Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Anisotropic Thermal Diffusion

NASA Astrophysics Data System (ADS)

Gardiner, Thomas

2013-10-01

Anisotropic thermal diffusion in magnetized plasmas is an important physical phenomena for a diverse set of physical conditions ranging from astrophysical plasmas to MFE and ICF. Yet numerically simulating this phenomenon accurately poses significant challenges when the computational mesh is misaligned with respect to the magnetic field. Particularly when the temperature gradients are unresolved, one frequently finds entropy violating solutions with heat flowing from cold to hot zones for χ∥ /χ⊥ >=102 which is substantially smaller than the range of interest which can reach 1010 or higher. In this talk we present a new implicit algorithm for solving the anisotropic thermal diffusion equations and demonstrate its characteristics on what has become a fairly standard set of test problems in the literature. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND2013-5687A.

Anisotropic rotational diffusion studied by passage saturation transfer electron paramagnetic resonance

NASA Astrophysics Data System (ADS)

Robinson, Bruce H.; Dalton, Larry R.

1980-01-01

The stochastic Liouville equation for the spin density matrix is modified to consider the effects of Brownian anisotropic rotational diffusion upon electron paramagnetic resonance (EPR) and saturation transfer electron paramagnetic resonance (ST-EPR) spectra. Spectral shapes and the ST-EPR parameters L″/L, C'/C, and H″/H defined by Thomas, Dalton, and Hyde at X-band microwave frequencies [J. Chem. Phys. 65, 3006 (1976)] are examined and discussed in terms of the rotational times τ∥ and τ⊥ and in terms of other defined correlation times for systems characterized by magnetic tensors of axial symmetry and for systems characterized by nonaxially symmetric magnetic tensors. For nearly axially symmetric magnetic tensors, such as nitroxide spin labels studied employing 1-3 GHz microwaves, ST-EPR spectra for systems undergoing anisotropic rotational diffusion are virtually indistinguishable from spectra for systems characterized by isotropic diffusion. For nonaxially symmetric magnetic tensors, such as nitroxide spin labels studied employing 8-35 GHz microwaves, the high field region of the ST-EPR spectra, and hence the H″/H parameter, will be virtually indistinguishable from spectra, and parameter values, obtained for isotropic diffusion. On the other hand, the central spectral region at x-band microwave frequencies, and hence the C'/C parameter, is sensitive to the anisotropic diffusion model provided that a unique and static relationship exists between the magnetic and diffusion tensors. Random labeling or motion of the spin label relative to the biomolecule whose hydrodynamic properties are to be investigated will destroy spectral sensitivity to anisotropic motion. The sensitivity to anisotropic motion is enhanced in proceeding to 35 GHz with the increased sensitivity evident in the low field half of the EPR and ST-EPR spectra. The L″/L parameter is thus a meaningful indicator of anisotropic motion when compared with H″/H parameter analysis. However, consideration of spectral shapes suggests that the C'/C parameter definition is not meaningfully extended from 9.5 to 35 GHz. Alternative definitions of the L″/L and C'/C parameters are proposed for those microwave frequencies for which the electron Zeeman anisotropy is comparable to or greater than the electron-nitrogen nuclear hyperfine anisotropy.

Texture formation mechanism and constitutive equation for anisotropic thermorheological rare-earth permanent magnets

NASA Astrophysics Data System (ADS)

Zhu, Minggang; Li, Wei

2017-05-01

The study investigates the mechanism and constitutive equations describing oriented texture formation in anisotropic thermorheological rare-earth permanent magnets. The thermorheological process cannot be considered as creep, since the related phenomena are not suitably explained by the diffusion creep model. A mathematical model describing the relationship between the rheological deformation rate and texture orientation was established, and a theoretical expression was obtained for the orientation factor of thermorheological magnets. In addition, nanocrystalline Nd-Fe-B magnets were fabricated, with intrinsic coercivity Hcj=760.1 kA/m, remanence Br=1.469 T, and maximum energy product (BH)max=427.1 kJ/m3.

Recursive recovery of Markov transition probabilities from boundary value data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes.

PubMed

Ghysels, An; Venable, Richard M; Pastor, Richard W; Hummer, Gerhard

2017-06-13

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

A New Numerical Scheme for Cosmic-Ray Transport

NASA Astrophysics Data System (ADS)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

Evaluation of the telegrapher's equation and multiple-flux theories for calculating the transmittance and reflectance of a diffuse absorbing slab.

PubMed

Kong, Steven H; Shore, Joel D

2007-03-01

We study the propagation of light through a medium containing isotropic scattering and absorption centers. With a Monte Carlo simulation serving as the benchmark solution to the radiative transfer problem of light propagating through a turbid slab, we compare the transmission and reflection density computed from the telegrapher's equation, the diffusion equation, and multiple-flux theories such as the Kubelka-Munk and four-flux theories. Results are presented for both normally incident light and diffusely incident light. We find that we can always obtain very good results from the telegrapher's equation provided that two parameters that appear in the solution are set appropriately. We also find an interesting connection between certain solutions of the telegrapher's equation and solutions of the Kubelka-Munk and four-flux theories with a small modification to how the phenomenological parameters in those theories are traditionally related to the optical scattering and absorption coefficients of the slab. Finally, we briefly explore how well the theories can be extended to the case of anisotropic scattering by multiplying the scattering coefficient by a simple correction factor.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time stepping

NASA Astrophysics Data System (ADS)

Vaidya, Bhargav; Prasad, Deovrat; Mignone, Andrea; Sharma, Prateek; Rickler, Luca

2017-12-01

An important ingredient in numerical modelling of high temperature magnetized astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures. Magnetohydrodynamics typically involves solving the hyperbolic set of conservation equations along with the induction equation. Incorporating anisotropic thermal conduction requires to also treat parabolic terms arising from the diffusion operator. An explicit treatment of parabolic terms will considerably reduce the simulation time step due to its dependence on the square of the grid resolution (Δx) for stability. Although an implicit scheme relaxes the constraint on stability, it is difficult to distribute efficiently on a parallel architecture. Treating parabolic terms with accelerated super-time-stepping (STS) methods has been discussed in literature, but these methods suffer from poor accuracy (first order in time) and also have difficult-to-choose tuneable stability parameters. In this work, we highlight a second-order (in time) Runge-Kutta-Legendre (RKL) scheme (first described by Meyer, Balsara & Aslam 2012) that is robust, fast and accurate in treating parabolic terms alongside the hyperbolic conversation laws. We demonstrate its superiority over the first-order STS schemes with standard tests and astrophysical applications. We also show that explicit conduction is particularly robust in handling saturated thermal conduction. Parallel scaling of explicit conduction using RKL scheme is demonstrated up to more than 104 processors.

Anisotropic Turbulence Models for Acoustic Propagation Through the Neutral Atmospheric Surface Layer

DTIC Science & Technology

1998-02-01

and Brost (1984). †Specific means per unit mass. 2 Observations Top-Down Approach Bottom-Up Approach Equations for the energy spectra Equations for...R. A. Brost (1984): Top-down and bottom-up diffusion of a scalar in the convective boundary layer. J. Atmos. Sci., 41, 102–112. 62 Distribution 63...Agency Attn W21 Longbothum 9800 Savage Rd FT George G Meade MD 20755-6000 TACOM Attn AMSTA-TR-R E Shalis Mail Stop 263 Warren MI 48090 US Army

Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haverkort, J.W.; Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven; Blank, H.J. de

Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. Amore » rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.« less

Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging

DTIC Science & Technology

2011-10-01

the deviatoric part of a tensor in the reference configuration and p = −∂Ψ ∂J is the hydrostatic pressure. Using the chain 4 rule, equation 13 can be...Kirchoff stress tensor S to the current configuration, and a scaling with the inverse of the volume ratio, transforms equation 16 to the Cauchy stress ...a characteristic of most soft tissues. Then, similar to equation 13, the second Piola-Kirchoff stress is given by: S = 2J−2/3DEV [ ∂Ψisoc ( C ) ∂C

A stochastic method for Brownian-like optical transport calculations in anisotropic biosuspensions and blood

NASA Astrophysics Data System (ADS)

Miller, Steven

1998-03-01

A generic stochastic method is presented that rapidly evaluates numerical bulk flux solutions to the one-dimensional integrodifferential radiative transport equation, for coherent irradiance of optically anisotropic suspensions of nonspheroidal bioparticles, such as blood. As Fermat rays or geodesics enter the suspension, they evolve into a bundle of random paths or trajectories due to scattering by the suspended bioparticles. Overall, this can be interpreted as a bundle of Markov trajectories traced out by a "gas" of Brownian-like point photons being scattered and absorbed by the homogeneous distribution of uncorrelated cells in suspension. By considering the cumulative vectorial intersections of a statistical bundle of random trajectories through sets of interior data planes in the space containing the medium, the effective equivalent information content and behavior of the (generally unknown) analytical flux solutions of the radiative transfer equation rapidly emerges. The fluxes match the analytical diffuse flux solutions in the diffusion limit, which verifies the accuracy of the algorithm. The method is not constrained by the diffusion limit and gives correct solutions for conditions where diffuse solutions are not viable. Unlike conventional Monte Carlo and numerical techniques adapted from neutron transport or nuclear reactor problems that compute scalar quantities, this vectorial technique is fast, easily implemented, adaptable, and viable for a wide class of biophotonic scenarios. By comparison, other analytical or numerical techniques generally become unwieldy, lack viability, or are more difficult to utilize and adapt. Illustrative calculations are presented for blood medias at monochromatic wavelengths in the visible spectrum.

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

Anisotropic scene geometry resampling with occlusion filling for 3DTV applications

NASA Astrophysics Data System (ADS)

Kim, Jangheon; Sikora, Thomas

2006-02-01

Image and video-based rendering technologies are receiving growing attention due to their photo-realistic rendering capability in free-viewpoint. However, two major limitations are ghosting and blurring due to their sampling-based mechanism. The scene geometry which supports to select accurate sampling positions is proposed using global method (i.e. approximate depth plane) and local method (i.e. disparity estimation). This paper focuses on the local method since it can yield more accurate rendering quality without large number of cameras. The local scene geometry has two difficulties which are the geometrical density and the uncovered area including hidden information. They are the serious drawback to reconstruct an arbitrary viewpoint without aliasing artifacts. To solve the problems, we propose anisotropic diffusive resampling method based on tensor theory. Isotropic low-pass filtering accomplishes anti-aliasing in scene geometry and anisotropic diffusion prevents filtering from blurring the visual structures. Apertures in coarse samples are estimated following diffusion on the pre-filtered space, the nonlinear weighting of gradient directions suppresses the amount of diffusion. Aliasing artifacts from low density are efficiently removed by isotropic filtering and the edge blurring can be solved by the anisotropic method at one process. Due to difference size of sampling gap, the resampling condition is defined considering causality between filter-scale and edge. Using partial differential equation (PDE) employing Gaussian scale-space, we iteratively achieve the coarse-to-fine resampling. In a large scale, apertures and uncovered holes can be overcoming because only strong and meaningful boundaries are selected on the resolution. The coarse-level resampling with a large scale is iteratively refined to get detail scene structure. Simulation results show the marked improvements of rendering quality.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Traytak, Sergey D., E-mail: sergtray@mail.ru; Le STUDIUM; Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow

The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problemmore » and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.« less

Cosmic-ray propagation with DRAGON2: I. numerical solver and astrophysical ingredients

NASA Astrophysics Data System (ADS)

Evoli, Carmelo; Gaggero, Daniele; Vittino, Andrea; Di Bernardo, Giuseppe; Di Mauro, Mattia; Ligorini, Arianna; Ullio, Piero; Grasso, Dario

2017-02-01

We present version 2 of the DRAGON code designed for computing realistic predictions of the CR densities in the Galaxy. The code numerically solves the interstellar CR transport equation (including inhomogeneous and anisotropic diffusion, either in space and momentum, advective transport and energy losses), under realistic conditions. The new version includes an updated numerical solver and several models for the astrophysical ingredients involved in the transport equation. Improvements in the accuracy of the numerical solution are proved against analytical solutions and in reference diffusion scenarios. The novel features implemented in the code allow to simulate the diverse scenarios proposed to reproduce the most recent measurements of local and diffuse CR fluxes, going beyond the limitations of the homogeneous galactic transport paradigm. To this end, several applications using DRAGON2 are presented as well. This new version facilitates the users to include their own physical models by means of a modular C++ structure.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

CRPropa 3.1—a low energy extension based on stochastic differential equations

NASA Astrophysics Data System (ADS)

Merten, Lukas; Becker Tjus, Julia; Fichtner, Horst; Eichmann, Björn; Sigl, Günter

2017-06-01

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ∥ and perpendicular κ⊥ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

GALACTIC WINDS DRIVEN BY ISOTROPIC AND ANISOTROPIC COSMIC-RAY DIFFUSION IN DISK GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pakmor, R.; Pfrommer, C.; Simpson, C. M.

2016-06-20

The physics of cosmic rays (CRs) is a promising candidate for explaining the driving of galactic winds and outflows. Recent galaxy formation simulations have demonstrated the need for active CR transport either in the form of diffusion or streaming to successfully launch winds in galaxies. However, due to computational limitations, most previous simulations have modeled CR transport isotropically. Here, we discuss high-resolution simulations of isolated disk galaxies in a 10{sup 11} M {sub ⊙} halo with the moving-mesh code Arepo that include injection of CRs from supernovae, advective transport, CR cooling, and CR transport through isotropic or anisotropic diffusion. Wemore » show that either mode of diffusion leads to the formation of strong bipolar outflows. However, they develop significantly later in the simulation with anisotropic diffusion compared to the simulation with isotropic diffusion. Moreover, we find that isotropic diffusion allows most of the CRs to quickly diffuse out of the disk, while in the simulation with anisotropic diffusion, most CRs remain in the disk once the magnetic field becomes dominated by its azimuthal component, which occurs after ∼300 Myr. This has important consequences for the gas dynamics in the disk. In particular, we show that isotropic diffusion strongly suppresses the amplification of the magnetic field in the disk compared to anisotropic or no diffusion models. We therefore conclude that reliable simulations which include CR transport inevitably need to account for anisotropic diffusion.« less

Strain-based diffusion solver for realistic representation of diffusion front in physical reactions

PubMed Central

2017-01-01

When simulating fluids, such as water or fire, interacting with solids, it is a challenging problem to represent details of diffusion front in physical reaction. Previous approaches commonly use isotropic or anisotropic diffusion to model the transport of a quantity through a medium or long interface. We have identified unrealistic monotonous patterns with previous approaches and therefore, propose to extend these approaches by integrating the deformation of the material with the diffusion process. Specifically, stretching deformation represented by strain is incorporated in a divergence-constrained diffusion model. A novel diffusion model is introduced to increase the global rate at which the solid acquires relevant quantities, such as heat or saturation. This ensures that the equations describing fluid flow are linked to the change of solid geometry, and also satisfy the divergence-free condition. Experiments show that our method produces convincing results. PMID:28448591

Steady state whistler turbulence and stability of thermal barriers in tandem mirrors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Litwin, C.; Sudan, R.N.

The effect of the whistler turbulence on anisotropic electrons in a thermal barrier is examined. The electron distribution function is derived self-consistently by solving the steady state quasilinear diffusion equation. Saturated amplitudes are computed using the resonance broadening theory or convective stabilization. Estimated power levels necessary for sustaining the steady state of a strongly anisotropic electron population are found to exceed by orders of magnitude the estimates based on Fokker--Planck calculations for the range of parameters of tandem mirror (TMX-U and MFTF-B) experiments (Nucl. Fusion 25, 1205 (1985)). Upper limits on the allowed degree of anisotropy for existing power densitiesmore » are calculated.« less

Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azhar, Mueed; Greiner, Andreas; Korvink, Jan G., E-mail: jan.korvink@kit.edu, E-mail: david.kauzlaric@imtek.uni-freiburg.de

We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. Aftermore » a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.« less

Cosmic-ray propagation with DRAGON2: I. numerical solver and astrophysical ingredients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evoli, Carmelo; Gaggero, Daniele; Vittino, Andrea

2017-02-01

We present version 2 of the DRAGON code designed for computing realistic predictions of the CR densities in the Galaxy. The code numerically solves the interstellar CR transport equation (including inhomogeneous and anisotropic diffusion, either in space and momentum, advective transport and energy losses), under realistic conditions. The new version includes an updated numerical solver and several models for the astrophysical ingredients involved in the transport equation. Improvements in the accuracy of the numerical solution are proved against analytical solutions and in reference diffusion scenarios. The novel features implemented in the code allow to simulate the diverse scenarios proposed tomore » reproduce the most recent measurements of local and diffuse CR fluxes, going beyond the limitations of the homogeneous galactic transport paradigm. To this end, several applications using DRAGON2 are presented as well. This new version facilitates the users to include their own physical models by means of a modular C++ structure.« less

Langevin Equation for DNA Dynamics

NASA Astrophysics Data System (ADS)

Grych, David; Copperman, Jeremy; Guenza, Marina

Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

Effects of anisotropic turbulent thermal diffusion on spherical magnetoconvection in the Earth's core

NASA Astrophysics Data System (ADS)

Ivers, D. J.; Phillips, C. G.

2018-03-01

We re-consider the plate-like model of turbulence in the Earth's core, proposed by Braginsky and Meytlis (1990), and show that it is plausible for core parameters not only in polar regions but extends to mid- and low-latitudes where rotation and gravity are not parallel, except in a very thin equatorial layer. In this model the turbulence is highly anisotropic with preferred directions imposed by the Earth's rotation and the magnetic field. Current geodynamo computations effectively model sub-grid scale turbulence by using isotropic viscous and thermal diffusion values significantly greater than the molecular values of the Earth's core. We consider a local turbulent dynamo model for the Earth's core in which the mean magnetic field, velocity and temperature satisfy the Boussinesq induction, momentum and heat equations with an isotropic turbulent Ekman number and Roberts number. The anisotropy is modelled only in the thermal diffusion tensor with the Earth's rotation and magnetic field as preferred directions. Nonlocal organising effects of gravity and rotation (but not aspect ratio in the Earth's core) such as an inverse cascade and nonlocal transport are assumed to occur at longer length scales, which computations may accurately capture with sufficient resolution. To investigate the implications of this anisotropy for the proposed turbulent dynamo model we investigate the linear instability of turbulent magnetoconvection on length scales longer than the background turbulence in a rotating sphere with electrically insulating exterior for no-slip and isothermal boundary conditions. The equations are linearised about an axisymmetric basic state with a conductive temperature, azimuthal magnetic field and differential rotation. The basic state temperature is a function of the anisotropy and the spherical radius. Elsasser numbers in the range 1-20 and turbulent Roberts numbers 0.01-1 are considered for both equatorial symmetries of the magnetic basic state. It is found that anisotropic turbulent thermal diffusivity has a strong destabilising effect on magneto-convective instabilities, which may relax the tight energy budget constraining geodynamo models. The enhanced instability is not due to a reduction of the total diffusivity. The anisotropy also strengthens instabilities which break the symmetry of the underlying state, which may facilitate magnetic field reversal. Geostrophic flow appears to suppress the symmetry breaking modes and magnetic instabilities. Through symmetry breaking and the geostrophic flow the anisotropy may provide a mechanism of magnetic field reversal and its suppression in computational dynamo models.

Logarithmic violation of scaling in anisotropic kinematic dynamo model

NASA Astrophysics Data System (ADS)

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

2016-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t')/k⊥d-1 +ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of power-like corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L.

CRPropa 3.1—a low energy extension based on stochastic differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merten, Lukas; Tjus, Julia Becker; Eichmann, Björn

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us tomore » use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.« less

Approximate methods for the fast computation of EPR and ST-EPR spectra. V. Application of the perturbation approach to the problem of anisotropic motion

NASA Astrophysics Data System (ADS)

Robinson, B. H.; Dalton, L. R.

1981-01-01

The modulation perturbation treatment of Galloway and Dalton is applied to the solution of the stochastic Liouville equation for the spin density matrix which incorporates an anisotropic rotational diffusion operator. Pseudosecular and saturation terms of the spin hamiltonian are explicitly considered as is the interaction of the electron spins with the applied Zeeman modulation field. The modulation perturbation treatment results in a factor of four improvement in computational speed relative to inversion of the full supermatrix with little or no loss of computational accuracy. The theoretical simulations of EPR and ST-EPR spectra are in nearly quantitative agreement with experimental spectra taken under high resolution conditions.

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

NASA Technical Reports Server (NTRS)

Salamon, N. J. (Principal Investigator); Sullivan, Roy M.; Lee, Sunpyo

1995-01-01

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Anisotropic diffusion and capture on surfaces: Time dependent modeling and visualization in 2 dimensions

NASA Astrophysics Data System (ADS)

Yang, Pu

Since the application of nanowires may lead to a new generation of electronic, optoelectronic and magnetic devices, there is much research on understanding the growth mechanism of various "self assembled" nanowires on semiconductor surfaces. The motivation of the present work is to use theoretical modeling to study the conditions required to form and grow elongated islands and nanowires. In this work, a modeling method is developed to study the time-dependent anisotropic diffusion and growth in two dimensions for an array of rectangular islands. This method uses discrete Fast Fourier Transformation (FFT) to solve the time-dependent diffusion equation on the surface. The ad-particles are captured and incorporated to the island edge to simulate island growth. Implemented in MATLABRTM programs, this model produces expected faceted shapes; the calculation runs very fast on a common personal computer. Time-dependent island growth and the evolving diffusion field have been visualized using simple MATLABRTM functions and can be made into MATLABRTM movies. This modeling method is applied to simulate elongated island and nanowire growth by incorporating anisotropic bonding at the island edge. When there is a full sink in one direction and partial sink in the other direction at the island edge, the model results in the growth of an elongated island with an aspect ratio that stabilizes after it reaches a certain value. This result agrees with experimental data on "endotaxial" nanowire growth. For the island edge with a full sink in one direction and no sink in the other direction, the island grows in length with constant width, which is comparable to experimental data on Bi nanoline and rare-earth metal nanowire growth.

On Pokrovskii's anisotropic gap equations in superconductivity theory

NASA Astrophysics Data System (ADS)

Yang, Yisong

2003-11-01

An existence and uniqueness theorem for Pokrovskii's zero-temperature anisotropic gap equation is proved. Furthermore, it is shown that Pokrovskii's finite-temperature equation is inconsistent with the Bardeen-Cooper-Schrieffer (BCS) theory. A reformulation of the anisotropic gap equation is presented along the line of Pokrovskii and it is shown that the new equation is consistent with the BCS theory for the whole temperature range. As an application, the Markowitz-Kadanoff model for anisotropic superconductivity is considered and a rigorous proof of the half-integer-exponent isotope effect is obtained. Furthermore, a sharp estimate of the gap solution near the transition temperature is established.

Theory and simulation of time-fractional fluid diffusion in porous media

NASA Astrophysics Data System (ADS)

Carcione, José M.; Sanchez-Sesma, Francisco J.; Luzón, Francisco; Perez Gavilán, Juan J.

2013-08-01

We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald-Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’.

Flexible and polarization-controllable diffusion metasurface with optical transparency

NASA Astrophysics Data System (ADS)

Zhuang, Yaqiang; Wang, Guangming; Liang, Jiangang; Cai, Tong; Guo, Wenlong; Zhang, Qingfeng

2017-11-01

In this paper, a novel coding metasurface is proposed to realize polarization-controllable diffusion scattering. The anisotropic Jerusalem-cross unit cell is employed as the basic coding element due to its polarization-dependent phase response. The isotropic random coding sequence is firstly designed to obtain diffusion scattering, and the anisotropic random coding sequence is subsequently realized by adding different periodic coding sequences to the original isotropic one along different directions. For demonstration, we designed and fabricated a flexible polarization-controllable diffusion metasurface (PCDM) with both chessboard diffusion and hedge diffusion under different polarizations. The specular scattering reduction performance of the anisotropic metasurface is better than the isotropic one because the scattered energies are redirected away from the specular reflection direction. For potential applications, the flexible PCDM wrapped around a cylinder structure is investigated and tested for polarization-controllable diffusion scattering. The numerical and experimental results coincide well, indicating anisotropic low scatterings with comparable performances. This paper provides an alternative approach for designing high-performance, flexible, low-scattering platforms.

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2011-01-01

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction

NASA Astrophysics Data System (ADS)

Ammari, Habib; Qiu, Lingyun; Santosa, Fadil; Zhang, Wenlong

2017-12-01

In this paper we present a mathematical and numerical framework for a procedure of imaging anisotropic electrical conductivity tensor by integrating magneto-acoutic tomography with data acquired from diffusion tensor imaging. Magneto-acoustic tomography with magnetic induction (MAT-MI) is a hybrid, non-invasive medical imaging technique to produce conductivity images with improved spatial resolution and accuracy. Diffusion tensor imaging (DTI) is also a non-invasive technique for characterizing the diffusion properties of water molecules in tissues. We propose a model for anisotropic conductivity in which the conductivity is proportional to the diffusion tensor. Under this assumption, we propose an optimal control approach for reconstructing the anisotropic electrical conductivity tensor. We prove convergence and Lipschitz type stability of the algorithm and present numerical examples to illustrate its accuracy and feasibility.

Phase-field modeling of two-dimensional crystal growth with anisotropic diffusion.

PubMed

Meca, Esteban; Shenoy, Vivek B; Lowengrub, John

2013-11-01

In the present article, we introduce a phase-field model for thin-film growth with anisotropic step energy, attachment kinetics, and diffusion, with second-order (thin-interface) corrections. We are mainly interested in the limit in which kinetic anisotropy dominates, and hence we study how the expected shape of a crystallite, which in the long-time limit is the kinetic Wulff shape, is modified by anisotropic diffusion. We present results that prove that anisotropic diffusion plays an important, counterintuitive role in the evolving crystal shape, and we add second-order corrections to the model that provide a significant increase in accuracy for small supersaturations. We also study the effect of different crystal symmetries and discuss the influence of the deposition rate.

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Molnár, E.; Niemi, H.; Rischke, D. H.

2016-12-01

In Molnár et al. Phys. Rev. D 93, 114025 (2016) the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.

Modeling fluid injection induced microseismicity in shales

NASA Astrophysics Data System (ADS)

Carcione, José M.; Currenti, Gilda; Johann, Lisa; Shapiro, Serge

2018-02-01

Hydraulic fracturing in shales generates a cloud of seismic—tensile and shear—events that can be used to evaluate the extent of the fracturing (event clouds) and obtain the hydraulic properties of the medium, such as the degree of anisotropy and the permeability. Firstly, we investigate the suitability of novel semi-analytical reference solutions for pore pressure evolution around a well after fluid injection in anisotropic media. To do so, we use cylindrical coordinates in the presence of a formation (a layer) and spherical coordinates for a homogeneous and unbounded medium. The involved differential equations are transformed to an isotropic diffusion equation by means of pseudo-spatial coordinates obtained from the spatial variables re-scaled by the permeability components. We consider pressure-dependent permeability components, which are independent of the spatial direction. The analytical solutions are compared to numerical solutions to verify their applicability. The comparison shows that the solutions are suitable for a limited permeability range and moderate to minor pressure dependences of the permeability. Once the pressure evolution around the well has been established, we can model the microseismic events. Induced seismicity by failure due to fluid injection in a porous rock depends on the properties of the hydraulic and elastic medium and in situ stress conditions. Here, we define a tensile threshold pressure above which there is tensile emission, while the shear threshold is obtained by using the octahedral stress criterion and the in situ rock properties and conditions. Subsequently, we generate event clouds for both cases and study the spatio-temporal features. The model considers anisotropic permeability and the results are spatially re-scaled to obtain an effective isotropic medium representation. For a 3D diffusion in spherical coordinates and exponential pressure dependence of the permeability, the results differ from those of the classical diffusion equation. Use of the classical front to fit cloud events spatially, provides good results but with a re-scaled value of these components. Modeling is required to evaluate the scaling constant in real cases.

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

Development and application of an exchange model for anisotropic water diffusion in the microporous MOF aluminum fumarate

NASA Astrophysics Data System (ADS)

Splith, Tobias; Fröhlich, Dominik; Henninger, Stefan K.; Stallmach, Frank

2018-06-01

Diffusion of water in aluminum fumarate was studied by means of pulsed field gradient (PFG) nuclear magnetic resonance (NMR). Due to water molecules exchanging between the intracrystalline anisotropic pore space and the isotropic intercrystalline void space the model of intracrystalline anisotropic diffusion fails to describe the experimental PFG NMR data at high observation times. Therefore, the two-site exchange model developed by Kärger is extended to the case of exchange between an anisotropic and an isotropic site. This extended exchange model is solved by numerical integration. It describes the experimental data very well and yields values for the intracrystalline diffusion coefficient and the mean residence times of the respective sites. Further PFG NMR studies were performed with coatings consisting of small aluminum fumarate crystals, which are used in adsorptive heat transformation applications. The diffusion coefficients of water in the small crystal coating are compared to the values expected from the extended two-site exchange model and from the model of long-range diffusion.

Anisotropic Diffusion Despeckling for High Resolution SAR Images

DTIC Science & Technology

2004-11-01

Chiang Mai , Thailand 323 Data Processing B-4.2 Anisotropic Diffusion Despeckling for High...18 324 25th ACRS 2004 Chiang Mai , Thailand B-4.2 Data Processing 2 NONLINEAR DIFFUSION FILTERING 2.1...edge-enhancing diffusion model is adopted. |)(|1 σϕ ug ∇= 2.02 =ϕ (4) 25th ACRS 2004 Chiang Mai , Thailand 325 Data

Entropy-guided switching trimmed mean deviation-boosted anisotropic diffusion filter

NASA Astrophysics Data System (ADS)

Nnolim, Uche A.

2016-07-01

An effective anisotropic diffusion (AD) mean filter variant is proposed for filtering of salt-and-pepper impulse noise. The implemented filter is robust to impulse noise ranging from low to high density levels. The algorithm involves a switching scheme in addition to utilizing the unsymmetric trimmed mean/median deviation to filter image noise while greatly preserving image edges, regardless of impulse noise density (ND). It operates with threshold parameters selected manually or adaptively estimated from the image statistics. It is further combined with the partial differential equations (PDE)-based AD for edge preservation at high NDs to enhance the properties of the trimmed mean filter. Based on experimental results, the proposed filter easily and consistently outperforms the median filter and its other variants ranging from simple to complex filter structures, especially the known PDE-based variants. In addition, the switching scheme and threshold calculation enables the filter to avoid smoothing an uncorrupted image, and filtering is activated only when impulse noise is present. Ultimately, the particular properties of the filter make its combination with the AD algorithm a unique and powerful edge-preservation smoothing filter at high-impulse NDs.

Spin diffusion from an inhomogeneous quench in an integrable system.

PubMed

Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž

2017-07-13

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

Asymptotic-Preserving methods and multiscale models for plasma physics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Deluzet, Fabrice

2017-05-01

The purpose of the present paper is to provide an overview of Asymptotic-Preserving methods for multiscale plasma simulations by addressing three singular perturbation problems. First, the quasi-neutral limit of fluid and kinetic models is investigated in the framework of non-magnetized as well as magnetized plasmas. Second, the drift limit for fluid descriptions of thermal plasmas under large magnetic fields is addressed. Finally efficient numerical resolutions of anisotropic elliptic or diffusion equations arising in magnetized plasma simulation are reviewed.

The origin of cosmic rays

NASA Technical Reports Server (NTRS)

Eichler, D.

1986-01-01

Data related to the development of cosmic rays are discussed. The relationship between cosmic ray production and the steady-state Boltzmann equation is analyzed. The importance of the power-law spectrum, the scattering rate, the theory of shock acceleration, anisotropic instabilities, and cosmic ray diffusion in the formation of cosmic rays is described. It is noted that spacecraft observations at the earth's bow shock are useful for studying cosmic rays and that the data support the collisionless shock-wave theory of cosmic ray origin.

Mechanism of anisotropic surface self-diffusivity at the prismatic ice-vapor interface.

PubMed

Gladich, Ivan; Oswald, Amrei; Bowens, Natalie; Naatz, Sam; Rowe, Penny; Roeselova, Martina; Neshyba, Steven

2015-09-21

Predictive theoretical models for mesoscopic roughening of ice require improved understanding of attachment kinetics occurring at the ice-vapor interface. Here, we use classical molecular dynamics to explore the generality and mechanics of a transition from anisotropic to isotropic self-diffusivity on exposed prismatic surfaces. We find that self-diffusion parallel to the crystallographic a-axis is favored over the c-axis at sub-melt temperatures below about -35 °C, for three different representations of the water-water intermolecular potential. In the low-temperature anisotropic regime, diffusion results from interstitial admolecules encountering entropically distinct barriers to diffusion in the two in-plane directions. At higher temperatures, isotropic self-diffusion occurring deeper within the quasi-liquid layer becomes the dominant mechanism, owing to its larger energy of activation.

Surface diffusivity measurements on 8mol.% yttrium oxide-zirconia bicrystals via grain boundary grooving experiments

NASA Astrophysics Data System (ADS)

Nassirou, Maissarath

Thermal grooving at grain boundaries (GBs) is a capillary-driven evolution of surface topography in the region where the grain boundary emerges at a free surface. The study of these topographic changes can provide insight into surface energetics, and in our particular case, the measurement of surface diffusivity. We have measured the surface diffusion coefficient of 8mol% Y 2O3-ZrO2 by studying the formation of thermal grooves. We studied a total of five bicrystals, with well defined orientation relationships; random [110] -60°, random [001] -30°, Sigma13 [001]/{510}, Sigma13 [001]/{320}, Sigma5 [001]/{210}. Our calculations employed the Herring relation (1951), in which the variation in the chemical potential is related to changes in topography. The samples were annealed at 1300°C and 1400°C for various period of time. Atomic Force Microscopy was used to determine the exact geometry of the thermal grooves. A first approach consisted of estimating the diffusion coefficient by using Mullins' equation. yx=0= dsDs1/ 4gb2g s12G 5/4( WkTgs) 1/4t 1/4 Where y(x =0) is the groove depth at the GB triple junction, O is the atomic volume, gs is the surface tension, gb is the grain boundary surface energy, ds is the thickness of the diffusion layer, t is the annealing time, and Ds is the surface diffusion coefficient. In Mullins' derivation, the atomic structure of the surface was ignored and it was assumed that the surface energy is independent of crystallographic orientation. In the case of zirconia, the surface energy is anisotropic. We will describe in this work a new approach to measuring surface diffusivity which accounts for the surface energy anisotropy. The study of these bicrystals will emphasize the effect of grain boundary structure on the surface diffusion coefficient, and it is for that purpose that we selected bicrystals with different tilt axes and angles. The results obtained using the equation set we have developed will be compared to those obtained by Mullins, and we show that the anisotropic groove evolution, even when perfectly symmetrical, is much slower than the corresponding isotropic case.

Turbulent solutions of equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1985-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases.

PubMed

Roniotis, Alexandros; Manikis, Georgios C; Sakkalis, Vangelis; Zervakis, Michalis E; Karatzanis, Ioannis; Marias, Kostas

2012-03-01

Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved. © 2012 IEEE

Anisotropic mesoscale eddy transport in ocean general circulation models

NASA Astrophysics Data System (ADS)

Reckinger, Scott; Fox-Kemper, Baylor; Bachman, Scott; Bryan, Frank; Dennis, John; Danabasoglu, Gokhan

2014-11-01

In modern climate models, the effects of oceanic mesoscale eddies are 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. However, the diffusive processes that the parameterization approximates, such as shear dispersion and potential vorticity barriers, typically have strongly anisotropic characteristics. Generalizing the eddy diffusivity tensor for anisotropy extends the number of parameters from one to three: major diffusivity, minor diffusivity, and alignment. The Community Earth System Model (CESM) with the anisotropic eddy parameterization is used to test various choices for the 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 temperature and salinity biases. These effects can be improved by parameterizing the oceanic anisotropic transport mechanisms.

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-05-31

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

Micromagnetic simulation of anisotropic grain boundary diffusion for sintered Nd-Fe-B magnets

NASA Astrophysics Data System (ADS)

Li, W.; Zhou, Q.; Zhao, L. Z.; Wang, Q. X.; Zhong, X. C.; Liu, Z. W.

2018-04-01

A systematic investigation on the anisotropic grain boundary diffusion in sintered Nd-Fe-B magnets is carried out by micromagnetic simulation. The results indicate that the critical reason for the anisotropic diffusion effect is not the difference in the amount of Dy diffused along different directions but the macroscopic demagnetizing field. The diffusion parallel to the easy axis from both pole surfaces of the magnet can increase the nucleation fields in the two major regions with large macroscopic demagnetizing fields, where the reverse domains can nucleate easily. As a consequence, the grain boundary diffusion along the directions parallel to the easy axis from two pole surfaces is more effective to improve the coercivity of the magnets than that along other directions. It is also found that, to enhance the coercivity, only a limited diffusion depth is required. The present result is in good agreement with the recent experimental findings.

Coarse-grained molecular dynamics simulation of water diffusion in the presence of carbon nanotubes.

PubMed

Lado Touriño, Isabel; Naranjo, Arisbel Cerpa; Negri, Viviana; Cerdán, Sebastián; Ballesteros, Paloma

2015-11-01

Computational modeling of the translational diffusion of water molecules in anisotropic environments entails vital relevance to understand correctly the information contained in the magnetic resonance images weighted in diffusion (DWI) and of the diffusion tensor images (DTI). In the present work we investigated the validity, strengths and weaknesses of a coarse-grained (CG) model based on the MARTINI force field to simulate water diffusion in a medium containing carbon nanotubes (CNTs) as models of anisotropic water diffusion behavior. We show that water diffusion outside the nanotubes follows Ficḱs law, while water diffusion inside the nanotubes is not described by a Ficḱs behavior. We report on the influence on water diffusion of various parameters such as length and concentration of CNTs, comparing the CG results with those obtained from the more accurate classic force field calculation, like the all-atom approach. Calculated water diffusion coefficients decreased in the presence of nanotubes in a concentration dependent manner. We also observed smaller water diffusion coefficients for longer CNTs. Using the CG methodology we were able to demonstrate anisotropic diffusion of water inside the nanotube scaffold, but we could not prove anisotropy in the surrounding medium, suggesting that grouping several water molecules in a single diffusing unit may affect the diffusional anisotropy calculated. The methodologies investigated in this work represent a first step towards the study of more complex models, including anisotropic cohorts of CNTs or even neuronal axons, with reasonable savings in computation time. Copyright © 2015 Elsevier Inc. All rights reserved.

Dynamic of charged planar geometry in tilted and non-tilted frames

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharif, M., E-mail: msharif.math@pu.edu.pk; Zaeem Ul Haq Bhatti, M., E-mail: mzaeem.math@pu.edu.pk

2015-05-15

We investigate the dynamics of charged planar symmetry with an anisotropic matter field subject to a radially moving observer called a tilted observer. The Einstein-Maxwell field equations are used to obtain a relation between non-tilted and tilted frames and between kinematical and dynamical quantities. Using the Taub mass formalism and conservation laws, two evolution equations are developed to analyze the inhomogeneities in the tilted congruence. It is found that the radial velocity (due to the tilted observer) and the electric charge have a crucial effect on the inhomogeneity factor. Finally, we discuss the stability in the non-tilted frame in themore » pure diffusion case and examine the effects of the electromagnetic field.« less

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Milne problem for non-absorbing medium with extremely anisotropic scattering kernel in the case of specular and diffuse reflecting boundaries

NASA Astrophysics Data System (ADS)

Güleçyüz, M. Ç.; Şenyiğit, M.; Ersoy, A.

2018-01-01

The Milne problem is studied in one speed neutron transport theory using the linearly anisotropic scattering kernel which combines forward and backward scatterings (extremely anisotropic scattering) for a non-absorbing medium with specular and diffuse reflection boundary conditions. In order to calculate the extrapolated endpoint for the Milne problem, Legendre polynomial approximation (PN method) is applied and numerical results are tabulated for selected cases as a function of different degrees of anisotropic scattering. Finally, some results are discussed and compared with the existing results in literature.

Fundamental Flux Equations for Fracture-Matrix Interactions with Linear Diffusion

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Rutqvist, J.; Birkholzer, J. T.

2017-12-01

The conventional dual-continuum models are only applicable for late-time behavior of pressure propagation in fractured rock, while discrete-fracture-network models may explicitly deal with matrix blocks at high computational expense. To address these issues, we developed a unified-form diffusive flux equation for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular matrix blocks (squares, cubes, rectangles, and rectangular parallelepipeds) by partitioning the entire dimensionless-time domain (Zhou et al., 2017a, b). For each matrix block, this flux equation consists of the early-time solution up until a switch-over time after which the late-time solution is applied to create continuity from early to late time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the coefficients dependent on dimensionless area-to-volume ratio and aspect ratios for rectangular blocks. For the late-time solutions, one exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic blocks. The time-partitioning method was also used for calculating pressure/concentration/temperature distribution within a matrix block. The approximate solution contains an error-function solution for early times and an exponential solution for late times, with relative errors less than 0.003. These solutions form the kernel of multirate and multidimensional hydraulic, solute and thermal diffusion in fractured reservoirs.

Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

DOE PAGES

Willert, Jeffrey; Park, H.; Taitano, William

2015-11-01

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

2014-09-01

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less

Understanding the anisotropic strain effects on lithium diffusion in graphite anodes: A first-principles study

NASA Astrophysics Data System (ADS)

Ji, Xiang; Wang, Yang; Zhang, Junqian

2018-06-01

The lithium diffusion in graphite anode, which is the most widely used commercial electrode material today, affects the charge/discharge performance of lithium-ion batteries. In this study, the anisotropic strain effects on lithium diffusion in graphite anodes are systematically investigated using first-principles calculations based on density functional theory (DFT) with van der Waals corrections. It is found that the effects of external applied strains along various directions of LixC6 (i.e., perpendicular or parallel to the basal planes of the graphite host) on lithium diffusivity are different. Along the direction perpendicular to the graphite planes, the tensile strain facilitates in-plane Li diffusion by reducing the energy barrier, and the compressive strain hinders in-plane Li diffusion by raising the energy barrier. In contrast, the in-plane biaxial tensile strain (parallel to the graphite planes) hinders in-plane Li diffusion, and the in-plane biaxial compressive strain facilitates in-plane Li diffusion. Furthermore, both in-plane and transverse shear strains slightly influence Li diffusion in graphite anodes. A discussion is presented to explain the anisotropic strain dependence of lithium diffusion. This research provides data for the continuum modelling of the electrodes in the lithium-ion batteries.

Anisotropic Rotational Diffusion Studied by Nuclear Spin Relaxation and Molecular Dynamics Simulation: An Undergraduate Physical Chemistry Laboratory

ERIC Educational Resources Information Center

Fuson, Michael M.

2017-01-01

Laboratories studying the anisotropic rotational diffusion of bromobenzene using nuclear spin relaxation and molecular dynamics simulations are described. For many undergraduates, visualizing molecular motion is challenging. Undergraduates rarely encounter laboratories that directly assess molecular motion, and so the concept remains an…

Field theory and diffusion creep predictions in polycrystalline aggregates

NASA Astrophysics Data System (ADS)

Villani, A.; Busso, E. P.; Forest, S.

2015-07-01

In polycrystals, stress-driven vacancy diffusion at high homologous temperatures leads to inelastic deformation. In this work, a novel continuum mechanics framework is proposed to describe the strain fields resulting from such a diffusion-driven process in a polycrystalline aggregate where grains and grain boundaries are explicitly considered. The choice of an anisotropic eigenstrain in the grain boundary region provides the driving force for the diffusive creep processes. The corresponding inelastic strain rate is shown to be related to the gradient of the vacancy flux. Dislocation driven deformation is then introduced as an additional mechanism, through standard crystal plasticity constitutive equations. The fully coupled diffusion-mechanical model is implemented into the finite element method and then used to describe the biaxial creep behaviour of FCC polycrystalline aggregates. The corresponding results revealed for the first time that such a coupled diffusion-stress approach, involving the gradient of the vacancy flux, can accurately predict the well-known macroscopic strain rate dependency on stress and grain size in the diffusion creep regime. They also predict strongly heterogeneous viscoplastic strain fields, especially close to grain boundaries triple junctions. Finally, a smooth transition from Herring and Coble to dislocation creep behaviour is predicted and compared to experimental results for copper.

Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

NASA Astrophysics Data System (ADS)

Chun, Sehun

2017-07-01

Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.

Gravitational decoupled anisotropies in compact stars

NASA Astrophysics Data System (ADS)

Gabbanelli, Luciano; Rincón, Ángel; Rubio, Carlos

2018-05-01

Simple generic extensions of isotropic Durgapal-Fuloria stars to the anisotropic domain are presented. These anisotropic solutions are obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors by means of the minimal geometric deformation approach are satisfied. Hence the anisotropic field equations are isolated resulting a more treatable set. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, observational effects of such anisotropies when measuring the surface redshift are discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations is shown. In this manner, different anisotropic sectors can be isolated of each other and modeled in a simple and systematic way.

A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

PubMed Central

Gottwald, Georg A.; Melbourne, Ian

2013-01-01

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481

Anisotropic diffusion of meteor trails due to the geomagnetic field over King Sejong Station (62.2°S, 58.8°W), Antarctica

NASA Astrophysics Data System (ADS)

Choi, Jong-Min; Kwak, Young-Sil; Kim, Yong Ha; Lee, Changsup; Kim, Jeong-Han; Jee, Geonhwa; Yang, Tae-Yong

2018-06-01

We analyzed meteor decay times measured by a VHF meteor radar at King Sejong Station, Antarctica (62.22°S, 58.78°W) to study diffusion processes of the meteor trails above the altitude of ˜93 km. Above this altitude, where the atmospheric density is so dilute that collisions between trail ions and ambient molecules become rare, diffusion of a meteor trail can be greatly affected by the geomagnetic field, resulting in anisotropic distribution of measured decay times over the azimuthal and elevation angles. Our preliminary analysis confirm the anisotropic nature of meteor decay times due to geomagnetic field.

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

Anisotropic Weyl symmetry and cosmology

NASA Astrophysics Data System (ADS)

Moon, Taeyoon; Oh, Phillial; Sohn, Jongsu

2010-11-01

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

Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

Diffusion tensor optical coherence tomography

NASA Astrophysics Data System (ADS)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Polymer scaling and dynamics in steady-state sedimentation at infinite Péclet number.

PubMed

Lehtola, V; Punkkinen, O; Ala-Nissila, T

2007-11-01

We consider the static and dynamical behavior of a flexible polymer chain under steady-state sedimentation using analytic arguments and computer simulations. The model system comprises a single coarse-grained polymer chain of N segments, which resides in a Newtonian fluid as described by the Navier-Stokes equations. The chain is driven into nonequilibrium steady state by gravity acting on each segment. The equations of motion for the segments and the Navier-Stokes equations are solved simultaneously using an immersed boundary method, where thermal fluctuations are neglected. To characterize the chain conformation, we consider its radius of gyration RG(N). We find that the presence of gravity explicitly breaks the spatial symmetry leading to anisotropic scaling of the components of RG with N along the direction of gravity RG, parallel and perpendicular to it RG, perpendicular, respectively. We numerically estimate the corresponding anisotropic scaling exponents nu parallel approximately 0.79 and nu perpendicular approximately 0.45, which differ significantly from the equilibrium scaling exponent nue=0.588 in three dimensions. This indicates that on the average, the chain becomes elongated along the sedimentation direction for large enough N. We present a generalization of the Flory scaling argument, which is in good agreement with the numerical results. It also reveals an explicit dependence of the scaling exponents on the Reynolds number. To study the dynamics of the chain, we compute its effective diffusion coefficient D(N), which does not contain Brownian motion. For the range of values of N used here, we find that both the parallel and perpendicular components of D increase with the chain length N, in contrast to the case of thermal diffusion in equilibrium. This is caused by the fluid-driven fluctuations in the internal configuration of the polymer that are magnified as polymer size becomes larger.

Anisotropic Mesoscale Eddy Transport in Ocean General Circulation Models

NASA Astrophysics Data System (ADS)

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.

Anisotropic thermal conduction with magnetic fields in galaxy clusters

NASA Astrophysics Data System (ADS)

Arth, Alexander; Dolag, Klaus; Beck, Alexander; Petkova, Margarita; Lesch, Harald

2015-08-01

Magnetic fields play an important role for the propagation and diffusion of charged particles, which are responsible for thermal conduction. In this poster, we present an implementation of thermal conduction including the anisotropic effects of magnetic fields for smoothed particle hydrodynamics (SPH). The anisotropic thermal conduction is mainly proceeding parallel to magnetic fields and suppressed perpendicular to the fields. We derive the SPH formalism for the anisotropic heat transport and solve the corresponding equation with an implicit conjugate gradient scheme. We discuss several issues of unphysical heat transport in the cases of extreme ansiotropies or unmagnetized regions and present possible numerical workarounds. We implement our algorithm into the cosmological simulation code GADGET and study its behaviour in several test cases. In general, we reproduce the analytical solutions of our idealised test problems, and obtain good results in cosmological simulations of galaxy cluster formations. Within galaxy clusters, the anisotropic conduction produces a net heat transport similar to an isotropic Spitzer conduction model with low efficiency. In contrast to isotropic conduction our new formalism allows small-scale structure in the temperature distribution to remain stable, because of their decoupling caused by magnetic field lines. Compared to observations, strong isotropic conduction leads to an oversmoothed temperature distribution within clusters, while the results obtained with anisotropic thermal conduction reproduce the observed temperature fluctuations well. A proper treatment of heat transport is crucial especially in the outskirts of clusters and also in high density regions. It's connection to the local dynamical state of the cluster also might contribute to the observed bimodal distribution of cool core and non cool core clusters. Our new scheme significantly advances the modelling of thermal conduction in numerical simulations and overall gives better results compared to observations.

Anisotropic hydrodynamics for conformal Gubser flow

NASA Astrophysics Data System (ADS)

Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael

2015-02-01

We derive the equations of motion for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse "Gubser flow" using leading-order anisotropic hydrodynamics. This is accomplished by assuming that the one-particle distribution function is ellipsoidally symmetric in the momenta conjugate to the de Sitter coordinates used to parametrize the Gubser flow. We then demonstrate that the S O (3 )q symmetry in de Sitter space further constrains the anisotropy tensor to be of spheroidal form. The resulting system of two coupled ordinary differential equations for the de Sitter-space momentum scale and anisotropy parameter are solved numerically and compared to a recently obtained exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We show that anisotropic hydrodynamics describes the spatiotemporal evolution of the system better than all currently known dissipative hydrodynamics approaches. In addition, we prove that anisotropic hydrodynamics gives the exact solution of the relaxation-time approximation Boltzmann equation in the ideal, η /s →0 , and free-streaming, η /s →∞, limits.

Singularity-free solutions for anisotropic charged fluids with Chaplygin equation of state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rahaman, Farook; Ray, Saibal; Jafry, Abdul Kayum

2010-11-15

We extend the Krori-Barua analysis of the static, spherically symmetric, Einstein-Maxwell field equations and consider charged fluid sources with anisotropic stresses. The inclusion of a new variable (tangential pressure) allows the use of a nonlinear, Chaplygin-type equation of state with coefficients fixed by the matching conditions at the boundary of the source. Some physical features are briefly discussed.

Brownian motion of a self-propelled particle.

PubMed

ten Hagen, B; van Teeffelen, S; Löwen, H

2011-05-18

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the 'active' particle is driven along its internal orientation axis. We calculate the first four moments of the probability distribution function for displacements as a function of time for a spherical particle with isotropic translational diffusion, as well as for an anisotropic ellipsoidal particle. In both cases the translational and rotational motion is either unconfined or confined to one or two dimensions. A significant non-Gaussian behaviour at finite times t is signalled by a non-vanishing kurtosis γ(t). To delimit the super-diffusive regime, which occurs at intermediate times, two timescales are identified. For certain model situations a characteristic t(3) behaviour of the mean-square displacement is observed. Comparing the dynamics of real and artificial microswimmers, like bacteria or catalytically driven Janus particles, to our analytical expressions reveals whether their motion is Brownian or not.

Directly measuring of thermal pulse transfer in one-dimensional highly aligned carbon nanotubes

PubMed Central

Zhang, Guang; Liu, Changhong; Fan, Shoushan

2013-01-01

Using a simple and precise instrument system, we directly measured the thermo-physical properties of one-dimensional highly aligned carbon nanotubes (CNTs). A kind of CNT-based macroscopic materials named super aligned carbon nanotube (SACNT) buckypapers was measured in our experiment. We defined a new one-dimensional parameter, the “thermal transfer speed” to characterize the thermal damping mechanisms in the SACNT buckypapers. Our results indicated that the SACNT buckypapers with different densities have obviously different thermal transfer speeds. Furthermore, we found that the thermal transfer speed of high-density SACNT buckypapers may have an obvious damping factor along the CNTs aligned direction. The anisotropic thermal diffusivities of SACNT buckypapers could be calculated by the thermal transfer speeds. The thermal diffusivities obviously increase as the buckypaper-density increases. For parallel SACNT buckypapers, the thermal diffusivity could be as high as 562.2 ± 55.4 mm2/s. The thermal conductivities of these SACNT buckypapers were also calculated by the equation k = Cpαρ. PMID:23989589

Directly measuring of thermal pulse transfer in one-dimensional highly aligned carbon nanotubes.

PubMed

Zhang, Guang; Liu, Changhong; Fan, Shoushan

2013-01-01

Using a simple and precise instrument system, we directly measured the thermo-physical properties of one-dimensional highly aligned carbon nanotubes (CNTs). A kind of CNT-based macroscopic materials named super aligned carbon nanotube (SACNT) buckypapers was measured in our experiment. We defined a new one-dimensional parameter, the "thermal transfer speed" to characterize the thermal damping mechanisms in the SACNT buckypapers. Our results indicated that the SACNT buckypapers with different densities have obviously different thermal transfer speeds. Furthermore, we found that the thermal transfer speed of high-density SACNT buckypapers may have an obvious damping factor along the CNTs aligned direction. The anisotropic thermal diffusivities of SACNT buckypapers could be calculated by the thermal transfer speeds. The thermal diffusivities obviously increase as the buckypaper-density increases. For parallel SACNT buckypapers, the thermal diffusivity could be as high as 562.2 ± 55.4 mm(2)/s. The thermal conductivities of these SACNT buckypapers were also calculated by the equation k = Cpαρ.

Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media.

PubMed

Guo, Z; Kumar, S

2000-08-20

An isotropic scaling formulation is evaluated for transient radiative transfer in a one-dimensional planar slab subject to collimated and/or diffuse irradiation. The Monte Carlo method is used to implement the equivalent scattering and exact simulations of the transient short-pulse radiation transport through forward and backward anisotropic scattering planar media. The scaled equivalent isotropic scattering results are compared with predictions of anisotropic scattering in various problems. It is found that the equivalent isotropic scaling law is not appropriate for backward-scattering media in transient radiative transfer. Even for an optically diffuse medium, the differences in temporal transmittance and reflectance profiles between predictions of backward anisotropic scattering and equivalent isotropic scattering are large. Additionally, for both forward and backward anisotropic scattering media, the transient equivalent isotropic results are strongly affected by the change of photon flight time, owing to the change of flight direction associated with the isotropic scaling technique.

A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.

PubMed

Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui

2018-06-01

The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.

A Numerical Method for Predicting Rayleigh Surface Wave Velocity in Anisotropic Crystals (Postprint)

DTIC Science & Technology

2017-09-05

generalized version of the equations are very difficult to derive, even in symbolic math languages such as Mathematica. As a result, the equations are...formalism, Math . Mech. Solids 9 (1) (2004) 5–15. [8] M. Destrade, The explicit secular equation for surface acoustic waves in monoclinic elastic crystals...Q. J. Mech. Appl. Math . 55 (2) (2002) 297–311. [10] D. Taylor, Surface waves in anisotropic media: the secular equation and its numerical solution

Equation of state and some structural and dynamical properties of the confined Lennard-Jones fluid into carbon nanotube: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Abbaspour, Mohsen; Akbarzadeh, Hamed; Salemi, Sirous; Abroodi, Mousarreza

2016-11-01

By considering the anisotropic pressure tensor, two separate equations of state (EoS) as functions of the density, temperature, and carbon nanotube (CNT) diameter have been proposed for the radial and axial directions for the confined Lennard-Jones (LJ) fluid into (11,11), (12,10), and (19,0) CNTs from 120 to 600 K using molecular dynamics (MD) simulations. We have also investigated the effects of the pore size, pore loading, chirality, and temperature on some of the structural and dynamical properties of the confined LJ fluid into (11,11), (12,10), (19,0), and (19,19) CNTs such as the radial density profile and self-diffusion coefficient. We have also determined the EoS for the confined LJ fluid into double and triple walled CNTs.

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

NASA Astrophysics Data System (ADS)

Triantafyllopoulos, A.; Stavrinos, P. C.

2018-04-01

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of general relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4‑velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein–Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.

Relativistic anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Alqahtani, Mubarak; Nopoush, Mohammad; Strickland, Michael

2018-07-01

In this paper we review recent progress in relativistic anisotropic hydrodynamics. We begin with a pedagogical introduction to the topic which takes into account the advances in our understanding of this topic since its inception. We consider both conformal and non-conformal systems and demonstrate how one can implement a realistic equation of state using a quasiparticle approach. We then consider the inclusion of non-spheroidal (non-ellipsoidal) corrections to leading-order anisotropic hydrodynamics and present the findings of the resulting second-order viscous anisotropic hydrodynamics framework. We compare the results obtained in both the conformal and non-conformal cases with exact solutions to the Boltzmann equation and demonstrate that, in all known cases, anisotropic hydrodynamics best reproduces the exact solutions. Based on this success, we then discuss the phenomenological application of anisotropic hydrodynamics. Along these lines, we review techniques which can be used to convert a momentum-space anisotropic fluid into hadronic degrees of freedom by generalizing the original idea of Cooper-Frye freeze-out to momentum-space anisotropic systems. And, finally, we present phenomenological results of 3 + 1 d quasiparticle anisotropic hydrodynamic simulations and compare them to experimental data produced in 2.76 TeV Pb-Pb collisions at the LHC. Our results indicate that anisotropic hydrodynamics provides a promising framework for describing the dynamics of the momentum-space anisotropic QGP created in heavy-ion collisions.

Holographic estimate of heavy quark diffusion in a magnetic field

NASA Astrophysics Data System (ADS)

Dudal, David; Mertens, Thomas G.

2018-03-01

We study the influence of a background magnetic field on the J /ψ vector meson in a Dirac-Born-Infeld-extension of the soft wall model, building upon our earlier work [D. Dudal and T. G. Mertens Phys. Rev. D 91, 086002 (2015), 10.1103/PhysRevD.91.086002]. In this specific holographic QCD model, we discuss the heavy quark number susceptibility and diffusion constants of charm quarks and their dependence on the magnetic field by either a hydrodynamic expansion or by numerically solving the differential equation. This allows us to determine the response of these transport coefficients to the magnetic field. The effects of the latter are considered both from a direct as indirect (medium) viewpoint. As expected, we find a magnetic field induced anisotropic diffusion, with a stronger diffusion in the longitudinal direction compared to the transversal one. We backup, at least qualitatively, our findings with a hanging string analysis of heavy quark diffusion in a magnetic field. From the quark number susceptibility we can extract an estimate for the effective deconfinement temperature in the heavy quark sector, reporting consistency with the phenomenon of inverse magnetic catalysis.

Anisotropic charged generalized polytropic models

NASA Astrophysics Data System (ADS)

Nasim, A.; Azam, M.

2018-06-01

In this paper, we found some new anisotropic charged models admitting generalized polytropic equation of state with spherically symmetry. An analytic solution of the Einstein-Maxwell field equations is obtained through the transformation introduced by Durgapal and Banerji (Phys. Rev. D 27:328, 1983). The physical viability of solutions corresponding to polytropic index η =1/2, 2/3, 1, 2 is analyzed graphically. For this, we plot physical quantities such as radial and tangential pressure, anisotropy, speed of sound which demonstrated that these models achieve all the considerable physical conditions required for a relativistic star. Further, it is mentioned here that previous results for anisotropic charged matter with linear, quadratic and polytropic equation of state can be retrieved.

Analysis of diffuse radiation data for Beer Sheva: Measured (shadow ring) versus calculated (global-horizontal beam) values

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kudish, A.I.; Ianetz, A.

1993-12-01

The authors have utilized concurrently measured global, normal incidence beam, and diffuse radiation data, the latter measured by means of a shadow ring pyranometer to study the relative magnitude of the anisotropic contribution (circumsolar region and nonuniform sky conditions) to the diffuse radiation. In the case of Beer Sheva, the monthly average hourly anisotropic correction factor varies from 2.9 to 20.9%, whereas the [open quotes]standard[close quotes] geometric correction factor varies from 5.6 to 14.0%. The monthly average hourly overall correction factor (combined anisotropic and geometric factors) varies from 8.9 to 37.7%. The data have also been analyzed using a simplemore » model of sky radiance developed by Steven in 1984. His anisotropic correction factor is a function of the relative strength and angular width of the circumsolar radiation region. The results of this analysis are in agreement with those previously reported for Quidron on the Dead Sea, viz. the anisotropy and relative strength of the circumsolar radiation are significantly greater than at any of the sites analyzed by Steven. In addition, the data have been utilized to validate a model developed by LeBaron et al. in 1990 for correcting shadow ring diffuse radiation data. The monthly average deviation between the corrected and true diffuse radiation values varies from 4.55 to 7.92%.« less

The one-dimensional asymmetric persistent random walk

NASA Astrophysics Data System (ADS)

Rossetto, Vincent

2018-04-01

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

Light radiation pressure upon an optically orthotropic surface

NASA Astrophysics Data System (ADS)

Nerovny, Nikolay A.; Lapina, Irina E.; Grigorjev, Anton S.

2017-11-01

In this paper, we discuss the problem of determination of light radiation pressure force upon an anisotropic surface. The optical parameters of such a surface are considered to have major and minor axes, so the model is called an orthotropic model. We derive the equations for force components from emission, absorption, and reflection, utilizing a modified Maxwell's specular-diffuse model. The proposed model can be used to model a flat solar sail with wrinkles. By performing Bayesian analysis for example of a wrinkled surface, we show that there are cases in which an orthotropic model of the optical parameters of a surface may be more accurate than an isotropic model.

Solutions for a local equation of anisotropic plant cell growth: an analytical study of expansin activity

PubMed Central

Pietruszka, Mariusz

2011-01-01

This paper presents a generalization of the Lockhart equation for plant cell/organ expansion in the anisotropic case. The intent is to take into account the temporal and spatial variation in the cell wall mechanical properties by considering the wall ‘extensibility’ (Φ), a time- and space-dependent parameter. A dynamic linear differential equation of a second-order tensor is introduced by describing the anisotropic growth process with some key biochemical aspects included. The distortion and expansion of plant cell walls initiated by expansins, a class of proteins known to enhance cell wall ‘extensibility’, is also described. In this approach, expansin proteins are treated as active agents participating in isotropic/anisotropic growth. Two-parameter models and an equation for describing α- and β-expansin proteins are proposed by delineating the extension of isolated wall samples, allowing turgor-driven polymer creep, where expansins weaken the non-covalent binding between wall polysaccharides. We observe that the calculated halftime (t1/2 = εΦ0 log 2) of stress relaxation due to expansin action can be described in mechanical terms. PMID:21227964

Experimental evaluation of electrical conductivity imaging of anisotropic brain tissues using a combination of diffusion tensor imaging and magnetic resonance electrical impedance tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sajib, Saurav Z. K.; Jeong, Woo Chul; Oh, Tong In

Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At lowmore » frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.« less

Modeling of charged anisotropic compact stars in general relativity

NASA Astrophysics Data System (ADS)

Dayanandan, Baiju; Maurya, S. K.; T, Smitha T.

2017-06-01

A charged compact star model has been determined for anisotropic fluid distribution. We have solved the Einstein-Maxwell field equations to construct the charged compact star model by using the radial pressure, the metric function e^{λ} and the electric charge function. The generic charged anisotropic solution is verified by exploring different physical conditions like causality condition, mass-radius relation and stability of the solution (via the adiabatic index, TOV equations and the Herrera cracking concept). It is observed that the present charged anisotropic compact star model is compatible with the star PSR 1937+21. Moreover, we also presented the EOS ρ = f(p) for the present charged compact star model.

Well behaved anisotropic compact star models in general relativity

NASA Astrophysics Data System (ADS)

Jasim, M. K.; Maurya, S. K.; Gupta, Y. K.; Dayanandan, B.

2016-11-01

Anisotropic compact star models have been constructed by assuming a particular form of a metric function e^{λ}. We solved the Einstein field equations for determining the metric function e^{ν}. For this purpose we have assumed a physically valid expression of radial pressure (pr). The obtained anisotropic compact star model is representing the realistic compact objects such as PSR 1937 +21. We have done an extensive study about physical parameters for anisotropic models and found that these parameters are well behaved throughout inside the star. Along with these we have also determined the equation of state for compact star which gives the radial pressure is purely the function of density i.e. pr=f(ρ).

3D early embryogenesis image filtering by nonlinear partial differential equations.

PubMed

Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

2010-08-01

We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which are artificially connected due to acquisition error intrinsically linked to physics of LSM. In all studied aspects it turned out that the nonlinear diffusion filter which is called geodesic mean curvature flow (GMCF) has the best performance. Copyright 2010 Elsevier B.V. All rights reserved.

Instantons in Lifshitz field theories

NASA Astrophysics Data System (ADS)

Fujimori, Toshiaki; Nitta, Muneto

2015-10-01

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

A Patient-Specific Anisotropic Diffusion Model for Brain Tumour Spread.

PubMed

Swan, Amanda; Hillen, Thomas; Bowman, John C; Murtha, Albert D

2018-05-01

Gliomas are primary brain tumours arising from the glial cells of the nervous system. The diffuse nature of spread, coupled with proximity to critical brain structures, makes treatment a challenge. Pathological analysis confirms that the extent of glioma spread exceeds the extent of the grossly visible mass, seen on conventional magnetic resonance imaging (MRI) scans. Gliomas show faster spread along white matter tracts than in grey matter, leading to irregular patterns of spread. We propose a mathematical model based on Diffusion Tensor Imaging, a new MRI imaging technique that offers a methodology to delineate the major white matter tracts in the brain. We apply the anisotropic diffusion model of Painter and Hillen (J Thoer Biol 323:25-39, 2013) to data from 10 patients with gliomas. Moreover, we compare the anisotropic model to the state-of-the-art Proliferation-Infiltration (PI) model of Swanson et al. (Cell Prolif 33:317-329, 2000). We find that the anisotropic model offers a slight improvement over the standard PI model. For tumours with low anisotropy, the predictions of the two models are virtually identical, but for patients whose tumours show higher anisotropy, the results differ. We also suggest using the data from the contralateral hemisphere to further improve the model fit. Finally, we discuss the potential use of this model in clinical treatment planning.

Turbulent solutions of the equations of fluid motion

NASA Technical Reports Server (NTRS)

Deissler, R. G.

1984-01-01

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

A signature of anisotropic cosmic-ray transport in the gamma-ray sky

NASA Astrophysics Data System (ADS)

Cerri, Silvio Sergio; Gaggero, Daniele; Vittino, Andrea; Evoli, Carmelo; Grasso, Dario

2017-10-01

A crucial process in Galactic cosmic-ray (CR) transport is the spatial diffusion due to the interaction with the interstellar turbulent magnetic field. Usually, CR diffusion is assumed to be uniform and isotropic all across the Galaxy. However, this picture is clearly inaccurate: several data-driven and theoretical arguments, as well as dedicated numerical simulations, show that diffusion exhibits highly anisotropic properties with respect to the direction of a background (ordered) magnetic field (i.e., parallel or perpendicular to it). In this paper we focus on a recently discovered anomaly in the hadronic CR spectrum inferred by the Fermi-LAT gamma-ray data at different positions in the Galaxy, i.e. the progressive hardening of the proton slope at low Galactocentric radii. We propose the idea that this feature can be interpreted as a signature of anisotropic diffusion in the complex Galactic magnetic field: in particular, the harder slope in the inner Galaxy is due, in our scenario, to the parallel diffusive escape along the poloidal component of the large-scale, regular, magnetic field. We implement this idea in a numerical framework, based on the DRAGON code, and perform detailed numerical tests on the accuracy of our setup. We discuss how the effect proposed depends on the relevant free parameters involved. Based on low-energy extrapolation of the few focused numerical simulations aimed at determining the scalings of the anisotropic diffusion coefficients, we finally present a set of plausible models that reproduce the behavior of the CR proton slopes inferred by gamma-ray data.

A signature of anisotropic cosmic-ray transport in the gamma-ray sky

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cerri, Silvio Sergio; Grasso, Dario; Gaggero, Daniele

A crucial process in Galactic cosmic-ray (CR) transport is the spatial diffusion due to the interaction with the interstellar turbulent magnetic field. Usually, CR diffusion is assumed to be uniform and isotropic all across the Galaxy. However, this picture is clearly inaccurate: several data-driven and theoretical arguments, as well as dedicated numerical simulations, show that diffusion exhibits highly anisotropic properties with respect to the direction of a background (ordered) magnetic field (i.e., parallel or perpendicular to it). In this paper we focus on a recently discovered anomaly in the hadronic CR spectrum inferred by the Fermi-LAT gamma-ray data at differentmore » positions in the Galaxy, i.e. the progressive hardening of the proton slope at low Galactocentric radii. We propose the idea that this feature can be interpreted as a signature of anisotropic diffusion in the complex Galactic magnetic field: in particular, the harder slope in the inner Galaxy is due, in our scenario, to the parallel diffusive escape along the poloidal component of the large-scale, regular, magnetic field. We implement this idea in a numerical framework, based on the DRAGON code, and perform detailed numerical tests on the accuracy of our setup. We discuss how the effect proposed depends on the relevant free parameters involved. Based on low-energy extrapolation of the few focused numerical simulations aimed at determining the scalings of the anisotropic diffusion coefficients, we finally present a set of plausible models that reproduce the behavior of the CR proton slopes inferred by gamma-ray data.« less

Anisotropic diffusion of fluorescently labeled ATP in rat cardiomyocytes determined by raster image correlation spectroscopy

PubMed Central

Vendelin, Marko; Birkedal, Rikke

2008-01-01

A series of experimental data points to the existence of profound diffusion restrictions of ADP/ATP in rat cardiomyocytes. This assumption is required to explain the measurements of kinetics of respiration, sarcoplasmic reticulum loading with calcium, and kinetics of ATP-sensitive potassium channels. To be able to analyze and estimate the role of intracellular diffusion restrictions on bioenergetics, the intracellular diffusion coefficients of metabolites have to be determined. The aim of this work was to develop a practical method for determining diffusion coefficients in anisotropic medium and to estimate the overall diffusion coefficients of fluorescently labeled ATP in rat cardiomyocytes. For that, we have extended raster image correlation spectroscopy (RICS) protocols to be able to discriminate the anisotropy in the diffusion coefficient tensor. Using this extended protocol, we estimated diffusion coefficients of ATP labeled with the fluorescent conjugate Alexa Fluor 647 (Alexa-ATP). In the analysis, we assumed that the diffusion tensor can be described by two values: diffusion coefficient along the myofibril and that across it. The average diffusion coefficients found for Alexa-ATP were as follows: 83 ± 14 μm2/s in the longitudinal and 52 ± 16 μm2/s in the transverse directions (n = 8, mean ± SD). Those values are ∼2 (longitudinal) and ∼3.5 (transverse) times smaller than the diffusion coefficient value estimated for the surrounding solution. Such uneven reduction of average diffusion coefficient leads to anisotropic diffusion in rat cardiomyocytes. Although the source for such anisotropy is uncertain, we speculate that it may be induced by the ordered pattern of intracellular structures in rat cardiomyocytes. PMID:18815224

Anisotropic charged stellar models in Generalized Tolman IV spacetime

NASA Astrophysics Data System (ADS)

Murad, Mohammad Hassan; Fatema, Saba

2015-01-01

With the presence of electric charge and pressure anisotropy some anisotropic stellar models have been developed. An algorithm recently presented by Herrera et al. (Phys. Rev. D 77, 027502 (2008)) to generate static spherically symmetric anisotropic solutions of Einstein's equations has been used to derive relativistic anisotropic charged fluid spheres. In the absence of pressure anisotropy the fluid spheres reduce to some well-known Generalized Tolman IV exact metrics. The astrophysical significance of the resulting equations of state (EOS) for a particular case (Wyman-Leibovitz-Adler) for the anisotropic charged matter distribution has been discussed. Physical analysis shows that the relativistic stellar structure obtained 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 like electrically charged bare strange quark stars.

Extended phase graphs with anisotropic diffusion

NASA Astrophysics Data System (ADS)

Weigel, M.; Schwenk, S.; Kiselev, V. G.; Scheffler, K.; Hennig, J.

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles.

Diffusion of flexible random-coil dextran polymers measured in anisotropic brain extracellular space by integrative optical imaging.

PubMed

Xiao, Fanrong; Nicholson, Charles; Hrabe, Jan; Hrabetová, Sabina

2008-08-01

There are a limited number of methods available to quantify the extracellular diffusion of macromolecules in an anisotropic brain region, e.g., an area containing numerous aligned fibers where diffusion is faster along the fibers than across. We applied the integrative optical imaging method to measure diffusion of the fluorophore Alexa Fluor 488 (molecular weight (MW) 547) and fluorophore-labeled flexible random-coil dextran polymers (dex3, MW 3000; dex75, MW 75,000; dex282, MW 282,000; dex525, MW 525,000) in the extracellular space (ECS) of the anisotropic molecular layer of the isolated turtle cerebellum. For all molecules, two-dimensional images acquired an elliptical shape with major and minor axes oriented along and across, respectively, the unmyelinated parallel fibers. The effective diffusion coefficients, D*(major) and D*(minor), decreased with molecular size. The diffusion anisotropy ratio (DAR = D*(major)/D*(minor)) increased for Alexa Fluor 488 through dex75 but then unexpectedly reached a plateau. We argue that dex282 and dex525 approach the ECS width and deform to diffuse. In support of this concept, scaling theory shows the diffusion behavior of dex282 and dex525 to be consistent with transition to a reptation regime, and estimates the average ECS width at approximately 31 nm. These findings have implications for the interstitial transport of molecules and drugs, and for modeling neurotransmitter diffusion during ectopic release and spillover.

Anisotropic elliptic optical fibers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kang, Soon Ahm

1991-01-01

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

Speckle reduction in echocardiography by temporal compounding and anisotropic diffusion filtering

NASA Astrophysics Data System (ADS)

Giraldo-Guzmán, Jader; Porto-Solano, Oscar; Cadena-Bonfanti, Alberto; Contreras-Ortiz, Sonia H.

2015-01-01

Echocardiography is a medical imaging technique based on ultrasound signals that is used to evaluate heart anatomy and physiology. Echocardiographic images are affected by speckle, a type of multiplicative noise that obscures details of the structures, and reduces the overall image quality. This paper shows an approach to enhance echocardiography using two processing techniques: temporal compounding and anisotropic diffusion filtering. We used twenty echocardiographic videos that include one or three cardiac cycles to test the algorithms. Two images from each cycle were aligned in space and averaged to obtain the compound images. These images were then processed using anisotropic diffusion filters to further improve their quality. Resultant images were evaluated using quality metrics and visual assessment by two medical doctors. The average total improvement on signal-to-noise ratio was up to 100.29% for videos with three cycles, and up to 32.57% for videos with one cycle.

Boundary conditions for gas flow problems from anisotropic scattering kernels

NASA Astrophysics Data System (ADS)

To, Quy-Dong; Vu, Van-Huyen; Lauriat, Guy; Léonard, Céline

2015-10-01

The paper presents an interface model for gas flowing through a channel constituted of anisotropic wall surfaces. Using anisotropic scattering kernels and Chapman Enskog phase density, the boundary conditions (BCs) for velocity, temperature, and discontinuities including velocity slip and temperature jump at the wall are obtained. Two scattering kernels, Dadzie and Méolans (DM) kernel, and generalized anisotropic Cercignani-Lampis (ACL) are examined in the present paper, yielding simple BCs at the wall fluid interface. With these two kernels, we rigorously recover the analytical expression for orientation dependent slip shown in our previous works [Pham et al., Phys. Rev. E 86, 051201 (2012) and To et al., J. Heat Transfer 137, 091002 (2015)] which is in good agreement with molecular dynamics simulation results. More important, our models include both thermal transpiration effect and new equations for the temperature jump. While the same expression depending on the two tangential accommodation coefficients is obtained for slip velocity, the DM and ACL temperature equations are significantly different. The derived BC equations associated with these two kernels are of interest for the gas simulations since they are able to capture the direction dependent slip behavior of anisotropic interfaces.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field

NASA Astrophysics Data System (ADS)

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

2015-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field-theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t') /k⊥d -1 +ξ , where k⊥=|k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow")—the d -dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990), 10.1007/BF02161420]. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: Instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L . The key point is that the matrices of scaling dimensions of the relevant families of composite operators appear nilpotent and cannot be diagonalized. The detailed proof of this fact is given for the correlation functions of arbitrary order.

Analysis of Electric Field Propagation in Anisotropically Absorbing and Reflecting Waveplates

NASA Astrophysics Data System (ADS)

Carnio, B. N.; Elezzabi, A. Y.

2018-04-01

Analytical expressions are derived for half-wave plates (HWPs) and quarter-wave plates (QWPs) based on uniaxial crystals. This general analysis describes the behavior of anisotropically absorbing and reflecting waveplates across the electromagnetic spectrum, which allows for correction to the commonly used equations determined assuming isotropic absorptions and reflections. This analysis is crucial to the design and implementation of HWPs and QWPs in the terahertz regime, where uniaxial crystals used for waveplates are highly birefringent and anisotropically absorbing. The derived HWP equations describe the rotation of linearly polarized light by an arbitrary angle, whereas the QWP analysis focuses on manipulating a linearly polarized electric field to obtain any ellipticity. The HWP and QWP losses are characterized by determining equations for the total electric field magnitude transmitted through these phase-retarding elements.

Innovative anisotropic phantoms for calibration of diffusion tensor imaging sequences.

PubMed

Kłodowski, Krzysztof; Krzyżak, Artur Tadeusz

2016-05-01

The paper describes a novel type of anisotropic phantoms designed for b-matrix spatial distribution diffusion tensor imaging (BSD-DTI). Cubic plate anisotropic phantom, cylinder capillary phantom and water reference phantom are described as a complete set necessary for calibration, validation and normalization of BSD-DTI. An innovative design of the phantoms basing on enclosing the anisotropic cores in glass balls filled with liquid made for the first time possible BSD calibration with usage of echo planar imaging (EPI) sequence. Susceptibility artifacts prone to occur in EPI sequences were visibly reduced in the central region of the phantoms. The phantoms were designed for usage in a clinical scanner's head coil, but can be scaled for other coil or scanner types. The phantoms can be also used for a pre-calibration of imaging of other types of phantoms having more specific applications. Copyright © 2015 Elsevier Inc. All rights reserved.

Multigrid treatment of implicit continuum diffusion

NASA Astrophysics Data System (ADS)

Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

2017-10-01

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms can be efficiently and implicitly handled by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for large numbers of processors. We built and present here a multigrid algorithm for these types of problems which outperforms a spectral solution that employs the highly optimized FFTW library. This multigrid algorithm is not only suitable for high performance computing but may also be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with idealized harmonic test functions as well as a turbulent 2D magnetohydrodynamic simulation. It is also shown that an anisotropic operator without cross-terms can improve model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation. This work was supported by DOE-SC-0010508. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

Extended phase graphs with anisotropic diffusion.

PubMed

Weigel, M; Schwenk, S; Kiselev, V G; Scheffler, K; Hennig, J

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles. Copyright 2010 Elsevier Inc. All rights reserved.

Two-relaxation-time lattice Boltzmann method for the anisotropic dispersive Henry problem

NASA Astrophysics Data System (ADS)

Servan-Camas, Borja; Tsai, Frank T.-C.

2010-02-01

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (TRT) to cope with anisotropic heterogeneous hydraulic conductivity and anisotropic velocity-dependent hydrodynamic dispersion in the saltwater intrusion problem. The directional-speed-of-sound technique is further developed to address anisotropic hydraulic conductivity and dispersion tensors. Forcing terms are introduced in the LBM to correct numerical errors that arise during the recovery procedure and to describe the sink/source terms in the flow and transport equations. In order to facilitate the LBM implementation, the forcing terms are combined with the equilibrium distribution functions (EDFs) to create pseudo-EDFs. This study performs linear stability analysis and derives LBM stability domains to solve the anisotropic advection-dispersion equation. The stability domains are used to select the time step at which the lattice Boltzmann method provides stable solutions to the numerical examples. The LBM was implemented for the anisotropic dispersive Henry problem with high ratios of longitudinal to transverse dispersivities, and the results compared well to the solutions in the work of Abarca et al. (2007).

Renormalization group analysis of anisotropic diffusion in turbulent shear flows

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Barton, J. Michael

1991-01-01

The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.

Magnetic Field Line Random Walk in Arbitrarily Stretched Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Wongpan, P.; Ruffolo, D.; Matthaeus, W. H.; Rowlands, G.

2006-12-01

Many types of space and laboratory plasmas involve turbulent fluctuations with an approximately uniform mean magnetic field B_0, and the field line random walk plays an important role in guiding particle motions. Much of the relevant literature concerns isotropic turbulence, and has mostly been perturbative, i.e., for small fluctuations, or based on numerical simulations for specific conditions. On the other hand, solar wind turbulence is apparently anisotropic, and has been modeled as a sum of idealized two-dimensional and one dimensional (slab) components, but with the deficiency of containing no oblique wave vectors. In the present work, we address the above issues with non-perturbative analytic calculations of diffusive field line random walks for unpolarized, arbitrarily stretched isotropic turbulence, including the limits of nearly one-dimensional (highly stretched) and nearly two-dimensional (highly squashed) turbulence. We develop implicit analytic formulae for the diffusion coefficients D_x and D_z, two coupled integral equations in which D_x and D_z appear inside 3-dimensional integrals over all k-space, are solved numerically with the aid of Mathematica routines for specific cases. We can vary the parameters B0 and β, the stretching along z for constant turbulent energy. Furthermore, we obtain analytic closed-form solutions in all extreme cases. We obtain 0.54 < D_z/D_x < 2, indicating an approximately isotropic random walk even for very anisotropic (unpolarized) turbulence, a surprising result. For a given β, the diffusion coefficient vs. B0 can be described by a Padé approximant. We find quasilinear behavior at high B0 and percolative behavior at low B_0. Partially supported by a Sritrangthong Scholarship from the Faculty of Science, Mahidol University; the Thailand Research Fund; NASA Grant NNG05GG83G; and Thailand's Commission for Higher Education.

Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli

2017-04-01

We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d  >  1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.

Relativistic Modelling of Stable Anisotropic Super-Dense Star

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Gupta, Y. K.; Jasim, M. K.

2015-08-01

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 solutions so obtained join continuously to the Schwarzschild exterior solution across the pressure-free boundary. It is observed that most of the new anisotropic solutions are well-behaved and are used to construct the super-dense star models such as neutron stars and pulsars.

Anisotropic thermal conductivity of thin polycrystalline oxide samples

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tiwari, A., E-mail: abhishektiwariiitr@gmail.com; Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800; Boussois, K.

2013-11-15

This paper reports about the development of a modified laser-flash technique and relation to measure the in-plane thermal diffusivity of thin polycrystalline oxide samples. Thermal conductivity is then calculated with the product of diffusivity, specific heat and density. Design and operating features for evaluating in-plane thermal conductivities are described. The technique is advantageous as thin samples are not glued together to measure in-plane thermal conductivities like earlier methods reported in literature. The approach was employed to study anisotropic thermal conductivity in alumina sheet, textured kaolin ceramics and montmorillonite. Since it is rare to find in-plane thermal conductivity values for suchmore » anisotropic thin samples in literature, this technique offers a useful variant to existing techniques.« less

Viscoacoustic anisotropic full waveform inversion

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Second-order (2 +1 ) -dimensional anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

2014-11-01

We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

Nondimensional Parameters and Equations for Nonlinear and Bifurcation Analyses of Thin Anisotropic Quasi-Shallow Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2010-01-01

A comprehensive development of nondimensional parameters and equations for nonlinear and bifurcations analyses of quasi-shallow shells, based on the Donnell-Mushtari-Vlasov theory for thin anisotropic shells, is presented. A complete set of field equations for geometrically imperfect shells is presented in terms general of lines-of-curvature coordinates. A systematic nondimensionalization of these equations is developed, several new nondimensional parameters are defined, and a comprehensive stress-function formulation is presented that includes variational principles for equilibrium and compatibility. Bifurcation analysis is applied to the nondimensional nonlinear field equations and a comprehensive set of bifurcation equations are presented. An extensive collection of tables and figures are presented that show the effects of lamina material properties and stacking sequence on the nondimensional parameters.

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, G. N.; Tasso, H.

2003-06-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η∥ and η⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η∥(ψ) or η⊥(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η∥ and η⊥ profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η⊥>η∥. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI2/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η⊥-η∥ for the reversed-field pinch scaling, Bp≈Bt, is nearly two times larger than that for the tokamak scaling, Bp≈0.1Bt (Bp and Bt are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch-Schlüter diffusion, indicate that parallel flows might result in a reduction of the diffusion observed in magnetically confined plasmas.

Iterative discrete ordinates solution of the equation for surface-reflected radiance

NASA Astrophysics Data System (ADS)

Radkevich, Alexander

2017-11-01

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Nanoscale Rheology and Anisotropic Diffusion Using Single Gold Nanorod Probes

NASA Astrophysics Data System (ADS)

Molaei, Mehdi; Atefi, Ehsan; Crocker, John C.

2018-03-01

The complex rotational and translational Brownian motion of anisotropic particles depends on their shape and the viscoelasticity of their surroundings. Because of their strong optical scattering and chemical versatility, gold nanorods would seem to provide the ultimate probes of rheology at the nanoscale, but the suitably accurate orientational tracking required to compute rheology has not been demonstrated. Here we image single gold nanorods with a laser-illuminated dark-field microscope and use optical polarization to determine their three-dimensional orientation to better than one degree. We convert the rotational diffusion of single nanorods in viscoelastic polyethylene glycol solutions to rheology and obtain excellent agreement with bulk measurements. Extensions of earlier models of anisotropic translational diffusion to three dimensions and viscoelastic fluids give excellent agreement with the observed motion of single nanorods. We find that nanorod tracking provides a uniquely capable approach to microrheology and provides a powerful tool for probing nanoscale dynamics and structure in a range of soft materials.

Assessment of polarization effect on aerosol retrievals from MODIS

NASA Astrophysics Data System (ADS)

Korkin, S.; Lyapustin, A.

2010-12-01

Light polarization affects the total intensity of scattered radiation. In this work, we compare aerosol retrievals performed by code MAIAC [1] with and without taking polarization into account. The MAIAC retrievals are based on the look-up tables (LUT). For this work, MAIAC was run using two different LUTs, the first one generated using the scalar code SHARM [2], and the second one generated with the vector code Modified Vector Discrete Ordinates Method (MVDOM). MVDOM is a new code suitable for computations with highly anisotropic phase functions, including cirrus clouds and snow [3]. To this end, the solution of the vector radiative transfer equation (VRTE) is represented as a sum of anisotropic and regular components. The anisotropic component is evaluated in the Small Angle Modification of the Spherical Harmonics Method (MSH) [4]. The MSH is formulated in the frame of reference of the solar beam where z-axis lies along the solar beam direction. In this case, the MSH solution for anisotropic part is nearly symmetric in azimuth, and is computed analytically. In scalar case, this solution coincides with the Goudsmit-Saunderson small-angle approximation [5]. To correct for an analytical separation of the anisotropic part of the signal, the transfer equation for the regular part contains a correction source function term [6]. Several examples of polarization impact on aerosol retrievals over different surface types will be presented. 1. Lyapustin A., Wang Y., Laszlo I., Kahn R., Korkin S., Remer L., Levy R., and Reid J. S. Multi-Angle Implementation of Atmospheric Correction (MAIAC): Part 2. Aerosol Algorithm. J. Geophys. Res., submitted (2010). 2. Lyapustin A., Muldashev T., Wang Y. Code SHARM: fast and accurate radiative transfer over spatially variable anisotropic surfaces. In: Light Scattering Reviews 5. Chichester: Springer, 205 - 247 (2010). 3. Budak, V.P., Korkin S.V. On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering. JQSRT, 109, 220-234 (2008). 4. Budak V.P., Sarmin S.E. Solution of radiative transfer equation by the method of spherical harmonics in the small angle modification. Atmospheric and Oceanic Optics, 3, 898-903 (1990). 5. Goudsmit S., Saunderson J.L. Multiple scattering of electrons. Phys. Rev., 57, 24-29 (1940). 6. Budak V.P, Klyuykov D.A., Korkin S.V. Convergence acceleration of radiative transfer equation solution at strongly anisotropic scattering. In: Light Scattering Reviews 5. Chichester: Springer, 147 - 204 (2010).

Rotational Dynamics of Proteins from Spin Relaxation Times and Molecular Dynamics Simulations.

PubMed

Ollila, O H Samuli; Heikkinen, Harri A; Iwaï, Hideo

2018-06-14

Conformational fluctuations and rotational tumbling of proteins can be experimentally accessed with nuclear spin relaxation experiments. However, interpretation of molecular dynamics from the experimental data is often complicated, especially for molecules with anisotropic shape. Here, we apply classical molecular dynamics simulations to interpret the conformational fluctuations and rotational tumbling of proteins with arbitrarily anisotropic shape. The direct calculation of spin relaxation times from simulation data did not reproduce the experimental data. This was successfully corrected by scaling the overall rotational diffusion coefficients around the protein inertia axes with a constant factor. The achieved good agreement with experiments allowed the interpretation of the internal and overall dynamics of proteins with significantly anisotropic shape. The overall rotational diffusion was found to be Brownian, having only a short subdiffusive region below 0.12 ns. The presented methodology can be applied to interpret rotational dynamics and conformation fluctuations of proteins with arbitrary anisotropic shape. However, a water model with more realistic dynamical properties is probably required for intrinsically disordered proteins.

Speckle-reducing scale-invariant feature transform match for synthetic aperture radar image registration

NASA Astrophysics Data System (ADS)

Wang, Xianmin; Li, Bo; Xu, Qizhi

2016-07-01

The anisotropic scale space (ASS) is often used to enhance the performance of a scale-invariant feature transform (SIFT) algorithm in the registration of synthetic aperture radar (SAR) images. The existing ASS-based methods usually suffer from unstable keypoints and false matches, since the anisotropic diffusion filtering has limitations in reducing the speckle noise from SAR images while building the ASS image representation. We proposed a speckle reducing SIFT match method to obtain stable keypoints and acquire precise matches for the SAR image registration. First, the keypoints are detected in a speckle reducing anisotropic scale space constructed by the speckle reducing anisotropic diffusion, so that speckle noise is greatly reduced and prominent structures of the images are preserved, consequently the stable keypoints can be derived. Next, the probabilistic relaxation labeling approach is employed to establish the matches of the keypoints then the correct match rate of the keypoints is significantly increased. Experiments conducted on simulated speckled images and real SAR images demonstrate the effectiveness of the proposed method.

Diffusion tensor driven contour closing for cell microinjection targeting.

PubMed

Becattini, Gabriele; Mattos, Leonardo S; Caldwell, Darwin G

2010-01-01

This article introduces a novel approach to robust automatic detection of unstained living cells in bright-field (BF) microscope images with the goal of producing a target list for an automated microinjection system. The overall image analysis process is described and includes: preprocessing, ridge enhancement, image segmentation, shape analysis and injection point definition. The developed algorithm implements a new version of anisotropic contour completion (ACC) based on the partial differential equation (PDE) for heat diffusion which improves the cell segmentation process by elongating the edges only along their tangent direction. The developed ACC algorithm is equivalent to a dilation of the binary edge image with a continuous elliptic structural element that takes into account local orientation of the contours preventing extension towards normal direction. Experiments carried out on real images of 10 to 50 microm CHO-K1 adherent cells show a remarkable reliability in the algorithm along with up to 85% success for cell detection and injection point definition.

A Model of Magnetic Braking of Solar Rotation that Satisfies Observational Constraints

NASA Astrophysics Data System (ADS)

Denissenkov, Pavel A.

2010-08-01

The model of magnetic braking of solar rotation considered by Charbonneau & MacGregor has been modified so that it is able to reproduce for the first time the rotational evolution of both the fastest and slowest rotators among solar-type stars in open clusters of different ages, without coming into conflict with other observational constraints, such as the time evolution of the atmospheric Li abundance in solar twins and the thinness of the solar tachocline. This new model assumes that rotation-driven turbulent diffusion, which is thought to amplify the viscosity and magnetic diffusivity in stellar radiative zones, is strongly anisotropic with the horizontal components of the transport coefficients strongly dominating over those in the vertical direction. Also taken into account is the poloidal field decay that helps to confine the width of the tachocline at the solar age. The model's properties are investigated by numerically solving the azimuthal components of the coupled momentum and magnetic induction equations in two dimensions using a finite element method.

Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

NASA Technical Reports Server (NTRS)

Earl, James A.

1992-01-01

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

A note on stress-driven anisotropic diffusion and its role in active deformable media.

PubMed

Cherubini, Christian; Filippi, Simonetta; Gizzi, Alessio; Ruiz-Baier, Ricardo

2017-10-07

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue. Copyright © 2017. Published by Elsevier Ltd.

Electromagnetism on anisotropic fractal media

NASA Astrophysics Data System (ADS)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

3D anisotropic modeling and identification for airborne EM systems based on the spectral-element method

NASA Astrophysics Data System (ADS)

Huang, Xin; Yin, Chang-Chun; Cao, Xiao-Yue; Liu, Yun-He; Zhang, Bo; Cai, Jing

2017-09-01

The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell's equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.

Turbulent Flow past High Temperature Surfaces

NASA Astrophysics Data System (ADS)

Mehmedagic, Igbal; Thangam, Siva; Carlucci, Pasquale; Buckley, Liam; Carlucci, Donald

2014-11-01

Flow over high-temperature surfaces subject to wall heating is analyzed with applications to projectile design. In this study, computations are performed using an anisotropic Reynolds-stress model to study flow past surfaces that are subject to radiative flux. The model utilizes a phenomenological treatment of the energy spectrum and diffusivities of momentum and heat to include the effects of wall heat transfer and radiative exchange. The radiative transport is modeled using Eddington approximation including the weighted effect of nongrayness of the fluid. The time-averaged equations of motion and energy are solved using the modeled form of transport equations for the turbulence kinetic energy and the scalar form of turbulence dissipation with an efficient finite-volume algorithm. The model is applied for available test cases to validate its predictive capabilities for capturing the effects of wall heat transfer. Computational results are compared with experimental data available in the literature. Applications involving the design of projectiles are summarized. Funded in part by U.S. Army, ARDEC.

Squeeze-film flow between a flat impermeable bearing and an anisotropic porous bed

NASA Astrophysics Data System (ADS)

Karmakar, Timir; Raja Sekhar, G. P.

2018-04-01

We consider a theoretical model of the squeeze film in the presence of a porous bed. The gap between the porous bed and the bearing is assumed to be filled with a Newtonian fluid. We use the Navier-Stokes equation in the fluid region and the Darcy equation in the fluid filled porous region. Lubrication approximation is used to derive the corresponding evolution equation for the film thickness. We use G. S. Beavers and D. D. Joseph ["Boundary conditions at a naturally permeable wall," J. Fluid. Mech. 30, 197-207 (1967)] and M. Le Bars and M. G. Worster ["Interfacial conditions between a pure fluid and a porous medium: Implications for binary alloy solidification," J. Fluid. Mech. 550, 149-173 (2006)] condition at the liquid porous interface and present a detailed analysis on the corresponding impact. We assume that the porous bed is anisotropic in nature with permeabilities K2 and K1 along the principal axes. Accordingly, the anisotropic angle ϕ is taken as the angle between the horizontal direction and principal axis with permeability K2. We show that the anisotropic permeability ratio and the anisotropic angle make a significant influence on the contact time, flux, velocity, etc. Contact time to meet the porous bed when a bearing approaches under a constant prescribed load is estimated. We present some important findings (relevant to the knee joint) based on the anisotropic properties of the human cartilage. For a prescribed constant load, we have estimated the time duration, during which a healthy human knee remains fluid lubricated.

Mathematical analysis of the multiband BCS gap equations in superconductivity

NASA Astrophysics Data System (ADS)

Yang, Yisong

2005-01-01

In this paper, we present a mathematical analysis for the phonon-dominated multiband isotropic and anisotropic BCS gap equations at any finite temperature T. We establish the existence of a critical temperature T so that, when TT, the only nonnegative gap solution is the zero solution, representing the normal phase. Furthermore, when T=T, we prove that the only gap solution is the zero solution and that the positive gap solution depend on the temperature T

Seismic wavefield propagation in 2D anisotropic media: Ray theory versus wave-equation simulation

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; Hu, Guang-yi; Zhang, Yan-teng; Li, Zhong-sheng

2014-05-01

Despite the ray theory that is based on the high frequency assumption of the elastic wave-equation, the ray theory and the wave-equation simulation methods should be mutually proof of each other and hence jointly developed, but in fact parallel independent progressively. For this reason, in this paper we try an alternative way to mutually verify and test the computational accuracy and the solution correctness of both the ray theory (the multistage irregular shortest-path method) and the wave-equation simulation method (both the staggered finite difference method and the pseudo-spectral method) in anisotropic VTI and TTI media. Through the analysis and comparison of wavefield snapshot, common source gather profile and synthetic seismogram, it is able not only to verify the accuracy and correctness of each of the methods at least for kinematic features, but also to thoroughly understand the kinematic and dynamic features of the wave propagation in anisotropic media. The results show that both the staggered finite difference method and the pseudo-spectral method are able to yield the same results even for complex anisotropic media (such as a fault model); the multistage irregular shortest-path method is capable of predicting similar kinematic features as the wave-equation simulation method does, which can be used to mutually test each other for methodology accuracy and solution correctness. In addition, with the aid of the ray tracing results, it is easy to identify the multi-phases (or multiples) in the wavefield snapshot, common source point gather seismic section and synthetic seismogram predicted by the wave-equation simulation method, which is a key issue for later seismic application.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Phase space analysis in anisotropic optical systems

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Laser induced heat source distribution in bio-tissues

NASA Astrophysics Data System (ADS)

Li, Xiaoxia; Fan, Shifu; Zhao, Youquan

2006-09-01

During numerical simulation of laser and tissue thermal interaction, the light fluence rate distribution should be formularized and constituted to the source term in the heat transfer equation. Usually the solution of light irradiative transport equation is given in extreme conditions such as full absorption (Lambert-Beer Law), full scattering (Lubelka-Munk theory), most scattering (Diffusion Approximation) et al. But in specific conditions, these solutions will induce different errors. The usually used Monte Carlo simulation (MCS) is more universal and exact but has difficulty to deal with dynamic parameter and fast simulation. Its area partition pattern has limits when applying FEM (finite element method) to solve the bio-heat transfer partial differential coefficient equation. Laser heat source plots of above methods showed much difference with MCS. In order to solve this problem, through analyzing different optical actions such as reflection, scattering and absorption on the laser induced heat generation in bio-tissue, a new attempt was made out which combined the modified beam broaden model and the diffusion approximation model. First the scattering coefficient was replaced by reduced scattering coefficient in the beam broaden model, which is more reasonable when scattering was treated as anisotropic scattering. Secondly the attenuation coefficient was replaced by effective attenuation coefficient in scattering dominating turbid bio-tissue. The computation results of the modified method were compared with Monte Carlo simulation and showed the model provided reasonable predictions of heat source term distribution than past methods. Such a research is useful for explaining the physical characteristics of heat source in the heat transfer equation, establishing effective photo-thermal model, and providing theory contrast for related laser medicine experiments.

Quark–gluon plasma phenomenology from anisotropic lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skullerud, Jon-Ivar; Kelly, Aoife; Aarts, Gert

The FASTSUM collaboration has been carrying out simulations of N{sub f} = 2 + 1 QCD at nonzero temperature in the fixed-scale approach using anisotropic lattices. Here we present the status of these studies, including recent results for electrical conductivity and charge diffusion, and heavy quarkonium (charm and beauty) physics.

Relativistic theory of particles in a scattering flow III: photon transport.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We use the theory developed in Achterberg & Norman (2018a) and Achterberg & Norman (2018b) to calculate the stress due to photons that are scattered elastically by a relativistic flow. We show that the energy-momentum tensor of the radiation takes the form proposed by Eckart (1940). In particular we show that no terms associated with a bulk viscosity appear if one makes the diffusion approximation for radiation transport and treats the radiation as a separate fluid. We find only shear (dynamic) viscosity terms and heat flow terms in our expression for the energy-momentum tensor. This conclusion holds quite generally for different forms of scattering: Krook-type integral scattering, diffusive (Fokker-Planck) scattering and Thomson scattering. We also derive the transport equation in the diffusion approximation that shows the effects of the flow on the photon gas in the form of a combination of adiabatic heating and an irreversible heating term. We find no diffusive changes to the comoving number density and energy density of the scattered photons, in contrast with some published results in Radiation Hydrodynamics. It is demonstrated that these diffusive corrections to the number- and energy density of the photons are in fact higher-order terms that can (and should) be neglected in the diffusion approximation. Our approach eliminates these terms at the root of the expansion that yields the anisotropic terms in the phase-space density of particles and photons, the terms responsible for the photon viscosity.

New integrable model of propagation of the few-cycle pulses in an anisotropic microdispersed medium

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2018-03-01

We investigate the propagation of the few-cycle electromagnetic pulses in the anisotropic microdispersed medium. The effects of the anisotropy and spatial dispersion of the medium are created by the two sorts of the two-level atoms. The system of the material equations describing an evolution of the states of the atoms and the wave equations for the ordinary and extraordinary components of the pulses is derived. By applying the approximation of the sudden excitation to exclude the material variables, we reduce this system to the single nonlinear wave equation that generalizes the modified sine-Gordon equation and the Rabelo-Fokas equation. It is shown that this equation is integrable by means of the inverse scattering transformation method if an additional restriction on the parameters is imposed. The multisoliton solutions of this integrable generalization are constructed and investigated.

Meso-scale anisotropic hydrogen segregation near grain-boundaries in polycrystalline nickel characterized by EBSD/SIMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oudriss, A.; Le Guernic, Solenne; Wang, Zhaoying

2016-02-15

To study anisotropic hydrogen segregation and diffusion in nickel polycrystalline, Secondary Ion Mass Spectrometry (SIMS) and Electron Back Scattered Diffraction (EBSD) are integrated to investigate hydrogen distribution around grain boundaries. Hydrogen distribution in pre-charged samples were correlated with grain boundary character by integrating high-resolution grain microstructure from EBSD inverse pole figure map and low-resolution hydrogen concentration profile map from SIMS. This multimodal imaging instrumentation shows that grain boundaries in nickel can be categorized into two families based on behavior of hydrogen distribution crossing grain boundary: the first one includes random grain boundaries with fast hydrogen diffusivity, showing a sharp gapmore » for hydrogen concentration profile cross the grain boundaries. The second family are special Σ3n grain boundaries with low hydrogen diffusivity, showing a smooth gradient of hydrogen concentration cross the grain boundary. Heterogeneous hydrogen distributions due to grain boundary family revealed by SIMS/EBSD on mesoscale further validate the recent hydrogen permeation data and anisotropic ab-initio calculations in nanoscale. The results highlight the fact that grain boundaries character impacts hydrogen distribution significantly.« less

Exact anisotropic viscous fluid solutions of Einstein's equations

NASA Astrophysics Data System (ADS)

Goenner, H. F. M.; Kowalewski, F.

1989-05-01

A method for obtaining anisotropic, rotationless viscous fluid matter solutions of Bianchi type I and Segré type [1, 111] with the barotropic equation of state is presented. Solutions for which the anisotropy decreases exponentially or with a power law as well as solutions with average Hubble parameterH ˜t -1 are discussed. Also, a class of solutions with constant anisotropy and Bianchi type VIh is found. The dominant energy condition holds and the transport coefficients show the right sign.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

NASA Technical Reports Server (NTRS)

Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

2012-01-01

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion.

PubMed

Zhao, Yi; Cao, Xiangyu; Gao, Jun; Liu, Xiao; Li, Sijia

2016-05-16

We demonstrate a simple reconfigurable metasurface with multiple functions. Anisotropic tiles are investigated and manufactured as fundamental elements. Then, the tiles are combined in a certain sequence to construct a metasurface. Each of the tiles can be adjusted independently which is like a jigsaw puzzle and the whole metasurface can achieve diverse functions by different layouts. For demonstration purposes, we realize polarization conversion, anomalous reflection and diffusion by a jigsaw puzzle metasurface with 6 × 6 pieces of anisotropic tile. Simulated and measured results prove that our method offers a simple and effective strategy for metasurface design.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Measurement and modeling of solar irradiance components on horizontal and tilted planes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padovan, Andrea; Col, Davide del

2010-12-15

In this work new measurements of global and diffuse solar irradiance on the horizontal plane and global irradiance on planes tilted at 20 and 30 oriented due South and at 45 and 65 oriented due East are used to discuss the modeling of solar radiation. Irradiance data are collected in Padova (45.4 N, 11.9 E, 12 m above sea level), Italy. Some diffuse fraction correlations have been selected to model the hourly diffuse radiation on the horizontal plane. The comparison with the present experimental data shows that their prediction accuracy strongly depends on the sky characteristics. The hourly irradiance measurementsmore » taken on the tilted planes are compared with the estimations given by one isotropic and three anisotropic transposition models. The use of an anisotropic model, based on a physical description of the diffuse radiation, provides a much better accuracy, especially when measurements of the diffuse irradiance on the horizontal plane are not available and thus transposition models have to be applied in combination with a diffuse fraction correlation. This is particularly significant for the planes oriented away from South. (author)« less

Arrhenius analysis of anisotropic surface self-diffusion on the prismatic facet of ice.

PubMed

Gladich, Ivan; Pfalzgraff, William; Maršálek, Ondřej; Jungwirth, Pavel; Roeselová, Martina; Neshyba, Steven

2011-11-28

We present an Arrhenius analysis of self-diffusion on the prismatic surface of ice calculated from molecular dynamics simulations. The six-site water model of Nada and van der Eerden was used in combination with a structure-based criterion for determining the number of liquid-like molecules in the quasi-liquid layer. Simulated temperatures range from 230 K-287 K, the latter being just below the melting temperature of the model, 289 K. Calculated surface diffusion coefficients agree with available experimental data to within quoted precision. Our results indicate a positive Arrhenius curvature, implying a change in the mechanism of self-diffusion from low to high temperature, with a concomitant increase in energy of activation from 29.1 kJ mol(-1) at low temperature to 53.8 kJ mol(-1) close to the melting point. In addition, we find that the surface self-diffusion is anisotropic at lower temperatures, transitioning to isotropic in the temperature range of 240-250 K. We also present a framework for self-diffusion in the quasi-liquid layer on ice that aims to explain these observations.

A partial differential equation-based general framework adapted to Rayleigh's, Rician's and Gaussian's distributed noise for restoration and enhancement of magnetic resonance image.

PubMed

Yadav, Ram Bharos; Srivastava, Subodh; Srivastava, Rajeev

2016-01-01

The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.

Spin generation by strong inhomogeneous electric fields

NASA Astrophysics Data System (ADS)

Finkler, Ilya; Engel, Hans-Andreas; Rashba, Emmanuel; Halperin, Bertrand

2007-03-01

Motivated by recent experiments [1], we propose a model with extrinsic spin-orbit interaction, where an inhomogeneous electric field E in the x-y plane can give rise, through nonlinear effects, to a spin polarization with non-zero sz, away from the sample boundaries. The field E induces a spin current js^z= z x(αjc+βE), where jc=σE is the charge current, and the two terms represent,respectively, the skew scattering and side-jump contributions. [2]. The coefficients α and β are assumed to be E- independent, but conductivity σ is field dependent. We find the spin density sz by solving the equation for spin diffusion and relaxation with a source term ∇.js^z. For sufficiently low fields, jc is linear in E, and the source term vanishes, implying that sz=0 away from the edges. However, for large fields, σ varies with E. Solving the diffusion equation in a T-shaped geometry, where the electric current propagates along the main channel, we find spin accumulation near the entrance of the side channel, similar to experimental findings [1]. Also, we present a toy model where spin accumulation away from the boundary results from a nonlinear and anisotropic conductivity. [1] V. Sih, et al, Phys. Rev. Lett. 97, 096605 (2006). [2] H.-A. Engel, B.I. Halperin, E.I.Rashba, Phys. Rev. Lett. 95, 166605 (2005).

Physical interpretation and application of principles of ultrasonic nondestructive evaluation of high-performance materials

NASA Technical Reports Server (NTRS)

Miller, James G.

1990-01-01

An ultrasonic measurement system employed in the experimental interrogation of the anisotropic properties (through the measurement of the elastic stiffness constants) of the uniaxial graphite-epoxy composites is presented. The continuing effort for the development of improved visualization techniques for physical parameters is discussed. The background is set for the understanding and visualization of the relationship between the phase and energy/group velocity for propagation in high-performance anisotropic materials by investigating the general requirements imposed by the classical wave equation. The consequences are considered when the physical parameters of the anisotropic material are inserted into the classical wave equation by a linear elastic model. The relationship is described between the phase velocity and the energy/group velocity three dimensional surfaces through graphical techniques.

Domainal cleavage as an Anisotropic Reaction-diffusion Process

NASA Astrophysics Data System (ADS)

Mulchrone, Kieran; Meere, Patrick

2017-04-01

Domainal cleavage comprises zones dominated by quartz and feldspar (QF-domains) and zones dominated by Mica (M-domains) which form at low metamorphic grades. The protolith is typically fairly homogeneous mudstone, siltstone, sandstone or limestone. Wet diffusion or pressure solution along grain boundaries is a key mechanism in the development of domanial cleavage. However, this does not explain why M-domains become sub-regularly spaced, visually evident in coarser-grained rocks, and take on an anastomising morphology. The ratio of M to QF-domains by volume can range from 1 to 0.1 and lower i.e. in extreme cases M-domains are intermittent but regularly spaced. It is suggested here that an anisotropic reaction-diffusion process model can explain these features. The imposed stress field instantaneously leads to anisotropy of diffusion by narrowing intergranular channels perpendicular to the principal stress. This leads to a preferred diffusion of chemicals parallel to the principal stress direction and lower diffusion rates in the normal direction. Combining this with the chemical reaction of pressure solution produces an anisotropic reaction-diffusion system. Both isotropic and anistropic reaction diffusion systems lead to pattern formation as discovered by Alan Turing on the 1950's as an explanation for patterns found in animal skins such as spots and stripes. Thus domanial cleavage is a striped pattern induced by diffusion anisotropy combined with a chemical reaction. Furthermore, rates of chemical reaction in intergranular fluids is likely to be many orders of magnitude greater that rates of deformation. Therefore we expect domanial cleavage to form relatively rapidly. As deformation progresses the M-domains behave less competently and may be the site of enhanced shearing. An example from Co. Cork, Ireland demonstrates shear folding in low-grade metasedimentary rocks with reverse shear along M-domains at a high angle to the maximum compressive stress.

Analytical close-to-source investigation for an isotropic point source in an unbounded, anisotropically scattering medium

NASA Astrophysics Data System (ADS)

Rinzema, Kees; ten Bosch, Jaap J.; Ferwerda, Hedzer A.; Hoenders, Bernhard J.

1995-01-01

The diffusion approximation, which is often used to describe the propagation of light in biological tissues, is only good at a sufficient distance from sources and boundaries. Light- tissue interaction is however most intense in the region close to the source. It would therefore be interesting to study this region more closely. Although scattering in biological tissues is predominantly forward peaked, explicit solutions to the transport equation have only been obtained in the case of isotropic scattering. Particularly, for the case of an isotropic point source in an unbounded, isotropically scattering medium the solution is well known. We show that this problem can also be solved analytically if the scattering is no longer isotropic, while everything else remains the same.

Mirror Instability: Quasi-linear Effects

NASA Astrophysics Data System (ADS)

Hellinger, P.; Travnicek, P. M.; Passot, T.; Sulem, P.; Kuznetsov, E. A.

2008-12-01

Nonlinear properties of the mirror instability are investigated by direct integration of the quasi-linear diffusion equation [Shapiro and Shevchenko, 1964] near threshold. The simulation results are compared to the results of standard hybrid simulations [Califano et al., 2008] and discussed in the context of the nonlinear dynamical model by Kuznetsov et al. [2007]. References: Califano, F., P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek (2008), Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, A08219, doi:10.1029/2007JA012898. Kuznetsov, E., T. Passot and P. L. Sulem (2007), Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 98, 235003 . Shapiro, V. D., and V. I. Shevchenko (1964), Quasilinear theory of instability of a plasma with an anisotropic ion velocity distribution, Sov. JETP, 18, 1109.

Anisotropic fractal media by vector calculus in non-integer dimensional space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

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

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

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

On the nature of the NAA diffusion attenuated MR signal in the central nervous system.

PubMed

Kroenke, Christopher D; Ackerman, Joseph J H; Yablonskiy, Dmitriy A

2004-11-01

In the brain, on a macroscopic scale, diffusion of the intraneuronal constituent N-acetyl-L-aspartate (NAA) appears to be isotropic. In contrast, on a microscopic scale, NAA diffusion is likely highly anisotropic, with displacements perpendicular to neuronal fibers being markedly hindered, and parallel displacements less so. In this report we first substantiate that local anisotropy influences NAA diffusion in vivo by observing differing diffusivities parallel and perpendicular to human corpus callosum axonal fibers. We then extend our measurements to large voxels within rat brains. As expected, the macroscopic apparent diffusion coefficient (ADC) of NAA is practically isotropic due to averaging of the numerous and diverse fiber orientations. We demonstrate that the substantially non-monoexponential diffusion-mediated MR signal decay vs. b value can be quantitatively explained by a theoretical model of NAA confined to an ensemble of differently oriented neuronal fibers. On the microscopic scale, NAA diffusion is found to be strongly anisotropic, with displacements occurring almost exclusively parallel to the local fiber axis. This parallel diffusivity, ADCparallel, is 0.36 +/- 0.01 microm2/ms, and ADCperpendicular is essentially zero. From ADCparallel the apparent viscosity of the neuron cytoplasm is estimated to be twice as large as that of a temperature-matched dilute aqueous solution. (c) 2004 Wiley-Liss, Inc.

Bianchi type-VIh string cloud cosmological models with bulk viscosity

NASA Astrophysics Data System (ADS)

Tripathy, Sunil K.; Behera, Dipanjali

2010-11-01

String cloud cosmological models are studied using spatially homogeneous and anisotropic Bianchi type VIh metric in the frame work of general relativity. The field equations are solved for massive string cloud in presence of bulk viscosity. A general linear equation of state of the cosmic string tension density with the proper energy density of the universe is considered. The physical and kinematical properties of the models have been discussed in detail and the limits of the anisotropic parameter responsible for different phases of the universe are explored.

Determination of the hydrodynamic friction matrix for various anisotropic particles

NASA Astrophysics Data System (ADS)

Kraft, Daniela; Wittkowksi, Raphael; Löwen, Hartmut; Pine, David

2013-03-01

The relationship between the shape of a colloidal particle and its Brownian motion can be captured by the hydrodynamic friction matrix. It fully describes the translational and rotational diffusion along the particle's main axes as well as the coupling between rotational and translational diffusion. We observed a wide variety of anisotropic colloidal particles with confocal microscopy and calculated the hydrodynamic friction matrix from the particle trajectories. We find that symmetries in the particle shape are reflected in the entries of the friction matrix. We compare our experimentally obtained results with numerical simulations and theoretical predictions. Financial support through a Rubicon grant by the Netherlands Organisation for Scientific Research.

A MODEL OF MAGNETIC BRAKING OF SOLAR ROTATION THAT SATISFIES OBSERVATIONAL CONSTRAINTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denissenkov, Pavel A., E-mail: pavel.denisenkov@gmail.co

The model of magnetic braking of solar rotation considered by Charbonneau and MacGregor has been modified so that it is able to reproduce for the first time the rotational evolution of both the fastest and slowest rotators among solar-type stars in open clusters of different ages, without coming into conflict with other observational constraints, such as the time evolution of the atmospheric Li abundance in solar twins and the thinness of the solar tachocline. This new model assumes that rotation-driven turbulent diffusion, which is thought to amplify the viscosity and magnetic diffusivity in stellar radiative zones, is strongly anisotropic withmore » the horizontal components of the transport coefficients strongly dominating over those in the vertical direction. Also taken into account is the poloidal field decay that helps to confine the width of the tachocline at the solar age. The model's properties are investigated by numerically solving the azimuthal components of the coupled momentum and magnetic induction equations in two dimensions using a finite element method.« less

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2014-01-01

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

Emergence of anisotropic Gilbert damping in ultrathin Fe layers on GaAs(001)

NASA Astrophysics Data System (ADS)

Chen, L.; Mankovsky, S.; Wimmer, S.; Schoen, M. A. W.; Körner, H. S.; Kronseder, M.; Schuh, D.; Bougeard, D.; Ebert, H.; Weiss, D.; Back, C. H.

2018-05-01

As a fundamental parameter in magnetism, the phenomenological Gilbert damping constant α determines the performance of many spintronic devices. For most magnetic materials, α is treated as an isotropic parameter entering the Landau-Lifshitz-Gilbert equation. However, could the Gilbert damping be anisotropic? Although several theoretical approaches have suggested that anisotropic α could appear in single-crystalline bulk systems, experimental evidence of its existence is scarce. Here, we report the emergence of anisotropic magnetic damping by exploring a quasi-two-dimensional single-crystalline ferromagnetic metal/semiconductor interface—that is, a Fe/GaAs(001) heterojunction. The observed anisotropic damping shows twofold C2v symmetry, which is expected from the interplay of interfacial Rashba and Dresselhaus spin-orbit interaction, and is manifested by the anisotropic density of states at the Fe/GaAs (001) interface. This discovery of anisotropic damping will enrich the understanding of magnetization relaxation mechanisms and can provide a route towards the search for anisotropic damping at other ferromagnetic metal/semiconductor interfaces.

Charged anisotropic matter with linear or nonlinear equation of state

NASA Astrophysics Data System (ADS)

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

2010-08-01

Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplifications achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua’s method to include pressure anisotropy and linear or nonlinear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge (1019C) and maximum electric field intensities are very large (1023-1024statvolt/cm) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

Anisotropic swim stress in active matter with nematic order

NASA Astrophysics Data System (ADS)

Yan, Wen; Brady, John F.

2018-05-01

Active Brownian particles (ABPs) transmit a swim pressure {{{\\Pi }}}{{swim}}=n\\zeta {D}{{swim}} to the container boundaries, where ζ is the drag coefficient, D swim is the swim diffusivity and n is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress {{\\boldsymbol{σ }}}{{swim}}=-n\\zeta {{\\boldsymbol{D}}}{{swim}}, which is related to the anisotropic swim diffusivity {{\\boldsymbol{D}}}{{swim}}. We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems. The anisotropy, defined as the ratio of the maximum to the minimum of the three principal stresses, is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure {{{\\Pi }}}{{swim}}=-({{\\boldsymbol{σ }}}{{swim}}\\cdot {\\boldsymbol{n}})\\cdot {\\boldsymbol{n}} on a wall with normal vector {\\boldsymbol{n}}, and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components—the normal stress difference—generates a net flow of ABPs along the wall, which is a generic property of active matter systems.

The dynamics of nucleation and growth of a particle in the ternary alloy melt with anisotropic surface tension.

PubMed

Chen, Ming-Wen; Li, Lin-Yan; Guo, Hui-Min

2017-08-28

The dynamics of nucleation and growth of a particle affected by anisotropic surface tension in the ternary alloy melt is studied. The uniformly valid asymptotic solution for temperature field, concentration field, and interface evolution of nucleation and particle growth is obtained by means of the multiple variable expansion method. The asymptotic solution reveals the critical radius of nucleation in the ternary alloy melt and an inward melting mechanism of the particle induced by the anisotropic effect of surface tension. The critical radius of nucleation is dependent on isotropic surface tension, temperature undercooling, and constitutional undercooling in the ternary alloy melt, and the solute diffusion melt decreases the critical radius of nucleation. Immediately after a nucleus forms in the initial stage of solidification, the anisotropic effect of surface tension makes some parts of its interface grow inward while some parts grow outward. Until the inward melting attains a certain distance (which is defined as "the melting depth"), these parts of interface start to grow outward with other parts. The interface of the particle evolves into an ear-like deformation, whose inner diameter may be less than two times the critical radius of nucleation within a short time in the initial stage of solidification. The solute diffusion in the ternary alloy melt decreases the effect of anisotropic surface tension on the interface deformation.

Anisotropic Brownian motion in ordered phases of DNA fragments.

PubMed

Dobrindt, J; Rodrigo Teixeira da Silva, E; Alves, C; Oliveira, C L P; Nallet, F; Andreoli de Oliveira, E; Navailles, L

2012-01-01

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

Probabilistic-driven oriented Speckle reducing anisotropic diffusion with application to cardiac ultrasonic images.

PubMed

Vegas-Sanchez-Ferrero, G; Aja-Fernandez, S; Martin-Fernandez, M; Frangi, A F; Palencia, C

2010-01-01

A novel anisotropic diffusion filter is proposed in this work with application to cardiac ultrasonic images. It includes probabilistic models which describe the probability density function (PDF) of tissues and adapts the diffusion tensor to the image iteratively. For this purpose, a preliminary study is performed in order to select the probability models that best fit the stastitical behavior of each tissue class in cardiac ultrasonic images. Then, the parameters of the diffusion tensor are defined taking into account the statistical properties of the image at each voxel. When the structure tensor of the probability of belonging to each tissue is included in the diffusion tensor definition, a better boundaries estimates can be obtained instead of calculating directly the boundaries from the image. This is the main contribution of this work. Additionally, the proposed method follows the statistical properties of the image in each iteration. This is considered as a second contribution since state-of-the-art methods suppose that noise or statistical properties of the image do not change during the filter process.

Multimodel analysis of anisotropic diffusive tracer-gas transport in a deep arid unsaturated zone

USGS Publications Warehouse

Green, Christopher T.; Walvoord, Michelle Ann; Andraski, Brian J.; Striegl, Robert G.; Stonestrom, David A.

2015-01-01

Gas transport in the unsaturated zone affects contaminant flux and remediation, interpretation of groundwater travel times from atmospheric tracers, and mass budgets of environmentally important gases. Although unsaturated zone transport of gases is commonly treated as dominated by diffusion, the characteristics of transport in deep layered sediments remain uncertain. In this study, we use a multimodel approach to analyze results of a gas-tracer (SF6) test to clarify characteristics of gas transport in deep unsaturated alluvium. Thirty-five separate models with distinct diffusivity structures were calibrated to the tracer-test data and were compared on the basis of Akaike Information Criteria estimates of posterior model probability. Models included analytical and numerical solutions. Analytical models provided estimates of bulk-scale apparent diffusivities at the scale of tens of meters. Numerical models provided information on local-scale diffusivities and feasible lithological features producing the observed tracer breakthrough curves. The combined approaches indicate significant anisotropy of bulk-scale diffusivity, likely associated with high-diffusivity layers. Both approaches indicated that diffusivities in some intervals were greater than expected from standard models relating porosity to diffusivity. High apparent diffusivities and anisotropic diffusivity structures were consistent with previous observations at the study site of rapid lateral transport and limited vertical spreading of gas-phase contaminants. Additional processes such as advective oscillations may be involved. These results indicate that gases in deep, layered unsaturated zone sediments can spread laterally more quickly, and produce higher peak concentrations, than predicted by homogeneous, isotropic diffusion models.

Scale-invariant streamline equations and strings of singular vorticity for perturbed anisotropic solutions of the Navier-Stokes equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Libin, A., E-mail: a_libin@netvision.net.il

2012-12-15

A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the stringsmore » of singular vorticity.« less

Dynamics of Geometrically Nonlinear Elastic Nonthin Anisotropic Shells of Variable Thickness

NASA Astrophysics Data System (ADS)

Marchuk, M. V.; Tuchapskii, R. I.

2017-11-01

A theory of dynamic elastic geometrically nonlinear deformation of nonthin anisotropic shells with variable thickness is constructed. Shells are assumed asymmetric about the reference surface. Functions are expanded into Legendre series. The basic equations are written in a coordinate system aligned with the lines of curvature of the reference surface. The equations of motion and appropriate boundary conditions are obtained using the Hamilton-Ostrogradsky variational principle. The change in metric across the thickness is taken into account. The theory assumes that the refinement process is regular and allows deriving equations including products of terms of Legendre series of unknown functions of arbitrary order. The behavior of a square metallic plate acted upon by a pressure pulse distributed over its face is studied.

Shear and compression buckling analysis for anisotropic panels with centrally located elliptical cutouts

NASA Technical Reports Server (NTRS)

Britt, V. O.

1993-01-01

An approximate analysis for buckling of biaxial- and shear-loaded anisotropic panels with centrally located elliptical cutouts is presented in the present paper. The analysis is composed of two parts, a prebuckling analysis and a buckling analysis. The prebuckling solution is determined using Lekhnitskii's complex variable equations of plane elastostatics combined with a Laurent series approximation and a boundary collocation method. The buckling solution is obtained using the principle of minimum potential energy. A by-product of the minimum potential energy equation is an integral equation which is solved using Gaussian quadrature. Comparisons with documented experimental results and finite element analyses indicate that the approximate analysis accurately predicts the buckling loads of square biaxial- and shear-loaded panels having elliptical cutouts with major axes up to sixty percent of the panel width. Results of a parametric study are presented for shear- and compression-loaded rectangular anisotropic panels with elliptical cutouts. The effects of panel aspect ratio, cutout shape, cutout size, cutout orientation, laminate anisotropy, and combined loading on the buckling load are examined.

Anisotropic ghost dark energy cosmological model with hybrid expansion law

NASA Astrophysics Data System (ADS)

Mahanta, Chandra Rekha; Sarma, Nitin

2017-11-01

In this paper, we study the anisotropic Bianchi type-VI0 metric filled with dark matter and anisotropic ghost dark energy. We have solved the Einstein's field equations by considering hybrid expansion law (HEL) for the average scale factor. It is found that at later times the universe becomes spatially homogeneous, isotropic and flat. From a state finder diagnosis, it is found that our model is having similar behavior like ɅCDM model at late phase of cosmic time.

Quantitative in vivo assessment of lung microstructure at the alveolar level with hyperpolarized 3He diffusion MRI

NASA Astrophysics Data System (ADS)

Yablonskiy, Dmitriy A.; Sukstanskii, Alexander L.; Leawoods, Jason C.; Gierada, David S.; Bretthorst, G. Larry; Lefrak, Stephen S.; Cooper, Joel D.; Conradi, Mark S.

2002-03-01

The study of lung emphysema dates back to the beginning of the 17th century. Nevertheless, a number of important questions remain unanswered because a quantitative localized characterization of emphysema requires knowledge of lung structure at the alveolar level in the intact living lung. This information is not available from traditional imaging modalities and pulmonary function tests. Herein, we report the first in vivo measurements of lung geometrical parameters at the alveolar level obtained with 3He diffusion MRI in healthy human subjects and patients with severe emphysema. We also provide the first experimental data demonstrating that 3He gas diffusivity in the acinus of human lung is highly anisotropic. A theory of anisotropic diffusion is presented. Our results clearly demonstrate substantial differences between healthy and emphysematous lung at the acinar level and may provide new insights into emphysema progression. The technique offers promise as a clinical tool for early diagnosis of emphysema.

Electrostatic and Small-Signal Analysis of CMUTs With Circular and Square Anisotropic Plates.

PubMed

Funding la Cour, Mette; Christiansen, Thomas Lehrmann; Jensen, Jørgen Arendt; Thomsen, Erik Vilain

2015-08-01

Traditionally, capacitive micromachined ultrasonic transducers (CMUTs) are modeled using the isotropic plate equation, and this leads to deviations between analytical calculations and finite element modeling (FEM). In this paper, the deflection is calculated for both circular and square plates using the full anisotropic plate equation. It is shown that the anisotropic calculations match excellently with FEM, whereas an isotropic approach causes up to 10% deviations in deflection. For circular plates, an exact solution can be found. For square plates using the Galerkin method, and utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The theory of multilayer plates is also applied to the CMUT. The deflection of a square plate was measured on fabricated CMUTs using a white light interferometer. Fitting the plate parameter for the anisotropic calculated deflection to the measurement, a deviation of 0.07% is seen. Electrostatic and small-signal dynamic analysis are performed using energy considerations including anisotropy. The stable position, effective spring constant, pullin distance, and pull-in voltage are found for both circular and square anisotropic plates, and the pressure dependence is included by comparison with the corresponding analysis for a parallel plate. Measurements on fabricated devices with both circular and square plates subjected to increasing bias voltage are performed, and it is observed that the models including anisotropic effects are within the uncertainty interval of the measurements. Finally, a lumped element small-signal model for both circular and square anisotropic plates is derived to describe the dynamics of the CMUT.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chandra, Mani; Gammie, Charles F.; Foucart, Francois, E-mail: manic@illinois.edu, E-mail: gammie@illinois.edu, E-mail: fvfoucart@lbl.gov

Hot, diffuse, relativistic plasmas such as sub-Eddington black-hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects such as heat conduction and viscosity can be important in a collisionless plasma and will potentially alter the dynamics and radiative properties of the flow from that in ideal fluid models; we refer to models that include these processes as Extended GRMHD. Here we describe a new conservative code, grim, that enables all of the above and additional physics to be efficiently incorporated. grim combines time evolution and primitive variablemore » inversion needed for conservative schemes into a single step using an algorithm that only requires the residuals of the governing equations as inputs. This algorithm enables the code to be physics agnostic as well as flexibility regarding time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same code. We formulate a performance model and use it to show that our implementation runs optimally on both architectures. grim correctly captures classical GRMHD test problems as well as a new suite of linear and nonlinear test problems with anisotropic conduction and viscosity in special and general relativity. As tests and example applications, we resolve the shock substructure due to the presence of dissipation, and report on relativistic versions of the magneto-thermal instability and heat flux driven buoyancy instability, which arise due to anisotropic heat conduction, and of the firehose instability, which occurs due to anisotropic pressure (i.e., viscosity). Finally, we show an example integration of an accretion flow around a Kerr black hole, using Extended GRMHD.« less

A Hybrid Seismic Inversion Method for V P/V S Ratio and Its Application to Gas Identification

NASA Astrophysics Data System (ADS)

Guo, Qiang; Zhang, Hongbing; Han, Feilong; Xiao, Wei; Shang, Zuoping

2018-03-01

The ratio of compressional wave velocity to shear wave velocity (V P/V S ratio) has established itself as one of the most important parameters in identifying gas reservoirs. However, considering that seismic inversion process is highly non-linear and geological conditions encountered may be complex, a direct estimation of V P/V S ratio from pre-stack seismic data remains a challenging task. In this paper, we propose a hybrid seismic inversion method to estimate V P/V S ratio directly. In this method, post- and pre-stack inversions are combined in which the pre-stack inversion for V P/V S ratio is driven by the post-stack inversion results (i.e., V P and density). In particular, the V P/V S ratio is considered as a model parameter and is directly inverted from the pre-stack inversion based on the exact Zoeppritz equation. Moreover, anisotropic Markov random field is employed in order to regularise the inversion process as well as taking care of geological structures (boundaries) information. Aided by the proposed hybrid inversion strategy, the directional weighting coefficients incorporated in the anisotropic Markov random field neighbourhoods are quantitatively calculated by the anisotropic diffusion method. The synthetic test demonstrates the effectiveness of the proposed inversion method. In particular, given low quality of the pre-stack data and high heterogeneity of the target layers in the field data, the proposed inversion method reveals the detailed model of V P/V S ratio that can successfully identify the gas-bearing zones.

Tissue signature characterisation of diffusion tensor abnormalities in cerebral gliomas.

PubMed

Price, Stephen J; Peña, Alonso; Burnet, Neil G; Jena, Raj; Green, Hadrian A L; Carpenter, T Adrian; Pickard, John D; Gillard, Jonathan H

2004-10-01

The inherent invasiveness of malignant cells is a major determinant of the poor prognosis of cerebral gliomas. Diffusion tensor MRI (DTI) can identify white matter abnormalities in gliomas that are not seen on conventional imaging. By breaking down DTI into its isotropic (p) and anisotropic (q) components, we can determine tissue diffusion "signatures". In this study we have characterised these abnormalities in peritumoural white matter tracts. Thirty-five patients with cerebral gliomas and seven normal volunteers were imaged with DTI and T2-weighted sequences at 3 T. Displaced, infiltrated and disrupted white matter tracts were identified using fractional anisotropy (FA) maps and directionally encoded colour maps and characterised using tissue signatures. The diffusion tissue signatures were normal in ROIs where the white matter was displaced. Infiltrated white matter was characterised by an increase in the isotropic component of the tensor (p) and a less marked reduction of the anisotropic component (q). In disrupted white matter tracts, there was a marked reduction in q and increase in p. The direction of water diffusion was grossly abnormal in these cases. Diffusion tissue signatures may be a useful method of assessing occult white matter infiltration. Copyright 2004 Springer-Verlag

Edge Probability and Pixel Relativity-Based Speckle Reducing Anisotropic Diffusion.

PubMed

Mishra, Deepak; Chaudhury, Santanu; Sarkar, Mukul; Soin, Arvinder Singh; Sharma, Vivek

2018-02-01

Anisotropic diffusion filters are one of the best choices for speckle reduction in the ultrasound images. These filters control the diffusion flux flow using local image statistics and provide the desired speckle suppression. However, inefficient use of edge characteristics results in either oversmooth image or an image containing misinterpreted spurious edges. As a result, the diagnostic quality of the images becomes a concern. To alleviate such problems, a novel anisotropic diffusion-based speckle reducing filter is proposed in this paper. A probability density function of the edges along with pixel relativity information is used to control the diffusion flux flow. The probability density function helps in removing the spurious edges and the pixel relativity reduces the oversmoothing effects. Furthermore, the filtering is performed in superpixel domain to reduce the execution time, wherein a minimum of 15% of the total number of image pixels can be used. For performance evaluation, 31 frames of three synthetic images and 40 real ultrasound images are used. In most of the experiments, the proposed filter shows a better performance as compared to the state-of-the-art filters in terms of the speckle region's signal-to-noise ratio and mean square error. It also shows a comparative performance for figure of merit and structural similarity measure index. Furthermore, in the subjective evaluation, performed by the expert radiologists, the proposed filter's outputs are preferred for the improved contrast and sharpness of the object boundaries. Hence, the proposed filtering framework is suitable to reduce the unwanted speckle and improve the quality of the ultrasound images.

Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution.

PubMed

Bangera, Nitin B; Schomer, Donald L; Dehghani, Nima; Ulbert, Istvan; Cash, Sydney; Papavasiliou, Steve; Eisenberg, Solomon R; Dale, Anders M; Halgren, Eric

2010-12-01

Forward solutions with different levels of complexity are employed for localization of current generators, which are responsible for the electric and magnetic fields measured from the human brain. The influence of brain anisotropy on the forward solution is poorly understood. The goal of this study is to validate an anisotropic model for the intracranial electric forward solution by comparing with the directly measured 'gold standard'. Dipolar sources are created at known locations in the brain and intracranial electroencephalogram (EEG) is recorded simultaneously. Isotropic models with increasing level of complexity are generated along with anisotropic models based on Diffusion tensor imaging (DTI). A Finite Element Method based forward solution is calculated and validated using the measured data. Major findings are (1) An anisotropic model with a linear scaling between the eigenvalues of the electrical conductivity tensor and water self-diffusion tensor in brain tissue is validated. The greatest improvement was obtained when the stimulation site is close to a region of high anisotropy. The model with a global anisotropic ratio of 10:1 between the eigenvalues (parallel: tangential to the fiber direction) has the worst performance of all the anisotropic models. (2) Inclusion of cerebrospinal fluid as well as brain anisotropy in the forward model is necessary for an accurate description of the electric field inside the skull. The results indicate that an anisotropic model based on the DTI can be constructed non-invasively and shows an improved performance when compared to the isotropic models for the calculation of the intracranial EEG forward solution.

A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

NASA Technical Reports Server (NTRS)

Schneider, Harold

1959-01-01

This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

PubMed

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Effects of Orientation and Anisometry of Magnetic Resonance Imaging Acquisitions on Diffusion Tensor Imaging and Structural Connectomes.

PubMed

Tudela, Raúl; Muñoz-Moreno, Emma; López-Gil, Xavier; Soria, Guadalupe

2017-01-01

Diffusion-weighted imaging (DWI) quantifies water molecule diffusion within tissues and is becoming an increasingly used technique. However, it is very challenging as correct quantification depends on many different factors, ranging from acquisition parameters to a long pipeline of image processing. In this work, we investigated the influence of voxel geometry on diffusion analysis, comparing different acquisition orientations as well as isometric and anisometric voxels. Diffusion-weighted images of one rat brain were acquired with four different voxel geometries (one isometric and three anisometric in different directions) and three different encoding orientations (coronal, axial and sagittal). Diffusion tensor scalar measurements, tractography and the brain structural connectome were analyzed for each of the 12 acquisitions. The acquisition direction with respect to the main magnetic field orientation affected the diffusion results. When the acquisition slice-encoding direction was not aligned with the main magnetic field, there were more artifacts and a lower signal-to-noise ratio that led to less anisotropic tensors (lower fractional anisotropic values), producing poorer quality results. The use of anisometric voxels generated statistically significant differences in the values of diffusion metrics in specific regions. It also elicited differences in tract reconstruction and in different graph metric values describing the brain networks. Our results highlight the importance of taking into account the geometric aspects of acquisitions, especially when comparing diffusion data acquired using different geometries.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures

NASA Astrophysics Data System (ADS)

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.

Surface ordering of (In,Ga)As quantum dots controlled by GaAs substrate indexes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Zh.M.; Seydmohamadi, Sh.; Lee, J.H.

Self-organized surface ordering of (In,Ga)As quantum dots in a GaAs matrix was investigated using stacked multiple quantum dot layers prepared by molecular-beam epitaxy. While one-dimensional chain-like ordering is formed on singular and slightly misorientated GaAs(100) surfaces, we report on two-dimensional square-like ordering that appears on GaAs(n11)B, where n is 7, 5, 4, and 3. Using a technique to control surface diffusion, the different ordering patterns are found to result from the competition between anisotropic surface diffusion and anisotropic elastic matrix, a similar mechanism suggested before by Solomon [Appl. Phys. Lett. 84, 2073 (2004)].

Effect of bulk Lorentz violation on anisotropic brane cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari-Fard, Malihe, E-mail: heydarifard@qom.ac.ir

2012-04-01

The effect of Lorentz invariance violation in cosmology has attracted a considerable amount of attention. By using a dynamical vector field assumed to point in the bulk direction, with Lorentz invariance holding on the brane, we extend the notation of Lorentz violation in four dimensions Jacobson to a five-dimensional brane-world. We obtain the general solution of the field equations in an exact parametric form for Bianchi type I space-time, with perfect fluid as a matter source. We show that the brane universe evolves from an isotropic/anisotropic state to an isotropic de Sitter inflationary phase at late time. The early timemore » behavior of anisotropic brane universe is largely dependent on the Lorentz violating parameters β{sub i},i = 1,2,3 and the equation of state of the matter, while its late time behavior is independent of these parameters.« less

Multiscale model reduction for shale gas transport in poroelastic fractured media

NASA Astrophysics Data System (ADS)

Akkutlu, I. Yucel; Efendiev, Yalchin; Vasilyeva, Maria; Wang, Yuhe

2018-01-01

Inherently coupled flow and geomechanics processes in fractured shale media have implications for shale gas production. The system involves highly complex geo-textures comprised of a heterogeneous anisotropic fracture network spatially embedded in an ultra-tight matrix. In addition, nonlinearities due to viscous flow, diffusion, and desorption in the matrix and high velocity gas flow in the fractures complicates the transport. In this paper, we develop a multiscale model reduction approach to couple gas flow and geomechanics in fractured shale media. A Discrete Fracture Model (DFM) is used to treat the complex network of fractures on a fine grid. The coupled flow and geomechanics equations are solved using a fixed stress-splitting scheme by solving the pressure equation using a continuous Galerkin method and the displacement equation using an interior penalty discontinuous Galerkin method. We develop a coarse grid approximation and coupling using the Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM constructs the multiscale basis functions in a systematic way to capture the fracture networks and their interactions with the shale matrix. Numerical results and an error analysis is provided showing that the proposed approach accurately captures the coupled process using a few multiscale basis functions, i.e. a small fraction of the degrees of freedom of the fine-scale problem.

Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media

NASA Astrophysics Data System (ADS)

Toner, John; Löwen, Hartmut; Wensink, Henricus H.

2016-06-01

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to t lnt of the mean-square displacement with time t . This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.

Heat source reconstruction from noisy temperature fields using a gradient anisotropic diffusion filter

NASA Astrophysics Data System (ADS)

Beitone, C.; Balandraud, X.; Delpueyo, D.; Grédiac, M.

2017-01-01

This paper presents a post-processing technique for noisy temperature maps based on a gradient anisotropic diffusion (GAD) filter in the context of heat source reconstruction. The aim is to reconstruct heat source maps from temperature maps measured using infrared (IR) thermography. Synthetic temperature fields corrupted by added noise are first considered. The GAD filter, which relies on a diffusion process, is optimized to retrieve as well as possible a heat source concentration in a two-dimensional plate. The influence of the dimensions and the intensity of the heat source concentration are discussed. The results obtained are also compared with two other types of filters: averaging filter and Gaussian derivative filter. The second part of this study presents an application for experimental temperature maps measured with an IR camera. The results demonstrate the relevancy of the GAD filter in extracting heat sources from noisy temperature fields.

Large-scale vortices in compressible turbulent medium with the magnetic field

NASA Astrophysics Data System (ADS)

Gvaramadze, V. V.; Dimitrov, B. G.

1990-08-01

An averaged equation which describes the large scale vortices and Alfven waves generation in a compressible helical turbulent medium with a constant magnetic field is presented. The presence of the magnetic field leads to anisotropization of the vortex generation. Possible applications of the anisotropic vortex dynamo effect are accretion disks of compact objects.

Vibrations and stresses in layered anisotropic cylinders

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

SIMULATION OF ENERGETIC PARTICLE TRANSPORT AND ACCELERATION AT SHOCK WAVES IN A FOCUSED TRANSPORT MODEL: IMPLICATIONS FOR MIXED SOLAR PARTICLE EVENTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kartavykh, Y. Y.; Dröge, W.; Gedalin, M.

2016-03-20

We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock formore » which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturally reproduce the morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.« less

Demonstration of Anisotropic Fluid Closure Capturing the Kinetic Structure of Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Ohia, Obioma

2012-10-01

Magnetic reconnection in collisionless plasmas plays an important role in space and laboratory plasmas. Allowing magnetic stress to be reduced by a rearrangement of magnetic line topology, this process is often accompanied by a large release of magnetic field energy, which can heat the plasma, drive large scale flows, or accelerate particles. Reconnection has been widely studied through fluid models and kinetic simulations. While two-fluid models often reproduce the fast reconnection that is observed in nature and seen in kinetic simulations, it is found that the structure surrounding the electron diffusion region and the electron current layer differ vastly between fluid models and kinetic simulations [1]. Recently, using an adiabatic solution of the Vlasov equation, a new fluid closure has been obtained for electrons that relate parallel and perpendicular pressures to the density and magnetic field [2]. Here we present the results of fluid simulation, developed using the HiFi framework [3], that implements new equations of state for guide-field reconnection. The new fluid closure accurately accounts for the anisotropic electron pressure that builds in the reconnection region due to electric and magnetic trapping of electrons. In contrast to previous fluid models, our fluid simulation reproduces the detailed reconnection region as observed in fully kinetic simulations [4]. We hereby demonstrate that the new fluid closure self-consistently captures all the physics relevant to the structure of the reconnection region, providing a gateway to a renewed and deeper theoretical understanding for reconnection in weakly collisional regimes.[4pt] [1] Daughton W et al., Phys. Plasmas 13, 072101 (2006).[0pt] [2] Le A et al., Phys. Rev. Lett. 102, 085001 (2009). [0pt] [3] Lukin VS, Linton MG, Nonlinear Proc. Geoph. 18, 871 (2011). [0pt] [4] Ohia O, et al., Phys. Rev. Lett. In Press (2012).

Ideal magnetohydrodynamic theory for localized interchange modes in toroidal anisotropic plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Tonghui, E-mail: thshi@ipp.ac.cn; Wan, B. N.; Sun, Y.

2016-08-15

Ideal magnetohydrodynamic theory for localized interchange modes is developed for toroidal plasmas with anisotropic pressure. The work extends the existing theories of Johnson and Hastie [Phys. Fluids 31, 1609 (1988)], etc., to the low n mode case, where n is the toroidal mode number. Also, the plasma compressibility is included, so that the coupling of the parallel motion to perpendicular one, i.e., the so-called apparent mass effect, is investigated in the anisotropic pressure case. The singular layer equation is obtained, and the generalized Mercier's criterion is derived.

Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution

PubMed Central

Schomer, Donald L.; Dehghani, Nima; Ulbert, Istvan; Cash, Sydney; Papavasiliou, Steve; Eisenberg, Solomon R.; Dale, Anders M.; Halgren, Eric

2010-01-01

Forward solutions with different levels of complexity are employed for localization of current generators, which are responsible for the electric and magnetic fields measured from the human brain. The influence of brain anisotropy on the forward solution is poorly understood. The goal of this study is to validate an anisotropic model for the intracranial electric forward solution by comparing with the directly measured ‘gold standard’. Dipolar sources are created at known locations in the brain and intracranial electroencephalogram (EEG) is recorded simultaneously. Isotropic models with increasing level of complexity are generated along with anisotropic models based on Diffusion tensor imaging (DTI). A Finite Element Method based forward solution is calculated and validated using the measured data. Major findings are (1) An anisotropic model with a linear scaling between the eigenvalues of the electrical conductivity tensor and water self-diffusion tensor in brain tissue is validated. The greatest improvement was obtained when the stimulation site is close to a region of high anisotropy. The model with a global anisotropic ratio of 10:1 between the eigenvalues (parallel: tangential to the fiber direction) has the worst performance of all the anisotropic models. (2) Inclusion of cerebrospinal fluid as well as brain anisotropy in the forward model is necessary for an accurate description of the electric field inside the skull. The results indicate that an anisotropic model based on the DTI can be constructed non-invasively and shows an improved performance when compared to the isotropic models for the calculation of the intracranial EEG forward solution. Electronic supplementary material The online version of this article (doi:10.1007/s10827-009-0205-z) contains supplementary material, which is available to authorized users. PMID:20063051

Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 2: image reconstruction.

PubMed

Correia, Teresa; Koch, Maximilian; Ale, Angelique; Ntziachristos, Vasilis; Arridge, Simon

2016-02-21

Fluorescence diffuse optical tomography (fDOT) provides 3D images of fluorescence distributions in biological tissue, which represent molecular and cellular processes. The image reconstruction problem is highly ill-posed and requires regularisation techniques to stabilise and find meaningful solutions. Quadratic regularisation tends to either oversmooth or generate very noisy reconstructions, depending on the regularisation strength. Edge preserving methods, such as anisotropic diffusion regularisation (AD), can preserve important features in the fluorescence image and smooth out noise. However, AD has limited ability to distinguish an edge from noise. We propose a patch-based anisotropic diffusion regularisation (PAD), where regularisation strength is determined by a weighted average according to the similarity between patches around voxels within a search window, instead of a simple local neighbourhood strategy. However, this method has higher computational complexity and, hence, we wavelet compress the patches (PAD-WT) to speed it up, while simultaneously taking advantage of the denoising properties of wavelet thresholding. Furthermore, structural information can be incorporated into the image reconstruction with PAD-WT to improve image quality and resolution. In this case, the weights used to average voxels in the image are calculated using the structural image, instead of the fluorescence image. The regularisation strength depends on both structural and fluorescence images, which guarantees that the method can preserve fluorescence information even when it is not structurally visible in the anatomical images. In part 1, we tested the method using a denoising problem. Here, we use simulated and in vivo mouse fDOT data to assess the algorithm performance. Our results show that the proposed PAD-WT method provides high quality and noise free images, superior to those obtained using AD.

THE STABILITY OF THE PINCH WITH ANISOTROPIC PRESSURE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jaggi, R.K.

1961-12-01

A dispersion equation was obtained for the stability of the pinch from the hydromagnetic equations supplemented by an equation for the pressure tensor of the ions. The dispersion equation was obtained for the marginal instability case only. It was observed that this dispersion equation coincides with the dispersion equation obtained from the Chew, Goldberger, and Low equations for the marginal instability case. It was concluded that the region of stability predicted from the equations that were used is slightly more than given by the kinetic equation used by Chandrasekhar, Kaufmann, and Watson. (auth)

Measurement and modeling of diffusion time dependence of apparent diffusion coefficient and fractional anisotropy in prostate tissue ex vivo.

PubMed

Bourne, Roger; Liang, Sisi; Panagiotaki, Eleftheria; Bongers, Andre; Sved, Paul; Watson, Geoffrey

2017-10-01

The purpose of this study was to measure and model the diffusion time dependence of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) derived from conventional prostate diffusion-weighted imaging methods as used in recommended multiparametric MRI protocols. Diffusion tensor imaging (DTI) was performed at 9.4 T with three radical prostatectomy specimens, with diffusion times in the range 10-120 ms and b-values 0-3000 s/mm 2 . ADC and FA were calculated from DTI measurements at b-values of 800 and 1600 s/mm 2 . Independently, a two-component model (restricted isotropic plus Gaussian anisotropic) was used to synthesize DTI data, from which ADC and FA were predicted and compared with the measured values. Measured ADC and FA exhibited a diffusion time dependence, which was closely predicted by the two-component model. ADC decreased by about 0.10-0.15 μm 2 /ms as diffusion time increased from 10 to 120 ms. FA increased with diffusion time at b-values of 800 and 1600 s/mm 2 but was predicted to be independent of diffusion time at b = 3000 s/mm 2 . Both ADC and FA exhibited diffusion time dependence that could be modeled as two unmixed water pools - one having isotropic restricted dynamics, and the other unrestricted anisotropic dynamics. These results highlight the importance of considering and reporting diffusion times in conventional ADC and FA calculations and protocol recommendations, and inform the development of improved diffusion methods for prostate cancer imaging. Copyright © 2017 John Wiley & Sons, Ltd.

Localized modes in optics of photonic liquid crystals with local anisotropy of absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belyakov, V. A., E-mail: bel1937@mail.ru, E-mail: bel@landau.ac.ru; Semenov, S. V.

2016-05-15

The localized optical modes in spiral photonic liquid crystals are theoretically studied for the certainty at the example of chiral liquid crystals (CLCs) for the case of CLC with an anisotropic local absorption. The model adopted here (absence of dielectric interfaces in the structures under investigation) makes it possible to get rid of mixing of polarizations on the surfaces of the CLC layer and of the defect structure and to reduce the corresponding equations to only the equations for light with polarization diffracting in the CLC. The dispersion equations determining connection of the edge mode (EM) and defect mode (DM)more » frequencies with the CLC layer parameters (anisotropy of local absorption, CLC order parameter) and other parameters of the DMS are obtained. Analytic expressions for the transmission and reflection coefficients of CLC layer and DMS for the case of CLC with an anisotropic local absorption are presented and analyzed. It is shown that the CLC layers with locally anisotropic absorption reduce the EM and DM lifetimes (and increase the lasing threshold) in the way different from the case of CLC with an isotropic local absorption. Due to the Borrmann effect revealing of which is different at the opposite stop-band edges in the case of CLC layers with an anisotropic local absorption the EM life-times for the EM frequencies at the opposite stop-bands edges may be significantly different. The options of experimental observations of the theoretically revealed phenomena are briefly discussed.« less

Localized modes in optics of photonic liquid crystals with local anisotropy of absorption

NASA Astrophysics Data System (ADS)

Belyakov, V. A.; Semenov, S. V.

2016-05-01

The localized optical modes in spiral photonic liquid crystals are theoretically studied for the certainty at the example of chiral liquid crystals (CLCs) for the case of CLC with an anisotropic local absorption. The model adopted here (absence of dielectric interfaces in the structures under investigation) makes it possible to get rid of mixing of polarizations on the surfaces of the CLC layer and of the defect structure and to reduce the corresponding equations to only the equations for light with polarization diffracting in the CLC. The dispersion equations determining connection of the edge mode (EM) and defect mode (DM) frequencies with the CLC layer parameters (anisotropy of local absorption, CLC order parameter) and other parameters of the DMS are obtained. Analytic expressions for the transmission and reflection coefficients of CLC layer and DMS for the case of CLC with an anisotropic local absorption are presented and analyzed. It is shown that the CLC layers with locally anisotropic absorption reduce the EM and DM lifetimes (and increase the lasing threshold) in the way different from the case of CLC with an isotropic local absorption. Due to the Borrmann effect revealing of which is different at the opposite stop-band edges in the case of CLC layers with an anisotropic local absorption the EM life-times for the EM frequencies at the opposite stop-bands edges may be significantly different. The options of experimental observations of the theoretically revealed phenomena are briefly discussed.

Measurement of Three-Dimensional Anisotropic Thermal Diffusivities for Carbon Fiber-Reinforced Plastics Using Lock-In Thermography

NASA Astrophysics Data System (ADS)

Ishizaki, Takuya; Nagano, Hosei

2015-11-01

A new measurement technique to measure the in-plane thermal diffusivity, the distribution of in-plane anisotropy, and the out-of-plane thermal diffusivity has been developed to evaluate the thermal conductivity of anisotropic materials such as carbon fiber-reinforced plastics (CFRPs). The measurements were conducted by using a laser-spot-periodic-heating method. The temperature of the sample is detected by using lock-in thermography. Thermography can analyze the phase difference between the periodic heat input and the temperature response of the sample. Two kinds of samples, unidirectional (UD) and cross-ply (CP) pitch-based CFRPs, were fabricated and tested in an atmospheric condition. All carbon fibers of the UD sample run in one direction [90°]. The carbon fibers of the CP sample run in two directions [0°/90°]. It is found that, by using lock-in thermography, it is able to visualize the thermal anisotropy and calculate the angular dependence of the in-plane thermal diffusivity of the CFRPs. The out-of-plane thermal diffusivity of CFRPs was also measured by analyzing the frequency dependence of the phase difference.

Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE) on a 3T clinical scanner

PubMed Central

Baete, Steven H.; Cho, Gene; Sigmund, Eric E.

2013-01-01

This paper describes the concepts and implementation of an MRI method, Multiple Echo Diffusion Tensor Acquisition Technique (MEDITATE), which is capable of acquiring apparent diffusion tensor maps in two scans on a 3T clinical scanner. In each MEDITATE scan, a set of RF-pulses generates multiple echoes whose amplitudes are diffusion-weighted in both magnitude and direction by a pattern of diffusion gradients. As a result, two scans acquired with different diffusion weighting strengths suffice for accurate estimation of diffusion tensor imaging (DTI)-parameters. The MEDITATE variation presented here expands previous MEDITATE approaches to adapt to the clinical scanner platform, such as exploiting longitudinal magnetization storage to reduce T2-weighting. Fully segmented multi-shot Cartesian encoding is used for image encoding. MEDITATE was tested on isotropic (agar gel), anisotropic diffusion phantoms (asparagus), and in vivo skeletal muscle in healthy volunteers with cardiac-gating. Comparisons of accuracy were performed with standard twice-refocused spin echo (TRSE) DTI in each case and good quantitative agreement was found between diffusion eigenvalues, mean diffusivity, and fractional anisotropy derived from TRSE-DTI and from the MEDITATE sequence. Orientation patterns were correctly reproduced in both isotropic and anisotropic phantoms, and approximately so for in vivo imaging. This illustrates that the MEDITATE method of compressed diffusion encoding is feasible on the clinical scanner platform. With future development and employment of appropriate view-sharing image encoding this technique may be used in clinical applications requiring time-sensitive acquisition of DTI parameters such as dynamical DTI in muscle. PMID:23828606

Generation of anisotropy in turbulent flows subjected to rapid distortion

NASA Astrophysics Data System (ADS)

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

2018-01-01

A computational tool for the anisotropic time-evolution of the spectral velocity correlation tensor is presented. We operate in the linear, rapid distortion limit of the mean-field-coupled equations. Each term of the equations is written in the form of an expansion to arbitrary order in the basis of irreducible representations of the SO(3) symmetry group. The computational algorithm for this calculation solves a system of coupled equations for the scalar weights of each generated anisotropic mode. The analysis demonstrates that rapid distortion rapidly but systematically generates higher-order anisotropic modes. To maintain a tractable computation, the maximum number of rotational modes to be used in a given calculation is specified a priori. The computed Reynolds stress converges to the theoretical result derived by Batchelor and Proudman [Quart. J. Mech. Appl. Math. 7, 83 (1954), 10.1093/qjmam/7.1.83] if a sufficiently large maximum number of rotational modes is utilized; more modes are required to recover the solution at later times. The emergence and evolution of the underlying multidimensional space of functions is presented here using a 64-mode calculation. Alternative implications for modeling strategies are discussed.

THEMIS Observations of the Magnetopause Electron Diffusion Region: Large Amplitude Waves and Heated Electrons

NASA Technical Reports Server (NTRS)

Tang, Xiangwei; Cattell, Cynthia; Dombeck, John; Dai, Lei; Wilson, Lynn B. III; Breneman, Aaron; Hupack, Adam

2013-01-01

We present the first observations of large amplitude waves in a well-defined electron diffusion region based on the criteria described by Scudder et al at the subsolar magnetopause using data from one Time History of Events and Macroscale Interactions during Substorms (THEMIS) satellite. These waves identified as whistler mode waves, electrostatic solitary waves, lower hybrid waves, and electrostatic electron cyclotron waves, are observed in the same 12 s waveform capture and in association with signatures of active magnetic reconnection. The large amplitude waves in the electron diffusion region are coincident with abrupt increases in electron parallel temperature suggesting strong wave heating. The whistler mode waves, which are at the electron scale and which enable us to probe electron dynamics in the diffusion region were analyzed in detail. The energetic electrons (approx. 30 keV) within the electron diffusion region have anisotropic distributions with T(sub e(right angle))/T(sub e(parallel)) > 1 that may provide the free energy for the whistler mode waves. The energetic anisotropic electrons may be produced during the reconnection process. The whistler mode waves propagate away from the center of the "X-line" along magnetic field lines, suggesting that the electron diffusion region is a possible source region of the whistler mode waves.

Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goffin, Mark A., E-mail: mark.a.goffin@gmail.com; Buchan, Andrew G.; Dargaville, Steven

2015-01-15

A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specifiedmore » functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.« less

Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic media

NASA Astrophysics Data System (ADS)

Liu, Ying; Xu, Zhenhuan; Li, Yuguo

2018-04-01

We present a goal-oriented adaptive finite element (FE) modelling algorithm for 3-D magnetotelluric fields in generally anisotropic conductivity media. The model consists of a background layered structure, containing anisotropic blocks. Each block and layer might be anisotropic by assigning to them 3 × 3 conductivity tensors. The second-order partial differential equations are solved using the adaptive finite element method (FEM). The computational domain is subdivided into unstructured tetrahedral elements, which allow for complex geometries including bathymetry and dipping interfaces. The grid refinement process is guided by a global posteriori error estimator and is performed iteratively. The system of linear FE equations for electric field E is solved with a direct solver MUMPS. Then the magnetic field H can be found, in which the required derivatives are computed numerically using cubic spline interpolation. The 3-D FE algorithm has been validated by comparisons with both the 3-D finite-difference solution and 2-D FE results. Two model types are used to demonstrate the effects of anisotropy upon 3-D magnetotelluric responses: horizontal and dipping anisotropy. Finally, a 3D sea hill model is modelled to study the effect of oblique interfaces and the dipping anisotropy.

Calculations of key magnetospheric parameters using the isotropic and anisotropic SPSU global MHD code

NASA Astrophysics Data System (ADS)

Samsonov, Andrey; Gordeev, Evgeny; Sergeev, Victor

2017-04-01

As it was recently suggested (e.g., Gordeev et al., 2015), the global magnetospheric configuration can be characterized by a set of key parameters, such as the magnetopause distance at the subsolar point and on the terminator plane, the magnetic field in the magnetotail lobe and the plasma sheet thermal pressure, the cross polar cap electric potential drop and the total field-aligned current. For given solar wind conditions, the values of these parameters can be obtained from both empirical models and global MHD simulations. We validate the recently developed global MHD code SPSU-16 using the key magnetospheric parameters mentioned above. The code SPSU-16 can calculate both the isotropic and anisotropic MHD equations. In the anisotropic version, we use the modified double-adiabatic equations in which the T⊥/T∥ (the ratio of perpendicular to parallel thermal pressures) has been bounded from above by the mirror and ion-cyclotron thresholds and from below by the firehose threshold. The results of validation for the SPSU-16 code well agree with the previously published results of other global codes. Some key parameters coincide in the isotropic and anisotropic MHD simulations, but some are different.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress

NASA Astrophysics Data System (ADS)

Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-01

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

Needlelike motion of prolate ellipsoids in the sea of spheres

NASA Astrophysics Data System (ADS)

Vasanthi, R.; Ravichandran, S.; Bagchi, Biman

2001-05-01

Molecular dynamics simulations of translational motion of isolated prolate ellipsoids in the sea of spheres have been carried out for several different values of the aspect ratio (κ), obtained by changing either the length or the diameter of the ellipsoids, at several different solvent densities. The interaction among the spheres is given by the Lennard-Jones pair potential while that between spheres and ellipsoids is given by a modified Gay-Berne potential. Both the mean-square displacements of the center of mass of the ellipsoids and their orientational time correlation function have been calculated. It is found that at short to intermediate times, the motion of ellipsoids is anisotropic and primarily needlelike—the molecules prefer to move parallel to their long axis. The ratio of these two diffusion constants (D∥ and D⊥) approaches κ, suggesting a decoupling of D∥ from the length of the ellipsoid. The diffusion becomes isotropic in the long time with the total diffusion coefficient given by D∥+2D⊥. The crossover from the anisotropic to the isotropic diffusion is surprisingly sharp and clear in most cases.

Deducing Shape of Anisotropic Particles in Solution from Light Scattering: Spindles and Nanorods

NASA Astrophysics Data System (ADS)

Tsuper, Ilona; Terrano, Daniel; Streletzky, Kiril A.; Dement'eva, Olga V.; Semyonov, Sergey A.; Rudoy, Victor M.

Depolarized Dynamic Light Scattering (DDLS) enables to measure rotational and translational diffusion of nanoparticles suspended in solution. The particle size, shape, diffusion, and interactions can then be inferred from the DDLS data using various models of diffusion. Incorporating the technique of DDLS to analyze the dimensions of easily imaged elongated particles, such as Iron (III) oxyhydroxide (FeOOH) Spindles and gold Nanorods, allows testing of the models for rotational and translational diffusion of elongated particles in solution. This, in turn, can help to better interpret DDLS data on hard-to-image anisotropic wet systems such as micelles, microgels, and protein complexes. This study focused on FeOOH Spindles and gold nanorod particles. The light scattering results on FeOOH analyzed using the basic model of non-interacting prolate ellipsoids yielded dimensions within 17% of the SEM measured dimensions. The dimensions of gold nanorod obtained from the straight cylinder model of DDLS data provided results within 25% of the sizes that were obtained from TEM. The nanorod DDLS data was also analyzed by a spherocylinder model.

Diffusion, Dispersion, and Uncertainty in Anisotropic Fractal Porous Media

NASA Astrophysics Data System (ADS)

Monnig, N. D.; Benson, D. A.

2007-12-01

Motivated by field measurements of aquifer hydraulic conductivity (K), recent techniques were developed to construct anisotropic fractal random fields, in which the scaling, or self-similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these 2-D "operator-scaling" fractional Brownian motion (fBm) ln(K) fields. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-stratified growth must be the result of other demonstrable factors, such as initial plume size. The addition of large local dispersion and diffusion does not significantly change the effective longitudinal dispersivity of the plumes. In the presence of significant local dispersion or diffusion, the concentration coefficient of variation CV={σc}/{\\langle c \\rangle} remains large at the leading edge of the plumes. This indicates that even with considerable mixing due to dispersion or diffusion, there is still substantial uncertainty in the leading edge of a plume moving in fractal porous media.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress.

PubMed

Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-21

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Passive Imaging in Nondiffuse Acoustic Wavefields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mulargia, Francesco; Castellaro, Silvia

2008-05-30

A main property of diffuse acoustic wavefields is that, taken any two points, each of them can be seen as the source of waves and the other as the recording station. This property is shown to follow simply from array azimuthal selectivity and Huygens principle in a locally isotropic wavefield. Without time reversal, this property holds approximately also in anisotropic azimuthally uniform wavefields, implying much looser constraints for undistorted passive imaging than those required by a diffuse field. A notable example is the seismic noise field, which is generally nondiffuse, but is found to be compatible with a finite aperturemore » anisotropic uniform wavefield. The theoretical predictions were confirmed by an experiment on seismic noise in the mainland of Venice, Italy.« less

Analysis and correction of gradient nonlinearity bias in ADC measurements

PubMed Central

Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.

2013-01-01

Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Middleton, Chad A.; Stanley, Ethan

2011-10-15

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore » the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.« less

The Shock and Vibration Digest. Volume 16, Number 11

DTIC Science & Technology

1984-11-01

wave [19], a secular equation for Rayleigh waves on ing, seismic risk, and related problems are discussed. the surface of an anisotropic half-space...waves in an !so- tive equation of an elastic-plastic rack medium was....... tropic linear elastic half-space with plane material used; the coefficient...pair of semi-linear hyperbolic partial differential -- " Conditions under which the equations of motion equations governing slow variations in amplitude

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

NASA Astrophysics Data System (ADS)

Amooshahi, Majid; Shoughi, Ali

2018-05-01

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Metric anisotropies and emergent anisotropic hydrodynamics

NASA Astrophysics Data System (ADS)

Dash, Ashutosh; Jaiswal, Amaresh

2018-05-01

Expansion of a locally equilibrated fluid is considered in an anisotropic space-time given by the Bianchi type-I metric. Starting from the isotropic equilibrium phase-space distribution function in the local rest frame, we obtain expressions for components of the energy-momentum tensor and conserved current, such as number density, energy density, and pressure components. In the case of an axissymmetric Bianchi type-I metric, we show that they are identical to those obtained within the setup of anisotropic hydrodynamics. We further consider the case in which the Bianchi type-I metric is a vacuum solution of the Einstein equation: the Kasner metric. For the axissymmetric Kasner metric, we discuss the implications of our results in the context of anisotropic hydrodynamics.

Generalized analytic solutions and response characteristics of magnetotelluric fields on anisotropic infinite faults

NASA Astrophysics Data System (ADS)

Bing, Xue; Yicai, Ji

2018-06-01

In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.

Refined BCF-type boundary conditions for mesoscale surface step dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Renjie; Ackerman, David M.; Evans, James W.

Deposition on a vicinal surface with alternating rough and smooth steps is described by a solid-on-solid model with anisotropic interactions. Kinetic Monte Carlo (KMC) simulations of the model reveal step pairing in the absence of any additional step attachment barriers. We explore the description of this behavior within an analytic Burton-Cabrera-Frank (BCF)-type step dynamics treatment. Without attachment barriers, conventional kinetic coefficients for the rough and smooth steps are identical, as are the predicted step velocities for a vicinal surface with equal terrace widths. However, we determine refined kinetic coefficients from a two-dimensional discrete deposition-diffusion equation formalism which accounts for stepmore » structure. These coefficients are generally higher for rough steps than for smooth steps, reflecting a higher propensity for capture of diffusing terrace adatoms due to a higher kink density. Such refined coefficients also depend on the local environment of the step and can even become negative (corresponding to net detachment despite an excess adatom density) for a smooth step in close proximity to a rough step. Incorporation of these refined kinetic coefficients into a BCF-type step dynamics treatment recovers quantitatively the mesoscale step-pairing behavior observed in the KMC simulations.« less

Refined BCF-type boundary conditions for mesoscale surface step dynamics

DOE PAGES

Zhao, Renjie; Ackerman, David M.; Evans, James W.

2015-06-24

Deposition on a vicinal surface with alternating rough and smooth steps is described by a solid-on-solid model with anisotropic interactions. Kinetic Monte Carlo (KMC) simulations of the model reveal step pairing in the absence of any additional step attachment barriers. We explore the description of this behavior within an analytic Burton-Cabrera-Frank (BCF)-type step dynamics treatment. Without attachment barriers, conventional kinetic coefficients for the rough and smooth steps are identical, as are the predicted step velocities for a vicinal surface with equal terrace widths. However, we determine refined kinetic coefficients from a two-dimensional discrete deposition-diffusion equation formalism which accounts for stepmore » structure. These coefficients are generally higher for rough steps than for smooth steps, reflecting a higher propensity for capture of diffusing terrace adatoms due to a higher kink density. Such refined coefficients also depend on the local environment of the step and can even become negative (corresponding to net detachment despite an excess adatom density) for a smooth step in close proximity to a rough step. Incorporation of these refined kinetic coefficients into a BCF-type step dynamics treatment recovers quantitatively the mesoscale step-pairing behavior observed in the KMC simulations.« less

Magnetic pumping of the solar wind

NASA Astrophysics Data System (ADS)

Egedal, Jan; Lichko, Emily; Daughton, William

2015-11-01

The transport of matter and radiation in the solar wind and terrestrial magnetosphere is a complicated problem involving competing processes of charged particles interacting with electric and magnetic fields. Given the rapid expansion of the solar wind, it would be expected that superthermal electrons originating in the corona would cool rapidly as a function of distance to the Sun. However, this is not observed, and various models have been proposed as candidates for heating the solar wind. In the compressional pumping mechanism explored by Fisk and Gloeckler particles are accelerated by random compressions by the interplanetary wave turbulence. This theory explores diffusion due to spatial non-uniformities and provides a mechanism for redistributing particle. For investigation of a related but different heating mechanism, magnetic pumping, in our work we include diffusion of anisotropic features that develops in velocity space. The mechanism allows energy to be transferred to the particles directly from the turbulence. Guided by kinetic simulations a theory is derived for magnetic pumping. At the heart of this work is a generalization of the Parker Equation to capture the role of the pressure anisotropy during the pumping process. Supported by NASA grant NNX15AJ73G.

Indentation of poroviscoelastic vocal fold tissue using an atomic force microscope.

PubMed

Heris, Hossein K; Miri, Amir K; Tripathy, Umakanta; Barthelat, Francois; Mongeau, Luc

2013-12-01

The elastic properties of the vocal folds (VFs) vary as a function of depth relative to the epithelial surface. The poroelastic anisotropic properties of porcine VFs, at various depths, were measured using atomic force microscopy (AFM)-based indentation. The minimum tip diameter to effectively capture the local properties was found to be 25µm, based on nonlinear laser scanning microscopy data and image analysis. The effects of AFM tip dimensions and AFM cantilever stiffness were systematically investigated. The indentation tests were performed along the sagittal and coronal planes for an evaluation of the VF anisotropy. Hertzian contact theory was used along with the governing equations of linear poroelasticity to calculate the diffusivity coefficient of the tissue from AFM indentation creep testing. The permeability coefficient of the porcine VF was found to be 1.80±0.32×10(-15)m(4)/Ns. Copyright © 2013 Elsevier Ltd. All rights reserved.

Postcoalescence evolution of growth stress in polycrystalline films.

PubMed

González-González, A; Polop, C; Vasco, E

2013-02-01

The growth stress generated once grains coalesce in Volmer-Weber-type thin films is investigated by time-multiscale simulations comprising complementary modules of (i) finite-element modeling to address the interactions between grains happening at atomic vibration time scales (~0.1 ps), (ii) dynamic scaling to account for the surface stress relaxation via morphology changes at surface diffusion time scales (~μs-ms), and (iii) the mesoscopic rate equation approach to simulate the bulk stress relaxation at deposition time scales (~sec-h). On the basis of addressing the main experimental evidence reported so far on the topic dealt with, the simulation results provide key findings concerning the interplay between anisotropic grain interactions at complementary space scales, deposition conditions (such as flux and mobility), and mechanisms of stress accommodation-relaxation, which underlies the origin, nature and spatial distribution, and the flux dependence of the postcoalescence growth stress.

Indentation of poroviscoelastic vocal fold tissue using an atomic force microscope☆

PubMed Central

Heris, Hossein K.; Miri, Amir K.; Tripathy, Umakanta; Barthelat, Francois; Mongeau, Luc

2013-01-01

The elastic properties of the vocal folds (VFs) vary as a function of depth relative to the epithelial surface. The poroelastic anisotropic properties of porcine VFs, at various depths, were measured using atomic force microscopy (AFM)-based indentation. The minimum tip diameter to effectively capture the local properties was found to be 25 µm, based on nonlinear laser scanning microscopy data and image analysis. The effects of AFM tip dimensions and AFM cantilever stiffness were systematically investigated. The indentation tests were performed along the sagittal and coronal planes for an evaluation of the VF anisotropy. Hertzian contact theory was used along with the governing equations of linear poroelasticity to calculate the diffusivity coefficient of the tissue from AFM indentation creep testing. The permeability coefficient of the porcine VF was found to be 1.80 ± 0.32 × 10−15 m4/N s. PMID:23829979

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Cracking on anisotropic neutron stars

NASA Astrophysics Data System (ADS)

Setiawan, A. M.; Sulaksono, A.

2017-07-01

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

He-3, Pierre Morel and Me—Early Work on Anisotropic Superfluidity

NASA Astrophysics Data System (ADS)

Anderson, Philip W.

2011-08-01

The idea that there are alternative, anisotropic solutions of BCS equations, which might apply to He-3, surfaced independently in at least three places, one of which was Pierre Morel's thesis project (for the ENS, under me at Bell Labs) I was skeptical of quantitative estimates of transition temperatures and instead focused, with Pierre, on conceptual and experimental properties of such states.

Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

NASA Astrophysics Data System (ADS)

Chen, Dongxiang; Wang, Yuxi; Zhang, Zhifei

2018-05-01

By using the paralinearization technique, we prove the well-posedness of the Prandtl equation for monotonic data in anisotropic Sobolev space with exponential weight and low regularity. The proof is very elementary, thus is expected to provide a new possible way for the zero-viscosity limit problem of the Navier-Stokes equations with the non-slip boundary condition.

Mechanisms Inducing Jet Rotation in Shear-Formed Shaped-Charge Liners.

DTIC Science & Technology

1990-03-01

of deviatoric strain, and compressibility affects only the equation of state , not the deviatoric stress /strain relation. An anisotropic formulation is...strains, a more accurate scalar equation of state should simultaneously be employed to account for non-linear compressibility effects . A4 A.3 Elastic... obtainable knowing the previous and present cycles’ average stress . However, many non-linear equations

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

NASA Astrophysics Data System (ADS)

Kumari, Nirmala; Chattopadhyay, Amares; Singh, Abhishek K.; Sahu, Sanjeev A.

2017-03-01

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker's asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot's gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

An artifacts removal post-processing for epiphyseal region-of-interest (EROI) localization in automated bone age assessment (BAA)

PubMed Central

2011-01-01

Background Segmentation is the most crucial part in the computer-aided bone age assessment. A well-known type of segmentation performed in the system is adaptive segmentation. While providing better result than global thresholding method, the adaptive segmentation produces a lot of unwanted noise that could affect the latter process of epiphysis extraction. Methods A proposed method with anisotropic diffusion as pre-processing and a novel Bounded Area Elimination (BAE) post-processing algorithm to improve the algorithm of ossification site localization technique are designed with the intent of improving the adaptive segmentation result and the region-of interest (ROI) localization accuracy. Results The results are then evaluated by quantitative analysis and qualitative analysis using texture feature evaluation. The result indicates that the image homogeneity after anisotropic diffusion has improved averagely on each age group for 17.59%. Results of experiments showed that the smoothness has been improved averagely 35% after BAE algorithm and the improvement of ROI localization has improved for averagely 8.19%. The MSSIM has improved averagely 10.49% after performing the BAE algorithm on the adaptive segmented hand radiograph. Conclusions The result indicated that hand radiographs which have undergone anisotropic diffusion have greatly reduced the noise in the segmented image and the result as well indicated that the BAE algorithm proposed is capable of removing the artifacts generated in adaptive segmentation. PMID:21952080

CFD-ACE+: a CAD system for simulation and modeling of MEMS

NASA Astrophysics Data System (ADS)

Stout, Phillip J.; Yang, H. Q.; Dionne, Paul; Leonard, Andy; Tan, Zhiqiang; Przekwas, Andrzej J.; Krishnan, Anantha

1999-03-01

Computer aided design (CAD) systems are a key to designing and manufacturing MEMS with higher performance/reliability, reduced costs, shorter prototyping cycles and improved time- to-market. One such system is CFD-ACE+MEMS, a modeling and simulation environment for MEMS which includes grid generation, data visualization, graphical problem setup, and coupled fluidic, thermal, mechanical, electrostatic, and magnetic physical models. The fluid model is a 3D multi- block, structured/unstructured/hybrid, pressure-based, implicit Navier-Stokes code with capabilities for multi- component diffusion, multi-species transport, multi-step gas phase chemical reactions, surface reactions, and multi-media conjugate heat transfer. The thermal model solves the total enthalpy from of the energy equation. The energy equation includes unsteady, convective, conductive, species energy, viscous dissipation, work, and radiation terms. The electrostatic model solves Poisson's equation. Both the finite volume method and the boundary element method (BEM) are available for solving Poisson's equation. The BEM method is useful for unbounded problems. The magnetic model solves for the vector magnetic potential from Maxwell's equations including eddy currents but neglecting displacement currents. The mechanical model is a finite element stress/deformation solver which has been coupled to the flow, heat, electrostatic, and magnetic calculations to study flow, thermal electrostatically, and magnetically included deformations of structures. The mechanical or structural model can accommodate elastic and plastic materials, can handle large non-linear displacements, and can model isotropic and anisotropic materials. The thermal- mechanical coupling involves the solution of the steady state Navier equation with thermoelastic deformation. The electrostatic-mechanical coupling is a calculation of the pressure force due to surface charge on the mechanical structure. Results of CFD-ACE+MEMS modeling of MEMS such as cantilever beams, accelerometers, and comb drives are discussed.

Callosal tracts and patterns of hemispheric dominance: a combined fMRI and DTI study.

PubMed

Häberling, Isabelle S; Badzakova-Trajkov, Gjurgjica; Corballis, Michael C

2011-01-15

Left-hemispheric dominance for language and right-hemispheric dominance for spatial processing are distinctive characteristics of the human brain. However, variations of these hemispheric asymmetries have been observed, with a minority showing crowding of both functions to the same hemisphere or even a mirror reversal of the typical lateralization pattern. Here, we used diffusion tensor imaging and functional magnetic imaging to investigate the role of the corpus callosum in participants with atypical hemispheric dominance. The corpus callosum was segmented according to the projection site of the underlying fibre tracts. Analyses of the microstructure of the identified callosal segments revealed that atypical hemispheric dominance for language was associated with high anisotropic diffusion through the corpus callosum as a whole. This effect was most evident in participants with crowding of both functions to the right. The enhanced anisotropic diffusion in atypical hemispheric dominance implies that in these individuals the two hemispheres are more heavily interconnected. Copyright © 2010 Elsevier Inc. All rights reserved.

MULTISCALE TENSOR ANISOTROPIC FILTERING OF FLUORESCENCE MICROSCOPY FOR DENOISING MICROVASCULATURE.

PubMed

Prasath, V B S; Pelapur, R; Glinskii, O V; Glinsky, V V; Huxley, V H; Palaniappan, K

2015-04-01

Fluorescence microscopy images are contaminated by noise and improving image quality without blurring vascular structures by filtering is an important step in automatic image analysis. The application of interest here is to automatically extract the structural components of the microvascular system with accuracy from images acquired by fluorescence microscopy. A robust denoising process is necessary in order to extract accurate vascular morphology information. For this purpose, we propose a multiscale tensor with anisotropic diffusion model which progressively and adaptively updates the amount of smoothing while preserving vessel boundaries accurately. Based on a coherency enhancing flow with planar confidence measure and fused 3D structure information, our method integrates multiple scales for microvasculature preservation and noise removal membrane structures. Experimental results on simulated synthetic images and epifluorescence images show the advantage of our improvement over other related diffusion filters. We further show that the proposed multiscale integration approach improves denoising accuracy of different tensor diffusion methods to obtain better microvasculature segmentation.

Stability enhancement of high Prandtl number chaotic convection in an anisotropic porous layer with feedback control

NASA Astrophysics Data System (ADS)

Mahmud, M. N.

2018-04-01

The chaotic dynamical behaviour of thermal convection in an anisotropic porous layer subject to gravity, heated from below and cooled from above, is studied based on theory of dynamical system in the presence of feedback control. The extended Darcy model, which includes the time derivative has been employed in the momentum equation to derive a low dimensional Lorenz-like equation by using Galerkin-truncated approximation. The classical fourth-order Runge-Kutta method is used to obtain the numerical solution in order to exemplify the dynamics of the nonlinear autonomous system. The results show that stability enhancement of chaotic convection is feasible via feedback control.

Instability analysis of expansion-free sphere in f(𝒢) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Ikram, Ayesha

The aim of this paper is to study the dynamical instability of expansion-free spherically symmetric anisotropic fluid in the framework of f(𝒢) gravity. We apply perturbation scheme of the first-order to the metric functions as well as matter variables and construct modified field equations for both static and perturbed configurations using power-law f(𝒢) model. To discuss the instability dynamics, we use the contracted Bianchi identities to formulate the dynamical equations in both Newtonian and post-Newtonian regimes. It is found that the range of instability is independent of adiabatic index for expansion-free fluid but depends on anisotropic pressures, energy density and Gauss-Bonnet (GB) terms.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

GRIZZLY Model of Multi-Reactive Species Diffusion, Moisture/Heat Transfer and Alkali-Silica Reaction for Simulating Concrete Aging and Degradation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Hai; Spencer, Benjamin W.; Cai, Guowei

Concrete is widely used in the construction of nuclear facilities because of its structural strength and its ability to shield radiation. The use of concrete in nuclear power plants for containment and shielding of radiation and radioactive materials has made its performance crucial for the safe operation of the facility. As such, when life extension is considered for nuclear power plants, it is critical to have accurate and reliable predictive tools to address concerns related to various aging processes of concrete structures and the capacity of structures subjected to age-related degradation. The goal of this report is to document themore » progress of the development and implementation of a fully coupled thermo-hydro-mechanical-chemical model in GRIZZLY code with the ultimate goal to reliably simulate and predict long-term performance and response of aged NPP concrete structures subjected to a number of aging mechanisms including external chemical attacks and volume-changing chemical reactions within concrete structures induced by alkali-silica reactions and long-term exposure to irradiation. Based on a number of survey reports of concrete aging mechanisms relevant to nuclear power plants and recommendations from researchers in concrete community, we’ve implemented three modules during FY15 in GRIZZLY code, (1) multi-species reactive diffusion model within cement materials; (2) coupled moisture and heat transfer model in concrete; and (3) anisotropic, stress-dependent, alkali-silica reaction induced swelling model. The multi-species reactive diffusion model was implemented with the objective to model aging of concrete structures subjected to aggressive external chemical attacks (e.g., chloride attack, sulfate attack, etc.). It considers multiple processes relevant to external chemical attacks such as diffusion of ions in aqueous phase within pore spaces, equilibrium chemical speciation reactions and kinetic mineral dissolution/precipitation. The moisture/heat transfer module was implemented to simulate long-term spatial and temporal evolutions of the moisture and temperature fields within concrete structures at both room and elevated temperatures. The ASR swelling model implemented in GRIZZLY code can simulate anisotropic expansions of ASR gel under either uniaxial, biaxial and triaxial stress states, and can be run simultaneously with the moisture/heat transfer model and coupled with various elastic/inelastic solid mechanics models that were implemented in GRIZZLY code previously. This report provides detailed descriptions of the governing equations, constitutive equations and numerical algorithms of the three modules implemented in GRIZZLY during FY15, simulation results of example problems and model validation results by comparing simulations with available experimental data reported in the literature. The close match between the experiments and simulations clearly demonstrate the potential of GRIZZLY code for reliable evaluation and prediction of long-term performance and response of aged concrete structures in nuclear power plants.« less

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Modeling the effect of orientation on the shock response of a damageable composite material

NASA Astrophysics Data System (ADS)

Lukyanov, Alexander A.

2012-10-01

A carbon fiber-epoxy composite (CFEC) shock response in the through thickness orientation and in one of the fiber directions is significantly different. The hydrostatic pressure inside anisotropic materials depends on deviatoric strain components as well as volumetric strain. Non-linear effects, such as shock effects, can be incorporated through the volumetric straining in the material. Thus, a new basis is required to couple the anisotropic material stiffness and strength with anisotropic shock effects, associated energy dependence, and damage softening process. This article presents these constitutive equations for shock wave modeling of a damageable carbon fiber-epoxy composite. Modeling the effect of fiber orientation on the shock response of a CFEC has been performed using a generalized decomposition of the stress tensor [A. A. Lukyanov, Int. J. Plast. 24, 140 (2008)] and Mie-Grüneisen's extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked CFEC materials. The three-wave structure (non-linear anisotropic, fracture, and isotropic elastic waves) that accompanies damage softening process is also proposed in this work for describing CFEC behavior under shock loading which allows to remove any discontinuities observed in the linear case for relation between shock velocities and particle velocities [A. A. Lukyanov, Eur. Phys. J. B 74, 35 (2010)]. Different Hugoniot stress levels are obtained when the material is impacted in different directions; their good agreement with the experiment demonstrates that the anisotropic equation of state, strength, and damage model are adequate for the simulation of shock wave propagation within damageable CFEC material. Remarkably, in the through thickness orientation, the material behaves similar to a simple polymer whereas in the fiber direction, the proposed in this paper model explains an initial ramp, before at sufficiently high stresses, and a much faster rising shock above it. The numerical results for shock wave modeling using proposed constitutive equations are presented, discussed, and future studies are outlined.

Noise-induced drift in two-dimensional anisotropic systems

NASA Astrophysics Data System (ADS)

Farago, Oded

2017-10-01

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Stability of anisotropic self-gravitating fluids

NASA Astrophysics Data System (ADS)

Ahmad, S.; Jami, A. Rehman; Mughal, M. Z.

2018-06-01

The aim of this paper is to study the stability as well as the existence of self-gravitating anisotropic fluids in Λ-dominated era. Taking a cylindrically symmetric and static spacetime, we computed the corresponding equations of motion in the background of anisotropic fluid distributions. The realistic formulation of energy momentum tensor as well as theoretical model of the scale factors are considered in order to describe some physical properties of the anisotropic fluids. To find the stability of the compact star, we have used Herrera’s technique which is based on finding the radial and the transverse components of the speed of sound. Moreover, the behaviors of other physical quantities are also discussed like anisotropy, matching conditions of interior metric and exterior metric and compactness of the compact structures are also discussed.

Elasticity and hydrodynamic properties of ``doped solvent dilute'' lamellar phases

NASA Astrophysics Data System (ADS)

Nallet, Frédéric; Roux, Didier; Quilliet, Catherine; Fabre, Pascale; Milner, Scott T.

1994-09-01

The equilibrium fluctuations and weakly out-of-equilibrium relaxation properties of “doped solvent" dilute lamellar phases are investigated, both theoretically and experimentally, in the low-frequency, long-wavelength limit. The physical system of interest is a three-component smectic A lyotropic liquid crystal where surfactant bilayers infinite in extent are periodically stacked along one direction in space and separated by a colloidal solution. Two experimentally relevant modes are found in the lowest frequency part of the fluctuation spectrum of such multicomponent systems. Both are associated to the relaxation of coupled layer displacement and colloid concentration waves. In the limit of small coupling, one mode is close to the well-known undulation/baroclinic mode of two-component lamellar phases, while the other corresponds to the Brownian diffusive motion of the colloid in an anisotropic medium. Elastic constants of the smectic liquid crystal and diffusion parameters of the colloidal solution may be deduced from a measurement of the anisotropic dispersion relation of these two modes, as illustrated by dynamic light scattering experiments on the ferrosmectic system. Les fluctuations à l'équilibre ainsi que la relaxation des états légèrement en dehors de l'équilibre des phases lamellaires à “solvant dopé” sont étudiées, aussi bien d'un point de vue théorique qu'expérimental, dans la limite de basses fréquences et de grandes longueurs d'onde. Les systèmes décrits sont des cristaux-liquides smectiques A lyotropes formés de trois constituants : un tensioactif en solution dans une suspension colloïdale forme des bicouches de grande extension latérale qui s'empilent de façon périodique le long d'une direction dans l'espace. Avec de tels systèmes anisotropes et à plusieurs constituants deux modes présents dans la partie à basse fréquence du spectre des fluctuations (associés à la relaxation d'ondes, couplées, de concentration colloïdale et de déplacement des couches smectiques) ont une certaine importance expérimentale. Dans la limite d'un couplage faible, l'un des deux modes est similaire au mode barocline des phases lamellaires à deux constituants ; le second s'identifie au mouvement brownien de diffusion d'un colloïde dans un substrat anisotrope. Les constantes élastiques du cristal liquide smectique de même que le coefficient de diffusion du colloïde peuvent en principe être déduits de la mesure des relations anisotropes de dispersion de ces deux modes ; cela est illustré par des expériences de diffusion quasi-élastique de la lumière sur des ferrosmectiques.

Anisotropic Thermal Diffusivities of Plasma-Sprayed Thermal Barrier Coatings

NASA Astrophysics Data System (ADS)

Akoshima, Megumi; Takahashi, Satoru

2017-09-01

Thermal barrier coatings (TBCs) are used to shield the blades of gas turbines from heat and wear. There is a pressing need to evaluate the thermal conductivity of TBCs in the thermal design of advanced gas turbines with high energy efficiency. These TBCs consist of a ceramic-based top coat and a bond coat on a superalloy substrate. Usually, the focus is on the thermal conductivity in the thickness direction of the TBC because heat tends to diffuse from the surface of the top coat to the substrate. However, the in-plane thermal conductivity is also important in the thermal design of gas turbines because the temperature distribution within the turbine cannot be ignored. Accordingly, a method is developed in this study for measuring the in-plane thermal diffusivity of the top coat. Yttria-stabilized zirconia top coats are prepared by thermal spraying under different conditions. The in-plane and cross-plane thermal diffusivities of the top coats are measured by the flash method to investigate the anisotropy of thermal conduction in a TBC. It is found that the in-plane thermal diffusivity is higher than the cross-plane one for each top coat and that the top coats have significantly anisotropic thermal diffusivity. The cross-sectional and in-plane microstructures of the top coats are observed, from which their porosities are evaluated. The thermal diffusivity and its anisotropy are discussed in detail in relation to microstructure and porosity.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Prestack reverse time migration for tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Jang, Seonghyung; Hien, Doan Huy

2013-04-01

According to having interest in unconventional resource plays, anisotropy problem is naturally considered as an important step for improving the seismic image quality. Although it is well known prestack depth migration for the seismic reflection data is currently one of the powerful tools for imaging complex geological structures, it may lead to migration error without considering anisotropy. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation of couple P- and SV wave modes that can be converted to a fourth order scalar partial differential equation (PDE). By setting the shear wave velocity equal zero, the fourth order PDE, called an acoustic wave equation for TI media, can be reduced to couple of second order PDE systems and we try to solve the second order PDE by the finite difference method (FDM). The result of this P wavefield simulation is kinematically similar to elastic and anisotropic wavefield simulation. We develop prestack depth migration algorithm for tilted transversely isotropic media using reverse time migration method (RTM). RTM is a method for imaging the subsurface using inner product of source wavefield extrapolation in forward and receiver wavefield extrapolation in backward. We show the subsurface image in TTI media using the inner product of partial derivative wavefield with respect to physical parameters and observation data. Since the partial derivative wavefields with respect to the physical parameters require extremely huge computing time, so we implemented the imaging condition by zero lag crosscorrelation of virtual source and back propagating wavefield instead of partial derivative wavefields. The virtual source is calculated directly by solving anisotropic acoustic wave equation, the back propagating wavefield on the other hand is calculated by the shot gather used as the source function in the anisotropic acoustic wave equation. According to the numerical model test for a simple geological model including syncline and anticline, the prestack depth migration using TTI-RTM in weak anisotropic media shows the subsurface image is similar to the true geological model used to generate the shot gathers.

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Elia, M.; Edwards, H. C.; Hu, J.

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE PAGES

D'Elia, M.; Edwards, H. C.; Hu, J.; ...

2018-01-18

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Improved spatial regression analysis of diffusion tensor imaging for lesion detection during longitudinal progression of multiple sclerosis in individual subjects

NASA Astrophysics Data System (ADS)

Liu, Bilan; Qiu, Xing; Zhu, Tong; Tian, Wei; Hu, Rui; Ekholm, Sven; Schifitto, Giovanni; Zhong, Jianhui

2016-03-01

Subject-specific longitudinal DTI study is vital for investigation of pathological changes of lesions and disease evolution. Spatial Regression Analysis of Diffusion tensor imaging (SPREAD) is a non-parametric permutation-based statistical framework that combines spatial regression and resampling techniques to achieve effective detection of localized longitudinal diffusion changes within the whole brain at individual level without a priori hypotheses. However, boundary blurring and dislocation limit its sensitivity, especially towards detecting lesions of irregular shapes. In the present study, we propose an improved SPREAD (dubbed improved SPREAD, or iSPREAD) method by incorporating a three-dimensional (3D) nonlinear anisotropic diffusion filtering method, which provides edge-preserving image smoothing through a nonlinear scale space approach. The statistical inference based on iSPREAD was evaluated and compared with the original SPREAD method using both simulated and in vivo human brain data. Results demonstrated that the sensitivity and accuracy of the SPREAD method has been improved substantially by adapting nonlinear anisotropic filtering. iSPREAD identifies subject-specific longitudinal changes in the brain with improved sensitivity, accuracy, and enhanced statistical power, especially when the spatial correlation is heterogeneous among neighboring image pixels in DTI.

Simulations of eddy kinetic energy transport in barotropic turbulence

NASA Astrophysics Data System (ADS)

Grooms, Ian

2017-11-01

Eddy energy transport in rotating two-dimensional turbulence is investigated using numerical simulation. Stochastic forcing is used to generate an inhomogeneous field of turbulence and the time-mean energy profile is diagnosed. An advective-diffusive model for the transport is fit to the simulation data by requiring the model to accurately predict the observed time-mean energy distribution. Isotropic harmonic diffusion of energy is found to be an accurate model in the case of uniform, solid-body background rotation (the f plane), with a diffusivity that scales reasonably well with a mixing-length law κ ∝V ℓ , where V and ℓ are characteristic eddy velocity and length scales. Passive tracer dynamics are added and it is found that the energy diffusivity is 75 % of the tracer diffusivity. The addition of a differential background rotation with constant vorticity gradient β leads to significant changes to the energy transport. The eddies generate and interact with a mean flow that advects the eddy energy. Mean advection plus anisotropic diffusion (with reduced diffusivity in the direction of the background vorticity gradient) is moderately accurate for flows with scale separation between the eddies and mean flow, but anisotropic diffusion becomes a much less accurate model of the transport when scale separation breaks down. Finally, it is observed that the time-mean eddy energy does not look like the actual eddy energy distribution at any instant of time. In the future, stochastic models of the eddy energy transport may prove more useful than models of the mean transport for predicting realistic eddy energy distributions.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

APC: A New Code for Atmospheric Polarization Computations

NASA Technical Reports Server (NTRS)

Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

2014-01-01

A new polarized radiative transfer code Atmospheric Polarization Computations (APC) is described. The code is based on separation of the diffuse light field into anisotropic and smooth (regular) parts. The anisotropic part is computed analytically. The smooth regular part is computed numerically using the discrete ordinates method. Vertical stratification of the atmosphere, common types of bidirectional surface reflection and scattering by spherical particles or spheroids are included. A particular consideration is given to computation of the bidirectional polarization distribution function (BPDF) of the waved ocean surface.

Self-Diffusion of Drops in a Dilute Sheared Emulsion

NASA Technical Reports Server (NTRS)

Loewenberg, Michael; Hinch, E. J.

1996-01-01

Self-diffusion coefficients that describe cross-flow migration of non-Brownian drops in a dilute sheared emulsion were obtained by trajectory calculations. A boundary integral formulation was used to describe pairwise interactions between deformable drops; interactions between undeformed drops were described with mobility functions for spherical drops. The results indicate that drops have large anisotropic self-diffusivities which depend strongly on the drop viscosity and modestly on the shear-rate. Pairwise interactions between drops in shear-flow do not appreciably promote drop breakup.

Integral Equation Method for Electromagnetic Wave Propagation in Stratified Anisotropic Dielectric-Magnetic Materials

NASA Astrophysics Data System (ADS)

Shu, Wei-Xing; Fu, Na; Lü, Xiao-Fang; Luo, Hai-Lu; Wen, Shuang-Chun; Fan, Dian-Yuan

2010-11-01

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics, which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

Deformation and stress response of composite laminated shells under internal pressure

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1991-01-01

This paper presents a theoretical study of the response of filament wound composite shells under internal pressure. Each layer of the material is generally cylindrically anisotropic. By using cylindrically anisotropic elasticity field equations and Lekhnitskii's stress functions, a system of sixth-order ordinary differential equations is obtained. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Stress distributions of (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio.

Dynamic wormhole solutions in Einstein-Cartan gravity

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Ziaie, Amir Hadi

2017-12-01

In the present work, we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory. The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state for energy density and pressure profiles. We introduce exact asymptotically flat and anti-de Sitter spacetimes that admit traversable wormholes and respect energy conditions throughout the spacetime. The rate of expansion of these evolving wormholes is determined only by the Friedmann equation in the presence of spin effects.

On the interpretation of continuous wave electron spin resonance spectra of tempo-palmitate in 5-cyanobiphenyl.

PubMed

Zerbetto, Mirco; Polimeno, Antonino; Cimino, Paola; Barone, Vincenzo

2008-01-14

Electron spin resonance (ESR) measurements are highly informative on the dynamic behavior of molecules, which is of fundamental importance to understand their stability, biological functions and activities, and catalytic action. The wealth of dynamic information which can be extracted from a continuous wave electron spin resonance (cw-ESR) spectrum can be inferred by a basic theoretical approach defined within the stochastic Liouville equation formalism, i.e., the direct inclusion of motional dynamics in the form of stochastic (Fokker-Planck/diffusive) operators in the super Hamiltonian H governing the time evolution of the system. Modeling requires the characterization of magnetic parameters (e.g., hyperfine and Zeeman tensors) and the calculation of ESR observables in terms of spectral densities. The magnetic observables can be pursued by the employment of density functional theory which is apt, provided that hybrid functionals are employed, for the accurate computation of structural properties of molecular systems. Recently, an ab initio integrated computational approach to the in silico interpretation of cw-ESR spectra of multilabeled systems in isotropic fluids has been discussed. In this work we present the extension to the case of nematic liquid crystalline environments by performing simulations of the ESR spectra of the prototypical nitroxide probe 4-(hexadecanoyloxy)-2,2,6,6-tetramethylpiperidine-1-oxy in isotropic and nematic phases of 5-cyanobiphenyl. We first discuss the basic ingredients of the integrated approach, i.e., (1) determination of geometric and local magnetic parameters by quantum-mechanical calculations, taking into account the solvent and, when needed, the vibrational averaging contributions; (2) numerical solution of a stochastic Liouville equation in the presence of diffusive rotational dynamics, based on (3) parameterization of diffusion rotational tensor provided by a hydrodynamic model. Next we present simulated spectra with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing three-dimensional structural and dynamic information on molecular systems in anisotropic environments.

Direct measurement of lateral transport in membranes by using time-resolved spatial photometry.

PubMed Central

Kapitza, H G; McGregor, G; Jacobson, K A

1985-01-01

Spatially resolving light detectors allow, with proper calibration, quantitative analysis of the variations in two-dimensional intensity distributions over time. An ultrasensitive microfluorometer was assembled by using as a detector a microchannel plate-intensified video camera. The camera was interfaced with a software-based digital video analysis system to digitize, average, and process images and to directly control the timing of the experiments to minimize exposure of the specimen to light. The detector system has been characterized to allow its use as a photometer. A major application has been to perform fluorescence recovery after photobleaching measurements by using the camera in place of a photomultiplier tube (video-FRAP) with the goal of detecting possible anisotropic diffusion or convective flow. Analysis of the data on macromolecular diffusion in homogenous aqueous glycol solutions yielded diffusion constants in agreement with previous measurements. Results on lipid probe diffusion in dimyristoylphosphatidylcholine multibilayers indicated that at temperatures above the gel-to-liquid crystalline phase transition diffusion is isotropic, and analysis of video-FRAP data yielded diffusion coefficients consistent with those measured previously by using spot photobleaching. However, lipid probes in these multibilayers held just below the main phase transition temperature exhibited markedly anisotropic diffusive fluxes when the bleaching beam was positioned proximate to domain boundaries in the P beta' phase. Lipid probes and lectin receptor complexes diffused isotropically in fibroblast surface membranes with little evidence for diffusion channeled parallel to stress fibers. A second application was to trace the time evolution of cell surface reactions such as patching. The feasibility of following, on the optical scale, the growth of individual receptor clusters induced by the ligand wheat germ agglutinin was demonstrated. PMID:3858869

Direct measurement of lateral transport in membranes by using time-resolved spatial photometry.

PubMed

Kapitza, H G; McGregor, G; Jacobson, K A

1985-06-01

Spatially resolving light detectors allow, with proper calibration, quantitative analysis of the variations in two-dimensional intensity distributions over time. An ultrasensitive microfluorometer was assembled by using as a detector a microchannel plate-intensified video camera. The camera was interfaced with a software-based digital video analysis system to digitize, average, and process images and to directly control the timing of the experiments to minimize exposure of the specimen to light. The detector system has been characterized to allow its use as a photometer. A major application has been to perform fluorescence recovery after photobleaching measurements by using the camera in place of a photomultiplier tube (video-FRAP) with the goal of detecting possible anisotropic diffusion or convective flow. Analysis of the data on macromolecular diffusion in homogenous aqueous glycol solutions yielded diffusion constants in agreement with previous measurements. Results on lipid probe diffusion in dimyristoylphosphatidylcholine multibilayers indicated that at temperatures above the gel-to-liquid crystalline phase transition diffusion is isotropic, and analysis of video-FRAP data yielded diffusion coefficients consistent with those measured previously by using spot photobleaching. However, lipid probes in these multibilayers held just below the main phase transition temperature exhibited markedly anisotropic diffusive fluxes when the bleaching beam was positioned proximate to domain boundaries in the P beta' phase. Lipid probes and lectin receptor complexes diffused isotropically in fibroblast surface membranes with little evidence for diffusion channeled parallel to stress fibers. A second application was to trace the time evolution of cell surface reactions such as patching. The feasibility of following, on the optical scale, the growth of individual receptor clusters induced by the ligand wheat germ agglutinin was demonstrated.

Nondimensional parameters and equations for buckling of symmetrically laminated thin elastic shallow shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

1991-01-01

A method of deriving nondimensional equations and identifying the fundamental parameters associated with bifurcation buckling of anisotropic shells subjected to combined loads is presented. The procedure and rationale used to obtain useful nondimensional forms of the transverse equilibrium and compatibility equations for buckling are presented. Fundamental parameters are identified that represent the importance of both membrane and bending orthotropy and anisotropy on the results.

The Shock and Vibration Digest. Volume 15. Number 2

DTIC Science & Technology

1983-02-01

plates - other analyses. Asymptotic solu- tions of the general three-dimensional elasticity equations for an anisotropic beam have been used by Sayir...34Operatorsand Fractional Deriva- tives for Viscoelastic Constitutive Equations " (Submitted to J. Rheology, Apr 1982). 53. Bagley, R.L and Torvik, P.J... equations governing free, undamped vibration modes, the hull is specified by sectional quaruties. They are: hull stiffness, as represented by bending

Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

NASA Astrophysics Data System (ADS)

Han, B.; Li, Y.

2016-12-01

We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

Improving temporal resolution and speed sensitivity of laser speckle contrast analysis imaging based on noise reduction with an anisotropic diffusion filter

NASA Astrophysics Data System (ADS)

Song, Lipei; Wang, Xueyan; Zhang, Ru; Zhang, Kuanshou; Zhou, Zhen; Elson, Daniel S.

2018-07-01

The fluctuation of contrast caused by statistical noise degenerates the temporal/spatial resolution of laser speckle contrast imaging (LSCI) and limits the maximum speed when imaging. In this study, we investigated the application of the anisotropic diffusion filter (ADF) to temporal LSCI and found that the edge magnitude parameter of the ADF can be determined by the mean of the contrast image. Because the edge magnitude parameter is usually denoted as K, we term this the K-constant ADF (KC-ADF) and show that temporal sensitivity is improved when imaging because of the enhanced signal-to-noise ratio when using the KC-ADF in small-animal experiments. The cardiac cycle of a rat as high as 390 bpm can be imaged with an industrial camera.

Model atmospheres and radiation of magnetic neutron stars. I - The fully ionized case

NASA Technical Reports Server (NTRS)

Shibanov, Iu. A.; Zavlin, V. E.; Pavlov, G. G.; Ventura, J.

1992-01-01

Model neutron star atmospheres are calculated for typical cooling stars with a strong magnetic field and effective temperatures of 10 exp 5 to 10 exp 6 K. The effect of anisotropic photon diffusion in two normal modes are examined under the assumption that the opacity is due solely to the bremsstrahlung and Thomson scattering processes under conditions of LTE that are expected to prevail at the temperatures and densities obtained. The main aspects of anisotropic photon diffusion, and an original procedure for calculating model atmospheres and emitted spectra are discussed. Representative calculated spectra are given, and it is found that the hard spectral excess characterizing the nonmagnetic case, while still present, becomes less prominent in the presence of magnetic fields in the range of 10 exp 11 to 10 exp 13 G.

Robust segmentation of trabecular bone for in vivo CT imaging using anisotropic diffusion and multi-scale morphological reconstruction

NASA Astrophysics Data System (ADS)

Chen, Cheng; Jin, Dakai; Zhang, Xiaoliu; Levy, Steven M.; Saha, Punam K.

2017-03-01

Osteoporosis is associated with an increased risk of low-trauma fractures. Segmentation of trabecular bone (TB) is essential to assess TB microstructure, which is a key determinant of bone strength and fracture risk. Here, we present a new method for TB segmentation for in vivo CT imaging. The method uses Hessian matrix-guided anisotropic diffusion to improve local separability of trabecular structures, followed by a new multi-scale morphological reconstruction algorithm for TB segmentation. High sensitivity (0.93), specificity (0.93), and accuracy (0.92) were observed for the new method based on regional manual thresholding on in vivo CT images. Mechanical tests have shown that TB segmentation using the new method improved the ability of derived TB spacing measure for predicting actual bone strength (R2=0.83).

A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bauer, Carl A., E-mail: bauerca@colorado.ed; Werner, Gregory R.; Cary, John R.

A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardsonmore » extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.« less

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

On axisymmetric resistive MHD equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, George N.; Tasso, Henri

2002-11-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic electrical conductivity and flows parallel to the magnetic field is investigated within the framework of the MHD theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order partial differential equation for the poloidal magnetic flux function along with a Bernoulli equation for the density identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the conductivities σ_allel and σ_⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic conductivity and parallel flows (see [1]) the equilibrium is compatible with non-vanishing poloidal currents. For incompressible flows exact solutions of the above mentioned set of equations can be constructed with σ_allel and σ_⊥ profiles compatible with collisional conductivity profiles, i.e. profiles peaked close to the magnetic axis, vanishing on the boundary and such that σ_allel> σ_⊥. In particular, an exact equilibrium describing a toroidal plasma of arbitrary aspect ratio being contained within a perfectly conducting boundary of rectangular cross-section and peaked toroidal current density profile vanishing on the boundary is further considered. For this equilibrium in the case of vanishing flows the difference σ_allel-σ_⊥ for the reversed field pinch scaling Bp Bt (where Bp and Bt are the poloidal and toroidal magnetic field components) is nearly two times larger than that for the tokamak scaling B_p 0.1 B_t. [1] G. N. Throumoulopoulos, H. Tasso, J. Plasma Physics 64, 601 (2000).

Analogies between the torque-free motion of a rigid body about a fixed point and light propagation in anisotropic media

NASA Astrophysics Data System (ADS)

Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo

2009-03-01

An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of the modulus of angular velocity ω. The equivalence between this plane construction and the well-known Poinsot's three-dimensional graphical procedure is also shown. From this equivalence, analogies have been found between the general plane wave equation (relation of dispersion) in anisotropic media and basic equations of torque-free motion of a rigid body about a fixed point. These analogies allow reciprocal transfer of results between optics and mechanics and, as an example, reinterpretation of the internal conical refraction phenomenon in biaxial media is carried out. This paper is intended as an interdisciplinary application of analogies for students and teachers in the context of intermediate physics courses at university level.

A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganapol, B.D., E-mail: ganapol@cowboy.ame.arizona.edu; Mostacci, D.; Previti, A.

2016-07-01

We present highly accurate solutions to the neutral particle transport equation in a half-space. While our initial motivation was in response to a recently published solution based on Chandrasekhar's H-function, the presentation to follow has taken on a more comprehensive tone. The solution by H-functions certainly did achieved high accuracy but was limited to isotropic scattering and emission from spatially uniform and linear sources. Moreover, the overly complicated nature of the H-function approach strongly suggests that its extension to anisotropic scattering and general sources is not at all practical. For this reason, an all encompassing theory for the determination ofmore » highly precise benchmarks, including anisotropic scattering for a variety of spatial source distributions, is presented for particle transport in a half-space. We illustrate the approach via a collection of cases including tables of 7-place flux benchmarks to guide transport methods developers. The solution presented can be applied to a considerable number of one and two half-space transport problems with variable sources and represents a state-of-the-art benchmark solution.« less

Towards a new multiscale air quality transport model using the fully unstructured anisotropic adaptive mesh technology of Fluidity (version 4.1.9)

NASA Astrophysics Data System (ADS)

Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.

2015-10-01

An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection-diffusion problems, 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 set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.

The role of anisotropic expansion for pulmonary acinar aerosol deposition

PubMed Central

Hofemeier, Philipp; Sznitman, Josué

2016-01-01

Lung deformations at the local pulmonary acinar scale are intrinsically anisotropic. Despite progress in imaging modalities, the true heterogeneous nature of acinar expansion during breathing remains controversial, where our understanding of inhaled aerosol deposition still widely emanates from studies under self-similar, isotropic wall motions. Building on recent 3D models of multi-generation acinar networks, we explore in numerical simulations how different hypothesized scenarios of anisotropic expansion influence deposition outcomes of inhaled aerosols in the acinar depths. While the broader range of particles acknowledged to reach the acinar region (dp = 0.005–5.0 μm) are largely unaffected by the details of anisotropic expansion under tidal breathing, our results suggest nevertheless that anisotropy modulates the deposition sites and fractions for a narrow band of sub-micron particles (dp ~ 0.5–0.75 μm), where the fate of aerosols is greatly intertwined with local convective flows. Our findings underscore how intrinsic aerosol motion (i.e. diffusion, sedimentation) undermines the role of anisotropic wall expansion that is often attributed in determining aerosol mixing and acinar deposition. PMID:27614613

The role of anisotropic expansion for pulmonary acinar aerosol deposition.

PubMed

Hofemeier, Philipp; Sznitman, Josué

2016-10-03

Lung deformations at the local pulmonary acinar scale are intrinsically anisotropic. Despite progress in imaging modalities, the true heterogeneous nature of acinar expansion during breathing remains controversial, where our understanding of inhaled aerosol deposition still widely emanates from studies under self-similar, isotropic wall motions. Building on recent 3D models of multi-generation acinar networks, we explore in numerical simulations how different hypothesized scenarios of anisotropic expansion influence deposition outcomes of inhaled aerosols in the acinar depths. While the broader range of particles acknowledged to reach the acinar region (d p =0.005-5.0μm) are largely unaffected by the details of anisotropic expansion under tidal breathing, our results suggest nevertheless that anisotropy modulates the deposition sites and fractions for a narrow band of sub-micron particles (d p ~0.5-0.75μm), where the fate of aerosols is greatly intertwined with local convective flows. Our findings underscore how intrinsic aerosol motion (i.e. diffusion, sedimentation) undermines the role of anisotropic wall expansion that is often attributed in determining aerosol mixing and acinar deposition. Copyright © 2016 Elsevier Ltd. All rights reserved.

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

Effective modeling and reverse-time migration for novel pure acoustic wave in arbitrary orthorhombic anisotropic media

NASA Astrophysics Data System (ADS)

Xu, Shigang; Liu, Yang

2018-03-01

The conventional pseudo-acoustic wave equations (PWEs) in arbitrary orthorhombic anisotropic (OA) media usually have coupled P- and SV-wave modes. These coupled equations may introduce strong SV-wave artifacts and numerical instabilities in P-wave simulation results and reverse-time migration (RTM) profiles. However, pure acoustic wave equations (PAWEs) completely decouple the P-wave component from the full elastic wavefield and naturally solve all the aforementioned problems. In this article, we present a novel PAWE in arbitrary OA media and compare it with the conventional coupled PWEs. Through decomposing the solution of the corresponding eigenvalue equation for the original PWE into an ellipsoidal differential operator (EDO) and an ellipsoidal scalar operator (ESO), the new PAWE in time-space domain is constructed by applying the combination of these two solvable operators and can effectively describe P-wave features in arbitrary OA media. Furthermore, we adopt the optimal finite-difference method (FDM) to solve the newly derived PAWE. In addition, the three-dimensional (3D) hybrid absorbing boundary condition (HABC) with some reasonable modifications is developed for reducing artificial edge reflections in anisotropic media. To improve computational efficiency in 3D case, we adopt graphic processing unit (GPU) with Compute Unified Device Architecture (CUDA) instead of traditional central processing unit (CPU) architecture. Several numerical experiments for arbitrary OA models confirm that the proposed schemes can produce pure, stable and accurate P-wave modeling results and RTM images with higher computational efficiency. Moreover, the 3D numerical simulations can provide us with a comprehensive and real description of wave propagation.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Thermal conductivity of III-V semiconductor superlattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mei, S., E-mail: song.mei@wisc.edu; Knezevic, I., E-mail: irena.knezevic@wisc.edu

2015-11-07

This paper presents a semiclassical model for the anisotropic thermal transport in III-V semiconductor superlattices (SLs). An effective interface rms roughness is the only adjustable parameter. Thermal transport inside a layer is described by the Boltzmann transport equation in the relaxation time approximation and is affected by the relevant scattering mechanisms (three-phonon, mass-difference, and dopant and electron scattering of phonons), as well as by diffuse scattering from the interfaces captured via an effective interface scattering rate. The in-plane thermal conductivity is obtained from the layer conductivities connected in parallel. The cross-plane thermal conductivity is calculated from the layer thermal conductivitiesmore » in series with one another and with thermal boundary resistances (TBRs) associated with each interface; the TBRs dominate cross-plane transport. The TBR of each interface is calculated from the transmission coefficient obtained by interpolating between the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM), where the weight of the AMM transmission coefficient is the same wavelength-dependent specularity parameter related to the effective interface rms roughness that is commonly used to describe diffuse interface scattering. The model is applied to multiple III-arsenide superlattices, and the results are in very good agreement with experimental findings. The method is both simple and accurate, easy to implement, and applicable to complicated SL systems, such as the active regions of quantum cascade lasers. It is also valid for other SL material systems with high-quality interfaces and predominantly incoherent phonon transport.« less

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

A Locally Adaptive Regularization Based on Anisotropic Diffusion for Deformable Image Registration of Sliding Organs

PubMed Central

Pace, Danielle F.; Aylward, Stephen R.; Niethammer, Marc

2014-01-01

We propose a deformable image registration algorithm that uses anisotropic smoothing for regularization to find correspondences between images of sliding organs. In particular, we apply the method for respiratory motion estimation in longitudinal thoracic and abdominal computed tomography scans. The algorithm uses locally adaptive diffusion tensors to determine the direction and magnitude with which to smooth the components of the displacement field that are normal and tangential to an expected sliding boundary. Validation was performed using synthetic, phantom, and 14 clinical datasets, including the publicly available DIR-Lab dataset. We show that motion discontinuities caused by sliding can be effectively recovered, unlike conventional regularizations that enforce globally smooth motion. In the clinical datasets, target registration error showed improved accuracy for lung landmarks compared to the diffusive regularization. We also present a generalization of our algorithm to other sliding geometries, including sliding tubes (e.g., needles sliding through tissue, or contrast agent flowing through a vessel). Potential clinical applications of this method include longitudinal change detection and radiotherapy for lung or abdominal tumours, especially those near the chest or abdominal wall. PMID:23899632

A locally adaptive regularization based on anisotropic diffusion for deformable image registration of sliding organs.

PubMed

Pace, Danielle F; Aylward, Stephen R; Niethammer, Marc

2013-11-01

We propose a deformable image registration algorithm that uses anisotropic smoothing for regularization to find correspondences between images of sliding organs. In particular, we apply the method for respiratory motion estimation in longitudinal thoracic and abdominal computed tomography scans. The algorithm uses locally adaptive diffusion tensors to determine the direction and magnitude with which to smooth the components of the displacement field that are normal and tangential to an expected sliding boundary. Validation was performed using synthetic, phantom, and 14 clinical datasets, including the publicly available DIR-Lab dataset. We show that motion discontinuities caused by sliding can be effectively recovered, unlike conventional regularizations that enforce globally smooth motion. In the clinical datasets, target registration error showed improved accuracy for lung landmarks compared to the diffusive regularization. We also present a generalization of our algorithm to other sliding geometries, including sliding tubes (e.g., needles sliding through tissue, or contrast agent flowing through a vessel). Potential clinical applications of this method include longitudinal change detection and radiotherapy for lung or abdominal tumours, especially those near the chest or abdominal wall.

Reverse ray tracing for transformation optics.

PubMed

Hu, Chia-Yu; Lin, Chun-Hung

2015-06-29

Ray tracing is an important technique for predicting optical system performance. In the field of transformation optics, the Hamiltonian equations of motion for ray tracing are well known. The numerical solutions to the Hamiltonian equations of motion are affected by the complexities of the inhomogeneous and anisotropic indices of the optical device. Based on our knowledge, no previous work has been conducted on ray tracing for transformation optics with extreme inhomogeneity and anisotropicity. In this study, we present the use of 3D reverse ray tracing in transformation optics. The reverse ray tracing is derived from Fermat's principle based on a sweeping method instead of finding the full solution to ordinary differential equations. The sweeping method is employed to obtain the eikonal function. The wave vectors are then obtained from the gradient of that eikonal function map in the transformed space to acquire the illuminance. Because only the rays in the points of interest have to be traced, the reverse ray tracing provides an efficient approach to investigate the illuminance of a system. This approach is useful in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. The performance and analysis of three transformation optics with inhomogeneous and anisotropic indices are explored. The ray trajectories and illuminances in these demonstration cases are successfully solved by the proposed reverse ray tracing method.

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Biasing anisotropic scattering kernels for deep-penetration Monte Carlo calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carter, L.L.; Hendricks, J.S.

1983-01-01

The exponential transform is often used to improve the efficiency of deep-penetration Monte Carlo calculations. This technique is usually implemented by biasing the distance-to-collision kernel of the transport equation, but leaving the scattering kernel unchanged. Dwivedi obtained significant improvements in efficiency by biasing an isotropic scattering kernel as well as the distance-to-collision kernel. This idea is extended to anisotropic scattering, particularly the highly forward Klein-Nishina scattering of gamma rays.

High-temperature electron-hole superfluidity with strong anisotropic gaps in double phosphorene monolayers

NASA Astrophysics Data System (ADS)

Saberi-Pouya, S.; Zarenia, M.; Perali, A.; Vazifehshenas, T.; Peeters, F. M.

2018-05-01

Excitonic superfluidity in double phosphorene monolayers is investigated using the BCS mean-field equations. Highly anisotropic superfluidity is predicted where we found that the maximum superfluid gap is in the Bose-Einstein condensate (BEC) regime along the armchair direction and in the BCS-BEC crossover regime along the zigzag direction. We estimate the highest Kosterlitz-Thouless transition temperature with maximum value up to ˜90 K with onset carrier densities as high as 4 ×1012cm-2 . This transition temperature is significantly larger than what is found in double electron-hole few-layers graphene. Our results can guide experimental research toward the realization of anisotropic condensate states in electron-hole phosphorene monolayers.

Generalized migration in frequency-wavenumber domain (MGF-K) in anisotropic media

NASA Astrophysics Data System (ADS)

Kostecki, Andrzej; Półchłopek, Anna

2013-06-01

In this paper, the background of MGF-K migration in dual domain (wavenumber-frequency K-F and space-time) in anisotropic media is presented. Algorithms for poststack (zero-offset) and prestack migration are based on downward extrapolation of acoustic wavefield by shift-phase with correction filter for lateral variability of medium's parameters. In anisotropic media, the vertical wavenumber was determined from full elastic wavefield equations for two dimensional (2D) tilted transverse isotropy (TTI) model. The method was tested on a synthetic wavefield for TTI anticlinal model (zero-offset section) and on strongly inhomogeneous vertical transverse isotropy (VTI) Marmousi model. In both cases, the proper imaging of assumed media was obtained.

Invariant Clustering Using Scattering Matrices.

DTIC Science & Technology

1983-02-23

general three-dimensional elasticity a discontinuous fiber, however. equations for an anisotropic beam have been used by Sayir [19] to show that shear...34 Exptl. tives for Viscoelastic Constitutive Equations " Tech.,6(2), pp 10-14 (Apr 1982). (Submitted to J. Rheology, Apr 1982). 63. Gibson, R.F., Yau, A...vibration modes up to about nine nodes [4], Added mass of water. The frequency range relevant In the Timoshenko beam equations governing free, for ship

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Anisotropy of anomalous diffusion improves the accuracy of differentiating low- and high-grade cerebral gliomas.

PubMed

Xu, Boyan; Su, Lu; Wang, Zhenxiong; Fan, Yang; Gong, Gaolang; Zhu, Wenzhen; Gao, Peiyi; Gao, Jia-Hong

2018-04-17

Anomalous diffusion model has been introduced and shown to be beneficial in clinical applications. However, only the directionally averaged values of anomalous diffusion parameters were investigated, and the anisotropy of anomalous diffusion remains unexplored. The aim of this study was to demonstrate the feasibility of using anisotropy of anomalous diffusion for differentiating low- and high-grade cerebral gliomas. Diffusion MRI images were acquired from brain tumor patients and analyzed using the fractional motion (FM) model. Twenty-two patients with histopathologically confirmed gliomas were selected. An anisotropy metric for the FM-related parameters, including the Noah exponent (α) and the Hurst exponent (H), was introduced and their values were statistically compared between the low- and high-grade gliomas. Additionally, multivariate logistic regression analysis was performed to assess the combination of the anisotropy metric and the directionally averaged value for each parameter. The diagnostic performances for grading gliomas were evaluated using a receiver operating characteristic (ROC) analysis. The Hurst exponent H was more anisotropic in high-grade than in low-grade gliomas (P = 0.015), while no significant difference was observed for the anisotropy of α. The ROC analysis revealed that larger areas under the ROC curves were produced for the combination of α (1) and the combination of H (0.813) compared with the directionally averaged α (0.979) and H (0.594), indicating an improved performance for tumor differentiation. The anisotropy of anomalous diffusion can provide distinctive information and benefit the differentiation of low- and high-grade gliomas. The utility of anisotropic anomalous diffusion may have an improved effect for investigating pathological changes in tissues. Copyright © 2018 Elsevier Inc. All rights reserved.

Anisotropic strange star with Tolman V potential

NASA Astrophysics Data System (ADS)

Shee, Dibyendu; Deb, Debabrata; Ghosh, Shounak; Ray, Saibal; Guha, B. K.

In this paper, we present a strange stellar model using Tolman V-type metric potential employing simplest form of the MIT bag equation of state (EOS) for the quark matter. We consider that the stellar system is spherically symmetric, compact and made of an anisotropic fluid. Choosing different values of n we obtain exact solutions of the Einstein field equations and finally conclude that for a specific value of the parameter n = 1/2, we find physically acceptable features of the stellar object. Further, we conduct different physical tests, viz., the energy condition, generalized Tolman-Oppeheimer-Volkoff (TOV) equation, Herrera’s cracking concept, etc., to confirm the physical validity of the presented model. Matching conditions provide expressions for different constants whereas maximization of the anisotropy parameter provides bag constant. By using the observed data of several compact stars, we derive exact values of some of the physical parameters and exhibit their features in tabular form. It is to note that our predicted value of the bag constant satisfies the report of CERN-SPS and RHIC.

Optimized growth and reorientation of anisotropic material based on evolution equations

NASA Astrophysics Data System (ADS)

Jantos, Dustin R.; Junker, Philipp; Hackl, Klaus

2018-07-01

Modern high-performance materials have inherent anisotropic elastic properties. The local material orientation can thus be considered to be an additional design variable for the topology optimization of structures containing such materials. In our previous work, we introduced a variational growth approach to topology optimization for isotropic, linear-elastic materials. We solved the optimization problem purely by application of Hamilton's principle. In this way, we were able to determine an evolution equation for the spatial distribution of density mass, which can be evaluated in an iterative process within a solitary finite element environment. We now add the local material orientation described by a set of three Euler angles as additional design variables into the three-dimensional model. This leads to three additional evolution equations that can be separately evaluated for each (material) point. Thus, no additional field unknown within the finite element approach is needed, and the evolution of the spatial distribution of density mass and the evolution of the Euler angles can be evaluated simultaneously.

Radiative heat transfer in strongly forward scattering media of circulating fluidized bed combustors

NASA Astrophysics Data System (ADS)

Ates, Cihan; Ozen, Guzide; Selçuk, Nevin; Kulah, Gorkem

2016-10-01

Investigation of the effect of particle scattering on radiative incident heat fluxes and source terms is carried out in the dilute zone of the lignite-fired 150 kWt Middle East Technical University Circulating Fluidized Bed Combustor (METU CFBC) test rig. The dilute zone is treated as an axisymmetric cylindrical enclosure containing grey/non-grey, absorbing, emitting gas with absorbing, emitting non/isotropically/anisotropically scattering particles surrounded by grey diffuse walls. A two-dimensional axisymmetric radiation model based on Method of Lines (MOL) solution of Discrete Ordinates Method (DOM) coupled with Grey Gas (GG)/Spectral Line-Based Weighted Sum of Grey Gases Model (SLW) and Mie theory/geometric optics approximation (GOA) is extended for incorporation of anisotropic scattering by using normalized Henyey-Greenstein (HG)/transport approximation for the phase function. Input data for the radiation model is obtained from predictions of a comprehensive model previously developed and benchmarked against measurements on the same CFBC burning low calorific value indigenous lignite with high volatile matter/fixed carbon (VM/FC) ratio in its own ash. Predictive accuracy and computational efficiency of nonscattering, isotropic scattering and forward scattering with transport approximation are tested by comparing their predictions with those of forward scattering with HG. GG and GOA based on reflectivity with angular dependency are found to be accurate and CPU efficient. Comparisons reveal that isotropic assumption leads to under-prediction of both incident heat fluxes and source terms for which discrepancy is much larger. On the other hand, predictions obtained by neglecting scattering were found to be in favorable agreement with those of forward scattering at significantly less CPU time. Transport approximation is as accurate and CPU efficient as HG. These findings indicate that negligence of scattering is a more practical choice in solution of the radiative transfer equation (RTE) in conjunction with conservation equations for the system under consideration.

Conformal collineations and anisotropic fluids in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duggal, K.L.; Sharma, R.

1986-10-01

Recently, Herrera et al. (L. Herrera, J. Jimenez, L. Leal, J. Ponce de Leon, M. Esculpi, and V. Galino, J. Math. Phys. 25, 3274 (1984)) studied the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter. They concluded that for special conformal motions, the stiff equation of state (p = ..mu..) is singled out in a unique way, provided the generating conformal vector field is orthogonal to the four-velocity. In this paper, the same problem is studied by using conformal collineations (which include conformal motions as subgroups). It is shown that, for a special conformalmore » collineation, the stiff equation of state is not singled out. Non-Einstein Ricci-recurrent spaces are considered as physical models for the fluid matter.« less

Zonal flow generation and its feedback on turbulence production in drift wave turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pushkarev, Andrey V.; Bos, Wouter J. T.; Nazarenko, Sergey V.

2013-04-15

Plasma turbulence described by the Hasegawa-Wakatani equations is simulated numerically for different models and values of the adiabaticity parameter C. It is found that for low values of C turbulence remains isotropic, zonal flows are not generated and there is no suppression of the meridional drift waves and particle transport. For high values of C, turbulence evolves towards highly anisotropic states with a dominant contribution of the zonal sector to the kinetic energy. This anisotropic flow leads to a decrease of turbulence production in the meridional sector and limits the particle transport across the mean isopycnal surfaces. This behavior allowsmore » to consider the Hasegawa-Wakatani equations a minimal PDE model, which contains the drift-wave/zonal-flow feedback loop mechanism.« less

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

NASA Astrophysics Data System (ADS)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

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

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Behavior of optical properties of coagulated blood sample at 633 nm wavelength

NASA Astrophysics Data System (ADS)

Morales Cruzado, Beatriz; Vázquez y Montiel, Sergio; Delgado Atencio, José Alberto

2011-03-01

Determination of tissue optical parameters is fundamental for application of light in either diagnostics or therapeutical procedures. However, in samples of biological tissue in vitro, the optical properties are modified by cellular death or cellular agglomeration that can not be avoided. This phenomena change the propagation of light within the biological sample. Optical properties of human blood tissue were investigated in vitro at 633 nm using an optical setup that includes a double integrating sphere system. We measure the diffuse transmittance and diffuse reflectance of the blood sample and compare these physical properties with those obtained by Monte Carlo Multi-Layered (MCML). The extraction of the optical parameters: absorption coefficient μa, scattering coefficient μs and anisotropic factor g from the measurements were carried out using a Genetic Algorithm, in which the search procedure is based in the evolution of a population due to selection of the best individual, evaluated by a function that compares the diffuse transmittance and diffuse reflectance of those individuals with the experimental ones. The algorithm converges rapidly to the best individual, extracting the optical parameters of the sample. We compare our results with those obtained by using other retrieve procedures. We found that the scattering coefficient and the anisotropic factor change dramatically due to the formation of clusters.

A note on flow reversal in a wavy channel filled with anisotropic porous material

NASA Astrophysics Data System (ADS)

Karmakar, Timir; Raja Sekhar, G. P.

2017-07-01

Viscous flow through a symmetric wavy channel filled with anisotropic porous material is investigated analytically. Flow inside the porous bed is assumed to be governed by the anisotropic Brinkman equation. It is assumed that the ratio of the channel width to the wavelength is small (i.e. δ2≪1). The problem is solved up to O(δ2) assuming that δ2λ2≪1, where λ is the anisotropic ratio. The key purpose of this paper is to study the effect of anisotropic permeability on flow near the crests of the wavy channel which causes flow reversal. We present a detailed analysis of the flow reversal at the crests. The ratio of the permeabilities (anisotropic ratio) is responsible for the flow separation near the crests of the wall where viscous forces are effective. For a flow configuration (say, low amplitude parameter) in which there is no separation if the porous media is isotropic, introducing anisotropy causes flow separation. On the other hand, interestingly, flow separation occurs even in the case of isotropic porous medium if the amplitude parameter a is large.

Non-Porod scattering and non-integer scaling of resistance in rough films

NASA Astrophysics Data System (ADS)

Bupathy, Arunkumar; Verma, Rupesh; Banerjee, Varsha; Puri, Sanjay

2017-04-01

In many physical systems, films are rough due to the stochastic behavior of depositing particles. They are characterized by non-Porod power law decays in the structure factor S (k) . Theoretical studies predict anomalous diffusion in such morphologies, with important implications for diffusivity, conductivity, etc. We use the non-Porod decay to accurately determine the fractal properties of two prototypical nanoparticle films: (i) Palladium (Pd) and (ii) Cu2O. Using scaling arguments, we find that the resistance of rough films of lateral size L obeys a non-integer power law R ∼L-ζ , in contrast to integer power laws for compact structures. The exponent ζ is anisotropic. We confirm our predictions by re-analyzing experimental data from Cu2O nano-particle films. Our results are valuable for understanding recent experiments that report anisotropic electrical properties in (rough) thin films.

Fractional domain varying-order differential denoising method

NASA Astrophysics Data System (ADS)

Zhang, Yan-Shan; Zhang, Feng; Li, Bing-Zhao; Tao, Ran

2014-10-01

Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.

A mathematical model for mesenchymal and chemosensitive cell dynamics.

PubMed

Häcker, Anita

2012-01-01

The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared. © Springer-Verlag 2011

Spatial dispersion effects upon local excitation of extrinsic plasmons in a graphene micro-disk

NASA Astrophysics Data System (ADS)

Mencarelli, D.; Bellucci, S.; Sindona, A.; Pierantoni, L.

2015-11-01

Excitation of surface plasmon waves in extrinsic graphene is studied using a full-wave electromagnetic field solver as analysis engine. Particular emphasis is placed on the role played by spatial dispersion due to the finite size of the two-dimensional material at the micro-scale. A simple instructive set up is considered where the near field of a wire antenna is held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of the simulation is the graphene conductivity tensor at terahertz frequencies, being modeled by the Boltzmann transport equation for the valence and conduction electrons at the Dirac points (where a linear wave-vector dependence of the band energies is assumed). The conductivity equation is worked out in different levels of approximations, based on the relaxation time ansatz with an additional constraint for particle number conservation. Both drift and diffusion currents are shown to significantly contribute to the spatially dispersive anisotropic features of micro-scale graphene. More generally, spatial dispersion effects are predicted to influence not only plasmon propagation free of external sources, but also typical scanning probe microscopy configurations. The paper sets the focus on plasmon excitation phenomena induced by near field probes, being a central issue for the design of optical devices and photonic circuits.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

Generating a Simulated Fluid Flow over a Surface Using Anisotropic Diffusion

NASA Technical Reports Server (NTRS)

Rodriguez, David L. (Inventor); Sturdza, Peter (Inventor)

2016-01-01

A fluid-flow simulation over a computer-generated surface is generated using a diffusion technique. The surface is comprised of a surface mesh of polygons. A boundary-layer fluid property is obtained for a subset of the polygons of the surface mesh. A gradient vector is determined for a selected polygon, the selected polygon belonging to the surface mesh but not one of the subset of polygons. A maximum and minimum diffusion rate is determined along directions determined using the gradient vector corresponding to the selected polygon. A diffusion-path vector is defined between a point in the selected polygon and a neighboring point in a neighboring polygon. An updated fluid property is determined for the selected polygon using a variable diffusion rate, the variable diffusion rate based on the minimum diffusion rate, maximum diffusion rate, and the gradient vector.

Resonant-state expansion for open optical systems: generalization to magnetic, chiral, and bi-anisotropic materials

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Weiss, T.

2018-05-01

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.

Comparison of different bioheat transfer models for assessment of burns injuries

NASA Astrophysics Data System (ADS)

Łapka, Piotr; Furmański, Piotr; Wiśniewski, Tomasz S.

2016-12-01

Two bioheat transfer models i.e.: the classical Pennes model and a more realistic two-equation model which accounted for blood vessel structure in the skin as well as heat transfer in the tissue and arteria blood were coupled with heat and mass transfer model in the protective multilayer garment. The clothing model included conductive-radiative heat transfer with water vapor diffusion in pores and air gaps as well as sorption and desorption of water in fibers. Thermal radiation was modeled rigorously e.g.: both the tissue and fabrics were assumed non-gray, absorbing, emitting and anisotropically scattering. Additionally different refractive indices of fabrics, air and tissue and resulting optical phenomena at separating interfaces were accounted for. Both bioheat models were applied for predicting skin temperature distributions and possibility of burns for different exposition times and radiative heat fluxes incident on external surface of the protective garment. Performed analyses revealed that heat transfer in the skin subjected to high heat flux is independent of the blood vessel structure.

Nonlinear Schrödinger equations for Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Galati, Luigi; Zheng, Shijun

2013-10-01

The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Anisotropic cosmological solutions in massive vector theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-11-01

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

Anisotropic cosmological solutions in massive vector theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji, E-mail: Lavinia.heisenberg@googlemail.com, E-mail: r.kase@rs.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant,more » the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v {sup 2} || φ{sup 2} are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w {sub DE} in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w {sub DE}{sup (iso)} typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.« less

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

Grain boundary grooving induced by the anisotropic surface drift diffusion driven by the capillary and electromigration forces: Simulations

NASA Astrophysics Data System (ADS)

Akyildiz, Oncu; Omer Ogurtani, Tarik

2011-08-01

The morphological evolution kinetics of a bicrystal thin film induced by anisotropic surface drift diffusion and driven by the applied electrostatic field is investigated via self consistent dynamical computer simulations. The physico-mathematical model, which is based upon the irreversible thermodynamic treatment of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)], provided us with auto-control on the otherwise free-motion of the triple junction at the intersection of the grooving surface and the grain boundary, without having any a priori assumption on the equilibrium dihedral angles. The destruction of the symmetry of the freshly formed grain boundary grooves under the anisotropic surface diffusion driven by the concurrent action of the capillarity and electromigration is observed. After prolonged exposure times the applied electric field above the well defined threshold level modifies Mullins' familiar stationary state time law as, t¯1/4, and causes the premature termination of the groove penetration because of the current crowding at the tips of counteracting grain boundary-grooves initiated on both sides of the test modulus. That finding indicates that the electromigration plays the same role as a healing agent [T. O. Ogurtani, J. Appl. Phys. 106, 053503 (2009)] in arresting the thermal grooving, thereby avoiding the premature interconnect failure as in the case of surface roughening and crack initiation caused by compressive stress gradients. The role of the electromigration and wetting parameter on the ridge/slit formations are thoroughly investigated in this study and the prerequisite conditions are also identified.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Spin echo versus stimulated echo diffusion tensor imaging of the in vivo human heart

PubMed Central

von Deuster, Constantin; Stoeck, Christian T.; Genet, Martin; Atkinson, David

2015-01-01

Purpose To compare signal‐to‐noise ratio (SNR) efficiency and diffusion tensor metrics of cardiac diffusion tensor mapping using acceleration‐compensated spin‐echo (SE) and stimulated echo acquisition mode (STEAM) imaging. Methods Diffusion weighted SE and STEAM sequences were implemented on a clinical 1.5 Tesla MR system. The SNR efficiency of SE and STEAM was measured (b = 50–450 s/mm2) in isotropic agar, anisotropic diffusion phantoms and the in vivo human heart. Diffusion tensor analysis was performed on mean diffusivity, fractional anisotropy, helix and transverse angles. Results In the isotropic phantom, the ratio of SNR efficiency for SE versus STEAM, SNRt(SE/STEAM), was 2.84 ± 0.08 for all tested b‐values. In the anisotropic diffusion phantom the ratio decreased from 2.75 ± 0.05 to 2.20 ± 0.13 with increasing b‐value, similar to the in vivo decrease from 2.91 ± 0.43 to 2.30 ± 0.30. Diffusion tensor analysis revealed reduced deviation of helix angles from a linear transmural model and reduced transverse angle standard deviation for SE compared with STEAM. Mean diffusivity and fractional anisotropy were measured to be statistically different (P < 0.001) between SE and STEAM. Conclusion Cardiac DTI using motion‐compensated SE yields a 2.3–2.9× increase in SNR efficiency relative to STEAM and improved accuracy of tensor metrics. The SE method hence presents an attractive alternative to STEAM based approaches. Magn Reson Med 76:862–872, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:26445426

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Generating a Simulated Fluid Flow Over an Aircraft Surface Using Anisotropic Diffusion

NASA Technical Reports Server (NTRS)

Rodriguez, David L. (Inventor); Sturdza, Peter (Inventor)

2013-01-01

A fluid-flow simulation over a computer-generated aircraft surface is generated using a diffusion technique. The surface is comprised of a surface mesh of polygons. A boundary-layer fluid property is obtained for a subset of the polygons of the surface mesh. A pressure-gradient vector is determined for a selected polygon, the selected polygon belonging to the surface mesh but not one of the subset of polygons. A maximum and minimum diffusion rate is determined along directions determined using a pressure gradient vector corresponding to the selected polygon. A diffusion-path vector is defined between a point in the selected polygon and a neighboring point in a neighboring polygon. An updated fluid property is determined for the selected polygon using a variable diffusion rate, the variable diffusion rate based on the minimum diffusion rate, maximum diffusion rate, and angular difference between the diffusion-path vector and the pressure-gradient vector.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Inflation in Einstein-Cartan theory with energy-momentum tensor with spin

NASA Technical Reports Server (NTRS)

Fennelly, A. J.; Bradas, James C.; Smalley, Larry L.

1988-01-01

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic (Bianchi Type I) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley (RS) improved energy-momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density.

Generalized Phenomenological Cyclic Stress-Strain-Strength Characterization of Anisotropic Granular Media.

DTIC Science & Technology

1985-06-27

can be rephrased to read: work hardening means that Useful energy over and above the elastic energy cannot be extracted - from the material and the...compactly write equation 159 as: A dp’ + B dp + C’ - 0 from which the solution for the roots are dij= -B VB2 - 4 A CI . (163) 2 A Equation 163 can be

Anisotropic nonequilibrium hydrodynamic attractor

NASA Astrophysics Data System (ADS)

Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.

2018-02-01

We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S.; Klang, Eric C.

2001-01-01

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium

NASA Astrophysics Data System (ADS)

Yang, Pengliang; Brossier, Romain; Métivier, Ludovic; Virieux, Jean

2016-10-01

In this paper, we study 3-D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter FWI for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3-D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parametrization can be related to the counterparts using P and S velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high-performance computing resources and the field data are available.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

String-fluid transition in systems with aligned anisotropic interactions.

PubMed

Brandt, P C; Ivlev, A V; Morfill, G E

2010-06-21

Systems with aligned anisotropic interactions between particles exhibit numerous phase transitions. A remarkable example of the fluid phase transition occurring in such systems is the formation of particle strings--the so-called "string" or "chain" fluids. We employ an approach based on the Ornstein-Zernike (OZ) equation, which allows us to calculate structural properties of fluids with aligned anisotropic interactions. We show that the string-fluid transition can be associated with the bifurcation of the "isotropic" correlation length into two distinct scales which characterize the longitudinal and transverse order in string fluids and, hence, may be used as a fingerprint of this transition. The comparison of the proposed OZ theory with the Monte Carlo simulations reveals fairly good agreement.

FIBER AND INTEGRATED OPTICS. OPTOELECTRONICS: Method for calculation of the parameters of guided waves in anisotropic dielectric waveguides

NASA Astrophysics Data System (ADS)

Goncharenko, I. A.

1989-07-01

The method of shift formulas is applied to anisotropic dielectric waveguides capable of conserving a given state of polarization of the transmitted signal. Equations are derived for calculation of the propagation constants and of the dispersion of the fundamental modes in waveguides with an anisotropic permittivity and a noncircular shape of the transverse cross section. Distributions of electric and magnetic fields of these modes are obtained in a transverse cross section of the waveguide. It is shown that under the influence of the anisotropy of the dielectric an energy spot describing the distribution of the mode field becomes of an ellipse with its axes oriented along the coordinates coinciding with the principal axes of the permittivity tensor.

Analysis of stresses in finite anisotropic panels with centrally located cutouts

NASA Technical Reports Server (NTRS)

Britt, Vicki O.

1992-01-01

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

Space, energy and anisotropy effects on effective cross sections and diffusion coefficients in the resonance region

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meftah, B.

1982-01-01

Present methods used in reactor analysis do not include adequately the effect of anisotropic scattering in the calculation of resonance effective cross sections. Also the assumption that the streaming term ..cap omega...del Phi is conserved when the total, absorption and transfer cross sections are conserved, is bad because the leakage from a heterogeneous cell will not be conserved and is strongly anisotropic. A third major consideration is the coupling between different regions in a multiregion reactor; currently this effect is being completely ignored. To assess the magnitude of these effects, a code based on integral transport formalism with linear anisotropicmore » scattering was developed. Also, a more adequate formulation of the diffusion coefficient in a heterogeneous cell was derived. Two reactors, one fast, ZPR-6/5, and one thermal, TRX-3, were selected for the study. The study showed that, in general, the inclusion of linear scattering anisotropy increases the cell effective capture cross section of U-238. The increase was up to 2% in TRX-3 and 0.5% in ZPR-6/5. The effect on the multiplication factor was -0.003% ..delta..k/k for ZPR-6/5 and -0.05% ..delta..k/k for TRX-3. For the case of the diffusion coefficient, the combined effect of heterogeneity and linear anisotropy gave an increase of up to 29% in the parallel diffusion coefficient of TRX-3 and 5% in the parallel diffusion coefficient of ZPR-6/5. In contrast, the change in the perpendicular diffusion coefficient did not exceed 2% in both systems.« less

Some notes on hydrogen-related point defects and their role in the isotope exchange and electrical conductivity in olivine

NASA Astrophysics Data System (ADS)

Karato, Shun-ichiro

2015-11-01

Nominally anhydrous minerals such as olivine dissolve hydrogen in a variety of forms including free (or interstitial) proton (Hrad) and two protons trapped at the M-site ((2 H)M×). The strength of chemical bonding between protons and the surrounding atoms are different among different species, and consequently protons belonging to different species likely have different mobility (diffusion coefficients). I discuss the role of diffusion of protons in different species in the isotope exchange and hydrogen-assisted electrical conductivity adding a few notes to the previous work by Karato (2013) including a new way to test the model. I conclude that in the case of isotope exchange, the interaction among these species is strong because diffusion is heterogeneous, whereas there is no strong interaction among different species in electrical conduction where diffusion is homogeneous (in an infinite crystal). Consequently, the slowest diffusing species controls the rate of isotope exchange, whereas the fastest diffusing species controls electrical conductivity leading to a different temperature dependence of activation energy and anisotropy. This model explains the differences in the activation energy and anisotropy between isotope diffusion and electrical conductivity, and predicts that the mechanism of electrical conductivity changes with temperature providing an explanation for most of the discrepancies among different experimental observations at different temperatures except for those by Poe et al. (2010) who reported anomalously high water content dependence and highly anisotropic activation energy. When the results obtained at high temperatures are used, most of the geophysically observed high and highly anisotropic electrical conductivity in the asthenosphere can be explained without invoking partial melting.

The exit-time problem for a Markov jump process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Examination of the four-fifths law for longitudinal third-order moments in incompressible magnetohydrodynamic turbulence in a periodic box.

PubMed

Yoshimatsu, Katsunori

2012-06-01

The four-fifths law for third-order longitudinal moments is examined, using direct numerical simulation (DNS) data on three-dimensional (3D) forced incompressible magnetohydrodynamic (MHD) turbulence without a uniformly imposed magnetic field in a periodic box. The magnetic Prandtl number is set to one, and the number of grid points is 512(3). A generalized Kármán-Howarth-Kolmogorov equation for second-order velocity moments in isotropic MHD turbulence is extended to anisotropic MHD turbulence by means of a spherical average over the direction of r. Here, r is a separation vector. The viscous, forcing, anisotropic and nonstationary terms in the generalized equation are quantified. It is found that the influence of the anisotropic terms on the four-fifths law is negligible at small scales, compared to that of the viscous term. However, the influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of r from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

NASA Astrophysics Data System (ADS)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

Transport of inertial anisotropic particles under surface gravity waves

NASA Astrophysics Data System (ADS)

Dibenedetto, Michelle; Koseff, Jeffrey; Ouellette, Nicholas

2016-11-01

The motion of neutrally and almost-neutrally buoyant particles under surface gravity waves is relevant to the transport of microplastic debris and other small particulates in the ocean. Consequently, a number of studies have looked at the transport of spherical particles or mobile plankton in these conditions. However, the effects of particle-shape anisotropy on the trajectories and behavior of irregularly shaped particles in this type of oscillatory flow are still relatively unknown. To better understand these issues, we created an idealized numerical model which simulates the three-dimensional behavior of anisotropic spheroids in flow described by Airy wave theory. The particle's response is calculated using a simplified Maxey-Riley equation coupled with Jeffery's equation for particle rotation. We show that the particle dynamics are strongly dependent on their initial conditions and shape, with some some additional dependence on Stokes number.

A new exact anisotropic solution of embedding class one

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Gupta, Y. K.; T. T., Smitha; Rahaman, Farook

2016-07-01

We have presented a new anisotropic solution of Einstein's field equations for compact-star models. Einstein's field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor ( Δ by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor ( Δ. The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2).

The mixing length parameter alpha. [in stellar structure calculations

NASA Technical Reports Server (NTRS)

Canuto, V. M.

1990-01-01

The standard mixing length theory, MLT, treats turbulent eddies as if they were isotropic, while the largest eddies that carry most of the flux are highly anisotropic. Recently, an anisotropic MLT was constructed, and the relevant equations derived. It is shown that these new equations can actually be cast in a form that is formally identical to that of the standard isotropic MLT, provided the mixing length parameter, derived from stellar structure calculations, is interpreted as an intermediate, auxiliary function alpha(x), where x, the degree of anisotropy is given as a function of the thermodynamic variables of the problem. The relation between alpha(x) and the physically relevant alpha(l = Hp) is also given. Once the value alpha is deduced, it is found to be a function of the local thermodynamic quantities, as expected.

An accurate discontinuous Galerkin method for solving point-source Eikonal equation in 2-D heterogeneous anisotropic media

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2018-03-01

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications.

Imaging of high-amylose starch tablets. 3. Initial diffusion and temperature effects.

PubMed

Thérien-Aubin, Héloïse; Baille, Wilms E; Zhu, Xiao Xia; Marchessault, Robert H

2005-01-01

The penetration of water into cross-linked high amylose starch tablets was studied at different temperatures by nuclear magnetic resonance (NMR) imaging, which follows the changes occurring at the surface and inside the starch tablets during swelling. It was found that the swelling was anisotropic, whereas water diffusion was almost isotropic. The water proton image profiles at the initial stage of water penetration were used to calculate the initial diffusion coefficient. The swelling and water concentration gradients in this controlled release system show significant temperature dependence. Diffusion behavior changed from Fickian to Case II diffusion with increasing temperature. The observed phenomena are attributed to the gelatinization of starch and the pseudo-cross-linking effect of double helix formation.

A practical implementation of 3D TTI reverse time migration with multi-GPUs

NASA Astrophysics Data System (ADS)

Li, Chun; Liu, Guofeng; Li, Yihang

2017-05-01

Tilted transversely isotropic (TTI) media are typical earth anisotropy media from practical observational studies. Accurate anisotropic imaging is recognized as a breakthrough in areas with complex anisotropic structures. TTI reverse time migration (RTM) is an important method for these areas. However, P and SV waves are coupled together in the pseudo-acoustic wave equation. The SV wave is regarded as an artifact for RTM of the P wave. We adopt matching of the anisotropy parameters to suppress the SV artifacts. Another problem in the implementation of TTI RTM is instability of the numerical solution for a variably oriented axis of symmetry. We adopt Fletcher's equation by setting a small amount of SV velocity without an acoustic approximation to stabilize the wavefield propagation. To improve calculation efficiency, we use NVIDIA graphic processing unit (GPU) with compute unified device architecture instead of traditional CPU architecture. To accomplish this, we introduced a random velocity boundary and an extended homogeneous anisotropic boundary for the remaining four anisotropic parameters in the source propagation. This process avoids large storage memory and IO requirements, which is important when using a GPU with limited bandwidth of PCI-E. Furthermore, we extend the single GPU code to multi-GPUs and present a corresponding high concurrent strategy with multiple asynchronous streams, which closely achieved an ideal speedup ratio of 2:1 when compared with a single GPU. Synthetic tests validate the correctness and effectiveness of our multi-GPUs-based TTI RTM method.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

Intermediate scattering function of an anisotropic active Brownian particle

PubMed Central

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-01-01

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations. PMID:27830719

Intermediate scattering function of an anisotropic active Brownian particle.

PubMed

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-10

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Intermediate scattering function of an anisotropic active Brownian particle

NASA Astrophysics Data System (ADS)

Kurzthaler, Christina; Leitmann, Sebastian; Franosch, Thomas

2016-10-01

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

On Coulomb collisions in the solar wind

NASA Astrophysics Data System (ADS)

Hellinger, P.; Travnicek, P. M.

2009-04-01

Collisional transport in anisotropic plasmas is investigated comparing theoretical predictions of the Fokker-Planck equation for bi-Maxwellian particle distribution functions (Kogan, 1961; Lehner, 1967) and results of the corresponding Langevin equation. References: Kogan, V. I., in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, edited by M. A. Leontovich, Pergamon Press, New York, , vol. 1, 153, 1961. Lehner, G., Zeitschrift fur Physik, 206, 284, 1967.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Diffusion-limited aggregation in two dimensions

NASA Astrophysics Data System (ADS)

Hurd, Alan J.; Schaefer, Dale W.

1985-03-01

We have studied the aggregation of silica microspheres confined to two dimensions at an air-water interface. Under microscopic observation, both monomers and clusters are seen to aggregate by a diffusion-limited process. The clusters' fractal dimension is 1.20+/-0.15, smaller than values obtained from current models of aggregation. We propose that anisotropic repulsive interactions account for the low dimensionality by more effectively repelling particles from the side of an existing dendrite than from the end.

Ellipsoidal Brownian self-driven particles in a magnetic field

NASA Astrophysics Data System (ADS)

Fan, Wai-Tong Louis; Pak, On Shun; Sandoval, Mario

2017-03-01

We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at a low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement, showing the effect of a particles's shape, activity, and magnetic field on the microswimmer's diffusion, is analytically obtained. Comparison between analytical and computational results shows good agreement. In addition, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is investigated.

Brownian motion of arbitrarily shaped particles in two dimensions.

PubMed

Chakrabarty, Ayan; Konya, Andrew; Wang, Feng; Selinger, Jonathan V; Sun, Kai; Wei, Qi-Huo

2014-11-25

We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.

Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

USGS Publications Warehouse

Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil

1984-01-01

The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.

Isogeometric Kirchhoff-Love shell formulations for biological membranes

PubMed Central

Tepole, Adrián Buganza; Kabaria, Hardik; Bletzinger, Kai-Uwe; Kuhl, Ellen

2015-01-01

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis. PMID:26251556

Magnetic field effect on charmonium formation in high energy nuclear collisions

DOE PAGES

Guo, Xingyu; Shi, Shuzhe; Xu, Nu; ...

2015-10-23

It is important to understand the strong external magnetic field generated at the very beginning of heavy ion collisions. We study the effect of the magnetic field on the anisotropic charmonium formation in Pb + Pb collisions at the LHC energy. The time dependent Schrödinger equation is employed to describe the motion ofmore » $$c\\bar{c}$$ pairs. We compare our model prediction of the non-collective anisotropic parameter v 2 of J/ψ with CMS data at high transverse momentum.« less

Laminated anisotropic reinforced plastic plates and shells

NASA Technical Reports Server (NTRS)

Korolev, V. I.

1981-01-01

Basic technical theories and engineering calculation equations for anisotropic plates and shells made of rigid reinforced plastics, mainly laminated fiberglass, are presented and discussed. Solutions are given for many problems of design of structural plates and shells, including curved sections and tanks, as well as two chapters on selection of the optimum materials, are given. Accounting for interlayer shearing and transverse separation, which are new engineering properties, are discussed. Application of the results obtained to thin three ply plates and shells wth a light elastic filler is presented and discussed.

The theory of transient radiation of a charged particle in a waveguide with an anisotropic magnetodielectric filling

NASA Astrophysics Data System (ADS)

Gevorkyan, E. A.

2015-08-01

We have considered transient radiation of a charged particle that moves at a constant velocity perpendicularly to the axis of a regular waveguide filled with an anisotropic magnetodielectric medium. Wave equations and analytical expressions for transverse electric (TE) and transverse magnetic (TM) fields in the waveguide have been found. Energies of transient radiation of the particle moving in a rectangular waveguide have been determined. We have obtained conditions of occurrence, the frequency, and the energy of Vavilov-Cherenkov radiation.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

NASA Astrophysics Data System (ADS)

Kushch, Volodymyr I.; Sevostianov, Igor; Giraud, Albert

2017-11-01

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

Anisotropic carrier mobility in single- and bi-layer C3N sheets

NASA Astrophysics Data System (ADS)

Wang, Xueyan; Li, Qingfang; Wang, Haifeng; Gao, Yan; Hou, Juan; Shao, Jianxin

2018-05-01

Based on the density functional theory combined with the Boltzmann transport equation with relaxation time approximation, we investigate the electronic structure and predict the carrier mobility of single- and bi-layer newly fabricated 2D carbon nitrides C3N. Although C3N sheets possess graphene-like planar hexagonal structure, the calculated carrier mobility is remarkably anisotropic, which is found mainly induced by the anisotropic effective masses and deformation potential constants. Importantly, we find that both the electron and hole mobilities are considerable high, for example, the hole mobility along the armchair direction of single-layer C3N sheets can arrive as high as 1.08 ×104 cm2 V-1 s-1, greatly larger than that of C2N-h2D and many other typical 2D materials. Owing to the high and anisotropic carrier mobility and appropriate band gap, single- and bi-layer semiconducting C3N sheets may have great potential applications in high performance electronic and optoelectronic devices.

The role of anisotropic thermal conduction in a collisionless magnetized hot accretion flow

NASA Astrophysics Data System (ADS)

Ghasemnezhad, Maryam

2018-06-01

We study the importance and the effects of anisotropic thermal conduction in a collisionless magnetized advection dominated accretion flow in the presence of discontinuity of mass, angular momentum and energy between inflow and outflow. In this paper, we have considered that the thermal conduction is a heating mechanism like viscosity and leads to an increase in the temperature of the gas. A set of self similar solutions are used for steady state and axisymmetric structure of such hot accretion disc to solve the MHD equations in our model. Based on these solutions, we have found that increasing the level of two parts of anisotropic thermal conduction (parallel & transverse) results in increasing the mass accretion rate or radial velocity but decreasing the rotational velocity. Also both radial and rotational velocities are sub-Keplerian. Also we have shown that the anisotropic thermal conduction can be effective in the parameter space of specific energy of outflow, toroidal and vertical components of magnetic field according to a physical constraint tinfall ≥ t⊥, conduction.

Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit

2017-03-01

The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.

A Numerical Model of Anisotropic Mass Transport Through Grain Boundary Networks

NASA Astrophysics Data System (ADS)

Wang, Yibo

Tin (Sn) thin films are commonly used in electronic circuit applications as coatings on contacts and solders for joining components. It is widely observed, for some such system, that whiskers---long, thin crystalline structures---emerge and grow from the film. The Sn whisker phenomenon has become a highly active research area since Sn whiskers have caused a large amount of damage and loss in manufacturing, military, medical and power industries. Though lead (Pb) addition to Sn has been used to solve this problem for over five decades, the adverse environmental and health effects of Pb have motivated legislation to severely constrain Pb use in society. People are researching and seeking the reasons which cause whiskers and corresponding methods to solve the problem. The contributing factors to cause a Sn whisker are potentially many and much still remains unknown. Better understanding of fundamental driving forces should point toward strategies to improve (a) the accuracy with which we can predict whisker formation, and (b) our ability to mitigate the phenomenon. This thesis summarizes recent important research achievements in understanding Sn whisker formation and growth, both experimentally and theoretically. Focus is then placed on examining the role that anisotropy in grain boundary diffusivity plays in determining whisker characteristics (specifically, whether they form and, if so, where on a surface). To study this aspect of the problem and to enable future studies on stress driven grain boundary diffusion, this thesis presents a numerical anisotropic mass transport model. In addition to presenting details of the model and implementation, model predictions for a set of increasingly complex grain boundary networks are discussed. Preliminary results from the model provide evidence that anisotropic grain boundary diffusion may be a primary driving mechanism in whisker formation.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Cosmic transit and anisotropic models in f(R,T) gravity

NASA Astrophysics Data System (ADS)

Sahu, S. K.; Tripathy, S. K.; Sahoo, P. K.; Nath, A.

2017-06-01

Accelerating cosmological models are constructed in a modified gravity theory dubbed as $f(R,T)$ gravity at the backdrop of an anisotropic Bianchi type-III universe. $f(R,T)$ is a function of the Ricci scalar $R$ and the trace $T$ of the energy-momentum tensor and it replaces the Ricci scalar in the Einstein-Hilbert action of General Relativity. The models are constructed for two different ways of modification of the Einstein-Hilbert action. Exact solutions of the field equations are obtained by a novel method of integration. We have explored the behaviour of the cosmic transit from an decelerated phase of expansion to an accelerated phase to get the dynamical features of the universe. Within the formalism of the present work, it is found that, the modification of the Einstein-Hilbert action does not affect the scale factor. However the dynamics of the effective dark energy equation of state is significantly affected.

A novel methodology for radiative transfer in a planetary atmosphere. I - The functions a exponent m and b exponent m of anisotropic scattering

NASA Technical Reports Server (NTRS)

Fymat, A. L.; Kalaba, R. E.

1977-01-01

The original problem of anisotropic scattering in an atmosphere illuminated by a unidirectional source is replaced by an analogous formulation where the incident light is omnidirectional. A radiative-transfer equation for the omnidirectional case is obtained in which the direction of illumination plays no role and the source-function analog, Sobolev's (1972) source function Phi exponent m, contains only a single integral term. For radiation incident on the top or the bottom of the atmosphere, this equation involves the functions b exponent m and h exponent m, respectively, with m corresponding to the order of the harmonic component of the scattered radiation field; these two functions are shown to be only one through some simple reciprocity relations. The transfer problem is then reformulated for the function a exponent m, in which case the source-function analog (Sobolev's function D exponent m) involves incident direction.

Plane waves in magneto-thermoelastic anisotropic medium based on (L-S) theory under the effect of Coriolis and centrifugal forces

NASA Astrophysics Data System (ADS)

Alesemi, Meshari

2018-04-01

The objective of this research is to illustrate the effectiveness of the thermal relaxation time based on the theory of Lord-Shulman (L-S), Coriolis and Centrifugal Forces on the reflection coefficients of plane waves in an anisotropic magneto-thermoelastic medium. Assuming the elastic medium is rotating with stable angular velocity and the imposed magnetic field is parallel to the boundary of the half-space. The basic equations of a transversely isotropic rotating magneto-thermoelastic medium are formulated according to thermoelasticity theory of Lord-Shulman (L-S). Next to that, getting the velocity equation which is illustrated to show existence of three quasi-plane waves propagating in the medium. The amplitude ratios coefficients of these plane waves have been given and then computed numerically and plotted graphically to demonstrate the influences of the rotation on the Zinc material.

Relativistic compact stars with charged anisotropic matter

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Banerjee, Ayan; Channuie, Phongpichit

2018-05-01

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.

A fiber-reinforced-fluid model of anisotropic plant root cell growth

NASA Astrophysics Data System (ADS)

Jensen, Oliver E.; Dyson, Rosemary J.

2009-11-01

We present a theoretical model of a single cell in the expansion zone of the primary root of the plant Arabidopsis thaliana. The cell undergoes rapid elongation with approximately constant radius. Growth is driven by high internal turgor pressure causing viscous stretching of the cell wall, with embedded cellulose microfibrils providing the wall with strongly anisotropic properties. We represent the cell as a thin cylindrical fiber-reinforced viscous sheet between rigid end plates. Asymptotic reduction of the governing equations, under simple sets of assumptions about fiber and wall properties, yields variants of the traditional Lockhart equation that relates the axial cell growth rate to the internal pressure. The model provides insights into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and shows how either dynamical changes in wall material properties or passive fibre reorientation may suppress cell elongation.

Non-interferometric determination of optical anisotropy in highly-oriented fibres using transport intensity equation technique

NASA Astrophysics Data System (ADS)

Sokkar, T. Z. N.; El-Farahaty, K. A.; El-Bakary, M. A.; Raslan, M. I.; Omar, E. Z.; Hamza, A. A.

2018-03-01

The optical setup of the transport intensity equation (TIE) technique is developed to be valid for measuring the optical properties of the highly-oriented anisotropic fibres. This development is based on the microstructure models of the highly-oriented anisotropic fibres and the principle of anisotropy. We provide the setup of TIE technique with polarizer which is controlled via stepper motor. This developed technique is used to investigate the refractive indices in the parallel and perpendicular polarization directions of light for the highly-oriented poly (ethylene terephthalate) (PET) fibres and hence its birefringence. The obtained results through the developed TIE technique for PET fibre are compared with that determined experimentally using the Mach-Zehnder interferometer under the same conditions. The comparison shows a good agreement between the obtained results from the developed technique and that obtained from the Mach-Zehnder interferometer technique.

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Juan, Pierre -Alexandre; Dingreville, Remi

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to themore » complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.« less

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

DOE PAGES

Juan, Pierre -Alexandre; Dingreville, Remi

2017-09-13

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to themore » complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.« less

A new anisotropic compact star model having Matese & Whitman mass function

NASA Astrophysics Data System (ADS)

Bhar, Piyali; Ratanpal, B. S.

2016-07-01

Present paper proposed a new singularity free model of anisotropic compact star. The Einstein field equations are solved in closed form by utilizing Matese & Whitman mass function. The model parameters ρ, pr and pt all are well behaved inside the stellar interior and our model satisfies all the required conditions to be physically acceptable. The model given in the present work is compatible with observational data of compact objects like SAX J 1808.4-3658 (SS1), SAX J 1808.4-3658 (SS2) and 4U 1820-30. A particular model of 4U 1820-30 is studied in detail and found that it satisfies all the condition needed for physically acceptable model. The present work is the generalization of Sharma and Ratanpal (Int. J. Mod. Phys. D 22:1350074, 2013) model for compact stars admitting quadratic equation of state.

Phase space analysis for anisotropic universe with nonlinear bulk viscosity

NASA Astrophysics Data System (ADS)

Sharif, M.; Mumtaz, Saadia

2018-06-01

In this paper, we discuss phase space analysis of locally rotationally symmetric Bianchi type I universe model by taking a noninteracting mixture of dust like and viscous radiation like fluid whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. An autonomous system of equations is established by defining normalized dimensionless variables. In order to investigate stability of the system, we evaluate corresponding critical points for different values of the parameters. We also compute power-law scale factor whose behavior indicates different phases of the universe model. It is found that our analysis does not provide a complete immune from fine-tuning because the exponentially expanding solution occurs only for a particular range of parameters. We conclude that stable solutions exist in the presence of nonlinear model for bulk viscosity with different choices of the constant parameter m for anisotropic universe.

Transport Mechanism of Guest Methane in Water-Filled Nanopores

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bui, Tai; Phan, Anh; Cole, David R.

We computed the transport of methane through 1 nm wide slit-shaped pores carved out of selected solid substrates using classical molecular dynamics simulations. The transport mechanism was elucidated via the implementation of the well-tempered metadynamics algorithm, which allowed for the quantification and visualization of the free energy landscape sampled by the guest molecule. Models for silica, magnesium oxide, alumina, muscovite, and calcite were used as solid substrates. Slit-shaped pores of width 1 nm were carved out of these materials and filled with liquid water. Methane was then inserted at low concentration. The results show that the diffusion of methane throughmore » the hydrated pores is strongly dependent on the solid substrate. While methane molecules diffuse isotropically along the directions parallel to the pore surfaces in most of the pores considered, anisotropic diffusion was observed in the hydrated calcite pore. The differences observed in the various pores are due to local molecular properties of confined water, including molecular structure and solvation free energy. The transport mechanism and the diffusion coefficients are dependent on the free energy barriers encountered by one methane molecule as it migrates from one preferential adsorption site to a neighboring one. It was found that the heterogeneous water distribution in different hydration layers and the low free energy pathways in the plane parallel to the pore surfaces yield the anisotropic diffusion of methane molecules in the hydrated calcite pore. Our observations contribute to an ongoing debate on the relation between local free energy profiles and diffusion coefficients and could have important practical consequences in various applications, ranging from the design of selective membranes for gas separations to the sustainable deployment of shale gas.« less

Brain tumor classification using the diffusion tensor image segmentation (D-SEG) technique.

PubMed

Jones, Timothy L; Byrnes, Tiernan J; Yang, Guang; Howe, Franklyn A; Bell, B Anthony; Barrick, Thomas R

2015-03-01

There is an increasing demand for noninvasive brain tumor biomarkers to guide surgery and subsequent oncotherapy. We present a novel whole-brain diffusion tensor imaging (DTI) segmentation (D-SEG) to delineate tumor volumes of interest (VOIs) for subsequent classification of tumor type. D-SEG uses isotropic (p) and anisotropic (q) components of the diffusion tensor to segment regions with similar diffusion characteristics. DTI scans were acquired from 95 patients with low- and high-grade glioma, metastases, and meningioma and from 29 healthy subjects. D-SEG uses k-means clustering of the 2D (p,q) space to generate segments with different isotropic and anisotropic diffusion characteristics. Our results are visualized using a novel RGB color scheme incorporating p, q and T2-weighted information within each segment. The volumetric contribution of each segment to gray matter, white matter, and cerebrospinal fluid spaces was used to generate healthy tissue D-SEG spectra. Tumor VOIs were extracted using a semiautomated flood-filling technique and D-SEG spectra were computed within the VOI. Classification of tumor type using D-SEG spectra was performed using support vector machines. D-SEG was computationally fast and stable and delineated regions of healthy tissue from tumor and edema. D-SEG spectra were consistent for each tumor type, with constituent diffusion characteristics potentially reflecting regional differences in tissue microstructure. Support vector machines classified tumor type with an overall accuracy of 94.7%, providing better classification than previously reported. D-SEG presents a user-friendly, semiautomated biomarker that may provide a valuable adjunct in noninvasive brain tumor diagnosis and treatment planning. © The Author(s) 2014. Published by Oxford University Press on behalf of the Society for Neuro-Oncology.

Transport Mechanism of Guest Methane in Water-Filled Nanopores

DOE PAGES

Bui, Tai; Phan, Anh; Cole, David R.; ...

2017-05-11

We computed the transport of methane through 1 nm wide slit-shaped pores carved out of selected solid substrates using classical molecular dynamics simulations. The transport mechanism was elucidated via the implementation of the well-tempered metadynamics algorithm, which allowed for the quantification and visualization of the free energy landscape sampled by the guest molecule. Models for silica, magnesium oxide, alumina, muscovite, and calcite were used as solid substrates. Slit-shaped pores of width 1 nm were carved out of these materials and filled with liquid water. Methane was then inserted at low concentration. The results show that the diffusion of methane throughmore » the hydrated pores is strongly dependent on the solid substrate. While methane molecules diffuse isotropically along the directions parallel to the pore surfaces in most of the pores considered, anisotropic diffusion was observed in the hydrated calcite pore. The differences observed in the various pores are due to local molecular properties of confined water, including molecular structure and solvation free energy. The transport mechanism and the diffusion coefficients are dependent on the free energy barriers encountered by one methane molecule as it migrates from one preferential adsorption site to a neighboring one. It was found that the heterogeneous water distribution in different hydration layers and the low free energy pathways in the plane parallel to the pore surfaces yield the anisotropic diffusion of methane molecules in the hydrated calcite pore. Our observations contribute to an ongoing debate on the relation between local free energy profiles and diffusion coefficients and could have important practical consequences in various applications, ranging from the design of selective membranes for gas separations to the sustainable deployment of shale gas.« less

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Effects of Magnetic Field and Rotation on 3P2 Superfluidity in Neutron Stars

NASA Astrophysics Data System (ADS)

Masuda, Kota; Nitta, Muneto

2014-09-01

It is believed that an anisotropic 3P2 superfluid state is realized in the core of neutron stars. Historically, a lot of works (Anderson et al. (1961), Hoffberg et al. (1970) and Tamagaki (1970)) discussed the properties of 3P2 superfluid state. Ginzburg-Landau (GL) equation was derived by Fujita, Tsuneto (1972) and Richardson (1972). After that, Mermin (1974) solved the problem of minimizing GL free energy density for d-wave pairing and showed what ground states are realized. By using these results, Sauls and Serene (1978) concluded that the unitary phase is realized in BCS limit, and Sauls et al. (1982) showed 3P2 vortices have a spontaneous magnetization. In this presentation, we firstly introduce GL equation and show some analogy to that of spin2-BEC. In BCS limit, degenerate ground states are parameterized by one parameter. We show effects of gradient terms, magnetic field and rotation on ground states and half-quantized 3P2 vortices are the most stable states under certain conditions. Next, by using an anisotropic GL equation, we discuss a spontaneous magnetization caused by half-quantized 3P2 vortices and compare results with that of integer vortices. Finally, we comment on possible effects of 3P2 superfluid state on neutron star observables. It is believed that an anisotropic 3P2 superfluid state is realized in the core of neutron stars. Historically, a lot of works (Anderson et al. (1961), Hoffberg et al. (1970) and Tamagaki (1970)) discussed the properties of 3P2 superfluid state. Ginzburg-Landau (GL) equation was derived by Fujita, Tsuneto (1972) and Richardson (1972). After that, Mermin (1974) solved the problem of minimizing GL free energy density for d-wave pairing and showed what ground states are realized. By using these results, Sauls and Serene (1978) concluded that the unitary phase is realized in BCS limit, and Sauls et al. (1982) showed 3P2 vortices have a spontaneous magnetization. In this presentation, we firstly introduce GL equation and show some analogy to that of spin2-BEC. In BCS limit, degenerate ground states are parameterized by one parameter. We show effects of gradient terms, magnetic field and rotation on ground states and half-quantized 3P2 vortices are the most stable states under certain conditions. Next, by using an anisotropic GL equation, we discuss a spontaneous magnetization caused by half-quantized 3P2 vortices and compare results with that of integer vortices. Finally, we comment on possible effects of 3P2 superfluid state on neutron star observables. JSPS Research Fellowship for Young Scientists and Grant-in-Aid for Scientific Research (No. 25400268 and 25103720) from MEXT of Japan.

Preprocessing of SAR interferometric data using anisotropic diffusion filter

NASA Astrophysics Data System (ADS)

Sartor, Kenneth; Allen, Josef De Vaughn; Ganthier, Emile; Tenali, Gnana Bhaskar

2007-04-01

The most commonly used smoothing algorithms for complex data processing are blurring functions (i.e., Hanning, Taylor weighting, Gaussian, etc.). Unfortunately, the filters so designed blur the edges in a Synthetic Aperture Radar (SAR) scene, reduce the accuracy of features, and blur the fringe lines in an interferogram. For the Digital Surface Map (DSM) extraction, the blurring of these fringe lines causes inaccuracies in the height of the unwrapped terrain surface. Our goal here is to perform spatially non-uniform smoothing to overcome the above mentioned disadvantages. This is achieved by using a Complex Anisotropic Non-Linear Diffuser (CANDI) filter that is a spatially varying. In particular, an appropriate choice of the convection function in the CANDI filter is able to accomplish the non-uniform smoothing. This boundary sharpening intra-region smoothing filter acts on interferometric SAR (IFSAR) data with noise to produce an interferogram with significantly reduced noise contents and desirable local smoothing. Results of CANDI filtering will be discussed and compared with those obtained by using the standard filters on simulated data.

Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models

NASA Astrophysics Data System (ADS)

Jeong, Hyun-Sik; Ahn, Yongjun; Ahn, Dujin; Niu, Chao; Li, Wei-Jia; Kim, Keun-Young

2018-01-01

We study a relation between the thermal diffusivity ( D T ) and two quantum chaotic properties, Lyapunov time (τ L ) and butterfly velocity ( v B ) in strongly correlated systems by using a holographic method. Recently, it was shown that E_i:={D}_{T,i}/({v}{^{B,i}}^2{τ}_L)(i=x,y) is universal in the sense that it is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, by analyzing the anisotropic IR scaling geometry carefully, we find the concrete expressions for E_i in terms of the critical dynamical exponents z i in each direction, E_i={z}_i/2({z}_i-1) . Furthermore, we find the lower bound of E_i is always 1 /2, which is not affected by anisotropy, contrary to the η/s case. However, there may be an upper bound determined by given fixed anisotropy.

Anisotropic reflectance from turbid media. I. Theory.

PubMed

Neuman, Magnus; Edström, Per

2010-05-01

It is shown that the intensity of light reflected from plane-parallel turbid media is anisotropic in all situations encountered in practice. The anisotropy, in the form of higher intensity at large polar angles, increases when the amount of near-surface bulk scattering is increased, which dominates in optically thin and highly absorbing media. The only situation with isotropic intensity is when a non-absorbing infinitely thick medium is illuminated diffusely. This is the only case where the Kubelka-Munk model gives exact results and there exists an exact translation between Kubelka-Munk and general radiative transfer. This also means that a bulk scattering perfect diffusor does not exist. Angle-resolved models are thus crucial for a correct understanding of light scattering in turbid media. The results are derived using simulations and analytical calculations. It is also shown that there exists an optimal angle for directional detection that minimizes the error introduced when using the Kubelka-Munk model to interpret reflectance measurements with diffuse illumination.

Combined measurement of surface, grain boundary and lattice diffusion coefficients on olivine bi-crystals

NASA Astrophysics Data System (ADS)

Marquardt, Katharina; Dohmen, Ralf; Wagner, Johannes

2014-05-01

Diffusion along interface and grain boundaries provides an efficient pathway and may control chemical transport in rocks as well as their mechanical strength. Besides the significant relevance of these diffusion processes for various geologic processes, experimental data are still very limited (e.g., Dohmen & Milke, 2010). Most of these data were measured using polycrystalline materials and the formalism of LeClaire (1951) to fit integrated concentration depth profiles. To correctly apply this formalism, certain boundary conditions of the diffusion problem need to be fulfilled, e.g., surface diffusion is ignored, and furthermore the lattice diffusion coefficient has to be known from other studies or is an additional fitting parameter, which produces some ambiguity in the derived grain boundary diffusion coefficients. We developed an experimental setup where we can measure the lattice and grain boundary diffusion coefficients simultaneously but independent and demonstrate the relevance of surface diffusion for typical grain boundary diffusion experiments. We performed Mg2SiO4 bicrystal diffusion experiments, where a single grain boundary is covered by a thin-film of pure Ni2SiO4 acting as diffusant source, produced by pulsed laser deposition. The investigated grain boundary is a 60° (011)/[100]. This specific grain boundary configuration was modeled using molecular dynamics for comparison with the experimental observations in the transmission electron microscope (TEM). Both, experiment and model are in good agreement regarding the misorientation, whereas there are still some disagreements regarding the strain fields along the grain boundary that are of outmost importance for the strengths of the material. The subsequent diffusion experiments were carried out in the temperature range between 800° and 1450° C. The inter diffusion profiles were measured using the TEMs energy dispersive x-ray spectrometer standardized using the Cliff-Lorimer equation and EMPA measurements. To evaluate the obtained diffusion profiles we adapted the isolated grain boundary model, first proposed by Fisher (1951) to match several observations: (i) Anisotropic diffusion in forsterite, (ii) fast diffusion along the grain boundary, (iii) fast diffusion on the surface of the sample. The latter process is needed to explain an additional flux of material from the surface into the grain boundary. Surface and grain boundary diffusion coefficients are on the order of 10000 times faster than diffusion in the lattice. Another observation was that in some regions the diffusion profiles in the lattice were greatly extended. TEM observations suggest here that surface defects (nano-cracks, ect.) have been present, which apparently enhanced the diffusion through the bulk lattice. Dohmen, R., & Milke, R. (2010). Diffusion in Polycrystalline Materials: Grain Boundaries, Mathematical Models, and Experimental Data. Reviews in Mineralogy and Geochemistry, 72(1), 921-970. Fisher, J. C. (1951). Calculations of Diffusion Penetration Curves for Surface and Grain Boundary Diffusion. Journal of Applied Physics, 22(1), 74-77. Le Claire, A. D. (1951). Grain boundary diffusion in metals. Philosophical Magazine A, 42(328), 468-474.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Anisotropic Damage Mechanics Modeling in Metal Matrix Composites

DTIC Science & Technology

1993-05-15

conducted on a titanium aluminide SiC-reinforced metal matrix composite. Center-cracked plates with laminate layups of (0/90) and (±45). were tested... interfacial damage mechanisms as debonding or delamination. Equations (2.14) and (2.15) represent the damage transformation equations for the stress... titanium aluminide SiC 46 continuous reinforced metal matrix composite. As a means of enforcing quality assurance, all manufacturing and cutting of the

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Ellipsoidal Brownian self-driven particles in a magnetic field

NASA Astrophysics Data System (ADS)

Sandoval, Mario; Wai-Tong, Fan; Shun Pak, On

We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement showing the effect of particles's shape, activity, and magnetic field on the microswimmer's diffusion is analytically obtained. A comparison among analytical and computational results is also made and we obtain good agreement. Additionally, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is also elucidated. CONACYT GRANT: CB 2014/237848.

A diffuse interface model of grain boundary faceting

NASA Astrophysics Data System (ADS)

Abdeljawad, F.; Medlin, D. L.; Zimmerman, J. A.; Hattar, K.; Foiles, S. M.

2016-06-01

Interfaces, free or internal, greatly influence the physical properties and stability of materials microstructures. Of particular interest are the processes that occur due to anisotropic interfacial properties. In the case of grain boundaries (GBs) in metals, several experimental observations revealed that an initially flat GB may facet into hill-and-valley structures with well defined planes and corners/edges connecting them. Herein, we present a diffuse interface model that is capable of accounting for strongly anisotropic GB properties and capturing the formation of hill-and-valley morphologies. The hallmark of our approach is the ability to independently examine the various factors affecting GB faceting and subsequent facet coarsening. More specifically, our formulation incorporates higher order expansions to account for the excess energy due to facet junctions and their non-local interactions. As a demonstration of the modeling capability, we consider the Σ5 <001 > tilt GB in body-centered-cubic iron, where faceting along the {210} and {310} planes was experimentally observed. Atomistic calculations were utilized to determine the inclination-dependent GB energy, which was then used as an input in our model. Linear stability analysis and simulation results highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. Broadly speaking, our modeling approach provides a general framework to examine the microstructural stability of polycrystalline systems with highly anisotropic GBs.

Effective orthorhombic anisotropic models for wavefield extrapolation

NASA Astrophysics Data System (ADS)

Ibanez-Jacome, Wilson; Alkhalifah, Tariq; Waheed, Umair bin

2014-09-01

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, we 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, 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.

Exact renormalization group equation for the Lifshitz critical point

NASA Astrophysics Data System (ADS)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Study of conformally flat polytropes with tilted congruence

NASA Astrophysics Data System (ADS)

Sharif, M.; Sadiq, Sobia

This paper is aimed to study the modeling of spherically symmetric spacetime in the presence of anisotropic dissipative fluid configuration. This is accomplished for an observer moving relative to matter content using two cases of polytropic equation-of-state under conformally flat condition. We formulate the corresponding generalized Tolman-Oppenheimer-Volkoff equation, mass equation, as well as energy conditions for both cases. The conformally flat condition is imposed to find an expression for anisotropy which helps to study spherically symmetric polytropes. Finally, Tolman mass is used to analyze stability of the resulting models.

Projecting diffusion along the normal bundle of a plane curve

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Relativistic model for anisotropic strange stars

NASA Astrophysics Data System (ADS)

Deb, Debabrata; Chowdhury, Sourav Roy; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2017-12-01

In this article, we attempt to find a singularity free solution of Einstein's field equations for compact stellar objects, precisely strange (quark) stars, considering Schwarzschild metric as the exterior spacetime. To this end, we consider that the stellar object is spherically symmetric, static and anisotropic in nature and follows the density profile given by Mak and Harko (2002) , which satisfies all the physical conditions. To investigate different properties of the ultra-dense strange stars we have employed the MIT bag model for the quark matter. Our investigation displays an interesting feature that the anisotropy of compact stars increases with the radial coordinate and attains its maximum value at the surface which seems an inherent property for the singularity free anisotropic compact stellar objects. In this connection we also perform several tests for physical features of the proposed model and show that these are reasonably acceptable within certain range. Further, we find that the model is consistent with the energy conditions and the compact stellar structure is stable with the validity of the TOV equation and Herrera cracking concept. For the masses below the maximum mass point in mass vs radius curve the typical behavior achieved within the framework of general relativity. We have calculated the maximum mass and radius of the strange stars for the three finite values of bag constant Bg.

Role of pressure anisotropy on relativistic compact stars

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Banerjee, Ayan; Hansraj, Sudan

2018-02-01

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [Phys. Rev. D 67, 104015 (2003), 10.1103/PhysRevD.67.104015]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this model, such as the energy conditions, speeds of sound, and compactness of the star, in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

A microscale turbine driven by diffusive mass flux.

PubMed

Yang, Mingcheng; Liu, Rui; Ripoll, Marisol; Chen, Ke

2015-10-07

An external diffusive mass flux is shown to be able to generate a mechanical torque on a microscale object based on anisotropic diffusiophoresis. In light of this finding, we propose a theoretical prototype micro-turbine driven purely by diffusive mass flux, which is in strong contrast to conventional turbines driven by convective mass flows. The rotational velocity of the proposed turbine is determined by the external concentration gradient, the geometry and the diffusiophoretic properties of the turbine. This scenario is validated by performing computer simulations. Our finding thus provides a new type of chemo-mechanical response which could be used to exploit existing chemical energies at small scales.

Anisotropic Diffusion of Surface Normals for Feature Preserving Surface Reconstruction

DTIC Science & Technology

2003-04-18

Jacobi Formulations”, J. Comp. Physics, 79, pp. 12–49, 1988. [9] R . Malladi , J. A. Sethian, and B. C. Vemuri, “Shape Modeling with Front Propagation...implement the constrained minimization with the following second-order PDE: T | T 0 >�� � � | r �m| `ih� ~��  GGa`���|�GdG �-� � `���| � (4.1...100 1000 Weight D is ta n ce ( r m s) Surface area Isotropic curvature Anisotropic curvature (a) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.001

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics.

PubMed

Hoover, Wm G; Hoover, Carol G

2010-04-01

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivanov, A. A., E-mail: aai@a5.kiam.ru; Martynov, A. A., E-mail: martynov@a5.kiam.ru; Medvedev, S. Yu., E-mail: medvedev@a5.kiam.ru

In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (withmore » arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented.« less

Three-dimensional magnetotelluric axial anisotropic forward modeling and inversion

NASA Astrophysics Data System (ADS)

Cao, Hui; Wang, Kunpeng; Wang, Tao; Hua, Boguang

2018-06-01

Magnetotelluric (MT) data has been widely used to image underground electrical structural. However, when the significant axial resistivity anisotropy presents, how this influences three-dimensional MT data has not been resolved clearly yet. We here propose a scheme for three-dimensional modeling of MT data in presence of axial anisotropic resistivity, where the electromagnetic fields are decomposed into primary and secondary components. A 3D staggered-grid finite difference method is then used to resolve the resulting 3D governing equations. Numerical tests have completed to validate the correctness and accuracy of the present algorithm. A limited-memory Broyden-Fletcher-Goldfarb-Shanno method is then utilized to realize the 3D MT axial anisotropic inversion. The testing results show that, compared to the results of isotropic resistivity inversion, taking account the axial anisotropy can much improve the inverted results.

(3+1)D Quasiparticle Anisotropic Hydrodynamics for Ultrarelativistic Heavy-Ion Collisions.

PubMed

Alqahtani, Mubarak; Nopoush, Mohammad; Ryblewski, Radoslaw; Strickland, Michael

2017-07-28

We present the first comparisons of experimental data with phenomenological results from (3+1)D quasiparticle anisotropic hydrodynamics (aHydroQP). We compare particle spectra, average transverse momentum, and elliptic flow. The dynamical equations used for the hydrodynamic stage utilize aHydroQP, which naturally includes both shear and bulk viscous effects. The (3+1)D aHydroQP evolution obtained is self-consistently converted to hadrons using anisotropic Cooper-Frye freeze-out. Hadron production and decays are modeled using a customized version of therminator 2. In this first study, we utilized smooth Glauber-type initial conditions and a single effective freeze-out temperature T_{FO}=130  MeV with all hadronic species in full chemical equilibrium. With this rather simple setup, we find a very good description of many heavy-ion observables.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

Methodological improvements in voxel-based analysis of diffusion tensor images: applications to study the impact of apolipoprotein E on white matter integrity.

PubMed

Newlander, Shawn M; Chu, Alan; Sinha, Usha S; Lu, Po H; Bartzokis, George

2014-02-01

To identify regional differences in apparent diffusion coefficient (ADC) and fractional anisotropy (FA) using customized preprocessing before voxel-based analysis (VBA) in 14 normal subjects with the specific genes that decrease (apolipoprotein [APO] E ε2) and that increase (APOE ε4) the risk of Alzheimer's disease. Diffusion tensor images (DTI) acquired at 1.5 Tesla were denoised with a total variation tensor regularization algorithm before affine and nonlinear registration to generate a common reference frame for the image volumes of all subjects. Anisotropic and isotropic smoothing with varying kernel sizes was applied to the aligned data before VBA to determine regional differences between cohorts segregated by allele status. VBA on the denoised tensor data identified regions of reduced FA in APOE ε4 compared with the APOE ε2 healthy older carriers. The most consistent results were obtained using the denoised tensor and anisotropic smoothing before statistical testing. In contrast, isotropic smoothing identified regional differences for small filter sizes alone, emphasizing that this method introduces bias in FA values for higher kernel sizes. Voxel-based DTI analysis can be performed on low signal to noise ratio images to detect subtle regional differences in cohorts using the proposed preprocessing techniques. Copyright © 2013 Wiley Periodicals, Inc.

Existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Alves, Claudianor O.; Miyagaki, Olímpio H.

2017-08-01

In this paper, we establish some results concerning the existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation. Variational methods are used to get an existence result, as well as, to study the concentration phenomenon, while the regularity is more delicate because we are leading with functions in an anisotropic Sobolev space.

LIMEPY: Lowered Isothermal Model Explorer in PYthon

NASA Astrophysics Data System (ADS)

Gieles, Mark; Zocchi, Alice

2017-10-01

LIMEPY solves distribution function (DF) based lowered isothermal models. It solves Poisson's equation used on input parameters and offers fast solutions for isotropic/anisotropic, single/multi-mass models, normalized DF values, density and velocity moments, projected properties, and generates discrete samples.

Green's function integral equation method for propagation of electromagnetic waves in an anisotropic dielectric-magnetic slab

NASA Astrophysics Data System (ADS)

Shu, Weixing; Lv, Xiaofang; Luo, Hailu; Wen, Shuangchun

2010-08-01

We extend the Green's function integral method to investigate the propagation of electromagnetic waves through an anisotropic dielectric-magnetic slab. From a microscopic perspective, we analyze the interaction of wave with the slab and derive the propagation characteristics by self-consistent analyses. Applying the results, we find an alternative explanation to the general mechanism for the photon tunneling. The results are confirmed by numerical simulations and disclose the underlying physics of wave propagation through slab. The method extended is applicable to other problems of propagation in dielectric-magnetic materials, including metamaterials.

Anisotropic mimetic cosmology

NASA Astrophysics Data System (ADS)

Abbassi, M. H.; Jozani, A.; Sepangi, H. R.

2018-06-01

We consider a mimetic set up in which the mimetic scalar is coupled to a vector field. It is shown that such a field with a timelike component does not contribute to the background equations and yet produces healthy isocurvature perturbations with respect to ghost and gradient instabilities in spite of the absence of any propagating curvature perturbations at the level of the quadratic action. We then consider a vector field with spacelike components, which leads to an anisotropic Bianchi universe, and show that the ghost and gradient instabilities are absent in the limit of high momenta and that the propagating curvature perturbations have healthy UV behavior.

An elementary singularity-free Rotational Brownian Dynamics algorithm for anisotropic particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ilie, Ioana M.; Briels, Wim J.; MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede

2015-03-21

Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.

Anisotropic light diffraction in crystals with a large acoustic-energy walk-off

NASA Astrophysics Data System (ADS)

Balakshy, V. I.; Voloshin, A. S.; Molchanov, V. Ya.

2014-11-01

The influence of energy walk-off in an acoustic beam on the characteristic of anisotropic Bragg diffraction of light has been investigated by the example of paratellurite crystal. The angular and frequency characteristics of acousto-optic diffraction have been calculated in wide ranges of ultrasound frequencies and Bragg angles using the modified Raman-Nath equations. It is shown that the walk-off of an acoustic beam may change (either widen or narrow) significantly the frequency and angular ranges. The calculation results have been experimentally checked on an acousto-optic cell made of 10.5°-cut paratellurite crystal.

Hexagonally ordered nanodots: Result of substrate rotation during oblique incidence low energy IBS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chowdhury, Debasree, E-mail: debasree.chowdhury@saha.ac.in; Ghose, Debabrata, E-mail: debasree.chowdhury@saha.ac.in

The anisotropic regular patterns are often results during oblique incidence ion beam sputtering (IBS). Simultaneous substrate rotation (SR) during IBS can suppress surface roughening and removes anisotropic nature of surface pattern. Here, the evolution of Si surface morphology as result of with and without SR is studied during oblique incidence low energy Ar{sup +} sputtering. Resultant topography shows smooth surface to hexagonally ordered nanodots at different rotating conditions. Interestingly, surface roughness exhibits non-monotonic dependence on rotation frequency. The underlying mechanism for dot formation can be described within the framework of isotropic DKS equation.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE PAGES

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; ...

2017-02-21

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

Worst case prediction of additives migration from polystyrene for food safety purposes: a model update.

PubMed

Martínez-López, Brais; Gontard, Nathalie; Peyron, Stéphane

2018-03-01

A reliable prediction of migration levels of plastic additives into food requires a robust estimation of diffusivity. Predictive modelling of diffusivity as recommended by the EU commission is carried out using a semi-empirical equation that relies on two polymer-dependent parameters. These parameters were determined for the polymers most used by packaging industry (LLDPE, HDPE, PP, PET, PS, HIPS) from the diffusivity data available at that time. In the specific case of general purpose polystyrene, the diffusivity data published since then shows that the use of the equation with the original parameters results in systematic underestimation of diffusivity. The goal of this study was therefore, to propose an update of the aforementioned parameters for PS on the basis of up to date diffusivity data, so the equation can be used for a reasoned overestimation of diffusivity.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

A Novel A Posteriori Investigation of Scalar Flux Models for Passive Scalar Dispersion in Compressible Boundary Layer Flows

NASA Astrophysics Data System (ADS)

Braman, Kalen; Raman, Venkat

2011-11-01

A novel direct numerical simulation (DNS) based a posteriori technique has been developed to investigate scalar transport modeling error. The methodology is used to test Reynolds-averaged Navier-Stokes turbulent scalar flux models for compressible boundary layer flows. Time-averaged DNS velocity and turbulence fields provide the information necessary to evolve the time-averaged scalar transport equation without requiring the use of turbulence modeling. With this technique, passive dispersion of a scalar from a boundary layer surface in a supersonic flow is studied with scalar flux modeling error isolated from any flowfield modeling errors. Several different scalar flux models are used. It is seen that the simple gradient diffusion model overpredicts scalar dispersion, while anisotropic scalar flux models underpredict dispersion. Further, the use of more complex models does not necessarily guarantee an increase in predictive accuracy, indicating that key physics is missing from existing models. Using comparisons of both a priori and a posteriori scalar flux evaluations with DNS data, the main modeling shortcomings are identified. Results will be presented for different boundary layer conditions.

Coherent 3D nanostructure of γ-Al{sub 2}O{sub 3}: Simulation of whole X-ray powder diffraction pattern

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pakharukova, V.P., E-mail: verapakh@catalysis.ru; Novosibirsk State University, Pirogova Street 2, 630090 Novosibirsk; Research and Educational Center for Energy Efficient Catalysis, Novosibirsk State University, Novosibirsk 630090

2017-02-15

The structure and nanostructure features of nanocrystalline γ-Al{sub 2}O{sub 3} obtained by dehydration of boehmite with anisotropic platelet-shaped particles were investigated. The original models of 3D coherent nanostructure of γ-Al{sub 2}O{sub 3} were constructed. The models of nanostructured γ-Al{sub 2}O{sub 3} particles were first confirmed by a direct simulation of powder X–Ray diffraction (XRD) patterns using the Debye Scattering Equation (DSE) with assistance of high-resolution transmission electron microscopy (HRTEM) study. The average crystal structure of γ-Al{sub 2}O{sub 3} was shown to be tetragonally distorted. The experimental results revealed that thin γ-Al{sub 2}O{sub 3} platelets were heterogeneous on a nanometer scalemore » and nanometer-sized building blocks were separated by partially coherent interfaces. The XRD simulation results showed that a specific packing of the primary crystalline blocks in the nanostructured γ-Al{sub 2}O{sub 3} particles with formation of planar defects on (001), (100), and (101) planes nicely accounted for pronounced diffuse scattering, anisotropic peak broadening and peak shifts in the experimental XRD pattern. The identified planar defects in cation sublattice seem to be described as filling cation non-spinel sites in existing crystallographic models of γ-Al{sub 2}O{sub 3} structure. The overall findings provided an insight into the complex nanostructure, which is intrinsic to the metastable γ-Al{sub 2}O{sub 3} oxide. - Highlights: • Thin plate-like crystallites of γ-Al{sub 2}O{sub 3} were obtained. • Models of 3D coherent nanostructure of γ-Al{sub 2}O{sub 3} were constructed. • Models were verified by simulating XRD patterns using the Debye Scattering Equation. • Specific broadening of XRD peaks was explained in terms of planar defects. • Primary crystalline blocks in γ-Al{sub 2}O{sub 3} are separated by partially coherent interfaces.« less

Scaling laws and reduced-order models for mixing and reactive-transport in heterogeneous anisotropic porous media

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Karra, S.; Nakshatrala, K. B.

2016-12-01

Fundamental to enhancement and control of the macroscopic spreading, mixing, and dilution of solute plumes in porous media structures is the topology of flow field and underlying heterogeneity and anisotropy contrast of porous media. Traditionally, in literature, the main focus was limited to the shearing effects of flow field (i.e., flow has zero helical density, meaning that flow is always perpendicular to vorticity vector) on scalar mixing [2]. However, the combined effect of anisotropy of the porous media and the helical structure (or chaotic nature) of the flow field on the species reactive-transport and mixing has been rarely studied. Recently, it has been experimentally shown that there is an irrefutable evidence that chaotic advection and helical flows are inherent in porous media flows [1,2]. In this poster presentation, we present a non-intrusive physics-based model-order reduction framework to quantify the effects of species mixing in-terms of reduced-order models (ROMs) and scaling laws. The ROM framework is constructed based on the recent advancements in non-negative formulations for reactive-transport in heterogeneous anisotropic porous media [3] and non-intrusive ROM methods [4]. The objective is to generate computationally efficient and accurate ROMs for species mixing for different values of input data and reactive-transport model parameters. This is achieved by using multiple ROMs, which is a way to determine the robustness of the proposed framework. Sensitivity analysis is performed to identify the important parameters. Representative numerical examples from reactive-transport are presented to illustrate the importance of the proposed ROMs to accurately describe mixing process in porous media. [1] Lester, Metcalfe, and Trefry, "Is chaotic advection inherent to porous media flow?," PRL, 2013. [2] Ye, Chiogna, Cirpka, Grathwohl, and Rolle, "Experimental evidence of helical flow in porous media," PRL, 2015. [3] Mudunuru, and Nakshatrala, "On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method," JCP, 2016. [4] Quarteroni, Manzoni, and Negri. "Reduced Basis Methods for Partial Differential Equations: An Introduction," Springer, 2016.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

An Exploration into Diffusion Tensor Imaging in the Bovine Ocular Lens

PubMed Central

Vaghefi, Ehsan; Donaldson, Paul J.

2013-01-01

We describe our development of the diffusion tensor imaging modality for the bovine ocular lens. Diffusion gradients were added to a spin-echo pulse sequence and the relevant parameters of the sequence were refined to achieve good diffusion weighting in the lens tissue, which demonstrated heterogeneous regions of diffusive signal attenuation. Decay curves for b-value (loosely summarizes the strength of diffusion weighting) and TE (determines the amount of magnetic resonance imaging-obtained signal) were used to estimate apparent diffusion coefficients (ADC) and T2 in different lens regions. The ADCs varied by over an order of magnitude and revealed diffusive anisotropy in the lens. Up to 30 diffusion gradient directions, and 8 signal acquisition averages, were applied to lenses in culture in order to improve maps of diffusion tensor eigenvalues, equivalent to ADC, across the lens. From these maps, fractional anisotropy maps were calculated and compared to known spatial distributions of anisotropic molecular fluxes in the lens. This comparison suggested new hypotheses and experiments to quantitatively assess models of circulation in the avascular lens. PMID:23459990

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE PAGES

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

2015-04-14

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goodman, Roy H.; Kevrekidis, P. G.; Carretero-González, R.

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. In this study, we uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals inmore » the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system, we are able to construct complex periodic orbits in the original, PDE, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.« less

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.