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
Finite-volume scheme for anisotropic diffusion
NASA Astrophysics Data System (ADS)
van Es, Bram; Koren, Barry; de Blank, Hugo J.
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.
Formation of pyramid elements for hexahedra to tetrahedra transitions
OWEN,STEVEN J.; SAIGAL,SUNIL
2000-02-24
New algorithms are proposed for the modification of a mixed hexahedra-tetrahedra element mesh to maintain compatibility by the insertion of pyramid elements. Several methods for generation of the pyramids are presented involving local tetrahedral transformations and/or node insertion near the hex/tet interface. Local smoothing and topological operations improve the quality of the transition region. Results show superior performance of the resulting elements in a commercial finite element code over non-conforming interface conditions.
Anisotropic Hydraulic Permeability Under Finite Deformation
Ateshian, Gerard A.; Weiss, Jeffrey A.
2011-01-01
The structural organization of biological tissues and cells often produces anisotropic transport properties. These tissues may also undergo large deformations under normal function, potentially inducing further anisotropy. A general framework for formulating constitutive relations for anisotropic transport properties under finite deformation is lacking in the literature. This study presents an approach based on representation theorems for symmetric tensor-valued functions and provides conditions to enforce positive semi-definiteness of the permeability or diffusivity tensor. Formulations are presented which describe materials that are orthotropic, transversely isotropic, or isotropic in the reference state, and where large strains induce greater anisotropy. Strain-induced anisotropy of the permeability of a solid-fluid mixture is illustrated for finite torsion of a cylinder subjected to axial permeation. It is shown that, in general, torsion can produce a helical flow pattern, rather than the rectilinear pattern observed when adopting a more specialized, unconditionally isotropic spatial permeability tensor commonly used in biomechanics. The general formulation presented in this study can produce both affine and non-affine reorientation of the preferred directions of material symmetry with strain, depending on the choice of material functions. This study addresses a need in the biomechanics literature by providing guidelines and formulations for anisotropic strain-dependent transport properties in porous-deformable media undergoing large deformations. PMID:21034145
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.
Finite-difference schemes for anisotropic diffusion
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.
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.
Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements
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
Finite-element implementation of reverse-time migration for anisotropic media
NASA Astrophysics Data System (ADS)
Zhang, Meigen; Li, Xiaofan; Wang, Miaoyue
2004-06-01
Reverse-time migration for post-stack seismic data in anisotropic media is implemented using the finite-element method. As an accurate digital method, the finite-element method is flexible for dealing with complicated geological structures, inner and man-made boundaries despite its intensive computation. Applying it in reverse-time migration may produce accurate images for anisotropic media. To eliminate man-made boundary reflections, the absorbing boundary condition for anisotropic elastic waves is also studied. An efficient and stable absorbing boundary scheme is presented combining a discrete transparent boundary condition with an attenuation boundary condition.
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.
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.
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.
Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers
NASA Astrophysics Data System (ADS)
Kiran, Ravi; Khandelwal, Kapil
2015-01-01
The main aim of this paper is to automate the implementation of finite strain anisotropic hyperelastic models into a general finite element framework. The automation presented in this paper enables the end-user to implement a hyperelastic model by programming its Helmholtz free energy function alone. The automation is achieved by employing hyper-dual number system to evaluate analytical quality derivatives. New perturbation techniques are introduced and are employed to extend the hyper-dual numbers system to evaluate tensor derivatives. The capability of the proposed automation scheme is demonstrated by implementing five finite strain anisotropic hyperelastic models. The merits and demerits of the proposed automation scheme are compared to an automation scheme based on the central difference method.
NASA Astrophysics Data System (ADS)
Latorre, Marcos; Montáns, Francisco Javier
2015-09-01
In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored energy is composed of distinct anisotropic equilibrated and non-equilibrated parts. The nonequilibrated strains are obtained from the multiplicative decomposition of the deformation gradient. The procedure can be considered as an extension of the Reese and Govindjee framework to anisotropic materials and reduces to such formulation for isotropic materials. The stress-point algorithmic implementation is based on an elastic-predictor viscous-corrector algorithm similar to that employed in plasticity. The consistent tangent moduli for the general anisotropic case are also derived. Numerical examples explain the procedure to obtain the material parameters, show the quadratic convergence of the algorithm and usefulness in multiaxial loading. One example also highlights the importance of prescribing a complete set of stress-strain curves in orthotropic materials.
Onset of convection in an anisotropic porous layer of finite lateral extent
Mahidjiba, A.; Robillard, L.; Vasseur, P.; Mamou, M.
2000-04-01
Despite the fact that the porous materials are anisotropic in several applications, natural convection in such media has received relatively little attention. Anisotropy is generally a consequence of asymmetric geometry of the grain or fibers or of a preferential orientation. Such media are in fact often encountered in numerous systems in industry and nature. Examples include fibrous materials, geological formations, oil extraction, some biological materials, etc. A linear stability analysis is performed to study the onset of convection in a horizontal saturated porous layer of finite aspect ratio and anisotropic in permeability. The critical Rayleigh number is established as a function of the permeability ratio, the inclination angle of the principal axes and the enclosure aspect ratio. A linear stability analysis is conducted through a numerical procedure. Also, for the weak finite amplitude convection, results are obtained by solving numerically the full governing equations.
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
Zhao, A P; Cvetkovic, S R
1994-08-20
An efficient, accurate, and automated vectorial finite-element software package (named WAVEGIDE), which is implemented within a PDE/Protran problem-solving environment, has been extended to general multilayer anisotropic waveguides. With our system, through an interactive question-and-answer session, the problem can be simply defined with high-level PDE/Protran commands. The problem can then be solved easily and quickly by the main processor within this intelligent environment. In particular, in our system the eigenvalue of waveguide problems may be either a propagation constant (β) or an operated light frequency (F). Furthermore, the cutoff frequencies of propagation modes in waveguides can be calculated. As an application of this approach, numerical results for both scalar and hybrid modes in multilayer anisotropic waveguides are presented and are also compared with results obtained with the domain-integral method. These results clearly illustrate the unique flexibility, accuracy, and the ease of use f the WAVEGIDE program. PMID:20935964
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.
NASA Astrophysics Data System (ADS)
Yan, Bo; Li, Yuguo; Liu, Ying
2016-07-01
In this paper, we present an adaptive finite element (FE) algorithm for direct current (DC) resistivity modeling in 2-D generally anisotropic conductivity structures. Our algorithm is implemented on an unstructured triangular mesh that readily accommodates complex structures such as topography and dipping layers and so on. We implement a self-adaptive, goal-oriented grid refinement algorithm in which the finite element analysis is performed on a sequence of refined grids. The grid refinement process is guided by an a posteriori error estimator. The problem is formulated in terms of total potentials where mixed boundary conditions are incorporated. This type of boundary condition is superior to the Dirichlet type of conditions and improves numerical accuracy considerably according to model calculations. We have verified the adaptive finite element algorithm using a two-layered earth with azimuthal anisotropy. The FE algorithm with incorporation of mixed boundary conditions achieves high accuracy. The relative error between the numerical and analytical solutions is less than 1% except in the vicinity of the current source location, where the relative error is up to 2.4%. A 2-D anisotropic model is used to demonstrate the effects of anisotropy upon the apparent resistivity in DC soundings.
Zharnikov, T V; Syresin, D E
2015-06-01
In this letter repulsion of phase-velocity dispersion curves of quasidipole eigenmodes of waveguides with non-circular cross section in non-axisymmetric anisotropic medium is studied by the semi-analytical finite element technique. Borehole waveguide is used as an example. The modeling helps in clarifying the nature of this phenomenon, which is accompanied by the rotation of the orientation of two quasidipole modes with frequency and by the exchange of their behavior at near-crossover point. The dispersion curves cross only in the presence of exact symmetry. Such a scenario is the alternative to the stress-induced anisotropy crossing of dispersion curves. PMID:26093446
Kao, Philip H; Lammers, Steven R; Hunter, Kendall; Stenmark, Kurt R; Shandas, Robin; Qi, H Jerry
2010-04-01
Many biological materials are composites composed of a soft matrix reinforced with stiffer fibers. These stiffer fibers may have a tortuous shape and wind through the soft matrix. At small material deformation, these fibers deform in a bending mode and contribute little to the material stiffness; at large material deformation, these fibers deform in a stretching mode and induce a stiffening effect in the material behavior. The transition from bending mode deformation to stretching mode deformation yields a characteristic J-shape stress-strain curve. In addition, the spatial distribution of these fibers may render the composite an anisotropic behavior. In this paper, we present an anisotropic finite-deformation hyperelastic constitutive model for such materials. Here, the matrix is modeled as an isotropic neo-Hookean material. "The behaviors of single tortuous fiber are represented by a crimped fiber model". The anisotropic behavior is introduced by a structure tensor representing the effective orientation distribution of crimped fibers. Parametric studies show the effect of fiber tortuosity and fiber orientation distribution on the overall stress-strain behaviors of the materials. PMID:21822502
Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM).
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. PMID:23455165
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.
Three-dimensional DC anisotropic resistivity modelling using finite elements on unstructured grids
NASA Astrophysics Data System (ADS)
Wang, Wei; Wu, Xiaoping; Spitzer, Klaus
2013-05-01
We present a newly developed finite element program for direct current resistivity modelling, which can handle arbitrary 3-D electric anisotropy. For this purpose, it is of particular importance to construct appropriate grids because artificial anisotropy can be introduced through preferential directions associated with regular grid structures. Therefore, results from different kinds of grids (structured hexahedral, structured tetrahedral and unstructured tetrahedral) are checked for symmetry. After a series of comparisons, we conclude that unstructured tetrahedral grids generally perform best. In addition, this grid type allows for local refinement, which greatly reduces the number of nodes and, consequently, lowers the computational costs significantly. A singularity removal technique is applied, which improves the accuracy considerably. The resulting system of linear equations is solved by a conjugate gradient method with a symmetric successive overrelaxation pre-conditioner. Comparisons with analytical solutions prove the code to be highly accurate for both isotropic and anisotropic models. More complex models are investigated to analyse the response of anisotropic structures, for example, in form of the P2 tensor invariant. Finally, we apply the code to a hot dry rock scenario and show that anisotropy reveals significant information on the hydraulically induced fracture system.
Abbasi, Mostafa; Barakat, Mohammed S; Vahidkhah, Koohyar; Azadani, Ali N
2016-09-01
Computational modeling has an important role in design and assessment of medical devices. In computational simulations, considering accurate constitutive models is of the utmost importance to capture mechanical response of soft tissue and biomedical materials under physiological loading conditions. Lack of comprehensive three-dimensional constitutive models for soft tissue limits the effectiveness of computational modeling in research and development of medical devices. The aim of this study was to use inverse finite element (FE) analysis to determine three-dimensional mechanical properties of bovine pericardial leaflets of a surgical bioprosthesis under dynamic loading condition. Using inverse parameter estimation, 3D anisotropic Fung model parameters were estimated for the leaflets. The FE simulations were validated using experimental in-vitro measurements, and the impact of different constitutive material models was investigated on leaflet stress distribution. The results of this study showed that the anisotropic Fung model accurately simulated the leaflet deformation and coaptation during valve opening and closing. During systole, the peak stress reached to 3.17MPa at the leaflet boundary while during diastole high stress regions were primarily observed in the commissures with the peak stress of 1.17MPa. In addition, the Rayleigh damping coefficient that was introduced to FE simulations to simulate viscous damping effects of surrounding fluid was determined. PMID:27173827
Finite-element analysis of vibration and flutter of cantilever anisotropic plates
NASA Technical Reports Server (NTRS)
Rossettos, J. N.; Tong, P.
1974-01-01
The hybrid stress finite element method is used to study the effects of filament angle and orthotropicity parameter on the vibration and flutter characteristics of cantilevered anisotropic plates. The results indicate a generally strong lack of monotonic dependence on filament angle. Also, the natural frequency in certain cases involving the first few modes, can become relatively insensitive to both filament angle and orthotropicity parameter for a range of filament angle beyond 70 deg. Values of critical dynamic pressure are obtained by a modal approach, in which the mode shapes are obtained by the hybrid stress method. Convergence of the modal method is rather rapid for the configurations analyzed, and a comparison of the method with an exact solution for the case of an isotropic simply supported plate shows that use of six modes gives excellent agreement.
AnisWave2D: User's Guide to the 2d Anisotropic Finite-DifferenceCode
Toomey, Aoife
2005-01-06
This document describes a parallel finite-difference code for modeling wave propagation in 2D, fully anisotropic materials. The code utilizes a mesh refinement scheme to improve computational efficiency. Mesh refinement allows the grid spacing to be tailored to the velocity model, so that fine grid spacing can be used in low velocity zones where the seismic wavelength is short, and coarse grid spacing can be used in zones with higher material velocities. Over-sampling of the seismic wavefield in high velocity zones is therefore avoided. The code has been implemented to run in parallel over multiple processors and allows large-scale models and models with large velocity contrasts to be simulated with ease.
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.
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.
AC losses in a finite Z stack using an anisotropic homogeneous-medium approximation
NASA Astrophysics Data System (ADS)
Clem, John R.; Claassen, J. H.; Mawatari, Yasunori
2007-12-01
A finite stack of thin superconducting tapes, all carrying a fixed current I, can be approximated by an anisotropic superconducting bar with critical current density Jc = Ic/2aD, where Ic is the critical current of each tape, 2a is the tape width, and D is the tape-to-tape periodicity. The current density J must obey the constraint \\int J\\, \\mathrm {d}x=I/D , where the tapes lie parallel to the x axis and are stacked along the z axis. We suppose that Jc is independent of field (Bean approximation) and look for a solution to the critical state for arbitrary height 2b of the stack. For c<|x|anisotropic homogeneous-medium approximation gives a reasonably accurate estimate of the ac losses in a finite Z stack. The results for a Z stack can be used to calculate the transport losses in a pancake coil wound with superconducting tape.
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.
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.
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin
2015-08-01
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.
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.
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 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
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.
NASA Astrophysics Data System (ADS)
Provost, A.; Langevin, C.
2012-12-01
A number of numerical methods exist for incorporating anisotropic diffusion tensors, such as hydraulic or thermal conductivity, into two- and three-dimensional numerical models. The methods vary in mathematical approach, complexity, performance, and applicability to different types of model grids. The CCLADS variant of the CCLAD (Cell-Centered LAgrangian Diffusion) method of Maire & Breil (2011) is applicable to two-dimensional, unstructured, cell-centered finite-volume grids. It has a local stencil and exhibits nearly second-order accuracy on smooth distorted grids. As originally derived, CCLADS is not directly generalizable to three dimensions, and the derivation breaks down when adjacent cell edges meet at 180 degrees. Here, we rederive CCLADS to overcome these limitations and investigate the performance of the generalized method in a suite of three-dimensional test problems on structured, rectangular grids. As in two dimensions, the generalized method should be applicable to unstructured grids. Maire, P.-H., and Breil J., 2012, A nominally second-order accurate finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids, J. Comput. Phys., 231 (5), 2259-2299.
Drag force of Anisotropic plasma at finite U(1) chemical potential
NASA Astrophysics Data System (ADS)
Cheng, Long; Ge, Xian-Hui; Wu, Shang-Yu
2016-05-01
We perform the calculation of the drag force acting on a massive quark moving through an anisotropic N=4 SU(N) Super Yang-Mills plasma in the presence of a U(1) chemical potential. We present the numerical results for any value of the anisotropy and arbitrary direction of the quark velocity with respect to the direction of the anisotropy. We find the effect of the chemical potential or charge density will enhance the drag force for our charged solution.
NASA Astrophysics Data System (ADS)
Grilo, Tiago J.; Vladimirov, Ivaylo N.; Valente, Robertt A. F.; Reese, Stefanie
2016-02-01
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.
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.
Carnelli, Davide; Lucchini, Riccardo; Ponzoni, Matteo; Contro, Roberto; Vena, Pasquale
2011-07-01
Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ∼3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ∼6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing. PMID:21570077
A curvilinear, anisotropic, p-version, brick finite element based on geometric entities
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1992-01-01
A 'brick' solid finite element is presently developed on the basis of the p-version analysis, and used to demonstrate the FEM concept of 'geometric entities'. This method eliminates interelement discontinuities between low- and high-order elements, allowing very fine control over the shape-function order in various parts of the model. Attention is given to the illustrative cases of a one-element model of an elliptic pipe, and a square cross-section cantilevered beam.
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.
NASA Astrophysics Data System (ADS)
Suh, Hyun Sang; Lee, Won Hee; Kim, Tae-Seong
2012-11-01
To establish safe and efficient transcranial direct current stimulation (tDCS), it is of particular importance to understand the electrical effects of tDCS in the brain. Since the current density (CD) and electric field (EF) in the brain generated by tDCS depend on various factors including complex head geometries and electrical tissue properties, in this work, we investigated the influence of anisotropic conductivity in the skull and white matter (WM) on tDCS via a 3D anatomically realistic finite element head model. We systematically incorporated various anisotropic conductivity ratios into the skull and WM. The effects of anisotropic tissue conductivity on the CD and EF were subsequently assessed through comparisons to the conventional isotropic solutions. Our results show that the anisotropic skull conductivity significantly affects the CD and EF distribution: there is a significant reduction in the ratio of the target versus non-target total CD and EF on the order of 12-14%. In contrast, the WM anisotropy does not significantly influence the CD and EF on the targeted cortical surface, only on the order of 1-3%. However, the WM anisotropy highly alters the spatial distribution of both the CD and EF inside the brain. This study shows that it is critical to incorporate anisotropic conductivities in planning of tDCS for improved efficacy and safety.
Lee, Won Hee; Deng, Zhi-De; Kim, Tae-Seong; Laine, Andrew F; Lisanby, Sarah H; Peterchev, Angel V
2012-02-01
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 paradigms
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.
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.
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
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. PMID:24527060
NASA Astrophysics Data System (ADS)
Kamppeter, T.; Mertens, F. G.; Sánchez, Angel; Gronbech-Jensen, N.; Bishop, A. R.; Dominguez-Adame, F.
The 2-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry bears non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. In order to study the dynamics of these vortices under thermal fluctuations we use the Landau-Lifshitz equation and add white noise and Gilbert damping. Using a collective variable theory we derive an equation of motion with stochastic forces which are shown to represent white noise with an effective diffusion constant. We compare the results with Langevin dynamics simulations for the Landau-Lifshitz equation and find three temperature regimes: For low temperatures the dynamics is described by a 3rd-order equation of motion, for intermediate temperatures by a 1st-order equation. For higher temperatures, but still below the Kosterlitz-Thouless transition temperature, the spontaneous appearance of vortex-antivortex pairs does not allow a single-particle description.
Barocas, V H; Tranquillo, R T
1997-08-01
We present a method for solving the governing equations from our anisotropic biphasic theory of tissue-equivalent mechanics (Barocas and Tranquillo, 1997) for axisymmetric problems. A mixed finite element method is used for discretization of the spatial derivatives, and the DASPK subroutine (Brown et al., 1994) is used to solve the resulting differential-algebraic equation system. The preconditioned GMRES algorithm, using a preconditioner based on an extension of Dembo's (1994) adaptation of the Uzawa algorithm for viscous flows, provides an efficient and scaleable solution method, with the finite element method discretization being first-order accurate in space. In the cylindrical isometric cell traction assay, the chosen test problem, a cylindrical tissue equivalent is adherent at either end to fixed circular platens. As the cells exert traction on the collagen fibrils, the force required to maintain constant sample length, or load, is measured. However, radial compaction occurs during the course of the assay, so that the cell and network concentrations increase and collagen fibrils become aligned along the axis of the cylinder, leading to cell alignment along the axis. Our simulations predict that cell contact guidance leads to an increase in the load measured in the assay, but this effect is diminished by the tendency of contact guidance to inhibit radial compaction of the sample, which in turn reduces concentrations and hence the measured load. PMID:9285339
NASA Astrophysics Data System (ADS)
Key, K.
2013-12-01
This work announces the public release of an open-source inversion code named MARE2DEM (Modeling with Adaptively Refined Elements for 2D Electromagnetics). Although initially designed for the rapid inversion of marine electromagnetic data, MARE2DEM now supports a wide variety of acquisition configurations for both offshore and onshore surveys that utilize electric and magnetic dipole transmitters or magnetotelluric plane waves. The model domain is flexibly parameterized using a grid of arbitrarily shaped polygonal regions, allowing for complicated structures such as topography or seismically imaged horizons to be easily assimilated. MARE2DEM efficiently solves the forward problem in parallel by dividing the input data parameters into smaller subsets using a parallel data decomposition algorithm. The data subsets are then solved in parallel using an automatic adaptive finite element method that iterative solves the forward problem on successively refined finite element meshes until a specified accuracy tolerance is met, thus freeing the end user from the burden of designing an accurate numerical modeling grid. Regularized non-linear inversion for isotropic or anisotropic conductivity is accomplished with a new implementation of Occam's method referred to as fast-Occam, which is able to minimize the objective function in much fewer forward evaluations than the required by the original method. This presentation will review the theoretical considerations behind MARE2DEM and use a few recent offshore EM data sets to demonstrate its capabilities and to showcase the software interface tools that streamline model building and data inversion.
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.
NASA Technical Reports Server (NTRS)
Reddy, J. N.
1986-01-01
An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.
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
Anisotropic universe with anisotropic sources
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.
Jacobs, Nathan T.; Cortes, Daniel H.; Peloquin, John M.; Vresilovic, Edward J.; Elliott, Dawn M.
2014-01-01
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. PMID:24998992
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. PMID:24998992
3D unstructured mesh discontinuous finite element hydro
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.
Sound field distribution influenced by anisotropic materials
Erhard, A.; Boehm, R.; Wuestenberg, H.
1993-12-31
Sound wave distributions in isotropic materials are often described using analytical or numerical solutions of the wave equation. In opposition to this, it is more difficult to find a solution for anisotropic mediums. One possible method is the elastic finite integration technique (EFIT). With this method, scalar and vectorial calculations of the sound distribution from a line source in anisotropic materials were carried out. This method needs a powerful computer in order to keep the computation time short. In the present paper another theoretical model was used -- the pulse integration model -- with which sound field distributions for scalar waves were calculated in the sound field distribution of longitudinal waves in anisotropic materials. The principle of the model is described briefly. Different sound field pattern generated with a phased array longitudinal wave probe were calculated during the propagation in a homogeneous isotropic material and in a homogeneous anisotropic material (single crystal).
A generalized anisotropic deformation formulation for geomaterials
NASA Astrophysics Data System (ADS)
Lei, Z.; Rougier, Esteban; Knight, E. E.; Munjiza, A.; Viswanathan, H.
2016-04-01
In this paper, the combined finite-discrete element method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of addressing anisotropic material problems, improved 2D FDEM formulations have been developed. These formulations feature the unified hypo-hyper elastic approach combined with a multiplicative decomposition-based selective integration for volumetric and shear deformation modes. This approach is significantly different from the co-rotational formulations typically encountered in finite element codes. Unlike the co-rotational formulation, the multiplicative decomposition-based formulation naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. This approach can be implemented for a whole family of finite elements from solids to shells and membranes. This novel 2D FDEM based material formulation was designed in such a way that the anisotropic properties of the solid can be specified in a cell by cell basis, therefore enabling the user to seed these anisotropic properties following any type of spatial variation, for example, following a curvilinear path. In addition, due to the selective integration, there are no problems with volumetric or shear locking with any type of finite element employed.
Improved Beam Theory for Anisotropic Materials
NASA Technical Reports Server (NTRS)
1984-01-01
The behavior of beams made of anisotropic material was investigated in order to develop an appropriate model of such behavior. Closed form solutions of the problem were derived using two alternative approaches. In the first approach, the axial displacements are expanded as a series of eigenwarpings. In the second approach, the axial stresses are expanded as a series of eigenwarpings. A finite element solution was also derived using the same displacement field as in the first approach.
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.
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
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.
Anisotropic Damage Analysis of HY100 Steel Under Quasistatic Loading Conditions
Los Alamos National Laboratory
2001-01-01
The effect of MnS inclusion orientation on damage evolution and fracture toughness in HYlOO steel is investigated in the context of anisotropic damage modeling at the continuum level. Experimental notched-bar data sets are analyzed and modeled using finite element calculations with constitutive behavior that assumes isotropic elastoplastic behavior in conjunction with anisotropic damage.
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.
Magnetospheric equilibrium with anisotropic pressure
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.
Magnetospheric equilibrium with anisotropic pressure
Cheng, C.Z. )
1992-02-01
Self-consistent magnetospheric equilibria with anisotropic pressure are 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 distributions or particle distributions measured along a satellite's path is presented. The numerical results of axisymmetric magnetospheric equilibria 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 owing 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 a significant effect on the magnetospheric equilibrium. For the outer flux boundary resembling the 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 taillike flux surface.
Anisotropic metamaterial optical fibers.
Pratap, Dheeraj; Anantha Ramakrishna, S; Pollock, Justin G; Iyer, Ashwin K
2015-04-01
Internal physical structure can drastically modify the properties of waveguides: photonic crystal fibers are able to confine light inside a hollow air core by Bragg scattering from a periodic array of holes, while metamaterial loaded waveguides for microwaves can support propagation at frequencies well below cutoff. Anisotropic metamaterials assembled into cylindrically symmetric geometries constitute light-guiding structures that support new kinds of exotic modes. A microtube of anodized nanoporous alumina, with nanopores radially emanating from the inner wall to the outer surface, is a manifestation of such an anisotropic metamaterial optical fiber. The nanopores, when filled with a plasmonic metal such as silver or gold, greatly increase the electromagnetic anisotropy. The modal solutions in such anisotropic circular waveguides can be uncommon Bessel functions with imaginary orders. PMID:25968741
Enhancement of non-resonant dielectric cloaks using anisotropic composites
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.
Enhancement of non-resonant dielectric cloaks using anisotropic composites
NASA Astrophysics Data System (ADS)
Takezawa, Akihiro; Kitamura, Mitsuru
2014-01-01
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.
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.
Anisotropic Ambient Volume Shading.
Ament, Marco; Dachsbacher, Carsten
2016-01-01
We present a novel method to compute anisotropic shading for direct volume rendering to improve the perception of the orientation and shape of surface-like structures. We determine the scale-aware anisotropy of a shading point by analyzing its ambient region. We sample adjacent points with similar scalar values to perform a principal component analysis by computing the eigenvectors and eigenvalues of the covariance matrix. In particular, we estimate the tangent directions, which serve as the tangent frame for anisotropic bidirectional reflectance distribution functions. Moreover, we exploit the ratio of the eigenvalues to measure the magnitude of the anisotropy at each shading point. Altogether, this allows us to model a data-driven, smooth transition from isotropic to strongly anisotropic volume shading. In this way, the shape of volumetric features can be enhanced significantly by aligning specular highlights along the principal direction of anisotropy. Our algorithm is independent of the transfer function, which allows us to compute all shading parameters once and store them with the data set. We integrated our method in a GPU-based volume renderer, which offers interactive control of the transfer function, light source positions, and viewpoint. Our results demonstrate the benefit of anisotropic shading for visualization to achieve data-driven local illumination for improved perception compared to isotropic shading. PMID:26529745
NASA Astrophysics Data System (ADS)
Gutzov, S.; Danchova, N.; Tsekov, R.; Barreno, I.; Ruiz del Portal, X.; Ulbikas, J.
2015-10-01
A new hybrid woven micromesh containing metal and polyester wires with a 2D porosity of about 30% has been created. The anisotropic microcomposite is developed as a new material with wide applications in thermal and electrical engineering. The mesh material is carefully characterized using electron microscopy, fluorescence microscopy, chemical analysis, thermal conductivity measurements and differential scanning calorimetry.
Dynamics of Anisotropic Universes
NASA Astrophysics Data System (ADS)
Perez, Jérôme
2006-11-01
We present a general study of the dynamical properties of Anisotropic Bianchi Universes in the context of Einstein General Relativity. Integrability results using Kovalevskaya exponents are reported and connected to general knowledge about Bianchi dynamics. Finally, dynamics toward singularity in Bianchi type VIII and IX universes are showed to be equivalent in some precise sence.
Glueball spectrum from an anisotropic lattice study
Morningstar, C.J.; Peardon, M.
1999-08-01
The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is investigated using Monte Carlo simulations of gluons on several anisotropic lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic errors from discretization and finite volume are studied, and the continuum spin quantum numbers are identified. Care is taken to distinguish single glueball states from two-glueball and torelon-pair states. Our determination of the spectrum significantly improves upon previous Wilson action calculations. {copyright} {ital 1999} {ital The American Physical Society}
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. PMID:26698490
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.
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.
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
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.
Anisotropic Total Variation Filtering
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.
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.
Optics of anisotropic nanostructures
NASA Astrophysics Data System (ADS)
Rokushima, Katsu; Antoš, Roman; Mistrík, Jan; Višňovský, Štefan; Yamaguchi, Tomuo
2006-07-01
The analytical formalism of Rokushima and Yamakita [J. Opt. Soc. Am. 73, 901-908 (1983)] treating the Fraunhofer diffraction in planar multilayered anisotropic gratings proved to be a useful introduction to new fundamental and practical situations encountered in laterally structured periodic (both isotropic and anisotropic) multilayer media. These are employed in the spectroscopic ellipsometry for modeling surface roughness and in-depth profiles, as well as in the design of various frequency-selective elements including photonic crystals. The subject forms the basis for the solution of inverse problems in scatterometry of periodic nanostructures including magnetic and magneto-optic recording media. It has no principal limitations as for the frequencies and period to radiation wavelength ratios and may include matter wave diffraction. The aim of the paper is to make this formalism easily accessible to a broader community of students and non-specialists. Many aspects of traditional electromagnetic optics are covered as special cases from a modern and more general point of view, e.g., plane wave propagation in isotropic media, reflection and refraction at interfaces, Fabry-Perot resonator, optics of thin films and multilayers, slab dielectric waveguides, crystal optics, acousto-, electro-, and magneto-optics, diffraction gratings, etc. The formalism is illustrated on a model simulating the diffraction on a ferromagnetic wire grating.
NASA Astrophysics Data System (ADS)
Gardiner, Thomas
2013-10-01
Anisotropic thermal diffusion in magnetized plasmas is an important physical phenomena for a diverse set of physical conditions ranging from astrophysical plasmas to MFE and ICF. Yet numerically simulating this phenomenon accurately poses significant challenges when the computational mesh is misaligned with respect to the magnetic field. Particularly when the temperature gradients are unresolved, one frequently finds entropy violating solutions with heat flowing from cold to hot zones for χ∥ /χ⊥ >=102 which is substantially smaller than the range of interest which can reach 1010 or higher. In this talk we present a new implicit algorithm for solving the anisotropic thermal diffusion equations and demonstrate its characteristics on what has become a fairly standard set of test problems in the literature. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND2013-5687A.
Simple types of anisotropic inflation
Barrow, John D.; Hervik, Sigbjoern
2010-01-15
We display some simple cosmological solutions of gravity theories with quadratic Ricci curvature terms added to the Einstein-Hilbert Lagrangian which exhibit anisotropic inflation. The Hubble expansion rates are constant and unequal in three orthogonal directions. We describe the evolution of the simplest of these homogeneous and anisotropic cosmological models from its natural initial state and evaluate the deviations they will create from statistical isotropy in the fluctuations produced during a period of anisotropic inflation. The anisotropic inflation is not a late-time attractor in these models but the rate of approach to a final isotropic de Sitter state is slow and is conducive to the creation of observable anisotropic statistical effects in the microwave background. The statistical anisotropy would not be scale invariant and the level of statistical anisotropy will grow with scale.
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.
Relativistic heavy quark spectrum on anisotropic lattices
NASA Astrophysics Data System (ADS)
Liao, Xiaodong
We report a fully relativistic quenched calculation of the heavy quark spectrum, including both charmonium and bottomonium, using anisotropic lattice QCD. We demonstrate that a fully relativistic treatment of a heavy quark system is well-suited to address the large systematic errors in non-relativistic calculations. In addition, the anisotropic lattice formulation is a very efficient framework for calculations requiring high temporal resolutions. A detailed excited charmonium spectrum is obtained, including both the exotic hybrids (with JPC = 1-+ , 0+-, 2+-) and orbitally excited mesons (with orbital angular momentum up to 3). Using three different lattice spacings (0.197, 0.131, and 0.092 fm), we perform a continuum extrapolation of the spectrum. The lowest lying exotic hybrid 1-+ lies at 4.428(41) GeV, slightly above the D**D (S + P wave) threshold of 4.287 GeV. Another two exotic hybrids 0+- and 2 +- are determined to be 4.70(17) GeV and 4.895(88) GeV, respectively. Our finite volume analysis confirms that our lattices are large enough to accommodate all the excited states reported here. We did the first relativistic calculation of the quenched bottomonium spectrum from anisotropic lattices. Using a very fine discretization in the temporal direction we were able to go beyond the non-relativistic approximation and perform a continuum extrapolation of our results from five different lattice spacings (0.04--0.17 fm) and two anisotropies (4 and 5). We investigate several systematic errors within the quenched approximation and compare our results with those from non-relativistic simulations.
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.
Anisotropic inflation with general potentials
NASA Astrophysics Data System (ADS)
Shi, JiaMing; Huang, XiaoTian; Qiu, TaoTao
2016-04-01
Anomalies in recent observational data indicate that there might be some "anisotropic hair" generated in an inflation period. To obtain general information about the effects of this anisotropic hair to inflation models, we studied anisotropic inflation models that involve one vector and one scalar using several types of potentials. We determined the general relationship between the degree of anisotropy and the fraction of the vector and scalar fields, and concluded that the anisotropies behave independently of the potentials. We also generalized our study to the case of multi-directional anisotropies.
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.
Vortex dynamics in anisotropic traps
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.
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.
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.
Anisotropic Alfven-ballooning modes in the Earth's magnetosphere
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
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.
Deficiencies in numerical models of anisotropic nonlinearly elastic materials.
Ní Annaidh, A; Destrade, M; Gilchrist, M D; Murphy, J G
2013-08-01
Incompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial finite element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a 'compressibility parameter' (or 'penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a 'bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in 'Poisson's ratio' close to the perfect incompressibility limit of 1/2 are made. PMID:23011411
Cloaking by shells with radially inhomogeneous anisotropic permittivity.
Reshetnyak, V Yu; Pinkevych, I P; Sluckin, T J; Evans, D R
2016-01-25
We model electromagnetic cloaking of a spherical or cylindrical nanoparticle enclosed by an optically anisotropic and optically inhomogeneous symmetric shell, by examining its electric response in a quasi-static uniform electric field. When the components of the shell permittivity are radially anisotropic and power-law dependent (ε~r(m)) whereris distance to the shell center, and m a positive or negative exponent which can be varied), the problem is analytically tractable. Formulas are calculated for the degree of cloaking in the general case, allowing the determination of a dielectric condition for the shells to be used as an invisibility cloak. Ideal cloaking is known to require that homogeneous shells exhibit an infinite ratio of tangential and radial components of the shell permittivity, but for radially inhomogeneous shells ideal cloaking can occur even for finite values of this ratio. PMID:26832575
A resistor interpretation of general anisotropic cardiac tissue.
Shao, Hai; Sampson, Kevin J; Pormann, John B; Rose, Donald J; Henriquez, Craig S
2004-02-01
This paper describes a spatial discretization scheme for partial differential equation systems that contain anisotropic diffusion. The discretization method uses unstructured finite volumes, or the boxes, that are formed as a secondary geometric structure from an underlying triangular mesh. We show how the discretization can be interpreted as a resistive circuit network, where each resistor is assigned at each edge of the triangular element. The resistor is computed as an anisotropy dependent geometric quantity of the local mesh structure. Finally, we show that under certain conditions, the discretization gives rise to negative resistors that can produce non-physical hyperpolarizations near depolarizing stimuli. We discuss how the proper choice of triangulation (anisotropic Delaunay triangulation) can ensure monotonicity (i.e. all resistors are positive). PMID:14739082
Superlens from complementary anisotropic metamaterials
NASA Astrophysics Data System (ADS)
Li, G. X.; Tam, H. L.; Wang, F. Y.; Cheah, K. W.
2007-12-01
Metamaterials with isotropic property have been shown to possess novel optical properties such as a negative refractive index that can be used to design a superlens. Recently, it was shown that metamaterials with anisotropic property can translate the high-frequency wave vector k values from evanescence to propagating. However, electromagnetic waves traveling in single-layer anisotropic metamaterial produce diverging waves of different spatial frequency. In this work, it is shown that, using bilayer metamaterials that have complementary anisotropic property, the diverging waves are recombined to produce a subwavelength image, i.e., a superlens device can be designed. The simulation further shows that the design can be achieved using a metal/oxide multilayer, and a resolution of 30 nm can be easily obtained in the optical frequency range.
NASA Astrophysics Data System (ADS)
Pekşen, Ertan; Yas, Türker; Kıyak, Alper
2014-09-01
We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.
3D time-domain airborne EM modeling for an arbitrarily anisotropic earth
NASA Astrophysics Data System (ADS)
Yin, Changchun; Qi, Yanfu; Liu, Yunhe
2016-08-01
Time-domain airborne EM data is currently interpreted based on an isotropic model. Sometimes, it can be problematic when working in the region with distinct dipping stratifications. In this paper, we simulate the 3D time-domain airborne EM responses over an arbitrarily anisotropic earth with topography by edge-based finite-element method. Tetrahedral meshes are used to describe the abnormal bodies with complicated shapes. We further adopt the Backward Euler scheme to discretize the time-domain diffusion equation for electric field, obtaining an unconditionally stable linear equations system. We verify the accuracy of our 3D algorithm by comparing with 1D solutions for an anisotropic half-space. Then, we switch attentions to effects of anisotropic media on the strengths and the diffusion patterns of time-domain airborne EM responses. For numerical experiments, we adopt three typical anisotropic models: 1) an anisotropic anomalous body embedded in an isotropic half-space; 2) an isotropic anomalous body embedded in an anisotropic half-space; 3) an anisotropic half-space with topography. The modeling results show that the electric anisotropy of the subsurface media has big effects on both the strengths and the distribution patterns of time-domain airborne EM responses; this effect needs to be taken into account when interpreting ATEM data in areas with distinct anisotropy.
Dynamical analysis of anisotropic inflation
NASA Astrophysics Data System (ADS)
Karčiauskas, Mindaugas
2016-06-01
The inflaton coupling to a vector field via the f(φ)2F μνFμν term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to support anisotropic inflation, and to circumvent the η-problem. In this work, I perform dynamical analysis of this system allowing for the most general Bianchi I initial conditions. I also confirm the stability of attractor fixed points along phase-space directions that had not been investigated before.
Anisotropic superfluidity in a dipolar Bose gas
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
Anisotropic inflation with the nonvacuum initial state
NASA Astrophysics Data System (ADS)
Emami, Razieh; Firouzjahi, Hassan; Zarei, Moslem
2014-07-01
In this work we study models of anisotropic inflation with the generalized nonvacuum initial states for the inflaton field and the gauge field. The effects of the non-Bunch-Davies initial condition on the anisotropic power spectrum and bispectrum are calculated. We show that the non-Bunch-Davies initial state can help to reduce the fine-tuning on the anisotropic power spectrum while reducing the level of anisotropic bispectrum.
NASA Astrophysics Data System (ADS)
Parente, Walter E. F.; Pacobahyba, J. T. M.; Araújo, Ijanílio G.; Neto, Minos A.; Ricardo de Sousa, J.
2015-11-01
We will study phase diagram the quantum spin-1/2 anisotropic Heisenberg antiferromagnet model in the presence of a Dzyaloshinskii-Moriya interaction (D) and a uniform longitudinal (H) magnetic field, where we have observed an anomaly at low temperatures. Using the effective-field theory with a finite cluster N=2 spin (EFT-2) we calculate the phase diagram in the H - D plane on a simple cubic lattice (z=6). We analyzed the cases: anisotropic Heisenberg - case I: (Δ = 1), anisotropic Heisenberg - case II: (Δ = 0.5) and anisotropic Heisenberg - case III: (Δ = 0), where only second order phase transitions are observed.
Velocity of Light in Anisotropic Spacetime
NASA Astrophysics Data System (ADS)
Fomin, I. V.
2016-05-01
The task of the present study is to describe local anisotropic spacetime and to discuss the possibility of its experimental detection. Anisotropic spacetime is treated as the flat isotropic Minkowski space with anisotropic perturbations. A determination of the components of the metric tensor is bound up with measurements of the velocity of light in different directions.
Fracture toughness of anisotropic graphites
Kennedy, C.R.; Kehne, M.T.
1985-01-01
Fracture toughness measurements have been made at 0, 30, 45, 60, and 90/sup 0/ from the extrusion axis on a reasonably anisotropic graphite, grade AGOT. It was found that the fracture toughness did not vary appreciably with orientation. An observed variation in strength was found to be the result of defect orientation.
PP/PS anisotropic stereotomography
NASA Astrophysics Data System (ADS)
Nag, Steinar; Alerini, Mathias; Ursin, Bjørn
2010-04-01
Stereotomography is a slope tomographic method which gives good results for background velocity model estimation in 2-D isotropic media. We develop here the extension of the method to 3-D general anisotropic media for PP and PS events. We do not take into account the issue of shear wave degeneracy. As in isotropic media, the sensitivity matrix of the inversion can be computed by paraxial ray tracing. We introduce a `constant Z stereotomography' approach, which can reduce the size of the sensitivity matrix. Based on ray perturbation theory, we give all the derivatives of stereotomography data parameters with respect to model parameters in a 3-D general anisotropic medium. These general formulas for the derivatives can also be used in other applications that rely on anisotropic ray perturbation theory. In particular, we obtain derivatives of the phase velocity with respect to position, phase angle and elastic medium parameters, all for general anisotropic media. The derivatives are expressed using the Voigt notation for the elastic medium parameters. We include a Jacobian that allows to change the model parametrization from Voigt to Thomsen parameters. Explicit expressions for the derivatives of the data are given for the case of 2-D tilted transversely isotropic (TTI) media. We validate the method by single-parameter estimation of each Thomsen parameter field of a 2-D TTI synthetic model, where data are modelled by ray tracing. For each Thomsen parameter, the estimated velocity field fits well with the true velocity field.
Anisotropic linear elastic properties of fractal-like composites.
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. PMID:21230552
NASA Astrophysics Data System (ADS)
Cui, Linyan
2016-07-01
Experiments and theoretical investigations have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, based on the anisotropic generalized von Karman spectrum and the Rytov approximation theory, new expression for the irradiance scintillation index of optical waves is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. Compared with previously published results, it considers simultaneously the asymmetry property of turbulence cells or eddies in the orthogonal xy-plane, the general spectral power law in the range 3-4 instead of constant value of 11/3 for the Kolmogorov turbulence, and the finite turbulence inner and outer scales. Two anisotropic factors are introduced to parameterize the anisotropy of turbulence cells or eddies in horizontal and vertical directions. In the special cases of these two anisotropic factors equaling one and the finite turbulence inner and outer scales equaling separately zero and infinite, the derived expression can reduce correctly to the previously published results. Calculations are performed to analyze the derived results.
Heavy quarks on anisotropic lattices: The charmonium spectrum
NASA Astrophysics Data System (ADS)
Chen, Ping
2000-10-01
We present results for the mass spectrum of cc¯ mesons simulated on anisotropic lattices where the temporal spacing is only half of the spatial spacing. The lattice QCD action is the Wilson gauge action plus the clover-improved Wilson fermion action. The two clover coefficients on an anisotropic lattice are estimated using mean links in Landau gauge. The bare velocity of light νt has been tuned to keep the anisotropic, heavy-quark Wilson action relativistic. Local meson operators and three box sources are used in obtaining clear statistics for the lowest lying and first excited charmonium states of 1 S0, 3S1, 1P1, 3P 0 and 3P1. The continuum limit is discussed by extrapolating from quenched simulations at four lattice spacings in the range 0.1-0.3 fm. Results are compared with the observed values in nature and other lattice approaches. Finite volume effects and dispersion relations are checked.
NASA Astrophysics Data System (ADS)
Barrow, John D.; Ganguly, Chandrima
2016-06-01
We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropization on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialize to consider the closed Bianchi type IX universe, and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate on approach to the singularity, it will be anisotropic. We include an isotropic ultra-stiff ghost fluid with negative energy density in order to create a cosmological bounce at finite volume in the absence of the anisotropic fluid. When the dominant anisotropic fluid is present it leads to an anisotropic cosmological singularity rather than an isotropic bounce. The inclusion of anisotropic stresses generated by collisionless particles in an anisotropically expanding universe is therefore essential for a full analysis of the consequences of a cosmological bounce or singularity in cyclic universes.
Non-linear dynamic analysis of anisotropic cylindrical shells
Lakis, A.A.; Selmane, A.; Toledano, A.
1996-12-01
A theory to predict the influence of geometric non-linearities on the natural frequencies of an empty anisotropic cylindrical shell is presented in this paper. It is a hybrid of finite element and classical thin shell theories. Sanders-Koiter non-linear and strain-displacement relations are used. Displacement functions are evaluated using linearized equations of motion. Modal coefficients are then obtained for these displacement functions. Expressions for the mass, linear and non-linear stiffness matrices are derived through the finite element method. The uncoupled equations are solved with the help of elliptic functions. The period and frequency variations are first determined as a function of shell amplitudes and then compared with the results in the literature.
Anisotropic models for compact stars
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Dayanandan, Baiju
2015-05-01
In the present paper we obtain an anisotropic analog of the Durgapal and Fuloria (Gen Relativ Gravit 17:671, 1985) perfect fluid solution. The methodology consists of contraction of the anisotropic factor with the help of both metric potentials and . Here we consider the same as Durgapal and Fuloria (Gen Relativ Gravit 17:671, 1985) did, whereas is as given by Lake (Phys Rev D 67:104015, 2003). The field equations are solved by the change of dependent variable method. The solutions set mathematically thus obtained are compared with the physical properties of some of the compact stars, strange star as well as white dwarf. It is observed that all the expected physical features are available related to the stellar fluid distribution, which clearly indicates the validity of the model.
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.
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.
Model-size reduction for the buckling and vibration analyses of anisotropic panels
NASA Technical Reports Server (NTRS)
Noor, A. K.; Whitworth, S. L.
1986-01-01
A computational procedure is presented for reducing the size of the model used in the buckling and vibration analyses of symmetric anisotropic panels to that of the corresponding orthotropic model. The key elements of the procedure are the application of an operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts and the use of a reduction method through successive application of the finite element method and the classical Rayleigh-Ritz technique. The effectiveness of the procedure is demonstrated by numerical examples.
Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models
NASA Astrophysics Data System (ADS)
Bakar, B.; Tirnakli, U.
2008-03-01
We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state (self-organized critical state). Corresponding growth exponent α for the Hamming distance and the dynamical exponent z are calculated. These values allow us to observe a clear data collapse of the finite size scaling for both versions of the Bak-Sneppen model. Moreover, it is shown that the growth exponent of the distance in the isotropic and anisotropic Bak-Sneppen models is strongly affected by the choice of the transient time.
Thermoelectric conductivities, shear viscosity, and stability in an anisotropic linear axion model
NASA Astrophysics Data System (ADS)
Ge, Xian-Hui; Ling, Yi; Niu, Chao; Sin, Sang-Jin
2015-11-01
We study thermoelectric conductivities and shear viscosities in a holographically anisotropic model, which is dual to a spatially anisotropic N =4 super-Yang-Mills theory at finite chemical potential. Momentum relaxation is realized through perturbing the linear axion field. Ac conductivity exhibits a coherent/incoherent metal transition. Deviations from the Wiedemann-Franz law are also observed in our model. The longitudinal shear viscosity for prolate anisotropy violates the bound conjectured by Kovtun-Son-Starinets. We also find that thermodynamic and dynamical instabilities are not always equivalent by examining the Gubser-Mitra conjecture.
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.
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.
Numerical investigation of nanoparticles transport in anisotropic porous media.
Salama, Amgad; Negara, Ardiansyah; El Amin, Mohamed; Sun, Shuyu
2015-10-01
In this work the problem related to the transport of nanoparticles in anisotropic porous media is investigated numerically using the multipoint flux approximation. Anisotropy of porous media properties is an essential feature that exists almost everywhere in subsurface formations. In anisotropic media, the flux and the pressure gradient vectors are no longer collinear and therefore interesting patterns emerge. The transport of nanoparticles in subsurface formations is affected by several complex processes including surface charges, heterogeneity of nanoparticles and soil grain collectors, interfacial dynamics of double-layer and many others. We use the framework of the theory of filtration in this investigation. Processes like particles deposition, entrapment, as well as detachment are accounted for. From the numerical methods point of view, traditional two-point flux finite difference approximation cannot handle anisotropy of media properties. Therefore, in this work we use the multipoint flux approximation (MPFA). In this technique, the flux components are affected by more neighboring points as opposed to the mere two points that are usually used in traditional finite volume methods. We also use the experimenting pressure field approach which automatically constructs the global system of equations by solving multitude of local problems. This approach facilitates to a large extent the construction of the global system. A set of numerical examples is considered involving two-dimensional rectangular domain. A source of nanoparticles is inserted in the middle of the anisotropic layer. We investigate the effects of both anisotropy angle and anisotropy ratio on the transport of nanoparticles in saturated porous media. It is found that the concentration plume and porosity contours follow closely the principal direction of anisotropy of permeability of the central domain. PMID:26212784
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
Application of Mass Lumped Higher Order Finite Elements
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.
Anomalous optical forces on radially anisotropic nanowires
NASA Astrophysics Data System (ADS)
Chen, H. L.; Gao, L.
2015-11-01
Full-wave electromagnetic scattering theory and Maxwell stress tensor integration techniques have been established to study the optical force on the radially anisotropic nanowires. The optical forces on the isotropic nanowires are dependent on the size of the nanowire and the wave vector in the media with the Rayleigh's law. However, the optical forces on the anisotropic nanowires have the anomalous behaviors under non-Rayleigh vanishing condition and non-Rayleigh diverging condition. Therefore, the optical forces on the anisotropic nanowires may be enhanced or reduced by tuning the anisotropic parameters. These results may promote the potential applications in the field of nanotechnology.
Planetary spectra for anisotropic scattering
NASA Technical Reports Server (NTRS)
Chamberlain, J. W.
1975-01-01
Some of the effects on planetary spectra that would be produced by departures from isotropic scattering are examined. The phase function is the simplest departure to handle analytically and the only phase function, other than the isotropic one, that can be incorporated into a Chandrasekhar first approximation. This approach has the advantage of illustrating trends resulting from anisotropies while retaining the simplicity that yields physical insight. An algebraic solution to the two sets of anisotropic H functions is developed in the appendix. It is readily adaptable to progammable desk calculators and gives emergent intensities accurate to 0.3 percent, which is sufficient even for spectroscopic analysis.
Tunneling spectroscopy of anisotropic superconductors
Kashiwaya, Satoshi; Koyanagi, Masao; Kajimura, Koji; Tanaka, Yukio
1996-12-31
Tunneling spectroscopy of normal-insulator-superconductor junction is investigated theoretically. In anisotropic superconductors, differently from the case of isotropic superconductor, the effective pair potentials felt by quasiparticles depend on the direction of their motion. By taking this effect into account, it is shown that the conductance spectra strongly depend on the crystal orientation. Using Green`s function method, local density of states (LDOS) in superconductor is also calculated. The close relation between conductance spectra and LDOS is presented. The calculation is compared with experimental spectra of high-{Tc} superconductors.
Spin precession in anisotropic cosmologies
NASA Astrophysics Data System (ADS)
Kamenshchik, A. Yu.; Teryaev, O. V.
2016-05-01
We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. We discuss in some detail the geodesics and the spin precession for both the Kasner and the Heckmann-Schucking solutions. In the Bianchi-IX universe the spin precession acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the very early universe may produce the sterile particles contributing to dark matter.
Remarks on inhomogeneous anisotropic cosmology
NASA Astrophysics Data System (ADS)
Kaya, Ali
2016-08-01
Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow of spacelike surfaces in Lorentzian manifolds. We show that singularities may form during cosmic evolution, and the theorems forbidding the global recollapse lose their validity. The time evolution of the spatial scalar curvature that may kinematically prevent the recollapse is determined in normal coordinates, which shows the impact of inhomogeneities explicitly. Our analysis indicates a caveat in numerical solutions that give rise to inflation.
Anisotropic fractional diffusion tensor imaging
Meerschaert, Mark M; Magin, Richard L; Ye, Allen Q
2015-01-01
Traditional diffusion tensor imaging (DTI) maps brain structure by fitting a diffusion model to the magnitude of the electrical signal acquired in magnetic resonance imaging (MRI). Fractional DTI employs anomalous diffusion models to obtain a better fit to real MRI data, which can exhibit anomalous diffusion in both time and space. In this paper, we describe the challenge of developing and employing anisotropic fractional diffusion models for DTI. Since anisotropy is clearly present in the three-dimensional MRI signal response, such models hold great promise for improving brain imaging. We then propose some candidate models, based on stochastic theory.
New charged anisotropic compact models
NASA Astrophysics Data System (ADS)
Kileba Matondo, D.; Maharaj, S. D.
2016-07-01
We find new exact solutions to the Einstein-Maxwell field equations which are relevant in the description of highly compact stellar objects. The relativistic star is charged and anisotropic with a quark equation of state. Exact solutions of the field equations are found in terms of elementary functions. It is interesting to note that we regain earlier quark models with uncharged and charged matter distributions. A physical analysis indicates that the matter distributions are well behaved and regular throughout the stellar structure. A range of stellar masses are generated for particular parameter values in the electric field. In particular the observed mass for a binary pulsar is regained.
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.
Electromagnetism on anisotropic fractal media
NASA Astrophysics Data System (ADS)
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Cryogenic microwave anisotropic artificial materials
NASA Astrophysics Data System (ADS)
Trang, Frank
This thesis addresses analysis and design of a cryogenic microwave anisotropic wave guiding structure that isolates an antenna from external incident fields from specific directions. The focus of this research is to design and optimize the radome's constituent material parameters for maximizing the isolation between an interior receiver antenna and an exterior transmitter without significantly disturbing the transmitter antenna far field characteristics. The design, characterization, and optimization of high-temperature superconducting metamaterials constitutive parameters are developed in this work at X-band frequencies. A calibrated characterization method for testing arrays of split-ring resonators at cryogenic temperature inside a TE10 waveguide was developed and used to back-out anisotropic equivalent material parameters. The artificial material elements (YBCO split-ring resonators on MgO substrate) are optimized to improve the narrowband performance of the metamaterial radome with respect to maximizing isolation and minimizing shadowing, defined as a reduction of the transmitted power external to the radome. The optimized radome is fabricated and characterized in a parallel plate waveguide in a cryogenic environment to demonstrate the degree of isolation and shadowing resulting from its presence. At 11.12 GHz, measurements show that the HTS metamaterial radome achieved an isolation of 10.5 dB and the external power at 100 mm behind the radome is reduced by 1.9 dB. This work demonstrates the feasibility of fabricating a structure that provides good isolation between two antennas and low disturbance of the transmitter's fields.
Mekhiche, M.; Pera, T.; Marechal, Y.
1995-05-01
The anisotropic and nonlinear behavior of doubly oriented and non-oriented sheets are modeled using the coenergy density. These models have been implemented in a finite element computation. A large generator has been modeled and the advantages of doubly oriented sheets compared to the conventional non-oriented ones are shown.
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.
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.
Materials with constant anisotropic conductivity as a thermal cloak or concentrator
NASA Astrophysics Data System (ADS)
Chen, Tungyang; Weng, Chung-Ning; Tsai, Yu-Lin
2015-02-01
An invisibility cloak based on transformation optics often requires material with inhomogeneous, anisotropic, and possibly extreme material parameters. In the present study, on the basis of the concept of neutral inclusion, we find that a spherical cloak can be achieved using a layer with finite constant anisotropic conductivity. We show that thermal localization can be tuned and controlled by anisotropy of the coating layer. A suitable balance of the degree of anisotropy of the cloaking layer and the layer thickness provides a cloaking effect. Additionally, by reversing the conductivities in two different directions, we find that a thermal concentrating effect can be simulated. This finding is of particular value in practical implementation as a material with constant material parameters is more feasible to fabricate. In addition to the theoretical analysis, we also demonstrate our solutions in numerical simulations based on finite element calculations to validate our results.
Anisotropic N=4 Super-Yang-Mills Plasma and Its Instabilities
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.
Effects of anisotropic dynamics on cosmic strings
Kunze, Kerstin E.
2011-08-01
The dynamics of cosmic strings is considered in anisotropic backgrounds. In particular, the behaviour of infinitely long straight cosmic strings and of cosmic string loops is determined. Small perturbations of a straight cosmic string are calculated. The relevance of these results is discussed with respect to the possible observational imprints of an anisotropic phase on the behaviour of a cosmic string network.
Phonon heat conduction in layered anisotropic crystals
NASA Astrophysics Data System (ADS)
Minnich, A. J.
2015-02-01
The thermal properties of anisotropic crystals are of both fundamental and practical interest, but transport phenomena in anisotropic materials such as graphite remain poorly understood because solutions of the Boltzmann equation often assume isotropy. Here, we extend an analytic solution of the transient, frequency-dependent Boltzmann equation to highly anisotropic solids and examine its predictions for graphite. We show that this simple model predicts key results, such as long c -axis phonon mean free paths and a negative correlation of cross-plane thermal conductivity with in-plane group velocity, that were previously observed with computationally expensive molecular-dynamics simulations. Further, using our analytic solution, we demonstrate a method to reconstruct the anisotropic mean free path spectrum of crystals with arbitrary dispersion relations without any prior knowledge of their harmonic or anharmonic properties using observations of quasiballistic heat conduction. These results provide a useful analytic framework to understand thermal transport in anisotropic crystals.
Designing anisotropic inflation with form fields
NASA Astrophysics Data System (ADS)
Ito, Asuka; Soda, Jiro
2015-12-01
We study inflation with anisotropic hair induced by form fields. In four dimensions, the relevant form fields are gauge (one-form) fields and two-form fields. Assuming the exponential form of potential and gauge kinetic functions, we find new exact power-law solutions endowed with anisotropic hair. We also explore the phase space of anisotropic inflation and find fixed points corresponding to the exact power-law solutions. Moreover, we perform the stability analysis around the fixed points to reveal the structure of the phase space. It turns out that one of the fixed points becomes an attractor and others (if any) are saddle points. In particular, the one corresponding to anisotropic inflation becomes an attractor when it exists. We also argue that various anisotropic inflation models can be designed by choosing coupling constants.
2-D Finite Element Heat Conduction
Energy Science and Technology Software Center (ESTSC)
1989-10-30
AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less
Jean, Aurélie; Engelmayr, George C
2012-01-11
Anisotropic collagen fibrillogenesis is demonstrated within the pores of an accordion-like honeycomb poly(glycerol sebacate) tissue engineering scaffold. Confocal reflectance microscopy and image analysis demonstrate increased fibril distribution order, fibril density, and alignment in accordion-like honeycomb pores compared with collagen gelled unconstrained. Finite element modeling predicts how collagen gel and scaffold mechanics couple in matching native heart muscle stiffness and anisotropy. PMID:23184695
Gravitational baryogenesis after anisotropic inflation
NASA Astrophysics Data System (ADS)
Fukushima, Mitsuhiro; Mizuno, Shuntaro; Maeda, Kei-ichi
2016-05-01
The gravitational baryogensis may not generate a sufficient baryon asymmetry in the standard thermal history of the Universe when we take into account the gravitino problem. Hence, it has been suggested that anisotropy of the Universe can enhance the generation of the baryon asymmetry through the increase of the time change of the Ricci scalar curvature. We study the gravitational baryogenesis in the presence of anisotropy, which is produced at the end of an anisotropic inflation. Although we confirm that the generated baryon asymmetry is enhanced compared with the original isotropic cosmological model, taking into account the constraint on the anisotropy by the recent CMB observations, we find that it is still difficult to obtain the observed baryon asymmetry only through the gravitational baryogenesis without suffering from the gravitino problem.
Anisotropic charged core envelope star
NASA Astrophysics Data System (ADS)
Mafa Takisa, P.; Maharaj, S. D.
2016-08-01
We study a charged compact object with anisotropic pressures in a core envelope setting. The equation of state is quadratic in the core and linear in the envelope. There is smooth matching between the three regions: the core, envelope and the Reissner-Nordström exterior. We show that the presence of the electric field affects the masses, radii and compactification factors of stellar objects with values which are in agreement with previous studies. We investigate in particular the effect of electric field on the physical features of the pulsar PSR J1614-2230 in the core envelope model. The gravitational potentials and the matter variables are well behaved within the stellar object. We demonstrate that the radius of the core and the envelope can vary by changing the parameters in the speed of sound.
Spatially anisotropic Heisenberg kagome antiferromagnet
NASA Astrophysics Data System (ADS)
Apel, W.; Yavors'kii, T.; Everts, H.-U.
2007-04-01
In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies (Hiroi et al 2001 J. Phys. Soc. Japan 70 3377; Fukaya et al 2003 Phys. Rev. Lett. 91 207603; Bert et al 2004 J. Phys.: Condens. Matter 16 S829; Bert et al 2005 Phys. Rev. Lett. 95 087203). It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the {\\mathrm {Sp}}(\\mathcal {N}) symmetric generalization of this model in the large \\mathcal {N} limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long-range order and a decoupled chain phase emerges.
Anisotropic scaling of magnetohydrodynamic turbulence.
Horbury, Timothy S; Forman, Miriam; Oughton, Sean
2008-10-24
We present a quantitative estimate of the anisotropic power and scaling of magnetic field fluctuations in inertial range magnetohydrodynamic turbulence, using a novel wavelet technique applied to spacecraft measurements in the solar wind. We show for the first time that, when the local magnetic field direction is parallel to the flow, the spacecraft-frame spectrum has a spectral index near 2. This can be interpreted as the signature of a population of fluctuations in field-parallel wave numbers with a k(-2)_(||) spectrum but is also consistent with the presence of a "critical balance" style turbulent cascade. We also find, in common with previous studies, that most of the power is contained in wave vectors at large angles to the local magnetic field and that this component of the turbulence has a spectral index of 5/3. PMID:18999759
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.
The Anisotropic Geometrodynamics For Cosmology
NASA Astrophysics Data System (ADS)
Siparov, Sergey V.
2009-05-01
The classical geometrodynamics (GRT) and its modern features based on the use of the Fridman-Robertson-Walker type metrics are still unable to explain several important issues of extragalactic observations like flat rotation curves of the spiral galaxies, Tully-Fisher law, globular clusters behavior in comparisson to that of the stars belonging to the galactic plane etc. The chalenging problem of the Universe expansion acceleration stemming from the supernovae observations demands the existence of the repulsion forces which brings one to the choice between the cosmological constant and some quintessence. The popular objects of discussion are now still dark (matter and energy), nevertheless, they are supposed to correspond to more than 95% of the Universe which seems to be far from satisfactory. According to the equivalence principle we can not experimentally distinguish between the inertial forces and the gravitational ones. Since there exist the inertial forces depending on velocity (Coriolis), it seems plausible to explore the velocity dependent gravitational forces. From the mathematical point of view it means that we should use the anisotropic metric. It immediately turns out that the expression for the Einstein-Hilbert action changes in a natural way - contrary to the cases of f(R)-theories, additional scalar fields, arbitrary MOND functions etc.. We use the linear approximation for the metric and derive the generalized geodesics and the equation for the gravity force that contains not only the Newton-Einstein term. The relation between the obtained results and those of Lense-Thirring approach are discussed. The resulting anisotropic geometrodynamics includes all the results of the GRT and is used to give the explanation to the problems mentioned above. One of the impressive consequences is the possibility to explain the observed Hubble red shift not by the Doppler effect as usually but by the gravitational red shift originating from the metric anisotropy.
Higher Order Lagrange Finite Elements In M3D
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.
Identifying Heterogeneous Anisotropic Properties in Cerebral Aneurysms: A Pointwise Approach
Zhao, Xuefeng; Raghavan, Madhavan L.; Lu, Jia
2014-01-01
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. PMID:20490886
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.
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.
Image Segmentation With Eigenfunctions of an Anisotropic Diffusion Operator.
Wang, Jingyue; Huang, Weizhang
2016-05-01
We propose the eigenvalue problem of an anisotropic diffusion operator for image segmentation. The diffusion matrix is defined based on the input image. The eigenfunctions and the projection of the input image in some eigenspace capture key features of the input image. An important property of the model is that for many input images, the first few eigenfunctions are close to being piecewise constant, which makes them useful as the basis for a variety of applications, such as image segmentation and edge detection. The eigenvalue problem is shown to be related to the algebraic eigenvalue problems resulting from several commonly used discrete spectral clustering models. The relation provides a better understanding and helps developing more efficient numerical implementation and rigorous numerical analysis for discrete spectral segmentation methods. The new continuous model is also different from energy-minimization methods such as active contour models in that no initial guess is required for in the current model. A numerical implementation based on a finite-element method with an anisotropic mesh adaptation strategy is presented. It is shown that the numerical scheme gives much more accurate results on eigenfunctions than uniform meshes. Several interesting features of the model are examined in numerical examples, and possible applications are discussed. PMID:26992021
Beam manipulating by metal-anisotropic-metal plasmonic lens
NASA Astrophysics Data System (ADS)
Bahramipanah, M.; Abrishamian, M. S.; Mirtaheri, S. A.
2012-10-01
Embedding anisotropic media in the slit region of a plasmonic nano-optic lens is proposed as a new method of actively modulating the output beam. The focal length can be controlled easily by exposing the plasmonic nano-optic lens to a constant external electric field. The physical principle of this phenomenon is evaluated from the phase of surface plasmon polaritons (SPPs) in the slits and the electro-optical effect of liquid crystals. Our numerical simulations using the finite-difference time-domain (FDTD) technique reveal that a large tuning range of the focal length up to 545 nm at the first communication window can be achieved. The special feature of the proposed structure gives it an opportunity to be used as an efficient element in ultrahigh nano-scale integrated photonic circuits for miniaturization and tuning purposes.
Glueball Spectrum and Matrix Elements on Anisotropic Lattices
Y. Chen; A. Alexandru; S.J. Dong; T. Draper; I. Horvath; F.X. Lee; K.F. Liu; N. Mathur; C. Morningstar; M. Peardon; S. Tamhankar; B.L. Young; J.B. Zhang
2006-01-01
The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in J/{psi} radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.
Anisotropic optical film embedded with cellulose nanowhisker.
Kim, Dah Hee; Song, Young Seok
2015-10-01
We investigated anisotropic optical behaviors of composite films embedded with CNWs. To control the orientation of CNWs, elongation was applied to the composite film. Morphological and mechanical analyses of the specimens were carried out to examine the influence of the applied extension. The CNWs were found to be aligned in the elongated direction, yielding remarkable anisotropic microstructure and optical properties. As the applied elongation and CNW loading increased, the resulting degree of polarization and birefringence increased due to increased interactions between the embedded particles. This study suggests a way to prepare an anisotropic optical component with nanoparticles of which the microstructures, such as orientation and filler content, can be controlled. PMID:26076646
Can cosmic parallax distinguish between anisotropic cosmologies?
Fontanini, Michele; West, Eric J.; Trodden, Mark
2009-12-15
In an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax--the relative angular motion of test galaxies over cosmic time. It was recently argued that the nonobservance of this effect in upcoming precision astrometry missions such as GAIA may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any observation of cosmic parallax would distinguish between different anisotropic evolutions.
Flow in horizontally anisotropic multilayered aquifer systems with leaky wells and aquitards
NASA Astrophysics Data System (ADS)
Cihan, Abdullah; Zhou, Quanlin; Birkholzer, Jens T.; Kraemer, Stephen R.
2014-01-01
Flow problems in an anisotropic domain can be transformed into ones in an equivalent isotropic domain by coordinate transformations. Once analytical solutions are obtained for the equivalent isotropic domain, they can be back transformed to the original anisotropic domain. The existing solutions presented by Cihan et al. (2011) for isotropic multilayered aquifer systems with alternating aquitards and multiple injection/pumping wells and leaky wells were modified to account for horizontal anisotropy in aquifers. The modified solutions for pressure buildup distribution and leakage rates through leaky wells can be used when the anisotropy direction and ratio (Kx/Ky) are assumed to be identical for all aquifers alternating with aquitards. However, for multilayered aquifers alternating with aquicludes, both the principal direction of the anisotropic horizontal conductivity and the anisotropy ratio can be different in each aquifer. With coordinate transformation, a circular well with finite radius becomes an ellipse, and thus in the transformed domain the head contours in the immediate vicinity of the well have elliptical shapes. Through a radial flow approximation around the finite radius wells, the elliptical well boundaries in the transformed domain are approximated by an effective well radius expression. The analytical solutions with the effective radius approximations were compared with exact solutions as well as a numerical solution for elliptic flow. The effective well radius approximation is sufficiently accurate to predict the head buildup at the well bore of the injection/pumping wells for moderately anisotropic systems (Kx/Ky≤25). The effective radius approximation gives satisfactory results for predicting head buildup at observation points and leakage through leaky wells away from the injection/pumping wells even for highly anisotropic aquifer systems >(Kx/Ky≤1000>).
Spatial interpolation approach based on IDW with anisotropic spatial structures
NASA Astrophysics Data System (ADS)
Li, Jia; Duan, Ping; Sheng, Yehua; Lv, Haiyang
2015-12-01
In many interpolation methods, with its simple interpolation principle, Inverse distance weighted (IDW) interpolation is one of the most common interpolation method. There are anisotropic spatial structures with actual geographical spatial phenomenon. When the IDW interpolation is used, anisotropic spatial structures should be considered. Geostatistical theory has a characteristics of exploring anisotropic spatial structures. In this paper, spatial interpolation approach based on IDW with anisotropic spatial structures is proposed. The DEM data is tested in this paper to prove reliability of the IDW interpolation considering anisotropic spatial structures. Experimental results show that IDW interpolation considering anisotropic spatial structures can improve interpolation precision when sampling data has anisotropic spatial structures feature.
Optical trapping of the anisotropic crystal nanorod.
Bareil, Paul B; Sheng, Yunlong
2015-05-18
We observed in the optical tweezers experiment that some anisotropic nanorod was stably trapped in an orientation tiled to the beam axis. We explain this trapping with the T-matrix calculation. As the vector spherical wave functions do not individually satisfy the anisotropic vector wave equation, we expand the incident and scattered fields in the isotropic buffer in terms of E→, and the internal field in the anisotropic nanoparticle in terms of D→, and use the boundary condition for the normal components of D→ to compute the T-matrix. We found that when the optical axes of an anisotropic nanorod are not aligned to the nanorod axis, the nanorod may be trapped stably at a tilted angle, under which the lateral torque equals to zero and the derivative of the torque is negative. PMID:26074566
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.
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.
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.
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.
Modelling Coulomb Collisions in Anisotropic Plasmas
NASA Astrophysics Data System (ADS)
Hellinger, P.; Travnicek, P. M.
2009-12-01
Collisional transport in anisotropic plasmas is investigated comparing the theoretical transport coefficients (Hellinger and Travnicek, 2009) for anisotropic particles with the results of the corresponding Langevin equation, obtained as a generalization of Manheimer et al. (1997). References: Hellinger, P., and P. M. Travnicek (2009), On Coulomb collisions in bi-Maxwellian plasmas, Phys. Plasmas, 16, 054501. Manheimer, W. M., M. Lampe and G. Joyce (1997), Langevin representation of Coulomb collisions in PIC simulations, J. Comput. Phys., 138, 563-584.
Overview of anisotropic flow measurements from ALICE
NASA Astrophysics Data System (ADS)
Zhou, You
2016-05-01
Anisotropic flow is an important observable to study the properties of the hot and dense matter, the Quark Gluon Plasma (QGP), created in heavy-ion collisions. Measurements of anisotropic flow for inclusive and identified charged hadrons are reported in Pb-Pb, p-Pb and pp collisions with the ALICE detector. The comparison of experimental measurements to various theoretical calculations are also presented in these proceedings.
Anisotropic System of Quasiparticles in Superfluid Helium
Adamenko, I.N.; Nemchenko, K.E.; Slipko, V.A.; Wyatt, A.F.G.
2006-02-17
The thermodynamic properties of anisotropic quasiparticle systems of He II are considered for all degrees of anisotropy. It is shown that the thermodynamic functions of a strongly anisotropic phonon-roton system are mainly determined by rotons at all temperatures. Analytical expressions for the roton thermodynamic functions are obtained for all degrees of anisotropy. The maximum anisotropy is limited by the criterion for thermodynamic stability, which is here derived for the whole temperature range.
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
Soft particles with anisotropic interactions
NASA Astrophysics Data System (ADS)
Schurtenberger, Peter
Responsive colloids such as thermo- or pH-sensitive microgels are ideal model systems to investigate the relationship between the nature of interparticle interactions and the plethora of self-assembled structures that can form in colloidal suspensions. They allow for a variation of the form, strength and range of the interaction potential almost at will. While microgels have extensively been used as model systems to investigate various condensed matter problems such as glass formation, jamming or crystallization, they can also be used to study systems with anisotropic interactions. Here we show results from a systematic investigation of the influence of softness and anisotropy on the structural and dynamic properties of strongly interacting suspensions. We focus first on ionic microgels. Due to their large number of internal counterions they possess very large polarisabilities, and we can thus use external electrical ac fields to generate large dipolar contributions to the interparticle interaction potential. This leads to a number of new crystal phases, and we can trigger crystal-crystal phase transitions through the appropriate choice of the field strength. We then show that this approach can be extended to more complex particle shapes in an attempt to copy nature's well documented success in fabricating complex nanostructures such as virus shells via self assembly. European Research Council (ERC-339678-COMPASS).
Modeling of anisotropic wound healing
NASA Astrophysics Data System (ADS)
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.; Menzel, A.
2015-06-01
Biological soft tissues exhibit non-linear complex properties, the quantification of which presents a challenge. Nevertheless, these properties, such as skin anisotropy, highly influence different processes that occur in soft tissues, for instance wound healing, and thus its correct identification and quantification is crucial to understand them. Experimental and computational works are required in order to find the most precise model to replicate the tissues' properties. In this work, we present a wound healing model focused on the proliferative stage that includes angiogenesis and wound contraction in three dimensions and which relies on the accurate representation of the mechanical behavior of the skin. Thus, an anisotropic hyperelastic model has been considered to analyze the effect of collagen fibers on the healing evolution of an ellipsoidal wound. The implemented model accounts for the contribution of the ground matrix and two mechanically equivalent families of fibers. Simulation results show the evolution of the cellular and chemical species in the wound and the wound volume evolution. Moreover, the local strain directions depend on the relative wound orientation with respect to the fibers.
Anisotropic diffusion-limited aggregation.
Popescu, M N; Hentschel, H G E; Family, F
2004-06-01
Using stochastic conformal mappings, we study the effects of anisotropic perturbations on diffusion-limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant measure on a unit circle. Here we map m preferred directions for growth to a distribution on the unit circle, which is a periodic function with m peaks in [-pi,pi) such that the angular width sigma of the peak defines the "strength" of anisotropy kappa= sigma(-1) along any of the m chosen directions. The two parameters (m,kappa) map out a parameter space of perturbations that allows a continuous transition from DLA (for small enough kappa ) to m needlelike fingers as kappa--> infinity. We show that at fixed m the effective fractal dimension of the clusters D(m,kappa) obtained from mass-radius scaling decreases with increasing kappa from D(DLA) approximately 1.71 to a value bounded from below by D(min) = 3 / 2. Scaling arguments suggest a specific form for the dependence of the fractal dimension D(m,kappa) on kappa for large kappa which compares favorably with numerical results. PMID:15244564
Electrostatic and Small-Signal Analysis of CMUTs With Circular and Square Anisotropic Plates.
Funding la Cour, Mette; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt; Thomsen, Erik Vilain
2015-08-01
Traditionally, capacitive micromachined ultrasonic transducers (CMUTs) are modeled using the isotropic plate equation, and this leads to deviations between analytical calculations and finite element modeling (FEM). In this paper, the deflection is calculated for both circular and square plates using the full anisotropic plate equation. It is shown that the anisotropic calculations match excellently with FEM, whereas an isotropic approach causes up to 10% deviations in deflection. For circular plates, an exact solution can be found. For square plates using the Galerkin method, and utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The theory of multilayer plates is also applied to the CMUT. The deflection of a square plate was measured on fabricated CMUTs using a white light interferometer. Fitting the plate parameter for the anisotropic calculated deflection to the measurement, a deviation of 0.07% is seen. Electrostatic and small-signal dynamic analysis are performed using energy considerations including anisotropy. The stable position, effective spring constant, pullin distance, and pull-in voltage are found for both circular and square anisotropic plates, and the pressure dependence is included by comparison with the corresponding analysis for a parallel plate. Measurements on fabricated devices with both circular and square plates subjected to increasing bias voltage are performed, and it is observed that the models including anisotropic effects are within the uncertainty interval of the measurements. Finally, a lumped element small-signal model for both circular and square anisotropic plates is derived to describe the dynamics of the CMUT. PMID:26492637
Azimuthally-dependent Finite Element Solution to the Cylindrical Resonator
NASA Technical Reports Server (NTRS)
Osegueda, R.; Pierluissi, J.; Gil, L.; Revilla, A.; Villalva, G.; Dick, G.; Wang, D. SantiagoR.
1994-01-01
The cylindrical cavity resonator loaded with an anisotropic dielectric is analyzed as a two-dimensional problem using a finite element approach that assumes sinusoidal dependence in azimuth. This methodology allows the first finite element treatment of the technically important case of a resonator containing a sapphire element with a cylindrically aligned c axis. Second order trial functions together with quadrilateral elements are adopted in the calculations. The method was validated through comparisons with the analytical solutions for the hollow metal cavity and a coaxial cavity, as well as through measurements on a shielded sapphire resonator.
Generalized Similarity in Finite Range Solar Wind Magnetohydrodynamic Turbulence
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.
Generalized similarity in finite range solar wind magnetohydrodynamic turbulence.
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. PMID:20366193
Instabilities of collisionless current sheets revisited: The role of anisotropic heating
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.
Stress distribution in a premolar 3D model with anisotropic and isotropic enamel.
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. PMID:25850984
Bianchi type-II models in the presence of perfect fluid and anisotropic dark energy
NASA Astrophysics Data System (ADS)
Kumar, Suresh; Akarsu, Özgür
2012-06-01
The spatially homogeneous but totally anisotropic and non-flat Bianchi type-II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical anisotropic fluid as the dark energy fluid. The Einstein field equations have been solved by applying two kinematical Ansätze: we have assumed the variation law for the mean Hubble parameter that yields a constant value of the deceleration parameter, and one of the components of the shear tensor has been considered proportional to the mean Hubble parameter. We have particularly dwelled on the accelerating models with non-divergent expansion anisotropy as the Universe evolves. Yielding the anisotropic pressure, the fluid we consider in the context of dark energy can produce results that can be produced in the presence of isotropic fluid in accordance with the ΛCDM cosmology. However, the derived model gives additional opportunities by being able to allow kinematics that cannot be produced in the presence of fluids that yield only isotropic pressure. We have obtained well-behaving cases where the anisotropy of the expansion and the anisotropy of the fluid converge to finite values (include zero) in the late Universe. We have also showed that, although the metric we consider is totally anisotropic, the anisotropy of the dark energy is constrained to be axially symmetric, as long as the overall energy momentum tensor possesses zero shear stress.
NASA Astrophysics Data System (ADS)
De Paoli, Marco; Zonta, Francesco; Soldati, Alfredo
2016-05-01
Solute convection in porous media at high Rayleigh-Darcy numbers has important fundamental features and may also bear implications for geological CO2 sequestration processes. With the aid of direct numerical simulations, we examine the role of anisotropic permeability on the distribution of solutal concentration in fluid saturated porous medium. Our computational analyses span over few decades of Rayleigh-Darcy number and confirm the linear scaling of Nusselt number that was previously found in the literature. In addition, we find that anisotropic permeability γ < 1, i.e., with vertical permeability smaller than horizontal permeability, effectively increases the Nusselt number compared with isotropic conditions. We link this seemingly counterintuitive effect with the occurring modifications to the flow topology in the anisotropic conditions. Finally, we use our data computed for the two-sided configuration (i.e., Dirichlet conditions on upper and lower boundaries) to examine the time evolution of solutal dynamics in the one-sided configuration, and we demonstrate that the finite-time (short-term) amount of CO2 that can be dissolved in anisotropic sedimentary rocks is much larger than in isotropic rocks.
Model-size reduction technique for the analysis of symmetric anisotropic structures
NASA Technical Reports Server (NTRS)
Noor, A. K.; Peters, J. M.
1985-01-01
A two-step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic (anisotropic) parts; and (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero nonorthotropic matrix and its various-order derivatives with respect to an anisotropic tracing parameter (identifying the nonorthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi-symmetric problems is discussed.
Dispersive Alfvén waves in a plasma with anisotropic superthermal particles
NASA Astrophysics Data System (ADS)
Liu, Y.; Wang, Y. F.; Hu, T. P.
2016-04-01
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.
Accelerating numerical modeling of wave propagation through 2-D anisotropic materials using OpenCL.
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. PMID:23290584
A microsphere-based remodelling formulation for anisotropic biological tissues.
Menzel, Andreas; Waffenschmidt, Tobias
2009-09-13
Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material's anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved. PMID:19657009
Application of Perona Malik anisotropic diffusion on digital radiographic image
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.
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.
Bauer, Carl A.; Werner, Gregory R.; Cary, John R.
2011-03-01
A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardson extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.
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.
Effective medium theory for anisotropic metamaterials
Zhang, Xiujuan; Wu, Ying
2015-01-01
Materials with anisotropic material parameters can be utilized to fabricate many fascinating devices, such as hyperlenses, metasolids, and one-way waveguides. In this study, we analyze the effects of geometric anisotropy on a two-dimensional metamaterial composed of a rectangular array of elliptic cylinders and derive an effective medium theory for such a metamaterial. We find that it is possible to obtain a closed-form analytical solution for the anisotropic effective medium parameters, provided the aspect ratio of the lattice and the eccentricity of the elliptic cylinder satisfy certain conditions. The derived effective medium theory not only recovers the well-known Maxwell-Garnett results in the quasi-static regime, but is also valid beyond the long-wavelength limit, where the wavelength in the host medium is comparable to the size of the lattice so that previous anisotropic effective medium theories fail. Such an advance greatly broadens the applicable realm of the effective medium theory and introduces many possibilities in the design of structures with desired anisotropic material characteristics. A real sample of a recently theoretically proposed anisotropic medium, with a near-zero index to control the flux, is achieved using the derived effective medium theory, and control of the electromagnetic waves in the sample is clearly demonstrated. PMID:25599847
Anisotropic nanomaterials: structure, growth, assembly, and functions
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
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.
Finite Volume Study of the Delta Magnetic Moments Using Dynamical Clover Fermions
Aubin, Christopher; Orginos, Konstantinos; Pascalutsa, Vladimir; Vanderhaeghen, Marc
2009-01-01
We calculate the magnetic dipole moment of the $\\Delta$ baryon using a background magnetic field on 2+1-flavors of clover fermions on anisotropic lattices. We focus on the finite volume effects that can be significant in background field studies, and thus we use two different spatial volumes in addition to several quark masses.
Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields
NASA Astrophysics Data System (ADS)
Hutt, Axel; Rougier, Nicolas
2010-11-01
The work studies the spatiotemporal activity propagation in a two-dimensional spatial system involving a finite transmission speed. We derive a numerical scheme in detail to integrate the corresponding evolution equation and validate the derived algorithm by a study of a spatially periodic system. Finally, the work demonstrates numerically transmission delay-induced breathers subjected to anisotropic external input.
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.
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.
Short-time dynamics of isotropic and anisotropic Bak-Sneppen model: extensive simulation results
NASA Astrophysics Data System (ADS)
Tirnakli, Ugur; Lyra, Marcelo L.
2004-12-01
In this work, the short-time dynamics of the isotropic and anisotropic versions of the Bak-Sneppen (BS) model has been investigated using the standard damage spreading technique. Since the system sizes attained in our simulations are larger than the ones employed in previous studies, our results for the dynamic scaling exponents are expected to be more accurate than the results of the existing literature. The obtained scaling exponents of both versions of the BS model are found to be greater than the ones given in previous works. These findings are in agreement with the recent claim of Cafiero et al. (Eur. Phys. J. B7 (1999) 505). Moreover, it is found that the short-time dynamics of the anisotropic model is only slightly affected by finite-size effects and the reported estimate of α≃0.53 can be considered as a good estimate of the true exponent in the thermodynamic limit.
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.
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.
Calculations of diffuser flows with an anisotropic K-epsilon model
NASA Astrophysics Data System (ADS)
Zhu, J.; Shih, T.-H.
1995-10-01
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.
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.
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.
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.
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.
Energy shift due to anisotropic blackbody radiation
NASA Astrophysics Data System (ADS)
Flambaum, V. V.; Porsev, S. G.; Safronova, M. S.
2016-02-01
In many applications a source of the blackbody radiation (BBR) can be highly anisotropic. This leads to the BBR shift that depends on tensor polarizability and on the projection of the total angular momentum of ions and atoms in a trap. We derived a formula for the anisotropic BBR shift and performed numerical calculations of this effect for Ca+and Yb+ transitions of experimental interest. These ions were used for a design of high-precision atomic clocks, fundamental physics tests such as the search for the Lorentz invariance violation and space-time variation of the fundamental constants, and quantum information. Anisotropic BBR shift may be one of the major systematic effects in these experiments.
Azimuthally Anisotropic 3D Velocity Continuation
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
Magnetization of anisotropic Type II superconductors
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.
Gravitational stresses in anisotropic rock masses
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.
Foam front propagation in anisotropic oil reservoirs.
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. PMID:27090239
Bouncing anisotropic universes with varying constants
NASA Astrophysics Data System (ADS)
Barrow, John D.; Sloan, David
2013-07-01
We examine the evolution of a closed, homogeneous and anisotropic cosmology subject to a variation of the fine structure “constant” α within the context of the theory introduced by Bekenstein and Sandvik et al. which generalizes Maxwell’s equations and general relativity The variation of α permits an effective ghost scalar field, whose negative energy density becomes dominant at small length scales, leading to a bouncing cosmology. A thermodynamically motivated coupling that describes energy exchange between the effective ghost field and the radiation field leads to an expanding, isotropizing sequence of bounces. In the absence of entropy production, we also find solutions with stable anisotropic oscillations around a static universe.
Inhomogeneous and anisotropic Universe and apparent acceleration
NASA Astrophysics Data System (ADS)
Fanizza, G.; Tedesco, L.
2015-01-01
In this paper, we introduce a Lemaître-Tolman-Bondi (LTB) Bianchi type I (plane symmetric) model of the Universe. We study and solve Einstein field equations. We investigate the effects of such a model of the Universe; in particular, these results are important in understanding the effect of the combined presence of an inhomogeneous and anisotropic universe. The observational magnitude-redshift data deviated from the UNION 2 catalog have been analyzed in the framework of this LTB anisotropic universe, and the fit has been achieved without the inclusion of any dark energy.
Evolution of multidimensional flat anisotropic cosmological models
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.
Anisotropic Gold Nanocrystals:. Synthesis and Characterization
NASA Astrophysics Data System (ADS)
Stiufiuc, R.; Toderas, F.; Iosin, M.; Stiufiuc, G.
In this letter we report on successful preparation and characterization of anisotropic gold nanocrystals bio-synthesized by reduction of aqueous chloroaurate ions in pelargonium plant extract. The nanocrystals have been characterized by means of Transmission Electron Microscopy (TEM), UV-VIS absorption spectroscopy and tapping mode atomic force microscopy (TM-AFM). Using these investigation techniques, the successful formation of anisotropic single nanocrystals with the preferential growth direction along the gold (111) plane has been confirmed. The high detail phase images could give us an explanation concerning the growth mechanism of the nanocrystals.
Controllable underwater anisotropic oil-wetting
Yong, Jiale; Chen, Feng Yang, Qing; Farooq, Umar; Bian, Hao; Du, Guangqing; Hou, Xun
2014-08-18
This Letter demonstrates a simple method to achieve underwater anisotropic oil-wetting using silicon surfaces with a microgroove array produced by femtosecond laser ablation. The oil contact angles along the direction perpendicular to the grooves are consistently larger than those parallel to the microgroove arrays in water because the oil droplet is restricted by the energy barrier that exists between the non-irradiated domain and the trapped water in the laser-ablated microgrooves. This underwater anisotropic oil-wetting is able to be controlled, and the anisotropy can be tuned from 0° to ∼20° by adjusting the period of the microgroove arrays.
Optical Activity of Anisotropic Achiral Surfaces
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.}
Directional wetting in anisotropic inverse opals.
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. PMID:24941308
Ballooning stability of anisotropic, rotating plasmas
NASA Technical Reports Server (NTRS)
Wang, X.-H.; Bhattacharjee, A.
1990-01-01
The linearized equation of motion is given in a Lagrangian representation for a rotating plasma with anisotropic pressure. A WKB theory is developed for large-n ballooning modes in an axisymmetric configuration with field-aligned and rigid toroidal flows. In the presence of field-aligned flows, it is shown that a resonance occurs which is strongly suggestive of a generalized mirror instability. In the presence of toroidal rotation, a possible stabilizing effect is identified for P(normal) greater than P(parallel). Finally, as a special case of the theory, the necessary and sufficient conditions for stability in a static, anisotropic plasma are obtained.
Anisotropic Peridotite Rheology and Regional Upper Mantle Flow Patterns
NASA Astrophysics Data System (ADS)
Blackman, D. K.; Boyce, D.; Dawson, P.; Castelnau, O.
2014-12-01
We investigate the rheologic impact of strong lattice preferred orientation (LPO), such as develops due to plate-driven shear, on the pattern of upper mantle flow near plate boundaries. We use finite element models to simulate a regional system of mantle flow, that includes LPO evolution in olivine polycrystal aggregates tracked along flow paths and anisotropic viscosity tensors based on the LPO. Our first, loosely coupled approach begins with a flow field based on a scalar viscosity. The results are postprocessed to compute LPO by integration along streamlines, and an anisotropic viscosity tensor field is derived from LPO. A new flow field is then computed based on the viscosity tensor field. For this case, the predicted flow field differed in a modest but geologically relevant way from the isotropic case. In preparation for incorporating the LPO and effective viscosity calculation directly into the flow code, we have been testing this step separately to assess the sensitivity of the computed tensor to specified deformation parameters. New work explores a power law stress:strain rate relation for the LPO development, upon which the aggregate's effective viscosity tensor depends. The pattern and amplitude of predicted deviation from isotropic viscosity are stronger than for the previously assumed linear stress:strain rate case, as expected. Initial runs that employ the power law viscosity tensor in updated flow calculations are underway at the time of this writing. In addition to the stress exponent for LPO and the resulting viscosity tensor, flow model parameters that notably impact the predictions include the specified stiffening as asthenosphere cools to lithospheric temperatures and mesh resolution within the axial and the base of lithosphere regions. We will present results for subaxial oceanic spreading center flow and report the outcomes of model parameter testing.
Anisotropic permeabilities evolution of reservoir rocks under pressure
NASA Astrophysics Data System (ADS)
Jeremie, D.; Nicolas, G.; Alexandre, D.; Olga, V.
2006-12-01
The aim of our study is to measure, to model and to forecast the evolutions of porosity and permeability under anisotropic stresses representative of hydrocarbon reservoir conditions. Reservoir field exploitation induces a decrease of the pore pressure, hence modifying the effective stress-state at the reservoir scale. To optimize production and recovery rates of the reservoir it is of fundamental interest to understand all the physical and mechanical evolutions of the host-rock and their influence on transport properties. In the case of weakly consolidated reservoirs the variations of stresses are modest, yet they can induce significant porosity and permeability changes due to their high compressibility. In the case of deeply buried and consolidated reservoirs the stress variations might be pronounced enough to influence flow properties as well. Because of reservoir boundaries conditions, the fluid pressure drop influences essentially the vertical stress. The recovery rate is a function of horizontal permeability. In order to understand how the anisotropic stress-states induced during production may influence the transport properties experiments must be designed to measure simultaneously both horizontal and vertical permeabilities under deviatoric stresses. For this purpose we developed a specific triaxial cell operating in conditions representative of the field conditions. Preliminary results obtained with low permeability sandstones allowed a coupled observation of deformation and directional permeability evolution. Because of complex geometrical conditions the results required numerical interpretations. A finite-element inversion of our data allowed the determination of the complete permeability tensor. In addition the study aims on the identification of the microphysical mechanics that induce the pore scale microstructural evolution, which is ultimately responsible of the permeability decrease. For this purpose we used synthetic hot-pressed calcite
Charged anisotropic matter with linear or nonlinear equation of state
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.
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.
δN formalism in anisotropic inflation and large anisotropic bispectrum and trispectrum
Abolhasani, Ali Akbar; Emami, Razieh; Firouzjaee, Javad T.; Firouzjahi, Hassan E-mail: emami@ipm.ir E-mail: firouz@mail.ipm.ir
2013-08-01
We present the consistent δN formalism for curvature perturbations in anisotropic cosmological backgrounds. We employ our δN formalism to calculate the power spectrum, the bispectrum and the trispectrum in models of anisotropic inflation with the background gauge fields in Bianchi I universe. Our results coincide exactly with the recent results obtained from in-in formalism. To satisfy the observational constraints the anisotropies generated on power spectrum are kept small but large orientation-dependent non-Gaussianities can be generated. We study the Suyama-Yamaguchi inequality for the amplitudes of the bispectrum and the trispectrum in the presence of anisotropic shapes.
Bad behavior of Godunov mixed methods for strongly anisotropic advection-dispersion equations
NASA Astrophysics Data System (ADS)
Mazzia, Annamaria; Manzini, Gianmarco; Putti, Mario
2011-09-01
We study the performance of Godunov mixed methods, which combine a mixed-hybrid finite element solver and a Godunov-like shock-capturing solver, for the numerical treatment of the advection-dispersion equation with strong anisotropic tensor coefficients. It turns out that a mesh locking phenomenon may cause ill-conditioning and reduce the accuracy of the numerical approximation especially on coarse meshes. This problem may be partially alleviated by substituting the mixed-hybrid finite element solver used in the discretization of the dispersive (diffusive) term with a linear Galerkin finite element solver, which does not display such a strong ill conditioning. To illustrate the different mechanisms that come into play, we investigate the spectral properties of such numerical discretizations when applied to a strongly anisotropic diffusive term on a small regular mesh. A thorough comparison of the stiffness matrix eigenvalues reveals that the accuracy loss of the Godunov mixed method is a structural feature of the mixed-hybrid method. In fact, the varied response of the two methods is due to the different way the smallest and largest eigenvalues of the dispersion (diffusion) tensor influence the diagonal and off-diagonal terms of the final stiffness matrix. One and two dimensional test cases support our findings.
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 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
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.
Data-driven imaging in anisotropic media
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.
On anisotropic black branes with Lifshitz scaling
NASA Astrophysics Data System (ADS)
Roychowdhury, Dibakar
2016-08-01
In this paper, based on the method of scalar perturbations, we construct the anisotropic charged Lifshitz background perturbatively up to leading order in the anisotropy. We perform our analysis both in the extremal as well as in the non-extremal limit. Finally, we probe the so called superfluid phase of the boundary theory and explore the effects of anisotropy on the superconducting condensate.
Wave simulation in anisotropic, saturated porous media
Carcione, J.M.
1995-12-31
Porous media are anisotropic due to bedding, compaction and the presence of aligned microcracks and fractures. Here, I assume that the skeleton (and not the solid itself) is anisotropic. The rheological model also includes anisotropic tortuosity and permeability. The poroelastic equations are based on a transversely isotropic extension of Biot`s theory, and the problem is of plane strain type, i.e., two dimensional, and describes qP - qS propagation. In the high-frequency case, the (two) viscodynamic operators are approximated by Zener relaxation functions, that allow a close differential formulation of Biot`s equation of motion. The propagation is solved numerically, with a direct grid method and a time splitting integration algorithm, allowing the solution of the stiff part of the differential equations in closed analytical form. Snapshots in sandstone show that three waves propagate when the fluid is ideal (zero viscosity): the fast compressional and shear waves and the slow compressional wave. Anisotropic tortuosity has not a major influence on the faster modes, but significantly affects the slow wavefront. On the other hand, when the fluid is viscous, the slow wave becomes diffusive and appears as a static mode at the source location.
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.
Highly Anisotropic, Highly Transparent Wood Composites.
Zhu, Mingwei; Song, Jianwei; Li, Tian; Gong, Amy; Wang, Yanbin; Dai, Jiaqi; Yao, Yonggang; Luo, Wei; Henderson, Doug; Hu, Liangbing
2016-07-01
For the first time, two types of highly anisotropic, highly transparent wood composites are demonstrated by taking advantage of the macro-structures in original wood. These wood composites are highly transparent with a total transmittance up to 90% but exhibit dramatically different optical and mechanical properties. PMID:27147136
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
Anisotropic Alfven-ballooning modes in Earth's magnetosphere
NASA Technical Reports Server (NTRS)
Chan, Anthony A.; Xia, Mengfen; Chen, Liu
1994-01-01
We have carried out a theoretical analysis of the stability and parallel structure of coupled shear Alfven and slow magnetosonic waves in Earth's inner magnetopause (i.e., at equatorial distances between about five and ten Earth radii) including effects of finite 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: (1) The field line eigenfrequency can be significantly lowered by finite pressure effects. (2) 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 as a result of increased pressure, especially when P(sub perpendicular to) is greater than P(sub parallel) (here P(sub perpendicular to) and P(sub parallel) are the perpendicular and parallel plasma pressure). (3) For the isotropic (P(sub parallel) = P(sub perpendicular to) = P) case ballooning instability can occur when the ratio of the plasma presure to the magnetic pressure, beta = P/(B squared/8 pi), exceeds a critical value beta(sup B)(sub 0) is approximately equal to 3.5 at the equator. (4) Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field line bending stabilization when P(sub parallel) is greater than P(sub perpendicular to) or due to increased ballooning-mirror destabilization when P(sub perpendicular to) is greater than P(sub parallel). (5) We use a beta-delta 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(sub perpendicular to)) is an
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.
NASA Astrophysics Data System (ADS)
Liu, B.; Arsenlis, A.; Aubry, S.
2016-06-01
Driven by the growing interest in numerical simulations of dislocation–interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple dislocation dynamics with a finite element or boundary element solver. The dislocation stress fields in elastically anisotropic media are made analytically accessible through the spherical harmonics expansion of the derivative of Green’s function, and analytical expressions for the forces on interface elements are derived by analytically integrating the spherical harmonics series recursively. Compared with numerical integration by Gaussian quadrature, the newly developed analytical algorithm for interface traction integration is highly beneficial in terms of both computation precision and speed.
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.
NASA Astrophysics Data System (ADS)
Poon, H.; Ahmad, M. F.
This study presents an effective and robust time integration procedure for general anisotropic, thermal rheologically simple viscoelasticity, that is suitable for implementation in a broad spectrum of general purpose nonlinear finite element programs. It features a judicious choice of state variables which record the extent of inelastic flow (creep), a stable backward Euler integration step, and a consistent tangent operator. Numerical examples involving homogeneous stress states such as uniaxial tension and simple shear, and non-uniform stress states such as a beam under tip load, were carried out by incorporating the present scheme into a general purpose FEM package. Excellent agreement with analytical results is observed.
Casimir-Polder force between anisotropic nanoparticles and gently curved surfaces
NASA Astrophysics Data System (ADS)
Bimonte, Giuseppe; Emig, Thorsten; Kardar, Mehran
2015-07-01
The Casimir-Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO2 and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.
Arkadan, A.A.; Russell, A.A. . Electrical and Computer Engineering Dept.)
1999-05-01
An indirectly coupled State Space-Finite Element (ICSS-FE) model of Axially Laminated Anisotropic (ALA) Synchronous Reluctance Motor (SynRM) drive systems is used to evaluate the impact of converter excitation on the machine performance characteristics., The model utilizes an iterative approach which includes the full impact of nonlinearities on the machine magnetic circuit, and which results in the nonsinusoidal flux waveforms in the different parts of the machine. The modeling approach is applied to a prototype ALA SynRM designed for use in hybrid vehicle applications.
Defect detection in aluminum laser welds using an anisotropic magnetoresistive sensor array
Allweins, K.; Kreutzbruck, M. von; Gierelt, G.
2005-05-15
For the detection of defects in aluminum laser welds an anisotropic magnetoresistive (AMR) sensor array was implemented in an eddy current testing system. The reliability of weld testing is strongly influenced by the texture of the laser weld whose field response significantly superimposes the defect's magnetic signature. A finite-element model was used to determine the influence of the weld's topology on the detection of defects such as porosities and inclusions hosted in the aluminum matrix. When using an AMR sensor array with field sensitivity of better than 1 nT/{radical}Hz defects with a radius smaller than 100 {mu}m could be detected and classified.
Collective Excitations of Bose-Einstein Condensates In Isotropic and Slightly Anisotropic Traps
NASA Astrophysics Data System (ADS)
Barentine, Andrew; Lobser, Dan; Lewandowski, Heather; Cornell, Eric
2014-05-01
Boltzmann proved that the monopole mode of a thermal gas in an isotropic, harmonic and 3D trap is undamped. Bose-Einstein Condensates (BECs) are not classical gases and their weakly interacting nature causes damping at finite temperature in a 3D monopole mode. The large parameter space of the TOP (Time-averaged Orbiting Potential) trap allows for precise control of the trap geometry. Exciting a monopole mode in a BEC as well as its canonical thermal cloud in the hydrodynamic regime will allow us to investigate damping effects in isotropic and slightly anisotropic traps. Funding : NSF,NIST,ONR
Durlofsky, L.J. )
1993-04-01
Triangle based discretization techniques offer great advantages relative to standard finite difference methods for the modeling of flow through geometrically complex geological features. The purpose of this paper is to develop and apply a triangle based method for the modeling of two phase flow through porous formations. The formulation includes the effects of gravity, compressibility, and capillary pressure. The technique entails a triangle based mixed finite element method for solution of the variable coefficient, parabolic pressure equation, and a second-order TVD-type (total variation diminishing) finite volume scheme for solution of the essentially hyperbolic saturation equation. The method is applied to a variety of example problems and is shown to perform very well on problems involving geometric complexity coupled with heterogeneous, generally anisotropic permeability descriptions. 20 refs., 20 figs.
QUARKONIUM AT FINITE TEMPERATURE.
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.
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
Homogenization of Periodic Masonry Using Self-Consistent Scheme and Finite Element Method
NASA Astrophysics Data System (ADS)
Kumar, Nitin; Lambadi, Harish; Pandey, Manoj; Rajagopal, Amirtham
2016-01-01
Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavior of the masonry, through rigorous application of the homogenization theory in one step and through a full three-dimensional behavior. We have considered the periodic Eshelby self-consistent method and the finite element method. Two representative unit cells that represent the microstructure of the masonry wall exactly are considered for calibration and numerical application of the theory.