-Mindlin form with optimization implemented to minimize the error. Transverse stresses and strains are recovered using the in-plane strain variables. Several numerical examples of different laminations and shapes are studied with the help of analytical solutions or shell elements in finite element codes. The constitutive relation is

  20. Anisotropic artificial substrates for microwave applications

    NASA Astrophysics Data System (ADS)

    Shahvarpour, Attieh

    The perfect electromagnetic conductor (PEMC) boundary is a novel fundamental electromagnetic concept. It is a generalized description of the electromagnetic boundary conditions including the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC) and due to its fundamental properties, it has the potential of enabling several electromagnetic applications. However, the PEMC boundaries concept had remained at the theoretical level and has not been practically realized. Therefore, motivated by the importance of this electromagnetic fundamental concept and its potential applications, the first contribution of this thesis is focused on the practical implementation of the PEMC boundaries by exploiting Faraday rotation principle and ground reflection in the ferrite materials which are intrinsically anisotropic. As a result, this thesis reports the first practical approach for the realization of PEMC boundaries. A generalized scattering matrix (GSM) is used for the analysis of the grounded-ferrite PEMC boundaries structure. As an application of the PEMC boundaries, a transverse electromagnetic (TEM) waveguide is experimentally demonstrated using grounded ferrite PMC (as particular case of the PEMC boundaries) side walls. Perfect electromagnetic conductor boundaries may find applications in various types of sensors, reflectors, polarization convertors and polarization-based radio frequency identifiers. Leaky-wave antennas perform as high directivity and frequency beam scanning antennas and as a result they enable applications in radar, point-to-point communications and MIMO systems. The second contribution of this thesis is introducing and analysing a novel broadband and highly directive two-dimensional leaky-wave antenna. This antenna operates differently in the lower and higher frequency ranges. Toward its lower frequencies, it allows full-space conical-beam scanning while at higher frequencies, it provides fixed-beam radiation (at a designable angle

  1. Holographic Wilson loops in anisotropic quark-gluon plasma.

    NASA Astrophysics Data System (ADS)

    Ageev, Dmitry

    2016-10-01

    The nonequilibrium properties of the anisotropic quark-gluon plasma are condidered from the holographic viewpoint. Lifshitz-like solution is considered as a holographic dual of anisotropic QGP. The black brane formation in such background is considered as a thermalization in dual theory. As a probe of thermalization we consider rectangular spatial Wilson loops with different orientation.

  2. Method for anisotropic etching in the manufacture of semiconductor devices

    DOEpatents

    Koontz, Steven L.; Cross, Jon B.

    1993-01-01

    Hydrocarbon polymer coatings used in microelectronic manufacturing processes are anisotropically etched by atomic oxygen beams (translational energies of 0.2-20 eV, preferably 1-10 eV). Etching with hyperthermal (kinetic energy>1 eV) oxygen atom species obtains highly anisotropic etching with sharp boundaries between etched and mask-protected areas.

  3. Anisotropic microporous supports impregnated with polymeric ion-exchange materials

    DOEpatents

    Friesen, Dwayne; Babcock, Walter C.; Tuttle, Mark

    1985-05-07

    Novel ion-exchange media are disclosed, the media comprising polymeric anisotropic microporous supports containing polymeric ion-exchange or ion-complexing materials. The supports are anisotropic, having small exterior pores and larger interior pores, and are preferably in the form of beads, fibers and sheets.

  4. Anisotropic microporous supports impregnated with polymeric ion-exchange materials

    DOEpatents

    Friesen, D.; Babcock, W.C.; Tuttle, M.

    1985-05-07

    Novel ion-exchange media are disclosed, the media comprising polymeric anisotropic microporous supports containing polymeric ion-exchange or ion-complexing materials. The supports are anisotropic, having small exterior pores and larger interior pores, and are preferably in the form of beads, fibers and sheets. 5 figs.

  5. Optical isotropy at terahertz frequencies using anisotropic metamaterials

    NASA Astrophysics Data System (ADS)

    Lee, In-Sung; Sohn, Ik-Bu; Kang, Chul; Kee, Chul-Sik; Yang, Jin-Kyu; Lee, Joong Wook

    2016-07-01

    We demonstrate optically isotropic filters in the terahertz (THz) frequency range using structurally anisotropic metamaterials. The proposed metamaterials with two-dimensional arrangements of anisotropic H-shaped apertures show polarization-independent transmission due to the combined effects of the dipole resonances of resonators and antennas. Our results may offer the potential for the design and realization of versatile THz devices and systems.

  6. Behavioral analysis of anisotropic diffusion in image processing.

    PubMed

    You, Y L; Xu, W; Tannenbaum, A; Kaveh, M

    1996-01-01

    In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator.

  7. Symmetric periodic solutions of the anisotropic Manev problem

    NASA Astrophysics Data System (ADS)

    Santoprete, Manuele

    2002-06-01

    We consider the Manev potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincaré continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.

  8. Method for anisotropic etching in the manufacture of semiconductor devices

    NASA Technical Reports Server (NTRS)

    Koontz, Steven L. (Inventor); Cross, Jon B. (Inventor)

    1993-01-01

    Hydrocarbon polymer coatings used in microelectronic manufacturing processes are anisotropically etched by hyperthermal atomic oxygen beams (translational energies of 0.2 to 20 eV, preferably 1 to 10 eV). Etching with hyperthermal oxygen atom species obtains highly anisotropic etching with sharp boundaries between etched and mask protected areas.

  9. Automatic finite element generators

    NASA Technical Reports Server (NTRS)

    Wang, P. S.

    1984-01-01

    The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.

  10. Anisotropic conductivity imaging with MREIT using equipotential projection algorithm.

    PubMed

    Değirmenci, Evren; Eyüboğlu, B Murat

    2007-12-21

    Magnetic resonance electrical impedance tomography (MREIT) combines magnetic flux or current density measurements obtained by magnetic resonance imaging (MRI) and surface potential measurements to reconstruct images of true conductivity with high spatial resolution. Most of the biological tissues have anisotropic conductivity; therefore, anisotropy should be taken into account in conductivity image reconstruction. Almost all of the MREIT reconstruction algorithms proposed to date assume isotropic conductivity distribution. In this study, a novel MREIT image reconstruction algorithm is proposed to image anisotropic conductivity. Relative anisotropic conductivity values are reconstructed iteratively, using only current density measurements without any potential measurement. In order to obtain true conductivity values, only either one potential or conductivity measurement is sufficient to determine a scaling factor. The proposed technique is evaluated on simulated data for isotropic and anisotropic conductivity distributions, with and without measurement noise. Simulation results show that the images of both anisotropic and isotropic conductivity distributions can be reconstructed successfully.

  11. Insights into Shallow Anisotropic Structure in the Forearc Hikurangi Subduction Zone, New Zealand via Splitting of Teleseisms

    NASA Astrophysics Data System (ADS)

    Karalliyadda, S.; Savage, M. K.

    2013-12-01

    subslab region and lithospheric shear beneath the upper-plate faulting. At crustal depths, there could be anisotropic contributions from fault structures and clay mineralization around them. To provide further constraints on the observed lateral variations, we will implement a finite-difference approach that enables us to verify whether the lateral variations in splitting parameters are due to discrepancies between anisotropic properties or the isotropic velocity variations of the different regimes in the subduction structure.

  12. Nonlinear, finite deformation, finite element analysis

    NASA Astrophysics Data System (ADS)

    Nguyen, Nhung; Waas, Anthony M.

    2016-06-01

    The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated

  13. Mixed models and reduction method for dynamic analysis of anisotropic shells

    NASA Technical Reports Server (NTRS)

    Noor, A. K.; Peters, J. M.

    1985-01-01

    A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

  14. Mixed models and reduction method for dynamic analysis of anisotropic shells

    NASA Technical Reports Server (NTRS)

    Noor, A. K.; Peters, J. M.

    1985-01-01

    A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

  15. Anisotropic heat diffusion on stochastic magnetic field in the Large Helical Device

    NASA Astrophysics Data System (ADS)

    Suzuki, Yasuhiro

    2016-10-01

    The magnetic topology is a key issue in fusion plasma researches. An example is the Resonant Magnetic Perturbation (RMP) to control the transport and MHD activities in tokamak and stellarator experiments. However, the physics how the RMP affects the transport and MHD is not clear. One reason is a role of the magnetic topology is unclear. That problem is connecting to the identification of the magnetic topology in the experiment. In the experiment, the finite temperature gradient is observed on the stochastic field where is stochastized by the theoretical prediction. In a classical theory, the electron temperature gradient should be zero on the stochastic magnetic field. We need to study the stochastic magnetic field can keep the finite temperature gradient or not. In this study, we study the anisotropic heat diffusion equation to simulate the heat transport on the stochastic magnetic field. Changing a ratio of κ∥ and κ⊥, the distribution of the temperature on the stochastic magnetic field is obtained. Hudson et al. pointed out the KAM surface is a barrier to keep the finite temperature. We simulate those results in realistic magnetic field of the Large Helical Device.

  16. Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system.

    PubMed

    Cai, Yangjian; Hu, Li

    2006-03-15

    By expanding the hard-aperture function into a finite sum of complex Gaussian functions, we derived an approximate analytical formula for a partially coherent twisted anisotropic Gaussian Schell-model (AGSM) beam propagating through an apertured paraxial general astigmatic (GA) optical system by use of a tensor method. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. Our formulas avoid time-consuming numerical integration and provide a convenient and effective way for studying the propagation and transformation of a partially coherent twisted AGSM beam through an apertured paraxial GA optical system.

  17. Inference for an Anisotropic Diffusion Model

    ERIC Educational Resources Information Center

    Eaves, David

    1976-01-01

    Vector sum of a white noise in an unknown hyperspace and an Ornstein-Uhlenbeck process in an unknown line is observed through sharp linear test functions over a finite time span. Parameters associated with white noise are determinable and index measure-equivalence classes in relevant sample space. Intraclass relative density provides a basis for…

  18. Routing of deep-subwavelength optical beams without reflection and diffraction using infinitely anisotropic metamaterials

    NASA Astrophysics Data System (ADS)

    Catrysse, Peter B.; Fan, Shanhui

    2015-03-01

    Media that are described by extreme electromagnetic parameters, such as very large/small permittivity/permeability, have generated significant fundamental and applied interest in recent years. Notable examples include epsilon-near-zero, ultra-low refractive-index, and ultra-high refractive-index materials. Many photonic structures, such as waveguides, lenses, and photonic band gap materials, benefit greatly from the large index contrast provided by such media. In this paper, I discuss our recent work on media with infinite anisotropy, i.e., infinite permittivity (permeability) in one direction and finite in the other directions. As an illustration of the unusual optical behaviors that result from infinite anisotropy, I describe efficient light transport in deep-subwavelength apertures filled with infinitely anisotropic media. I then point out some of the opportunities that exist for controlling light at the nano-scale using infinitely anisotropic media by themselves. First, I show that a single medium with infinite anisotropy enables diffraction-free propagation of deep-subwavelength beams. Next, I demonstrate interfaces between two infinitely anisotropic media that are impedancematched for complete deep-subwavelength beams and enable reflection-free routing with zero bend radius that is entirely free from diffraction effects even when deep-subwavelength information is encoded on the beams. These behaviors indicate an unprecedented possibility to use media with infinite anisotropy to manipulate beams with deepsubwavelength features, including complete images. To illustrate physical realizability, I demonstrate a metamaterial design using existing materials in a planar geometry, which can be implemented using well-established nanofabrication techniques. This approach provides a path to deep-subwavelength routing of information-carrying beams and far-field imaging unencumbered by diffraction and reflection.

  19. Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

    NASA Astrophysics Data System (ADS)

    Han, B.; Li, Y.

    2016-12-01

    We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

  20. A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

    NASA Astrophysics Data System (ADS)

    Carpio, Jaime; Prieto, Juan Luis; Vera, Marcos

    2016-02-01

    A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogen-air flame/vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.

  1. A quantum fidelity study of the anisotropic next-nearest-neighbour triangular lattice Heisenberg model.

    PubMed

    Thesberg, Mischa; Sørensen, Erik S

    2014-10-22

    Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.

  2. GVF-based anisotropic diffusion models.

    PubMed

    Yu, Hongchuan; Chua, Chin-Seng

    2006-06-01

    In this paper, the gradient vector flow fields are introduced in image restoration. Within the context of flow fields, the shock filter, mean curvature flow, and Perona-Malik equation are reformulated. Many advantages over the original models can be obtained; these include numerical stability, large capture range, and high-order derivative estimation. In addition, a fairing process is introduced in the anisotropic diffusion, which contains a fourth-order derivative and is reformulated as the intrinsic Laplacian of curvature under the level set framework. By applying this fairing process, the shape boundaries will become more apparent. In order to overcome numerical errors, the intrinsic Laplacian of curvature is computed from the gradient vector flow fields instead of the observed images.

  3. Adiabatic theory for anisotropic cold molecule collisions

    SciTech Connect

    Pawlak, Mariusz; Shagam, Yuval; Narevicius, Edvardas; Moiseyev, Nimrod

    2015-08-21

    We developed an adiabatic theory for cold anisotropic collisions between slow atoms and cold molecules. It enables us to investigate the importance of the couplings between the projection states of the rotational motion of the atom about the molecular axis of the diatom. We tested our theory using the recent results from the Penning ionization reaction experiment {sup 4}He(1s2s {sup 3}S) + HD(1s{sup 2}) → {sup 4}He(1s{sup 2}) + HD{sup +}(1s) + e{sup −} [Lavert-Ofir et al., Nat. Chem. 6, 332 (2014)] and demonstrated that the couplings have strong effect on positions of shape resonances. The theory we derived provides cross sections which are in a very good agreement with the experimental findings.

  4. Anisotropic criteria for the type of superconductivity

    SciTech Connect

    Kogan, Vladimir G; Prozorov, Ruslan

    2014-08-01

    The classical criterion for classification of superconductors as type I or type II based on the isotropic Ginzburg-Landau theory is generalized to arbitrary temperatures for materials with anisotropic Fermi surfaces and order parameters. We argue that the relevant quantity for this classification is the ratio of the upper and thermodynamic critical fields Hc2/Hc, rather than the traditional ratio of the penetration depth and the coherence length λ/ξ. Even in the isotropic case, Hc2/Hc coincides with 2√λ/ξ only at the critical temperature Tc and they differ as T decreases, the long-known fact. Anisotropies of Fermi surfaces and order parameters may amplify this difference and render false the criterion based on the value of κ=λ/ξ.

  5. Correlation energy of anisotropic quantum dots

    SciTech Connect

    Zhao Yan; Loos, Pierre-Francois; Gill, Peter M. W.

    2011-09-15

    We study the D-dimensional high-density correlation energy E{sub c} of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic and examine the behavior of E{sub c} as a function of the anisotropy {alpha}{sup -1}. In particular, we are interested in the limit where the anisotropy goes to infinity ({alpha}{yields}0) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of {alpha} from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model, in which a quantum dot is treated as a two-dimensional system, is inappropriate. Finally, we provide a simple function which reproduces the behavior of E{sub c} over the entire range of {alpha}.

  6. Model for the anisotropic reentry of albedo

    SciTech Connect

    Koenig, P.J.

    1981-02-01

    The trajectory-tracing technique was used to obtain the angles of incidence, and hence 'intensities,' of negatively charged 0.88-GV particles reentrant at Palestine, Texas. Splash albedo trajectories were traced from the conjugate point, and also from Palestine itself, for those trajectories that were unable to complete a full gyration before reentry into the shadow cone at Palestine. Both isotropic and anisotropic ejection configurations were used at these two locations. These simulations predict a north-south anisotropy (hence also a zenithal anisotropy) for reentrant albedo, with a dearth of trajectories incident from the south. The anisotropy is large enough to explain experimentally determined north-south anisotropies for lower-energy particles, as observed by other groups in the Northern Hemisphere. The results are in agreement with measurements and simulations previously obtained in the Southern Hemisphere.

  7. An Anisotropic Hardening Model for Springback Prediction

    SciTech Connect

    Zeng, Danielle; Xia, Z. Cedric

    2005-08-05

    As more Advanced High-Strength Steels (AHSS) are heavily used for automotive body structures and closures panels, accurate springback prediction for these components becomes more challenging because of their rapid hardening characteristics and ability to sustain even higher stresses. In this paper, a modified Mroz hardening model is proposed to capture realistic Bauschinger effect at reverse loading, such as when material passes through die radii or drawbead during sheet metal forming process. This model accounts for material anisotropic yield surface and nonlinear isotropic/kinematic hardening behavior. Material tension/compression test data are used to accurately represent Bauschinger effect. The effectiveness of the model is demonstrated by comparison of numerical and experimental springback results for a DP600 straight U-channel test.

  8. Highly Anisotropic Dirac Fermions in Square Graphynes.

    PubMed

    Zhang, L Z; Wang, Z F; Wang, Zhiming M; Du, S X; Gao, H-J; Liu, Feng

    2015-08-06

    We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.

  9. Anisotropic Absorption of Pure Spin Currents

    NASA Astrophysics Data System (ADS)

    Baker, A. A.; Figueroa, A. I.; Love, C. J.; Cavill, S. A.; Hesjedal, T.; van der Laan, G.

    2016-01-01

    Spin transfer in magnetic multilayers offers the possibility of ultrafast, low-power device operation. We report a study of spin pumping in spin valves, demonstrating that a strong anisotropy of spin pumping from the source layer can be induced by an angular dependence of the total Gilbert damping parameter, α , in the spin sink layer. Using lab- and synchrotron-based ferromagnetic resonance, we show that an in-plane variation of damping in a crystalline Co50 Fe50 layer leads to an anisotropic α in a polycrystalline Ni81 Fe19 layer. This anisotropy is suppressed above the spin diffusion length in Cr, which is found to be 8 nm, and is independent of static exchange coupling in the spin valve. These results offer a valuable insight into the transmission and absorption of spin currents, and a mechanism by which enhanced spin torques and angular control may be realized for next-generation spintronic devices.

  10. Particle Behavior at Anisotropically Curved Liquid Interfaces

    NASA Astrophysics Data System (ADS)

    McEnnis, Kathleen; Zeng, Chuan; Davidovitch, Benny; Dinsmore, Anthony; Russell, Thomas

    2011-03-01

    A particle bound to an anisotropically curved liquid interface, such as a cylinder or catenoid, cannot maintain a constant contact angle without deforming the interface. Theory suggests that the particles will experience a force that depends on the interfacial shape and migrate to minimize the total interfacial energy. To test these predictions, particles were deposited on top of liquid semi-cylinders of ionic liquid or melted polystyrene confined on chemically patterned surfaces. Particles were also deposited on liquid catenoid structures created by placing a melted polymer film under an electric field. The location of the particles on these structures was observed by optical, confocal, and scanning electron microscopy. The implications for the directed assembly of particles and stability of Pickering emulsions are also discussed.

  11. Disordered spherical bead packs are anisotropic

    NASA Astrophysics Data System (ADS)

    Schröder-Turk, G. E.; Mickel, W.; Schröter, M.; Delaney, G. W.; Saadatfar, M.; Senden, T. J.; Mecke, K.; Aste, T.

    2010-05-01

    Investigating how tightly objects pack space is a long-standing problem, with relevance for many disciplines from discrete mathematics to the theory of glasses. Here we report on the fundamental yet so far overlooked geometric property that disordered mono-disperse spherical bead packs have significant local structural anisotropy manifest in the shape of the free space associated with each bead. Jammed disordered packings from several types of experiments and simulations reveal very similar values of the cell anisotropy, showing a linear decrease with packing fraction. Strong deviations from this trend are observed for unjammed configurations and for partially crystalline packings above 64%. These findings suggest an inherent geometrical reason why, in disordered packings, anisotropic shapes can fill space more efficiently than spheres, and have implications for packing effects in non-spherical liquid crystals, foams and structural glasses.

  12. Translation correlations in anisotropically scattering media

    NASA Astrophysics Data System (ADS)

    Judkewitz, Benjamin; Horstmeyer, Roarke; Vellekoop, Ivo M.; Papadopoulos, Ioannis N.; Yang, Changhuei

    2015-08-01

    Controlling light propagation across scattering media by wavefront shaping holds great promise for a wide range of communications and imaging applications. But, finding the right shape for the wavefront is a challenge when the mapping between input and output scattered wavefronts (that is, the transmission matrix) is not known. Correlations in transmission matrices, especially the so-called memory effect, have been exploited to address this limitation. However, the traditional memory effect applies to thin scattering layers at a distance from the target, which precludes its use within thick scattering media, such as fog and biological tissue. Here, we theoretically predict and experimentally verify new transmission matrix correlations within thick anisotropically scattering media, with important implications for biomedical imaging and adaptive optics.

  13. Anisotropic star on pseudo-spheroidal spacetime

    NASA Astrophysics Data System (ADS)

    Ratanpal, B. S.; Thomas, V. O.; Pandya, D. M.

    2016-02-01

    A new class of exact solutions of Einstein's field equations representing anisotropic distribution of matter on pseudo-spheroidal spacetime is obtained. The parameters appearing in the model are restricted through physical requirements of the model. It is found that the models given in the present work is compatible with observational data of a wide variety of compact objects like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4, Cen X-3. A particular model of pulsar PSR J1614-2230 is studied in detail and found that it satisfies all physical requirements needed for physically acceptable model.

  14. Far field expansion for anisotropic wave equations

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.; Hagstrom, Thomas

    1989-01-01

    A necessary ingredient for the numerical simulation of many time dependent phenomena in acoustics and aerodynamics is the imposition of accurate radiation conditions at artificial boundaries. The asymptotic analysis of propagating waves provides a rational approach to the development of such conditions. A far field asymptotic expansion of solutions of anisotropic wave equations is derived. This generalizes the well known Friedlander expansion for the standard wave operator. The expansion is used to derive a hierarchy of radiation conditions of increasing accuracy. Two numerical experiments are given to illustrate the utility of this approach. The first application is the study of unsteady vortical disturbances impinging on a flat plate; the second is the simulation of inviscid flow past an impulsively started cylinder.

  15. Anisotropic Particle Acceleration in Relativistic Shear Layers

    NASA Astrophysics Data System (ADS)

    Boettcher, Markus; Liang, Edison P.; Fu, Wen

    2017-08-01

    We present results of Particle in Cell (PIC) simulations of relativistic shear layers as relevant to the relativistic jets of acive galactic nuclei and gamma-ray bursts. We study the self-generation of electro-magnetic fields and particle acceleration for various different plasma compositions (electron-ion vs. electron-positron pair vs. hybrid). Special emphasis is placed on the angular distribution of accelerated particles. We find that electron-ion shear layers lead to highly anisotropic particle distributions in the frame of the fast-moving inner spine. The beaming pattern of the highest-energy particles is much narrower than the characteristic beaming angle of 1/Gamma resulting from relativistic aberration of a co-moving isotropic distribution. This may pose a possible solution to the Lorentz-Factor crisis in blazars and explain very hard X-ray / soft gamma-ray spectra of some gamma-ray bursts.

  16. Anisotropic compact stars in Karmarkar spacetime

    NASA Astrophysics Data System (ADS)

    Newton Singh, Ksh.; Pant, Neeraj; Govender, M.

    2017-01-01

    We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of Class One reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the grr metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We use this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348+0432, PSR B0943+10 and XTE J1739-285.

  17. Observable effects of anisotropic bubble nucleation

    SciTech Connect

    Blanco-Pillado, Jose J.; Salem, Michael P. E-mail: salem@cosmos.phy.tufts.edu

    2010-07-01

    Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension — the modulus of which tunnels out of a metastable minimum during bubble nucleation — which subsequently grows to become one of our three large spatial dimensions. Then the reduced symmetry of the background is equivalent to anisotropic initial conditions in our bubble universe. We compute the inflationary spectrum in such a scenario and, as a first step toward understanding the effects of anisotropy, project it onto spherical harmonics. The resulting spectrum exhibits anomalous multipole correlations, their relative amplitude set by the present curvature parameter, which appear to extend to arbitrarily large multipole moments. This raises the possibility of future detection, if slow-roll inflation does not last too long within our bubble. A full understanding of the observational signal must account for the effects of background anisotropy on photon free streaming, and is left to future work.

  18. Turbulent Output-Based Anisotropic Adaptation

    NASA Technical Reports Server (NTRS)

    Park, Michael A.; Carlson, Jan-Renee

    2010-01-01

    Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10(exp 7)) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori.

  19. Anisotropic Shock Propagation in Single Crystals

    SciTech Connect

    Eggert, J; Hicks, D; Celliers, P; Bradley, D; Cox, J; Unites, W; Collins, G; McWilliams, R; Jeanloz, R; Bruygoo, S; Loubeyre, P

    2005-05-26

    Most single-crystal shock experiments have been performed in high-symmetry directions while the nature of shock propagation in low-symmetry directions remains relatively unstudied. It is well known that small-amplitude, linear acoustic waves propagating in low-symmetry directions can focus and/or form caustics (Wolfe, 1995). In this report we provide evidence for similar focusing behavior in nonlinear (shock) waves propagating in single crystals of silicon and diamond. Using intense lasers, we have driven non-planar (divergent geometry) shock waves through single-crystals of silicon or diamond and into an isotropic backing plate. On recovery of the backing plates we observe a depression showing evidence of anisotropic plastic strain with well-defined crystallographic registration. We observe 4-, 2-, and 3-fold symmetric impressions for [100], [110], and [111] oriented crystals respectively.

  20. Effects of anisotropic heat conduction on solidification

    NASA Technical Reports Server (NTRS)

    Weaver, J. A.; Viskanta, R.

    1989-01-01

    Two-dimensional solidification influenced by anisotropic heat conduction has been considered. The interfacial energy balance was derived to account for the heat transfer in one direction (x or y) depending on the temperature gradient in both the x and y directions. A parametric study was made to determine the effects of the Stefan number, aspect ratio, initial superheat, and thermal conductivity ratios on the solidification rate. Because of the imposed boundary conditions, the interface became skewed and sometimes was not a straight line between the interface position at the upper and lower adiabatic walls (spatially nonlinear along the height). This skewness depends on the thermal conductivity ratio k(yy)/k(yx). The nonlinearity of the interface is influenced by the solidification rate, aspect ratio, and k(yy/k(yx).