WANG, LIANG; Wu, Zheyang; Yang, Chun; Zheng, Jie; Bach, Richard; Muccigrosso, David; Billiar, Kristen; Maehara, Akiko; Mintz, Gary S; Tang, Dalin
2014-01-01
Atherosclerotic plaque progression is believed to be associated with mechanical stress conditions. Patient follow-up in vivo intravascular ultrasound coronary plaque data were acquired to construct fluid-structure interaction (FSI) models with cyclic bending to obtain flow wall shear stress (WSS), plaque wall stress (PWS) and strain (PWSn) data and investigate correlations between plaque progression measured by wall thickness increase (WTI), cap thickness increase (CTI), lipid depth increase ...
Applicability of the Godunov's method for fundamental four-equations FSI model
The present paper addresses mathematical and numerical model needed for description of the axial pipe movement induced with transient fluid motion. This phenomenon is also known as Fluid-Structure Interaction (FSI). Standard Skalak's four-equation model was applied and solved with improved second-order accurate numerical method that is based on Godounov's upwind first-order accurate method. Special attention was made to applicability of the numerical method for solution of the mathematical model. The method was verified using standard Delft Hydraulics Benchmark Problem A, and the preliminary results are very promising. (author)
Three-band decomposition analysis in multiscale FSI models of abdominal aortic aneurysms
Nestola, Maria G. C.; Gizzi, Alessio; Cherubini, Christian; Filippi, Simonetta
2016-07-01
Computational modeling plays an important role in biology and medicine to assess the effects of hemodynamic alterations in the onset and development of vascular pathologies. Synthetic analytic indices are of primary importance for a reliable and effective a priori identification of the risk. In this scenario, we propose a multiscale fluid-structure interaction (FSI) modeling approach of hemodynamic flows, extending the recently introduced three-band decomposition (TBD) analysis for moving domains. A quantitative comparison is performed with respect to the most common hemodynamic risk indicators in a systematic manner. We demonstrate the reliability of the TBD methodology also for deformable domains by assuming a hyperelastic formulation of the arterial wall and a Newtonian approximation of the blood flow. Numerical simulations are performed for physiologic and pathologic axially symmetric geometry models with particular attention to abdominal aortic aneurysms (AAAs). Risk assessment, limitations and perspectives are finally discussed.
Model anisotropic quantum Hall states
Qiu, R. -Z.; Haldane, F.D.M.; Wan, Xin; Yang, Kun; Yi, Su
2012-01-01
Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body Hamiltonians, and explicitly illustrate the existence of geometric degrees of in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeri...
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.
Model for Anisotropic Directed Percolation
Nguyen, V. Lien; Canessa, Enrique
1997-01-01
We propose a simulation model to study the properties of directed percolation in two-dimensional (2D) anisotropic random media. The degree of anisotropy in the model is given by the ratio $\\mu$ between the axes of a semi-ellipse enclosing the bonds that promote percolation in one direction. At percolation, this simple model shows that the average number of bonds per site in 2D is an invariant equal to 2.8 independently of $\\mu$. This result suggests that Sinai's theorem proposed originally fo...
New charged anisotropic compact models
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.
Simulation a Disposable mass flow meter by an advanced FSI Modeling and Finite Element Analysis.
zadeh, Siavash Hooshmand
2014-01-01
Abstract -In this thesis a design of a Coriolis mass flow-meter is chosen by considering all advantages and disadvantages and the project requirements. The chosen geometry is imported into COMSOL, because modelling is implemented by FEM and two different physics should be coupled. To consider both applications of the device include measuring density and flow rate, modeling is divided into two parts: Coriolis density meter and Coriolis mass flow-meter. Both applications are based on Fluid Stru...
ITM-Based FSI-Models for Rooms with Absorptive Boundaries
Buchschmid, Martin
2012-01-01
A method for room acoustical simulations has been developed in order to compute the sound field in acoustic cavities with compound absorbers, mounted at the walls. To reduce the number of degrees of freedom and therefore the numerical effort, a model reduction method, based on a Component Mode Synthesis (CMS), is applied. Macrostructures are assembled out of single substructures applying shape functions at the interfaces. These substructures contain acoustic components like porous absorbers o...
Warm anisotropic inflationary universe model
Sharif, M.; Saleem, Rabia [University of the Punjab, Department of Mathematics, Lahore (Pakistan)
2014-02-15
This paper is devoted to the study of warm inflation using vector fields in the background of a locally rotationally symmetric Bianchi type I model of the universe. We formulate the field equations, and slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) in the slow-roll approximation. We evaluate all these parameters in terms of the directional Hubble parameter during the intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of the scalar field as well as a constant. In each case, we calculate the observational parameter of interest, i.e., the tensor-scalar ratio in terms of the inflaton. The graphical behavior of these parameters shows that the anisotropic model is also compatible with WMAP7 and the Planck observational data. (orig.)
Warm Anisotropic Inflationary Universe Model
Sharif, M
2014-01-01
This paper is devoted to study the warm inflation using vector fields in the background of locally rotationally symmetric Bianchi type I universe model. We formulate the field equations, slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) under slow-roll approximation. We evaluate all these parameters in terms of directional Hubble parameter during intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of scalar field as well as a constant. In each case, we calculate the observational parameter of interest, i.e., tensor-scalar ratio in terms of inflation. The graphical behavior of these parameters shows that the anisotropic model is also compatible with WMAP7 and Planck observational data.
Ebna Hai, Bhuiyan Shameem Mahmood; Bause, Markus
2014-01-01
Advanced composite materials such as Carbon Fibre Reinforced Polymers (CFRP) tend to be used in aerospace industry to keep the weight at its minimum and yet retain a great strength. CFRP have a strong, stiff fibres in a matrix. The resulting material is very strong as it has the best strength to weight ratio of all construction materials. However, aircraft structures such as wings can break due to Fluid-Structure Interaction (FSI) oscillations or material fatigue. Material inspection by piezo...
Anisotropic invariance in minisuperspace models
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.
Khe, A. K.; Cherevko, A. A.; Chupakhin, A. P.; Bobkova, M. S.; Krivoshapkin, A. L.; Orlov, K. Yu
2016-06-01
In this paper a computer simulation of a blood flow in cerebral vessels with a giant saccular aneurysm at the bifurcation of the basilar artery is performed. The modelling is based on patient-specific clinical data (both flow domain geometry and boundary conditions for the inlets and outlets). The hydrodynamic and mechanical parameters are calculated in the frameworks of three models: rigid-wall assumption, one-way FSI approach, and full (two-way) hydroelastic model. A comparison of the numerical solutions shows that mutual fluid- solid interaction can result in qualitative changes in the structure of the fluid flow. Other characteristics of the flow (pressure, stress, strain and displacement) qualitatively agree with each other in different approaches. However, the quantitative comparison shows that accounting for the flow-vessel interaction, in general, decreases the absolute values of these parameters. Solving of the hydroelasticity problem gives a more detailed solution at a cost of highly increased computational time.
Evolution of multidimensional flat anisotropic cosmological models
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
Bond diluted anisotropic quantum Heisenberg model
Akıncı, Ümit
2013-01-01
Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigat...
Bond diluted anisotropic quantum Heisenberg model
Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found. - Highlights: • Anisotropic quantum Heisenberg model with bond dilution investigated. • Bond percolation threshold values given for 2D and 3D lattices in isotropic case. • Phase diagrams and ground state magnetizations investigated in detail. • Variation of the bond percolation threshold values with anisotropy determined
Isotropic and anisotropic pointing models
Pál, András; Mészáros, László; Mező, György
2015-01-01
This paper describes an alternative approach for generating pointing models for telescopes equipped with serial kinematics, esp. equatorial or alt-az mounts. Our model construction does not exploit any assumption for the underlying physical constraints of the mount, however, one can assign various effects to the respective components of the equations. In order to recover the pointing model parameters, classical linear least squares fitting procedures can be applied. This parameterization also lacks any kind of parametric singularity. We demonstrate the efficiency of this type of model on real measurements with meter-class telescopes where the results provide a root mean square accuracy of 1.5-2 arcseconds.
Some analytical models of anisotropic strange stars
Murad, Mohammad Hassan
2016-01-01
Over the years of the concept of local isotropy has become a too stringent condition in modeling relativistic self-gravitating objects. Taking local anisotropy into consideration, in this work, some analytical models of relativistic anisotropic charged strange stars have been developed. The Einstein-Maxwell gravitational field equations have been solved with a particular form of one of the metric potentials. The radial pressure and the energy density have been assumed to follow the usual linear equation of state of strange quark matter, the MIT bag model.
Generalized model for anisotropic compact stars
Maurya, S K; Ray, Saibal; Deb, Debabrata
2016-01-01
In the present investigation an exact generalized model for anisotropic compact stars of embedding class one is sought for under general relativistic background. The generic solutions are verified by exploring different physical aspects, viz. energy conditions, mass-radius relation, stability of the models, in connection to their validity. It is observed that the model present here for compact stars is compatible with all these physical tests and thus physically acceptable as far as the compact star candidates $RXJ~1856-37$, $SAX~J~1808.4-3658~(SS1)$ and $SAX~J~1808.4-3658~(SS2)$ are concerned.
Czechowicz, K.; Badur, J.; Narkiewicz, K.
2014-08-01
Flow parameters can induce pathological changes in the arteries. We propose a method to asses those parameters using a 3D computer model of the flow in the Common Carotid Artery. Input data was acquired using an automatic 2D ultrasound wall tracking system. This data has been used to generate a 3D geometry of the artery. The diameter and wall thickness have been assessed individually for every patient, but the artery has been taken as a 75mm straight tube. The Young's modulus for the arterial walls was calculated using the pulse pressure, diastolic (minimal) diameter and wall thickness (IMT). Blood flow was derived from the pressure waveform using a 2-parameter Windkessel model. The blood is assumed to be non-Newtonian. The computational models were generated and calculated using commercial code. The coupling method required the use of Arbitrary Lagrangian-Euler formulation to solve Navier-Stokes and Navier-Lame equations in a moving domain. The calculations showed that the distention of the walls in the model is not significantly different from the measurements. Results from the model have been used to locate additional risk factors, such as wall shear stress or circumferential stress, that may predict adverse hypertension complications.
Flow parameters can induce pathological changes in the arteries. We propose a method to asses those parameters using a 3D computer model of the flow in the Common Carotid Artery. Input data was acquired using an automatic 2D ultrasound wall tracking system. This data has been used to generate a 3D geometry of the artery. The diameter and wall thickness have been assessed individually for every patient, but the artery has been taken as a 75mm straight tube. The Young's modulus for the arterial walls was calculated using the pulse pressure, diastolic (minimal) diameter and wall thickness (IMT). Blood flow was derived from the pressure waveform using a 2-parameter Windkessel model. The blood is assumed to be non-Newtonian. The computational models were generated and calculated using commercial code. The coupling method required the use of Arbitrary Lagrangian-Euler formulation to solve Navier-Stokes and Navier-Lame equations in a moving domain. The calculations showed that the distention of the walls in the model is not significantly different from the measurements. Results from the model have been used to locate additional risk factors, such as wall shear stress or circumferential stress, that may predict adverse hypertension complications.
A model for anisotropic strange stars
Deb, Debabrata; Ray, Saibal; Rahaman, Farook; Guha, B K
2016-01-01
We attempt to find a singularity free interior solution for a neutral and static stellar model. We consider that (i) the star is made up of anisotropic fluid and (ii) the MIT bag model can be used. The total system is defined by assuming the density profile given by Mak and Harko \\cite{Mak2002}, which satisfies all the physical conditions of a stellar system and is stable by nature. We find that those stellar systems which obey such a non-linear density function must have maximum anisotropy at the surface. We also perform several tests for physical features of the proposed model and show that these are mostly acceptable within certain range. As a special mention, from our investigation we find that the maximum mass and radius of the quark star are $11.811 km$ and $3.53 {M}_{\\odot}$ respectively.
Effective orthorhombic anisotropic models for wavefield extrapolation
Ibanez-Jacome, W.
2014-07-18
Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth\\'s subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the firstarrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.
Relativistic modelling of stable anisotropic super-dense star
Maurya, S K; Jasim, M K
2015-01-01
In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al.[1] algorithm. The anisotropic fluid spheres so obtained join continuously to Schwarzschild exterior solution across the pressure free boundary.It is observed that most of the new anisotropic solutions are well behaved and utilized to construct the super-dense star models such as neutron star and pulsars.
Modeling and Measurements of CMUTs with Square Anisotropic Plates
la Cour, Mette Funding; Christiansen, Thomas Lehrmann; Dahl-Petersen, Christian;
2013-01-01
The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic ...
Critical exponents of the anisotropic Bak-Sneppen model
Maslov, Sergei; Rios, Paolo De Los; Marsili, Matteo; Zhang, Yi-Cheng
1998-01-01
We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then det...
Modelling anisotropic damage and permeability of mortar under dynamic loads
Chen, W.; MAUREL, O.; REESS, T.; MATALLAH, M.; FERRON, A.; C. La Borderie; G. Pijaudier-Cabot
2011-01-01
This paper deals with the development of a model for concrete subjected to dynamic loads. Shock waves are generated by Pulsed Arc Electro-hydraulic Discharges (PAED) in water and applied to mortar samples. A diphasic model (liquid water and vapour) is implemented in order to describe the electrical discharge and the propagation of shock waves in water. An anisotropic damage model is devised, which takes account of the strain rate effect and the crack closure effect. Coupling between anisotrop...
Anisotropic Cosmological Model with Variable G and Lambda
Tripathy, S K; Routray, T R
2015-01-01
Anisotropic Bianchi-III cosmological model is investigated with variable gravitational and cosmological constants in the framework of Einstein's general relativity. The shear scalar is considered to be proportional to the expansion scalar. The dynamics of the anisotropic universe with variable G and Lambda are discussed. Without assuming any specific forms for Lambda and the metric potentials, we have tried to extract the time variation of G and Lambda from the anisotropic model. The extracted G and Lambda are in conformity with the present day observation. Basing upon the observational limits, the behaviour and range of the effective equation of state parameter are discussed.
Modelling of anisotropic compact star of emending class one
Bhar, Piyali; Manna, Tuhina
2016-01-01
In the present article, we have constructed static anisotropic compact star models of Einstein field equations for the spherical symmetric metric of embedding class one. By assuming the particular form of metric function $\
Anisotropic static solutions in modelling highly compact bodies
M Chaisi; S D Maharaj
2006-03-01
Einstein field equations for static anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case ∝ -2 for the energy density which arises in many astrophysical applications. In the second class the singularity at the centre of the star is not present in the energy density
Modeling operations back extrusion billets thick-walled anisotropic
ПЛАТОНОВ В.И.; Яковлев, С. С.
2014-01-01
The mathematical model is an inverse extrusion thick-walled tube blanks of material having anisotropic mechanical properties cylindrical. Relations are given to assess the kinematics of course materials la, stress and strain states, power operation modes reverse extrusion. The results of theoretical investigations of power modes. You are the manifest effects of process parameters on the power mode of operation isothermal reverse extrusion billets of high anisotropic materials in the short-ter...
Anisotropic models are unitary: A rejuvenation of standard quantum cosmology
Pal, Sridip
2016-01-01
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint extension as long as it is constructed to be a symmetric operator, thereby making the problem of non-unitarity in context of anisotropic homogeneous model a ghost. Moreover, it is indicated that the self-adjoint extension is not unique and this non-uniqueness is suspected not to be a feature of Anisotropic model only, in the sense that there exists operator orderings such that Hamiltonian for an isotropic homogeneous cosmological model does not have unique self-adjoint extension, albeit for isotropic model, there is a special unique extension associated with quadratic form of Hamiltonian i.e {\\it Friedrichs extension}. Details of calculations are carried out for a Bianchi III model.
Critical exponents of the anisotropic Bak-Sneppen model
Maslov, S. [Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 (United States); De Los Rios, P.; Marsili, M.; Zhang, Y. [Institut de Physique Theorique, Universite de Fribourg Perolles, Fribourg CH-1700 (Switzerland); Marsili, M. [International School for Advanced Studies (SISSA) and INFM Unit, Trieste I-34014 (Italy)
1998-12-01
We analyze the behavior of the spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents {tau} and {mu}=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For the one-dimensional anisotropic Bak-Sneppen model, we derive an exact equation for the distribution of avalanche spatial sizes, and extract the value {gamma}=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation. {copyright} {ital 1998} {ital The American Physical Society}
Hysteresis modeling of anisotropic and isotropic nanocrystalline hard magnetic films
Cornejo, D. R.; Azevedo, A.; Rezende, S. M.
2003-05-01
In the Hauser model, the magnetic state of a system is obtained by minimizing the so-called total energy function for a statistical set of magnetic domains. In this article, this energetic model of ferromagnetic materials is used in order to calculate hysteresis loops of isotropic and anisotropic nanocrystalline SmCo films at room temperature. A qualitative very good agreement between the calculated and experimental curves is obtained, mainly in the anisotropic case. Also, it has been verified that, under suitable approximations, the free parameters of the model can tie with intrinsic characteristics of the reversal magnetization process.
The anisotropic \\lambda-deformed SU(2) model is integrable
Sfetsos, Konstantinos
2014-01-01
The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax pair formulation. We derive its underlying symmetry current algebra and use it to show that the Poisson brackets of the spatial part of the Lax pair, assume the Maillet form. In this way we procure the corresponding r and s matrices which provide non-trivial solutions to the modified Yang-Baxter equation.
Gauge-invariant perturbations in anisotropic homogeneous cosmological models
Perturbations in spatially flat anisotropic homogeneous cosmological models with arbitrary dimension N are classified into three types I, II, and III and gauge-invariant quantities are defined in each type. Equations for them are derived for arbitrary anisotropic flat models. It is found that density perturbations are described by two second-order differential equations, as in the treatment of Perko, Matzner, and Shepley for the pressureless fluid. The solutions are obtained for approximate Kasner-type anisotropic models and their characteristic behaviors are shown for the fluids with nonzero pressure as well as the pressureless fluid. They are consistent with the counterparts of Perko, Matzner, and Shepley for the pressureless fluid. The instability problem in a Kaluza-Klein multidimensional universe also is discussed
Shear-free anisotropic cosmological models in {f (R)} gravity
Abebe, Amare; Momeni, Davood; Myrzakulov, Ratbay
2016-04-01
We study a class of shear-free, homogeneous but anisotropic cosmological models with imperfect matter sources in the context of f( R) gravity. We show that the anisotropic stresses are related to the electric part of the Weyl tensor in such a way that they balance each other. We also show that within the class of orthogonal f( R) models, small perturbations of shear are damped, and that the electric part of the Weyl tensor and the anisotropic stress tensor decay with the expansion as well as the heat flux of the curvature fluid. Specializing in locally rotationally symmetric spacetimes in orthonormal frames, we examine the late-time behaviour of the de Sitter universe in f( R) gravity. For the Starobinsky model of f( R), we study the evolutionary behavior of the Universe by numerically integrating the Friedmann equation, where the initial conditions for the expansion, acceleration and jerk parameters are taken from observational data.
The Derived Equivalent Circuit Model for Magnetized Anisotropic Graphene
Cao, Ying S; Ruehli, Albert E
2015-01-01
Due to the static magnetic field, the conductivity for graphene becomes a dispersive and anisotropic tensor, which complicates most modeling methodologies. In this paper, a novel equivalent circuit model is proposed for graphene with the magnetostatic bias based on the electric field integral equation (EFIE). To characterize the anisotropic property of the biased graphene, the resistive part of the unit circuit is replaced by a resistor in series with current control voltage sources (CCVSs). The CCVSs account for the off-diagonal parts of the surface conductivity tensor for the magnetized graphene. Furthermore, the definitions of the absorption cross section and the scattering cross section are revisited to make them feasible for derived circuit analysis. This proposed method is benchmarked with several numerical examples. This paper also provides a new equivalent circuit model to deal with dispersive and anisotropic materials.
Numerical modelling of tunnel construction in anisotropic foliated soft rock
Markovič, Jernej
2009-01-01
The present work focuses on the influence on tunnelling in the anisotropic foliated soft rock. The excavation initiates stress redistribution around an opening and thus causes the deformation to occur. The numerical problem of the tunnel excavation was modelled in the Plaxis 2D code using different soil constitutive models for modelling the rock mass behaviour. A parametric study was performed to obtain the model response to alteration of the rock mass parameters. The analysis was divided int...
Anisotropic cosmological models and generalized scalar tensor theory
Subenoy Chakraborty; Batul Chandra Santra; Nabajit Chakravarty
2003-10-01
In this paper generalized scalar tensor theory has been considered in the background of anisotropic cosmological models, namely, axially symmetric Bianchi-I, Bianchi-III and Kortowski–Sachs space-time. For bulk viscous ﬂuid, both exponential and power-law solutions have been studied and some assumptions among the physical parameters and solutions have been discussed.
Mathematical model of non-isothermal creep based anisotropic damage
Галаган, Ю. Н.; Лысенко, С. В.; Львов, Г. И.
2008-01-01
А mathematical model of nonisothermic creep for anisotropic damage case is considered. Constitutive relation of creep rate and kinematic equation of damage evolution are assumed temperature dependent. A second range tensor is used for description damage. A technique based on existing experimental curves for the identification of material creep constants is presented.
Computing realization of group analysis of FSI problems
Following the rational thought, that the computational realization of the mechanical-mathematical modelling of thin walled structural components has to supplement harmonically any powerful theoretical (analytical) methods, an investigation containing the three components: (i) Powerful analytical method (Lie group method); (ii) computational method and numerical realization of the analytical investigation including the code 'MAYA-MAXI' (to construct the corresponding group and compathability conditions of the FSI problem); (iii) results of an example for computational design of a circular thinwalled nonlinear shell (of PWR core), is performed in the present paper. (orig.)
FSI ANALYSIS OF SUBMARINE OUTFALL
Engin GÜCÜYEN
2016-06-01
Full Text Available In the scope of this study, main pipe of the diffuser, risers, ports, internal and external environments forming the discharge system which is used in application are modelled by Finite Elements Analysis (FEA program to obtain discharge and structural behaviour. The last two spans of the system (20 m and four ports on these spans are investigated. While the diameter and geometry of the risers and ports remain constant, the diffuser pipe is modelled in three different ways. These are constant sectioned (Model 1, contracting with sharp edge entrance sectioned (Model 2 and gradually contracting sectioned (Model 3 respectively. Among them, only Model 1 is treated as Single Degree of Freedom (SDOF system and it is simulated by FEA to verify FEA solver in the first place. After structural suitability is confirmed, rest of the models are analysed to determine reaction forces and stresses. The discharge is performed as unsteady external flow as well as steady external flow assumption which is widely used in external flow model in the literature. The discharge analyses are performed in two different ways to verify FEA program. Iterative method is accompanying to FEA program. As a result of this study, proper model for structural and discharge behaviour and external flow effects on discharge velocities are obtained.
Prestack exploding reflector modelling and migration for anisotropic media
Alkhalifah, Tariq Ali
2014-10-09
The double-square-root equation is commonly used to image data by downward continuation using one-way depth extrapolation methods. A two-way time extrapolation of the double-square-root-derived phase operator allows for up and downgoing wavefields but suffers from an essential singularity for horizontally travelling waves. This singularity is also associated with an anisotropic version of the double-square-root extrapolator. Perturbation theory allows us to separate the isotropic contribution, as well as the singularity, from the anisotropic contribution to the operator. As a result, the anisotropic residual operator is free from such singularities and can be applied as a stand alone operator to correct for anisotropy. We can apply the residual anisotropy operator even if the original prestack wavefield was obtained using, for example, reverse-time migration. The residual correction is also useful for anisotropic parameter estimation. Applications to synthetic data demonstrate the accuracy of the new prestack modelling and migration approach. It also proves useful in approximately imaging the Vertical Transverse Isotropic Marmousi model.
Efficient anisotropic wavefield extrapolation using effective isotropic models
Alkhalifah, Tariq Ali
2013-06-10
Isotropic wavefield extrapolation is more efficient than anisotropic extrapolation, and this is especially true when the anisotropy of the medium is tilted (from the vertical). We use the kinematics of the wavefield, appropriately represented in the high-frequency asymptotic approximation by the eikonal equation, to develop effective isotropic models, which are used to efficiently and approximately extrapolate anisotropic wavefields using the isotropic, relatively cheaper, operators. These effective velocity models are source dependent and tend to embed the anisotropy in the inhomogeneity. Though this isotropically generated wavefield theoretically shares the same kinematic behavior as that of the first arrival anisotropic wavefield, it also has the ability to include all the arrivals resulting from a complex wavefield propagation. In fact, the effective models reduce to the original isotropic model in the limit of isotropy, and thus, the difference between the effective model and, for example, the vertical velocity depends on the strength of anisotropy. For reverse time migration (RTM), effective models are developed for the source and receiver fields by computing the traveltime for a plane wave source stretching along our source and receiver lines in a delayed shot migration implementation. Applications to the BP TTI model demonstrates the effectiveness of the approach.
A new model for spherically symmetric anisotropic compact star
Maurya, S K; Dayanandan, Baiju; Ray, Saibal
2016-01-01
In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of both objects by solving numerically the Einstein field equations under with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if anisotropy is zero everywhere inside the star then the density and pressures will become zero and metric turns out to be flat. We report our results and compare with the above mentioned two compact objects on a number of key aspects: the central density, the surface density onset and the critical scaling behavior, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications...
A new model for spherically symmetric anisotropic compact star
Maurya, S. K.; Gupta, Y. K.; Dayanandan, Baiju; Ray, Saibal
2016-05-01
In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star.
Effective Elliptic Models for Efficient Wavefield Extrapolation in Anisotropic Media
Waheed, Umair bin
2014-05-01
Wavefield extrapolation operator for elliptically anisotropic media offers significant cost reduction compared to that of transversely isotropic media (TI), especially when the medium exhibits tilt in the symmetry axis (TTI). However, elliptical anisotropy does not provide accurate focusing for TI media. Therefore, we develop effective elliptically anisotropic models that correctly capture the kinematic behavior of the TTI wavefield. Specifically, we use an iterative elliptically anisotropic eikonal solver that provides the accurate traveltimes for a TI model. The resultant coefficients of the elliptical eikonal provide the effective models. These effective models allow us to use the cheaper wavefield extrapolation operator for elliptic media to obtain approximate wavefield solutions for TTI media. Despite the fact that the effective elliptic models are obtained by kinematic matching using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including the frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy tradeoff for wavefield computations in TTI media, considering the cost prohibitive nature of the problem. We demonstrate the applicability of the proposed approach on the BP TTI model.
Anisotropic dark energy model with a hybrid scale factor
Mishra, B
2015-01-01
Anisotropic dark energy model with dynamic pressure anisotropies along different spatial directions is constructed at the backdrop of a spatially homogeneous diagonal Bianchi type $V$ $(BV)$ space-time in the framework of General Relativity. A time varying deceleration parameter generating a hybrid scale factor is considered to simulate a cosmic transition from early deceleration to late time acceleration. We found that the pressure anisotropies along the $y-$ and $z-$ axes evolve dynamically and continue along with the cosmic expansion without being subsided even at late times. The anisotropic pressure along the $x-$axis becomes equal to the mean fluid pressure. At a late phase of cosmic evolution, the model enters into a phantom region. From a state finder diagnosis, it is found that the model overlaps with $\\Lambda$CDM at late phase of cosmic time.
Modelling of ultrasonic nondestructive testing in anisotropic materials - Rectangular crack
Nondestructive testing with ultrasound is a standard procedure in the nuclear power industry when searching for defects, in particular cracks. To develop and qualify testing procedures extensive experimental work on test blocks is usually required. This can take a lot of time and therefore be quite costly. A good mathematical model of the testing situation is therefore of great value as it can reduce the experimental work to a great extent. A good model can be very useful for parametric studies and as a pedagogical tool. A further use of a model is as a tool in the qualification of personnel. In anisotropic materials, e.g. austenitic welds, the propagation of ultrasound becomes much more complicated as compared to isotropic materials. Therefore, modelling is even more useful for anisotropic materials, and it in particular has a greater pedagogical value. The present project has been concerned with a further development of the anisotropic capabilities of the computer program UTDefect, which has so far only contained a strip-like crack as the single defect type for anisotropic materials. To be more specific, the scattering by a rectangular crack in an anisotropic component has been studied and the result is adapted to include transmitting and receiving ultrasonic probes. The component under study is assumed to be anisotropic with arbitrary anisotropy. On the other hand, it is assumed to be homogeneous, and this in particular excludes most welds, where it is seldom an adequate approximation to assume homogeneity. The anisotropy may be arbitrarily oriented and the same is true of the rectangular crack. The crack may also be located near a backside of the component. To solve the scattering problem for the crack an integral equation method is used. The probe model has been developed in an earlier project and to compute the signal response in the receiving probe an electromechanical reciprocity argument is employed. As a rectangle is a truly 3D scatterer the sizes of the
Anisotropic neutron star models: stability against radial and nonradial pulsations
The problem of stability of fully relativistic neutron star models, which are constructed from plausible assumptions about an anisotropic equation of state, is analysed in the framework of general relativity. The differential equations for radial pulsation of such models are derived and results of numerical solutions are presented. It is shown that there exists a static stability criterion similar to the one obtained for isotropic models. Moreover there is in principle no limiting mass for arbitrarily large anisotropy and these models are still stable against radial pulsations. Non-radial pulsations are analysed in the Newtonian approximation for some simplified models. Again we do not find any dynamical instabilities. (orig.)
The Anisotropic Bak-Sneppen Model
Head, DA; Rodgers, GJ
1998-01-01
The Bak-Sneppen model is shown to fall into a different universality class with the introduction of a preferred direction, mirroring the situation in spin systems. This is first demonstrated by numerical simulations and subsequently confirmed by analysis of the multi-trait version of the model, which admits exact solutions in the extremes of zero and maximal anisotropy. For intermediate anisotropies, we show that the spatiotemporal evolution of the avalanche has a power law ``tail'' which pas...
Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models
Reckinger, S. J.; Fox-Kemper, B.; Bachman, S.; Bryan, F.; Dennis, J.; Danabasoglu, G.
2014-12-01
Modern climate models are limited to coarse-resolution representations of large-scale ocean circulation that rely on parameterizations for mesoscale eddies. The effects of eddies are typically introduced by relating subgrid eddy fluxes to the resolved gradients of buoyancy or other tracers, where the proportionality is, in general, governed by an eddy transport tensor. The symmetric part of the tensor, which represents the diffusive effects of mesoscale eddies, is universally treated isotropically in general circulation models. Thus, only a single parameter, namely the eddy diffusivity, is used at each spatial and temporal location to impart the influence of mesoscale eddies on the resolved flow. However, the diffusive processes that the parameterization approximates, such as shear dispersion, potential vorticity barriers, oceanic turbulence, and instabilities, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters to three: a major diffusivity, a minor diffusivity, and the principal axis of alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the newly introduced parameters, which are motivated by observations and the eddy transport tensor diagnosed from high resolution simulations. Simply setting the ratio of major to minor diffusivities to a value of five globally, while aligning the major axis along the flow direction, improves biogeochemical tracer ventilation and reduces global temperature and salinity biases. These effects can be improved even further by parameterizing the anisotropic transport mechanisms in the ocean.
Inflationary Weak Anisotropic Model with General Dissipation Coefficient
Sharif, M
2015-01-01
This paper explores the dynamics of warm intermediate and logamediate inflationary models during weak dissipative regime with a general form of dissipative coefficient. We analyze these models within the framework of locally rotationally symmetric Bianchi type I universe. In both cases, we evaluate solution of inflaton, effective scalar potential, dissipative coefficient, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio under slow-roll approximation. We constrain the model parameters using recent data and conclude that anisotropic inflationary universe model with generalized dissipation coefficient remains compatible with WMAP9, Planck and BICEP2 data.
Anisotropic propagation model of ventricular myocardium
Hren, Rok; Simelius, Kim; Nenonen, Jukka; Horáček, B Milan
2015-01-01
We describe a hybrid model for propagated excitaion in three-dimensional human ventricles. The subtreshold behaviour of the excitable elements is governed by a reaction-diffusion equation derived from the bidomain theory, while in the supratreshold state the elements obey cellular automata rules. The ventricles consist of two million discrete cubes (cells) with the side length of 0.5 mm. Each cell is assigned a principal fiber direction according to the fiber arhitecture in the human heart. W...
Critical state model with anisotropic critical current density
Bhagwat, K V; Ravikumar, G
2003-01-01
Analytical solutions of Bean's critical state model with critical current density J sub c being anisotropic are obtained for superconducting cylindrical samples of arbitrary cross section in a parallel geometry. We present a method for calculating the flux fronts and magnetization curves. Results are presented for cylinders with elliptical cross section with a specific form of the anisotropy. We find that over a certain range of the anisotropy parameter the flux fronts have shapes similar to those for an isotropic sample. However, in general, the presence of anisotropy significantly modifies the shape of the flux fronts. The field for full flux penetration also depends on the anisotropy parameter. The method is extended to the case of anisotropic J sub c that also depends on the local field B, and magnetization hysteresis curves are presented for typical values of the anisotropy parameter for the case of |J sub c | that decreases exponentially with |B|.
Wang, Hui
2014-05-01
This thesis addresses the efficiency improvement of seismic wave modeling and migration in anisotropic media. This improvement becomes crucial in practice as the process of imaging complex geological structures of the Earth\\'s subsurface requires modeling and migration as building blocks. The challenge comes from two aspects. First, the underlying governing equations for seismic wave propagation in anisotropic media are far more complicated than that in isotropic media which demand higher computational costs to solve. Second, the usage of whole prestack seismic data still remains a burden considering its storage volume and the existing wave equation solvers. In this thesis, I develop two approaches to tackle the challenges. In the first part, I adopt the concept of prestack exploding reflector model to handle the whole prestack data and bridge the data space directly to image space in a single kernel. I formulate the extrapolation operator in a two-way fashion to remove he restriction on directions that waves propagate. I also develop a generic method for phase velocity evaluation within anisotropic media used in this extrapolation kernel. The proposed method provides a tool for generating prestack images without wavefield cross correlations. In the second part of this thesis, I approximate the anisotropic models using effective isotropic models. The wave phenomena in these effective models match that in anisotropic models both kinematically and dynamically. I obtain the effective models through equating eikonal equations and transport equations of anisotropic and isotropic models, thereby in the high frequency asymptotic approximation sense. The wavefields extrapolation costs are thus reduced using isotropic wave equation solvers while the anisotropic effects are maintained through this approach. I benchmark the two proposed methods using synthetic datasets. Tests on anisotropic Marmousi model and anisotropic BP2007 model demonstrate the applicability of my
A completely analytical family of anisotropic Plummer models
In spherical stellar systems a given mass density allows an infinity of distribution functions. This indeterminacy is illustrated with a one-parameter family of anisotropic models. They all satisfy the Plummer law in the mass density, but have different velocity dispersions. Moreover, the stars are not confined to a particular subset of the total accessible phase space. This family is explored analytically in detail. Even when both the mass density and the velocity dispersion profiles are required to be the same, a degeneracy in the model space persists, which can be shown with a three-parameter generalization of the above family. (author)
The anisotropic material constitutive models for the human cornea.
Li, Long-yuan; Tighe, Brian
2006-03-01
This paper presents an anisotropic analysis model for the human cornea. The model is based on the assumption that the fibrils in the cornea are organised into lamellae, which may have preferential orientation along the superior-inferior and nasal-temporal directions, while the alignment of lamellae with different orientations is assumed to be random. Hence, the cornea can be regarded as a laminated composite shell. The constitutive equation describing the relationships between membrane forces, bending moments, and membrane strains, bending curvatures are derived. The influences of lamella orientations and the random alignment of lamellae on the stiffness coefficients of the constitutive equation are discussed. PMID:16426861
Secondary Cosmic Positrons in an Anisotropic Diffusion Model
Kappl, Rolf
2016-01-01
One aim of cosmic ray measurements is the search for possible signatures of annihilating or decaying dark matter. The so-called positron excess has attracted a lot of attention in this context. On the other hand it has been proposed that the data might challenge the established diffusion model for cosmic ray propagation. We investigate an anisotropic diffusion model by solving the corresponding equations analytically. Depending on the propagation parameters we find that the spectral features of the positron spectrum are affected significantly. We also discuss the influence of the anisotropy on hadronic spectra.
Power-law models of totally anisotropic scattering
Tuntsov, Artem V; Walker, Mark A; 10.1093/mnras/sts527
2012-01-01
The interstellar scattering responsible for pulsar parabolic arcs, and for intra-day variability of compact radio quasars, is highly anisotropic in some cases. We numerically simulate these observed phenomena using totally anisotropic, power-law models for the electron density fluctuations which cause the scattering. By comparing our results to the scattered image of PSR B0834+06 and, independently, to dual-frequency light curves of the quasar PKS1257-326, we constrain the nature of the scattering media on these lines of sight. We find that models with spectral indices slightly below \\beta=3, including the one-dimensional Kolmogorov model, are broadly consistent with both data sets. We confirm that a single physical model suffices for both sources, with the scattering medium simply being more distant in the case of B0834+06. This reinforces the idea that intra-day variability and parabolic arcs have a common cause in a type of interstellar structure which, though obscure, is commonplace. However, the implied ...
Critical dynamics of anisotropic Bak-Sneppen model
Tirnakli, Ugur; Lyra, Marcelo L.
2004-10-01
A new damage spreading algorithm, which was introduced very recently in (Int. J. Mod. Phys. C 14 (2003) 85) has been applied to anisotropic Bak-Sneppen model of biological evolution. Since this new algorithm is able to capture both the short-time and long-time dynamics of extended systems which exhibits self-organized criticality, this analysis is expected to shed further light to the recent claim that the dynamics of such systems is similar to the one observed at the usual critical point of continuous phase-transitions and at the chaos threshold of low-dimensional dissipative maps.
Anisotropic cosmology and inflation from tilted Bianchi IX model
Sundell, Peter
2015-01-01
The dynamics of the tilted Bianchi IX cosmological models are explored allowing energy flux in the source fluid. The equation of state and the tilt angle of the fluid are the two free parameters and the shear, the vorticity and the curvature of the spacetime span a three-dimensional phase space that contains seven fixed points. One of them is an attractor that inflates the universe anisotropically, thus providing a counter example to the cosmic no-hair conjecture. Also, an example of a realistic though fine-tuned cosmology is presented wherein the rotation can grow significant towards the present epoch but the shear stays within the observational bounds.
Anisotropic Third-Order Regularization for Sparse Digital Elevation Models
Lellmann, Jan
2013-01-01
We consider the problem of interpolating a surface based on sparse data such as individual points or level lines. We derive interpolators satisfying a list of desirable properties with an emphasis on preserving the geometry and characteristic features of the contours while ensuring smoothness across level lines. We propose an anisotropic third-order model and an efficient method to adaptively estimate both the surface and the anisotropy. Our experiments show that the approach outperforms AMLE and higher-order total variation methods qualitatively and quantitatively on real-world digital elevation data. © 2013 Springer-Verlag.
Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos
Nguyen, P H
2013-01-01
Spherical systems with a polytropic equation of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense that their equiprobability surfaces in velocity space are non-spherical, leading to an overabundance of radial or circular orbits, depending on the parameters of the model in consideration. Among the family, we find the post-Newtonian generalization of the Plummer and Hernquist models. A close inspection of their equation of state reveals that these solutions interpolate smoothly between a polytropic sphere in the asymptoti...
Anisotropic Coarse-Grained Model for Proteins Based On Gay–Berne and Electric Multipole Potentials
Shen, Hujun; LI Yan; Ren, Pengyu; Zhang, Dinglin; Li, Guohui
2014-01-01
Gay–Berne anisotropic potential has been widely used to evaluate the nonbonded interactions between coarse-grained particles being described as elliptical rigid bodies. In this paper, we are presenting a coarse-grained model for twenty kinds of amino acids and proteins, based on the anisotropic Gay–Berne and point electric multipole (EMP) potentials. We demonstrate that the anisotropic coarse-grained model, namely GBEMP model, is able to reproduce many key features observed from experimental ...
Modeling space plasma dynamics with anisotropic Kappa distributions
Lazar, M; Poedts, S; Schlickeiser, R
2012-01-01
Space plasmas are collisionpoor and kinetic effects prevail leading to wave fluctuations, which transfer the energy to small scales: wave-particle interactions replace collisions and enhance dispersive effects heating particles and producing suprathermal populations observed at any heliospheric distance in the solar wind. At large distances collisions are not efficient, and the selfgenerated instabilities constrain the solar wind anisotropy including the thermal core and the suprathermal components. The generalized power-laws of Kappa-type are the best fitting model for the observed distributions of particles, and a convenient mathematical tool for modeling their dynamics. But the anisotropic Kappa models are not correlated with the observations leading, in general, to inconsistent effects. This review work aims to reconcile some of the existing Kappa models with the observations.
Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm
Lee Hyoungsuk
2014-09-01
Full Text Available A reliable steady/transient hydro-elastic analysis is developed for flexible (composite marine propeller blade design which deforms according to its environmental load (ship speed, revolution speed, wake distribution, etc. Hydro-elastic analysis based on CFD and FEM has been widely used in the engineering field because of its accurate results however it takes large computation time to apply early propeller design stage. Therefore the analysis based on a boundary element method-Finite Element Method (BEM-FEM Fluid-Structure Interaction (FSI is introduced for computational efficiency and accuracy. The steady FSI analysis, and its application to reverse engineering, is designed for use regarding optimum geometry and ply stack design. A time domain two-way coupled transient FSI analysis is developed by considering the hydrodynamic damping ffects of added mass due to fluid around the propeller blade. The analysis makes possible to evaluate blade strength and also enable to do risk assessment by estimating the change in performance and the deformation depending on blade position in the ship’s wake. To validate this hydro-elastic analysis methodology, published model test results of P5479 and P5475 are applied to verify the steady and the transient FSI analysis, respectively. As the results, the proposed steady and unsteady analysis methodology gives sufficient accuracy to apply flexible marine propeller design
Efficient Multigrid Preconditioners for Anisotropic Problems in Geophysical Modelling
Dedner, Andreas; Scheichl, Robert
2014-01-01
Many problems in geophysical modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor-product approach originally analysed by B\\"{o}rm and Hiptmair ...
Effective Orthorhombic Anisotropic Models for Wave field Extrapolation
Ibanez Jacome, Wilson
2013-05-01
Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models, to reproduce wave propagation phenomena in the Earth\\'s subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, I generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, I develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic one, is represented by a sixth order polynomial equation that includes the fastest solution corresponding to outgoing P-waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, which is done by explicitly solving the isotropic eikonal equation for the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. I extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the
Anisotropic rock physics models for interpreting pore structures in carbonate reservoirs
Li, Sheng-Jie; Shao, Yu; Chen, Xu-Qiang
2016-03-01
We developed an anisotropic effective theoretical model for modeling the elastic behavior of anisotropic carbonate reservoirs by combining the anisotropic self-consistent approximation and differential effective medium models. By analyzing the measured data from carbonate samples in the TL area, a carbonate pore-structure model for estimating the elastic parameters of carbonate rocks is proposed, which is a prerequisite in the analysis of carbonate reservoirs. A workflow for determining elastic properties of carbonate reservoirs is established in terms of the anisotropic effective theoretical model and the pore-structure model. We performed numerical experiments and compared the theoretical prediction and measured data. The result of the comparison suggests that the proposed anisotropic effective theoretical model can account for the relation between velocity and porosity in carbonate reservoirs. The model forms the basis for developing new tools for predicting and evaluating the properties of carbonate reservoirs.
Anisotropic damage coupled modeling of saturated porous rock
无
2010-01-01
It is widely acknowledged that the natural rock mass is anisotropic and its failing type is also non-isotropic. An orthotropic elastic damaged model has been proposed in which the elastic deformation,the damaged deformation and irreversible deformation can be identified respectively. A second rank damage tensor is employed to characterize the induced damage and damage evolution related to the propagation conditions of microcracks. A specific form of the Gibbs free energy function is used to obtain the effective elastic stiffness and the limited scopes of damage parameters are suggested. The model’s parameter determination is proposed by virtue of conventional tri-axial test. Then,the proposed model is developed to simulate the coupled hydraulic mechanical responses and traction behaviors in different loading paths of porous media.
Lattice models of directed and semiflexible polymers in anisotropic environment
Haydukivska, K.; Blavatska, V.
2015-10-01
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to existing of three characteristic length scales in the system. At each fixed concentration of disorder we found a transition point, where the influence of extended defects is exactly counterbalanced by the stretching field. Numerical simulations of BSAWs in anisotropic environment reveal an increase of polymer stiffness. In particular, the persistence length of semiflexible polymers increases in presence of disorder.
Lattice models of directed and semiflexible polymers in anisotropic environment
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to existing of three characteristic length scales in the system. At each fixed concentration of disorder we found a transition point, where the influence of extended defects is exactly counterbalanced by the stretching field. Numerical simulations of BSAWs in anisotropic environment reveal an increase of polymer stiffness. In particular, the persistence length of semiflexible polymers increases in presence of disorder. (paper)
Distance-redshift relations in an anisotropic cosmological model
In this paper we study an anisotropic model generated from a particular Bianchi type-III metric, which is a generalization of Gödel's metric and an exact solution of Einstein's field equations. We analyse type Ia supernova data, namely the SDSS sample calibrated with the MLCS2k2 fitter, and we verify in which ranges of distances and redshifts the anisotropy could be observed. We also consider, in a joint analysis, the position of the first peak in the CMB anisotropy spectrum, as well as current observational constraints on the Hubble constant. We conclude that a small anisotropy is permitted by the data, and that more accurate measurements of supernova distances above z = 2 might indicate the existence of such anisotropy in the universe
Anisotropic magnetoresistivity in structured elastomer composites: modelling and experiments.
Mietta, José Luis; Tamborenea, Pablo I; Martin Negri, R
2016-08-14
A constitutive model for the anisotropic magnetoresistivity in structured elastomer composites (SECs) is proposed. The SECs considered here are oriented pseudo-chains of conductive-magnetic inorganic materials inside an elastomer organic matrix. The pseudo-chains are formed by fillers which are simultaneously conductive and magnetic dispersed in the polymer before curing or solvent evaporation. The SEC is then prepared in the presence of a uniform magnetic field, referred to as Hcuring. This procedure generates the pseudo-chains, which are preferentially aligned in the direction of Hcuring. Electrical conduction is present in that direction only. The constitutive model for the magnetoresistance considers the magnetic pressure, Pmag, induced on the pseudo-chains by an external magnetic field, H, applied in the direction of the pseudo-chains. The relative changes in conductivity as a function of H are calculated by evaluating the relative increase of the electron tunnelling probability with Pmag, a magneto-elastic coupling which produces an increase of conductivity with magnetization. The model is used to adjust experimental results of magnetoresistance in a specific SEC where the polymer is polydimethylsiloxane, PDMS, and fillers are microparticles of magnetite-silver (referred to as Fe3O4[Ag]). Simulations of the expected response for other materials in both superparamagnetic and blocked magnetic states are presented, showing the influence of the Young's modulus of the matrix and filler's saturation magnetization. PMID:27418417
Anisotropic Effects on Constitutive Model Parameters of Aluminum Alloys
Brar, Nachhatter; Joshi, Vasant
2011-06-01
Simulation of low velocity impact on structures or high velocity penetration in armor materials heavily rely on constitutive material models. The model constants are required input to computer codes (LS-DYNA, DYNA3D or SPH) to accurately simulate fragment impact on structural components made of high strength 7075-T651 aluminum alloys. Johnson-Cook model constants determined for Al7075-T651 alloy bar material failed to simulate correctly the penetration into 1' thick Al-7075-T651plates. When simulations go well beyond minor parameter tweaking and experimental results are drastically different it is important to determine constitutive parameters from the actual material used in impact/penetration experiments. To investigate anisotropic effects on the yield/flow stress of this alloy we performed quasi-static and high strain rate tensile tests on specimens fabricated in the longitudinal, transverse, and thickness directions of 1' thick Al7075-T651 plate. Flow stresses at a strain rate of ~1100/s in the longitudinal and transverse direction are similar around 670MPa and decreases to 620 MPa in the thickness direction. These data are lower than the flow stress of 760 MPa measured in Al7075-T651 bar stock.
Some anisotropic non-static perfect fluid cosmological models in general relativity
Perfect fluid cosmological models are derived which are anisotropic, non-static and have homogeneous distributions of density and pressure. Various physical properties of the models are explored. (author)
Sari, Rr. Kurnia Novita; Neswan, Oki
2015-12-01
Anisotropic semivariogram modeling can be aplied in petroleum industry where the angle between a pair of wells has important function in defining the spatial correlation between wells. In geometry anisotropic, function of range is formulated in trigonometric functions of the angle between pairs of wells that have periodicity property. The fluctuations of range will affect on shifting geometry anisotropic models with different properties for each quadrant of angle. In three semivariogram models (exponential, spherical and gaussian), the increasing of angle give difference influence for range function and the shifting of semivariogram value.
A robust absorbing layer method for anisotropic seismic wave modeling
Métivier, L., E-mail: ludovic.metivier@ujf-grenoble.fr [LJK, CNRS, Université de Grenoble, BP 53, 38041 Grenoble Cedex 09 (France); ISTerre, Université de Grenoble I, BP 53, 38041 Grenoble Cedex 09 (France); Brossier, R. [ISTerre, Université de Grenoble I, BP 53, 38041 Grenoble Cedex 09 (France); Labbé, S. [LJK, CNRS, Université de Grenoble, BP 53, 38041 Grenoble Cedex 09 (France); Operto, S. [Géoazur, Université de Nice Sophia-Antipolis, CNRS, IRD, OCA, Villefranche-sur-Mer (France); Virieux, J. [ISTerre, Université de Grenoble I, BP 53, 38041 Grenoble Cedex 09 (France)
2014-12-15
When applied to wave propagation modeling in anisotropic media, Perfectly Matched Layers (PML) exhibit instabilities. Incoming waves are amplified instead of being absorbed. Overcoming this difficulty is crucial as in many seismic imaging applications, accounting accurately for the subsurface anisotropy is mandatory. In this study, we present the SMART layer method as an alternative to PML approach. This method is based on the decomposition of the wavefield into components propagating inward and outward the domain of interest. Only outgoing components are damped. We show that for elastic and acoustic wave propagation in Transverse Isotropic media, the SMART layer is unconditionally dissipative: no amplification of the wavefield is possible. The SMART layers are not perfectly matched, therefore less accurate than conventional PML. However, a reasonable increase of the layer size yields an accuracy similar to PML. Finally, we illustrate that the selective damping strategy on which is based the SMART method can prevent the generation of spurious S-waves by embedding the source in a small zone where only S-waves are damped.
An anisotropic minijets model for the GRB prompt emission
Duran, Rodolfo Barniol; Giannios, Dimitrios
2015-01-01
In order to explain rapid light curve variability in the context of gamma-ray bursts (GRBs) and jets from active galactic nuclei (AGNs), several authors have proposed the existence of "blobs" or "minijets" that move with relativistic speed relative to the main flow of the jet. Here we consider the possibility that these minijets, instead of being isotropically distributed in the co-moving frame of the jet, form primarily perpendicular to the direction of the flow. This anisotropic collection of minijets yields two robust features. First, the main burst of emission is significantly delayed compared with the isotropic case. This delay allows for the peak of the afterglow emission to appear during the prompt emission, in contrast to the simplest isotropic model, where the afterglow peak appears at or after the end of the main burst. Second, the flux decline following the end of the main burst of emission will be steeper than the isotropic case. We find that these two features are realized in the case of GRBs: 1....
Modeling the anisotropic shock response of single-crystal RDX
Luscher, Darby
Explosives initiate under impacts whose energy, if distributed homogeneously throughout the material, translates to temperature increases that are insufficient to drive the rapid chemistry observed. Heterogeneous thermomechanical interactions at the meso-scale (i.e. between single-crystal and macroscale) leads to the formation of localized hot spots. Direct numerical simulations of mesoscale response can contribute to our understanding of hot spots if they include the relevant deformation mechanisms that are essential to the nonlinear thermomechanical response of explosive molecular crystals. We have developed a single-crystal model for the finite deformation thermomechanical response of cyclotrimethylene trinitramine (RDX). Because of the low symmetry of RDX, a complete description of nonlinear thermoelasticity requires a careful decomposition of free energy into components that represent the pressure-volume-temperature (PVT) response and the coupling between isochoric deformation and both deviatoric and hydrostatic stresses. An equation-of-state (EOS) based on Debye theory that defines the PVT response was constructed using experimental data and density functional theory calculations. This EOS replicates the equilibrium states of phase transformation from alpha to gamma polymorphs observed in static high-pressure experiments. Lattice thermoelastic parameters defining the coupled isochoric free energy were obtained from molecular dynamics calculations and previous experimental data. Anisotropic crystal plasticity is modeled using Orowan's expression relating slip rate to dislocation density and velocity. Details of the theory will be presented followed by discussion of simulations of flyer plate impact experiments, including recent experiments diagnosed with in situ X-ray diffraction at the Advanced Photon Source. Impact conditions explored within the experimental effort have spanned shock pressures ranging from 1-10 GPa for several crystallographic orientations
Bianchi type II models in the presence of perfect fluid and anisotropic dark energy
Akarsu, Özgur; Kumar, Suresh
2011-01-01
arXiv:1110.2408v2 [gr-qc] 15 Jun 2012 Bianchi type II models in the presence of perfect fluid and anisotropic dark energy Suresh Kumar ¨O zg¨ur Akarsu † June 18, 2012 Abstract 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 Ein...
3D time-domain airborne EM modeling for an arbitrarily anisotropic earth
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.
Effects of Staggered Magnetic Field on Entanglement in the Anisotropic XY Model
SUN Zhe; WANG Xiao-Guang
2006-01-01
We investigate effects of staggered magnetic field on thermal entanglement in the anisotropic XY model.The analytic results of entanglement for the two-site cases are obtained. For the general case of even sites, we show that when the anisotropic parameter is zero, the entanglement in the XY model with a staggered magnetic field is the same as that with a uniform magnetic field.
An analytical model of anisotropic low-field electron mobility in wurtzite indium nitride
Wang, Shulong; Liu, Hongxia; Song, Xin; Guo, Yulong; Yang, Zhaonian [Xidian University, School of Microelectronics, Key Laboratory of Wide Band-Gap Semiconductor Materials and Devices, Xi' an (China)
2014-03-15
This paper presents a theoretical analysis of anisotropic transport properties and develops an anisotropic low-field electron analytical mobility model for wurtzite indium nitride (InN). For the different effective masses in the Γ-A and Γ-M directions of the lowest valley, both the transient and steady state transport behaviors of wurtzite InN show different transport characteristics in the two directions. From the relationship between velocity and electric field, the difference is more obvious when the electric field is low in the two directions. To make an accurate description of the anisotropic transport properties under low field, for the first time, we present an analytical model of anisotropic low-field electron mobility in wurtzite InN. The effects of different ionized impurity scattering models on the low-field mobility calculated by Monte Carlo method (Conwell-Weisskopf and Brooks-Herring method) are also considered. (orig.)
3D, 9-C anisotropic seismic modeling and inversion
Rusmanugroho, Herurisa
The most complete representation of an elastic medium consists of an elastic tensor with 21 independent moduli. All 21 can be estimated from compressional and shear wave polarization and slowness vectors corresponding to wide apertures of polar and azimuth angles. In isotropic media, when seismic source and receiver components have the same orientation (such as XX and YY), the reflection amplitude contours align approximately perpendicular to the particle motions. The mixed components (such as XY and YX) have amplitude patterns that are in symmetrical pairs of either the same, or of opposite, polarity on either side of the diagonal of the 9-C response matrix. In anisotropic media, amplitude variations with azimuth show the same basic patterns and symmetries as for isotropic, but with a superimposed tendency for alignment parallel to the strike of the vertical cracks. Solutions for elastic tensor elements from synthetic slowness and polarization data calculated directly from the Christoffel equation are more sensitive to the polar angle aperture than to the azimuth aperture. Nine-component synthetic elastic vertical seismic profile data for a model with triclinic symmetry calculated by finite-differencing allows estimation of the elastic 21 tensor elements in the vicinity of a three-component borehole receiver. Wide polar angle and azimuth apertures are needed for accurately estimating the elastic tensor elements. The tensor elements become less independent as the data apertures decrease. Results obtained by extracting slowness and polarization data from the corresponding synthetic seismograms show similar results. The inversion algorithm has produced good results from field vertical seismic profile data set from the Weyburn Field in Southern Saskatchewan in Canada. Synthetic nine-component seismograms calculated from the extracted tensor are able to explain most of the significant features in the field data. The inverted stiffness elastic tensor shows orthorhombic
Asymptotic modelling of a thermopiezoelastic anisotropic smart plate
Long, Yufei
Motivated by the requirement of modelling for space flexible reflectors as well as other applications of plate structures in engineering, a general anisotropic laminated thin plate model and a monoclinic Reissner-Mindlin plate model with thermal deformation, two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structure helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. For the zeroth-order approximation, the asymptotically correct expression of energy is derived into the form of energetic equation in classical laminated plate theory, which will be enough to predict the behavior of plate structures as thin as a space flexible reflector. A through-the-thickness strain field can be expressed in terms of material constants and two-dimensional membrane and bending strains, while the transverse normal and shear stresses are not predictable yet. In the first-order approximation, the warping functions are further disturbed into a high order and an asymptotically correct energy expression with derivatives of the two-dimensional strains is acquired. For the convenience of practical use, the expression is transformed into a Reissner-Mindlin form with optimization implemented to minimize the error. Transverse stresses and strains are recovered using the in-plane strain variables. Several numerical examples of different laminations and shapes are studied with the help of analytical solutions or shell elements in finite element codes. The constitutive relation is
Generalized anisotropic strange star models for compact stars
Mauryaa, S K; Dayanandan, Baiju; Jasim, M K; Al-Jamel, Ahmed
2015-01-01
We present new anisotropic generalization of Buchdahl [1] type perfect fluid solution by using the method of earlier work [2]. In similar approach we have constructed the new pressure anisotropy factor {\\Delta} by the help both the metric potential e^{\\lambda} and e^{\
Applied Models of Static Deformation of Anisotropic Micropolar Elastic Thin Bars
Alvajyan Sh. I.; Sargsyan S.H.
2011-01-01
In this paper, using the method of hypothesis, which has an asymptotic study, two dimension boundary problem of micropolar elasticity theory for an anisotropic surrounding in a thin rectangular aria is reduced to the applied one-dimensional problem and, depending on the values of the dimensionless physical parameters used to construct general models of micropolar anisotropic elastic thin bars with free rotation, with constrained rotation, ''with small shift rigidity'', in which fully takes in...
Shawish, Samir El; CIZELJ Leon; SIMONOVSKI IGOR
2012-01-01
In this work we propose an anisotropic elasto-plastic finite element model to account for various observations in the tensile test experiments on stainless steel specimen. Using Voronoi construction for the grains, grain boundaries and anisotropic Hill’s plastic potential function, we find a clear correlation between the computed average misorientation angle, measuring the change of local crystal orientations, and the applied plastic strain, in agreement with the electron backscatter diffract...
Magnetic phase diagram of the anisotropic double-exchange model: a Monte Carlo study
The magnetic phase diagram of highly anisotropic double-exchange model systems is investigated as a function of the ratio of the anisotropic hopping integrals, i.e., tc/tab, on a three-dimensional lattice by using Monte Carlo calculations. The magnetic domain structure at low temperature is found to be a generic property of the strong anisotropy region. Moreover, the tc/tab ratio is crucial in determining the anisotropic charge transport due to the relative spin orientation of the magnetic domains. As a result, we show the anisotropic hopping integral is the most likely cause of the magnetic domain structure. It is noted that the competition between the reduced interlayer double-exchange coupling and the thermal frustration of the ordered two-dimensional ferromagnetic layer seems to be crucial in understanding the properties of layered manganites
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
A continuum-mechanical model for the flow of anisotropic polar ice
Greve, Ralf; Seddik, Hakime
2009-01-01
In order to study the mechanical behaviour of polar ice masses, the method of continuum mechanics is used. The newly developed CAFFE model (Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor) is described, which comprises an anisotropic flow law as well as a fabric evolution equation. The flow law is an extension of the isotropic Glen's flow law, in which anisotropy enters via an enhancement factor that depends on the deformability of the polycrystal. The fabric evolution equation results from an orientational mass balance and includes constitutive relations for grain rotation and recrystallization. The CAFFE model fulfills all the fundamental principles of classical continuum mechanics, is sufficiently simple to allow numerical implementations in ice-flow models and contains only a limited number of free parameters. The applicability of the CAFFE model is demonstrated by a case study for the site of the EPICA (European Project for Ice Coring in Antarctica) ice core ...
In the present article we resume some of our results on homogeneous anisotropic models of the Poincare gauge theory of gravity based on the Riemann-Cartan spacetime. Namely, within the framework of the minimum quadratic Poincare gauge theory of gravity the dynamics of homogeneous anisotropic Bianchi types I-IX spinning-fluid cosmological models is studied. A basic equation set for these models is obtained and analyzed. In particular, exact solutions for the Bianchi type-I spinning-fluid and Bianchi type-V perfect-fluid models are found in integral form. (author). 30 refs, 2 tabs
Implementation of an anisotropic turbulence model in the COMMIX- 1C/ATM computer code
The computer code COMMIX-1C/ATM, which describes single-phase, three-dimensional transient thermofluiddynamic problems, has provided the framework for the extension of the standard k-var-epsilon turbulence model to a six-equation model with additional transport equations for the turbulence heat fluxes and the variance of temperature fluctuations. The new, model, which allows simulation of anisotropic turbulence in stratified shear flows, is referred to as the Anisotropic Turbulence Model (ATM) has been verified with numerical computations of stable and unstable stratified shear flow between parallel plates
Qing, Hai; Mishnaevsky, Leon
2010-01-01
A 3D anisotropic continuum damage model is developed for the computational analysis of the elastic–brittle behaviour of fibre-reinforced composite. The damage model is based on a set of phenomenological failure criteria for fibre-reinforced composite, which can distinguish the matrix and fibre...... failure under tensile and compressive loading. The homogenized continuum theory is adopted for the anisotropic elastic damage constitutive model. The damage modes occurring in the longitudinal and transverse directions of a ply are represented by a damage vector. The elastic damage model is implemented in...
Anisotropic Cosmological Model in Modified Brans--Dicke Theory
Rasouli, S. M. M.; Farhoudi, Mehrdad; Sepangi, Hamid R.
2011-01-01
It has been shown that four dimensional Brans-Dicke theory with effective matter field and self interacting potential can be achieved from vacuum 5D BD field equations, where we refer to as modified Brans-Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing obtained formalism, we derive induced-matter on any 4D hypersurface in context of the MBDT. We illustrate that if the usual spatial scale factors are functions of time whi...
Modeling anisotropic flow and heat transport by using mimetic finite differences
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.
Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models
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.
Shear-free Anisotropic Cosmological Models in f(R) Gravity
Abebe, Amare; Myrzakulov, Ratbay
2015-01-01
We study a class of shear-free, homogeneous but anisotropic cosmological models with imperfect matter sources in the context of f(R) gravity. We show that the anisotropic stresses are related to the electric part of the Weyl tensor in such a way that they balance each other. We also show that within the class of orthogonal f(R) models, small perturbations of shear are damped, and that the electric part of the Weyl tensor and the anisotropic stress tensor decay with the expansion as well as the heat flux of the curvature fluid. Specializing in locally rotationally symmetric spacetimes in orthonormal frames, we examine the late-time behaviour of the de Sitter universe in $f(R)$ gravity. For the Starobinsky model of f(R), we study the evolutionary behavior of the Universe by numerically integrating the Friedmann equation, where the initial conditions for the expansion, acceleration and jerk parameters are taken from observational data.
Bianchi type II models in the presence of perfect fluid and anisotropic dark energy
Kumar, Suresh
2011-01-01
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's field equations have been solved by applying two kinematical ans\\"{a}tze: we have assumed the variation law for the mean Hubble parameter that yields a constant value of 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 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 \\Lambda CDM cosmology. However, the derived model gives additional opportunities by being able to allow kinematics th...
Validation of Modified Lemaitre’s Anisotropic Damage Model with the Cross Die Drawing Test
Niazi, M.S.; Wisselink, H.H.; Meinders, T.
2012-01-01
Dual Phase (DP) steels are widely replacing the traditional forming steels in automotive industry. Advanced damage models are required to accurately predict the formability of DP steels. In this work, Lemaitre’s anisotropic damage model has been slightly modified for sheet metal forming applications
Luchini, Chris B.
1997-01-01
Development of camera and instrument simulations for space exploration requires the development of scientifically accurate models of the objects to be studied. Several planned cometary missions have prompted the development of a three dimensional, multi-spectral, anisotropic multiple scattering model of cometary coma.
Modelling anisotropic water transport in polymer composite reinforced with aligned triangular bars
Bryan Pajarito; Masatoshi Kubouchi; Saiko Aoki
2014-02-01
This work reports anisotropic water transport in a polymer composite consisting of an epoxy matrix reinforced with aligned triangular bars made of vinyl ester. By gravimetric experiments, water diffusion in resin and polymer composites were characterized. Parameters for Fickian diffusion and polymer relaxation models were determined by least-square curve fitting to the experimental data. Diffusion parameters of epoxy and vinyl ester resin were used as input during development of finite element (FE) model of polymer composite. Through transient FE diffusion analysis, anisotropic water transport in thickness direction of the polymer composite was numerically predicted and validated against experimental results. The case of using impermeable triangular bars was also numerically simulated. The diffusivity of reinforced aligned triangular bars was confirmed to affect anisotropic water transport in the composite. The results of this work suggest possible use of polymer composite for barrier and fluid removal applications.
How real-time cosmology can distinguish between different anisotropic models
Amendola, Luca [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D–69120 Heidelberg (Germany); Bjælde, Ole Eggers [Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK–8000 Aarhus C (Denmark); Valkenburg, Wessel [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden (Netherlands); Wong, Yvonne Y.Y., E-mail: l.amendola@thphys.uni-heidelberg.de, E-mail: oeb@phys.au.dk, E-mail: valkenburg@lorentz.leidenuniv.nl, E-mail: yvonne.y.wong@unsw.edu.au [School of Physics, The University of New South Wales, Sydney NSW 2052 (Australia)
2013-12-01
We present a new analysis on how to distinguish between isotropic and anisotropic cosmological models based on tracking the angular displacements of a large number of distant quasars over an extended period of time, and then performing a multipole-vector decomposition of the resulting displacement maps. We find that while the GAIA mission operating at its nominal specifications does not have sufficient angular resolution to resolve anisotropic universes from isotropic ones using this method within a reasonable timespan of ten years, a next-generation GAIA-like survey with a resolution ten times better should be equal to the task. Distinguishing between different anisotropic models is however more demanding. Keeping the observational timespan to ten years, we find that the angular resolution of the survey will need to be of order 0.1 μas in order for certain rotating anisotropic models to produce a detectable signature that is also unique to models of this class. However, should such a detection become possible, it would immediately allow us to rule out large local void models.
Chen, Yu [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gao, Kai [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Huang, Lianjie [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sabin, Andrew [Geothermal Program Office, China Lake, CA (United States)
2016-03-31
Accurate imaging and characterization of fracture zones is crucial for geothermal energy exploration. Aligned fractures within fracture zones behave as anisotropic media for seismic-wave propagation. The anisotropic properties in fracture zones introduce extra difficulties for seismic imaging and waveform inversion. We have recently developed a new anisotropic elastic-waveform inversion method using a modified total-variation regularization scheme and a wave-energy-base preconditioning technique. Our new inversion method uses the parameterization of elasticity constants to describe anisotropic media, and hence it can properly handle arbitrary anisotropy. We apply our new inversion method to a seismic velocity model along a 2D-line seismic data acquired at Eleven-Mile Canyon located at the Southern Dixie Valley in Nevada for geothermal energy exploration. Our inversion results show that anisotropic elastic-waveform inversion has potential to reconstruct subsurface anisotropic elastic parameters for imaging and characterization of fracture zones.
Modeling anisotropic plasmon excitations in self-assembled fullerenes
Iurov, Andrii; Gumbs, Godfrey; Gao, Bo; Huang, Danhong
2014-05-01
The plasmon excitations in Coulomb-coupled spherical two-dimensional electron gases (S2DEGs) reveal an interesting dependence on the displacement vector between the centers of the spheres with respect to the axis of quantization for the angular momentum quantum number L. Specifically, plasmon modes for a bundle of three S2DEGs have been obtained within the random-phase approximation. The inter-sphere Coulomb interaction matrix elements and their symmetry properties were also investigated in detail. The case of a bundle gives an adequate picture of the way in which the Coulomb interaction depends on the orbital angular momentum quantum number L and its projection M. We concluded that the interaction between the S2DEGs aligned at an angle of 45° with the axis of quantization is negligible compared to the interaction along and perpendicular to the quantization axis, which are themselves unequal to each other. Consequently, the plasmon excitation frequencies reveal an interesting orientational anisotropic coupling to an external electromagnetic field probing the charge density oscillations. Our result on the spatial correlation may be experimentally observable. In this connection, there have already been some experimental reports pointing to a similar effect in nanoparticles.
Anisotropic Cosmological Model in Modified Brans--Dicke Theory
Rasouli, S M M; Sepangi, Hamid R
2011-01-01
It has been shown that four dimensional Brans-Dicke theory with effective matter field and self interacting potential can be achieved from vacuum 5D BD field equations, where we refer to as modified Brans-Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing obtained formalism, we derive induced-matter on any 4D hypersurface in context of the MBDT. We illustrate that if the usual spatial scale factors are functions of time while scale factor of extra dimension is constant, and scalar field depends on time and fifth coordinate, then in general, one will encounter inconsistencies in field equations. Then, we assume the scale factors and scalar field depend on time and extra coordinate as separated variables in power law forms. Hence, we find a few classes of solutions in 5D spacetime through which, we probe the one which leads to a generalized Kasner relations among Kasner parameters. The induced scalar potential is found to be in power law or i...
Bianchi type-II models in the presence of perfect fluid and anisotropic dark energy
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.
Study on stress characteristics of Francis hydraulic turbine runner based on two-way FSI
Zhu, W. R.; Xiao, R. F.; Yang, W.; Liu, J.; Wang, F. J.
2012-11-01
In recent years, cracking phenomenon occurs in many large-sized turbines both nationally and internationally, which has threatened the stable operation of hydraulic turbines. Consequently, Stress characteristics calculation and analysis of a Francis hydraulic turbine runner by application of fluid-structure interaction (FSI) technology become significantly important. In order to introduce two-way coupling technology to hydraulic machinery, two-way FSI technology is applied in this article to calculate and analyze stress characteristics. Through coordinate system transformation, the continuity equations and Navier-Stokes equations in the Cartesian coordinates system are firstly transformed to ALE coordinates system. The fluid field control equations are then constructed and discrete equations can be obtained by using flow-condition-based interpolation (FBIC-C). The structure static mechanics equations used are established in rotation coordinate system, and modeled with the finite method. Two-way coupling is computed by using iteration method. The fluid equations and structure equations are iterated until coupling coefficients converge. According to structure result, the maximum stress, displacement as well as its location can be found. As a result, the most easily wear position can be discovered which provides valuable basis for optimized design and stable operation of Francis hydraulic turbines. After comparing the results with that of one-way coupling, it is discovered that displacements is the key factors which affects the results of one-way and two-way coupling.
Study on stress characteristics of Francis hydraulic turbine runner based on two-way FSI
In recent years, cracking phenomenon occurs in many large-sized turbines both nationally and internationally, which has threatened the stable operation of hydraulic turbines. Consequently, Stress characteristics calculation and analysis of a Francis hydraulic turbine runner by application of fluid-structure interaction (FSI) technology become significantly important. In order to introduce two-way coupling technology to hydraulic machinery, two-way FSI technology is applied in this article to calculate and analyze stress characteristics. Through coordinate system transformation, the continuity equations and Navier-Stokes equations in the Cartesian coordinates system are firstly transformed to ALE coordinates system. The fluid field control equations are then constructed and discrete equations can be obtained by using flow-condition-based interpolation (FBIC-C). The structure static mechanics equations used are established in rotation coordinate system, and modeled with the finite method. Two-way coupling is computed by using iteration method. The fluid equations and structure equations are iterated until coupling coefficients converge. According to structure result, the maximum stress, displacement as well as its location can be found. As a result, the most easily wear position can be discovered which provides valuable basis for optimized design and stable operation of Francis hydraulic turbines. After comparing the results with that of one-way coupling, it is discovered that displacements is the key factors which affects the results of one-way and two-way coupling.
Evaluation of Springback for DP980 S Rail Using Anisotropic Hardening Models
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.
Microscopic model of the Knight shift in anisotropic and correlated metals
Hall, Bianca E.; Klemm, Richard A.
2016-01-01
We present a microscopic model of nuclear magnetic resonance in metals. The spin-1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant \\boldsymbol{B}{0} and perpendicular time-oscillatory magnetic inductions \\boldsymbol{B}{1}(t) and with each other via an anisotropic hyperfine interaction. An Anderson-like Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each band described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin \\boldsymbol{g} tensor. Local orbital electron correlation effects are included using the mean-field decoupling procedure of Lacroix. The Knight resonance frequency and corresponding linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to {{≤ft({{B}1}/{{B}0}\\right)}2} and a constant for weak {{B}0}\\gg {{B}1} , both highly anisotropic shifts depend strongly upon \\boldsymbol{B}{0} when a Landau level is near the Fermi energy. Electron correlations affect the anisotropy of the linewidth shift. The model is easily generalizable to arbitrary nuclear spin I.
Debbaut, Charlotte; Vierendeels, Jan; Siggers, Jennifer H.; Repetto, Rodolfo; Monbaliu, Diethard; Segers, Patrick
2014-01-01
The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computat...
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.
2014-07-01
Stable partitioned algorithms for fluid-structure interaction (FSI) problems are developed and analyzed in this two-part paper. Part I describes an algorithm for incompressible flow coupled with compressible elastic solids, while Part II discusses an algorithm for incompressible flow coupled with structural shells. Importantly, these new added-mass partitioned (AMP) schemes are stable and retain full accuracy with no sub-iterations per time step, even in the presence of strong added-mass effects (e.g. for light solids). The numerical approach described here for bulk compressible solids extends the scheme of Banks et al. [1,2] for inviscid compressible flow, and uses Robin (mixed) boundary conditions with the fluid and solid solvers at the interface. The basic AMP Robin conditions, involving a linear combination of velocity and stress, are determined from the outgoing solid characteristic relation normal to the fluid-solid interface combined with the matching conditions on the velocity and traction. Two alternative forms of the AMP conditions are then derived depending on whether the fluid equations are advanced with a fractional-step method or not. The stability and accuracy of the AMP algorithm is evaluated for linearized FSI model problems; the full nonlinear case being left for future consideration. A normal mode analysis is performed to show that the new AMP algorithm is stable for any ratio of the solid and fluid densities, including the case of very light solids when added-mass effects are large. In contrast, it is shown that a traditional partitioned algorithm involving a Dirichlet-Neumann coupling for the same FSI problem is formally unconditionally unstable for any ratio of densities. Exact traveling wave solutions are derived for the FSI model problems, and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the AMP algorithm for the cases of light, medium and heavy solids.
The long-term and short-term anisotropic mechanical behaviour of a biaxially stretched polyethylene terephthalate foil is measured. The orientation of the crystalline phase is characterized and the representative foil microstructure is discussed. Using the obtained information, a mean-field model is used to simulate the elasto-viscoplastic behaviour of the oriented polymer foil, taking into account the different constitutive behaviour of the phases. The material is modelled as an aggregate of connected two-phase domains. The parameters of the constitutive behaviour of the crystalline and non-crystalline phases have been determined, and the ability to simulate the large-strain anisotropic behaviour of polyethylene terephthalate in the strain-rate-controlled regime and the long-term creep has been demonstrated. The model is extended to include pre-orientation of the non-crystalline phase. In addition, deformation at the microscopic level is analysed using the model results. (paper)
An anisotropic thermomechanical damage model for concrete at transient elevated temperatures.
Baker, Graham; de Borst, René
2005-11-15
The behaviour of concrete at elevated temperatures is important for an assessment of integrity (strength and durability) of structures exposed to a high-temperature environment, in applications such as fire exposure, smelting plants and nuclear installations. In modelling terms, a coupled thermomechanical analysis represents a generalization of the computational mechanics of fracture and damage. Here, we develop a fully coupled anisotropic thermomechanical damage model for concrete under high stress and transient temperature, with emphasis on the adherence of the model to the laws of thermodynamics. Specific analytical results are given, deduced from thermodynamics, of a novel interpretation on specific heat, evolution of entropy and the identification of the complete anisotropic, thermomechanical damage surface. The model is also shown to be stable in a computational sense, and to satisfy the laws of thermodynamics. PMID:16243703
SOL–divertor plasma simulations introducing anisotropic temperature with virtual divertor model
A 1D SOL–divertor plasma simulation code by introducing the anisotropic ion temperature with virtual divertor model has been developed. By introducing the anisotropic ion temperature directly, the second-order derivative parallel ion viscosity term in the momentum transport equation can be excluded and the boundary condition at the divertor plate will not be required in the simulation. In order to express the effects of the divertor plate and accompanying sheath implicitly, a virtual divertor model which has artificial sinks for the particle, momentum and energy has been introduced. Periodic boundary condition becomes available by the use of the virtual divertor model. By using this model, SOL–divertor plasmas which satisfy the Bohm condition has been successfully obtained. The dependence of the ion temperature anisotropy on the normalized mean free path of ion and the validity of the parallel ion viscous flux for the Braginskii expression and the limited one are also investigated
Anisotropic cosmological models in $f (R, T)$ theory of gravitation
Shri Ram; Priyanka; Manish Kumar Singh
2013-07-01
A class of non-singular bouncing cosmological models of a general class of Bianchi models filled with perfect fluid in the framework of $f (R, T)$ gravity is presented. The model initially accelerates for a certain period of time and decelerates thereafter. The physical behaviour of the model is also studied.
Invisibility Cloaks Modeled by Anisotropic Metamaterials Based on Inductor-capacitor Networks
Liu, Xiao; Li, Chao; Yao, Kan; Meng, Xiankun; Li, Fang
2009-01-01
Based on the transformation optics, a novel transmission-line (TL) approach to realize invisibility cloaking using planar anisotropic metamaterials (MTMs) is proposed. The two-dimensional cylindrical cloaks are modeled based on inductor-capacitor (L-C) MTMs networks. The three elements of the constitutive parameters are all allowed to be spatially inhomogeneous which lead to the full parameter realization of a cylindrical cloak. As an example, a cloak working at VHF band is modeled and its in...
A rock physics model for analysis of anisotropic parameters in a shale reservoir in Southwest China
Qian, Keran; Zhang, Feng; Chen, Shuangquan; Li, Xiangyang; Zhang, Hui
2016-02-01
A rock physics model is a very effective tool to describe the anisotropy and mechanical properties of rock from a seismology perspective. Compared to a conventional reservoir, modelling a shale reservoir requires us to face two main challenges in modelling: the existence of organic matter and strong anisotropy. We construct an anisotropic rock physics workflow for a typical shale reservoir in Southwest China, in which the organic matter is treated separately from other minerals by using a combination of anisotropic self-consistent approximation and the differential effective medium method. The standard deviation of the distribution function is used to model the degree of lamination of clay and kerogen. A double scan workflow is introduced to invert the probability of pore aspect ratio and lamination simultaneously, which can give us a better understanding of the shale formation. The anisotropic properties of target formation have been analysed based on the proposed model. Inverted Thomsen parameters, especially the sign of delta, are analysed in terms of the physical properties of rock physics modelling.
Hallez, Hans; Staelens, Steven; Lemahieu, Ignace [Department of Electronics and Information Systems, Institute of Broadband Technology (IBBT) Medical Image and Signal Processing (MEDISIP), Ghent University, Sint-Pietersnieuwstraat 41, 9000 Ghent (Belgium)], E-mail: hans.hallez@ugent.be
2009-10-21
EEG source analysis is a valuable tool for brain functionality research and for diagnosing neurological disorders, such as epilepsy. It requires a geometrical representation of the human head or a head model, which is often modeled as an isotropic conductor. However, it is known that some brain tissues, such as the skull or white matter, have an anisotropic conductivity. Many studies reported that the anisotropic conductivities have an influence on the calculated electrode potentials. However, few studies have assessed the influence of anisotropic conductivities on the dipole estimations. In this study, we want to determine the dipole estimation errors due to not taking into account the anisotropic conductivities of the skull and/or brain tissues. Therefore, head models are constructed with the same geometry, but with an anisotropically conducting skull and/or brain tissue compartment. These head models are used in simulation studies where the dipole location and orientation error is calculated due to neglecting anisotropic conductivities of the skull and brain tissue. Results show that not taking into account the anisotropic conductivities of the skull yields a dipole location error between 2 and 25 mm, with an average of 10 mm. When the anisotropic conductivities of the brain tissues are neglected, the dipole location error ranges between 0 and 5 mm. In this case, the average dipole location error was 2.3 mm. In all simulations, the dipole orientation error was smaller than 10 deg. We can conclude that the anisotropic conductivities of the skull have to be incorporated to improve the accuracy of EEG source analysis. The results of the simulation, as presented here, also suggest that incorporation of the anisotropic conductivities of brain tissues is not necessary. However, more studies are needed to confirm these suggestions.
EEG source analysis is a valuable tool for brain functionality research and for diagnosing neurological disorders, such as epilepsy. It requires a geometrical representation of the human head or a head model, which is often modeled as an isotropic conductor. However, it is known that some brain tissues, such as the skull or white matter, have an anisotropic conductivity. Many studies reported that the anisotropic conductivities have an influence on the calculated electrode potentials. However, few studies have assessed the influence of anisotropic conductivities on the dipole estimations. In this study, we want to determine the dipole estimation errors due to not taking into account the anisotropic conductivities of the skull and/or brain tissues. Therefore, head models are constructed with the same geometry, but with an anisotropically conducting skull and/or brain tissue compartment. These head models are used in simulation studies where the dipole location and orientation error is calculated due to neglecting anisotropic conductivities of the skull and brain tissue. Results show that not taking into account the anisotropic conductivities of the skull yields a dipole location error between 2 and 25 mm, with an average of 10 mm. When the anisotropic conductivities of the brain tissues are neglected, the dipole location error ranges between 0 and 5 mm. In this case, the average dipole location error was 2.3 mm. In all simulations, the dipole orientation error was smaller than 10 deg. We can conclude that the anisotropic conductivities of the skull have to be incorporated to improve the accuracy of EEG source analysis. The results of the simulation, as presented here, also suggest that incorporation of the anisotropic conductivities of brain tissues is not necessary. However, more studies are needed to confirm these suggestions.
Short-time dynamics of isotropic and anisotropic Bak-Sneppen model: extensive simulation results
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.
The behaviour of concrete, considered as isotropic for a sound material, becomes anisotropic and unilateral as soon as microcracks are initiated. Concrete also shows a different behaviour in tension than in compression. However, isotropic models, which are more simple and time costless, are still widely used for industrial applications. An anisotropic and unilateral model, with few parameters, is thus proposed in the present work, which enhances the accuracy of the description of concrete's behaviour, while remaining suitable for industrial studies. The validation of the model is based on experimental results. Numerical simulations of structures are also proposed, among which one concerns a representative volume of a confinement vessel. Finally, a non local theory is investigated to overcome the problems induced by strain localisation. (author)
Kondoh, Hiroshi; Matsushita, Mitsugu
1986-10-01
Diffusion-limited aggregation (DLA) model with anisotropic sticking probability Ps is computer-simulated on two dimensional square lattice. The cluster grows from a seed particle at the origin in the positive y area with the absorption-type boundary along x-axis. The cluster is found to grow anisotropically as R//˜Nν// and R\\bot˜Nν\\bot, where R\\bot and R// are the radii of gyration of the cluster along x- and y-axes, respectively, and N is the particle number constituting the cluster. The two exponents are shown to become assymptotically ν//{=}2/3, ν\\bot{=}1/3 whenever the sticking anisotropy exists. It is also found that the present model is fairly consistent with Hack’s law of river networks, suggesting that it is a good candidate of a prototype model for the evolution of the river network.
Modeling of plates with multiple anisotropic layers and residual stress
Engholm, Mathias; Pedersen, Thomas; Thomsen, Erik Vilain
2016-01-01
an excellent agreement between the two models is seen with a relative difference of less than 2% for all calculations. The model was also used to extract the cell capacitance, the parasitic capacitance and the residual stress of a pressure sensor composed of a multilayered plate of silicon and...
Implementation of an anisotropic mechanical model for shale in Geodyn
Attia, A; Vorobiev, O; Walsh, S
2015-05-15
The purpose of this report is to present the implementation of a shale model in the Geodyn code, based on published rock material models and properties that can help a petroleum engineer in his design of various strategies for oil/gas recovery from shale rock formation.
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.
Garion, C
2004-01-01
A majority of the thin-walled components subjected to intensive plastic straining at cryogenic temperatures are made of stainless steels. The examples of such components can be found in the interconnections of particle accelerators, containing the superconducting magnets, where the thermal contraction is absorbed by thin-walled, axisymetric shells called bellows expansion joints. The stainless steels show three main phenomena induced by plastic strains at cryogenic temperatures: serrated (discontinuous) yielding, gamma->alpha' phase transformation and anisotropic ductile damage. In the present paper, a coupled constitutive model of gamma->alpha' phase transformation and orthotropic ductile damage is presented. A kinetic law of phase transformation, and a kinetic law of evolution of orthotropic damage are presented. The model is extended to anisotropic plasticity comprising a constant anisotropy (texture effect), which can be classically taken into account by the Hill yield surface, and plastic strain induced ...
Magnetized Anisotropic Dark Energy Models in Barber’s Second Self-Creation Theory
D. D. Pawar
2014-01-01
Full Text Available The present paper deals with Bianchi type IX cosmological model with magnetized anisotropic dark energy by using Barber’s self-creation theory. The energy momentum tensor consists of anisotropic fluid with EoS parameter ω and a uniform magnetic field of energy density ρB. In order to obtain the exact solution we have assumed that dark energy components and the components of magnetic field interact minimally and obey the law of conservation of energy momentum tensors. We have also used the special law of variation for the mean generalized Hubble parameter and power law relation between scalar field and scale factor. Some physical and kinematical properties of the models have been discussed.
Multi-scale modelling of AISI H11 martensitic tool steel surface anisotropic mechanical behaviour
Zouaghi Ahmed; Velay Vincent; Soveja Adriana; Rézaï-Aria Farhad
2014-01-01
In this work, a numerical investigation is carried out on the anisotropic and heterogeneous behaviour of the AISI H11 martensitic tool steel surface using finite element method and a multi-scale approach. An elasto-viscoplastic model that considers nonlinear isotropic and kinematic hardenings is implemented in the finite elements code ABAQUS using small strain assumption. The parameters of the constitutive equations are identified using macroscopic quasi-static and cyclic material responses b...
Serigne Saliou Mbengue; Nicolas Buiron; Vincent Lanfranchi
2016-01-01
During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material’s behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for...
Large scale behavior of a two-dimensional model of anisotropic branched polymers.
Knežević, Milan; Knežević, Dragica
2013-10-28
We study critical properties of anisotropic branched polymers modeled by semi-directed lattice animals on a triangular lattice. Using the exact transfer-matrix approach on strips of quite large widths and phenomenological renormalization group analysis, we obtained pretty good estimates of various critical exponents in the whole high-temperature region, including the point of collapse transition. Our numerical results suggest that this collapse transition belongs to the universality class of directed percolation. PMID:24182076
Large scale behavior of a two-dimensional model of anisotropic branched polymers
Knežević, Milan; Knežević, Dragica
2013-10-01
We study critical properties of anisotropic branched polymers modeled by semi-directed lattice animals on a triangular lattice. Using the exact transfer-matrix approach on strips of quite large widths and phenomenological renormalization group analysis, we obtained pretty good estimates of various critical exponents in the whole high-temperature region, including the point of collapse transition. Our numerical results suggest that this collapse transition belongs to the universality class of directed percolation.
Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models
Bakar, Burhan; Tirnakli, Ugur
2008-01-01
The conventional Hamming distance measurement captures only the short-time dynamics of the displacement between the uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod. Phys. C 14, 805 (2003)] is used to study the short-time and long-time dynamics of the two distinct random configurations of the isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to 1-dimensional case, the time evolution of the displacement is...
Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models
Bakar, Burhan; Tirnakli, Ugur
2007-01-01
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 $\\alpha$ 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...
Dani, I.; Tahiri, N.; Ez-Zahraouy, H.; Benyoussef, A.
2016-08-01
In this paper we study, using mean field theory (MFT), the effect of the anisotropic Dzyaloshinskii-Moriya (DM) interaction on the phase diagrams of the spin-half Ashkin-Teller model on hypercubic lattice. Different new phase diagrams are found by varying the anisotropy of DM interaction. The multicritical behavior is studied as a function of four-spin interaction coefficient J4 /J1 and for two fixed values of spin interaction coefficient J2 /J1.
Anisotropic Hubbard model on a triangular lattice - spin dynamics in HoMnO3
Saptarshi Ghosh; Avinash Singh
2008-01-01
The recent neutron scattering data for spin-wave dispersion in HoMnO3 are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO3 correspond to the strong-coupling limit / > ∼ 15, with planar exchange energy = 42/ ≃ 2.5 meV and planar anisotropy ≃ 0.35 meV.
Zhong-yan Liu; Huan-zhen Chen
2014-01-01
By choosing the trial function space to the immersed finite element space and the test function space to be piecewise constant function space, we develop a discontinuous Galerkin immersed finite volume element method to solve numerically a kind of anisotropic diffusion models governed by the elliptic interface problems with discontinuous tensor-conductivity. The existence and uniqueness of the discrete scheme are proved, and an optimal-order energy-norm estimate and ${L}^{2}$ -norm estimate f...
Safety estimation of high-pressure hydraulic cylinder using FSI method
KIM J.H.; HAN S.M.; KIM Y.J.
2016-01-01
Hydraulic cylinder is a primary component of the hydraulic valve systems.The numerical study of hydraulic cylinder to evaluate the stress analysis,the life assessment and the performance of operation characteristics in hydraulic cylinder were described.The calculation of safety factor,fatigue life,piston chamber pressure,rod chamber pressure and the change of velocity of piston with flow time after the beginning of hydraulic cylinder were incorporated.Numerical analysis was performed using the commercial CFD code,ANSYS with unsteady,dynamic mesh model,two-way FSI (fluid-struc-ture interaction)method and k-εturbulent model.The internal pressure in hydraulic cylinder through stress analysis show higher than those of the yield strength.
Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.
2015-06-01
A new anisotropic hr-adaptive mesh technique has been applied to modelling of multiscale transport phenomena, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been setup for two-dimensional (2-D) transport phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes.
Viscoelastic response of anisotropic biological membranes. Part II: Constitutive models
Lubarda Vlado A.
2014-01-01
Full Text Available In Part I of this series [7] we described the structure of the biopolymer interlayers found in the shell of the mollusk Haliotis rufescens (the red abalone. There we described how the layers can be viewed as a viscoelastic composite reinforced by a network of chitin fibrils arranged in an often nearly unidirectional architecture. Mechanical testing documented the response to tensile testing of layers removed via demineralization. Herein in Part II we describe a general viscoelastic constitutive model for such layers that may be both transversely isotropic or orthotropic as would follow from the network of nearly aligned chitin fibrils described by Bezares et al. in Part I [7]. Part III of this series will be concerned with applying the models to more fully describing the response of these types of biological membranes to mechanical loading.
Anisotropic 3D Modeling for Long Offset VSP Survey Design
Today's seismic techniques allow the geoscientist to do the interpretation more quantitatively. AVO and anisotropy measurements are the examples of DHI (Direct Hydrocarbon Indication). These measurements can be done accurately using long offset borehole seismic survey such as walk away VSP, having the geophones located down hole close to the target formation. This paper will show the importance 3D seismic modeling prior to the survey, by simulating the seismic wave propagation in three-dimensional volume filled with continuous material properties. This pre-survey modeling can help us suppressing the uncertainties and narrowing the error bars on the real survey. Some examples from offshore Nigeria showed dramatic geometrical differences between ordinary 2D compared to 3D observations Assumption that the seismic wave travels in 2D plane is not always acceptable for survey design. The examples also demonstrated the ability to observe some critical information such as the limit of incidence angle, compromise between resolution and image coverage, effects of velocity anomalies, anisotropy and dipping formations on lateral coverage. Fluid effect in 3D modeling will also be discussed here. Amplitude anomalies are predicted by replacing different type of fluids effect in the target reservoirs, as well as various types of AVO classes. A well-prepared long offset VSP survey is very critical to provide us high quality and high accuracy information that can be used to calibrate and optimise the full 3D seismic processing and interpretation in the area. This process is known as Well Driven Seismic (WDS)
Multi-scale modelling of AISI H11 martensitic tool steel surface anisotropic mechanical behaviour
Zouaghi Ahmed
2014-06-01
Full Text Available In this work, a numerical investigation is carried out on the anisotropic and heterogeneous behaviour of the AISI H11 martensitic tool steel surface using finite element method and a multi-scale approach. An elasto-viscoplastic model that considers nonlinear isotropic and kinematic hardenings is implemented in the finite elements code ABAQUS using small strain assumption. The parameters of the constitutive equations are identified using macroscopic quasi-static and cyclic material responses by the mean of a localization rule. Virtual realistic microstructures, consisting of laths and grains, are generated using particular Voronoï tessellations. These microstructures consider the specific crystallographic orientations α’/γ. Finite element investigation is then performed. The local heterogeneous and anisotropic behaviour of the surface as well as the subsurface is shown under quasi-static and cyclic mechanical loadings. The laths morphology and crystallographic orientation have an important impact on the local mechanical fields.
Dayanandan, Baiju; Maurya, S. K.; Gupta, Y. K.; Smitha, T. T.
2016-05-01
We present a detailed investigation of the stability of anisotropic compact star models by introducing Matese and Whitman (Phys. Rev. D 11:1270, 1980) solution in general relativity. We have particularly looked into the detailed investigation of the measurements of basic physical parameters such as radial pressure, tangential pressure, energy density, red shift, sound velocity, masses and radii are affected by unknown effects such as loss, accretion and diffusion of mass. Those give insight into the characteristics of the compact astrophysical object with anisotropic matter distribution as well as the physical reality. The results obtained for the physical feature of compact stars such as, Her. X-1, RXJ 1856-37, SAX J1808.4-3658(SS2) and SAX J1808.4-3658(SS1) are compared to the recently observed massive compact object.
Spreading and wandering of Gaussian–Schell model laser beams in an anisotropic turbulent ocean
Wu, Yuqian; Zhang, Yixin; Zhu, Yun; Hu, Zhengda
2016-09-01
The effect of anisotropic turbulence on the spreading and wandering of Gaussian–Schell model (GSM) laser beams propagating in an ocean is studied. The long-term spreading of a GSM beam propagating through the paraxial channel of a turbulent ocean is also developed. Expressions of random wander for such laser beams are derived in an anisotropic turbulent ocean based on the extended Huygens–Fresnel principle. We investigate the influence of parameters in a turbulent ocean on the beam wander and spreading. Our results indicate that beam spreading and random beam wandering are smaller without considering the anisotropy of turbulence in the oceanic channel. Salinity fluctuation has a greater contribution to both the beam spreading and beam wander than that of temperature fluctuations in a turbulent ocean. Our results could be helpful for designing a free-space optical wireless communication system in an oceanic environment.
Modeling Anisotropic Stars Obeying Chaplygin Equation of State
Bhar, Piyali; Sharma, Ranjan
2016-01-01
In this work we provide a framework for modeling compact stars in which the interior matter distribution obeys a generalised Chaplygin equation of state. The interior geometry of the stellar object is described by a spherically symmetric line element which is simultaneously comoving and isotropic with the exterior spacetime being vacuum. We are able to integrate the Einstein field equations and present closed form solutions which adequately describe compact strange star candidates like Her X-1, RX J 1856-37, PSRJ 1614-2230 and SAX J1808.4-3658.
Anisotropic creep modeling for f.c.c. single crystals
The one-dimensional behavior of single crystal superalloys at high temperatures under constant and cyclic creep conditions is described by means of a 4-parameter rheological model based on linear viscoelasticity. Tertiary creep is taken into account by reducing the effective cross section by means of an additional damage parameter. Tensile creep tests have been used for the identification of the material constants by a non-linear optimization procedure. For the generalization to threee dimensions, a complete tensor-representation of cubic material symmetry is given. It contains twelve (temperature dependent) material parameters. Some results by finite element analysis will be presented. (orig.)
Spin-density functional for exchange anisotropic Heisenberg model
Prata, G.N.; Penteado, P.H.; Souza, F.C. [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, Sao Carlos - SP (Brazil); Libero, Valter L., E-mail: valter@if.sc.usp.b [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, Sao Carlos - SP (Brazil)
2009-10-15
Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.
Towards an Anisotropic Whole Mantle 3D Elastic Velocity Model
Panning, M. P.; Romanowicz, B.; Gung, Y.
2001-12-01
Many studies have documented the existence of anisotropy in the earth's upper mantle, concentrated in the top 200 km. This evidence comes from the study of surface waves as well as shear wave splitting. There is also evidence for shear wave splitting in D", at least in well sampled regions. There are some hints of anisotropy at the base of the transition zone. Tomographic models of the upper mantle have been developed with simplifying assumptions about the nature of the anisotropy, in order to minimize the number of free parameters in the inversions. Some assume transverse isotropy (e.g Ekström and Dziewonski, 1997), others include additional degrees of freedom with some realistic constraints on mineralogy (e.g. Montagner and Tanimoto, 1991). Our goal is to investigate anisotropy in the whole mantle, using the framework of waveform inversion, and the nonlinear asymptotic mode coupling theory (NACT), previously developed and applied to the construction of whole-mantle SH velocity models (Li and Romanowicz, 1996; Mégnin and Romanowicz, 2000). For this we require a 3 component dataset, and we have extended our automatic transverse (T) component wavepicking procedures to the vertical (Z) and longitudinal (L) component - a non-trivial task given the large number of phases present in the coupled P-SV system. A useful initial assumption, for which the theory has been readily adapted, is that of transverse isotropy. As a first step towards this, we have been investigating inversions using T component and Z,L component data separately. In particular, this allows us to explore the sampling that can be achieved with Z,L component data alone in the deepest part of the mantle. Indeed, D" is in general much better sampled in SH than in SV, owing to the availability of SHdiff at large distances, while SVdiff decays more rapidly due to mantle-core coupling. We present the results of our resolution experiments and discuss the differences between the 3D SV model obtained in well
Spin-density functional for exchange anisotropic Heisenberg model
Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.
Anisotropic Heisenberg model for a semi-infinite crystal
A semi-infinite Heisenberg model with exchange interactions between nearest and next-nearest neighbors in a simple cubic lattice. The free surface from the other layers of magnetic ions, by choosing a single ion uniaxial anisotropy in the surface (Ds) different from the anisotropy in the other layers (D). Using the Green function formalism, the behavior of magnetization as a function of the temperature for each layer, as well as the spectrum localized magnons for several values of ratio Ds/D for surface magnetization. Above this critical ratio, a ferromagnetic surface layer is obtained white the other layers are already in the paramagnetic phase. In this situation the critical temperature of surface becomes larger than the critical temperature of the bulk. (Author)
Barrow, John D
2015-01-01
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 isotropisation on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialise 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 collisionl...
Linjiang, QIN; Changfu, YANG
2016-03-01
The rocks in the crust and the upper mantle of the Earth are believed to exhibit electrical anisotropy to some extent. It is beneficial to further understand and recognize the propagation of the electromagnetic waves in the Earth by investigating the magnetotelluric (which is one of the main geophysical techniques to probe the deep structures in the Earth) responses of the media with anisotropic conductivity structures. In the present study, we examine the magnetotelluric fields over an idealized 2-D model consisting of two segments with axially anisotropic conductivity structures overlying a perfect conductor basement by a quasi-static analytic approach. The resulting analytic solution could not only contribute to the electromagnetic induction theory in the anisotropic Earth but also serve as at least an initial standard solution which could be used to validate the reliability and accuracy of the numerical algorithms developed for modeling the magnetotelluric responses of the 2-D media with much more general anisotropic conductivity.
Qin, Linjiang; Yang, Changfu
2016-06-01
The rocks in the crust and the upper mantle of the Earth are believed to exhibit electrical anisotropy to some extent. It is beneficial to further understand and recognize the propagation of the electromagnetic waves in the Earth by investigating the magnetotelluric (which is one of the main geophysical techniques to probe the deep structures in the Earth) responses of the media with anisotropic conductivity structures. In this study, we examine the magnetotelluric fields over an idealized 2-D model consisting of two segments with axially anisotropic conductivity structures overlying a perfect conductor basement by a quasi-static analytic approach. The resulting analytic solution could not only contribute to the electromagnetic induction theory in the anisotropic Earth but also serve as at least an initial standard solution which could be used to validate the reliability and accuracy of the numerical algorithms developed for modelling the magnetotelluric responses of the 2-D media with much more general anisotropic conductivity.
Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature
Pandey, Sachin
2016-01-01
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.
Spin superfluidity in the anisotropic XY model in the triangular lattice
Lima, L. S.
2016-07-01
We use the SU(3) Schwinger's boson theory to study the spin transport properties in the two-dimensional anisotropic frustrated Heisenberg model in the triangular lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents an single-ion anisotropy. We study the spin transport in the Bose-Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid: = = t . Our results show a metallic spin transport for ω > 0 and a superfluid spin transport in the limit of DC conductivity, ω → 0 , where σ(ω) tends to infinity in this limit of ω.
Debbaut, Charlotte; Vierendeels, Jan; Siggers, Jennifer H; Repetto, Rodolfo; Monbaliu, Diethard; Segers, Patrick
2014-01-01
The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computational fluid dynamics. VS inclusion resulted in more spatially homogeneous perfusion. Anisotropic permeability resulted in a larger axial velocity component than isotropic permeability. A parameter study revealed that results are most sensitive to the lobule size and radial pressure drop. Our model provides insight into hepatic microhaemodynamics, and suggests that inclusion of VS in the model leads to perfusion patterns that are likely to reflect physiological reality. The model has potential for applications to unphysiological and pathological conditions. PMID:23237543
Zheng Miao; Jin-Liang Xu; Ya-Ling He
2014-01-01
The transport phenomena in a passive direct methanol fuel cell (DMFC) were numerically simulated by the proposed two-dimensional two-phase nonisothermal mass transport model. The anisotropic transport characteristic and deformation of the gas diffusion layer (GDL) were considered in this model. The natural convection boundary conditions were adopted for the transport of methanol, oxygen, and heat at the GDL outer surface. The effect of methanol concentration in the reservoir on cell performan...
Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM).
Xia, Kelin; Opron, Kristopher; Wei, Guo-Wei
2015-11-28
Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions. PMID:26627949
Vitillo, F.; Vitale Di Maio, D.; Galati, C.; Caruso, G.
2015-11-01
A CFD analysis has been carried out to study the thermal-hydraulic behavior of liquid metal coolant in a fuel assembly of triangular lattice. In order to obtain fast and accurate results, the isotropic two-equation RANS approach is often used in nuclear engineering applications. A different approach is provided by Non-Linear Eddy Viscosity Models (NLEVM), which try to take into account anisotropic effects by a nonlinear formulation of the Reynolds stress tensor. This approach is very promising, as it results in a very good numerical behavior and in a potentially better fluid flow description than classical isotropic models. An Anisotropic Shear Stress Transport (ASST) model, implemented into a commercial software, has been applied in previous studies, showing very trustful results for a large variety of flows and applications. In the paper, the ASST model has been used to perform an analysis of the fluid flow inside the fuel assembly of the ALFRED lead cooled fast reactor. Then, a comparison between the results of wall-resolved conjugated heat transfer computations and the results of a decoupled analysis using a suitable thermal wall-function previously implemented into the solver has been performed and presented.
MacFarlane, Jake; Thiel, Stephan; Pek, Josef; Peacock, Jared; Heinson, Graham
2014-11-01
As opinions regarding the future of energy production shift towards renewable sources, enhanced geothermal systems (EGS) are becoming an attractive prospect. The characterisation of fracture permeability at depth is central to the success of EGS. Recent magnetotelluric (MT) studies of the Paralana geothermal system (PGS), an EGS in South Australia, have measured changes in MT responses which were attributed to fracture networks generated during fluid injection experiments. However, extracting permeabilities from these measurements remains problematic as conventional isotropic MT modelling is unable to accommodate for the complexities present within an EGS. To circumvent this problem, we introduce an electrical anisotropy representation to allow better characterisation of volumes at depth. Forward modelling shows that MT measurements are sensitive to subtle variations in anisotropy. Subsequent two-dimensional anisotropic forward modelling shows that electrical anisotropy is able to reproduce the directional response associated with fractures generated by fluid injection experiments at the PGS. As such, we conclude that MT monitoring combined with anisotropic modelling is a promising alternative to the micro-seismic method when characterising fluid reservoirs within geothermal and coal seam gas reservoirs.
Cosmological model with anisotropic dark energy and self-similarity of the second kind
We study the evolution of an anisotropic fluid with self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (pr =ωρ) and that the fluid moves along time-like geodesics. The equation of state and the anisotropy with self-similarity of second kind imply ω = -1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that for the parameter α=-1/2 , it may represent a Big Rip cosmological model. (author)
The wave propagation problem in anisotropic media is modeled by the Gauss-Hermite beam and tile finite element method and their results are compared. Gauss-Hermite mettled is computationally fast and simple, and explicitly incorporates beam spreading. In the 2-D model problem chosen, the ultrasonic beam leaves a transducer, propagates through a layer of ferritic steel and through a planar interface into a region of columnar cast stainless steel with two directions. After propagation to a reference plane, comparison .if made of the time-domain waveforms predicted by tile two models. The predictions of the two models are found to be in good agreement near the center of the beam, with deviations developing as one moves away from tile central ray. These are interpreted to be a consequence of the Fresnel approximation, made in the Gauss-Hermite model.
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.
Anisotropic Bianchi-III cosmological model in f (R, T) gravity
Sahoo, P. K.; Sahu, S. K.; Nath, A.
2016-01-01
An anisotropic Bianchi type-III universe is investigated in the presence of a perfect fluid within the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the source of matter. Here we have considered the first two cases of the f(R,T) model, i.e. f(R,T)=R+2f(T) and f(R,T)=f1(R)+f2(T). We have shown that the field equations of f(R,T) gravity are solvable for any arbitrary function of a scale factor. To get a physically realistic model of the universe, we have assumed a simple power-law form of a scale factor. The exact solutions of the field equations are obtained, which represent an expanding model of the universe which starts expanding with a big bang at t = 0 . The physical behaviours of the model are discussed.
Haider, Mohammad Faisal; Haider, Md. Mushfique; Yasmeen, Farzana
2016-07-01
Heterogeneous materials, such as composites consist of clearly distinguishable constituents (or phases) that show different electrical properties. Multifunctional composites have anisotropic electrical properties that can be tailored for a particular application. The effective anisotropic electrical conductivity of composites is strongly affected by many parameters including volume fractions, distributions, and orientations of constituents. Given the electrical properties of the constituents, one important goal of micromechanics of materials consists of predicting electrical response of the heterogeneous material on the basis of the geometries and properties of the individual phases, a task known as homogenization. The benefit of homogenization is that the behavior of a heterogeneous material can be determined without resorting or testing it. Furthermore, continuum micromechanics can predict the full multi-axial properties and responses of inhomogeneous materials, which are anisotropic in nature. Effective electrical conductivity estimation is performed by using classical micromechanics techniques (composite cylinder assemblage method) that investigates the effect of the fiber/matrix electrical properties and their volume fractions on the micro scale composite response. The composite cylinder assemblage method (CCM) is an analytical theory that is based on the assumption that composites are in a state of periodic structure. The CCM was developed to extend capabilities variable fiber shape/array availability with same volume fraction, interphase analysis, etc. The CCM is a continuum-based micromechanics model that provides closed form expressions for upper level length scales such as macro-scale composite responses in terms of the properties, shapes, orientations and constituent distributions at lower length levels such as the micro-scale.
Filippov, Alexander E.; Gorb, Stanislav N.
2016-03-01
Previous experimental data clearly revealed anisotropic friction on the ventral scale surface of snakes. However, it is known that frictional properties of the ventral surface of the snake skin range in a very broad range and the degree of anisotropy ranges as well to a quite strong extent. This might be due to the variety of species studied, diversity of approaches used for the friction characterization, and/or due to the variety of substrates used as a counterpart in the experiments. In order to understand the interactions between the nanostructure arrays of the ventral surface of the snake skin, this study was undertaken, which is aimed at numerical modeling of frictional properties of the structurally anisotropic surfaces in contact with various size of asperities. The model shows that frictional anisotropy appears on the snake skin only on the substrates with a characteristic range of roughness, which is less or comparable with dimensions of the skin microstructure. In other words, scale of the skin relief should reflect an adaptation to the particular range of surfaces asperities of the substrate.
Wang, Lei; Wang, Xiaodong
2014-06-01
Resulting from the nature of anisotropy of coal media, it is a meaningful work to evaluate pressure transient behavior and flow characteristics within coals. In this article, a complete analytical model called the elliptical flow model is established by combining the theory of elliptical flow in anisotropic media and Fick's laws about the diffusion of coalbed methane. To investigate pressure transient behavior, analytical solutions were first obtained through introducing a series of special functions (Mathieu functions), which are extremely complex and are hard to calculate. Thus, a computer program was developed to establish type curves, on which the effects of the parameters, including anisotropy coefficient, storage coefficient, transfer coefficient and rate constant, were analyzed in detail. Calculative results show that the existence of anisotropy would cause great pressure depletion. To validate new analytical solutions, previous results were used to compare with the new results. It is found that a better agreement between the solutions obtained in this work and the literature was achieved. Finally, a case study is used to explain the effects of the parameters, including rock total compressibility coefficient, coal medium porosity and anisotropic permeability, sorption time constant, Langmuir volume and fluid viscosity, on bottom-hole pressure behavior. It is necessary to coordinate these parameters so as to reduce the pressure depletion.
Resulting from the nature of anisotropy of coal media, it is a meaningful work to evaluate pressure transient behavior and flow characteristics within coals. In this article, a complete analytical model called the elliptical flow model is established by combining the theory of elliptical flow in anisotropic media and Fick's laws about the diffusion of coalbed methane. To investigate pressure transient behavior, analytical solutions were first obtained through introducing a series of special functions (Mathieu functions), which are extremely complex and are hard to calculate. Thus, a computer program was developed to establish type curves, on which the effects of the parameters, including anisotropy coefficient, storage coefficient, transfer coefficient and rate constant, were analyzed in detail. Calculative results show that the existence of anisotropy would cause great pressure depletion. To validate new analytical solutions, previous results were used to compare with the new results. It is found that a better agreement between the solutions obtained in this work and the literature was achieved. Finally, a case study is used to explain the effects of the parameters, including rock total compressibility coefficient, coal medium porosity and anisotropic permeability, sorption time constant, Langmuir volume and fluid viscosity, on bottom-hole pressure behavior. It is necessary to coordinate these parameters so as to reduce the pressure depletion. (paper)
Serigne Saliou Mbengue
2016-04-01
Full Text Available During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material’s behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI method. Measurements on the test bench and Finite Elements results are presented.
Mbengue, Serigne Saliou; Buiron, Nicolas; Lanfranchi, Vincent
2016-01-01
During the manufacturing process and use of ferromagnetic sheets, operations such as rolling, cutting, and tightening induce anisotropy that changes the material's behavior. Consequently for more accuracy in magnetization and magnetostriction calculations in electric devices such as transformers, anisotropic effects should be considered. In the following sections, we give an overview of a macroscopic model which takes into account the magnetic and magnetoelastic anisotropy of the material for both magnetization and magnetostriction computing. Firstly, a comparison between the model results and measurements from a Single Sheet Tester (SST) and values will be shown. Secondly, the model is integrated in a finite elements code to predict magnetostrictive deformation of an in-house test bench which is a stack of 40 sheets glued together by the Vacuum-Pressure Impregnation (VPI) method. Measurements on the test bench and Finite Elements results are presented. PMID:27092513
Anisotropic quantum cosmological models a discrepancy between many-worlds and dBB interpretations
Alvarenga, F G; Fabris, J C; Gonçalves, S V B
2002-01-01
In the isotropic quantum cosmological perfect fluid model, the initial singularity can be avoided, while the classical behaviour is recovered asymptotically. We verify if initial anisotropies can also be suppressed in a quantum version of a classical anisotropic model where gravity is coupled to a perfect fluid. Employing a Bianchi I cosmological model, we obtain a "Schr\\"odinger-like" equation where the matter variables play de role of time. This equation has a hyperbolic signature. It can be explicitly solved and a wave packet is constructed. The expectation value of the scale factor, evaluated in the spirit of the many-worlds interpretation, reveals an isotropic Universe. On the other hand, the bohmian trajectories indicate the existence of anisotropies. This is an example where the Bohm-de Broglie and the many-worlds interpretations are not equivalent. It is argued that this inequivalence is due to the hyperbolic structure of the "Schr\\"odinger-like" equation.
In the general relativity theory Bianki's homogeneous axisymmetrical cosmological model of type 5 is considered. This model belongs to the class of anisotropic models with 4-velocity nonorthogonal to invariant varieties (homogeneous spaces) V3. Matter possesses a velocity and a nonzero (with the exception of dustlike matter) value of 4-acceleration. A transition from a synchronous system with geodetic time line orthogonal to space-like V3 to the concomitant system reveals the presence of horizon surfaces and a possible incompleteness of the initial synchronous system. This necessitates also the introduction of a semigeodetic system with geodetic orthogonal invariant varieties V3 that are space-like. Gravitational equations are qualitatively analyzed. The hydrodynamic specificity of continuous motion of matter with 4-acceleration manifests itself as bifoliate solutions (the presence of limiting lines). The motion of matter with the studied symmetry in the Galilean space-time is also analyzed
Short intergranular cracks in the piecewise anisotropic continuum model of the microstructure
Computational algorithms aiming at modeling and visualization of the initiation and growth of intergranular stress corrosion cracks (e.g., in the steam generator tubes) on the grain-size scale have already been proposed [6]. The main focus of the paper is given to the influence of randomly oriented neighboring grains on the microscopic stress fields at crack tips. The incompatibility strains, which develop along the boundaries of randomly oriented anisotropic grains, are shown to influence the local stress fields at crack tips significantly. Special attention has been paid to the implementation and comparison of different numerical methods estimating the local stress fields at crack tips, aiming at optimizing the computational time and the numerical accuracy of the results. The limited number of calculations indicate that the anisotropic arrangement of grains with local incompatibility strains causes on average about 10% (plane strain) and 26% (plane stress) higher J-integral values at the crack tips than expected from the calculations in the isotropic case.(author)
A Whole-Mantle Three Dimensional Radially Anisotropic S Velocity Model
Panning, M. P.; Romanowicz, B. A.
2004-12-01
We present a 3D radially anisotropic model of the whole mantle obtained using a large three component surface and body waveform dataset and an iterative inversion for structure and source parameters based on Nonlinear Asymptotic Coupling Theory (NACT) (Li and Romanowicz, 1995). The model is parameterized by isotropic VS up to spherical harmonic degree 24 and ξ (ξ = VSH2 / VSV2), a measurement of radial anisotropy in shear velocity, up to degree 16. While the isotropic portion of the model is consistent with previous shear velocity tomographic models, the anisotropic portion suggests relationships between flow and anisotropy in a vairety of depth ranges. In the uppermost mantle, we confirm observations of regions with VSH}>V{SV starting at ˜80 km under oceanic regions and ˜250 km under old continental lithosphere, suggesting horizontal flow beneath the lithosphere (Gung et al., 2003). We also observe a VSV}>V{SH signature at ˜200-300 km depth beneath major ridge systems with amplitude significantly correlated with spreading rate for fast-spreading segments. In the transition zone (400-700 km depth), regions of subducted slab material are associated with VSV}>V{SH. We also confirm the observation of strong radially symmetric VSH}>V{SV in the lowermost 300 km (Panning and Romanowicz, 2004). The 3D deviations from this degree 0 signature are associated with the transition to the large-scale low-velocity superplumes under the central Pacific and Africa, suggesting that VSH}>V{SV is generated in the predominant horizontal flow of a mechanical boundary layer, with a change in signature related to transition to upwelling at the superplumes. We also solve for source perturbations in an interative procedure. Source perturbations are generally small compared to published Harvard CMT solutions, but significantly improve the fit to the data. The sources in the circum-Pacific subduction zones show small but clearly systematic shifts in location due to an improved structural
Impact of Extended Starobinsky Model on Evolution of Anisotropic Axially Symmetric Sources
Noureen, Ifra
2014-01-01
We study the implications of $R^n$ extension of Starobinsky model on dynamical instability of axially symmetric gravitating body. The matter distribution is considered to be anisotropic for which modified field equations are formed in context of $f(R)$ gravity. In order to achieve the collapse equation, we make use of the dynamical equations, extracted from linearly perturbed contracted Bianchi identities. The collapse equation carries adiabatic index $\\Gamma$ in terms of usual and dark source components, defining the range of stability/insatbility in Newtonian (N) and post-Newtonian (pN) eras. It is found that supersymmetric supergravity $f(R)$ model represents the more practical substitute of higher order curvature corrections.
Lima, L. S.
2016-07-01
We use the SU(3) Schwinger's boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents a single-ion anisotropy and J1 and J2 exchange interactions. We study the spin transport in the Bose-Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid: = = t. Our results show a metallic spin transport for ω > 0 and a superconductor spin transport in the limit of DC conductivity, ω → 0, where σ(ω) tends to infinity in this limit of ω.
Anisotropic Bulk Viscous String Cosmological Model in a Scalar-Tensor Theory of Gravitation
D. R. K. Reddy
2013-01-01
Full Text Available Spatially homogeneous, anisotropic, and tilted Bianchi type-VI0 model is investigated in a new scalar-tensor theory of gravitation proposed by Saez and Ballester (1986 when the source for energy momentum tensor is a bulk viscous fluid containing one-dimensional cosmic strings. Exact solution of the highly nonlinear field equations is obtained using the following plausible physical conditions: (i scalar expansion of the space-time which is proportional to the shear scalar, (ii the barotropic equations of state for pressure and energy density, and (iii a special law of variation for Hubble’s parameter proposed by Berman (1983. Some physical and kinematical properties of the model are also discussed.
Chai, Zhenhua; Guo, Zhaoli
2016-01-01
In this paper, based on the previous work [B. Shi, Z. Guo, Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E 79 (2009) 016701], we develop a general multiple-relaxation-time (MRT) lattice Boltzmann model for nonlinear anisotropic convection-diffusion equation (NACDE), and show that the NACDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the MRT model through some classic CDEs, and find that the numerical results are in good agreement with analytical solutions or some available results. Besides, the numerical results also show that similar to the single-relaxation-time (SRT) lattice Boltzmann model or so-called BGK model, the present MRT model also has a second-order convergence rate in space. Finally, we also perform a comparative study on the accuracy and stability of the MRT model and BGK model by using two examples. In terms of the accuracy, both the theoretical analysis and numerical results show that a \\emph{numerical}...
Li, Guohui; Shen, Hujun; Zhang, Dinglin; Li, Yan; Wang, Honglei
2016-02-01
In this work, we attempt to apply a coarse-grained (CG) model, which is based on anisotropic Gay-Berne and electric multipole (EMP) potentials, to the modeling of nucleic acids. First, a comparison has been made between the CG and atomistic models (AMBER point-charge model) in the modeling of DNA and RNA hairpin structures. The CG results have demonstrated a good quality in maintaining the nucleic acid hairpin structures, in reproducing the dynamics of backbone atoms of nucleic acids, and in describing the hydrogen-bonding interactions between nucleic acid base pairs. Second, the CG and atomistic AMBER models yield comparable results in modeling double-stranded DNA and RNA molecules. It is encouraging that our CG model is capable of reproducing many elastic features of nucleic acid base pairs in terms of the distributions of the interbase pair step parameters (such as shift, slide, tilt, and twist) and the intrabase pair parameters (such as buckle, propeller, shear, and stretch). Finally, The GBEMP model has shown a promising ability to predict the melting temperatures of DNA duplexes with different lengths. PMID:26717419
CAI; Ruixian; GOU; Chenhua; ZHANG; Na
2005-01-01
Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.
An advanced Thermal-FSI approach to flow heating/cooling
Actually, two-way thermal-energy exchange between working fluid and solid material of a casing is a leading problem for modern – semi automatic – design techniques. Many questions should be solved, especially, the turbulent mode of thermal energy transport both in fluid and solid, should be re-examined and reformulated from the primary principles. In the present paper, a group of researchers from Energy Conversion Department of IMP PAN at Gdańsk, tries to summarise a last three-years efforts towards to mathematical modelling of advanced models of thermal energy transport. This extremely difficult problem in 'thermal-FSI' ('Fluid Solid Interaction') means that the both for solid and fluid mathematical model of a surface layer should be self-equilibrated and self-concise. Taking these requirements into account, an advanced Reynolds-Stanton analogy has been discussed and implemented. Some numerical examples concerning of the benchmarks experiments and industrial applications have also been developed and presented.
Anisotropic viscoelastic-viscoplastic continuum model for high-density cellulose-based materials
Tjahjanto, D. D.; Girlanda, O.; Östlund, S.
2015-11-01
A continuum material model is developed for simulating the mechanical response of high-density cellulose-based materials subjected to stationary and transient loading. The model is formulated in an infinitesimal strain framework, where the total strain is decomposed into elastic and plastic parts. The model adopts a standard linear viscoelastic solid model expressed in terms of Boltzmann hereditary integral form, which is coupled to a rate-dependent viscoplastic formulation to describe the irreversible plastic part of the overall strain. An anisotropic hardening law with a kinematic effect is particularly adopted in order to capture the complex stress-strain hysteresis typically observed in polymeric materials. In addition, the present model accounts for the effects of material densification associated with through-thickness compression, which are captured using an exponential law typically applied in the continuum description of elasticity in porous media. Material parameters used in the present model are calibrated to the experimental data for high-density (press)boards. The experimental characterization procedures as well as the calibration of the parameters are highlighted. The results of the model simulations are systematically analyzed and validated against the corresponding experimental data. The comparisons show that the predictions of the present model are in very good agreement with the experimental observations for both stationary and transient load cases.
Anisotropic string cosmological models in Heckmann-Schucking space-time
Goswami, G. K.; Dewangan, R. N.; Yadav, A. K.; Pradhan, A.
2016-02-01
In the present work we have searched the existence of the late time acceleration of the universe with string fluid as source of matter in anisotropic Heckmann-Schucking space-time by using 287 high red shift (0.3 ≤ z≤1.4) SN Ia data of observed absolute magnitude along with their possible error from Union 2.1 compilation. It is found that the best fit values for (\\varOmegam)0, (\\varOmega_{\\varLambda})0, (\\varOmega_{σ })0 and (q)0 are 0.2820, 0.7177, 0.0002 & -0.5793 respectively. Several physical aspects and geometrical properties of the model are discussed in detail.
Anisotropic String Cosmological Models in Heckmann-Suchuking Space-Time
Goswami, G K; Yadav, A K; Pradhan, A
2016-01-01
In the present work we have searched the existence of the late time acceleration of the universe with string fluid as source of matter in anisotropic Heckmann-Suchking space-time by using 287 high red shift $(0.3 \\leq z\\leq 1.4)$ SN Ia data of observed absolute magnitude along with their possible error from Union 2.1 compilation. It is found that the best fit values for $(\\Omega_{m})_{0}$, $(\\Omega_{\\Lambda})_{0}$, $(\\Omega_{\\sigma})_{0}$ and $(q)_{0}$ are 0.2820, 0.7177, 0.0002 $\\&$ -0.5793 respectively. Several physical aspects and geometrical properties of the model are discussed in detail.
The luminosity law of ellipticals; a test of a family of anisotropic models on eight galaxies.
Bertin, G.; Saglia, R. P.; Stiavelli, M.
An important clue to the structure and dynamics of elliptical galaxies is provided by the empirical r1/4 luminosity law proposed by de Vaucouleurs (1948). The existence of such a law is indicative of a common underlying mass distribution in these galaxies. The fact that this law is universal suggests that essentially a single physical mechanism characterizes the formation of ellipticals. The authors report on a recent study where they have analyzed published photometric and kinematical data for a set of bright elliptical galaxies (NGC 3379, NGC 4374, NGC 4472, NGC 4486, NGC 4636, NGC 7562, NGC 7619, and NGC 7626) in terms of self-consistent anisotropic models under the assumption of constant mass-to-light ratio.
Convergence dynamics of 2-dimensional isotropic and anisotropic Bak Sneppen models
Bakar, Burhan; Tirnakli, Ugur
2008-09-01
The conventional Hamming distance measurement captures only short-time dynamics of the displacement between uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [U. Tirnakli, M.L. Lyra. Int. J. Mod. Phys. C 14 (2003) 805] is used to study short-time and long-time dynamics of the two distinct random configurations of isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to a 1-dimensional case, the time evolution of the displacement is intermittent. The scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial-temporal scales in the mechanism of displacement jumps used to quantify convergence dynamics.
Hills, M E; Olsen, A L; Nichols, L W
1968-08-01
Cary model 14 spectrophotometers like other prism and grating instruments have polarization characteristics that affect the transmittance values of anisotropic or dichroic materials. In the uv, the degree of polarization is fairly constant from 3000 A to 4000 A, whereas in the visible, it shows some variation with wavelength. In the near ir, the variation of the degree of polarization with wavelength is large, showing sharply defined maxima at approximately 0.77 micro, 0.97 micro, and 1.27 micro. The spectral transmittance of optical quality sapphire, a uniaxial crystal, cut at 45 degrees , 60 degrees , and 90 degrees to the c axis, showed undulations for certain orientations of the privileged directions. PMID:20068821
Rama, S Kalyana
2016-01-01
The dynamics of a (3 + 1) dimensional homogeneous anisotropic universe is modified by Loop Quantum Cosmology and, consequently, it has generically a big bounce in the past instead of a big-bang singularity. This modified dynamics can be well described by effective equations of motion. We generalise these effective equations of motion empirically to (d + 1) dimensions. The generalised equations involve two functions and may be considered as a class of LQC -- inspired models for (d + 1) dimensional early universe cosmology. As a special case, one can now obtain a universe which has neither a big bang singularity nor a big bounce but approaches asymptotically a `Hagedorn like' phase in the past where its density and volume remain constant. In a few special cases, we also obtain explicit solutions.
Daogang Lu
2015-01-01
Full Text Available Huge water storage tank on the top of many buildings may affect the safety of the structure caused by fluid-structure interaction (FSI under the earthquake. AP1000 passive containment cooling system water storage tank (PCCWST placed at the top of shield building is a key component to ensure the safety of nuclear facilities. Under seismic loading, water will impact the wall of PCCWST, which may pose a threat to the integrity of the shield building. In the present study, an FE model of AP1000 shield building is built for the modal and transient seismic analysis considering the FSI. Six different water levels in PCCWST were discussed by comparing the modal frequency, seismic acceleration response, and von Mises stress distribution. The results show the maximum von Mises stress emerges at the joint of shield building roof and water around the air inlet. However, the maximum von Mises stress is below the yield strength of reinforced concrete. The results may provide a reference for design of the AP1000 and CAP1400 in the future.
Khayyeri, Hanifeh; Longo, Giacomo; Gustafsson, Anna; Isaksson, Hanna
2016-08-01
The incidence of tendon injury (tendinopathy) has increased over the past decades due to greater participation in sports and recreational activities. But little is known about the aetiology of tendon injuries because of our limited knowledge in the complex structure-function relationship in tendons. Computer models can capture the biomechanical behaviour of tendons and its structural components, which is essential for understanding the underlying mechanisms of tendon injuries. This study compares three structural constitutive material models for the Achilles tendon and discusses their application on different biomechanical simulations. The models have been previously used to describe cardiovascular tissue and articular cartilage, and one model is novel to this study. All three constitutive models captured the tensile behaviour of rat Achilles tendon (root mean square errors between models and experimental data are 0.50-0.64). They further showed that collagen fibres are the main load-bearing component and that the non-collagenous matrix plays a minor role in tension. By introducing anisotropic behaviour also in the non-fibrillar matrix, the new biphasic structural model was also able to capture fluid exudation during tension and high values of Poisson׳s ratio that is reported in tendon experiments. PMID:27108350
Anisotropic Multishell Analytical Modeling of an Intervertebral Disk Subjected to Axial Compression.
Demers, Sébastien; Nadeau, Sylvie; Bouzid, Abdel-Hakim
2016-04-01
Studies on intervertebral disk (IVD) response to various loads and postures are essential to understand disk's mechanical functions and to suggest preventive and corrective actions in the workplace. The experimental and finite-element (FE) approaches are well-suited for these studies, but validating their findings is difficult, partly due to the lack of alternative methods. Analytical modeling could allow methodological triangulation and help validation of FE models. This paper presents an analytical method based on thin-shell, beam-on-elastic-foundation and composite materials theories to evaluate the stresses in the anulus fibrosus (AF) of an axisymmetric disk composed of multiple thin lamellae. Large deformations of the soft tissues are accounted for using an iterative method and the anisotropic material properties are derived from a published biaxial experiment. The results are compared to those obtained by FE modeling. The results demonstrate the capability of the analytical model to evaluate the stresses at any location of the simplified AF. It also demonstrates that anisotropy reduces stresses in the lamellae. This novel model is a preliminary step in developing valuable analytical models of IVDs, and represents a distinctive groundwork that is able to sustain future refinements. This paper suggests important features that may be included to improve model realism. PMID:26833355
Stopin, A.
2001-12-01
As the jump from 2D to 3D, seismic exploration lives a new revolution with the use of converted PS waves. Indeed PS converted waves are proving their potential as a tool for imaging through gas; lithology discrimination; structural confirmation; and more. Nevertheless, processing converted shear data and in particular determining accurate P and S velocity models for depth imaging of these data is still a challenging problem, especially when the subsurface is anisotropic. To solve this velocity model determination problem we propose to use reflection travel time tomography. In a first step, we derive a new approximation of the exact phase velocity equation of the SV wave in anisotropic (TI) media. This new approximation is valid for non-weak anisotropy and is mathematically simpler to handle than the exact equation. Then, starting from an isotropic reflection tomography tool developed at Lt-'P, we extend the isotropic bending ray tracing method to the anisotropic case and we implement the quantities necessary for the determination of the anisotropy parameters from the travel time data. Using synthetic data we then study the influence of the different anisotropy parameters on the travel times. From this analysis we propose a methodology to determine a complete anisotropic subsurface model (P and S layer velocities, interface geometries, anisotropy parameters). Finally, on a real data set from the Gulf of Mexico we demonstrate that this new anisotropic reflection tomography tool allows us to obtain a reliable subsurface model yielding kinematically correct and mutually coherent PP and PS images in depth; such a result could not be obtained with an isotropic velocity model. Similar results are obtained on a North Sea data set. (author)
Jiao, Yang, E-mail: yang.jiao.2@asu.edu; Chawla, Nikhilesh [Materials Science and Engineering, Arizona State University, Arizona 85287-6206 (United States)
2014-03-07
We present a framework to model and characterize the microstructure of heterogeneous materials with anisotropic inclusions of secondary phases based on the directional correlation functions of the inclusions. Specifically, we have devised an efficient method to incorporate both directional two-point correlation functions S{sub 2} and directional two-point cluster functions C{sub 2} that contain non-trivial topological connectedness information into the simulated annealing microstructure reconstruction procedure. Our framework is applied to model an anisotropic aluminum alloy and the accuracy of the reconstructed structural models is assessed by quantitative comparison with the actual microstructure obtained via x-ray tomography. We show that incorporation of directional clustering information via C{sub 2} significantly improves the accuracy of the reconstruction. In addition, a set of analytical “basis” correlation functions are introduced to approximate the actual S{sub 2} and C{sub 2} of the material. With the proper choice of basis functions, the anisotropic microstructure can be represented by a handful of parameters including the effective linear sizes of the iron-rich and silicon-rich inclusions along three orthogonal directions. This provides a general and efficient means for heterogeneous material modeling that enables one to significantly reduce the data set required to characterize the anisotropic microstructure.
We present a framework to model and characterize the microstructure of heterogeneous materials with anisotropic inclusions of secondary phases based on the directional correlation functions of the inclusions. Specifically, we have devised an efficient method to incorporate both directional two-point correlation functions S2 and directional two-point cluster functions C2 that contain non-trivial topological connectedness information into the simulated annealing microstructure reconstruction procedure. Our framework is applied to model an anisotropic aluminum alloy and the accuracy of the reconstructed structural models is assessed by quantitative comparison with the actual microstructure obtained via x-ray tomography. We show that incorporation of directional clustering information via C2 significantly improves the accuracy of the reconstruction. In addition, a set of analytical “basis” correlation functions are introduced to approximate the actual S2 and C2 of the material. With the proper choice of basis functions, the anisotropic microstructure can be represented by a handful of parameters including the effective linear sizes of the iron-rich and silicon-rich inclusions along three orthogonal directions. This provides a general and efficient means for heterogeneous material modeling that enables one to significantly reduce the data set required to characterize the anisotropic microstructure
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.
Kim, Byunghyun; Sanders, Brett F.; Famiglietti, James S.; Guinot, Vincent
2015-04-01
Porous shallow-water models (porosity models) simulate urban flood flows orders of magnitude faster than classical shallow-water models due to a relatively coarse grid and large time step, enabling flood hazard mapping over far greater spatial extents than is possible with classical shallow-water models. Here the errors of both isotropic and anisotropic porosity models are examined in the presence of anisotropic porosity, i.e., unevenly spaced obstacles in the cross-flow and along-flow directions, which is common in practical applications. We show that porosity models are affected by three types of errors: (a) structural model error associated with limitations of the shallow-water equations, (b) scale errors associated with use of a relatively coarse grid, and (c) porosity model errors associated with the formulation of the porosity equations to account for sub-grid scale obstructions. Results from a unique laboratory test case with strong anisotropy indicate that porosity model errors are smaller than structural model errors, and that porosity model errors in both depth and velocity are substantially smaller for anisotropic versus isotropic porosity models. Test case results also show that the anisotropic porosity model is equally accurate as classical shallow-water models when compared directly to gage measurements, while the isotropic model is less accurate. Further, results show the anisotropic porosity model resolves flow variability at smaller spatial scales than the isotropic model because the latter is restricted by the assumption of a Representative Elemental Volume (REV) which is considerably larger than the size of obstructions. These results point to anisotropic porosity models as being well-suited to whole-city urban flood prediction, but also reveal that point-scale flow attributes relevant to flood risk such as localized wakes and wave reflections from flow obstructions may not be resolved.
Chandel S; Ram Shri
2016-03-01
The paper deals with the study of particle creation and bulk viscosity in the evolution of spatially homogeneous and anisotropic Bianchi type-V cosmological models in the framework of Saez–Ballester theory of gravitation. Particle creation and bulk viscosity are considered as separate irreversible processes. The energy–momentum tensor is modified to accommodate the viscous pressure and creation pressure which is associated with the creation of matter out of gravitational field. A special law of variation of Hubble parameter is applied to obtain exact solutions of field equations in two types of cosmologies, one with power-law expansion and the other with exponential expansion. Cosmological model with power-law expansion has a Big-Bang singularity at time $t = 0$, whereas the model with exponential expansion has no finite singularity. We study bulk viscosity and particle creation in each model in four different cases. The bulk viscosity coefficient is obtained for full causal, Eckart’s and truncated theories. All physical parameters are calculated and thoroughly discussed in both models.
Explaining anisotropic macroseismic fields in terms of fault zone attenuation-A simple model
Sovic, Ivica; Sariri, Kristina
2016-06-01
In this work, we present a simple model of anisotropic macroseismic field based on the assumption that local and regional geological structures change the shape of the isotropic macroseismic field (as expected in 1D media). Local geological structures, like water saturated stratified media, may increase intensity level by multiple reflections, constructive interference and resonant effects, but inelastic attenuation, significantly stronger in water-saturated soils, as well as destructive interference, may decrease intensities. On the other hand, large geological structures like seismotectonically active fault zones decrease intensities due to energy redistribution and inelastic attenuation. This model has been developed for the Karst region of the Outer Dinarides where site effects may be neglected because of specific building construction. Neglecting of site effects simplifies the model, so we just need a map of seismically active faults acting as modulator of macroseismic field. In order to demonstrate how the model works, we have calculated the standard error for 10 earthquakes and the macroseismic fields for three of them with epicenters in the Outer Dinarides and compared the model to empiric isoseismals.
Reduced-order FSI simulation of NREL 5 MW wind turbine in atmospheric boundary layer turbulence
Motta-Mena, Javier; Campbell, Robert; Lavely, Adam; Jha, Pankaj
2015-11-01
A partitioned fluid-structure interaction (FSI) solver based on an actuator-line method solver and a finite-element modal-dynamic structural solver is used to evaluate the effect of blade deformation in the presence of a day-time, moderately convective atmospheric boundary layer (ABL). The solver components were validated separately and the integrated solver was partially validated against FAST. An overview of the solver is provided in addition to results of the validation study. A finite element model of the NREL 5 MW rotor was developed for use in the present simulations. The effect of blade pitching moment and the inherent bend/twist coupling of the rotor blades are assessed for both uniform inflow and the ABL turbulence cases. The results suggest that blade twisting in response to pitching moment and the bend/twist coupling can have a significant impact on rotor out-of-plane bending moment and power generated for both the uniform inflow and the ABL turbulence cases.
A class of spherical, truncated, anisotropic models for application to globular clusters
de Vita, Ruggero; Bertin, Giuseppe; Zocchi, Alice
2016-05-01
Recently, a class of non-truncated, radially anisotropic models (the so-called f(ν)-models), originally constructed in the context of violent relaxation and modelling of elliptical galaxies, has been found to possess interesting qualities in relation to observed and simulated globular clusters. In view of new applications to globular clusters, we improve this class of models along two directions. To make them more suitable for the description of small stellar systems hosted by galaxies, we introduce a "tidal" truncation by means of a procedure that guarantees full continuity of the distribution function. The new fT(ν)-models are shown to provide a better fit to the observed photometric and spectroscopic profiles for a sample of 13 globular clusters studied earlier by means of non-truncated models; interestingly, the best-fit models also perform better with respect to the radial-orbit instability. Then, we design a flexible but simple two-component family of truncated models to study the separate issues of mass segregation and multiple populations. We do not aim at a fully realistic description of globular clusters to compete with the description currently obtained by means of dedicated simulations. The goal here is to try to identify the simplest models, that is, those with the smallest number of free parameters, but still have the capacity to provide a reasonable description for clusters that are evidently beyond the reach of one-component models. With this tool, we aim at identifying the key factors that characterize mass segregation or the presence of multiple populations. To reduce the relevant parameter space, we formulate a few physical arguments based on recent observations and simulations. A first application to two well-studied globular clusters is briefly described and discussed.
Anisotropic thermo-mechanical damage modelling for cementitious materials at high temperature
The behavior of concrete at elevated temperatures is important for an assessment of integrity (strength and durability) of structures exposed to high temperature environment, in application such as fire exposure, smelting plants, nuclear installations. This paper we develop numerical algorithms for the integration of a thermo-mechanical damage model for concrete at high temperature. The model has been derived within the consistent framework of thermodynamics, drawing on the iso-thermal damage of Ortiz and Yazdani and Schreyer and the thermo-mechanical coupling aspects of Simo and Miehe. In addition, account has been taken of the known stress-temperature dependence of concrete through the descriptions of thermal and thermo-mechanical damage, and the thermal softening. Mechanical damage is related directly to compliance, with additional flexibility due to thermal damage. Explicit expressions have been derived for the free energy including elastic energy, damage due to micro-crack formation, thermal-mechanical coupling and thermal energy. The damage function is shown to be flexible in being able to capture the temperature dependent shape and size of failure surfaces: the model generally incorporates features of anisotropic damage, dilatation and inelastic strain responses. In a wider context, the damage model presented forms part of a study aimed at the development of a completely generalized analysis of concrete at transient elevated temperatures, including the coupling of damage, hygral diffusion and heat conduction through the material. Refs. 4 (author)
The aim of this work is the study and the modelization of the anisotropic viscoplastic behaviour of zircaloy 4 in two metallurgical states: recrystallized and cold-worked stress-relieved. The results of experiments performed in the intermediate temperature domain (20 - 450 deg C) are presented. In order to characterize the anisotropy, especially at 350 deg C, the tests were made under both monotonic and cyclic uni- and bidirectional loadings, i.e. tension-compression, tension-torsion and tension-internal pressure tests. The results would seem to indicate that the set of anisotropy coefficients do not depend or temperature. An important feature of the behaviour of this alloy in the neighbourhood of 300 deg C is attributed to the dynamic strain aging frequently observed in solid insertion solutions. This material also presents a slight supplementary hardening during out-of-phase cyclic loading (tension-torsion with a 90 deg C phase lag). In the last part, we propose to extend the formulation of a unified viscoplastic model, developed and identified elsewhere for other isotropic materials, to the case of zircaloy 4. From a general point of view, the introduction of anisotropy in the model is performed by the introduction cf four tensors of rank 4 affecting the flow directions, the linear parts of the kinematical hardening variables, the dynamic and static recoveries of these hardening variables. The identification of this model is performed at 350 deg C. (author)
Marcotte, D.
2016-04-01
The turning bands method (TBM) is a commonly used method of simulation for large Gaussian fields, its O(N) complexity being unsurpassed (N denotes the number of points to simulate). TBM can be implemented either in the spatial or the spectral domains. In the multivariate anisotropic case, spatial versions of TBM are currently available only for the linear model of coregionalization (LMC). For anisotropic non-LMC with symmetrical covariances only the spectral version is currently available. The spectral domain approach can be slow in the case of non-differentiable covariances due to the numerous frequencies to sample. Here a derivation of the equations is provided for simulating the anisotropic non-LMC directly in the spatial domain and the method is illustrated with two synthetic examples. The approach allows the specification of many different direct and cross-covariance components, each with possibly different geometric anisotropies and different model types. The complexity of the new multivariate approach remains O(N). Hence, a case of two variables defining an anisotropic non-LMC is simulated over one billion points in less than one hour on a desktop computer. These results help enlarge the scope of application of the TBM. The method can be easily implemented in any existing TBM program.
Anisotropic problem and one-dimensional VSP modeling in EDA medium
Zhusheng, Z.
1991-01-01
One-dimensional elastic wave equation in anisotropic EDA medium is derived by using Hooke's law and the kinematic equation of non-individual body in elastic theory, followed by a series of hypotheses. Then, synthetic one-dimensional VSP record in anisotropic EDA medium is obtained by solving the elastic wave equation with the use of Fourier algorithm. The numerical synthetic record and hodograph clearly show rich wave field, S-wave splitting, attenuation or absorption of amplitude and frequency in the anisotropic medium.
Full text: In this paper, is a study of the transport properties in anisotropic polycrystalline superconducting. The presence of certain order of orientation of grains in polycrystalline superconducting (Bi,Pb)2 Sr2 Ca2 Cu3 O10+delta, is modeled by introducing a probability of orientation, gamma factor. In addition, is included in the model the concentration c, which characterize the contribution of porosity to the decrease in the conductivity of the Crystal, transparent. Assumes that pores and pimples are ellipsoid flattened with similar dimensions and takes into account the values of conductivity of beads in each direction. The calculation is based on the application of a generalization of the approximation of the effective way to the study of heterogeneous media, which is called coherent potential approximation (APC). The results are compared with an empirical model developed recently for samples of YBa2 Cu3 O7-delta (YBCO) which enriches its employment and applied to ceramic superconducting in general. (author)
Models of polycrystalline microstructures, representative for sintered permanent magnets with various grain size distributions and alignment degrees, were generated by the Voronoï tessellation technique. The polycrystalline models were meshed and then a stress/strain analysis was performed with the Finite Element Method (FEM) in order to derive the relation between the homogenized properties (thermal expansion coefficient, elastic constants) and the degree of grain alignment. Residual stresses after sintering were also analyzed and a possible mechanism involved in the decrease in mechanical strength is discussed. It is argued that small sized and poorly aligned grains dispersed in the polycrystalline material are highly stressed after elaboration and could be responsible for the initiation of failure. - Highlights: • A new methodology for generating models of polycrystalline microstructures is presented. • Broad grain size distribution and dependence of the alignment on grain size are accounted. • Thermal residual stresses develop along grain boundary in anisotropic sintered magnets. • Localization of the residual stressed around small grains may cause failure initiation
The accuracy of an electroencephalography (EEG) forward problem partially depends on the head tissue conductivities. These conductivities are anisotropic and inhomogeneous in nature. This paper investigates the effects of conductivity uncertainty and analyses its sensitivity on an EEG forward problem for a spherical and a realistic head models. We estimate the uncertain conductivities using an efficient constraint based on an optimization method and perturb it by means of the volume and directional constraints. Assigning the uncertain conductivities, we construct spherical and realistic head models by means of a stochastic finite element method for fixed dipolar sources. We also compute EEG based on the constructed head models. We use a probabilistic sensitivity analysis method to determine the sensitivity indexes. These indexes characterize the conductivities with the most or the least effects on the computed outputs. These results demonstrate that conductivity uncertainty has significant effects on EEG. These results also show that the uncertain conductivities of the scalp, the radial direction of the skull and transversal direction in the white matter are more sensible.
A three-dimensional radially anisotropic model of shear velocity in the whole mantle
Panning, Mark; Romanowicz, Barbara
2006-10-01
We present a 3-D radially anisotropic S velocity model of the whole mantle (SAW642AN), obtained using a large three component surface and body waveform data set and an iterative inversion for structure and source parameters based on Non-linear Asymptotic Coupling Theory (NACT). The model is parametrized in level 4 spherical splines, which have a spacing of ~ 8°. The model shows a link between mantle flow and anisotropy in a variety of depth ranges. In the uppermost mantle, we confirm observations of regions with VSH > VSV starting at ~80 km under oceanic regions and ~200 km under stable continental lithosphere, suggesting horizontal flow beneath the lithosphere. We also observe a VSV > VSH signature at ~150-300 km depth beneath major ridge systems with amplitude correlated with spreading rate for fast-spreading segments. In the transition zone (400-700 km depth), regions of subducted slab material are associated with VSV > VSH, while the ridge signal decreases. While the mid-mantle has lower amplitude anisotropy ( VSV in the lowermost 300 km, which appears to be a robust conclusion, despite an error in our previous paper which has been corrected here. The 3-D deviations from this signature are associated with the large-scale low-velocity superplumes under the central Pacific and Africa, suggesting that VSH > VSV is generated in the predominant horizontal flow of a mechanical boundary layer, with a change in signature related to transition to upwelling at the superplumes.
Shen, Hujun; Li, Yan; Ren, Pengyu; Zhang, Dinglin; Li, Guohui
2014-02-10
Gay-Berne anisotropic potential has been widely used to evaluate the non-bonded interactions between coarse-grained particles being described as elliptical rigid bodies. In this paper, we are presenting a coarse-grained model for twenty kinds of amino acids and proteins, based on the anisotropic Gay-Berne and point electric multipole (EMP) potentials. We demonstrate that the anisotropic coarse-grained model, namely GBEMP model, is able to reproduce many key features observed from experimental protein structures (Dunbrack Library) as well as from atomistic force field simulations (using AMOEBA, AMBER and CHARMM force fields) while saving the computational cost by a factor of about 10~200 depending on specific cases and atomistic models. More importantly, unlike other coarse-grained approaches, our framework is based on the fundamental intermolecular forces with explicit treatment of electrostatic and repulsion-dispersion forces. As a result, the coarse-grained protein model presented an accurate description of non-bonded interactions (particularly electrostatic component) between hetero-/homo-dimers (such as peptide-peptide, peptide-water). In addition, the encouraging performance of the model was reflected by the excellent correlation between GBEMP and AMOEBA models in the calculations of the dipole moment of peptides. In brief, the GBEMP model given here is general and transferable, suitable for simulating complex biomolecular systems. PMID:24659927
Augustins, L.; Billardon, R.; Hild, F.
2016-01-01
The present paper details an elasto-viscoplastic constitutive model for automotive brake discs made of flake graphite cast iron. In a companion paper (Augustins et al. in Contin Mech Thermodyn, 2015), the authors proposed a one-dimensional setting appropriate for representing the complex behavior of the material (i.e., asymmetry between tensile and compressive loadings) under anisothermal conditions. The generalization of this 1D model to 3D cases on a volume element and the associated challenges are addressed. A direct transposition is not possible, and an alternative solution without unilateral conditions is first proposed. Induced anisotropic damage and associated constitutive laws are then introduced. The transition from the volume element to the real structure and the numerical implementation require a specific basis change. Brake disc simulations with this constitutive model show that unilateral conditions are needed for the friction bands. A damage deactivation procedure is therefore defined.
Anisotropic cosmologies with ghost dark energy models in f (R, T) gravity
Fayaz, V.; Hossienkhani, H.; Zarei, Z.; Azimi, N.
2016-02-01
In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. For this purpose, we use the squared sound speed vs2 whose sign determines the stability of the model. At first, the non-interacting ghost dark energy in a Bianchi type-I (BI) background is discussed. Then the equation-of-state parameter, ω_D=pD/ρD, the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It is shown that the equation-of-state parameter of the ghost dark energy can cross the phantom line ( ω=-1 in some range of the parameter spaces. Then, this investigation was extended to the general scheme for modified f(R,T) gravity reconstruction from a realistic case in an anisotropic Bianchi type-I cosmology, using the dark matter and ghost dark energy. Special attention is taken into account for the case in which the function f is given by f(R,T)=f1(R) +f2(T). We consider a specific model which permits the standard continuity equation in this modified theory. Besides Ω_{Λ} and Ω in standard Einstein cosmology, another density parameter, Ω_{σ}, is expected by the anisotropy. This theory implies that if Ω_{σ} is zero then it yields the FRW universe model. Interestingly enough, we find that the corresponding f ( R, T) gravity of the ghost DE model can behave like phantom or quintessence of the selected models which describe the accelerated expansion of the universe.
Bodaghi, M.; Damanpack, A. R.; Liao, W. H.
2016-07-01
The aim of this article is to develop a robust macroscopic bi-axial model to capture self-accommodation, martensitic transformation/orientation/reorientation, normal–shear deformation coupling and asymmetric/anisotropic strain generation in polycrystalline shape memory alloys. By considering the volume fraction of martensite and its preferred direction as scalar and directional internal variables, constitutive relations are derived to describe basic mechanisms of accommodation, transformation and orientation/reorientation of martensite variants. A new definition is introduced for maximum recoverable strain, which allows the model to capture the effects of tension–compression asymmetry and transformation anisotropy. Furthermore, the coupling effects between normal and shear deformation modes are considered by merging inelastic strain components together. By introducing a calibration approach, material and kinetic parameters of the model are recast in terms of common quantities that characterize a uniaxial phase kinetic diagram. The solution algorithm of the model is presented based on an elastic-predictor inelastic-corrector return mapping process. In order to explore and demonstrate capabilities of the proposed model, theoretical predictions are first compared with existing experimental results on uniaxial tension, compression, torsion and combined tension–torsion tests. Afterwards, experimental results of uniaxial tension, compression, pure bending and buckling tests on {{NiTi}} rods and tubes are replicated by implementing a finite element method along with the Newton–Raphson and Riks techniques to trace non-linear equilibrium path. A good qualitative and quantitative correlation is observed between numerical and experimental results, which verifies the accuracy of the model and the solution procedure.
Mizuno, Daisuke; Head, David; Ikebe, Emi; Nakamasu, Akiko; Kinoshita, Suguru; Peijuan, Zhang; Ando, Shoji
2013-03-01
Forces are generated heterogeneously in living cells and transmitted through cytoskeletal networks that respond highly non-linearly. Here, we carry out high-bandwidth passive microrheology on vimentin networks reconstituted in vitro, and observe the nonlinear mechanical response due to forces propagating from a local source applied by an optical tweezer. Since the applied force is constant, the gel becomes equilibrated and the fluctuation-dissipation theorem can be employed to deduce the viscoelasticity of the local environment from the thermal fluctuations of colloidal probes. Our experiments unequivocally demonstrate the anisotropic stiffening of the cytoskeletal network behind the applied force, with greater stiffening in the parallel direction. Quantitative agreement with an affine continuum model is obtained, but only for the response at certain frequency ~ 10-1000 Hz which separates the high-frequency power law and low-frequency elastic behavior of the network. We argue that the failure of the model at lower frequencies is due to the presence of non-affinity, and observe that zero-frequency changes in particle separation can be fitted when an independently-measured, empirical nonaffinity factor is applied.
Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data
Groeneboom, Nicolaas E
2008-01-01
We extend the previously described CMB Gibbs sampling framework to allow for exact Bayesian analysis of anisotropic universe models, and apply this method to the 5-year WMAP temperature observations. This involves adding support for non-diagonal signal covariance matrices, and implementing a general spectral parameter MCMC sampler. As a worked example we apply these techniques to the model recently introduced by Ackerman et al., describing for instance violations of rotational invariance during the inflationary epoch. After verifying the code with simulated data, we analyze the foreground-reduced 5-year WMAP temperature sky maps. For l < 400 and the W-band data, we find tentative evidence for a preferred direction pointing towards (l,b) = (110 deg, 10 deg) with an anisotropy amplitude of g* = 0.15 +- 0.039, nominally equivalent to a 3.8 sigma detection. Similar results are obtained from the V-band data [g* = 0.11 +- 0.039; (l,b) = (130 deg, 20 deg)]. Further, the preferred direction is stable with respect ...
Multi-component induction logging provides great assistance in the exploration of thinly laminated reservoirs. The 1D parametric inversion following an adaptive borehole correction is the key step in the data processing of multi-component induction logging responses. To make the inversion process reasonably fast, an efficient forward modelling method is necessary. In this paper, a modelling method has been developed to simulate the multi-component induction tools in deviated wells drilled in layered anisotropic formations. With the introduction of generalized reflection coefficients, the analytic expressions of magnetic field in the form of a Sommerfeld integral were derived. The fast numerical computation of the integral has been completed by using the fast Fourier–Hankel transform and fast Hankel transform methods. The latter is so time efficient that it is competent enough for real-time multi-parameter inversion. In this paper, some simulated results have been presented and they are in excellent agreement with the finite difference method code's solution. (paper)
Model of Anisotropic Magnetization of In(1-x)Mn(x)S: Comparison to Experiment
Garner, J.; Franzese, G.; Byrd, Ashlee; Pekarek, T. M.; Miotkowski, I.; Ramdas, A. K.
2004-03-01
Calculations of and experimental results for the anisotropic magnetization of the new III-VI dilute magnetic semiconductor, In(1-x)Mn(x)S, are presented. The model Hamiltonian incorporates the interaction of the incomplete shell of Mn 3d-electrons with the crystal lattice within the point-ion approximation. Other terms in the Hamiltonian include the Zeeman interaction, the spin-orbit and the spin-spin terms. It is assumed the Mn atoms do not interact with each other (this is the singlet model, which is appropriate when x is small, here 2%). The temperature- and field- dependent magnetization is found from the energy eigenvalues of the Hamiltonian matrix, which was expressed in terms of an uncoupled angular momentum basis set. Magnetization versus temperature results are found for several field values, B, pointing along various directions relative to the underlying dilute magnetic semiconductor crystal lattice. In addition, the magnetization versus field is computed for several fixed temperatures and for various B-field directions and magnitudes. Overall, the agreement of this simple model with the experimental data is very good except at low temperatures ( a few Tesla). It would be useful for quantitative comparison purposes to have optical absorption data in order to better fix the crystal potential parameters that are input parameters in the theory. In addition, the model could be improved by going beyond the point-ion approximation to better model the covalent bonds in the crystal.* Supported by UNF Research Grants, Research Corporation Award, CC4845, NSF Grant Nos. DMR-03-05653, DMR-01-02699, and ECS-01-29853 and Donors of the American Chemical Society Petroleum Research Fund PRF#40209-B5M, and a Purdue Univ. Academic Reimbursement Grant.
Ding, Guilin; Lü, Baida
2002-03-01
The generalized Huygens-Fresnel diffraction integral for misaligned asymmetric first-order optical systems is derived by using the canonical operator method, which enables us to study propagation properties of anisotropic Gaussian Schell-model (AGSM) beams through misaligned asymmetric first-order optical systems. It is shown that under the action of misaligned asymmetric first-order optical systems AGSM beams do not preserve the closed property. Therefore generalized partially coherent anisotropic Gaussian Schell-model beams called decentered anisotropic Gaussian Schell-model (DAGSM) beams are introduced, and AGSM beams can be regarded as a special case of DAGSM beams. PMID:11876311
Lisjak, Andrea; Tatone, Bryan S. A.; Grasselli, Giovanni; Vietor, Tim
2014-01-01
The Opalinus Clay (OPA) is an argillaceous rock formation selected to host a deep geologic repository for high-level nuclear waste in Switzerland. It has been shown that the excavation damaged zone (EDZ) in this formation is heavily affected by the anisotropic mechanical response of the material related to the presence of bedding planes. In this context, the purpose of this study is twofold: (i) to illustrate the new developments that have been introduced into the combined finite-discrete element method (FEM/DEM) to model layered materials and (ii) to demonstrate the effectiveness of this new modelling approach in simulating the short-term mechanical response of OPA at the laboratory-scale. A transversely isotropic elastic constitutive law is implemented to account for the anisotropic elastic modulus, while a procedure to incorporate a distribution of preferentially oriented defects is devised to capture the anisotropic strength. Laboratory results of indirect tensile tests and uniaxial compression tests are used to calibrate the numerical model. Emergent strength and deformation properties, together with the simulated damage mechanisms, are shown to be in strong agreement with experimental observations. Subsequently, the calibrated model is validated by investigating the effect of confinement and the influence of the loading angle with respect to the specimen anisotropy. Simulated fracture patterns are discussed in the context of the theory of brittle rock failure and analyzed with reference to the EDZ formation mechanisms observed at the Mont Terri Underground Research Laboratory.
Cortez, S; Alves, J L
2016-01-01
In articular cartilage the orientation of collagen fibres is not uniform, varying mostly with the depth on the tissue. Besides, the biomechanical response of each layer of the articular cartilage differs from the neighbouring ones, evolving through thickness as a function of the distribution, density and orientation of the collagen fibres. Based on a finite element implementation, a new continuum formulation is proposed to describe the remodelling and reorientation of the collagen fibres under arbitrary mechanical loads: the cartilaginous tissue is modelled based on a hyperelastic formulation, being the ground isotropic matrix described by a neo-Hookean law and the fibrillar anisotropic part modelled by a new anisotropic formulation introduced for the first time in the present work, in which both reorientation and remodelling are taken into account. To characterize the orientation of fibres, a structure tensor is defined to represent the expected distribution and orientation of fibres around a reference direc...
Labus, Kevin M; Puttlitz, Christian M
2016-09-01
Computational models of the brain require accurate and robust constitutive models to characterize the mechanical behavior of brain tissue. The anisotropy of white matter has been previously demonstrated; however, there is a lack of data describing the effects of multi-axial loading, even though brain tissue experiences multi-axial stress states. Therefore, a biaxial tensile experiment was designed to more fully characterize the anisotropic behavior of white matter in a quasi-static loading state, and the mechanical data were modeled with an anisotropic hyperelastic continuum model. A probabilistic analysis was used to quantify the uncertainty in model predictions because the mechanical data of brain tissue can show a high degree of variability, and computational studies can benefit from reporting the probability distribution of model responses. The axonal structure in white matter can be heterogeneous and regionally dependent, which can affect computational model predictions. Therefore, corona radiata and corpus callosum regions were tested, and histology and transmission electron microscopy were performed on tested specimens to relate the distribution of axon orientations and the axon volume fraction to the mechanical behavior. These measured properties were implemented into a structural constitutive model. Results demonstrated a significant, but relatively low anisotropic behavior, yet there were no conclusive mechanical differences between the two regions tested. The inclusion of both biaxial and uniaxial tests in model fits improved the accuracy of model predictions. The mechanical anisotropy of individual specimens positively correlated with the measured axon volume fraction, and, accordingly, the structural model exhibited slightly decreased uncertainty in model predictions compared to the model without structural properties. PMID:27214689
Milde, Frank; R{ö}mer, Rudolf A.
1998-01-01
Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders $W_c$ have been obtained within the accuracy of the data. We now employ energy level statistics (ELS) to further characterize the MIT. We find a crossover of the nearest-neighbor level spacing distribution $P(s)$ from GOE statistics at small disorder indicati...
Mimoso, José P.; Le Delliou, Morgan; Mena, Filipe C.
2013-08-01
We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a separating shell dividing expanding and collapsing regions. We resort to a 3+1 splitting and obtain gauge invariant conditions relating intrinsic spacetime quantities to properties of the matter source. We find that the separating shell is defined by a generalization of the Tolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a nonlocal character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stresses. We have cast the governing equations in terms of local, gauge invariant quantities that are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyze a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and co-workers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses.
Negara, Ardiansyah
2015-05-01
Anisotropy of hydraulic properties of the subsurface geologic formations is an essential feature that has been established as a consequence of the different geologic processes that undergo during the longer geologic time scale. With respect to subsurface reservoirs, in many cases, anisotropy plays significant role in dictating the direction of flow that becomes no longer dependent only on driving forces like the pressure gradient and gravity but also on the principal directions of anisotropy. Therefore, there has been a great deal of motivation to consider anisotropy into the subsurface flow and transport models. In this dissertation, we present subsurface flow modeling in single and dual continuum anisotropic porous media, which include the single-phase groundwater flow coupled with the solute transport in anisotropic porous media, the two-phase flow with gravity effect in anisotropic porous media, and the natural gas flow in anisotropic shale reservoirs. We have employed the multipoint flux approximation (MPFA) method to handle anisotropy in the flow model. The MPFA method is designed to provide correct discretization of the flow equations for general orientation of the principal directions of the permeability tensor. The implementation of MPFA method is combined with the experimenting pressure field approach, a newly developed technique that enables the solution of the global problem breaks down into the solution of multitude of local problems. The numerical results of the study demonstrate the significant effects of anisotropy of the subsurface formations. For the single-phase groundwater flow coupled with the solute transport modeling in anisotropic porous media, the results shows the strong impact of anisotropy on the pressure field and the migration of the solute concentration. For the two-phase flow modeling with gravity effect in anisotropic porous media, it is observed that the buoyancy-driven flow, which emerges due to the density differences between the
Jeppesen, Claus; Flyvbjerg, Henrik; Ole G. Mouritsen
1989-01-01
Monte Carlo computer-simulation techniques are used to elucidate the equilibrium phase behavior as well as the late-stage ordering dynamics of some two-dimensional models with ground-state ordering of a high degeneracy, Q. The models are Q-state Potts models with anisotropic grain-boundary potential on triangular lattices—essentially clock models, except that the potential is not a cosine, but a sine function of the angle between neighboring grain orientations. For not too small Q, these mode...
Starinshak, David P.; Smith, Nathan D.; Wilson, Jeffrey D.
2008-01-01
The electromagnetic effects of conventional dielectrics, anisotropic dielectrics, and metamaterials were modeled in a terahertz-frequency folded-waveguide slow-wave circuit. Results of attempts to utilize these materials to increase efficiency are presented.
Anisotropic matter in cosmology: locally rotationally symmetric Bianchi I and VII o models
Sloan, David
2016-05-01
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types I and VII o in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence of perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic sector. Thus we find that there is more ‘matter that matters’ close to a homogeneous singularity than the usual stiff fluid. Example metrics are given for cosmologies whose matter sources are magnetic fields, relativistic particles, cosmic strings and domain walls.
Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VII_o$ Models
Sloan, David
2016-01-01
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$ in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic sector. Thus we find that there is more `matter that matters' close to a homogeneous singularity than the usual stiff fluid. Example metrics are given for cosmologies whose matter sources are magnetic fields, relativistic particles, cosmic strings and domain walls.
Stender, Michael E; Regueiro, Richard A; Klisch, Stephen M; Ferguson, Virginia L
2015-08-01
Traumatic injuries and gradual wear-and-tear of articular cartilage (AC) that can lead to osteoarthritis (OA) have been hypothesized to result from tissue damage to AC. In this study, a previous equilibrium constitutive model of AC was extended to a constitutive damage articular cartilage (CDAC) model. In particular, anisotropic collagen (COL) fibril damage and isotropic glycosaminoglycan (GAG) damage were considered in a 3D formulation. In the CDAC model, time-dependent effects, such as viscoelasticity and poroelasticity, were neglected, and thus all results represent the equilibrium response after all time-dependent effects have dissipated. The resulting CDAC model was implemented in two different finite-element models. The first simulated uniaxial tensile loading to failure, while the second simulated spherical indentation with a rigid indenter displaced into a bilayer AC sample. Uniaxial tension to failure simulations were performed for three COL fibril Lagrangian failure strain (i.e., the maximum elastic COL fibril strain) values of 15%, 30%, and 45%, while spherical indentation simulations were performed with a COL fibril Lagrangian failure strain of 15%. GAG damage parameters were held constant for all simulations. Our results indicated that the equilibrium postyield tensile response of AC and the macroscopic tissue failure strain are highly dependent on COL fibril Lagrangian failure strain. The uniaxial tensile response consisted of an initial nonlinear ramp region due to the recruitment of intact fibrils followed by a rapid decrease in tissue stress at initial COL fibril failure, as a result of COL fibril damage which continued until ultimate tissue failure. In the spherical indentation simulation, damage to both the COL fibril and GAG constituents was located only in the superficial zone (SZ) and near the articular surface with tissue thickening following unloading. Spherical indentation simulation results are in agreement with published experimental
Nemeth, Noel
2013-01-01
Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software
B B Bhowmik; A Rajput
2004-06-01
Anisotropic Bianchi Type-I cosmological models have been studied on the basis of Lyra's geometry. Two types of models, one with constant deceleration parameter and the other with variable deceleration parameter have been derived by considering a time-dependent displacement field.
Ultrasound Evaluation of an Abdominal Aortic Fluid-Structure Interaction Model
Traberg, Marie Sand; Jensen, Jørgen Arendt
Ultrasound measurements are used for evaluating biomechanics of the abdominal aorta (AA) predicted by a fluid- structure interaction (FSI) simulation model. FSI simulation models describe the complete arterial physiology by quantify- ing the mechanical response in the vessel wall caused by the...... agreement except for 1 volunteer (Male, 23 yrs.). The magnitude of the displacement in simulation, u fsi , and in vivo , u iv , is within the same order of magnitude for the young ( u iv = 1 : 48 mm, u fsi = 1 : 12 mm) and middle-aged volunteer ( u iv = 0 : 783 mm, u fsi = 1 : 31 mm). For the elderly...
Averaging anisotropic cosmologies
We examine the effects of spatial inhomogeneities on irrotational anisotropic cosmologies by looking at the average properties of anisotropic pressure-free models. Adopting the Buchert scheme, we recast the averaged scalar equations in Bianchi-type form and close the standard system by introducing a propagation formula for the average shear magnitude. We then investigate the evolution of anisotropic average vacuum models and those filled with pressureless matter. In the latter case we show that the backreaction effects can modify the familiar Kasner-like singularity and potentially remove Mixmaster-type oscillations. The presence of nonzero average shear in our equations also allows us to examine the constraints that a phase of backreaction-driven accelerated expansion might put on the anisotropy of the averaged domain. We close by assessing the status of these and other attempts to define and calculate 'average' spacetime behaviour in general relativity
PACMAN STUDY OF FSI AND MICRO-TRIANGULATION FOR THE PRE-ALIGNMENT OF CLIC
Kamugasa, William Solomon
2015-01-01
The alignment precision of linear colliders is extremely demanding owing to the very narrow beam size at the interaction point. Unlike circular colliders, particles in linear colliders have only one chance to collide and are hence tightly focused to maximise the number of interactions per collision. The PACMAN* project is dedicated to study the integration of both fiducialization and alignment of the components on a common support. FSI (Frequency Scanning Interferometry) and Micro-triangulation will contribute to this goal. FSI realized by Etalon AG’s Absolute Multiline system and Micro-triangulation implemented by QDaedalus system developed at ETH Zurich offer precision of 0.5 μm/m and 2.4 μm/m respectively. However, these systems need to be improved in order to provide the necessary geometric information via distance measurements (multilateration) and angle measurements (triangulation), respectively. The paper describes the current status and the future developments of Absolute Multiline and QDaedalus, ...
Pierre, C.
2015-12-01
The Earthscope TA deployment across the continental United-State (US) has reached its eastern part, providing the opportunity for high-resolution 3D seismic velocity imaging of both lithosphere and asthenosphere across the entire north-American continent (NA). Previously (Yuan et al., 2014), we presented a 3D radially anisotropic shear wave (Vs) model of North America (NA) lithospheric mantle based on full waveform tomography, combining teleseismic and regional distance data sampling the NA. Regional wavefield computations were performed numerically, using a regional Spectral Element code (RegSEM, Cupillard et al., 2012), while teleseismic computations were performed approximately, using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995). For both datasets, the inversion was performed iteratively, using a Gauss-Newton scheme, with kernels computed using either NACT or the surface wave, path average approximation (PAVA), depending on the source-station distance. We here present a new radially anisotropic lithospheric/asthenospheric model of Vs for NA based entirely on SEM-based numerical waveforms from an augmented dataset of 155 regional events and 70 teleseismic events. The forward wavefield computations are performed using RegSEM down to 40s, starting from our most recent whole mantle 3D radially anisotropic Vs model (SEMUCB-wm1, French and Romanowicz, 2014). To model teleseismic wavefields within our regional computational domain, we developed a new modeling technique which allows us to replace a distant source by virtual sources at the boundary of the computational domain (Masson et al., 2014). Computing virtual sources requires one global simulation per teleseismic events.We then compare two models obtained: one using NACT/PAVA kernels as in our previous work, and another using hybrid kernels, where the Hessian is computed using NACT/PAVA, but the gradient is computed numerically from the adjoint wavefield, providing more accurate kernels
An anisotropic cosmological model in a modified Brans-Dicke theory
Rasouli, S. M. M.; Farhoudi, Mehrdad; Sepangi, Hamid R.
2011-08-01
Recently, it has been shown that a four-dimensional (4D) Brans-Dicke (BD) theory with an effective matter field and a self-interacting potential can be achieved from the vacuum 5D BD field equations, where we refer to as a modified Brans-Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing the obtained formalism, we derive the induced matter on any 4D hypersurface in the context of the MBDT. We illustrate that if the usual spatial scale factors are functions of the time while the scale factor of extra dimension is constant, and the scalar field depends on the time and the fifth coordinate, then, in general, one will encounter inconsistencies in the field equations. Then, we assume that the scale factors and the scalar field depend on the time and the extra coordinate as separated variables in the power-law forms. Hence, we find a few classes of solutions in 5D spacetime through which we probe the one which leads to a generalized Kasner relation among the Kasner parameters. The induced scalar potential is found to be in the power law or in the logarithmic form; however, for a constant scalar field and even when the scalar field only depends on the fifth coordinate, it vanishes. The conservation law is indeed valid in this MBDT approach for the derived induced energy-momentum tensor (EMT). We proceed our investigations for a few cosmological quantities, where for simplicity we assume that the metric and the scalar field are functions of the time. Hence, the EMT satisfies the barotropic equation of state, and the model indicates that the constant mean Hubble parameter is not allowed. Thus, by appealing to the variation of the Hubble parameter, we assume a fixed deceleration parameter, and set the evolution of the quantities with respect to the fixed deceleration, the BD coupling and the state parameters. The WEC allows a shrinking extra dimension for a decelerating expanding universe that, in the
A stable partitioned FSI algorithm for incompressible flow and deforming beams
Li, L.; Henshaw, W. D.; Banks, J. W.; Schwendeman, D. W.; Main, A.
2016-05-01
An added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier-Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler-Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet-Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one
Modeling of Anisotropic Two-Dimensional Materials Monolayer HfS2 and Phosphorene MOSFETs
Chang, Jiwon
2015-01-01
Ballistic transport characteristics of metal-oxide semiconductor field effect transistors (MOSFETs) based on anisotropic two-dimensional (2-D) materials monolayer HfS2 and phosphorene are explored through quantum transport simulations. We focus on the effects of the channel crystal orientation and the channel length scaling on device performances. Especially, the role of degenerate conduction band (CB) valleys in monolayer HfS2 is comprehensively analyzed. Benchmarking monolayer HfS2 with pho...
A variational finite element-spherical harmonics method is presented for the solution of the even-parity multigroup equations with anisotropic scattering and sources. It is shown that by using a simple and natural formulation the numerical implementation of the method for any desired geometry is greatly eased and the anisotropy of scatter treated without any difficulty. Numerical examples demonstrate the ability of the resulting code to solve geometrically complex multigroup problems. (Author)
The objective of this research thesis is to develop the most precise possible numeric modelling of reinforced concrete behaviour with application to the design of structures of protection of nuclear plants against violent dynamic loadings (explosions, impacts). After a discussion of existing models, of their benefits and weaknesses, a multi-axial model of anisotropic damage is proposed and implemented with the finite element method. A new procedure of failure management is also proposed which allows the induced anisotropic damage to be taken into account. Impact tests on concrete beams and concrete cubes with longitudinal steel have been performed in order to validate the model
Loredo, A.; Castel, A.
2013-01-01
In this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10×10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2×2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios between the stiffnesses of layers - up to 106 - are present. This work is related to Woodcock's model, so it can be seen as a reformulation of his work. However, it brings several enhancements: the displacement field is made explicit; it is reformulated with commonly used plate notations; laminate equations of motion are fully detailed; the place of this model among other plate models is now easy to see and is discussed; the link between this formulation and the original one is completely written with all necessary proofs; misses and errors have been found in the energy coefficients of the original work and have been corrected; it is now easy to improve or to adapt the model for specific applications with the choice of refined or specific warping functions. Static deflection and natural frequencies for isotropic and anisotropic sandwich plates are given and compared to other models: they show that the present model is very accurate for the simulation of such structures.
In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein-Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30. (orig.)
Humeida, Yousif; Pinfield, Valerie J.; Challis, Richard E.
2013-08-01
Ultrasonic arrays have seen increasing use for the characterisation of composite materials. In this paper, ultrasonic wave propagation in multilayer anisotropic materials has been modelled using plane wave and angular spectrum decomposition techniques. Different matrix techniques, such as the stiffness matrix method and the transfer matrix method, are used to calculate the reflection and transmission coefficients of ultrasonic plane waves in the considered media. Then, an angular decomposition technique is used to derive the bounded beams from finite-width ultrasonic array elements from the plane wave responses calculated earlier. This model is considered to be an analytical exact solution for the problem; hence the diffraction of waves in such composite materials can be calculated for different incident angles for a very wide range of frequencies. This model is validated against experimental measurements using the Full-Matrix Capture (FMC) of array data in both a homogeneous isotropic material, i.e. aluminium, and an inhomogeneous multilayer anisotropic material, i.e. a carbon fibre reinforced composite.
Murad, Mohammad Hassan [BRAC University, Department of Mathematics and Natural Sciences, Dhaka (Bangladesh); Fatema, Saba [Daffodil International University, Department of Natural Sciences, Dhaka (Bangladesh)
2015-11-15
In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein-Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30. (orig.)
Ultrasonic arrays have seen increasing use for the characterisation of composite materials. In this paper, ultrasonic wave propagation in multilayer anisotropic materials has been modelled using plane wave and angular spectrum decomposition techniques. Different matrix techniques, such as the stiffness matrix method and the transfer matrix method, are used to calculate the reflection and transmission coefficients of ultrasonic plane waves in the considered media. Then, an angular decomposition technique is used to derive the bounded beams from finite-width ultrasonic array elements from the plane wave responses calculated earlier. This model is considered to be an analytical exact solution for the problem; hence the diffraction of waves in such composite materials can be calculated for different incident angles for a very wide range of frequencies. This model is validated against experimental measurements using the Full-Matrix Capture (FMC) of array data in both a homogeneous isotropic material, i.e. aluminium, and an inhomogeneous multilayer anisotropic material, i.e. a carbon fibre reinforced composite
FSY30型林木枝丫切碎机试验分析%Experimental Analysis of FSY30 Tree Branch Chopper
牛晓华; 吴兆迁; 樊涛; 王晓军
2011-01-01
FSY30型林木枝丫切碎机是林区林木剩余物碎化处理的专用设备,该机采用圆盘式切碎装置,结构简单实用,解决了我国现有林木剩余物碎化处理设备野外作业性能差、切削效率低和原料适应面窄等问题,为我国林区人工林迹地整理更新、抚育和采伐等作业产生的各种林木剩余物碎化处理提供了适用的设备。该机性能和生产试验结果表明：其作业效率比现有机型提高20%以上,作业成本减少15%以上,具有显著的经济效益和一定的生态效益。%FSY30 tree branch chopper is a machine specially used for chopping forest residuals in forest areas. The machine uses a disc type chopping device, with a simple and practical structure, and has solved the problems with poor Operation performance in the field, low chopping efficiency and narrow adaptive scope of raw materials of the existing equipment and provided proper equipment for regeneration, tending and harvesting operations in the plantation area in China. Performance and production experiments show that the operation efficiency of the machine has improved by 20% over the current machine types and the operation cost has reduced by15%, with noticeable economic and social benefits.