Hybrid discrete ordinates and characteristics method for solving the linear Boltzmann equation

NASA Astrophysics Data System (ADS)

Yi, Ce

With the ability of computer hardware and software increasing rapidly, deterministic methods to solve the linear Boltzmann equation (LBE) have attracted some attention for computational applications in both the nuclear engineering and medical physics fields. Among various deterministic methods, the discrete ordinates method (SN) and the method of characteristics (MOC) are two of the most widely used methods. The SN method is the traditional approach to solve the LBE for its stability and efficiency. While the MOC has some advantages in treating complicated geometries. However, in 3-D problems requiring a dense discretization grid in phase space (i.e., a large number of spatial meshes, directions, or energy groups), both methods could suffer from the need for large amounts of memory and computation time. In our study, we developed a new hybrid algorithm by combing the two methods into one code, TITAN. The hybrid approach is specifically designed for application to problems containing low scattering regions. A new serial 3-D time-independent transport code has been developed. Under the hybrid approach, the preferred method can be applied in different regions (blocks) within the same problem model. Since the characteristics method is numerically more efficient in low scattering media, the hybrid approach uses a block-oriented characteristics solver in low scattering regions, and a block-oriented SN solver in the remainder of the physical model. In the TITAN code, a physical problem model is divided into a number of coarse meshes (blocks) in Cartesian geometry. Either the characteristics solver or the SN solver can be chosen to solve the LBE within a coarse mesh. A coarse mesh can be filled with fine meshes or characteristic rays depending on the solver assigned to the coarse mesh. Furthermore, with its object-oriented programming paradigm and layered code structure, TITAN allows different individual spatial meshing schemes and angular quadrature sets for each coarse mesh. Two quadrature types (level-symmetric and Legendre-Chebyshev quadrature) along with the ordinate splitting techniques (rectangular splitting and PN-TN splitting) are implemented. In the S N solver, we apply a memory-efficient 'front-line' style paradigm to handle the fine mesh interface fluxes. In the characteristics solver, we have developed a novel 'backward' ray-tracing approach, in which a bi-linear interpolation procedure is used on the incoming boundaries of a coarse mesh. A CPU-efficient scattering kernel is shared in both solvers within the source iteration scheme. Angular and spatial projection techniques are developed to transfer the angular fluxes on the interfaces of coarse meshes with different discretization grids. The performance of the hybrid algorithm is tested in a number of benchmark problems in both nuclear engineering and medical physics fields. Among them are the Kobayashi benchmark problems and a computational tomography (CT) device model. We also developed an extra sweep procedure with the fictitious quadrature technique to calculate angular fluxes along directions of interest. The technique is applied in a single photon emission computed tomography (SPECT) phantom model to simulate the SPECT projection images. The accuracy and efficiency of the TITAN code are demonstrated in these benchmarks along with its scalability. A modified version of the characteristics solver is integrated in the PENTRAN code and tested within the parallel engine of PENTRAN. The limitations on the hybrid algorithm are also studied.

Isotropic stochastic rotation dynamics

NASA Astrophysics Data System (ADS)

Mühlbauer, Sebastian; Strobl, Severin; Pöschel, Thorsten

2017-12-01

Stochastic rotation dynamics (SRD) is a widely used method for the mesoscopic modeling of complex fluids, such as colloidal suspensions or multiphase flows. In this method, however, the underlying Cartesian grid defining the coarse-grained interaction volumes induces anisotropy. We propose an isotropic, lattice-free variant of stochastic rotation dynamics, termed iSRD. Instead of Cartesian grid cells, we employ randomly distributed spherical interaction volumes. This eliminates the requirement of a grid shift, which is essential in standard SRD to maintain Galilean invariance. We derive analytical expressions for the viscosity and the diffusion coefficient in relation to the model parameters, which show excellent agreement with the results obtained in iSRD simulations. The proposed algorithm is particularly suitable to model systems bound by walls of complex shape, where the domain cannot be meshed uniformly. The presented approach is not limited to SRD but is applicable to any other mesoscopic method, where particles interact within certain coarse-grained volumes.

A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

NASA Astrophysics Data System (ADS)

Karimi-Fard, M.; Durlofsky, L. J.

2016-10-01

A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.

Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations

NASA Technical Reports Server (NTRS)

Jentink, Thomas Neil; Usab, William J., Jr.

1990-01-01

An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.

A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2000-01-01

Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

Electrostatic interactions in soft particle systems: mesoscale simulations of ionic liquids.

PubMed

Wang, Yong-Lei; Zhu, You-Liang; Lu, Zhong-Yuan; Laaksonen, Aatto

2018-05-21

Computer simulations provide a unique insight into the microscopic details, molecular interactions and dynamic behavior responsible for many distinct physicochemical properties of ionic liquids. Due to the sluggish and heterogeneous dynamics and the long-ranged nanostructured nature of ionic liquids, coarse-grained meso-scale simulations provide an indispensable complement to detailed first-principles calculations and atomistic simulations allowing studies over extended length and time scales with a modest computational cost. Here, we present extensive coarse-grained simulations on a series of ionic liquids of the 1-alkyl-3-methylimidazolium (alkyl = butyl, heptyl-, and decyl-) family with Cl, [BF4], and [PF6] counterions. Liquid densities, microstructures, translational diffusion coefficients, and re-orientational motion of these model ionic liquid systems have been systematically studied over a wide temperature range. The addition of neutral beads in cationic models leads to a transition of liquid morphologies from dispersed apolar beads in a polar framework to that characterized by bi-continuous sponge-like interpenetrating networks in liquid matrices. Translational diffusion coefficients of both cations and anions decrease upon lengthening of the neutral chains in the cationic models and by enlarging molecular sizes of the anionic groups. Similar features are observed in re-orientational motion and time scales of different cationic models within the studied temperature range. The comparison of the liquid properties of the ionic systems with their neutral counterparts indicates that the distinctive microstructures and dynamical quantities of the model ionic liquid systems are intrinsically related to Coulombic interactions. Finally, we compared the computational efficiencies of three linearly scaling O(N log N) Ewald summation methods, the particle-particle particle-mesh method, the particle-mesh Ewald summation method, and the Ewald summation method based on a non-uniform fast Fourier transform technique, to calculate electrostatic interactions. Coarse-grained simulations were performed using the GALAMOST and the GROMACS packages and hardware efficiently utilizing graphics processing units on a set of extended [1-decyl-3-methylimidazolium][BF4] ionic liquid systems of up to 131 072 ion pairs.

The Influence of Mesh Density on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Lyle, Karen H.; Spellman, Regina L.

2004-01-01

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0- in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA version 960 for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at five discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density. As a final comparison, the model with a fine panel and fine foam mesh was executed with slightly different material properties for the RCC. For this model, the average degraded properties of the RCC were replaced with the maximum degraded properties. Similar comparisons of panel and foam responses were made for the average and maximum degraded models.

Refreshing Music: Fog Harvesting with Harps

NASA Astrophysics Data System (ADS)

Shi, Weiwei; Anderson, Mark; Kennedy, Brook; Boreyko, Jonathan

2017-11-01

Fog harvesting is a useful technique for obtaining fresh water in arid climates. The wire meshes currently utilized for fog harvesting suffer from dual constraints: coarse meshes cannot efficiently capture fog, while fine meshes suffer from clogging issues. Here, we design a new type of fog harvester comprised of an array of vertical wires, which we call ``fog harps.'' To investigate the water collection efficiency, three fog harps were designed with different diameters (254 μm, 508 μm and 1.30 mm) but the same pitch-to-diameter ratio of 2. For comparison, three different size meshes were purchased with equivalent dimensions. As expected for the mesh structures, the mid-sized wires performed the best, with a drop-off in performance for the fine or coarse meshes. In contrast, the fog harvesting rate continually increased with decreasing wire diameter for the fog harps, due to its low hysteresis that prevented droplet clogging. This resulted in a 3-fold enhancement in the fog harvesting rate for the harp form factor compared to the mesh. The lack of a performance ceiling for the harps suggest that even greater enhancements could be achieved by scaling down to yet smaller sizes.

Multiscale modeling and simulation for nano/micro materials

NASA Astrophysics Data System (ADS)

Wang, Xianqiao

Continuum description and atomic description used to be two distinct methods in the community of modeling and simulations. Science and technology have become so advanced that our understanding of many physical phenomena involves the concepts of both. So our goal now is to build a bridge to make atoms and continua communicate with each other. Micromorphic theory (MMT) envisions a material body as a continuous collection of deformable particles; each possesses finite size and inner structure. It is considered as the most successful top-down formulation of a two-level continuum model to bridge the gap between the micro level and macro level. Therefore MMT can be expected to unveil many new classes of physical phenomena that fall beyond classical field theories. In this work, the constitutive equations for generalized Micromorphic thermoviscoelastic solid and generalized Micromorphic fluid have been formulated. To enlarge the domain of applicability of MMT, from nano, micro to macro, we take a bottom-up approach to re-derive the generalized atomistic field theory (AFT) comprehensively and completely and establish the relationship between AFT and MMT. Finite element (FE) method is then implemented to pursue the numerical solutions of the governing equations derived in AFT. When the finest mesh is used, i.e., the size of FE mesh is equal to the lattice constant of the material, the computational model becomes identical to molecular dynamics simulation. When a coarse mesh is used, the resulting model is a coarse-grained model, the majority of the degrees of freedom are eliminated and the computational cost is largely reduced. When the coarse mesh and finest mesh exist concurrently, i.e., the finest mesh is used in the critical regions and the coarser mesh is used in the far field, it leads naturally to a concurrent atomistic/continuum model. Atomic scale, coarse-grained scale and concurrent atomistic/continuum simulations have demonstrated the potential capability of AFT to simulate most grand challenging problems in nano/micro physics, and shown that AFT has the advantages of both atomic model and MMT. Therefore, AFT has accomplished the mission to bridge the gap between continuum mechanics and atomic physics.

Automatic generation of endocardial surface meshes with 1-to-1 correspondence from cine-MR images

NASA Astrophysics Data System (ADS)

Su, Yi; Teo, S.-K.; Lim, C. W.; Zhong, L.; Tan, R. S.

2015-03-01

In this work, we develop an automatic method to generate a set of 4D 1-to-1 corresponding surface meshes of the left ventricle (LV) endocardial surface which are motion registered over the whole cardiac cycle. These 4D meshes have 1- to-1 point correspondence over the entire set, and is suitable for advanced computational processing, such as shape analysis, motion analysis and finite element modelling. The inputs to the method are the set of 3D LV endocardial surface meshes of the different frames/phases of the cardiac cycle. Each of these meshes is reconstructed independently from border-delineated MR images and they have no correspondence in terms of number of vertices/points and mesh connectivity. To generate point correspondence, the first frame of the LV mesh model is used as a template to be matched to the shape of the meshes in the subsequent phases. There are two stages in the mesh correspondence process: (1) a coarse matching phase, and (2) a fine matching phase. In the coarse matching phase, an initial rough matching between the template and the target is achieved using a radial basis function (RBF) morphing process. The feature points on the template and target meshes are automatically identified using a 16-segment nomenclature of the LV. In the fine matching phase, a progressive mesh projection process is used to conform the rough estimate to fit the exact shape of the target. In addition, an optimization-based smoothing process is used to achieve superior mesh quality and continuous point motion.

Unstructured Polyhedral Mesh Thermal Radiation Diffusion

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

Palmer, T.S.; Zika, M.R.; Madsen, N.K.

2000-07-27

Unstructured mesh particle transport and diffusion methods are gaining wider acceptance as mesh generation, scientific visualization and linear solvers improve. This paper describes an algorithm that is currently being used in the KULL code at Lawrence Livermore National Laboratory to solve the radiative transfer equations. The algorithm employs a point-centered diffusion discretization on arbitrary polyhedral meshes in 3D. We present the results of a few test problems to illustrate the capabilities of the radiation diffusion module.

Recovery of macroinvertebrates by screening in the field: a comparison between coarse (1.18 mm) and fine (0.60 mm) mesh sieves

USGS Publications Warehouse

Dukerschein, J.T.; Gent, R.; Sauer, J.

1996-01-01

We evaluated the potential loss of target benthic macroinvertebrates from coarse-mesh field wash down of samples through a 1.18-mm mesh sieve nested on a 0.60-mm mesh sieve. Visible target organisms (midges, mayflies, and fingernail clams) in the 1.18-mm mesh sieve were removed from the sample and enumerated in the field. The entire contents of both sieves were preserved for subsequent laboratory enumeration under 4X magnification. Percent recoveries from each treatment were based on total intact organisms found in all sieves. Percent recovery for fingernail clams found in the field (31%) was lower than for mayflies (79%) and midges (88%). Laboratory enumeration of organisms retained by the 1.18-mm sieve yielded additional fingernail clams (to total 74% recovered in the field and lab), mayflies (to total 89%), and midges (to total 91%). If the 1.18-mm sieve is used alone in the field, it is adequate to monitor mayflies, midges >1 cm, and adult fingernail clams greater than or equal to 5.0 mm shell length.

High-fidelity meshes from tissue samples for diffusion MRI simulations.

PubMed

Panagiotaki, Eleftheria; Hall, Matt G; Zhang, Hui; Siow, Bernard; Lythgoe, Mark F; Alexander, Daniel C

2010-01-01

This paper presents a method for constructing detailed geometric models of tissue microstructure for synthesizing realistic diffusion MRI data. We construct three-dimensional mesh models from confocal microscopy image stacks using the marching cubes algorithm. Random-walk simulations within the resulting meshes provide synthetic diffusion MRI measurements. Experiments optimise simulation parameters and complexity of the meshes to achieve accuracy and reproducibility while minimizing computation time. Finally we assess the quality of the synthesized data from the mesh models by comparison with scanner data as well as synthetic data from simple geometric models and simplified meshes that vary only in two dimensions. The results support the extra complexity of the three-dimensional mesh compared to simpler models although sensitivity to the mesh resolution is quite robust.

Convergence study of global meshing on enamel-cement-bracket finite element model

NASA Astrophysics Data System (ADS)

Samshuri, S. F.; Daud, R.; Rojan, M. A.; Basaruddin, K. S.; Abdullah, A. B.; Ariffin, A. K.

2017-09-01

This paper presents on meshing convergence analysis of finite element (FE) model to simulate enamel-cement-bracket fracture. Three different materials used in this study involving interface fracture are concerned. Complex behavior ofinterface fracture due to stress concentration is the reason to have a well-constructed meshing strategy. In FE analysis, meshing size is a critical factor that influenced the accuracy and computational time of analysis. The convergence study meshing scheme involving critical area (CA) and non-critical area (NCA) to ensure an optimum meshing sizes are acquired for this FE model. For NCA meshing, the area of interest are at the back of enamel, bracket ligature groove and bracket wing. For CA meshing, area of interest are enamel area close to cement layer, the cement layer and bracket base. The value of constant NCA meshing tested are meshing size 1 and 0.4. The value constant CA meshing tested are 0.4 and 0.1. Manipulative variables are randomly selected and must abide the rule of NCA must be higher than CA. This study employed first principle stresses due to brittle failure nature of the materials used. Best meshing size are selected according to convergence error analysis. Results show that, constant CA are more stable compare to constant NCA meshing. Then, 0.05 constant CA meshing are tested to test the accuracy of smaller meshing. However, unpromising result obtained as the errors are increasing. Thus, constant CA 0.1 with NCA mesh of 0.15 until 0.3 are the most stable meshing as the error in this region are lowest. Convergence test was conducted on three selected coarse, medium and fine meshes at the range of NCA mesh of 0.15 until 3 and CA mesh area stay constant at 0.1. The result shows that, at coarse mesh 0.3, the error are 0.0003% compare to 3% acceptable error. Hence, the global meshing are converge as the meshing size at CA 0.1 and NCA 0.15 for this model.

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

2002-09-03

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Influence of vegetation and gravel mesh on the tertiary treatment of wastewater from a cosmetics industry.

PubMed

Vlyssides, Apostolos G; Mai, Sofia T H; Barampouti, Elli Maria P; Loukakis, Haralampos N

2009-07-01

To estimate the influence of gravel mesh (fine and coarse) and vegetation (Phragmites and Arundo) on the efficiency of a reed bed, a pilot plant was included after the wastewater treatment plant of a cosmetic industry treatment system according to a 22 factorial experimental design. The maximum biochemical oxygen demand (BOD5), chemical oxygen demand (COD) and total phosphorous (TP) reduction was observed in the reactor, where Phragmites and fine gravel were used. In the reactor with Phragmites and coarse gravel, the maximum total Kjeldahl nitrogen (TKN) and total suspended solids (TSS) reduction was observed. The maximum total solids reduction was measured in the reed bed, which was filled with Arundo and coarse gravel. Conclusively, the treatment of a cosmetic industry's wastewater by reed beds as a tertiary treatment method is quite effective.

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

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

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

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr; CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex; Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity ofmore » the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less

3-D inversion of airborne electromagnetic data parallelized and accelerated by local mesh and adaptive soundings

NASA Astrophysics Data System (ADS)

Yang, Dikun; Oldenburg, Douglas W.; Haber, Eldad

2014-03-01

Airborne electromagnetic (AEM) methods are highly efficient tools for assessing the Earth's conductivity structures in a large area at low cost. However, the configuration of AEM measurements, which typically have widely distributed transmitter-receiver pairs, makes the rigorous modelling and interpretation extremely time-consuming in 3-D. Excessive overcomputing can occur when working on a large mesh covering the entire survey area and inverting all soundings in the data set. We propose two improvements. The first is to use a locally optimized mesh for each AEM sounding for the forward modelling and calculation of sensitivity. This dedicated local mesh is small with fine cells near the sounding location and coarse cells far away in accordance with EM diffusion and the geometric decay of the signals. Once the forward problem is solved on the local meshes, the sensitivity for the inversion on the global mesh is available through quick interpolation. Using local meshes for AEM forward modelling avoids unnecessary computing on fine cells on a global mesh that are far away from the sounding location. Since local meshes are highly independent, the forward modelling can be efficiently parallelized over an array of processors. The second improvement is random and dynamic down-sampling of the soundings. Each inversion iteration only uses a random subset of the soundings, and the subset is reselected for every iteration. The number of soundings in the random subset, determined by an adaptive algorithm, is tied to the degree of model regularization. This minimizes the overcomputing caused by working with redundant soundings. Our methods are compared against conventional methods and tested with a synthetic example. We also invert a field data set that was previously considered to be too large to be practically inverted in 3-D. These examples show that our methodology can dramatically reduce the processing time of 3-D inversion to a practical level without losing resolution. Any existing modelling technique can be included into our framework of mesh decoupling and adaptive sampling to accelerate large-scale 3-D EM inversions.

Segmented Domain Decomposition Multigrid For 3-D Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Celestina, M. L.; Adamczyk, J. J.; Rubin, S. G.

2001-01-01

A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for three-dimensional viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.

Reducing numerical costs for core wide nuclear reactor CFD simulations by the Coarse-Grid-CFD

NASA Astrophysics Data System (ADS)

Viellieber, Mathias; Class, Andreas G.

2013-11-01

Traditionally complete nuclear reactor core simulations are performed with subchannel analysis codes, that rely on experimental and empirical input. The Coarse-Grid-CFD (CGCFD) intends to replace the experimental or empirical input with CFD data. The reactor core consists of repetitive flow patterns, allowing the general approach of creating a parametrized model for one segment and composing many of those to obtain the entire reactor simulation. The method is based on a detailed and well-resolved CFD simulation of one representative segment. From this simulation we extract so-called parametrized volumetric forces which close, an otherwise strongly under resolved, coarsely-meshed model of a complete reactor setup. While the formulation so far accounts for forces created internally in the fluid others e.g. obstruction and flow deviation through spacers and wire wraps, still need to be accounted for if the geometric details are not represented in the coarse mesh. These are modelled with an Anisotropic Porosity Formulation (APF). This work focuses on the application of the CGCFD to a complete reactor core setup and the accomplishment of the parametrization of the volumetric forces.

Adaptive Skin Meshes Coarsening for Biomolecular Simulation

PubMed Central

Shi, Xinwei; Koehl, Patrice

2011-01-01

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137

Seamless atmospheric modeling across the hydrostatic-nonhydrostatic scales - preliminary results using an unstructured-Voronoi mesh for weather prediction.

NASA Astrophysics Data System (ADS)

Skamarock, W. C.

2015-12-01

One of the major problems in atmospheric model applications is the representation of deep convection within the models; explicit simulation of deep convection on fine meshes performs much better than sub-grid parameterized deep convection on coarse meshes. Unfortunately, the high cost of explicit convective simulation has meant it has only been used to down-scale global simulations in weather prediction and regional climate applications, typically using traditional one-way interactive nesting technology. We have been performing real-time weather forecast tests using a global non-hydrostatic atmospheric model (the Model for Prediction Across Scales, MPAS) that employs a variable-resolution unstructured Voronoi horizontal mesh (nominally hexagons) to span hydrostatic to nonhydrostatic scales. The smoothly varying Voronoi mesh eliminates many downscaling problems encountered using traditional one- or two-way grid nesting. Our test weather forecasts cover two periods - the 2015 Spring Forecast Experiment conducted at the NOAA Storm Prediction Center during the month of May in which we used a 50-3 km mesh, and the PECAN field program examining nocturnal convection over the US during the months of June and July in which we used a 15-3 km mesh. An important aspect of this modeling system is that the model physics be scale-aware, particularly the deep convection parameterization. These MPAS simulations employ the Grell-Freitas scale-aware convection scheme. Our test forecasts show that the scheme produces a gradual transition in the deep convection, from the deep unstable convection being handled entirely by the convection scheme on the coarse mesh regions (dx > 15 km), to the deep convection being almost entirely explicit on the 3 km NA region of the meshes. We will present results illustrating the performance of critical aspects of the MPAS model in these tests.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement.

PubMed

Garcia-Cantero, Juan J; Brito, Juan P; Mata, Susana; Bayona, Sofia; Pastor, Luis

2017-01-01

Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells' overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma's morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes.

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.

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

NASA Astrophysics Data System (ADS)

Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander

2012-02-01

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.

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.

Application of the discrete generalized multigroup method to ultra-fine energy mesh in infinite medium calculations

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

Gibson, N. A.; Forget, B.

2012-07-01

The Discrete Generalized Multigroup (DGM) method uses discrete Legendre orthogonal polynomials to expand the energy dependence of the multigroup neutron transport equation. This allows a solution on a fine energy mesh to be approximated for a cost comparable to a solution on a coarse energy mesh. The DGM method is applied to an ultra-fine energy mesh (14,767 groups) to avoid using self-shielding methodologies without introducing the cost usually associated with such energy discretization. Results show DGM to converge to the reference ultra-fine solution after a small number of recondensation steps for multiple infinite medium compositions. (authors)

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

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

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Comparison of copepod collection efficiencies by three commonly used plankton nets: A case study in Bohai Sea, China

NASA Astrophysics Data System (ADS)

Chen, Hongju; Yu, Hao; Liu, Guangxing

2016-12-01

Selection of net with a suitable mesh size is a key concern in the quantitative assessment of zooplankton, which is crucial to understand pelagic ecosystem processes. This study compared the copepod collecting efficiency of three commonly used plankton nets, namely, the China standard coarse net (505 μm mesh), the China standard fine net (77 μm), and the WP-2 net (200 μm). The experiment was performed at six stations in the Bohai Sea during the autumn of 2012. The coarse net substantially under-sampled small individuals (body widths < 672 μm) and led to the lowest species number in each tow, whereas the fine net collected all small copepod species but failed to collect rare species. The WP-2 net appeared to be a compromise of the two other nets, collecting both small copepods and rare species. The abundance of copepods collected by the coarse net (126.4 ± 86.5 ind m-3) was one to two orders of magnitude lower than that by the WP-2 net (5802.4 ± 2595.4 ind m-3), and the value of the fine net (11117.0 ± 4563.41 ind m-3) was nearly twice that of the WP-2 net. The abundance of large copepods ( i.e., adult Calanus sinicus) in the three nets showed no significant differences, but the abundance of small copepods declined with decreasing mesh size. The difference in abundance resulted from the under-sampling of small copepods with body widths < 672 μm and < 266 μm by the coarse and WP-2 nets, respectively.

Polyhedral meshing in numerical analysis of conjugate heat transfer

NASA Astrophysics Data System (ADS)

Sosnowski, Marcin; Krzywanski, Jaroslaw; Grabowska, Karolina; Gnatowska, Renata

2018-06-01

Computational methods have been widely applied in conjugate heat transfer analysis. The very first and crucial step in such research is the meshing process which consists in dividing the analysed geometry into numerous small control volumes (cells). In Computational Fluid Dynamics (CFD) applications it is desirable to use the hexahedral cells as the resulting mesh is characterized by low numerical diffusion. Unfortunately generating such mesh can be a very time-consuming task and in case of complicated geometry - it may not be possible to generate cells of good quality. Therefore tetrahedral cells have been implemented into commercial pre-processors. Their advantage is the ease of its generation even in case of very complex geometry. On the other hand tetrahedrons cannot be stretched excessively without decreasing the mesh quality factor, so significantly larger number of cells has to be used in comparison to hexahedral mesh in order to achieve a reasonable accuracy. Moreover the numerical diffusion of tetrahedral elements is significantly higher. Therefore the polyhedral cells are proposed within the paper in order to combine the advantages of hexahedrons (low numerical diffusion resulting in accurate solution) and tetrahedrons (rapid semi-automatic generation) as well as to overcome the disadvantages of both the above mentioned mesh types. The major benefit of polyhedral mesh is that each individual cell has many neighbours, so gradients can be well approximated. Polyhedrons are also less sensitive to stretching than tetrahedrons which results in better mesh quality leading to improved numerical stability of the model. In addition, numerical diffusion is reduced due to mass exchange over numerous faces. This leads to a more accurate solution achieved with a lower cell count. Therefore detailed comparison of numerical modelling results concerning conjugate heat transfer using tetrahedral and polyhedral meshes is presented in the paper.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

NASA Astrophysics Data System (ADS)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

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

Gao, Kai; Fu, Shubin; Chung, Eric T.

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-04

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

The Influence of Shredder Feeding on Fungal Activity in a Nutrient-Enriched Stream and an Unaltered Stream

NASA Astrophysics Data System (ADS)

Chung, N.; Suberkopp, K.

2005-05-01

The effect of shredder feeding on aquatic hyphomycete communities associated with submerged leaves was studied in two southern Appalachian headwater streams in North Carolina. Coarse and fine mesh litter bags containing red maple (Acer rubrum) leaves were placed in the nutrient-enriched stream and in the reference stream and were retrieved monthly. Both shredder feeding and nutrient enrichment enhanced breakdown rates. The breakdown rates of leaves in coarse mesh bags in the reference stream (k = 0.0275) and fine mesh bags in the nutrient enriched stream (k = 0.0272) were not significantly different, suggesting that the shredding effect on litter breakdown was offset by higher fungal activity as a result of nutrient enrichment. Fungal sporulation rates and biomass (based on ergosterol concentrations) were higher in the nutrient enriched than in the reference stream, but neither fungal biomass nor sporulation rate was affected by shredder feeding. Species richness was higher in the nutrient-enriched than in the reference stream. The enrichment with nutrients altered fungal community composition more than shredder feeding.

Floating shock fitting via Lagrangian adaptive meshes

NASA Technical Reports Server (NTRS)

Vanrosendale, John

1994-01-01

In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2001-01-01

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement

PubMed Central

Garcia-Cantero, Juan J.; Brito, Juan P.; Mata, Susana; Bayona, Sofia; Pastor, Luis

2017-01-01

Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells’ overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma’s morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes. PMID:28690511

Mesh refinement strategy for optimal control problems

NASA Astrophysics Data System (ADS)

Paiva, L. T.; Fontes, F. A. C. C.

2013-10-01

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

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

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

DOE PAGES

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin; ...

2017-07-08

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Compact cell-centered discretization stencils at fine-coarse block structured grid interfaces

NASA Astrophysics Data System (ADS)

Pletzer, Alexander; Jamroz, Ben; Crockett, Robert; Sides, Scott

2014-03-01

Different strategies for coupling fine-coarse grid patches are explored in the context of the adaptive mesh refinement (AMR) method. We show that applying linear interpolation to fill in the fine grid ghost values can produce a finite volume stencil of comparable accuracy to quadratic interpolation provided the cell volumes are adjusted. The volume of fine cells expands whereas the volume of neighboring coarse cells contracts. The amount by which the cells contract/expand depends on whether the interface is a face, an edge, or a corner. It is shown that quadratic or better interpolation is required when the conductivity is spatially varying, anisotropic, the refinement ratio is other than two, or when the fine-coarse interface is concave.

Grid adaption using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Grid adaptation using chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1994-01-01

The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.

Grid adaptation using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

An Engineering Solution for Solving Mesh Size Effects in the Simulation of Delamination with Cohesive Zone Models

NASA Technical Reports Server (NTRS)

Turon, A.; Davila, C. G.; Camanho, P. P.; Costa, J.

2007-01-01

This paper presents a methodology to determine the parameters to be used in the constitutive equations of Cohesive Zone Models employed in the simulation of delamination in composite materials by means of decohesion finite elements. A closed-form expression is developed to define the stiffness of the cohesive layer. A novel procedure that allows the use of coarser meshes of decohesion elements in large-scale computations is also proposed. The procedure ensures that the energy dissipated by the fracture process is computed correctly. It is shown that coarse-meshed models defined using the approach proposed here yield the same results as the models with finer meshes normally used for the simulation of fracture processes.

Tetrahedral and polyhedral mesh evaluation for cerebral hemodynamic simulation--a comparison.

PubMed

Spiegel, Martin; Redel, Thomas; Zhang, Y; Struffert, Tobias; Hornegger, Joachim; Grossman, Robert G; Doerfler, Arnd; Karmonik, Christof

2009-01-01

Computational fluid dynamic (CFD) based on patient-specific medical imaging data has found widespread use for visualizing and quantifying hemodynamics in cerebrovascular disease such as cerebral aneurysms or stenotic vessels. This paper focuses on optimizing mesh parameters for CFD simulation of cerebral aneurysms. Valid blood flow simulations strongly depend on the mesh quality. Meshes with a coarse spatial resolution may lead to an inaccurate flow pattern. Meshes with a large number of elements will result in unnecessarily high computation time which is undesirable should CFD be used for planning in the interventional setting. Most CFD simulations reported for these vascular pathologies have used tetrahedral meshes. We illustrate the use of polyhedral volume elements in comparison to tetrahedral meshing on two different geometries, a sidewall aneurysm of the internal carotid artery and a basilar bifurcation aneurysm. The spatial mesh resolution ranges between 5,119 and 228,118 volume elements. The evaluation of the different meshes was based on the wall shear stress previously identified as a one possible parameter for assessing aneurysm growth. Polyhedral meshes showed better accuracy, lower memory demand, shorter computational speed and faster convergence behavior (on average 369 iterations less).

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

NASA Technical Reports Server (NTRS)

Lee-Rausch, E. M.; Park, M. A.; Jones, W. T.; Hammond, D. P.; Nielsen, E. J.

2005-01-01

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Hybrid continuum-coarse-grained modeling of erythrocytes

NASA Astrophysics Data System (ADS)

Lyu, Jinming; Chen, Paul G.; Boedec, Gwenn; Leonetti, Marc; Jaeger, Marc

2018-06-01

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE-POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum-coarse-grained model for the study of RBCs in fluid flows.

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-13

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscalemore » basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.« less

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

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

Gao, Kai; Fu, Shubin; Chung, Eric T.

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscalemore » basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.« less

A multi-block adaptive solving technique based on lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zhang, Yang; Xie, Jiahua; Li, Xiaoyue; Ma, Zhenghai; Zou, Jianfeng; Zheng, Yao

2018-05-01

In this paper, a CFD parallel adaptive algorithm is self-developed by combining the multi-block Lattice Boltzmann Method (LBM) with Adaptive Mesh Refinement (AMR). The mesh refinement criterion of this algorithm is based on the density, velocity and vortices of the flow field. The refined grid boundary is obtained by extending outward half a ghost cell from the coarse grid boundary, which makes the adaptive mesh more compact and the boundary treatment more convenient. Two numerical examples of the backward step flow separation and the unsteady flow around circular cylinder demonstrate the vortex structure of the cold flow field accurately and specifically.

System and method for producing metallic iron nodules

DOEpatents

Bleifuss, Rodney L [Grand Rapids, MN; Englund, David J [Bovey, MN; Iwasaki, Iwao [Grand Rapids, MN; Lindgren, Andrew J [Grand Rapids, MN; Kiesel, Richard F [Hibbing, MN

2011-09-20

A method for producing metallic iron nodules by assembling a shielding entry system to introduce coarse carbonaceous material greater than 6 mesh in to the furnace atmosphere at location(s) where the temperature of the furnace atmosphere adjacent at least partially reduced reducible iron bearing material is between about 2200 and 2650.degree. F. (1200 and 1450.degree. C.), the shielding entry system adapted to inhibit emission of infrared radiation from the furnace atmosphere and seal the furnace atmosphere from exterior atmosphere while introducing coarse carbonaceous material greater than 6 mesh into the furnace to be distributed over the at least partially reduced reducible iron bearing material, and heating the covered at least partially reduced reducible iron bearing material in a fusion atmosphere to assist in fusion and inhibit reoxidation of the reduced material during fusion to assist in fusion and inhibit reoxidation of the reduced material in forming metallic iron nodules.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Texturing of continuous LOD meshes with the hierarchical texture atlas

NASA Astrophysics Data System (ADS)

Birkholz, Hermann

2006-02-01

For the rendering of detailed virtual environments, trade-offs have to be made between image quality and rendering time. An immersive experience of virtual reality always demands high frame-rates with the best reachable image qual-ity. Continuous Level of Detail (cLoD) triangle-meshes provide an continuous spectrum of detail for a triangle mesh that can be used to create view-dependent approximations of the environment in real-time. This enables the rendering with a constant number of triangles and thus with constant frame-rates. Normally the construction of such cLoD mesh representations leads to the loss of all texture information of the original mesh. To overcome this problem, a parameter domain can be created, in order to map the surface properties (colour, texture, normal) to it. This parameter domain can be used to map the surface properties back to arbitrary approximations of the original mesh. The parameter domain is often a simplified version of the mesh to be parameterised. This limits the reachable simplification to the domain mesh which has to map the surface of the original mesh with the least possible stretch. In this paper, a hierarchical domain mesh is presented, that scales between very coarse domain meshes and good property-mapping.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Composition of riparian litter input regulates organic matter decomposition: Implications for headwater stream functioning in a managed forest landscape.

PubMed

Lidman, Johan; Jonsson, Micael; Burrows, Ryan M; Bundschuh, Mirco; Sponseller, Ryan A

2017-02-01

Although the importance of stream condition for leaf litter decomposition has been extensively studied, little is known about how processing rates change in response to altered riparian vegetation community composition. We investigated patterns of plant litter input and decomposition across 20 boreal headwater streams that varied in proportions of riparian deciduous and coniferous trees. We measured a suite of in-stream physical and chemical characteristics, as well as the amount and type of litter inputs from riparian vegetation, and related these to decomposition rates of native (alder, birch, and spruce) and introduced (lodgepole pine) litter species incubated in coarse- and fine-mesh bags. Total litter inputs ranged more than fivefold among sites and increased with the proportion of deciduous vegetation in the riparian zone. In line with differences in initial litter quality, mean decomposition rate was highest for alder, followed by birch, spruce, and lodgepole pine (12, 55, and 68% lower rates, respectively). Further, these rates were greater in coarse-mesh bags that allow colonization by macroinvertebrates. Variance in decomposition rate among sites for different species was best explained by different sets of environmental conditions, but litter-input composition (i.e., quality) was overall highly important. On average, native litter decomposed faster in sites with higher-quality litter input and (with the exception of spruce) higher concentrations of dissolved nutrients and open canopies. By contrast, lodgepole pine decomposed more rapidly in sites receiving lower-quality litter inputs. Birch litter decomposition rate in coarse-mesh bags was best predicted by the same environmental variables as in fine-mesh bags, with additional positive influences of macroinvertebrate species richness. Hence, to facilitate energy turnover in boreal headwaters, forest management with focus on conifer production should aim at increasing the presence of native deciduous trees along streams, as they promote conditions that favor higher decomposition rates of terrestrial plant litter.

Coarse-grained hydrodynamics from correlation functions

NASA Astrophysics Data System (ADS)

Palmer, Bruce

2018-02-01

This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

2016-08-01

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

Numerical benchmarking of a Coarse-Mesh Transport (COMET) Method for medical physics applications

NASA Astrophysics Data System (ADS)

Blackburn, Megan Satterfield

2009-12-01

Radiation therapy has become a very import method for treating cancer patients. Thus, it is extremely important to accurately determine the location of energy deposition during these treatments, maximizing dose to the tumor region and minimizing it to healthy tissue. A Coarse-Mesh Transport Method (COMET) has been developed at the Georgia Institute of Technology in the Computational Reactor and Medical Physics Group for use very successfully with neutron transport to analyze whole-core criticality. COMET works by decomposing a large, heterogeneous system into a set of smaller fixed source problems. For each unique local problem that exists, a solution is obtained that we call a response function. These response functions are pre-computed and stored in a library for future use. The overall solution to the global problem can then be found by a linear superposition of these local problems. This method has now been extended to the transport of photons and electrons for use in medical physics problems to determine energy deposition from radiation therapy treatments. The main goal of this work was to develop benchmarks for testing in order to evaluate the COMET code to determine its strengths and weaknesses for these medical physics applications. For response function calculations, legendre polynomial expansions are necessary for space, angle, polar angle, and azimuthal angle. An initial sensitivity study was done to determine the best orders for future testing. After the expansion orders were found, three simple benchmarks were tested: a water phantom, a simplified lung phantom, and a non-clinical slab phantom. Each of these benchmarks was decomposed into 1cm x 1cm and 0.5cm x 0.5cm coarse meshes. Three more clinically relevant problems were developed from patient CT scans. These benchmarks modeled a lung patient, a prostate patient, and a beam re-entry situation. As before, the problems were divided into 1cm x 1cm, 0.5cm x 0.5cm, and 0.25cm x 0.25cm coarse mesh cases. Multiple beam energies were also tested for each case. The COMET solutions for each case were compared to a reference solution obtained by pure Monte Carlo results from EGSnrc. When comparing the COMET results to the reference cases, a pattern of differences appeared in each phantom case. It was found that better results were obtained for lower energy incident photon beams as well as for larger mesh sizes. Possible changes may need to be made with the expansion orders used for energy and angle to better model high energy secondary electrons. Heterogeneity also did not pose a problem for the COMET methodology. Heterogeneous results were found in a comparable amount of time to the homogeneous water phantom. The COMET results were typically found in minutes to hours of computational time, whereas the reference cases typically required hundreds or thousands of hours. A second sensitivity study was also performed on a more stringent problem and with smaller coarse meshes. Previously, the same expansion order was used for each incident photon beam energy so better comparisons could be made. From this second study, it was found that it is optimal to have different expansion orders based on the incident beam energy. Recommendations for future work with this method include more testing on higher expansion orders or possible code modification to better handle secondary electrons. The method also needs to handle more clinically relevant beam descriptions with an energy and angular distribution associated with it.

An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions

NASA Astrophysics Data System (ADS)

Zahr, M. J.; Persson, P.-O.

2018-07-01

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin or finite volume methods. The proposed method aims to align inter-element boundaries with discontinuities in the solution by deforming the computational mesh. A discontinuity-aligned mesh ensures the discontinuity is represented through inter-element jumps while smooth basis functions interior to elements are only used to approximate smooth regions of the solution, thereby avoiding Gibbs' phenomena that create well-known stability issues. Therefore, very coarse high-order discretizations accurately resolve the piecewise smooth solution throughout the domain, provided the discontinuity is tracked. Central to the proposed discontinuity-tracking framework is a discrete PDE-constrained optimization formulation that simultaneously aligns the computational mesh with discontinuities in the solution and solves the discretized conservation law on this mesh. The optimization objective is taken as a combination of the deviation of the finite-dimensional solution from its element-wise average and a mesh distortion metric to simultaneously penalize Gibbs' phenomena and distorted meshes. It will be shown that our objective function satisfies two critical properties that are required for this discontinuity-tracking framework to be practical: (1) possesses a local minima at a discontinuity-aligned mesh and (2) decreases monotonically to this minimum in a neighborhood of radius approximately h / 2, whereas other popular discontinuity indicators fail to satisfy the latter. Another important contribution of this work is the observation that traditional reduced space PDE-constrained optimization solvers that repeatedly solve the conservation law at various mesh configurations are not viable in this context since severe overshoot and undershoot in the solution, i.e., Gibbs' phenomena, may make it impossible to solve the discrete conservation law on non-aligned meshes. Therefore, we advocate a gradient-based, full space solver where the mesh and conservation law solution converge to their optimal values simultaneously and therefore never require the solution of the discrete conservation law on a non-aligned mesh. The merit of the proposed method is demonstrated on a number of one- and two-dimensional model problems including the L2 projection of discontinuous functions, Burgers' equation with a discontinuous source term, transonic flow through a nozzle, and supersonic flow around a bluff body. We demonstrate optimal O (h p + 1) convergence rates in the L1 norm for up to polynomial order p = 6 and show that accurate solutions can be obtained on extremely coarse meshes.

Numerical simulation of immiscible viscous fingering using adaptive unstructured meshes

NASA Astrophysics Data System (ADS)

Adam, A.; Salinas, P.; Percival, J. R.; Pavlidis, D.; Pain, C.; Muggeridge, A. H.; Jackson, M.

2015-12-01

Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability.Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as consistent interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.

Simulation of stochastic diffusion via first exit times

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

Lötstedt, Per, E-mail: perl@it.uu.se; Meinecke, Lina, E-mail: lina.meinecke@it.uu.se

2015-11-01

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a methodmore » based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions.« less

Simulation of stochastic diffusion via first exit times

PubMed Central

Lötstedt, Per; Meinecke, Lina

2015-01-01

In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions. PMID:26600600

A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

DOE PAGES

Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...

2016-10-06

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less

A survey of nested grid techniques and their potential for use within the MASS weather prediction model

NASA Technical Reports Server (NTRS)

Koch, Steven E.; Mcqueen, Jeffery T.

1987-01-01

A survey of various one- and two-way interactive nested grid techniques used in hydrostatic numerical weather prediction models is presented and the advantages and disadvantages of each method are discussed. The techniques for specifying the lateral boundary conditions for each nested grid scheme are described in detail. Averaging and interpolation techniques used when applying the coarse mesh grid (CMG) and fine mesh grid (FMG) interface conditions during two-way nesting are discussed separately. The survey shows that errors are commonly generated at the boundary between the CMG and FMG due to boundary formulation or specification discrepancies. Methods used to control this noise include application of smoothers, enhanced diffusion, or damping-type time integration schemes to model variables. The results from this survey provide the information needed to decide which one-way and two-way nested grid schemes merit future testing with the Mesoscale Atmospheric Simulation System (MASS) model. An analytically specified baroclinic wave will be used to conduct systematic tests of the chosen schemes since this will allow for objective determination of the interfacial noise in the kind of meteorological setting for which MASS is designed. Sample diagnostic plots from initial tests using the analytic wave are presented to illustrate how the model-generated noise is ascertained. These plots will be used to compare the accuracy of the various nesting schemes when incorporated into the MASS model.

Three dimensional unstructured multigrid for the Euler equations

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1991-01-01

The three dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback. Results indicate: (1) The new method exhibits quadratic convergence for homogeneous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. ?? 2002 Elsevier Science Ltd. All rights reserved.

Reconciling transport models across scales: The role of volume exclusion

NASA Astrophysics Data System (ADS)

Taylor, P. R.; Yates, C. A.; Simpson, M. J.; Baker, R. E.

2015-10-01

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the role of volume exclusion, which can significantly alter diffusive transport, particularly within biological systems where the diffusing particles might occupy a significant fraction of the available space. In this work we use a random walk approach to provide a means to reconcile models that incorporate crowding effects on different spatial scales. Our work demonstrates that coarse-grained models incorporating simplified descriptions of excluded volume can be used in many circumstances, but that care must be taken in pushing the coarse-graining process too far.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2016-08-18

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

Green-noise halftoning with dot diffusion

NASA Astrophysics Data System (ADS)

Lippens, Stefaan; Philips, Wilfried

2007-02-01

Dot diffusion is a halftoning technique that is based on the traditional error diffusion concept, but offers a high degree of parallel processing by its block based approach. Traditional dot diffusion however suffers from periodicity artifacts. To limit the visibility of these artifacts, we propose grid diffusion, which applies different class matrices for different blocks. Furthermore, in this paper we will discuss two approaches in the dot diffusion framework to generate green-noise halftone patterns. The first approach is based on output dependent feedback (hysteresis), analogous to the standard green-noise error diffusion techniques. We observe that the resulting halftones are rather coarse and highly dependent on the used dot diffusion class matrices. In the second approach we don't limit the diffusion to the nearest neighbors. This leads to less coarse halftones, compared to the first approach. The drawback is that it can only cope with rather limited cluster sizes. We can reduce these drawbacks by combining the two approaches.

Diffusion of Zonal Variables Using Node-Centered Diffusion Solver

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

Yang, T B

2007-08-06

Tom Kaiser [1] has done some preliminary work to use the node-centered diffusion solver (originally developed by T. Palmer [2]) in Kull for diffusion of zonal variables such as electron temperature. To avoid numerical diffusion, Tom used a scheme developed by Shestakov et al. [3] and found their scheme could, in the vicinity of steep gradients, decouple nearest-neighbor zonal sub-meshes leading to 'alternating-zone' (red-black mode) errors. Tom extended their scheme to couple the sub-meshes with appropriate chosen artificial diffusion and thereby solved the 'alternating-zone' problem. Because the choice of the artificial diffusion coefficient could be very delicate, it is desirablemore » to use a scheme that does not require the artificial diffusion but still able to avoid both numerical diffusion and the 'alternating-zone' problem. In this document we present such a scheme.« less

Parallel flow diffusion battery

DOEpatents

Yeh, H.C.; Cheng, Y.S.

1984-01-01

A parallel flow diffusion battery for determining the mass distribution of an aerosol has a plurality of diffusion cells mounted in parallel to an aerosol stream, each diffusion cell including a stack of mesh wire screens of different density.

Parallel flow diffusion battery

DOEpatents

Yeh, Hsu-Chi; Cheng, Yung-Sung

1984-08-07

A parallel flow diffusion battery for determining the mass distribution of an aerosol has a plurality of diffusion cells mounted in parallel to an aerosol stream, each diffusion cell including a stack of mesh wire screens of different density.

Computer-Aided Design and Optimization of High-Performance Vacuum Electronic Devices

DTIC Science & Technology

2006-08-15

approximations to the metric, and space mapping wherein low-accuracy (coarse mesh) solutions can potentially be used more effectively in an...interface and algorithm development. • Work on space - mapping or related methods for utilizing models of varying levels of approximation within an

Hybrid finite difference/finite element immersed boundary method.

PubMed

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

Long-term behaviour of solid oxide fuel cell interconnect materials in contact with Ni-mesh during exposure in simulated anode gas at 700 and 800 °C

NASA Astrophysics Data System (ADS)

Garcia-Fresnillo, L.; Shemet, V.; Chyrkin, A.; de Haart, L. G. J.; Quadakkers, W. J.

2014-12-01

In the present study the long-term behaviour of two ferritic steels, Crofer 22 APU and Crofer 22H, in contact with a Ni-mesh during exposure in simulated anode gas, Ar-4%H2-2%H2O, at 700 and 800 °C for exposure times up to 3000 h was investigated. Ni diffusion from the Ni-mesh into the steel resulted in the formation of an austenitic zone whereas diffusion of iron and chromium from the steel into the Ni-mesh resulted in the formation of chromia base oxides in the Ni-mesh. Depending on the chemical composition of the steel, the temperature and the exposure time, interdiffusion processes between ferritic steel and Ni-mesh also resulted in σ-phase formation at the austenite-ferrite interface and in Laves-phase dissolution in the austenitic zone. The extent and morphology of the σ-phase formation are discussed on the basis of thermodynamic considerations, including reaction paths in the ternary alloy system Fe-Ni-Cr.

Do Invertebrate Activity and Current Velocity Affect Fungal Assemblage Structure in Leaves?

NASA Astrophysics Data System (ADS)

Ferreira, Verónica; Graça, Manuel A. S.

2006-02-01

In this study we assessed the effect of current velocity and shredder presence, manipulated in artificial channels, on the structure of the fungal assemblage colonizing alder (Alnus glutinosa (L.) Gaertner) leaves incubated in coarse and fine mesh bags. Fungal sporulation rates, cumulative conidial production and number of species of aquatic hyphomycetes were higher in leaves exposed to high rather than to low current velocity. The opposite was observed regarding Simpson's index (D) on the fungal assemblage. Some species of aquatic hyphomycetes were consistently stimulated in high current channels. No effect of shredders or of mesh type was observed.

Generating unstructured nuclear reactor core meshes in parallel

DOE PAGES

Jain, Rajeev; Tautges, Timothy J.

2014-10-24

Recent advances in supercomputers and parallel solver techniques have enabled users to run large simulations problems using millions of processors. Techniques for multiphysics nuclear reactor core simulations are under active development in several countries. Most of these techniques require large unstructured meshes that can be hard to generate in a standalone desktop computers because of high memory requirements, limited processing power, and other complexities. We have previously reported on a hierarchical lattice-based approach for generating reactor core meshes. Here, we describe efforts to exploit coarse-grained parallelism during reactor assembly and reactor core mesh generation processes. We highlight several reactor coremore » examples including a very high temperature reactor, a full-core model of the Korean MONJU reactor, a ¼ pressurized water reactor core, the fast reactor Experimental Breeder Reactor-II core with a XX09 assembly, and an advanced breeder test reactor core. The times required to generate large mesh models, along with speedups obtained from running these problems in parallel, are reported. A graphical user interface to the tools described here has also been developed.« less

The optimization of high resolution topographic data for 1D hydrodynamic models

NASA Astrophysics Data System (ADS)

Ales, Ronovsky; Michal, Podhoranyi

2016-06-01

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domain and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.

The optimization of high resolution topographic data for 1D hydrodynamic models

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

Ales, Ronovsky, E-mail: ales.ronovsky@vsb.cz; Michal, Podhoranyi

2016-06-08

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domainmore » and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.« less

Conservative and dissipative force field for simulation of coarse-grained alkane molecules: A bottom-up approach

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

Trément, Sébastien; Rousseau, Bernard, E-mail: bernard.rousseau@u-psud.fr; Schnell, Benoît

2014-04-07

We apply operational procedures available in the literature to the construction of coarse-grained conservative and friction forces for use in dissipative particle dynamics (DPD) simulations. The full procedure rely on a bottom-up approach: large molecular dynamics trajectories of n-pentane and n-decane modeled with an anisotropic united atom model serve as input for the force field generation. As a consequence, the coarse-grained model is expected to reproduce at least semi-quantitatively structural and dynamical properties of the underlying atomistic model. Two different coarse-graining levels are studied, corresponding to five and ten carbon atoms per DPD bead. The influence of the coarse-graining levelmore » on the generated force fields contributions, namely, the conservative and the friction part, is discussed. It is shown that the coarse-grained model of n-pentane correctly reproduces self-diffusion and viscosity coefficients of real n-pentane, while the fully coarse-grained model for n-decane at ambient temperature over-predicts diffusion by a factor of 2. However, when the n-pentane coarse-grained model is used as a building block for larger molecule (e.g., n-decane as a two blobs model), a much better agreement with experimental data is obtained, suggesting that the force field constructed is transferable to large macro-molecular systems.« less

A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh

NASA Astrophysics Data System (ADS)

Sun, Wenjun; Jiang, Song; Xu, Kun

2017-12-01

In order to extend the unified gas kinetic scheme (UGKS) to solve radiative transfer equations in a complex geometry, a multidimensional asymptotic preserving implicit method on unstructured mesh is constructed in this paper. With an implicit formulation, the CFL condition for the determination of the time step in UGKS can be much relaxed, and a large time step is used in simulations. Differently from previous direction-by-direction UGKS on orthogonal structured mesh, on unstructured mesh the interface flux transport takes into account multi-dimensional effect, where gradients of radiation intensity and material temperature in both normal and tangential directions of a cell interface are included in the flux evaluation. The multiple scale nature makes the UGKS be able to capture the solutions in both optically thin and thick regions seamlessly. In the optically thick region the condition of cell size being less than photon's mean free path is fully removed, and the UGKS recovers a solver for diffusion equation in such a limit on unstructured mesh. For a distorted quadrilateral mesh, the UGKS goes to a nine-point scheme for the diffusion equation, and it naturally reduces to the standard five-point scheme for a orthogonal quadrilateral mesh. Numerical computations covering a wide range of transport regimes on unstructured and distorted quadrilateral meshes will be presented to validate the current approach.

Advanced Multi-Physics (AMP)

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

Philip, Bobby

2012-06-01

The Advanced Multi-Physics (AMP) code, in its present form, will allow a user to build a multi-physics application code for existing mechanics and diffusion operators and extend them with user-defined material models and new physics operators. There are examples that demonstrate mechanics, thermo-mechanics, coupled diffusion, and mechanical contact. The AMP code is designed to leverage a variety of mathematical solvers (PETSc, Trilinos, SUNDIALS, and AMP solvers) and mesh databases (LibMesh and AMP) in a consistent interchangeable approach.

Full-mesh T- and O-band wavelength router based on arrayed waveguide gratings.

PubMed

Idris, Nazirul A; Yoshizawa, Katsumi; Tomomatsu, Yasunori; Sudo, Makoto; Hajikano, Tadashi; Kubo, Ryogo; Zervas, Georgios; Tsuda, Hiroyuki

2016-01-11

We propose an ultra-broadband full-mesh wavelength router supporting the T- and O-bands using 3 stages of cascaded arrayed waveguide gratings (AWGs). The router architecture is based on a combination of waveband and channel routing by coarse and fine AWGs, respectively. We fabricated several T-band-specific silica-based AWGs and quantum dot semiconductor optical ampliers as part of the router, and demonstrated 10 Gbps data transmission for several wavelengths throughout a range of 7.4 THz. The power penalties were below 1 dB. Wavelength routing was also demonstrated, where tuning time within a 9.4-nm-wide waveband was below 400 ms.

Recycled Coarse Aggregate Produced by Pulsed Discharge in Water

NASA Astrophysics Data System (ADS)

Namihira, Takao; Shigeishi, Mitsuhiro; Nakashima, Kazuyuki; Murakami, Akira; Kuroki, Kaori; Kiyan, Tsuyoshi; Tomoda, Yuichi; Sakugawa, Takashi; Katsuki, Sunao; Akiyama, Hidenori; Ohtsu, Masayasu

In Japan, the recycling ratio of concrete scraps has been kept over 98 % after the Law for the Recycling of Construction Materials was enforced in 2000. In the present, most of concrete scraps were recycled as the Lower Subbase Course Material. On the other hand, it is predicted to be difficult to keep this higher recycling ratio in the near future because concrete scraps increase rapidly and would reach to over 3 times of present situation in 2010. In addition, the demand of concrete scraps as the Lower Subbase Course Material has been decreased. Therefore, new way to reuse concrete scraps must be developed. Concrete scraps normally consist of 70 % of coarse aggregate, 19 % of water and 11 % of cement. To obtain the higher recycling ratio, the higher recycling ratio of coarse aggregate is desired. In this paper, a new method for recycling coarse aggregate from concrete scraps has been developed and demonstrated. The system includes a Marx generator and a point to hemisphere mesh electrode immersed in water. In the demonstration, the test piece of concrete scrap was located between the electrodes and was treated by the pulsed discharge. After discharge treatment of test piece, the recycling coarse aggregates were evaluated under JIS and TS and had enough quality for utilization as the coarse aggregate.

Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles

NASA Astrophysics Data System (ADS)

Katsoulakis, Markos A.; Vlachos, Dionisios G.

2003-11-01

We derive a hierarchy of successively coarse-grained stochastic processes and associated coarse-grained Monte Carlo (CGMC) algorithms directly from the microscopic processes as approximations in larger length scales for the case of diffusion of interacting particles on a lattice. This hierarchy of models spans length scales between microscopic and mesoscopic, satisfies a detailed balance, and gives self-consistent fluctuation mechanisms whose noise is asymptotically identical to the microscopic MC. Rigorous, detailed asymptotics justify and clarify these connections. Gradient continuous time microscopic MC and CGMC simulations are compared under far from equilibrium conditions to illustrate the validity of our theory and delineate the errors obtained by rigorous asymptotics. Information theory estimates are employed for the first time to provide rigorous error estimates between the solutions of microscopic MC and CGMC, describing the loss of information during the coarse-graining process. Simulations under periodic boundary conditions are used to verify the information theory error estimates. It is shown that coarse-graining in space leads also to coarse-graining in time by q2, where q is the level of coarse-graining, and overcomes in part the hydrodynamic slowdown. Operation counting and CGMC simulations demonstrate significant CPU savings in continuous time MC simulations that vary from q3 for short potentials to q4 for long potentials. Finally, connections of the new coarse-grained stochastic processes to stochastic mesoscopic and Cahn-Hilliard-Cook models are made.

Microstructures of Randall's plaques and their interfaces with calcium oxalate monohydrate kidney stones reflect underlying mineral precipitation mechanisms.

PubMed

Sethmann, Ingo; Wendt-Nordahl, Gunnar; Knoll, Thomas; Enzmann, Frieder; Simon, Ludwig; Kleebe, Hans-Joachim

2017-06-01

Randall's plaques (RP) are preferred sites for the formation of calcium oxalate monohydrate (COM) kidney stones. However, although processes of interstitial calcium phosphate (CaP) plaque formation are not well understood, the potential of plaque microstructures as indicators of CaP precipitation conditions received only limited attention. We investigated RP-associated COM stones for structural details of the calcified tissues and microstructural features of plaque-stone interfaces as indicators of the initial processes of stone formation. Significantly increased CaP supersaturation can be expected for interstitial fluid, if reabsorbed ions from the tubular system continuously diffuse into the collagenous connective tissue. Densely packed, fine-grained CaP particles were found in dense textures of basement membranes while larger, laminated particles were scattered in coarse-meshed interstitial tissue, which we propose to be due to differential spatial confinements and restrictions of ion diffusion. Particle morphologies suggest an initial precipitation as metastable amorphous calcium phosphate (ACP). Morphologies and arrangements of first COM crystals at the RP-stone interface ranged from stacked euhedral platelets to skeletal morphologies and even porous, dendritic structures, indicating, in this order, increasing levels of COM supersaturation. Furthermore, these first COM crystals were often coated with CaP. On this basis, we propose that ions from CaP-supersaturated interstitial fluid may diffuse through porous RP into the urine, where a resulting local increase in COM supersaturation could trigger crystal nucleation and, hence, initiate stone formation. Ion-depleted fluid in persistent pores of initial COM layers may get replenished from interstitial fluid, leading to CaP precipitation in porous COM.

Application of Interface Technology in Nonlinear Analysis of a Stitched/RFI Composite Wing Stub Box

NASA Technical Reports Server (NTRS)

Wang, John T.; Ransom, Jonathan B.

1997-01-01

A recently developed interface technology was successfully employed in the geometrically nonlinear analysis of a full-scale stitched/RFI composite wing box loaded in bending. The technology allows mismatched finite element models to be joined in a variationally consistent manner and reduces the modeling complexity by eliminating transition meshing. In the analysis, local finite element models of nonlinearly deformed wide bays of the wing box are refined without the need for transition meshing to the surrounding coarse mesh. The COMET-AR finite element code, which has the interface technology capability, was used to perform the analyses. The COMET-AR analysis is compared to both a NASTRAN analysis and to experimental data. The interface technology solution is shown to be in good agreement with both. The viability of interface technology for coupled global/local analysis of large scale aircraft structures is demonstrated.

An adaptive embedded mesh procedure for leading-edge vortex flows

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.; Beer, Michael A.; Law, Glenn W.

1989-01-01

A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.

A new coarse-grained model for E. coli cytoplasm: accurate calculation of the diffusion coefficient of proteins and observation of anomalous diffusion.

PubMed

Hasnain, Sabeeha; McClendon, Christopher L; Hsu, Monica T; Jacobson, Matthew P; Bandyopadhyay, Pradipta

2014-01-01

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Monte Carlo charged-particle tracking and energy deposition on a Lagrangian mesh.

PubMed

Yuan, J; Moses, G A; McKenty, P W

2005-10-01

A Monte Carlo algorithm for alpha particle tracking and energy deposition on a cylindrical computational mesh in a Lagrangian hydrodynamics code used for inertial confinement fusion (ICF) simulations is presented. The straight line approximation is used to follow propagation of "Monte Carlo particles" which represent collections of alpha particles generated from thermonuclear deuterium-tritium (DT) reactions. Energy deposition in the plasma is modeled by the continuous slowing down approximation. The scheme addresses various aspects arising in the coupling of Monte Carlo tracking with Lagrangian hydrodynamics; such as non-orthogonal severely distorted mesh cells, particle relocation on the moving mesh and particle relocation after rezoning. A comparison with the flux-limited multi-group diffusion transport method is presented for a polar direct drive target design for the National Ignition Facility. Simulations show the Monte Carlo transport method predicts about earlier ignition than predicted by the diffusion method, and generates higher hot spot temperature. Nearly linear speed-up is achieved for multi-processor parallel simulations.

A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

NASA Astrophysics Data System (ADS)

Wang, Shuai; Hang, Xudeng; Yuan, Guangwei

2017-12-01

In this paper, a new cell-centered finite volume scheme is proposed for three-dimensional diffusion equations on polyhedral meshes, which is called as pyramid scheme (P-scheme). The scheme is designed for polyhedral cells with nonplanar cell-faces. The normal flux on a nonplanar cell-face is discretized on a planar face, which is determined by a simple optimization procedure. The resulted discrete form of the normal flux involves only cell-centered and cell-vertex unknowns, and is free from face-centered unknowns. In the case of hexahedral meshes with skewed nonplanar cell-faces, a quite simple expression is obtained for the discrete normal flux. Compared with the second order accurate O-scheme [31], the P-scheme is more robust and the discretization cost is reduced remarkably. Numerical results are presented to show the performance of the P-scheme on various kinds of distorted meshes. In particular, the P-scheme is shown to be second order accurate.

Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

DOE PAGES

Chen, Zheng; Huang, Hongying; Yan, Jue

2015-12-21

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

NASA Astrophysics Data System (ADS)

Hurtado, Daniel E.; Rojas, Guillermo

2018-04-01

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.

The interplay between tissue plasminogen activator domains and fibrin structures in the regulation of fibrinolysis: kinetic and microscopic studies

PubMed Central

Thelwell, Craig; Williams, Stella C.; Silva, Marta M. C. G.; Szabó, László; Kolev, Krasimir

2011-01-01

Regulation of tissue-type plasminogen activator (tPA) depends on fibrin binding and fibrin structure. tPA structure/function relationships were investigated in fibrin formed by high or low thrombin concentrations to produce a fine mesh and small pores, or thick fibers and coarse structure, respectively. Kinetics studies were performed to investigate plasminogen activation and fibrinolysis in the 2 types of fibrin, using wild-type tPA (F-G-K1-K2-P, F and K2 binding), K1K1-tPA (F-G-K1-K1-P, F binding), and delF-tPA (G-K1-K2-P, K2 binding). There was a trend of enzyme potency of tPA > K1K1-tPA > delF-tPA, highlighting the importance of the finger domain in regulating activity, but the differences were less apparent in fine fibrin. Fine fibrin was a better surface for plasminogen activation but more resistant to lysis. Scanning electron and confocal microscopy using orange fluorescent fibrin with green fluorescent protein-labeled tPA variants showed that tPA was strongly associated with agglomerates in coarse but not in fine fibrin. In later lytic stages, delF-tPA-green fluorescent protein diffused more rapidly through fibrin in contrast to full-length tPA, highlighting the importance of finger domain-agglomerate interactions. Thus, the regulation of fibrinolysis depends on the starting nature of fibrin fibers and complex dynamic interaction between tPA and fibrin structures that vary over time. PMID:20966169

AMR on the CM-2

NASA Technical Reports Server (NTRS)

Berger, Marsha J.; Saltzman, Jeff S.

1992-01-01

We describe the development of a structured adaptive mesh algorithm (AMR) for the Connection Machine-2 (CM-2). We develop a data layout scheme that preserves locality even for communication between fine and coarse grids. On 8K of a 32K machine we achieve performance slightly less than 1 CPU of the Cray Y-MP. We apply our algorithm to an inviscid compressible flow problem.

On Spurious Numerics in Solving Reactive Equations

NASA Technical Reports Server (NTRS)

Kotov, D. V; Yee, H. C.; Wang, W.; Shu, C.-W.

2013-01-01

The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here "coarse grids" means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed.

Evaluation of flotation for purification of pyrite for use in thermal batteries

NASA Astrophysics Data System (ADS)

Guidotti, R. A.; Reinhardt, F. W.

1992-07-01

The purification of pyrite (FeS2) used in Li-alloy/FeS2 thermal batteries by the physical process of flotation was evaluated for reduction of the quartz impurity. The process was compared to the standard process of leaching with concentrated hydrofluoric acid. Flotation was an attractive alternative because it avoided many of the safety and environmental concerns posed by the use of concentrated HF. The effects of particle size and initial purity of the pyrite feed material upon the final purity and yield of the product concentrate were examined for batch sizes from 3.5 to 921 kg. Feed materials as coarse as 8 mm and as fine as -325 mesh were treated; the coarse pyrite was ground wet in a rod mill or dry in a vibratory mill to -230 mesh prior to flotation. Both the HF-leached and the flotation-treated pyrite were leached with HCI (1:1 v/v) to remove acid-soluble impurities. The flotation-purified pyrite concentrates were formulated into catholytes; their electrochemical performance was evaluated in both single cells and 5-cell batteries for comparison to data generated under the same discharge conditions for catholytes formulated with HF/HCI purified pyrite.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

Ab initio velocity-field curves in monoclinic β-Ga2O3

NASA Astrophysics Data System (ADS)

Ghosh, Krishnendu; Singisetti, Uttam

2017-07-01

We investigate the high-field transport in monoclinic β-Ga2O3 using a combination of ab initio calculations and full band Monte Carlo (FBMC) simulation. Scattering rate calculation and the final state selection in the FBMC simulation use complete wave-vector (both electron and phonon) and crystal direction dependent electron phonon interaction (EPI) elements. We propose and implement a semi-coarse version of the Wannier-Fourier interpolation method [Giustino et al., Phys. Rev. B 76, 165108 (2007)] for short-range non-polar optical phonon (EPI) elements in order to ease the computational requirement in FBMC simulation. During the interpolation of the EPI, the inverse Fourier sum over the real-space electronic grids is done on a coarse mesh while the unitary rotations are done on a fine mesh. This paper reports the high field transport in monoclinic β-Ga2O3 with deep insight into the contribution of electron-phonon interactions and velocity-field characteristics for electric fields ranging up to 450 kV/cm in different crystal directions. A peak velocity of 2 × 107 cm/s is estimated at an electric field of 200 kV/cm.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

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

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Botti, Lorenzo; Di Pietro, Daniele A.

2018-10-01

We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes featuring curved elements. HHO methods are based on discrete unknowns that are broken polynomials on the mesh and its skeleton. We propose here the use of physical frame polynomials over mesh elements and reference frame polynomials over mesh faces. With this choice, the degree of face unknowns must be suitably selected in order to recover on curved meshes the same convergence rates as on straight meshes. We provide an estimate of the optimal face polynomial degree depending on the element polynomial degree and on the so-called effective mapping order. The estimate is numerically validated through specifically crafted numerical tests. All test cases are conducted considering two- and three-dimensional pure diffusion problems, and include comparisons with discontinuous Galerkin discretizations. The extension to agglomerated meshes with curved boundaries is also considered.

Impact of Variable-Resolution Meshes on Regional Climate Simulations

NASA Astrophysics Data System (ADS)

Fowler, L. D.; Skamarock, W. C.; Bruyere, C. L.

2014-12-01

The Model for Prediction Across Scales (MPAS) is currently being used for seasonal-scale simulations on globally-uniform and regionally-refined meshes. Our ongoing research aims at analyzing simulations of tropical convective activity and tropical cyclone development during one hurricane season over the North Atlantic Ocean, contrasting statistics obtained with a variable-resolution mesh against those obtained with a quasi-uniform mesh. Analyses focus on the spatial distribution, frequency, and intensity of convective and grid-scale precipitations, and their relative contributions to the total precipitation as a function of the horizontal scale. Multi-month simulations initialized on May 1st 2005 using ERA-Interim re-analyses indicate that MPAS performs satisfactorily as a regional climate model for different combinations of horizontal resolutions and transitions between the coarse and refined meshes. Results highlight seamless transitions for convection, cloud microphysics, radiation, and land-surface processes between the quasi-uniform and locally- refined meshes, despite the fact that the physics parameterizations were not developed for variable resolution meshes. Our goal of analyzing the performance of MPAS is twofold. First, we want to establish that MPAS can be successfully used as a regional climate model, bypassing the need for nesting and nudging techniques at the edges of the computational domain as done in traditional regional climate modeling. Second, we want to assess the performance of our convective and cloud microphysics parameterizations as the horizontal resolution varies between the lower-resolution quasi-uniform and higher-resolution locally-refined areas of the global domain.

Impact of Variable-Resolution Meshes on Regional Climate Simulations

NASA Astrophysics Data System (ADS)

Fowler, L. D.; Skamarock, W. C.; Bruyere, C. L.

2013-12-01

The Model for Prediction Across Scales (MPAS) is currently being used for seasonal-scale simulations on globally-uniform and regionally-refined meshes. Our ongoing research aims at analyzing simulations of tropical convective activity and tropical cyclone development during one hurricane season over the North Atlantic Ocean, contrasting statistics obtained with a variable-resolution mesh against those obtained with a quasi-uniform mesh. Analyses focus on the spatial distribution, frequency, and intensity of convective and grid-scale precipitations, and their relative contributions to the total precipitation as a function of the horizontal scale. Multi-month simulations initialized on May 1st 2005 using NCEP/NCAR re-analyses indicate that MPAS performs satisfactorily as a regional climate model for different combinations of horizontal resolutions and transitions between the coarse and refined meshes. Results highlight seamless transitions for convection, cloud microphysics, radiation, and land-surface processes between the quasi-uniform and locally-refined meshes, despite the fact that the physics parameterizations were not developed for variable resolution meshes. Our goal of analyzing the performance of MPAS is twofold. First, we want to establish that MPAS can be successfully used as a regional climate model, bypassing the need for nesting and nudging techniques at the edges of the computational domain as done in traditional regional climate modeling. Second, we want to assess the performance of our convective and cloud microphysics parameterizations as the horizontal resolution varies between the lower-resolution quasi-uniform and higher-resolution locally-refined areas of the global domain.

LES on unstructured deforming meshes: Towards reciprocating IC engines

NASA Technical Reports Server (NTRS)

Haworth, D. C.; Jansen, K.

1996-01-01

A variable explicit/implicit characteristics-based advection scheme that is second-order accurate in space and time has been developed recently for unstructured deforming meshes (O'Rourke & Sahota 1996a). To explore the suitability of this methodology for Large-Eddy Simulation (LES), three subgrid-scale turbulence models have been implemented in the CHAD CFD code (O'Rourke & Sahota 1996b): a constant-coefficient Smagorinsky model, a dynamic Smagorinsky model for flows having one or more directions of statistical homogeneity, and a Lagrangian dynamic Smagorinsky model for flows having no spatial or temporal homogeneity (Meneveau et al. 1996). Computations have been made for three canonical flows, progressing towards the intended application of in-cylinder flow in a reciprocating engine. Grid sizes were selected to be comparable to the coarsest meshes used in earlier spectral LES studies. Quantitative results are reported for decaying homogeneous isotropic turbulence, and for a planar channel flow. Computations are compared to experimental measurements, to Direct-Numerical Simulation (DNS) data, and to Rapid-Distortion Theory (RDT) where appropriate. Generally satisfactory evolution of first and second moments is found on these coarse meshes; deviations are attributed to insufficient mesh resolution. Issues include mesh resolution and computational requirements for a specified level of accuracy, analytic characterization of the filtering implied by the numerical method, wall treatment, and inflow boundary conditions. To resolve these issues, finer-mesh simulations and computations of a simplified axisymmetric reciprocating piston-cylinder assembly are in progress.

Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation.

PubMed

Bui, Huu Phuoc; Tomar, Satyendra; Courtecuisse, Hadrien; Audette, Michel; Cotin, Stéphane; Bordas, Stéphane P A

2018-05-01

An error-controlled mesh refinement procedure for needle insertion simulations is presented. As an example, the procedure is applied for simulations of electrode implantation for deep brain stimulation. We take into account the brain shift phenomena occurring when a craniotomy is performed. We observe that the error in the computation of the displacement and stress fields is localised around the needle tip and the needle shaft during needle insertion simulation. By suitably and adaptively refining the mesh in this region, our approach enables to control, and thus to reduce, the error whilst maintaining a coarser mesh in other parts of the domain. Through academic and practical examples we demonstrate that our adaptive approach, as compared with a uniform coarse mesh, increases the accuracy of the displacement and stress fields around the needle shaft and, while for a given accuracy, saves computational time with respect to a uniform finer mesh. This facilitates real-time simulations. The proposed methodology has direct implications in increasing the accuracy, and controlling the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anaesthesia, or cryotherapy. Moreover, the proposed approach can be helpful in the development of robotic surgeries because the simulation taking place in the control loop of a robot needs to be accurate, and to occur in real time. Copyright © 2018 John Wiley & Sons, Ltd.

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

Sehgal, Ray M.; Maroudas, Dimitrios, E-mail: maroudas@ecs.umass.edu, E-mail: ford@ecs.umass.edu; Ford, David M., E-mail: maroudas@ecs.umass.edu, E-mail: ford@ecs.umass.edu

We have developed a coarse-grained description of the phase behavior of the isolated 38-atom Lennard-Jones cluster (LJ{sub 38}). The model captures both the solid-solid polymorphic transitions at low temperatures and the complex cluster breakup and melting transitions at higher temperatures. For this coarse model development, we employ the manifold learning technique of diffusion mapping. The outcome of the diffusion mapping analysis over a broad temperature range indicates that two order parameters are sufficient to describe the cluster's phase behavior; we have chosen two such appropriate order parameters that are metrics of condensation and overall crystallinity. In this well-justified coarse-variable space,more » we calculate the cluster's free energy landscape (FEL) as a function of temperature, employing Monte Carlo umbrella sampling. These FELs are used to quantify the phase behavior and onsets of phase transitions of the LJ{sub 38} cluster.« less

Short-range, overpressure-driven methane migration in coarse-grained gas hydrate reservoirs

DOE PAGES

Nole, Michael; Daigle, Hugh; Cook, Ann E.; ...

2016-08-31

Two methane migration mechanisms have been proposed for coarse-grained gas hydrate reservoirs: short-range diffusive gas migration and long-range advective fluid transport from depth. Herein we demonstrate that short-range fluid flow due to overpressure in marine sediments is a significant additional methane transport mechanism that allows hydrate to precipitate in large quantities in thick, coarse-grained hydrate reservoirs. Two-dimensional simulations demonstrate that this migration mechanism, short-range advective transport, can supply significant amounts of dissolved gas and is unencumbered by limitations of the other two end-member mechanisms. Here, short-range advective migration can increase the amount of methane delivered to sands as compared tomore » the slow process of diffusion, yet it is not necessarily limited by effective porosity reduction as is typical of updip advection from a deep source.« less

Short-range, overpressure-driven methane migration in coarse-grained gas hydrate reservoirs

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

Nole, Michael; Daigle, Hugh; Cook, Ann E.

Two methane migration mechanisms have been proposed for coarse-grained gas hydrate reservoirs: short-range diffusive gas migration and long-range advective fluid transport from depth. Herein we demonstrate that short-range fluid flow due to overpressure in marine sediments is a significant additional methane transport mechanism that allows hydrate to precipitate in large quantities in thick, coarse-grained hydrate reservoirs. Two-dimensional simulations demonstrate that this migration mechanism, short-range advective transport, can supply significant amounts of dissolved gas and is unencumbered by limitations of the other two end-member mechanisms. Here, short-range advective migration can increase the amount of methane delivered to sands as compared tomore » the slow process of diffusion, yet it is not necessarily limited by effective porosity reduction as is typical of updip advection from a deep source.« less

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt

NASA Astrophysics Data System (ADS)

Pazmiño Betancourt, Beatriz A.; Starr, Francis W.; Douglas, Jack F.

2018-03-01

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

Computationally Guided Design of Polymer Electrolytes for Battery Applications

NASA Astrophysics Data System (ADS)

Wang, Zhen-Gang; Webb, Michael; Savoie, Brett; Miller, Thomas

We develop an efficient computational framework for guiding the design of polymer electrolytes for Li battery applications. Short-times molecular dynamics (MD) simulations are employed to identify key structural and dynamic features in the solvation and motion of Li ions, such as the structure of the solvation shells, the spatial distribution of solvation sites, and the polymer segmental mobility. Comparative studies on six polyester-based polymers and polyethylene oxide (PEO) yield good agreement with experimental data on the ion conductivities, and reveal significant differences in the ion diffusion mechanism between PEO and the polyesters. The molecular insights from the MD simulations are used to build a chemically specific coarse-grained model in the spirit of the dynamic bond percolation model of Druger, Ratner and Nitzan. We apply this coarse-grained model to characterize Li ion diffusion in several existing and yet-to-be synthesized polyethers that differ by oxygen content and backbone stiffness. Good agreement is obtained between the predictions of the coarse-grained model and long-timescale atomistic MD simulations, thus providing validation of the model. Our study predicts higher Li ion diffusivity in poly(trimethylene oxide-alt-ethylene oxide) than in PEO. These results demonstrate the potential of this computational framework for rapid screening of new polymer electrolytes based on ion diffusivity.

Regulation Mechanism of the Lateral Diffusion of Band 3 in Erythrocyte Membranes by the Membrane Skeleton

PubMed Central

Tomishige, Michio; Sako, Yasushi; Kusumi, Akihiro

1998-01-01

Mechanisms that regulate the movement of a membrane spanning protein band 3 in erythrocyte ghosts were investigated at the level of a single or small groups of molecules using single particle tracking with an enhanced time resolution (0.22 ms). Two-thirds of band 3 undergo macroscopic diffusion: a band 3 molecule is temporarily corralled in a mesh of 110 nm in diameter, and hops to an adjacent mesh an average of every 350 ms. The rest (one-third) of band 3 exhibited oscillatory motion similar to that of spectrin, suggesting that these band 3 molecules are bound to spectrin. When the membrane skeletal network was dragged and deformed/translated using optical tweezers, band 3 molecules that were undergoing hop diffusion were displaced toward the same direction as the skeleton. Mild trypsin treatment of ghosts, which cleaves off the cytoplasmic portion of band 3 without affecting spectrin, actin, and protein 4.1, increased the intercompartmental hop rate of band 3 by a factor of 6, whereas it did not change the corral size and the microscopic diffusion rate within a corral. These results indicate that the cytoplasmic portion of band 3 collides with the membrane skeleton, which causes temporal confinement of band 3 inside a mesh of the membrane skeleton. PMID:9722611

Separation of the Stern and diffuse layer in coarse-grained models: the cases of phosphatidyl serine, phosphatidic acid, and PIP2 monolayers.

PubMed

Vangaveti, S; Travesset, A

2014-12-28

We present here a method to separate the Stern and diffuse layer in general systems into two regions that can be analyzed separately. The Stern layer can be described in terms of Bjerrum pairing and the diffuse layer in terms of Poisson-Boltzmann theory (monovalent) or strong coupling theory plus a slowly decaying tail (divalent). We consider three anionic phospholipids: phosphatidyl serine, phosphatidic acid, and phosphatidylinositol(4,5)bisphosphate (PIP2), which we describe within a minimal coarse-grained model as a function of ionic concentration. The case of mixed lipid systems is also considered, which shows a high level of binding cooperativity as a function of PIP2 localization. Implications for existing experimental systems of lipid heterogeneities are also discussed.

Separation of the Stern and diffuse layer in coarse-grained models: The cases of phosphatidyl serine, phosphatidic acid, and PIP2 monolayers

NASA Astrophysics Data System (ADS)

Vangaveti, S.; Travesset, A.

2014-12-01

We present here a method to separate the Stern and diffuse layer in general systems into two regions that can be analyzed separately. The Stern layer can be described in terms of Bjerrum pairing and the diffuse layer in terms of Poisson-Boltzmann theory (monovalent) or strong coupling theory plus a slowly decaying tail (divalent). We consider three anionic phospholipids: phosphatidyl serine, phosphatidic acid, and phosphatidylinositol(4,5)bisphosphate (PIP2), which we describe within a minimal coarse-grained model as a function of ionic concentration. The case of mixed lipid systems is also considered, which shows a high level of binding cooperativity as a function of PIP2 localization. Implications for existing experimental systems of lipid heterogeneities are also discussed.

Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex

PubMed Central

Heinemann, Fabian; Vogel, Sven K.; Schwille, Petra

2013-01-01

Diffusion of lipids and proteins within the cell membrane is essential for numerous membrane-dependent processes including signaling and molecular interactions. It is assumed that the membrane-associated cytoskeleton modulates lateral diffusion. Here, we use a minimal actin cortex to directly study proposed effects of an actin meshwork on the diffusion in a well-defined system. The lateral diffusion of a lipid and a protein probe at varying densities of membrane-bound actin was characterized by fluorescence correlation spectroscopy (FCS). A clear correlation of actin density and reduction in mobility was observed for both the lipid and the protein probe. At high actin densities, the effect on the protein probe was ∼3.5-fold stronger compared to the lipid. Moreover, addition of myosin filaments, which contract the actin mesh, allowed switching between fast and slow diffusion in the minimal system. Spot variation FCS was in accordance with a model of fast microscopic diffusion and slower macroscopic diffusion. Complementing Monte Carlo simulations support the analysis of the experimental FCS data. Our results suggest a stronger interaction of the actin mesh with the larger protein probe compared to the lipid. This might point toward a mechanism where cortical actin controls membrane diffusion in a strong size-dependent manner. PMID:23561523

Diffuse interface simulation of bubble rising process: a comparison of adaptive mesh refinement and arbitrary lagrange-euler methods

NASA Astrophysics Data System (ADS)

Wang, Ye; Cai, Jiejin; Li, Qiong; Yin, Huaqiang; Yang, Xingtuan

2018-06-01

Gas-liquid two phase flow exists in several industrial processes and light-water reactors (LWRs). A diffuse interface based finite element method with two different mesh generation methods namely, the Adaptive Mesh Refinement (AMR) and the Arbitrary Lagrange Euler (ALE) methods is used to model the shape and velocity changes in a rising bubble. Moreover, the calculating speed and mesh generation strategies of AMR and ALE are contrasted. The simulation results agree with the Bhagat's experiments, indicating that both mesh generation methods can simulate the characteristics of bubble accurately. We concluded that: the small bubble rises as elliptical with oscillation, whereas a larger bubble (11 mm > d > 7 mm) rises with a morphology between the elliptical and cap type with a larger oscillation. When the bubble is large (d > 11 mm), it rises up as a cap type, and the amplitude becomes smaller. Moreover, it takes longer to achieve the stable shape from the ellipsoid to the spherical cap type with the increase of the bubble diameter. The results also show that for smaller diameter case, the ALE method uses fewer grids and has a faster calculation speed, but the AMR method can solve the case of a large geometry deformation efficiently.

Hybrid Multiscale Finite Volume method for multiresolution simulations of flow and reactive transport in porous media

NASA Astrophysics Data System (ADS)

Barajas-Solano, D. A.; Tartakovsky, A. M.

2017-12-01

We present a multiresolution method for the numerical simulation of flow and reactive transport in porous, heterogeneous media, based on the hybrid Multiscale Finite Volume (h-MsFV) algorithm. The h-MsFV algorithm allows us to couple high-resolution (fine scale) flow and transport models with lower resolution (coarse) models to locally refine both spatial resolution and transport models. The fine scale problem is decomposed into various "local'' problems solved independently in parallel and coordinated via a "global'' problem. This global problem is then coupled with the coarse model to strictly ensure domain-wide coarse-scale mass conservation. The proposed method provides an alternative to adaptive mesh refinement (AMR), due to its capacity to rapidly refine spatial resolution beyond what's possible with state-of-the-art AMR techniques, and the capability to locally swap transport models. We illustrate our method by applying it to groundwater flow and reactive transport of multiple species.

Development of an adaptive hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1994-01-01

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

Progressive simplification and transmission of building polygons based on triangle meshes

NASA Astrophysics Data System (ADS)

Li, Hongsheng; Wang, Yingjie; Guo, Qingsheng; Han, Jiafu

2010-11-01

Digital earth is a virtual representation of our planet and a data integration platform which aims at harnessing multisource, multi-resolution, multi-format spatial data. This paper introduces a research framework integrating progressive cartographic generalization and transmission of vector data. The progressive cartographic generalization provides multiple resolution data from coarse to fine as key scales and increments between them which is not available in traditional generalization framework. Based on the progressive simplification algorithm, the building polygons are triangulated into meshes and encoded according to the simplification sequence of two basic operations, edge collapse and vertex split. The map data at key scales and encoded increments between them are stored in a multi-resolution file. As the client submits requests to the server, the coarsest map is transmitted first and then the increments. After data decoding and mesh refinement the building polygons with more details will be visualized. Progressive generalization and transmission of building polygons is demonstrated in the paper.

Performance Characteristics of the Multi-Zone NAS Parallel Benchmarks

NASA Technical Reports Server (NTRS)

Jin, Haoqiang; VanderWijngaart, Rob F.

2003-01-01

We describe a new suite of computational benchmarks that models applications featuring multiple levels of parallelism. Such parallelism is often available in realistic flow computations on systems of grids, but had not previously been captured in bench-marks. The new suite, named NPB Multi-Zone, is extended from the NAS Parallel Benchmarks suite, and involves solving the application benchmarks LU, BT and SP on collections of loosely coupled discretization meshes. The solutions on the meshes are updated independently, but after each time step they exchange boundary value information. This strategy provides relatively easily exploitable coarse-grain parallelism between meshes. Three reference implementations are available: one serial, one hybrid using the Message Passing Interface (MPI) and OpenMP, and another hybrid using a shared memory multi-level programming model (SMP+OpenMP). We examine the effectiveness of hybrid parallelization paradigms in these implementations on three different parallel computers. We also use an empirical formula to investigate the performance characteristics of the multi-zone benchmarks.

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

PubMed

MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H

2016-03-15

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR

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

Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.

2015-02-01

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L 2 norm.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric

2018-03-01

The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

Effects of alternatives to clearcutting on invertebrate and organic detritus transport from headwaters in southeastern Alaska.

Treesearch

Jake Musslewhite; Mark S. Wipfli

2004-01-01

We examined the transport of invertebrates and coarse organic detritus from headwater streams draining timber harvest units in a selective timber harvesting study, alternatives to clearcutting (ATC) in southeastern Alaska. Transport in 17 small streams (mean measured discharge range: 1.2 to 14.6 L/s) was sampled with 250- µ m-mesh drift nets in spring, summer, and fall...

MPACT Theory Manual, Version 2.2.0

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

Downar, Thomas; Collins, Benjamin S.; Gehin, Jess C.

2016-06-09

This theory manual describes the three-dimensional (3-D) whole-core, pin-resolved transport calculation methodology employed in the MPACT code. To provide sub-pin level power distributions with sufficient accuracy, MPACT employs the method of characteristics (MOC) solutions in the framework of a 3-D coarse mesh finite difference (CMFD) formulation. MPACT provides a 3D MOC solution, but also a 2D/1D solution in which the 2D planar solution is provided by MOC and the axial coupling is resolved by one-dimensional (1-D) lower order (diffusion or P3) solutions. In Chapter 2 of the manual, the MOC methodology is described for calculating the regional angular and scalarmore » fluxes from the Boltzmann transport equation. In Chapter 3, the 2D/1D methodology is described, together with the description of the CMFD iteration process involving dynamic homogenization and solution of the multigroup CMFD linear system. A description of the MPACT depletion algorithm is given in Chapter 4, followed by a discussion of the subgroup and ESSM resonance processing methods in Chapter 5. The final Chapter 6 describes a simplified thermal hydraulics model in MPACT.« less

Evaluation of the UnTRIM model for 3-D tidal circulation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; ,

2001-01-01

A family of numerical models, known as the TRIM models, shares the same modeling philosophy for solving the shallow water equations. A characteristic analysis of the shallow water equations points out that the numerical instability is controlled by the gravity wave terms in the momentum equations and by the transport terms in the continuity equation. A semi-implicit finite-difference scheme has been formulated so that these terms and the vertical diffusion terms are treated implicitly and the remaining terms explicitly to control the numerical stability and the computations are carried out over a uniform finite-difference computational mesh without invoking horizontal or vertical coordinate transformations. An unstructured grid version of TRIM model is introduced, or UnTRIM (pronounces as "you trim"), which preserves these basic numerical properties and modeling philosophy, only the computations are carried out over an unstructured orthogonal grid. The unstructured grid offers the flexibilities in representing complex study areas so that fine grid resolution can be placed in regions of interest, and coarse grids are used to cover the remaining domain. Thus, the computational efforts are concentrated in areas of importance, and an overall computational saving can be achieved because the total number of grid-points is dramatically reduced. To use this modeling approach, an unstructured grid mesh must be generated to properly reflect the properties of the domain of the investigation. The new modeling flexibility in grid structure is accompanied by new challenges associated with issues of grid generation. To take full advantage of this new model flexibility, the model grid generation should be guided by insights into the physics of the problems; and the insights needed may require a higher degree of modeling skill.

Approach to identifying pollutant source and matching flow field

NASA Astrophysics Data System (ADS)

Liping, Pang; Yu, Zhang; Hongquan, Qu; Tao, Hu; Wei, Wang

2013-07-01

Accidental pollution events often threaten people's health and lives, and it is necessary to identify a pollutant source rapidly so that prompt actions can be taken to prevent the spread of pollution. But this identification process is one of the difficulties in the inverse problem areas. This paper carries out some studies on this issue. An approach using single sensor information with noise was developed to identify a sudden continuous emission trace pollutant source in a steady velocity field. This approach first compares the characteristic distance of the measured concentration sequence to the multiple hypothetical measured concentration sequences at the sensor position, which are obtained based on a source-three-parameter multiple hypotheses. Then we realize the source identification by globally searching the optimal values with the objective function of the maximum location probability. Considering the large amount of computation load resulting from this global searching, a local fine-mesh source search method based on priori coarse-mesh location probabilities is further used to improve the efficiency of identification. Studies have shown that the flow field has a very important influence on the source identification. Therefore, we also discuss the impact of non-matching flow fields with estimation deviation on identification. Based on this analysis, a method for matching accurate flow field is presented to improve the accuracy of identification. In order to verify the practical application of the above method, an experimental system simulating a sudden pollution process in a steady flow field was set up and some experiments were conducted when the diffusion coefficient was known. The studies showed that the three parameters (position, emission strength and initial emission time) of the pollutant source in the experiment can be estimated by using the method for matching flow field and source identification.

Experiments with the Mesoscale Atmospheric Simulation System (MASS) using the synthetic relative humidity

NASA Technical Reports Server (NTRS)

Chang, Chia-Bo

1994-01-01

This study is intended to examine the impact of the synthetic relative humidity on the model simulation of mesoscale convective storm environment. The synthetic relative humidity is derived from the National Weather Services surface observations, and non-conventional sources including aircraft, radar, and satellite observations. The latter sources provide the mesoscale data of very high spatial and temporal resolution. The synthetic humidity data is used to complement the National Weather Services rawinsonde observations. It is believed that a realistic representation of initial moisture field in a mesoscale model is critical for the model simulation of thunderstorm development, and the formation of non-convective clouds as well as their effects on the surface energy budget. The impact will be investigated based on a real-data case study using the mesoscale atmospheric simulation system developed by Mesoscale Environmental Simulations Operations, Inc. The mesoscale atmospheric simulation system consists of objective analysis and initialization codes, and the coarse-mesh and fine-mesh dynamic prediction models. Both models are a three dimensional, primitive equation model containing the essential moist physics for simulating and forecasting mesoscale convective processes in the atmosphere. The modeling system is currently implemented at the Applied Meteorology Unit, Kennedy Space Center. Two procedures involving the synthetic relative humidity to define the model initial moisture fields are considered. It is proposed to perform several short-range (approximately 6 hours) comparative coarse-mesh simulation experiments with and without the synthetic data. They are aimed at revealing the model sensitivities should allow us both to refine the specification of the observational requirements, and to develop more accurate and efficient objective analysis schemes. The goal is to advance the MASS (Mesoscal Atmospheric Simulation System) modeling expertise so that the model output can provide reliable guidance for thunderstorm forecasting.

A coarse-grained Monte Carlo approach to diffusion processes in metallic nanoparticles

NASA Astrophysics Data System (ADS)

Hauser, Andreas W.; Schnedlitz, Martin; Ernst, Wolfgang E.

2017-06-01

A kinetic Monte Carlo approach on a coarse-grained lattice is developed for the simulation of surface diffusion processes of Ni, Pd and Au structures with diameters in the range of a few nanometers. Intensity information obtained via standard two-dimensional transmission electron microscopy imaging techniques is used to create three-dimensional structure models as input for a cellular automaton. A series of update rules based on reaction kinetics is defined to allow for a stepwise evolution in time with the aim to simulate surface diffusion phenomena such as Rayleigh breakup and surface wetting. The material flow, in our case represented by the hopping of discrete portions of metal on a given grid, is driven by the attempt to minimize the surface energy, which can be achieved by maximizing the number of filled neighbor cells.

Hopping Diffusion of Nanoparticles in Polymer Matrices

PubMed Central

2016-01-01

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae. Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus. PMID:25691803

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three dimension

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Benson, T. J.

1983-01-01

A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.

Numerical solution to the glancing sidewall oblique shock wave/turbulent boundary layer interaction in three-dimension

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Benson, T. J.

1983-01-01

A supersonic three-dimensional viscous forward-marching computer design code called PEPSIS is used to obtain a numerical solution of the three-dimensional problem of the interaction of a glancing sidewall oblique shock wave and a turbulent boundary layer. Very good results are obtained for a test case that was run to investigate the use of the wall-function boundary-condition approximation for a highly complex three-dimensional shock-boundary layer interaction. Two additional test cases (coarse mesh and medium mesh) are run to examine the question of near-wall resolution when no-slip boundary conditions are applied. A comparison with experimental data shows that the PEPSIS code gives excellent results in general and is practical for three-dimensional supersonic inlet calculations.

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.

Hydrogen atom kinetics in capacitively coupled plasmas

NASA Astrophysics Data System (ADS)

Nunomura, Shota; Katayama, Hirotaka; Yoshida, Isao

2017-05-01

Hydrogen (H) atom kinetics has been investigated in capacitively coupled very high frequency (VHF) discharges at powers of 16-780 mW cm-2 and H2 gas pressures of 0.1-2 Torr. The H atom density has been measured using vacuum ultra violet absorption spectroscopy (VUVAS) with a micro-discharge hollow cathode lamp as a VUV light source. The measurements have been performed in two different electrode configurations of discharges: conventional parallel-plate diode and triode with an intermediate mesh electrode. We find that in the triode configuration, the H atom density is strongly reduced across the mesh electrode. The H atom density varies from ˜1012 cm-3 to ˜1010 cm-3 by crossing the mesh with 0.2 mm in thickness and 36% in aperture ratio. The fluid model simulations for VHF discharge plasmas have been performed to study the H atom generation, diffusion and recombination kinetics. The simulations suggest that H atoms are generated in the bulk plasma, by the electron impact dissociation (e + H2 \\to e + 2H) and the ion-molecule reaction (H2 + + H2 \\to {{{H}}}3+ + H). The diffusion of H atoms is strongly limited by a mesh electrode, and thus the mesh geometry influences the spatial distribution of the H atoms. The loss of H atoms is dominated by the surface recombination.

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.

FINE PORE DIFFUSER CASE HISTORY FOR FRANKENMUTH, MICHIGAN

EPA Science Inventory

Frankenmuth is a community of 4,000 people in central Michigan. bout 25-3O% of the flow and 50-70% of the BOD load to the wastewater treatment plant are contributed by a brewery. In January 1986, conversion from a stainless steel broad band coarse bubble diffuser system to fine ...

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

Final Report of the Project "From the finite element method to the virtual element method"

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

Manzini, Gianmarco; Gyrya, Vitaliy

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for themore » numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.« less

Coarse graining Escherichia coli chemotaxis: from multi-flagella propulsion to logarithmic sensing.

PubMed

Curk, Tine; Matthäus, Franziska; Brill-Karniely, Yifat; Dobnikar, Jure

2012-01-01

Various sensing mechanisms in nature can be described by the Weber-Fechner law stating that the response to varying stimuli is proportional to their relative rather than absolute changes. The chemotaxis of bacteria Escherichia coli is an example where such logarithmic sensing enables sensitivity over large range of concentrations. It has recently been experimentally demonstrated that under certain conditions E. coli indeed respond to relative gradients of ligands. We use numerical simulations of bacteria in food gradients to investigate the limits of validity of the logarithmic behavior. We model the chemotactic signaling pathway reactions, couple them to a multi-flagella model for propelling and take the effects of rotational diffusion into account to accurately reproduce the experimental observations of single cell swimming. Using this simulation scheme we analyze the type of response of bacteria subject to exponential ligand profiles and identify the regimes of absolute gradient sensing, relative gradient sensing, and a rotational diffusion dominated regime. We explore dependance of the swimming speed, average run time and the clockwise (CW) bias on ligand variation and derive a small set of relations that define a coarse grained model for bacterial chemotaxis. Simulations based on this coarse grained model compare well with microfluidic experiments on E. coli diffusion in linear and exponential gradients of aspartate.

Nanorod Mobility within Entangled Wormlike Micelle Solutions

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

Lee, Jonghun; Grein-Iankovski, Aline; Narayanan, Suresh

In the semi-dilute regime, wormlike micelles form an isotropic entangled microstructure that is similar to that of an entangled polymer solution with a characteristic, nanometer-scale entanglement mesh size. We report a combined x-ray photon correlation spectroscopy (XPCS) and rheology study to investigate the translational dynamics of gold nanorods in semi-dilute solutions of entangled wormlike micelles formed by the surfactant cetylpyridinium chloride (CPyCl) and the counter-ion sodium salicylate (NaSal). The CPyCl concentration is varied to tune the entanglement mesh size over a range that spans from approximately equal to the nanorod diameter to larger than the nanorod length. The NaSal concentrationmore » is varied along with the CPyCl concentration so that the solutions have the maximum viscosity for given CPyCl concentration. On short time scales the nanorods are localized on a length scale matching that expected from the high-frequency elastic modulus of the solutions as long as the mesh size is smaller than the rod length. On longer time scales, the nanorods undergo free diffusion. At the highest CPyCl concentrations, the nanorod diffusivity approaches the value expected based on the macroscopic viscosity of the solutions, but it increases with decreasing CPyCl concentration more rapidly than expected from the macroscopic viscosity. A recent model by Cai et al. [Cai, L.-H.; Panyukov, S.; Rubinstein, M. Macromolecules 2015, 48, 847-862.] for nanoparticle “hopping” diffusion in entangled polymer solutions accounts quantitatively for this enhanced diffusivity.« less

Nanorod Mobility within Entangled Wormlike Micelle Solutions

DOE PAGES

Lee, Jonghun; Grein-Iankovski, Aline; Narayanan, Suresh; ...

2016-12-20

In the semi-dilute regime, wormlike micelles form an isotropic entangled microstructure that is similar to that of an entangled polymer solution with a characteristic, nanometer-scale entanglement mesh size. We report a combined x-ray photon correlation spectroscopy (XPCS) and rheology study to investigate the translational dynamics of gold nanorods in semi-dilute solutions of entangled wormlike micelles formed by the surfactant cetylpyridinium chloride (CPyCl) and the counter-ion sodium salicylate (NaSal). The CPyCl concentration is varied to tune the entanglement mesh size over a range that spans from approximately equal to the nanorod diameter to larger than the nanorod length. The NaSal concentrationmore » is varied along with the CPyCl concentration so that the solutions have the maximum viscosity for given CPyCl concentration. On short time scales the nanorods are localized on a length scale matching that expected from the high-frequency elastic modulus of the solutions as long as the mesh size is smaller than the rod length. On longer time scales, the nanorods undergo free diffusion. At the highest CPyCl concentrations, the nanorod diffusivity approaches the value expected based on the macroscopic viscosity of the solutions, but it increases with decreasing CPyCl concentration more rapidly than expected from the macroscopic viscosity. A recent model by Cai et al. [Cai, L.-H.; Panyukov, S.; Rubinstein, M. Macromolecules 2015, 48, 847-862.] for nanoparticle “hopping” diffusion in entangled polymer solutions accounts quantitatively for this enhanced diffusivity.« less

a Non-Overlapping Discretization Method for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Rosas-Medina, A.; Herrera, I.

2013-05-01

Mathematical models of many systems of interest, including very important continuous systems of Engineering and Science, lead to a great variety of partial differential equations whose solution methods are based on the computational processing of large-scale algebraic systems. Furthermore, the incredible expansion experienced by the existing computational hardware and software has made amenable to effective treatment problems of an ever increasing diversity and complexity, posed by engineering and scientific applications. The emergence of parallel computing prompted on the part of the computational-modeling community a continued and systematic effort with the purpose of harnessing it for the endeavor of solving boundary-value problems (BVPs) of partial differential equations. Very early after such an effort began, it was recognized that domain decomposition methods (DDM) were the most effective technique for applying parallel computing to the solution of partial differential equations, since such an approach drastically simplifies the coordination of the many processors that carry out the different tasks and also reduces very much the requirements of information-transmission between them. Ideally, DDMs intend producing algorithms that fulfill the DDM-paradigm; i.e., such that "the global solution is obtained by solving local problems defined separately in each subdomain of the coarse-mesh -or domain-decomposition-". Stated in a simplistic manner, the basic idea is that, when the DDM-paradigm is satisfied, full parallelization can be achieved by assigning each subdomain to a different processor. When intensive DDM research began much attention was given to overlapping DDMs, but soon after attention shifted to non-overlapping DDMs. This evolution seems natural when the DDM-paradigm is taken into account: it is easier to uncouple the local problems when the subdomains are separated. However, an important limitation of non-overlapping domain decompositions, as that concept is usually understood today, is that interface nodes are shared by two or more subdomains of the coarse-mesh and, therefore, even non-overlapping DDMs are actually overlapping when seen from the perspective of the nodes used in the discretization. In this talk we present and discuss a discretization method in which the nodes used are non-overlapping, in the sense that each one of them belongs to one and only one subdomain of the coarse-mesh.

CFD methodology and validation for turbomachinery flows

NASA Astrophysics Data System (ADS)

Hirsch, Ch.

1994-05-01

The essential problem today, in the application of 3D Navier-Stokes simulations to the design and analysis of turbomachinery components, is the validation of the numerical approximation and of the physical models, in particular the turbulence modelling. Although most of the complex 3D flow phenomena occurring in turbomachinery bladings can be captured with relatively coarse meshes, many detailed flow features are dependent on mesh size, on the turbulence and transition models. A brief review of the present state of the art of CFD methodology is given with emphasis on quality and accuracy of numerical approximations related to viscous flow computations. Considerations related to the mesh influence on solution accuracy are stressed. The basic problems of turbulence and transition modelling are discussed next, with a short summary of the main turbulence models and their applications to representative turbomachinery flows. Validations of present turbulence models indicate that none of the available turbulence models is able to predict all the detailed flow behavior in complex flow interactions. In order to identify the phenomena that can be captured on coarser meshes a detailed understanding of the complex 3D flow in compressor and turbines is necessary. Examples of global validations for different flow configurations, representative of compressor and turbine aerodynamics are presented, including secondary and tip clearance flows.

Improving finite element results in modeling heart valve mechanics.

PubMed

Earl, Emily; Mohammadi, Hadi

2018-06-01

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

S-HARP: A parallel dynamic spectral partitioner

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

Sohn, A.; Simon, H.

1998-01-01

Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. The authors present in this report a fast parallel dynamic partitioner, called S-HARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. S-HARP partitions a graph from scratch, requiring no partition information from previous iterations. Two types of parallelism have been exploited in S-HARP, fine grain loop level parallelism and coarse grain recursive parallelism. The parallel partitioner has been implemented in Messagemore » Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that S-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.2 seconds on a 64 processor Cray T3E. S-HARP is much more scalable than other dynamic partitioners, giving over 15 fold speedup on 64 processors while ParaMeTiS1.0 gives a few fold speedup. Experimental results demonstrate that S-HARP is three to 10 times faster than the dynamic partitioners ParaMeTiS and Jostle on six computational meshes of size over 100,000 vertices.« less

Reaction rates for mesoscopic reaction-diffusion kinetics

DOE PAGES

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2015-02-23

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In thismore » paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. Finally, we show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.« less

Reaction rates for mesoscopic reaction-diffusion kinetics

PubMed Central

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2016-01-01

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results. PMID:25768640

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

NASA Technical Reports Server (NTRS)

Eliasson, Peter; Engquist, Bjoern

1996-01-01

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

DISCO: A 3D Moving-mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks

NASA Astrophysics Data System (ADS)

Duffell, Paul C.

2016-09-01

This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.

DISCO: A 3D MOVING-MESH MAGNETOHYDRODYNAMICS CODE DESIGNED FOR THE STUDY OF ASTROPHYSICAL DISKS

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

Duffell, Paul C., E-mail: duffell@berkeley.edu

2016-09-01

This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide varietymore » of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.« less

Investigation of Grid Adaptation to Reduce Computational Efforts for a 2-D Hydrogen-Fueled Dual-Mode Scramjet

NASA Astrophysics Data System (ADS)

Foo, Kam Keong

A two-dimensional dual-mode scramjet flowpath is developed and evaluated using the ANSYS Fluent density-based flow solver with various computational grids. Results are obtained for fuel-off, fuel-on non-reacting, and fuel-on reacting cases at different equivalence ratios. A one-step global chemical kinetics hydrogen-air model is used in conjunction with the eddy-dissipation model. Coarse, medium and fine computational grids are used to evaluate grid sensitivity and to investigate a lack of grid independence. Different grid adaptation strategies are performed on the coarse grid in an attempt to emulate the solutions obtained from the finer grids. The goal of this study is to investigate the feasibility of using various mesh adaptation criteria to significantly decrease computational efforts for high-speed reacting flows.

Network Confinement and Heterogeneity Slows Nanoparticle Diffusion in Polymer Gels

NASA Astrophysics Data System (ADS)

Parrish, Emmabeth; Caporizzo, Matthew; Composto, Russell

Nanoparticle (NP) diffusion was measured in polyacrylamide gels (PAG) with a mesh size comparable to NP size, 20nm. The confinement ratio (CR), NP diameter/mesh, increased from 0.4 to 3.8 by increasing crosslinker density and 0.4 to 2 by adding acetone, which collapsed PAG. In all gels, NPs either became localized (<200nm) or diffused microns, as measured by single particle tracking. Mean squared displacements (MSD) of mobile NPs decreased as CR increased. In collapsed gels, the localized NP population increased and MSD of mobile NPs decreased compared to crosslinked PAG. For all CRs, van Hove distributions exhibited non-Gaussian displacements consistent with intermittent localization of NPs. The non-Gaussian parameter increased from a maximum of 1.5 for crosslinked PAG to 5 for collapsed PAG, consistent with greater network heterogeneity. Diffusion coefficients, D, decreased exponentially as CR increased for crosslinked gels, but in collapsed gels D decreased more strongly, suggesting CR alone was insufficient to capture diffusion. Collapsing the gel resulted in an increasingly tortuous pathway for NPs, slowing diffusion at a given CR. Understanding how gel structure affects NP mobility will allow the design of gels with improved ability to separate and release molecules. ACS/PRF 54028-ND7, NSF/MWN DMR-1210379.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

Sliding of proteins non-specifically bound to DNA: Brownian dynamics studies with coarse-grained protein and DNA models.

PubMed

Ando, Tadashi; Skolnick, Jeffrey

2014-12-01

DNA binding proteins efficiently search for their cognitive sites on long genomic DNA by combining 3D diffusion and 1D diffusion (sliding) along the DNA. Recent experimental results and theoretical analyses revealed that the proteins show a rotation-coupled sliding along DNA helical pitch. Here, we performed Brownian dynamics simulations using newly developed coarse-grained protein and DNA models for evaluating how hydrodynamic interactions between the protein and DNA molecules, binding affinity of the protein to DNA, and DNA fluctuations affect the one dimensional diffusion of the protein on the DNA. Our results indicate that intermolecular hydrodynamic interactions reduce 1D diffusivity by 30%. On the other hand, structural fluctuations of DNA give rise to steric collisions between the CG-proteins and DNA, resulting in faster 1D sliding of the protein. Proteins with low binding affinities consistent with experimental estimates of non-specific DNA binding show hopping along the CG-DNA. This hopping significantly increases sliding speed. These simulation studies provide additional insights into the mechanism of how DNA binding proteins find their target sites on the genome.

Molecular Simulation Studies of Covalently and Ionically Grafted Nanoparticles

NASA Astrophysics Data System (ADS)

Hong, Bingbing

Solvent-free covalently- or ionically-grafted nanoparticles (CGNs and IGNs) are a new class of organic-inorganic hybrid composite materials exhibiting fluid-like behaviors around room temperature. With similar structures to prior systems, e.g. nanocomposites, neutral or charged colloids, ionic liquids, etc, CGNs and IGNs inherit the functionality of inorganic nanopariticles, the facile processibility of polymers, as well as conductivity and nonvolatility from their constituent materials. In spite of the extensive prior experimental research having covered synthesis and measurements of thermal and dynamic properties, little progress in understanding of these new materials at the molecular level has been achieved, because of the lack of simulation work in this new area. Atomistic and coarse-grained molecular dynamics simulations have been performed in this thesis to investigate the thermodynamics, structure, and dynamics of these systems and to seek predictive methods predictable for their properties. Starting from poly(ethylene oxide) oligomers (PEO) melts, we established atomistic models based on united-atom representations of methylene. The Green-Kubo and Einstein-Helfand formulas were used to calculate the transport properties. The simulations generate densities, viscosities, diffusivities, in good agreement with experimental data. The chain-length dependence of the transport properties suggests that neither Rouse nor reptation models are applicable in the short-chain regime investigated. Coupled with thermodynamic integration methods, the models give good predictions of pressure-composition-density relations for CO 2 + PEO oligomers. Water effects on the Henry's constant of CO 2 in PEO have also been investigated. The dependence of the calculated Henry's constants on the weight percentage of water falls on a temperature-dependent master curve, irrespective of PEO chain length. CGNs are modeled by the inclusion of solid-sphere nanoparticles into the atomistic oligomers. The calculated viscosities from Green-Kubo relationships and temperature extrapolation are of the same order of magnitude as experimental values, but show a smaller activation energy relative to real CGNs systems. Grafted systems have higher viscosities, smaller diffusion coefficients, and slower chain dynamics than the ungrafted counterparts - nanocomposites - at high temperatures. At lower temperatures, grafted systems exhibit faster dynamics for both nanoparticles and chains relative to ungrafted systems, because of lower aggregation of nanoparticles and enhanced correlations between nanoparticles and chains. This agrees with the experimental observation that the new materials have liquid-like behavior in the absence of a solvent. To lower the simulated temperatures into the experimental range, we established a coarse-grained CGNs model by matching structural distribution functions to atomistic simulation data. In contrast with linear polymer systems, for which coarse-graining always accelerate dynamics, coarse-graining of grafted nanoparticles can either accelerate or slowdown the core motions, depending on the length of the grafted chains. This can be qualitatively predicted by a simple transition-state theory. Similar atomistic models to CGNs were developed for IGNs, with ammonium counterions described by an explicit-hydrogen way; these were in turn compared with "generic" coarse-grained IGNs. The elimination of chemical details in the coarse-grained models does not bring in qualitative changes to the radial distribution functions and diffusion of atomistic IGNs, but saves considerable simulation resources and make simulations near room temperatures affordable. The chain counterions in both atomistic and coarse-grained models are mobile, moving from site to site and from nanoparticle to nanoparticle. At the same temperature and the same core volume fractions, the nanoparticle diffusivities in coarse-grained IGNs are slower by a factor ten than the cores of CGNs. The coarse-grained IGNs models are later used to investigate the system dynamics through analysis of the dependence on temperature and structural parameters of the transport properties (self-diffusion coefficients, viscosities and conductivities). Further, migration kinetics of oligomeric counterions is analyzed in a manner analogous to unimer exchange between micellar aggregates. The counterion migrations follow the "double-core" mechanism and are kinetically controlled by neighboring-core collisions. (Abstract shortened by UMI.)

Adenosine triphosphate diffusion through poly(ethylene glycol) diacrylate hydrogels can be tuned by cross-link density as measured by PFG-NMR

NASA Astrophysics Data System (ADS)

Majer, Günter; Southan, Alexander

2017-06-01

The diffusion of small molecules through hydrogels is of great importance for many applications. Especially in biological contexts, the diffusion of nutrients through hydrogel networks defines whether cells can survive inside the hydrogel or not. In this contribution, hydrogels based on poly(ethylene glycol) diacrylate with mesh sizes ranging from ξ = 1.1 to 12.9 nm are prepared using polymers with number-average molecular weights between Mn = 700 and 8000 g/mol. Precise measurements of diffusion coefficients D of adenosine triphosphate (ATP), an important energy carrier in biological systems, in these hydrogels are performed by pulsed field gradient nuclear magnetic resonance. Depending on the mesh size, ξ, and on the polymer volume fraction of the hydrogel after swelling, ϕ, it is possible to tune the relative ATP diffusion coefficient D/D0 in the hydrogels to values between 0.14 and 0.77 compared to the ATP diffusion coefficient D0 in water. The diffusion coefficients of ATP in these hydrogels are compared with predictions of various mathematical expressions developed under different model assumptions. The experimental data are found to be in good agreement with the predictions of a modified obstruction model or the free volume theory in combination with the sieving behavior of the polymer chains. No reasonable agreement was found with the pure hydrodynamic model.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Biological decomposition efficiency in different woodland soils.

PubMed

Herlitzius, H

1983-03-01

The decomposition (meaning disappearance) of different leaf types and artificial leaves made from cellulose hydrate foil was studied in three forests - an alluvial forest (Ulmetum), a beech forest on limestone soil (Melico-Fagetum), and a spruce forest in soil overlying limestone bedrock.Fine, medium, and coarse mesh litter bags of special design were used to investigate the roles of abiotic factors, microorganisms, and meso- and macrofauna in effecting decomposition in the three habitats. Additionally, the experimental design was carefully arranged so as to provide information about the effects on decomposition processes of the duration of exposure and the date or moment of exposure. 1. Exposure of litter samples oor 12 months showed: a) Litter enclosed in fine mesh bags decomposed to some 40-44% of the initial amount placed in each of the three forests. Most of this decomposition can be attributed to abiotic factors and microoganisms. b) Litter placed in medium mesh litter bags reduced by ca. 60% in alluvial forest, ca. 50% in beech forest and ca. 44% in spruce forest. c) Litter enclosed in coarse mesh litter bags was reduced by 71% of the initial weights exposed in alluvial and beech forests; in the spruce forest decomposition was no greater than observed with fine and medium mesh litter bags. Clearly, in spruce forest the macrofauna has little or no part to play in effecting decomposition. 2. Sequential month by month exposure of hazel leaves and cellulose hydrate foil in coarse mesh litter bags in all three forests showed that one month of exposure led to only slight material losses, they did occur smallest between March and May, and largest between June and October/November. 3. Coarse mesh litter bags containing either hazel or artificial leaves of cellulose hydrate foil were exposed to natural decomposition processes in December 1977 and subsampled monthly over a period of one year, this series constituted the From-sequence of experiments. Each of the From-sequence samples removed was immediately replaced by a fresh litter bag which was left in place until December 1978, this series constituted the To-sequence of experiments. The results arising from the designated From- and To-sequences showed: a) During the course of one year hazel leaves decomposed completely in alluvial forest, almost completely in beech forest but to only 50% of the initial value in spruce forest. b) Duration of exposure and not the date of exposure is the major controlling influence on decomposition in alluvial forest, a characteristic reflected in the mirror-image courses of the From- and To-sequences curves with respect to the abscissa or time axis. Conversely the date of exposure and not the duration of exposure is the major controlling influence on decomposition in the spruce forest, a characteristic reflected in the mirror-image courses of the From-and To-sequences with respect to the ordinate or axis of percentage decomposition. c) Leaf powder amendment increased the decomposition rate of the hazel and cellulose hydrate leaves in the spruce forest but had no significant effect on their decomposition rate in alluvial and beech forests. It is concluded from this, and other evidence, that litter amendment by leaf fragments of phytophage frass in sites of low biological decomposition activity (eg. spruce) enhances decomposition processes. d) The time course of hazel leaf decomposition in both alluvial and beech forest is sigmoidal. Three s-phases are distinguished and correspond to the activity of microflora/microfauna, mesofauna/macrofauna, and then microflora/microfauna again. In general, the sigmoidal pattern of the curve can be considered valid for all decomposition processes occurring in terrestrial situations. It is contended that no decomposition (=disappearance) curve actually follows an e-type exponential function. A logarithmic linear regression can be constructed from the sigmoid curve data and although this facilitates inter-system comparisons it does not clearly express the dynamics of decomposition. 4. The course of the curve constructed from information about the standard deviations of means derived from the From- and To-sequence data does reflect the dynamics of litter decomposition. The three s-phases can be recognised and by comparing the actual From-sequence deviation curve with a mirror inversion representation of the To-sequence curve it is possible to determine whether decomposition is primarily controlled by the duration of exposure or the date of exposure. As is the case for hazel leaf decomposition in beech forest intermediate conditions can be readily recognised.

Coarse analysis of collective behaviors: Bifurcation analysis of the optimal velocity model for traffic jam formation

NASA Astrophysics Data System (ADS)

Miura, Yasunari; Sugiyama, Yuki

2017-12-01

We present a general method for analyzing macroscopic collective phenomena observed in many-body systems. For this purpose, we employ diffusion maps, which are one of the dimensionality-reduction techniques, and systematically define a few relevant coarse-grained variables for describing macroscopic phenomena. The time evolution of macroscopic behavior is described as a trajectory in the low-dimensional space constructed by these coarse variables. We apply this method to the analysis of the traffic model, called the optimal velocity model, and reveal a bifurcation structure, which features a transition to the emergence of a moving cluster as a traffic jam.

A discontinuous Galerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics

NASA Astrophysics Data System (ADS)

He, Ying; Puckett, Elbridge Gerry; Billen, Magali I.

2017-02-01

Mineral composition has a strong effect on the properties of rocks and is an essentially non-diffusive property in the context of large-scale mantle convection. Due to the non-diffusive nature and the origin of compositionally distinct regions in the Earth the boundaries between distinct regions can be nearly discontinuous. While there are different methods for tracking rock composition in numerical simulations of mantle convection, one must consider trade-offs between computational cost, accuracy or ease of implementation when choosing an appropriate method. Existing methods can be computationally expensive, cause over-/undershoots, smear sharp boundaries, or are not easily adapted to tracking multiple compositional fields. Here we present a Discontinuous Galerkin method with a bound preserving limiter (abbreviated as DG-BP) using a second order Runge-Kutta, strong stability-preserving time discretization method for the advection of non-diffusive fields. First, we show that the method is bound-preserving for a point-wise divergence free flow (e.g., a prescribed circular flow in a box). However, using standard adaptive mesh refinement (AMR) there is an over-shoot error (2%) because the cell average is not preserved during mesh coarsening. The effectiveness of the algorithm for convection-dominated flows is demonstrated using the falling box problem. We find that the DG-BP method maintains sharper compositional boundaries (3-5 elements) as compared to an artificial entropy-viscosity method (6-15 elements), although the over-/undershoot errors are similar. When used with AMR the DG-BP method results in fewer degrees of freedom due to smaller regions of mesh refinement in the neighborhood of the discontinuity. However, using Taylor-Hood elements and a uniform mesh there is an over-/undershoot error on the order of 0.0001%, but this error increases to 0.01-0.10% when using AMR. Therefore, for research problems in which a continuous field method is desired the DG-BP method can provide improved tracking of sharp compositional boundaries. For applications in which strict bound-preserving behavior is desired, use of an element that provides a divergence-free condition on the weak formulation (e.g., Raviart-Thomas) and an improved mesh coarsening scheme for the AMR are required.

LES-based generation of high-frequency fluctuation in wind turbulence obtained by meteorological model

NASA Astrophysics Data System (ADS)

Tamura, Tetsuro; Kawaguchi, Masaharu; Kawai, Hidenori; Tao, Tao

2017-11-01

The connection between a meso-scale model and a micro-scale large eddy simulation (LES) is significant to simulate the micro-scale meteorological problem such as strong convective events due to the typhoon or the tornado using LES. In these problems the mean velocity profiles and the mean wind directions change with time according to the movement of the typhoons or tornadoes. Although, a fine grid micro-scale LES could not be connected to a coarse grid meso-scale WRF directly. In LES when the grid is suddenly refined at the interface of nested grids which is normal to the mean advection the resolved shear stresses decrease due to the interpolation errors and the delay of the generation of smaller scale turbulence that can be resolved on the finer mesh. For the estimation of wind gust disaster the peak wind acting on buildings and structures has to be correctly predicted. In the case of meteorological model the velocity fluctuations have a tendency of diffusive variation without the high frequency component due to the numerically filtering effects. In order to predict the peak value of wind velocity with good accuracy, this paper proposes a LES-based method for generating the higher frequency components of velocity and temperature fields obtained by meteorological model.

A Critical Study of Agglomerated Multigrid Methods for Diffusion

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.

2011-01-01

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.

A Critical Study of Agglomerated Multigrid Methods for Diffusion

NASA Technical Reports Server (NTRS)

Thomas, James L.; Nishikawa, Hiroaki; Diskin, Boris

2009-01-01

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.

Super-nodal methods for space-time kinetics

NASA Astrophysics Data System (ADS)

Mertyurek, Ugur

The purpose of this research has been to develop an advanced Super-Nodal method to reduce the run time of 3-D core neutronics models, such as in the NESTLE reactor core simulator and FORMOSA nuclear fuel management optimization codes. Computational performance of the neutronics model is increased by reducing the number of spatial nodes used in the core modeling. However, as the number of spatial nodes decreases, the error in the solution increases. The Super-Nodal method reduces the error associated with the use of coarse nodes in the analyses by providing a new set of cross sections and ADFs (Assembly Discontinuity Factors) for the new nodalization. These so called homogenization parameters are obtained by employing consistent collapsing technique. During this research a new type of singularity, namely "fundamental mode singularity", is addressed in the ANM (Analytical Nodal Method) solution. The "Coordinate Shifting" approach is developed as a method to address this singularity. Also, the "Buckling Shifting" approach is developed as an alternative and more accurate method to address the zero buckling singularity, which is a more common and well known singularity problem in the ANM solution. In the course of addressing the treatment of these singularities, an effort was made to provide better and more robust results from the Super-Nodal method by developing several new methods for determining the transverse leakage and collapsed diffusion coefficient, which generally are the two main approximations in the ANM methodology. Unfortunately, the proposed new transverse leakage and diffusion coefficient approximations failed to provide a consistent improvement to the current methodology. However, improvement in the Super-Nodal solution is achieved by updating the homogenization parameters at several time points during a transient. The update is achieved by employing a refinement technique similar to pin-power reconstruction. A simple error analysis based on the relative residual in the 3-D few group diffusion equation at the fine mesh level is also introduced in this work.

Theory of wavelet-based coarse-graining hierarchies for molecular dynamics.

PubMed

Rinderspacher, Berend Christopher; Bardhan, Jaydeep P; Ismail, Ahmed E

2017-07-01

We present a multiresolution approach to compressing the degrees of freedom and potentials associated with molecular dynamics, such as the bond potentials. The approach suggests a systematic way to accelerate large-scale molecular simulations with more than two levels of coarse graining, particularly applications of polymeric materials. In particular, we derive explicit models for (arbitrarily large) linear (homo)polymers and iterative methods to compute large-scale wavelet decompositions from fragment solutions. This approach does not require explicit preparation of atomistic-to-coarse-grained mappings, but instead uses the theory of diffusion wavelets for graph Laplacians to develop system-specific mappings. Our methodology leads to a hierarchy of system-specific coarse-grained degrees of freedom that provides a conceptually clear and mathematically rigorous framework for modeling chemical systems at relevant model scales. The approach is capable of automatically generating as many coarse-grained model scales as necessary, that is, to go beyond the two scales in conventional coarse-grained strategies; furthermore, the wavelet-based coarse-grained models explicitly link time and length scales. Furthermore, a straightforward method for the reintroduction of omitted degrees of freedom is presented, which plays a major role in maintaining model fidelity in long-time simulations and in capturing emergent behaviors.

Wake orientation and its influence on the performance of diffusers with inlet distortion

NASA Astrophysics Data System (ADS)

Coffman, Jesse M.

Distortion at the inlet to diffusers is very common in internal flow applications. Inlet velocity distortion influences the pressure recovery and flow regimes of diffusers. This work introduced a centerline wake at the square inlet of a plane wall diffuser in two orthogonal orientations to investigate its influence on the diffuser performance. Two different wakes were generated. One was from a mesh strip which produced a velocity deficit with low turbulence intensity and two shear layers. The other wake generator was a D-shaped cylinder which produced a wake with high turbulence intensity and large length scales. These inlet conditions were generated for a diffuser with a diffusion angle of 3° and 6°. A pair of RANS simulations were used to investigate the influence of the orthogonal inlet orientations on the solution. The inlet conditions were taken from the inlet velocity field measured for the mesh strip. The flow development and exit conditions showed some similarities and some differences with the experimental results. The performance of a diffuser is typically measured through the static pressure recovery coefficient and the total pressure losses. The definition of these metrics commonly found in the literature were insufficient to discern differences between the wake orientations. New metrics were derived using the momentum flux profile parameter which related the static pressure recovery, the total pressure losses, and the velocity uniformity at the inlet and exit of the diffuser. These metrics revealed a trade-off between the total pressure losses and the uniformity of the velocity field.

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Summation rules for a fully nonlocal energy-based quasicontinuum method

NASA Astrophysics Data System (ADS)

Amelang, J. S.; Venturini, G. N.; Kochmann, D. M.

2015-09-01

The quasicontinuum (QC) method coarse-grains crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. A crucial cornerstone of all QC techniques, summation or quadrature rules efficiently approximate the thermodynamic quantities of interest. Here, we investigate summation rules for a fully nonlocal, energy-based QC method to approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of all atoms in the crystal lattice. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. We review traditional summation rules and discuss their strengths and weaknesses with a focus on energy approximation errors and spurious force artifacts. Moreover, we introduce summation rules which produce no residual or spurious force artifacts in centrosymmetric crystals in the large-element limit under arbitrary affine deformations in two dimensions (and marginal force artifacts in three dimensions), while allowing us to seamlessly bridge to full atomistics. Through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions, we compare the accuracy of the new scheme to various previous ones. Our results confirm that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors. Our numerical benchmark examples include the calculation of elastic constants from completely random QC meshes and the inhomogeneous deformation of aggressively coarse-grained crystals containing nano-voids. In the elastic regime, we directly compare QC results to those of full atomistics to assess global and local errors in complex QC simulations. Going beyond elasticity, we illustrate the performance of the energy-based QC method with the new second-order summation rule by the help of nanoindentation examples with automatic mesh adaptation. Overall, our findings provide guidelines for the selection of summation rules for the fully nonlocal energy-based QC method.

Time-marching multi-grid seismic tomography

NASA Astrophysics Data System (ADS)

Tong, P.; Yang, D.; Liu, Q.

2016-12-01

From the classic ray-based traveltime tomography to the state-of-the-art full waveform inversion, because of the nonlinearity of seismic inverse problems, a good starting model is essential for preventing the convergence of the objective function toward local minima. With a focus on building high-accuracy starting models, we propose the so-called time-marching multi-grid seismic tomography method in this study. The new seismic tomography scheme consists of a temporal time-marching approach and a spatial multi-grid strategy. We first divide the recording period of seismic data into a series of time windows. Sequentially, the subsurface properties in each time window are iteratively updated starting from the final model of the previous time window. There are at least two advantages of the time-marching approach: (1) the information included in the seismic data of previous time windows has been explored to build the starting models of later time windows; (2) seismic data of later time windows could provide extra information to refine the subsurface images. Within each time window, we use a multi-grid method to decompose the scale of the inverse problem. Specifically, the unknowns of the inverse problem are sampled on a coarse mesh to capture the macro-scale structure of the subsurface at the beginning. Because of the low dimensionality, it is much easier to reach the global minimum on a coarse mesh. After that, finer meshes are introduced to recover the micro-scale properties. That is to say, the subsurface model is iteratively updated on multi-grid in every time window. We expect that high-accuracy starting models should be generated for the second and later time windows. We will test this time-marching multi-grid method by using our newly developed eikonal-based traveltime tomography software package tomoQuake. Real application results in the 2016 Kumamoto earthquake (Mw 7.0) region in Japan will be demonstrated.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

Shrink-wrapped isosurface from cross sectional images

PubMed Central

Choi, Y. K.; Hahn, J. K.

2010-01-01

Summary This paper addresses a new surface reconstruction scheme for approximating the isosurface from a set of tomographic cross sectional images. Differently from the novel Marching Cubes (MC) algorithm, our method does not extract the iso-density surface (isosurface) directly from the voxel data but calculates the iso-density point (isopoint) first. After building a coarse initial mesh approximating the ideal isosurface by the cell-boundary representation, it metamorphoses the mesh into the final isosurface by a relaxation scheme, called shrink-wrapping process. Compared with the MC algorithm, our method is robust and does not make any cracks on surface. Furthermore, since it is possible to utilize lots of additional isopoints during the surface reconstruction process by extending the adjacency definition, theoretically the resulting surface can be better in quality than the MC algorithm. According to experiments, it is proved to be very robust and efficient for isosurface reconstruction from cross sectional images. PMID:20703361

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

Greve, L., E-mail: lars.greve@volkswagen.de; Medricky, M., E-mail: miloslav.medricky@volkswagen.de; Andres, M., E-mail: miloslav.medricky@volkswagen.de

A comprehensive strain hardening and fracture characterization of different grades of boron steel blanks has been performed, providing the foundation for the implementation into the modular material model (MMM) framework developed by Volkswagen Group Research for an explicit crash code. Due to the introduction of hardness-based interpolation rules for the characterized main grades, the hardening and fracture behavior is solely described by the underlying Vickers hardness. In other words, knowledge of the hardness distribution within a hot-formed component is enough to set up the newly developed computational model. The hardness distribution can be easily introduced via an experimentally measured hardnessmore » curve or via hardness mapping from a corresponding hot-forming simulation. For industrial application using rather coarse and computationally inexpensive shell element meshes, the user material model has been extended by a necking/post-necking model with reduced mesh-dependency as an additional failure mode. The present paper mainly addresses the necking/post-necking model.« less

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.

Network confinement and heterogeneity slows nanoparticle diffusion in polymer gels

NASA Astrophysics Data System (ADS)

Parrish, Emmabeth; Caporizzo, Matthew A.; Composto, Russell J.

2017-05-01

Nanoparticle (NP) diffusion was measured in polyacrylamide gels (PAGs) with a mesh size comparable to the NP size, 21 nm. The confinement ratio (CR), NP diameter/mesh size, increased from 0.4 to 3.8 by increasing crosslinker density and from 0.4 to 2.1 by adding acetone, which collapsed the PAGs. In all gels, NPs either became localized, moving less than 200 nm, diffused microns, or exhibited a combination of these behaviors, as measured by single particle tracking. Mean squared displacements (MSDs) of mobile NPs decreased as CR increased. In collapsed gels, the localized NP population increased and MSD of mobile NPs decreased compared to crosslinked PAGs. For all CRs, van Hove distributions exhibited non-Gaussian displacements, consistent with intermittent localization of NPs. The non-Gaussian parameter increased from a maximum of 1.5 for crosslinked PAG to 5 for collapsed PAG, consistent with greater network heterogeneity in these gels. Diffusion coefficients decreased exponentially as CR increased for crosslinked gels; however, in collapsed gels, the diffusion coefficients decreased more strongly, which was attributed to network heterogeneity. Collapsing the gel resulted in an increasingly tortuous pathway for NPs, slowing diffusion at a given CR. Understanding how gel structure affects NP mobility will allow the design and enhanced performance of gels that separate and release molecules in membranes and drug delivery platforms.

Diesel engine emissions and combustion predictions using advanced mixing models applicable to fuel sprays

NASA Astrophysics Data System (ADS)

Abani, Neerav; Reitz, Rolf D.

2010-09-01

An advanced mixing model was applied to study engine emissions and combustion with different injection strategies ranging from multiple injections, early injection and grouped-hole nozzle injection in light and heavy duty diesel engines. The model was implemented in the KIVA-CHEMKIN engine combustion code and simulations were conducted at different mesh resolutions. The model was compared with the standard KIVA spray model that uses the Lagrangian-Drop and Eulerian-Fluid (LDEF) approach, and a Gas Jet spray model that improves predictions of liquid sprays. A Vapor Particle Method (VPM) is introduced that accounts for sub-grid scale mixing of fuel vapor and more accurately and predicts the mixing of fuel-vapor over a range of mesh resolutions. The fuel vapor is transported as particles until a certain distance from nozzle is reached where the local jet half-width is adequately resolved by the local mesh scale. Within this distance the vapor particle is transported while releasing fuel vapor locally, as determined by a weighting factor. The VPM model more accurately predicts fuel-vapor penetrations for early cycle injections and flame lift-off lengths for late cycle injections. Engine combustion computations show that as compared to the standard KIVA and Gas Jet spray models, the VPM spray model improves predictions of in-cylinder pressure, heat released rate and engine emissions of NOx, CO and soot with coarse mesh resolutions. The VPM spray model is thus a good tool for efficiently investigating diesel engine combustion with practical mesh resolutions, thereby saving computer time.

Numerical modeling of pulsed laser-material interaction and of laser plume dynamics

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

Zhao, Qiang; Shi, Yina

2015-03-10

We have developed two-dimensional Arbitrary Lagrangian Eulerian (ALE) code which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. A new second order accurate diffusion solver has been implemented for the thermal conduction and radiation transport on distorted mesh. The results of numerical simulation of pulsed laser ablation are presented. The influences of different processes, such as time evolution of the surfacemore » temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas are examined. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.« less

Establishment of a Physical Model for Solute Diffusion in Hydrogel: Understanding the Diffusion of Proteins in Poly(sulfobetaine methacrylate) Hydrogel.

PubMed

Zhou, Yuhang; Li, Junjie; Zhang, Ying; Dong, Dianyu; Zhang, Ershuai; Ji, Feng; Qin, Zhihui; Yang, Jun; Yao, Fanglian

2017-02-02

Prediction of the diffusion coefficient of solute, especially bioactive molecules, in hydrogel is significant in the biomedical field. Considering the randomness of solute movement in a hydrogel network, a physical diffusion RMP-1 model based on obstruction theory was established in this study. The physical properties of the solute and the polymer chain and their interactions were introduced into this model. Furthermore, models RMP-2 and RMP-3 were established to understand and predict the diffusion behaviors of proteins in hydrogel. In addition, zwitterionic poly(sulfobetaine methacrylate) (PSBMA) hydrogels with wide range and fine adjustable mesh sizes were prepared and used as efficient experimental platforms for model validation. The Flory characteristic ratios, Flory-Huggins parameter, mesh size, and polymer chain radii of PSBMA hydrogels were determined. The diffusion coefficients of the proteins (bovine serum albumin, immunoglobulin G, and lysozyme) in PSBMA hydrogels were studied by the fluorescence recovery after photobleaching technique. The measured diffusion coefficients were compared with the predictions of obstruction models, and it was found that our model presented an excellent predictive ability. Furthermore, the assessment of our model revealed that protein diffusion in PSBMA hydrogel would be affected by the physical properties of the protein and the PSBMA network. It was also confirmed that the diffusion behaviors of protein in zwitterionic hydrogels can be adjusted by changing the cross-linking density of the hydrogel and the ionic strength of the swelling medium. Our model is expected to possess accurate predictive ability for the diffusion coefficient of solute in hydrogel, which will be widely used in the biomedical field.

Evaluation of an improved finite-element thermal stress calculation technique

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1982-01-01

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

A coarse-grained polarizable force field for the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate

NASA Astrophysics Data System (ADS)

Zeman, Johannes; Uhlig, Frank; Smiatek, Jens; Holm, Christian

2017-12-01

We present a coarse-grained polarizable molecular dynamics force field for the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIm][PF6]). For the treatment of electronic polarizability, we employ the Drude model. Our results show that the new explicitly polarizable force field reproduces important static and dynamic properties such as mass density, enthalpy of vaporization, diffusion coefficients, or electrical conductivity in the relevant temperature range. In situations where an explicit treatment of electronic polarizability might be crucial, we expect the force field to be an improvement over non-polarizable models, while still profiting from the reduction of computational cost due to the coarse-grained representation.

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

NASA Technical Reports Server (NTRS)

Movriplis, Dimitri J.

1998-01-01

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method

NASA Astrophysics Data System (ADS)

Fu, Shubin; Gao, Kai

2017-11-01

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

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 molecule-centered method for accelerating the calculation of hydrodynamic interactions in Brownian dynamics simulations containing many flexible biomolecules

PubMed Central

Elcock, Adrian H.

2013-01-01

Inclusion of hydrodynamic interactions (HIs) is essential in simulations of biological macromolecules that treat the solvent implicitly if the macromolecules are to exhibit correct translational and rotational diffusion. The present work describes the development and testing of a simple approach aimed at allowing more rapid computation of HIs in coarse-grained Brownian dynamics simulations of systems that contain large numbers of flexible macromolecules. The method combines a complete treatment of intramolecular HIs with an approximate treatment of the intermolecular HIs which assumes that the molecules are effectively spherical; all of the HIs are calculated at the Rotne-Prager-Yamakawa level of theory. When combined with Fixman’s Chebyshev polynomial method for calculating correlated random displacements, the proposed method provides an approach that is simple to program but sufficiently fast that it makes it computationally viable to include HIs in large-scale simulations. Test calculations performed on very coarse-grained models of the pyruvate dehydrogenase (PDH) E2 complex and on oligomers of ParM (ranging in size from 1 to 20 monomers) indicate that the method reproduces the translational diffusion behavior seen in more complete HI simulations surprisingly well; the method performs less well at capturing rotational diffusion but its discrepancies diminish with increasing size of the simulated assembly. Simulations of residue-level models of two tetrameric protein models demonstrate that the method also works well when more structurally detailed models are used in the simulations. Finally, test simulations of systems containing up to 1024 coarse-grained PDH molecules indicate that the proposed method rapidly becomes more efficient than the conventional BD approach in which correlated random displacements are obtained via a Cholesky decomposition of the complete diffusion tensor. PMID:23914146

Development of an efficient multigrid method for the NEM form of the multigroup neutron diffusion equation

NASA Astrophysics Data System (ADS)

Al-Chalabi, Rifat M. Khalil

1997-09-01

Development of an improvement to the computational efficiency of the existing nested iterative solution strategy of the Nodal Exapansion Method (NEM) nodal based neutron diffusion code NESTLE is presented. The improvement in the solution strategy is the result of developing a multilevel acceleration scheme that does not suffer from the numerical stalling associated with a number of iterative solution methods. The acceleration scheme is based on the multigrid method, which is specifically adapted for incorporation into the NEM nonlinear iterative strategy. This scheme optimizes the computational interplay between the spatial discretization and the NEM nonlinear iterative solution process through the use of the multigrid method. The combination of the NEM nodal method, calculation of the homogenized, neutron nodal balance coefficients (i.e. restriction operator), efficient underlying smoothing algorithm (power method of NESTLE), and the finer mesh reconstruction algorithm (i.e. prolongation operator), all operating on a sequence of coarser spatial nodes, constitutes the multilevel acceleration scheme employed in this research. Two implementations of the multigrid method into the NESTLE code were examined; the Imbedded NEM Strategy and the Imbedded CMFD Strategy. The main difference in implementation between the two methods is that in the Imbedded NEM Strategy, the NEM solution is required at every MG level. Numerical tests have shown that the Imbedded NEM Strategy suffers from divergence at coarse- grid levels, hence all the results for the different benchmarks presented here were obtained using the Imbedded CMFD Strategy. The novelties in the developed MG method are as follows: the formulation of the restriction and prolongation operators, and the selection of the relaxation method. The restriction operator utilizes a variation of the reactor physics, consistent homogenization technique. The prolongation operator is based upon a variant of the pin power reconstruction methodology. The relaxation method, which is the power method, utilizes a constant coefficient matrix within the NEM non-linear iterative strategy. The choice of the MG nesting within the nested iterative strategy enables the incorporation of other non-linear effects with no additional coding effort. In addition, if an eigenvalue problem is being solved, it remains an eigenvalue problem at all grid levels, simplifying coding implementation. The merit of the developed MG method was tested by incorporating it into the NESTLE iterative solver, and employing it to solve four different benchmark problems. In addition to the base cases, three different sensitivity studies are performed, examining the effects of number of MG levels, homogenized coupling coefficients correction (i.e. restriction operator), and fine-mesh reconstruction algorithm (i.e. prolongation operator). The multilevel acceleration scheme developed in this research provides the foundation for developing adaptive multilevel acceleration methods for steady-state and transient NEM nodal neutron diffusion equations. (Abstract shortened by UMI.)

Diffusion and surface alloying of gradient nanostructured metals

PubMed Central

Lu, Ke

2017-01-01

Gradient nanostructures (GNSs) have been optimized in recent years for desired performance. The diffusion behavior in GNS metals is crucial for understanding the diffusion mechanism and relative characteristics of different interfaces that provide fundamental understanding for advancing the traditional surface alloying processes. In this paper, atomic diffusion, reactive diffusion, and surface alloying processes are reviewed for various metals with a preformed GNS surface layer. We emphasize the promoted atomic diffusion and reactive diffusion in the GNS surface layer that are related to a higher interfacial energy state with respect to those in relaxed coarse-grained samples. Accordingly, different surface alloying processes, such as nitriding and chromizing, have been modified significantly, and some diffusion-related properties have been enhanced. Finally, the perspectives on current research in this field are discussed. PMID:28382244

Winner of the society for biomaterials student award in the Ph.D. category for the annual meeting of the society for biomaterials, april 11-14, 2018, Atlanta, GA: Development of a bimodal, in situ crosslinking method to achieve multifactor release from electrospun gelatin.

PubMed

Kishan, Alysha; Walker, Taneidra; Sears, Nick; Wilems, Thomas; Cosgriff-Hernandez, Elizabeth

2018-05-01

To better mimic native tissue microenvironments, current efforts have moved beyond single growth factor delivery to more complex multiple growth factor delivery with distinct release profiles. Electrospun gelatin, a widely investigated drug delivery vehicle, requires postprocessing crosslinking techniques that generate a mesh with uniform crosslinking density, limiting the ability to deliver multiple factors at different rates. Herein, we describe a method to independently control release of multiple factors from a single electrospun gelatin mesh. Two in situ crosslinking modalities, photocrosslinking of methacyrlated gelatin and reactive crosslinking of gelatin with a diisocyanate, are coelectrospun to generate distinct fiber populations with different crosslinking chemistry and density in a single mesh. The photocrosslinked gelatin-methacrylate resulted in a relatively rapid release of a model protein (48 ± 12% at day 1, 96 ± 3% at day 10) due to diffusion of embedded protein from the crosslinked fibers. The reactive crosslinking system displayed a more sustained release (7 ± 5% at day 1, 33 ± 2% at day 10) that was attributed to the conjugation of protein to gelatin with the diisocyanate, requiring degradation of gelatin prior to diffusion out of the fibers. Both modalities displayed tunable release profiles. Subsequent release studies of a cospun mesh with two different crosslinked fiber populations confirmed that the cospun mesh displayed multifactor release with independent release profiles. Overall, this bimodal, in situ crosslinking approach enables the delivery of multiple factors with distinct release kinetics from a single mesh and is expected to have broad utility in tissue engineering. © 2018 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 106A: 1155-1164, 2018. © 2018 Wiley Periodicals, Inc.

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.

Brownian dynamics simulations of lipid bilayer membrane with hydrodynamic interactions in LAMMPS

NASA Astrophysics Data System (ADS)

Fu, Szu-Pei; Young, Yuan-Nan; Peng, Zhangli; Yuan, Hongyan

2016-11-01

Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 6 nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane (such as gel-fluid-gas phase transitions of lipids, diffusion, and bending rigidity). In this work we implement such interaction potential in LAMMPS to simulate large-scale lipid systems such as vesicles and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for red blood cell (RBC) dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. We focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with varying enclosed volume; 2. RBC shape transitions with different enclosed volume. This work is funded by NSF under Grant DMS-1222550.

Brownian dynamics simulations of lipid bilayer membrane with hydrodynamic interactions in LAMMPS

NASA Astrophysics Data System (ADS)

Fu, Szu-Pei; Young, Yuan-Nan; Peng, Zhangli; Yuan, Hongyan

Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiency has been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 6 nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane (such as gel-fluid-gas phase transitions of lipids, diffusion, and bending rigidity). In this work we implement such interaction potential in LAMMPS to simulate large-scale lipid systems such as vesicles and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for red blood cell (RBC) dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. We focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with varying enclosed volume; 2. RBC shape transitions with different enclosed volume.

3D unstructured-mesh radiation transport codes

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

Morel, J.

1997-12-31

Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options:more » $$S{_}n$$ (discrete-ordinates), $$P{_}n$$ (spherical harmonics), and $$SP{_}n$$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $$S{_}n$$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.« less

Application of a multi-level grid method to transonic flow calculations

NASA Technical Reports Server (NTRS)

South, J. C., Jr.; Brandt, A.

1976-01-01

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.

Variable-free exploration of stochastic models: a gene regulatory network example.

PubMed

Erban, Radek; Frewen, Thomas A; Wang, Xiao; Elston, Timothy C; Coifman, Ronald; Nadler, Boaz; Kevrekidis, Ioannis G

2007-04-21

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [R. Erban et al., J. Chem. Phys. 124, 084106 (2006)] the authors assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e., effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [R. Coifman et al., Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005)] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free, coarse-grained computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.

Reaction-diffusion basis of retroviral infectivity

NASA Astrophysics Data System (ADS)

Sadiq, S. Kashif

2016-11-01

Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env3) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env3 molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env3 diffuses comparably to Gag-absent Env3. Initial immobility of Env3 is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env3 diffusion, and permits Env3 clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric

2017-04-01

Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For finite element methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary Lagrangian-Eulerian (ALE) formulation, the mesh can be adapted to increase the resolution in regions with strong shear or stratification. In such an application, consistency and conservativity must be strictly enforced. SLIM 3D, a discontinuous-Galerkin finite element model for shallow-water flows (www.climate.be/slim, e.g. Kärnä et al., 2013, Delandmeter et al., 2015), was designed to be strictly consistent and conservative in its discrete formulation. In this context, special care must be paid to the coupling of the external and internal modes of the model and the moving mesh algorithm. In this framework, the mesh can be adapted arbitrarily in the vertical direction. Two moving mesh algorithms were implemented: the first one computes an a-priori optimal mesh; the second one diffuses vertically the mesh (Burchard et al., 2004, Hofmeister et al., 2010). The criteria used to define the optimal mesh and the diffusion function are related to a suitable measure of shear and stratification. We will present in detail the design of the model and how the consistency and conservativity is obtained. Then we will apply it to both idealised benchmarks and the wind-forced thermocline oscillations in Lake Tanganyika (Naithani et al. 2002). References Tuomas Kärnä, Vincent Legat and Eric Deleersnijder. A baroclinic discontinuous Galerkin finite element model for coastal flows, Ocean Modelling, 61:1-20, 2013. Philippe Delandmeter, Stephen E Lewis, Jonathan Lambrechts, Eric Deleersnijder, Vincent Legat and Eric Wolanski. The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167:336-346, 2015. Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Modelling, 6:51-81, 2004. Richard Hofmeister, Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids for 3d numerical ocean models. Ocean Modelling, 33:70-86, 2010. Jaya Naithani, Eric Deleersnijder and Pierre-Denis Plisnier. Origin of intraseasonal variability in Lake Tanganyika. Geophysical Research Letters, 29(23), doi:10.1029/2002GL015843, 2002.

Solute diffusion through fibrotic tissue formed around protective cage system for implantable devices.

PubMed

Prihandana, Gunawan Setia; Ito, Hikaru; Tanimura, Kohei; Yagi, Hiroshi; Hori, Yuki; Soykan, Orhan; Sudo, Ryo; Miki, Norihisa

2015-08-01

This article presents the concept of an implantable cage system that can house and protect implanted biomedical sensing and therapeutic devices in the body. Cylinder-shaped cages made of porous polyvinyl alcohol (PVA) sheets with an 80-µm pore size and/or stainless steel meshes with 0.54-mm openings were implanted subcutaneously in the dorsal region of rats for 5 weeks. Analysis of the explanted cages showed the formation of fibrosis tissue around the cages. PVA cages had fibrotic tissue growing mostly along the outer surface of cages, while stainless steel cages had fibrotic tissue growing into the inside surface of the cage structure, due to the larger porosity of the stainless steel meshes. As the detection of target molecules with short time lags for biosensors and mass transport with low diffusion resistance into and out of certain therapeutic devices are critical for the success of such devices, we examined whether the fibrous tissue formed around the cages were permeable to molecules of our interest. For that purpose, bath diffusion and microfluidic chamber diffusion experiments using solutions containing the target molecules were performed. Diffusion of sodium, potassium and urea through the fibrosis tissue was confirmed, thus suggesting the potential of these cylindrical cages surrounded by fibrosis tissue to successfully encase implantable sensors and therapeutic apparatus. © 2014 Wiley Periodicals, Inc.

Influence of mesh density, cortical thickness and material properties on human rib fracture prediction.

PubMed

Li, Zuoping; Kindig, Matthew W; Subit, Damien; Kent, Richard W

2010-11-01

The purpose of this paper was to investigate the sensitivity of the structural responses and bone fractures of the ribs to mesh density, cortical thickness, and material properties so as to provide guidelines for the development of finite element (FE) thorax models used in impact biomechanics. Subject-specific FE models of the second, fourth, sixth and tenth ribs were developed to reproduce dynamic failure experiments. Sensitivity studies were then conducted to quantify the effects of variations in mesh density, cortical thickness, and material parameters on the model-predicted reaction force-displacement relationship, cortical strains, and bone fracture locations for all four ribs. Overall, it was demonstrated that rib FE models consisting of 2000-3000 trabecular hexahedral elements (weighted element length 2-3mm) and associated quadrilateral cortical shell elements with variable thickness more closely predicted the rib structural responses and bone fracture force-failure displacement relationships observed in the experiments (except the fracture locations), compared to models with constant cortical thickness. Further increases in mesh density increased computational cost but did not markedly improve model predictions. A ±30% change in the major material parameters of cortical bone lead to a -16.7 to 33.3% change in fracture displacement and -22.5 to +19.1% change in the fracture force. The results in this study suggest that human rib structural responses can be modeled in an accurate and computationally efficient way using (a) a coarse mesh of 2000-3000 solid elements, (b) cortical shells elements with variable thickness distribution and (c) a rate-dependent elastic-plastic material model. Copyright © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.

Edge delamination of composite laminates subject to combined tension and torsional loading

NASA Technical Reports Server (NTRS)

Hooper, Steven J.

1990-01-01

Delamination is a common failure mode of laminated composite materials. Edge delamination is important since it results in reduced stiffness and strength of the laminate. The tension/torsion load condition is of particular significance to the structural integrity of composite helicopter rotor systems. Material coupons can easily be tested under this type of loading in servo-hydraulic tension/torsion test stands using techniques very similar to those used for the Edge Delamination Tensile Test (EDT) delamination specimen. Edge delamination of specimens loaded in tension was successfully analyzed by several investigators using both classical laminate theory and quasi-three dimensional (Q3D) finite element techniques. The former analysis technique can be used to predict the total strain energy release rate, while the latter technique enables the calculation of the mixed-mode strain energy release rates. The Q3D analysis is very efficient since it produces a three-dimensional solution to a two-dimensional domain. A computer program was developed which generates PATRAN commands to generate the finite element model. PATRAN is a pre- and post-processor which is commonly used with a variety of finite element programs such as MCS/NASTRAN. The program creates a sufficiently dense mesh at the delamination crack tips to support a mixed-mode fracture mechanics analysis. The program creates a coarse mesh in those regions where the gradients in the stress field are low (away from the delamination regions). A transition mesh is defined between these regions. This program is capable of generating a mesh for an arbitrarily oriented matrix crack. This program significantly reduces the modeling time required to generate these finite element meshes, thus providing a realistic tool with which to investigate the tension torsion problem.

Drag Prediction for the NASA CRM Wing-Body-Tail Using CFL3D and OVERFLOW on an Overset Mesh

NASA Technical Reports Server (NTRS)

Sclafani, Anthony J.; DeHaan, Mark A.; Vassberg, John C.; Rumsey, Christopher L.; Pulliam, Thomas H.

2010-01-01

In response to the fourth AIAA CFD Drag Prediction Workshop (DPW-IV), the NASA Common Research Model (CRM) wing-body and wing-body-tail configurations are analyzed using the Reynolds-averaged Navier-Stokes (RANS) flow solvers CFL3D and OVERFLOW. Two families of structured, overset grids are built for DPW-IV. Grid Family 1 (GF1) consists of a coarse (7.2 million), medium (16.9 million), fine (56.5 million), and extra-fine (189.4 million) mesh. Grid Family 2 (GF2) is an extension of the first and includes a superfine (714.2 million) and an ultra-fine (2.4 billion) mesh. The medium grid anchors both families with an established build process for accurate cruise drag prediction studies. This base mesh is coarsened and enhanced to form a set of parametrically equivalent grids that increase in size by a factor of roughly 3.4 from one level to the next denser level. Both CFL3D and OVERFLOW are run on GF1 using a consistent numerical approach. Additional OVERFLOW runs are made to study effects of differencing scheme and turbulence model on GF1 and to obtain results for GF2. All CFD results are post-processed using Richardson extrapolation, and approximate grid-converged values of drag are compared. The medium grid is also used to compute a trimmed drag polar for both codes.

Application of closed-form solutions to a mesh point field in silicon solar cells

NASA Technical Reports Server (NTRS)

Lamorte, M. F.

1985-01-01

A computer simulation method is discussed that provides for equivalent simulation accuracy, but that exhibits significantly lower CPU running time per bias point compared to other techniques. This new method is applied to a mesh point field as is customary in numerical integration (NI) techniques. The assumption of a linear approximation for the dependent variable, which is typically used in the finite difference and finite element NI methods, is not required. Instead, the set of device transport equations is applied to, and the closed-form solutions obtained for, each mesh point. The mesh point field is generated so that the coefficients in the set of transport equations exhibit small changes between adjacent mesh points. Application of this method to high-efficiency silicon solar cells is described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing, carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been investigated using Fermi-Dirac statistics, and these results show that bandgap narrowing is more pronounced and that it is temperature-dependent in contrast to the results based on Boltzmann statistics.

Relationship between the anomalous diffusion and the fractal dimension of the environment

NASA Astrophysics Data System (ADS)

Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter

2018-03-01

In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

eBits: Compact stream of mesh refinements for remote visualization

DOE PAGES

Sati, Mukul; Lindstrom, Peter; Rossignac, Jarek

2016-05-12

Here, we focus on applications where a remote client needs to visualize or process a complex, manifold triangle mesh, M, but only in a relatively small, user controlled, Region of Interest (RoI) at a time. The client first downloads a coarse base mesh, pre-computed on the server via a series of simplification passes on M, one per Level of Detail (LoD), each pass identifying an independent set of triangles, collapsing them, and, for each collapse, storing, in a Vertex Expansion Record (VER), the information needed to reverse the collapse. On each client initiated RoI modification request, the server pushes tomore » the client a selected subset of these VERs, which, when decoded and applied to refine the mesh locally, ensure that the portion in the RoI is always at full resolution. The eBits approach proposed here offers state of the art compression ratios (using less than 2.5 bits per new full resolution RoI triangle when the RoI has more than 2000 vertices to transmit the connectivity for the selective refinements) and fine-grain control (allowing the user to adjust the RoI by small increments). The effectiveness of eBits results from several novel ideas and novel variations of previous solutions. We represent the VERs using persistent labels so that they can be applied in different orders within a given LoD. The server maintains a shadow copy of the client’s mesh. To avoid sending IDs identifying which vertices should be expanded, we either transmit, for each new vertex, a compact encoding of its death tag–the LoD at which it will be expanded if it lies in the Rol–or transmit vertex masks for the RoI and its neighboring vertices. We also propose a three-step simplification that reduces the overall transmission cost by increasing both the simplification effectiveness and the regularity of the valences in the resulting meshes.« less

eBits: Compact stream of mesh refinements for remote visualization

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

Sati, Mukul; Lindstrom, Peter; Rossignac, Jarek

2016-05-12

Here, we focus on applications where a remote client needs to visualize or process a complex, manifold triangle mesh, M, but only in a relatively small, user controlled, Region of Interest (RoI) at a time. The client first downloads a coarse base mesh, pre-computed on the server via a series of simplification passes on M, one per Level of Detail (LoD), each pass identifying an independent set of triangles, collapsing them, and, for each collapse, storing, in a Vertex Expansion Record (VER), the information needed to reverse the collapse. On each client initiated RoI modification request, the server pushes tomore » the client a selected subset of these VERs, which, when decoded and applied to refine the mesh locally, ensure that the portion in the RoI is always at full resolution. The eBits approach proposed here offers state of the art compression ratios (using less than 2.5 bits per new full resolution RoI triangle when the RoI has more than 2000 vertices to transmit the connectivity for the selective refinements) and fine-grain control (allowing the user to adjust the RoI by small increments). The effectiveness of eBits results from several novel ideas and novel variations of previous solutions. We represent the VERs using persistent labels so that they can be applied in different orders within a given LoD. The server maintains a shadow copy of the client’s mesh. To avoid sending IDs identifying which vertices should be expanded, we either transmit, for each new vertex, a compact encoding of its death tag ​–the LoD at which it will be expanded if it lies in the RoI–or transmit vertex masks for the RoI and its neighboring vertices. We also propose a three-step simplification that reduces the overall transmission cost by increasing both the simplification effectiveness and the regularity of the valences in the resulting meshes.« less

Hopping Diffusion of Nanoparticles Subjected to Topological Constraints

NASA Astrophysics Data System (ADS)

Cai, Li-Heng; Panyukov, Sergey; Rubinstein, Michael

2013-03-01

We describe a novel hopping mechanism for diffusion of large non-sticky nanoparticles subjected to topological constraints in polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size of unentangled polymer networks (tube diameter of entangled polymer liquids) are trapped by the network (entanglement) cages at time scales longer than the relaxation time of the network (entanglement) strand. At long time scales, however, these particles can move further by hopping between neighboring confinement cages. This hopping is controlled by fluctuations of surrounding confinement cages, which could be large enough to allow particles to slip through. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size slightly larger than the network mesh size (tube diameter). Very large particles in polymer solids will be permanently trapped by local network cages, whereas they can still move in polymer liquids by waiting for entanglement cages to rearrange on the relaxation time scale of the liquids. We would like to acknowledge the financial support of NSF CHE-0911588, DMR-0907515, DMR-1121107, DMR-1122483, and CBET-0609087, NIH R01HL077546 and P50HL107168, and Cystic Fibrosis Foundation under grant RUBIN09XX0.

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation. PMID:28239346

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers.

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation.

Noncontact diffuse correlation tomography of human breast tumor

PubMed Central

He, Lian; Lin, Yu; Huang, Chong; Irwin, Daniel; Szabunio, Margaret M.; Yu, Guoqiang

2015-01-01

Abstract. Our first step to adapt our recently developed noncontact diffuse correlation tomography (ncDCT) system for three-dimensional (3-D) imaging of blood flow distribution in human breast tumors is reported. A commercial 3-D camera was used to obtain breast surface geometry, which was then converted to a solid volume mesh. An ncDCT probe scanned over a region of interest on the mesh surface and the measured boundary data were combined with a finite element framework for 3-D image reconstruction of blood flow distribution. This technique was tested in computer simulations and in vivo human breasts with low-grade carcinoma. Results from computer simulations suggest that relatively high accuracy can be achieved when the entire tumor is within the sensitive region of diffuse light. Image reconstruction with a priori knowledge of the tumor volume and location can significantly improve the accuracy in recovery of tumor blood flow contrasts. In vivo imaging results from two breast carcinomas show higher average blood flow contrasts (5.9- and 10.9-fold) in the tumor regions compared to the surrounding tissues, which are comparable with previous findings using diffuse correlation spectroscopy. The ncDCT system has the potential to image blood flow distributions in soft and vulnerable tissues without distorting tissue hemodynamics. PMID:26259706

A Diffuse Interface Model with Immiscibility Preservation

PubMed Central

Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos

2013-01-01

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results. PMID:24058207

Coarse-grained molecular dynamics simulation of activated penetrant transport in glassy polymers.

PubMed

Zhang, Kai; Meng, Dong; Müller-Plathe, Florian; Kumar, Sanat K

2018-01-17

Membrane separations of gas mixtures strive to maximize the permeability of a desired species while keeping out undesired ones. Permeability vs. selectivity data from many polymer membranes for a given gas pair with diameters d A and d B are typically collected in a "Robeson plot"', and are bound from above by a line with a slope λ = (d B /d A ) 2 - 1. A microscopic understanding of this relationship, especially λ, is still missing. We perform molecular dynamics simulations of penetrant diffusion using three different coarse-grained polymer models over a wide range of penetrant sizes, temperatures, and monomer densities. The empirically relevant λ = (d B /d A ) 2 - 1 is only found for polymers that are either supercooled liquids with caged segmental dynamics or glasses and when the penetrant size is approximately half the Kuhn length of the chains, for which the penetrant diffusion is an activated process.

Mathematical model for the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.

1986-01-01

In a major technical breakthrough, a computer model for Bridgman-Stockbarger crystal growth was developed. The model includes melt convection, solute effects, thermal conduction in the ampule, melt, and crystal, and the determination of the curved moving crystal-melt interface. The key to the numerical method is the use of a nonuniform computational mesh which moves with the interface, so that the interface is a mesh surface. In addition, implicit methods are used for advection and diffusion of heat, concentration, and vorticity, for interface movement, and for internal gracity waves. This allows large time-steps without loss of stability or accuracy. Numerical results are presented for the interface shape, temperature distribution, and concentration distribution, in steady-state crystl growth. Solutions are presented for two test cases using water, with two different salts in solution. The two diffusivities differ by a factor of ten, and the concentrations differ by a factor of twenty.

Vectorization, threading, and cache-blocking considerations for hydrocodes on emerging architectures

DOE PAGES

Fung, J.; Aulwes, R. T.; Bement, M. T.; ...

2015-07-14

This work reports on considerations for improving computational performance in preparation for current and expected changes to computer architecture. The algorithms studied will include increasingly complex prototypes for radiation hydrodynamics codes, such as gradient routines and diffusion matrix assembly (e.g., in [1-6]). The meshes considered for the algorithms are structured or unstructured meshes. The considerations applied for performance improvements are meant to be general in terms of architecture (not specifically graphical processing unit (GPUs) or multi-core machines, for example) and include techniques for vectorization, threading, tiling, and cache blocking. Out of a survey of optimization techniques on applications such asmore » diffusion and hydrodynamics, we make general recommendations with a view toward making these techniques conceptually accessible to the applications code developer. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.« less

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Modeling of Turbulent Natural Convection in Enclosed Tall Cavities

NASA Astrophysics Data System (ADS)

Goloviznin, V. M.; Korotkin, I. A.; Finogenov, S. A.

2017-12-01

It was shown in our previous work (J. Appl. Mech. Tech. Phys 57 (7), 1159-1171 (2016)) that the eddy-resolving parameter-free CABARET scheme as applied to two-and three-dimensional de Vahl Davis benchmark tests (thermal convection in a square cavity) yields numerical results on coarse (20 × 20 and 20 × 20 × 20) grids that agree surprisingly well with experimental data and highly accurate computations for Rayleigh numbers of up to 1014. In the present paper, the sensitivity of this phenomenon to the cavity shape (varying from cubical to highly elongated) is analyzed. Box-shaped computational domains with aspect ratios of 1: 4, 1: 10, and 1: 28.6 are considered. The results produced by the CABARET scheme are compared with experimental data (aspect ratio of 1: 28.6), DNS results (aspect ratio of 1: 4), and an empirical formula (aspect ratio of 1: 10). In all the cases, the CABARET-based integral parameters of the cavity flow agree well with the other authors' results. Notably coarse grids with mesh refinement toward the walls are used in the CABARET calculations. It is shown that acceptable numerical accuracy on extremely coarse grids is achieved for an aspect ratio of up to 1: 10. For higher aspect ratios, the number of grid cells required for achieving prescribed accuracy grows significantly.

Factors controlling bark decomposition and its role in wood decomposition in five tropical tree species

PubMed Central

Dossa, Gbadamassi G. O.; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D.

2016-01-01

Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11–1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition. PMID:27698461

A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations

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

Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert

2015-11-15

The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence aremore » mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE PAGES

Svyatsky, Daniil; Lipnikov, Konstantin

2017-03-18

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

A Computational Icing Effects Study for a Three-Dimensional Wing: Comparison with Experimental Data and Investigation of Spanwise Variation

NASA Technical Reports Server (NTRS)

Thompson, D.; Mogili, P.; Chalasani, S.; Addy, H.; Choo, Y.

2004-01-01

Steady-state solutions of the Reynolds-averaged Navier-Stokes (RANS) equations were computed using the Colbalt flow solver for a constant-section, rectangular wing based on an extruded two-dimensional glaze ice shape. The one equation Spalart-Allmaras turbulence model was used. The results were compared with data obtained from a recent wind tunnel test. Computed results indicate that the steady RANS solutions do not accurately capture the recirculating region downstream of the ice accretion, even after a mesh refinement. The resulting predicted reattachment is farther downstream than indicated by the experimental data. Additionally, the solutions computed on a relatively coarse baseline mesh had detailed flow characteristics that were different from those computed on the refined mesh or the experimental data. Steady RANS solutions were also computed to investigate the effects of spanwise variation in the ice shape. The spanwise variation was obtained via a bleeding function that merged the ice shape with the clean wing using a sinusoidal spanwise variation. For these configurations, the results predicted for the extruded shape provided conservative estimates for the performance degradation of the wing. Additionally, the spanwise variation in the ice shape and the resulting differences in the flow fields did not significantly change the location of the primary reattachment.

Experimentally simulated global warming and nitrogen enrichment effects on microbial litter decomposers in a marsh.

PubMed

Flury, Sabine; Gessner, Mark O

2011-02-01

Atmospheric warming and increased nitrogen deposition can lead to changes of microbial communities with possible consequences for biogeochemical processes. We used an enclosure facility in a freshwater marsh to assess the effects on microbes associated with decomposing plant litter under conditions of simulated climate warming and pulsed nitrogen supply. Standard batches of litter were placed in coarse-mesh and fine-mesh bags and submerged in a series of heated, nitrogen-enriched, and control enclosures. They were retrieved later and analyzed for a range of microbial parameters. Fingerprinting profiles obtained by denaturing gradient gel electrophoresis (DGGE) indicated that simulated global warming induced a shift in bacterial community structure. In addition, warming reduced fungal biomass, whereas bacterial biomass was unaffected. The mesh size of the litter bags and sampling date also had an influence on bacterial community structure, with the apparent number of dominant genotypes increasing from spring to summer. Microbial respiration was unaffected by any treatment, and nitrogen enrichment had no clear effect on any of the microbial parameters considered. Overall, these results suggest that microbes associated with decomposing plant litter in nutrient-rich freshwater marshes are resistant to extra nitrogen supplies but are likely to respond to temperature increases projected for this century.

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

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

Svyatsky, Daniil; Lipnikov, Konstantin

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Recent developments in multidimensional transport methods for the APOLLO 2 lattice code

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

Zmijarevic, I.; Sanchez, R.

1995-12-31

A usual method of preparation of homogenized cross sections for reactor coarse-mesh calculations is based on two-dimensional multigroup transport treatment of an assembly together with an appropriate leakage model and reaction-rate-preserving homogenization technique. The actual generation of assembly spectrum codes based on collision probability methods is capable of treating complex geometries (i.e., irregular meshes of arbitrary shape), thus avoiding the modeling error that was introduced in codes with traditional tracking routines. The power and architecture of current computers allow the treatment of spatial domains comprising several mutually interacting assemblies using fine multigroup structure and retaining all geometric details of interest.more » Increasing safety requirements demand detailed two- and three-dimensional calculations for very heterogeneous problems such as control rod positioning, broken Pyrex rods, irregular compacting of mixed- oxide (MOX) pellets at an MOX-UO{sub 2} interface, and many others. An effort has been made to include accurate multi- dimensional transport methods in the APOLLO 2 lattice code. These include extension to three-dimensional axially symmetric geometries of the general-geometry collision probability module TDT and the development of new two- and three-dimensional characteristics methods for regular Cartesian meshes. In this paper we discuss the main features of recently developed multidimensional methods that are currently being tested.« less

Factors controlling bark decomposition and its role in wood decomposition in five tropical tree species.

PubMed

Dossa, Gbadamassi G O; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D

2016-10-04

Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11-1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition.

Accelerated life test of sputtering and anode deposit spalling in a small mercury ion thruster

NASA Technical Reports Server (NTRS)

Power, J. L.

1975-01-01

Tantalum and molybdenum sputtered from discharge chamber components during operation of a 5 centimeter diameter mercury ion thruster adhered much more strongly to coarsely grit blasted anode surfaces than to standard surfaces. Spalling of the sputtered coating did occur from a coarse screen anode surface but only in flakes less than a mesh unit long. The results were obtained in a 200 hour accelerated life test conducted at an elevated discharge potential of 64.6 volts. The test approximately reproduced the major sputter erosion and deposition effects that occur under normal operation but at approximately 75 times the normal rate. No discharge chamber component suffered sufficient erosion in the test to threaten its structural integrity or further serviceability. The test indicated that the use of tantalum-surfaced discharge chamber components in conjunction with a fine wire screen anode surface should cure the problems of sputter erosion and sputtered deposits spalling in long term operation of small mercury ion thrusters.

CFD Simulation of a Wing-In-Ground-Effect UAV

NASA Astrophysics Data System (ADS)

Lao, C. T.; Wong, E. T. T.

2018-05-01

This paper reports a numerical analysis on a wing section used for a Wing-In-Ground-Effect (WIG) unmanned aerial vehicle (UAV). The wing geometry was created by SolidWorks and the incompressible Reynolds-averaged Navier-Stokes (RANS) equations were solved with the Spalart–Allmaras turbulence model using CFD software ANSYS FLUENT. In FLUENT, the Spalart-Allmaras model has been implemented to use wall functions when the mesh resolution is not sufficiently fine. This might make it the best choice for relatively crude simulations on coarse meshes where accurate turbulent flow computations are not critical. The results show that the lift coefficient and lift-drag ratio derived excellent performance enhancement by ground effect. However, the moment coefficient shows inconsistency when the wing is operating in very low altitude - this is owing to the difficulty on the stability control of WIG vehicle. A drag polar estimation based on the analysis also indicated that the Oswald (or span) efficiency of the wing was improved by ground effect.

Laws, causation and dynamics at different levels.

PubMed

Butterfield, Jeremy

2012-02-06

I have two main aims. The first is general, and more philosophical (§2). The second is specific, and more closely related to physics (§§3 and 4). The first aim is to state my general views about laws and causation at different 'levels'. The main task is to understand how the higher levels sustain notions of law and causation that 'ride free' of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to give a framework for describing dynamics at different levels, emphasizing how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed 'micro' and 'macro', which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation.

Simplified Models for the Study of Postbuckled Hat-Stiffened Composite Panels

NASA Technical Reports Server (NTRS)

Vescovini, Riccardo; Davila, Carlos G.; Bisagni, Chiara

2012-01-01

The postbuckling response and failure of multistringer stiffened panels is analyzed using models with three levels of approximation. The first model uses a relatively coarse mesh to capture the global postbuckling response of a five-stringer panel. The second model can predict the nonlinear response as well as the debonding and crippling failure mechanisms in a single stringer compression specimen (SSCS). The third model consists of a simplified version of the SSCS that is designed to minimize the computational effort. The simplified model is well-suited to perform sensitivity analyses for studying the phenomena that lead to structural collapse. In particular, the simplified model is used to obtain a deeper understanding of the role played by geometric and material modeling parameters such as mesh size, inter-laminar strength, fracture toughness, and fracture mode mixity. Finally, a global/local damage analysis method is proposed in which a detailed local model is used to scan the global model to identify the locations that are most critical for damage tolerance.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Time scale of diffusion in molecular and cellular biology

NASA Astrophysics Data System (ADS)

Holcman, D.; Schuss, Z.

2014-05-01

Diffusion is the driver of critical biological processes in cellular and molecular biology. The diverse temporal scales of cellular function are determined by vastly diverse spatial scales in most biophysical processes. The latter are due, among others, to small binding sites inside or on the cell membrane or to narrow passages between large cellular compartments. The great disparity in scales is at the root of the difficulty in quantifying cell function from molecular dynamics and from simulations. The coarse-grained time scale of cellular function is determined from molecular diffusion by the mean first passage time of molecular Brownian motion to a small targets or through narrow passages. The narrow escape theory (NET) concerns this issue. The NET is ubiquitous in molecular and cellular biology and is manifested, among others, in chemical reactions, in the calculation of the effective diffusion coefficient of receptors diffusing on a neuronal cell membrane strewn with obstacles, in the quantification of the early steps of viral trafficking, in the regulation of diffusion between the mother and daughter cells during cell division, and many other cases. Brownian trajectories can represent the motion of a molecule, a protein, an ion in solution, a receptor in a cell or on its membrane, and many other biochemical processes. The small target can represent a binding site or an ionic channel, a hidden active site embedded in a complex protein structure, a receptor for a neurotransmitter on the membrane of a neuron, and so on. The mean time to attach to a receptor or activator determines diffusion fluxes that are key regulators of cell function. This review describes physical models of various subcellular microdomains, in which the NET coarse-grains the molecular scale to a higher cellular-level, thus clarifying the role of cell geometry in determining subcellular function.

Grain boundary and triple junction diffusion in nanocrystalline copper

NASA Astrophysics Data System (ADS)

Wegner, M.; Leuthold, J.; Peterlechner, M.; Song, X.; Divinski, S. V.; Wilde, G.

2014-09-01

Grain boundary and triple junction diffusion in nanocrystalline Cu samples with grain sizes, , of ˜35 and ˜44 nm produced by spark plasma sintering were investigated by the radiotracer method using the 63Ni isotope. The measured diffusivities, Deff, are comparable with those determined previously for Ni grain boundary diffusion in well-annealed, high purity, coarse grained, polycrystalline copper, substantiating the absence of a grain size effect on the kinetic properties of grain boundaries in a nanocrystalline material at grain sizes d ≥ 35 nm. Simultaneously, the analysis predicts that if triple junction diffusion of Ni in Cu is enhanced with respect to the corresponding grain boundary diffusion rate, it is still less than 500ṡDgb within the temperature interval from 420 K to 470 K.

Electrochemical properties of electrodes with different shapes and diffusion kinetic analysis of microbial fuel cells on ocean floor

NASA Astrophysics Data System (ADS)

Fu, Yubin; Liu, Jia; Su, Jia; Zhao, Zhongkai; Liu, Yang; Xu, Qian

2012-03-01

Microbial fuel cell (MFC) on the ocean floor is a kind of novel energy- harvesting device that can be developed to drive small instruments to work continuously. The shape of electrode has a great effect on the performance of the MFC. In this paper, several shapes of electrode and cell structure were designed, and their performance in MFC were compared in pairs: Mesh (cell-1) vs. flat plate (cell-2), branch (cell-3) vs. cylinder (cell-4), and forest (cell-5) vs. disk (cell-6) FC. Our results showed that the maximum power densities were 16.50, 14.20, 19.30, 15.00, 14.64, and 9.95 mWm-2 for cell-1, 2, 3, 4, 5 and 6 respectively. And the corresponding diffusion-limited currents were 7.16, 2.80, 18.86, 10.50, 18.00, and 6.900 mA. The mesh and branch anodes showed higher power densities and much higher diffusion-limited currents than the flat plate and the cylinder anodes respectively due to the low diffusion hindrance with the former anodes. The forest cathode improved by 47% of the power density and by 161% of diffusion-limited current than the disk cathode due to the former's extended solid/liquid/gas three-phase boundary. These results indicated that the shape of electrode is a major parameter that determining the diffusion-limited current of an MFC, and the differences in the electrode shape lead to the differences in cell performance. These results would be useful for MFC structure design in practical applications.

Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane

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

Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V., E-mail: aneimark@rutgers.edu

2016-01-07

Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. Themore » DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.« less

An Evaluation of Recently Developed RANS-Based Turbulence Models for Flow Over a Two-Dimensional Block Subjected to Different Mesh Structures and Grid Resolutions

NASA Astrophysics Data System (ADS)

Kardan, Farshid; Cheng, Wai-Chi; Baverel, Olivier; Porté-Agel, Fernando

2016-04-01

Understanding, analyzing and predicting meteorological phenomena related to urban planning and built environment are becoming more essential than ever to architectural and urban projects. Recently, various version of RANS models have been established but more validation cases are required to confirm their capability for wind flows. In the present study, the performance of recently developed RANS models, including the RNG k-ɛ , SST BSL k-ω and SST ⪆mma-Reθ , have been evaluated for the flow past a single block (which represent the idealized architecture scale). For validation purposes, the velocity streamlines and the vertical profiles of the mean velocities and variances were compared with published LES and wind tunnel experiment results. Furthermore, other additional CFD simulations were performed to analyze the impact of regular/irregular mesh structures and grid resolutions based on selected turbulence model in order to analyze the grid independency. Three different grid resolutions (coarse, medium and fine) of Nx × Ny × Nz = 320 × 80 × 320, 160 × 40 × 160 and 80 × 20 × 80 for the computational domain and nx × nz = 26 × 32, 13 × 16 and 6 × 8, which correspond to number of grid points on the block edges, were chosen and tested. It can be concluded that among all simulated RANS models, the SST ⪆mma-Reθ model performed best and agreed fairly well to the LES simulation and experimental results. It can also be concluded that the SST ⪆mma-Reθ model provides a very satisfactory results in terms of grid dependency in the fine and medium grid resolutions in both regular and irregular structure meshes. On the other hand, despite a very good performance of the RNG k-ɛ model in the fine resolution and in the regular structure grids, a disappointing performance of this model in the coarse and medium grid resolutions indicates that the RNG k-ɛ model is highly dependent on grid structure and grid resolution. These quantitative validations are essential to access the accuracy of RANS models for the simulation of flow in urban environment.

A hybrid multiview stereo algorithm for modeling urban scenes.

PubMed

Lafarge, Florent; Keriven, Renaud; Brédif, Mathieu; Vu, Hoang-Hiep

2013-01-01

We present an original multiview stereo reconstruction algorithm which allows the 3D-modeling of urban scenes as a combination of meshes and geometric primitives. The method provides a compact model while preserving details: Irregular elements such as statues and ornaments are described by meshes, whereas regular structures such as columns and walls are described by primitives (planes, spheres, cylinders, cones, and tori). We adopt a two-step strategy consisting first in segmenting the initial meshbased surface using a multilabel Markov Random Field-based model and second in sampling primitive and mesh components simultaneously on the obtained partition by a Jump-Diffusion process. The quality of a reconstruction is measured by a multi-object energy model which takes into account both photo-consistency and semantic considerations (i.e., geometry and shape layout). The segmentation and sampling steps are embedded into an iterative refinement procedure which provides an increasingly accurate hybrid representation. Experimental results on complex urban structures and large scenes are presented and compared to state-of-the-art multiview stereo meshing algorithms.

Non-Gaussian diffusion in static disordered media

NASA Astrophysics Data System (ADS)

Luo, Liang; Yi, Ming

2018-04-01

Non-Gaussian diffusion is commonly considered as a result of fluctuating diffusivity, which is correlated in time or in space or both. In this work, we investigate the non-Gaussian diffusion in static disordered media via a quenched trap model, where the diffusivity is spatially correlated. Several unique effects due to quenched disorder are reported. We analytically estimate the diffusion coefficient Ddis and its fluctuation over samples of finite size. We show a mechanism of population splitting in the non-Gaussian diffusion. It results in a sharp peak in the distribution of displacement P (x ,t ) around x =0 , that has frequently been observed in experiments. We examine the fidelity of the coarse-grained diffusion map, which is reconstructed from particle trajectories. Finally, we propose a procedure to estimate the correlation length in static disordered environments, where the information stored in the sample-to-sample fluctuation has been utilized.

Complex Geometric Models of Diffusion and Relaxation in Healthy and Damaged White Matter

PubMed Central

Farrell, Jonathan A.D.; Smith, Seth A.; Reich, Daniel S.; Calabresi, Peter A.; van Zijl, Peter C.M.

2010-01-01

Which aspects of tissue microstructure affect diffusion weighted MRI signals? Prior models, many of which use Monte-Carlo simulations, have focused on relatively simple models of the cellular microenvironment and have not considered important anatomic details. With the advent of higher-order analysis models for diffusion imaging, such as high-angular-resolution diffusion imaging (HARDI), more realistic models are necessary. This paper presents and evaluates the reproducibility of simulations of diffusion in complex geometries. Our framework is quantitative, does not require specialized hardware, is easily implemented with little programming experience, and is freely available as open-source software. Models may include compartments with different diffusivities, permeabilities, and T2 time constants using both parametric (e.g., spheres and cylinders) and arbitrary (e.g., mesh-based) geometries. Three-dimensional diffusion displacement-probability functions are mapped with high reproducibility, and thus can be readily used to assess reproducibility of diffusion-derived contrasts. PMID:19739233

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS

NASA Astrophysics Data System (ADS)

Fu, S.-P.; Peng, Z.; Yuan, H.; Kfoury, R.; Young, Y.-N.

2017-01-01

Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4 ∼ 6 nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane, such as gel-fluid-gas phase transitions of lipids, diffusion, and bending rigidity Yuan et al. (2010). In this work we implement such an interaction potential in LAMMPS to simulate large-scale lipid systems such as a giant unilamellar vesicle (GUV) and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for RBC dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. To demonstrate that the proposed methods do capture the observed dynamics of vesicles and RBCs, we focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with enclosed volume; 2. RBC shape transitions with different enclosed volume. Finally utilizing the parallel computing capability in LAMMPS, we provide some timing results for parallel coarse-grained simulations to illustrate that it is possible to use LAMMPS to simulate large-scale realistic complex biological membranes for more than 1 ms.

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches

PubMed Central

Taylor, P. R.; Baker, R. E.; Simpson, M. J.; Yates, C. A.

2016-01-01

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are ‘compartment-based’: the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise. PMID:27383421

Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

NASA Technical Reports Server (NTRS)

Jameson, Antony

1994-01-01

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

Characterization of a Dynamic String Method for the Construction of Transition Pathways in Molecular Reactions

PubMed Central

Johnson, Margaret E.; Hummer, Gerhard

2012-01-01

We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion, and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method. PMID:22616575

Effects of mesh style and grid convergence on particle deposition in bifurcating airway models with comparisons to experimental data.

PubMed

Longest, P Worth; Vinchurkar, Samir

2007-04-01

A number of research studies have employed a wide variety of mesh styles and levels of grid convergence to assess velocity fields and particle deposition patterns in models of branching biological systems. Generating structured meshes based on hexahedral elements requires significant time and effort; however, these meshes are often associated with high quality solutions. Unstructured meshes that employ tetrahedral elements can be constructed much faster but may increase levels of numerical diffusion, especially in tubular flow systems with a primary flow direction. The objective of this study is to better establish the effects of mesh generation techniques and grid convergence on velocity fields and particle deposition patterns in bifurcating respiratory models. In order to achieve this objective, four widely used mesh styles including structured hexahedral, unstructured tetrahedral, flow adaptive tetrahedral, and hybrid grids have been considered for two respiratory airway configurations. Initial particle conditions tested are based on the inlet velocity profile or the local inlet mass flow rate. Accuracy of the simulations has been assessed by comparisons to experimental in vitro data available in the literature for the steady-state velocity field in a single bifurcation model as well as the local particle deposition fraction in a double bifurcation model. Quantitative grid convergence was assessed based on a grid convergence index (GCI), which accounts for the degree of grid refinement. The hexahedral mesh was observed to have GCI values that were an order of magnitude below the unstructured tetrahedral mesh values for all resolutions considered. Moreover, the hexahedral mesh style provided GCI values of approximately 1% and reduced run times by a factor of 3. Based on comparisons to empirical data, it was shown that inlet particle seedings should be consistent with the local inlet mass flow rate. Furthermore, the mesh style was found to have an observable effect on cumulative particle depositions with the hexahedral solution most closely matching empirical results. Future studies are needed to assess other mesh generation options including various forms of the hybrid configuration and unstructured hexahedral meshes.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

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

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems: DIFFUSION-DRIVEN HYDRATE GROWTH IN SANDS

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

Nole, Michael; Daigle, Hugh; Cook, Ann E.

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1 to 20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two- dimensional and basin-scalemore » three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. As a result, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial.« less

Linking basin-scale and pore-scale gas hydrate distribution patterns in diffusion-dominated marine hydrate systems: DIFFUSION-DRIVEN HYDRATE GROWTH IN SANDS

DOE PAGES

Nole, Michael; Daigle, Hugh; Cook, Ann E.; ...

2017-02-01

The goal of this study is to computationally determine the potential distribution patterns of diffusion-driven methane hydrate accumulations in coarse-grained marine sediments. Diffusion of dissolved methane in marine gas hydrate systems has been proposed as a potential transport mechanism through which large concentrations of hydrate can preferentially accumulate in coarse-grained sediments over geologic time. Using one-dimensional compositional reservoir simulations, we examine hydrate distribution patterns at the scale of individual sand layers (1 to 20 m thick) that are deposited between microbially active fine-grained material buried through the gas hydrate stability zone (GHSZ). We then extrapolate to two- dimensional and basin-scalemore » three-dimensional simulations, where we model dipping sands and multilayered systems. We find that properties of a sand layer including pore size distribution, layer thickness, dip, and proximity to other layers in multilayered systems all exert control on diffusive methane fluxes toward and within a sand, which in turn impact the distribution of hydrate throughout a sand unit. In all of these simulations, we incorporate data on physical properties and sand layer geometries from the Terrebonne Basin gas hydrate system in the Gulf of Mexico. We demonstrate that diffusion can generate high hydrate saturations (upward of 90%) at the edges of thin sands at shallow depths within the GHSZ, but that it is ineffective at producing high hydrate saturations throughout thick (greater than 10 m) sands buried deep within the GHSZ. As a result, we find that hydrate in fine-grained material can preserve high hydrate saturations in nearby thin sands with burial.« less

Accurate reconstruction of 3D cardiac geometry from coarsely-sliced MRI.

PubMed

Ringenberg, Jordan; Deo, Makarand; Devabhaktuni, Vijay; Berenfeld, Omer; Snyder, Brett; Boyers, Pamela; Gold, Jeffrey

2014-02-01

We present a comprehensive validation analysis to assess the geometric impact of using coarsely-sliced short-axis images to reconstruct patient-specific cardiac geometry. The methods utilize high-resolution diffusion tensor MRI (DTMRI) datasets as reference geometries from which synthesized coarsely-sliced datasets simulating in vivo MRI were produced. 3D models are reconstructed from the coarse data using variational implicit surfaces through a commonly used modeling tool, CardioViz3D. The resulting geometries were then compared to the reference DTMRI models from which they were derived to analyze how well the synthesized geometries approximate the reference anatomy. Averaged over seven hearts, 95% spatial overlap, less than 3% volume variability, and normal-to-surface distance of 0.32 mm was observed between the synthesized myocardial geometries reconstructed from 8 mm sliced images and the reference data. The results provide strong supportive evidence to validate the hypothesis that coarsely-sliced MRI may be used to accurately reconstruct geometric ventricular models. Furthermore, the use of DTMRI for validation of in vivo MRI presents a novel benchmark procedure for studies which aim to substantiate their modeling and simulation methods using coarsely-sliced cardiac data. In addition, the paper outlines a suggested original procedure for deriving image-based ventricular models using the CardioViz3D software. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Patch-based Adaptive Mesh Refinement for Multimaterial Hydrodynamics

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

Lomov, I; Pember, R; Greenough, J

2005-10-18

We present a patch-based direct Eulerian adaptive mesh refinement (AMR) algorithm for modeling real equation-of-state, multimaterial compressible flow with strength. Our approach to AMR uses a hierarchical, structured grid approach first developed by (Berger and Oliger 1984), (Berger and Oliger 1984). The grid structure is dynamic in time and is composed of nested uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which the coarse grids are advanced, then the fine grids are advanced multiple steps to reach the same time, and finally the coarse and fine grids are synchronized tomore » remove conservation errors during the separate advances. The methodology presented here is based on a single grid algorithm developed for multimaterial gas dynamics by (Colella et al. 1993), refined by(Greenough et al. 1995), and extended to the solution of solid mechanics problems with significant strength by (Lomov and Rubin 2003). The single grid algorithm uses a second-order Godunov scheme with an approximate single fluid Riemann solver and a volume-of-fluid treatment of material interfaces. The method also uses a non-conservative treatment of the deformation tensor and an acoustic approximation for shear waves in the Riemann solver. This departure from a strict application of the higher-order Godunov methodology to the equation of solid mechanics is justified due to the fact that highly nonlinear behavior of shear stresses is rare. This algorithm is implemented in two codes, Geodyn and Raptor, the latter of which is a coupled rad-hydro code. The present discussion will be solely concerned with hydrodynamics modeling. Results from a number of simulations for flows with and without strength will be presented.« less

Employing a Modified Diffuser Momentum Model to Simulate Ventilation of the Orion CEV

NASA Technical Reports Server (NTRS)

Straus, John; Lewis, John F.

2011-01-01

The Ansys CFX CFD modeling tool was used to support the design efforts of the ventilation system for the Orion CEV. CFD modeling was used to establish the flow field within the cabin for several supply configurations. A mesh and turbulence model sensitivity study was performed before the design studies. Results were post-processed for comparison with performance requirements. Most configurations employed straight vaned diffusers to direct and throw the flow. To manage the size of the models, the diffuser vanes were not resolved. Instead, a momentum model was employed to account for the effect of the diffusers. The momentum model was tested against a separate, vane-resolved side study. Results are presented for a single diffuser configuration for a low supply flow case.

Three distinct modes in a surface micro-discharge in atmospheric pressure He + N{sub 2} mixtures

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

Li, Dong; Liu, Dingxin, E-mail: liudingxin@mail.xjtu.edu.cn; He, Tongtong

2015-12-15

A surface micro-discharge in atmospheric pressure He + N{sub 2} mixtures is studied in this paper with an emphasis on the discharge modes. With the N{sub 2} admixture increasing from 0.1% to 20%, the discharge evolves from a spatially diffuse mode to a filamentary mode during positive half-cycles of the applied voltage. However during the negative half-cycles, an additional patterned mode emerges between the diffuse and the filamentary modes, which has not been reported before to exist in surface micro-discharges. In the diffuse and patterned modes, the plasmas cover almost the entirety of the mesh area during one cycle after plasma ignitionmore » in all mesh elements, and the discharge power increases linearly with the applied voltage. In contrast, plasma coverage of the mesh area is only partial in the filamentary mode and the plasma is more unstable with the discharge power increasing exponentially with the applied voltage. As the surface micro-discharge evolves through the three modes, the density of excited species changes significantly, for instance, the density of N{sub 2}{sup +}(B) drops by ∼20-fold from [N{sub 2}] = 0.2% to 20%. The N{sub 2}{sup +}(B) is predicted to be generated mainly through successive processes of Penning ionization by helium metastables and electron-impact excitation of N{sub 2}{sup +}(X), the latter is most responsible for the density decrease of N{sub 2}{sup +}(B) because much more N{sub 2}{sup +}(X) is converted to N{sub 4}{sup +}(X) as the increase of N{sub 2} fraction. Also, the electron density and electron temperature decrease with the discharge mode transition.« less

Fast segmentation and high-quality three-dimensional volume mesh creation from medical images for diffuse optical tomography

NASA Astrophysics Data System (ADS)

Jermyn, Michael; Ghadyani, Hamid; Mastanduno, Michael A.; Turner, Wes; Davis, Scott C.; Dehghani, Hamid; Pogue, Brian W.

2013-08-01

Multimodal approaches that combine near-infrared (NIR) and conventional imaging modalities have been shown to improve optical parameter estimation dramatically and thus represent a prevailing trend in NIR imaging. These approaches typically involve applying anatomical templates from magnetic resonance imaging/computed tomography/ultrasound images to guide the recovery of optical parameters. However, merging these data sets using current technology requires multiple software packages, substantial expertise, significant time-commitment, and often results in unacceptably poor mesh quality for optical image reconstruction, a reality that represents a significant roadblock for translational research of multimodal NIR imaging. This work addresses these challenges directly by introducing automated digital imaging and communications in medicine image stack segmentation and a new one-click three-dimensional mesh generator optimized for multimodal NIR imaging, and combining these capabilities into a single software package (available for free download) with a streamlined workflow. Image processing time and mesh quality benchmarks were examined for four common multimodal NIR use-cases (breast, brain, pancreas, and small animal) and were compared to a commercial image processing package. Applying these tools resulted in a fivefold decrease in image processing time and 62% improvement in minimum mesh quality, in the absence of extra mesh postprocessing. These capabilities represent a significant step toward enabling translational multimodal NIR research for both expert and nonexpert users in an open-source platform.

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 flow scarcity on leaf-litter processing under oceanic climate conditions in calcareous streams.

PubMed

Martínez, Aingeru; Pérez, Javier; Molinero, Jon; Sagarduy, Mikel; Pozo, Jesús

2015-01-15

Although temporary streams represent a high proportion of the total number and length of running waters, historically the study of intermittent streams has received less attention than that of perennial ones. The goal of the present study was to assess the effects of flow cessation on litter decomposition in calcareous streams under oceanic climate conditions. For this, leaf litter of alder was incubated in four streams (S1, S2, S3 and S4) with different flow regimes (S3 and S4 with zero-flow periods) from northern Spain. To distinguish the relative importance and contribution of decomposers and detritivores, fine- and coarse-mesh litter bags were used. We determined processing rates, leaf-C, -N and -P concentrations, invertebrate colonization in coarse bags and benthic invertebrates. Decomposition rates in fine bags were similar among streams. In coarse bags, only one of the intermittent streams, S4, showed a lower rate than that in the other ones as a consequence of lower invertebrate colonization. The material incubated in fine bags presented higher leaf-N and -P concentrations than those in the coarse ones, except in S4, pointing out that the decomposition in this stream was driven mainly by microorganisms. Benthic macroinvertebrate and shredder density and biomass were lower in intermittent streams than those in perennial ones. However, the bags in S3 presented a greater amount of total macroinvertebrates and shredders comparing with the benthos. The most suitable explanation is that the fauna find a food substrate in bags less affected by calcite precipitation, which is common in the streambed at this site. Decomposition rate in coarse bags was positively related to associated shredder biomass. Thus, droughts in streams under oceanic climate conditions affect mainly the macroinvertebrate detritivore activity, although macroinvertebrates may show distinct behavior imposed by the physicochemical properties of water, mainly travertine precipitation, which can override the flow intermittence effects. Copyright © 2014. Published by Elsevier B.V.

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

NASA Astrophysics Data System (ADS)

Philip, B.; Wang, Z.; Berrill, M. A.; Birke, M.; Pernice, M.

2014-04-01

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Spectral Upscaling for Graph Laplacian Problems with Application to Reservoir Simulation

DOE PAGES

Barker, Andrew T.; Lee, Chak S.; Vassilevski, Panayot S.

2017-10-26

Here, we consider coarsening procedures for graph Laplacian problems written in a mixed saddle-point form. In that form, in addition to the original (vertex) degrees of freedom (dofs), we also have edge degrees of freedom. We extend previously developed aggregation-based coarsening procedures applied to both sets of dofs to now allow more than one coarse vertex dof per aggregate. Those dofs are selected as certain eigenvectors of local graph Laplacians associated with each aggregate. Additionally, we coarsen the edge dofs by using traces of the discrete gradients of the already constructed coarse vertex dofs. These traces are defined on themore » interface edges that connect any two adjacent aggregates. The overall procedure is a modification of the spectral upscaling procedure developed in for the mixed finite element discretization of diffusion type PDEs which has the important property of maintaining inf-sup stability on coarse levels and having provable approximation properties. We consider applications to partitioning a general graph and to a finite volume discretization interpreted as a graph Laplacian, developing consistent and accurate coarse-scale models of a fine-scale problem.« less

Adaptive Implicit Non-Equilibrium Radiation Diffusion

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

Philip, Bobby; Wang, Zhen; Berrill, Mark A

2013-01-01

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Effects of termite activities on coarse woody debris decomposition in an intact lowland mixed dipterocarp forest of Brunei Darussalam

NASA Astrophysics Data System (ADS)

Lee, S.; Kim, S.; Roh, Y.; Son, Y.

2016-12-01

Tropical forests play a critical role in mitigating climate change, because they sequester carbon more than any other terrestrial ecosystems. In addition, coarse woody debris is one of the main carbon storages, accounting for 10 - 40% of the tropical forest carbon. Carbon in coarse woody debris is released by various activities of organisms, and particularly termite's feeding activities are known to be a main process in tropical forests. Therefore, investigating the effects of termite activities on coarse woody debris decomposition is important to understanding carbon cycles of tropical forests. This study was conducted in an intact lowland mixed dipterocarp forest (MDF) of Brunei Darussalam, and three main MDF tree species (Dillenia beccariana, Macaranga bancana, and Elateriospermum tapos) were selected. Coarse woody debris samples of both 10 cm diameter and length were prepared, and half of samples were covered twice with nylon net (mesh size 1.5 mm × 1.5 mm) to prevent termite's approach. Three permanent plots were installed in January, 2015 and 36 samples per plot (3 species × 2 treatments × 6 replicates) were placed at the soil surface. Weights of each sample were recorded at initial time, and weighed again at an interval of 6 months until July, 2016. On average, uncovered and covered samples lost 32.4 % and 20.0 % of their initial weights, respectively. Weight loss percentage was highest in uncovered samples of M. bancana (43.8 %), and lowest in covered samples of E. tapos (14.7 %). Two-way ANOVA showed that the effects of the tree species and the termite exclusion treatment on coarse woody debris decomposition were statistically significant (P < 0.001). Also the interaction between the tree species and the termite exclusion treatment was significant (P < 0.001). The results reveal that termite activities promote the coarse woody debris decomposition and they influence differently along the tree species. In addition, as a result of repeated ANOVA, weight loss rates were accelerated over time and this time-acceleration effects were significantly different among the tree species (P < 0.05) and the termite exclusion treatment (P< 0.001). * Supported by research grants from the National Research Foundation of Korea (R1D1A1A01) * Supported by BK21Plus Eco-Leader Education Center.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

NASA Astrophysics Data System (ADS)

Grain, Julien; Vennin, Vincent

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ``slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Effect of temperature and grain size on the dominant diffusion process for superplastic flow in an AZ61 magnesium alloy

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

Watanabe, H.; Mukai, T.; Kohzu, M.

1999-10-26

The effect of temperature and grain size on superplastic flow was investigated using a relatively coarse-grained ({approximately}20 {micro}m) Mg-Al-Zn alloy for the inclusive understanding of the dominant diffusion process. Tensile tests revealed that the strain rate was inversely proportional to the square of the grain size and to the second power of stress. The activation energy was close to that for grain boundary diffusion at 523--573 K, and was close to that for lattice diffusion at 598--673 K. From the analysis of the stress exponent, the grain size exponent and activation energy, it was suggested that the dominant diffusion processmore » was influenced by temperature and grain size. It was demonstrated that the notion of effective diffusivity explained the experimental results.« less

OFF-GAS ANALYSIS RESULTS AND FINE PORE RETROFIT INFORMATION FOR GLASTONBURY, CONNECTICUT

EPA Science Inventory

In the summer of 1984, the Glastonbury, Connecticut Water Pollution Control Plant underwent a retrofit from a spiral roll coarse bubble to a spiral roll fine pore aeration system. Only diffuser replacement was performed in the aeration tanks. From November 1985 through Septembe...

CASE HISTORY OF FINE PORE DIFFUSER RETROFIT AT RIDGEWOOD, NEW JERSEY

EPA Science Inventory

In April 1983, the Ridgewood, New Jersey Wastewater Treatment Plant underwent a retrofit from a coarse bubble to a fine pore aeration system. Also, process modification from contact stabilization to tapered aeration occurred. This report presents a case history of plant and aer...

Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.

PubMed

Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong

2016-05-01

In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Summary of results of January climate simulations with the GISS coarse-mesh model

NASA Technical Reports Server (NTRS)

Spar, J.; Cohen, C.; Wu, P.

1981-01-01

The large scale climates generated by extended runs of the model are relatively independent of the initial atmospheric conditions, if the first few months of each simulation are discarded. The perpetual January simulations with a specified SST field produced excessive snow accumulation over the continents of the Northern Hemisphere. Mass exchanges between the cold (warm) continents and the warm (cold) adjacent oceans produced significant surface pressure changes over the oceans as well as over the land. The effect of terrain and terrain elevation on the amount of precipitation was examined. The evaporation of continental moisture was calculated to cause large increases in precipitation over the continents.

The influence of initial and surface boundary conditions on a model-generated January climatology

NASA Technical Reports Server (NTRS)

Wu, K. F.; Spar, J.

1981-01-01

The influence on a model-generated January climate of various surface boundary conditions, as well as initial conditions, was studied by using the GISS coarse-mesh climate model. Four experiments - two with water planets, one with flat continents, and one with mountains - were used to investigate the effects of initial conditions, and the thermal and dynamical effects of the surface on the model generated-climate. However, climatological mean zonal-symmetric sea surface temperature is used in all four runs over the model oceans. Moreover, zero ground wetness and uniform ground albedo except for snow are used in the last experiments.

Some effects of topography, soil moisture, and sea-surface temperature on continental precipitation as computed with the GISS coarse mesh climate model

NASA Technical Reports Server (NTRS)

Spar, J.; Cohen, C.

1981-01-01

The effects of terrain elevation, soil moisture, and zonal variations in sea/surface temperature on the mean daily precipitation rates over Australia, Africa, and South America in January were evaluated. It is suggested that evaporation of soil moisture may either increase or decrease the model generated precipitation, depending on the surface albedo. It was found that a flat, dry continent model best simulates the January rainfall over Australia and South America, while over Africa the simulation is improved by the inclusion of surface physics, specifically soil moisture and albedo variations.

MOC Efficiency Improvements Using a Jacobi Inscatter Approximation

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

Stimpson, Shane; Collins, Benjamin; Kochunas, Brendan

2016-08-31

In recent weeks, attention has been given to resolving the convergence issues encountered with TCP 0 by trying a Jacobi (J) inscatter approach when group sweeping, where the inscatter source is constructed using the previous iteration flux. This is in contrast to a Gauss-Seidel (GS) approach, which has been the default to-date, where the scattering source uses the most up-to-date flux values. The former is consistent with CASMO, which has no issues with TCP 0 convergence. Testing this out on a variety of problems has demonstrated that the Jacobi approach does indeed provide substantially more stability, though can take moremore » outer iterations to converge. While this is not surprising, there are improvements that can be made to the MOC sweeper to capitalize on the Jacobi approximation and provide substantial speedup. For example, the loop over groups, which has traditionally been the outermost loop in MPACT, can be moved to the interior, avoiding duplicate modular ray trace and coarse ray trace setup (mapping coarse mesh surface indexes), which needs to be performed repeatedly when group is outermost.« less

Investigation of Coupled model of Pore network and Continuum in shale gas

NASA Astrophysics Data System (ADS)

Cao, G.; Lin, M.

2016-12-01

Flow in shale spanning over many scales, makes the majority of conventional treatment methods disabled. For effectively simulating, a coupled model of pore-scale and continuum-scale was proposed in this paper. Based on the SEM image, we decompose organic-rich-shale into two subdomains: kerogen and inorganic matrix. In kerogen, the nanoscale pore-network is the main storage space and migration pathway so that the molecular phenomena (slip and diffusive transport) is significant. Whereas, inorganic matrix, with relatively large pores and micro fractures, the flow is approximate to Darcy. We use pore-scale network models (PNM) to represent kerogen and continuum-scale models (FVM or FEM) to represent matrix. Finite element mortars are employed to couple pore- and continuum-scale models by enforcing continuity of pressures and fluxes at shared boundary interfaces. In our method, the process in the coupled model is described by pressure square equation, and uses Dirichlet boundary conditions. We discuss several problems: the optimal element number of mortar faces, two categories boundary faces of pore network, the difference between 2D and 3D models, and the difference between continuum models FVM and FEM in mortars. We conclude that: (1) too coarse mesh in mortars will decrease the accuracy, while too fine mesh will lead to an ill-condition even singular system, the optimal element number is depended on boundary pores and nodes number. (2) pore network models are adjacent to two different mortar faces (PNM to PNM, PNM to continuum model), incidental repeated mortar nodes must be deleted. (3) 3D models can be replaced by 2D models under certain condition. (4) FVM is more convenient than FEM, for its simplicity in assigning interface nodes pressure and calculating interface fluxes. This work is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB10020302), the 973 Program (2014CB239004), the Key Instrument Developing Project of the CAS (ZDYZ2012-1-08-02), the National Natural Science Foundation of China (41574129).

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

NASA Astrophysics Data System (ADS)

Salvalaglio, Marco; Backofen, Rainer; Voigt, Axel; Elder, Ken R.

2017-08-01

One of the major difficulties in employing phase-field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work, we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free-energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite-element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Murman, S. M.; Kwak, Dochan (Technical Monitor)

2002-01-01

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH

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

Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu

2011-12-01

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less

Utilisation of steel furnace slag coarse aggregate in a low calcium fly ash geopolymer concrete

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

Khan, M. S.H.,; Castel, Arnaud; Akbarnezhad, A.

This paper evaluates the performance of steel furnace slag (SFS) coarse aggregate in blended slag and low calcium fly ash geopolymer concrete (GPC). The geopolymer binder is composed of 90% of low calcium fly ash and 10% of ground granulated blast furnace slag (GGBFS). Mechanical and physical properties, shrinkage, and detailed microstructure analysis were carried out. The results showed that geopolymer concrete with SFS aggregate offered higher compressive strength, surface resistivity and pulse velocity than that of GPC with traditional aggregate. The shrinkage results showed no expansion or swelling due to delayed calcium oxide (CaO) hydration after 320 days. Nomore » traditional porous interfacial transition zone (ITZ) was detected using scanning electron microscopy, indicating a better bond between SFS aggregate and geopolymer matrix. Energy dispersive spectroscopy results further revealed calcium (Ca) diffusion at the vicinity of ITZ. Raman spectroscopy results showed no new crystalline phase formed due to Ca diffusion. X-ray fluorescence result showed Mg diffusion from SFS aggregate towards geopolymer matrix. The incorporation of Ca and Mg into the geopolymer structure and better bond between SFS aggregate and geopolymer matrix are the most likely reasons for the higher compressive strength observed in GPC with SFS aggregate.« less

Adiabatic elimination of inertia of the stochastic microswimmer driven by α -stable noise

NASA Astrophysics Data System (ADS)

Noetel, Joerg; Sokolov, Igor M.; Schimansky-Geier, Lutz

2017-10-01

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α -stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τϕ, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t ≫τϕ , is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Adiabatic elimination of inertia of the stochastic microswimmer driven by α-stable noise.

PubMed

Noetel, Joerg; Sokolov, Igor M; Schimansky-Geier, Lutz

2017-10-01

We consider a microswimmer that moves in two dimensions at a constant speed and changes the direction of its motion due to a torque consisting of a constant and a fluctuating component. The latter will be modeled by a symmetric Lévy-stable (α-stable) noise. The purpose is to develop a kinetic approach to eliminate the angular component of the dynamics to find a coarse-grained description in the coordinate space. By defining the joint probability density function of the position and of the orientation of the particle through the Fokker-Planck equation, we derive transport equations for the position-dependent marginal density, the particle's mean velocity, and the velocity's variance. At time scales larger than the relaxation time of the torque τ_{ϕ}, the two higher moments follow the marginal density and can be adiabatically eliminated. As a result, a closed equation for the marginal density follows. This equation, which gives a coarse-grained description of the microswimmer's positions at time scales t≫τ_{ϕ}, is a diffusion equation with a constant diffusion coefficient depending on the properties of the noise. Hence, the long-time dynamics of a microswimmer can be described as a normal, diffusive, Brownian motion with Gaussian increments.

Effect of Solute Diffusion on Dendrite Growth in the Molten Pool of Al-Cu Alloy

NASA Astrophysics Data System (ADS)

Zhan, Xiaohong; Gu, Cheng; Liu, Yun; Wei, Yanhong

2017-10-01

A cellular automaton (CA)-finite difference model is developed to simulate dendrite growth and solute diffusion during solidification process in the molten pool of Al-Cu alloy. In order to explain the interaction between the dendritic growth and solute distribution, a series of CA simulations with different solute diffusion velocity coefficients are carried out. It is concluded that the solute concentration increases with dendrite growing and solute accumulation in the dendrite tip. Converged value of the dendrite tip growth velocity is about 480 μm/s if the mesh size is refined to 2 μm or less. Growth of the primary dendrite and the secondary dendrite is mainly influenced by solute diffusion at the dendrite tips. And growth of secondary and tertiary dendrites is mainly influenced by solute diffusion at interdendrite.

AN EXTENSION OF THE ATHENA++ CODE FRAMEWORK FOR GRMHD BASED ON ADVANCED RIEMANN SOLVERS AND STAGGERED-MESH CONSTRAINED TRANSPORT

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

White, Christopher J.; Stone, James M.; Gammie, Charles F.

2016-08-01

We present a new general relativistic magnetohydrodynamics (GRMHD) code integrated into the Athena++ framework. Improving upon the techniques used in most GRMHD codes, ours allows the use of advanced, less diffusive Riemann solvers, in particular HLLC and HLLD. We also employ a staggered-mesh constrained transport algorithm suited for curvilinear coordinate systems in order to maintain the divergence-free constraint of the magnetic field. Our code is designed to work with arbitrary stationary spacetimes in one, two, or three dimensions, and we demonstrate its reliability through a number of tests. We also report on its promising performance and scalability.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Coarse-grained model of nanoscale segregation, water diffusion, and proton transport in Nafion membranes

NASA Astrophysics Data System (ADS)

Vishnyakov, Aleksey; Mao, Runfang; Lee, Ming-Tsung; Neimark, Alexander V.

2018-01-01

We present a coarse-grained model of the acid form of Nafion membrane that explicitly includes proton transport. This model is based on a soft-core bead representation of the polymer implemented into the dissipative particle dynamics (DPD) simulation framework. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with water beads. Morse bond formation and breakup artificially mimics the Grotthuss hopping mechanism of proton transport. The proposed DPD model is parameterized to account for the specifics of the conformations and flexibility of the Nafion backbone and sidechains; it treats electrostatic interactions in the smeared charge approximation. The simulation results qualitatively, and in many respects quantitatively, predict the specifics of nanoscale segregation in the hydrated Nafion membrane into hydrophobic and hydrophilic subphases, water diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from a collection of isolated water clusters to a 3D network of pores filled with water embedded in the hydrophobic matrix. The segregated morphology is characterized in terms of the pore size distribution with the average size growing with hydration from ˜1 to ˜4 nm. Comparison of the predicted water diffusivity with the experimental data taken from different sources shows good agreement at high and moderate hydration and substantial deviation at low hydration, around and below the percolation threshold. This discrepancy is attributed to the dynamic percolation effects of formation and rupture of merging bridges between the water clusters, which become progressively important at low hydration, when the coarse-grained model is unable to mimic the fine structure of water network that includes singe molecule bridges. Selected simulations of water diffusion are performed for the alkali metal substituted membrane which demonstrate the effects of the counter-ions on membrane self-assembly and transport. The hydration dependence of the proton diffusivity reproduces semi-qualitatively the trend of the diverse experimental data, showing a sharp decrease around the percolation threshold. Overall, the proposed model opens up an opportunity to study self-assembly and water and proton transport in polyelectrolytes using computationally efficient DPD simulations, and, with further refinement, it may become a practical tool for theory informed design and optimization of perm-selective and ion-conducting membranes with improved properties.

Silicon-fiber blanket solar-cell array concept

NASA Technical Reports Server (NTRS)

Eliason, J. T.

1973-01-01

Proposed economical manufacture of solar-cell arrays involves parallel, planar weaving of filaments made of doped silicon fibers with diffused radial junction. Each filament is a solar cell connected either in series or parallel with others to form a blanket of deposited grids or attached electrode wire mesh screens.

Mesh and Time-Step Independent Computational Fluid Dynamics (CFD) Solutions

ERIC Educational Resources Information Center

Nijdam, Justin J.

2013-01-01

A homework assignment is outlined in which students learn Computational Fluid Dynamics (CFD) concepts of discretization, numerical stability and accuracy, and verification in a hands-on manner by solving physically realistic problems of practical interest to engineers. The students solve a transient-diffusion problem numerically using the common…

Evaluation of an Oxygen-Diffusion Dressing for Accelerated Healing of Donor-Site Wounds

DTIC Science & Technology

2014-06-01

such as fine- mesh gauze, scarlet-red gauze, Xeroform gauze, and other dressings. Slow healing times, cellulitis , and pain are perennial problems in...burn wound cellulitis preoperatively, and critically ill patients on mechanical ventilation who would be unable to provide consent for the study or

The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions.

PubMed

Arridge, S R; Dehghani, H; Schweiger, M; Okada, E

2000-01-01

We present a method for handling nonscattering regions within diffusing domains. The method develops from an iterative radiosity-diffusion approach using Green's functions that was computationally slow. Here we present an improved implementation using a finite element method (FEM) that is direct. The fundamental idea is to introduce extra equations into the standard diffusion FEM to represent nondiffusive light propagation across a nonscattering region. By appropriate mesh node ordering the computational time is not much greater than for diffusion alone. We compare results from this method with those from a discrete ordinate transport code, and with Monte Carlo calculations. The agreement is very good, and, in addition, our scheme allows us to easily model time-dependent and frequency domain problems.

Simulation tools for particle-based reaction-diffusion dynamics in continuous space

PubMed Central

2014-01-01

Particle-based reaction-diffusion algorithms facilitate the modeling of the diffusional motion of individual molecules and the reactions between them in cellular environments. A physically realistic model, depending on the system at hand and the questions asked, would require different levels of modeling detail such as particle diffusion, geometrical confinement, particle volume exclusion or particle-particle interaction potentials. Higher levels of detail usually correspond to increased number of parameters and higher computational cost. Certain systems however, require these investments to be modeled adequately. Here we present a review on the current field of particle-based reaction-diffusion software packages operating on continuous space. Four nested levels of modeling detail are identified that capture incrementing amount of detail. Their applicability to different biological questions is discussed, arching from straight diffusion simulations to sophisticated and expensive models that bridge towards coarse grained molecular dynamics. PMID:25737778

Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

NASA Astrophysics Data System (ADS)

Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

2017-11-01

Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

Electromagnetic forward modelling for realistic Earth models using unstructured tetrahedral meshes and a meshfree approach

NASA Astrophysics Data System (ADS)

Farquharson, C.; Long, J.; Lu, X.; Lelievre, P. G.

2017-12-01

Real-life geology is complex, and so, even when allowing for the diffusive, low resolution nature of geophysical electromagnetic methods, we need Earth models that can accurately represent this complexity when modelling and inverting electromagnetic data. This is particularly the case for the scales, detail and conductivity contrasts involved in mineral and hydrocarbon exploration and development, but also for the larger scale of lithospheric studies. Unstructured tetrahedral meshes provide a flexible means of discretizing a general, arbitrary Earth model. This is important when wanting to integrate a geophysical Earth model with a geological Earth model parameterized in terms of surfaces. Finite-element and finite-volume methods can be derived for computing the electric and magnetic fields in a model parameterized using an unstructured tetrahedral mesh. A number of such variants have been proposed and have proven successful. However, the efficiency and accuracy of these methods can be affected by the "quality" of the tetrahedral discretization, that is, how many of the tetrahedral cells in the mesh are long, narrow and pointy. This is particularly the case if one wants to use an iterative technique to solve the resulting linear system of equations. One approach to deal with this issue is to develop sophisticated model and mesh building and manipulation capabilities in order to ensure that any mesh built from geological information is of sufficient quality for the electromagnetic modelling. Another approach is to investigate other methods of synthesizing the electromagnetic fields. One such example is a "meshfree" approach in which the electromagnetic fields are synthesized using a mesh that is distinct from the mesh used to parameterized the Earth model. There are then two meshes, one describing the Earth model and one used for the numerical mathematics of computing the fields. This means that there are no longer any quality requirements on the model mesh, which makes the process of building a geophysical Earth model from a geological model much simpler. In this presentation we will explore the issues that arise when working with realistic Earth models and when synthesizing geophysical electromagnetic data for them. We briefly consider meshfree methods as a possible means of alleviating some of these issues.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

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

Grain, Julien; Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue.more » The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.« less

Variable role of aquatic macroinvertebrates in initial breakdown of seasonal leaf litter inputs to a cold-desert river

USGS Publications Warehouse

Nelson, S.M.; Andersen, D.C.

2007-01-01

We used coarse-mesh and fine-mesh leafpacks to examine the importance of aquatic macroinvertebrates in the breakdown of floodplain tree leaf litter that seasonally entered a sand-bedded reach of the sixth-order Yampa River in semiarid Colorado. Leafpacks were positioned off the easily mobilized channel bed, mimicking litter trapped in debris piles. Organic matter (OM) loss was fastest for leaves collected from the floodplain and placed in the river in spring (k = 0.029/day) and slowest for leaves collected and placed in the river in winter (0.006/day). Macroinvertebrates were most abundant in winter and spring leaves, but seemed important to processing only in spring, when exclusion by fine mesh reduced OM loss by 25% and nitrogen loss by 65% in spring leaves. Macroinvertebrates seemed to have little role in processing of autumn, winter, or summer leaves over the 50-day to 104-day monitoring periods. Desiccation during bouts of low discharge and sediment deposition on leaves limited invertebrate processing in summer and autumn, whereas processing of winter leaves, which supported relatively large numbers of shredders, might have been restricted by ice formation and low water temperatures. These results were consistent with the concept that microbial processing dominates in higher-order rivers, but suggested that macroinvertebrate processing can be locally important in higher-order desert rivers in seasons or years with favorable discharge and water quality conditions.

Subplane-based Control Rod Decusping Techniques for the 2D/1D Method in MPACT

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

Graham, Aaron M; Collins, Benjamin S; Downar, Thomas

2017-01-01

The MPACT transport code is being jointly developed by Oak Ridge National Laboratory and the University of Michigan to serve as the primary neutron transport code for the Virtual Environment for Reactor Applications Core Simulator. MPACT uses the 2D/1D method to solve the transport equation by decomposing the reactor model into a stack of 2D planes. A fine mesh flux distribution is calculated in each 2D plane using the Method of Characteristics (MOC), then the planes are coupled axially through a 1D NEM-Pmore » $$_3$$ calculation. This iterative calculation is then accelerated using the Coarse Mesh Finite Difference method. One problem that arises frequently when using the 2D/1D method is that of control rod cusping. This occurs when the tip of a control rod falls between the boundaries of an MOC plane, requiring that the rodded and unrodded regions be axially homogenized for the 2D MOC calculations. Performing a volume homogenization does not properly preserve the reaction rates, causing an error known as cusping. The most straightforward way of resolving this problem is by refining the axial mesh, but this can significantly increase the computational expense of the calculation. The other way of resolving the partially inserted rod is through the use of a decusping method. This paper presents new decusping methods implemented in MPACT that can dynamically correct the rod cusping behavior for a variety of problems.« less

Summary of the Third AIAA CFD Drag Prediction Workshop

NASA Technical Reports Server (NTRS)

Vassberg, John C.; Tinoco, Edward N.; Mani, Mori; Brodersen, Olaf P.; Eisfeld, Bernhard; Wahls, Richard A.; Morrison, Joseph H.; Zickuhr, Tom; Laflin, Kelly R.; Mavriplis, DImitri J.

2007-01-01

The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-al;one configurations of that are representative of transonic transport aircraft. The baseline DLR-F6 wing-body geometry, previously utilized in DPW-II, is also augmented with a side-body fairing to help reduce the complexity of the flow physics in the wing-body juncture region. In addition, two new wing-alone geometries have been developed for the DPW-II. Numerical calculations are performed using industry-relevant test cases that include lift-specific and fixed-alpha flight conditions, as well as full drag polars. Drag, lift, and pitching moment predictions from previous Reynolds-Averaged Navier-Stokes computational fluid Dynamics Methods are presented, focused on fully-turbulent flows. Solutions are performed on structured, unstructured, and hybrid grid systems. The structured grid sets include point-matched multi-block meshes and over-set grid systems. The unstructured and hybrid grid sets are comprised of tetrahedral, pyramid, and prismatic elements. Effort was made to provide a high-quality and parametrically consistent family of grids for each grid type about each configuration under study. The wing-body families are comprised of a coarse, medium, and fine grid, while the wing-alone families also include an extra-fine mesh. These mesh sequences are utilized to help determine how the provided flow solutions fair with respect to asymptotic grid convergence, and are used to estimate an absolute drag of each configuration.

A Software Architecture for the Construction and Management of Real-Time Virtual Worlds

DTIC Science & Technology

1993-06-01

University of California, Berkeley [FUNK921. The second improvement was the addition of a radiosity light model. The use of radiosity and its use of diffuse...the viewpoint is stationary, the coarse polygon model is replaced by progressively more complex radiosity lit scenes. The area of molecular modeling

Principal component analysis for protein folding dynamics.

PubMed

Maisuradze, Gia G; Liwo, Adam; Scheraga, Harold A

2009-01-09

Protein folding is considered here by studying the dynamics of the folding of the triple beta-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.

A strategy for characterized aerosol-sampling transport efficiency.

NASA Astrophysics Data System (ADS)

Schwarz, J. P.

2017-12-01

A fundamental concern when sampling aerosol in the laboratory or in situ, on the ground or (especially) from aircraft, is characterizing transport losses due to particles contacting the walls of tubing used for transport. Depending on the size range of the aerosol, different mechanisms dominate these losses: diffusion for the ultra-fine, and inertial and gravitational settling losses for the coarse mode. In the coarse mode, losses become intractable very quickly with increasing particle size above 5 µm diameter. Here we present these issues, with a concept approach to reducing aerosol losses via strategic dilution with porous tubing including results of laboratory testing of a prototype. We infer the potential value of this approach to atmospheric aerosol sampling.

Low modulus and bioactive Ti/α-TCP/Ti-mesh composite prepared by spark plasma sintering.

PubMed

Guo, Yu; Tan, Yanni; Liu, Yong; Liu, Shifeng; Zhou, Rui; Tang, Hanchun

2017-11-01

A titanium mesh scaffold composite filled with Ti/α-TCP particles was prepared by spark plasma sintering (SPS). The microstructures and interfacial reactions of the composites were investigated by scanning electron microscopy (SEM), Energy Dispersive Spectroscopy (EDS) and X-ray diffraction (XRD) analyses. The compressive strength and elastic modulus were also measured. In vitro bioactivity and biocompatibility was evaluated by using simulated body fluid and cells culture, respectively. After high temperature sintering, Ti oxides, Ti x P y and CaTiO 3 were formed. The formation of Ti oxides and Ti x P y were resulted from the diffusion of O and P elements from α-TCP to Ti. CaTiO 3 was the reaction product of Ti and α-TCP. The composite of 70Ti/α-TCP incorporated with Ti mesh showed a high compressive strength of 589MPa and a low compressive modulus of 30GPa. The bioactivity test showed the formation of a thick apatite layer on the composite and well-spread cells attachment. A good combination of mechanical properties and bioactivity indicated a high potential application of Ti/α-TCP/Ti-mesh composite for orthopedic implants. Copyright © 2017. Published by Elsevier B.V.

Interplay between inhibited transport and reaction in nanoporous materials

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

Ackerman, David Michael

2013-01-01

This work presents a detailed formulation of reaction and diffusion dynamics of molecules in confined pores such as mesoporous silica and zeolites. A general reaction-diffusion model and discrete Monte Carlo simulations are presented. Both transient and steady state behavior is covered. Failure of previous mean-field models for these systems is explained and discussed. A coarse-grained, generalized hydrodynamic model is developed that accurately captures the interplay between reaction and restricted transport in these systems. This method incorporates the non-uniform chemical diffusion behavior present in finite pores with multi-component diffusion. Two methods of calculating these diffusion values are developed: a random walkmore » based approach and a driven diffusion model based on an extension of Fick's law. The effects of reaction, diffusion, pore length, and catalytic site distribution are investigated. In addition to strictly single file motion, quasi-single file diffusion is incorporated into the model to match a range of experimental systems. The connection between these experimental systems and model parameters is made through Langevin dynamics modeling of particles in confined pores.« less

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

Garcia, Andres

Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems canmore » be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use Langevin Molecular Dynamics (MD) simulations to assess these parameters.« less

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

Chen, Zheng; Huang, Hongying; Yan, Jue

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0,β 1) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried outmore » to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.« less

On accuracy of the wave finite element predictions of wavenumbers and power flow: A benchmark problem

NASA Astrophysics Data System (ADS)

Søe-Knudsen, Alf; Sorokin, Sergey

2011-06-01

This rapid communication is concerned with justification of the 'rule of thumb', which is well known to the community of users of the finite element (FE) method in dynamics, for the accuracy assessment of the wave finite element (WFE) method. An explicit formula linking the size of a window in the dispersion diagram, where the WFE method is trustworthy, with the coarseness of a FE mesh employed is derived. It is obtained by the comparison of the exact Pochhammer-Chree solution for an elastic rod having the circular cross-section with its WFE approximations. It is shown that the WFE power flow predictions are also valid within this window.

The effect of surface boundary conditions on the climate generated by a coarse-mesh general circulation model

NASA Technical Reports Server (NTRS)

Cohen, C.

1981-01-01

A hierarchy of experiments was run, starting with an all water planet with zonally symmetric sea surface temperatures, then adding, one at a time, flat continents, mountains, surface physics, and realistic sea surface temperatures. The model was run with the sun fixed at a perpetual January. Ensemble means and standard deviations were computed and the t-test was used to determine the statistical significance of the results. The addition of realistic surface physics does not affect the model climatology to as large as extent as does the addition of mountains. Departures from zonal symmetry of the SST field result in a better simulation of the real atmosphere.

Diffusion of 99-technetium in compacted bentonite under aerobic and anaerobic conditions

NASA Astrophysics Data System (ADS)

Večerník, P.; Jedináková-Křížová, V.

2006-01-01

The main aim of this study was to investigate diffusion of technetium 99Tc under different conditions. Because technetium represents one of the most dangerous fission products due to its very long halftime and high mobility in aerobic conditions diffusion experiments of technetium (as 99TcO 4 - anion) in Czech bentonite from Rokle locality have been carried out. For performance and evaluation of experiments the through-diffusion method was chosen and apparent (Da) and effective (De) diffusion coefficients were evaluated. The effects of particle mesh-size, dry bulk density and aerobic or anaerobic conditions on diffusion were studied. In the presence of oxygen, technetium occurs in oxidation state VII, as an anion, soluble and mobile in the environment. However, under reducing conditions it occurs in a lower oxidation states, mainly as insoluble oxides or hydroxides. Aerobic experiments were carried out under laboratory conditions and anaerobic experiments were performed in a nitrogen atmosphere in a glove box, to simulate the real underground conditions.

Influence of wind-speed on short-duration NO2 measurements using Palmes and Ogawa passive diffusion samplers

NASA Astrophysics Data System (ADS)

Masey, Nicola; Gillespie, Jonathan; Heal, Mathew R.; Hamilton, Scott; Beverland, Iain J.

2017-07-01

We assessed the precision and accuracy of nitrogen dioxide (NO2) concentrations over 2-day, 3-day and 7-day exposure periods measured with the following types of passive diffusion samplers: standard (open) Palmes tubes; standard Ogawa samplers with commercially-prepared Ogawa absorbent pads (Ogawa[S]); and modified Ogawa samplers with absorbent-impregnated stainless steel meshes normally used in Palmes tubes (Ogawa[P]). We deployed these passive samplers close to the inlet of a chemiluminescence NO2 analyser at an urban background site in Glasgow, UK over 32 discrete measurement periods. Duplicate relative standard deviation was <7% for all passive samplers. The Ogawa[P], Ogawa[S] and Palmes samplers explained 93%, 87% and 58% of temporal variation in analyser concentrations respectively. Uptake rates for Palmes and Ogawa[S] samplers were positively and linearly associated with wind-speed (P < 0.01 and P < 0.05 respectively). Computation of adjusted uptake rates using average wind-speed observed during each sampling period increased the variation in analyser concentrations explained by Palmes and Ogawa[S] estimates to 90% and 92% respectively, suggesting that measurements can be corrected for shortening of diffusion path lengths due to wind-speed to improve the accuracy of estimates of short-term NO2 exposure. Monitoring situations where it is difficult to reliably estimate wind-speed variations, e.g. across multiple sites with different unknown exposures to local winds, and personal exposure monitoring, are likely to benefit from protection of these sampling devices from the effects of wind, for example by use of a mesh or membrane across the open end. The uptake rate of Ogawa[P] samplers was not associated with wind-speed resulting in a high correlation between estimated concentrations and observed analyser concentrations. The use of Palmes meshes in Ogawa[P] samplers reduced the cost of sampler preparation and removed uncertainty associated with the unknown manufacturing process for the commercially-prepared collection pads.

GRAPE- TWO-DIMENSIONAL GRIDS ABOUT AIRFOILS AND OTHER SHAPES BY THE USE OF POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

ULTRAFINE AEROSOL INFLUENCE ON THE SAMPLING BY CASCADE IMPACTOR.

PubMed

Vasyanovich, M; Mostafa, M Y A; Zhukovsky, M

2017-11-01

Cascade impactors based on inertial deposition of aerosols are widely used to determine the size distribution of radioactive aerosols. However, there are situations where radioactive aerosols are represented by particles with a diameter of 1-5 nm. In this case, ultrafine aerosols can be deposited on impactor cascades by diffusion mechanism. The influence of ultrafine aerosols (1-5 nm) on the response of three different types of cascade impactors was studied. It was shown that the diffusion deposition of ultrafine aerosols can distort the response of the cascade impactor. The influence of diffusion deposition of ultrafine aerosols can be considerably removed by the use of mesh screens or diffusion battery installed before cascade impactor during the aerosol sampling. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

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

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

Experimental advances and preliminary mathematical modeling of the Swiss-roll mixed-reactant direct borohydride fuel cell

NASA Astrophysics Data System (ADS)

Aziznia, Amin; Oloman, Colin W.; Gyenge, Előd L.

2014-11-01

The Swiss-roll single-cell mixed reactant (SR-MRFC) borohydride - oxygen fuel cell equipped with Pt/carbon cloth 3D anode and either MnO2 or Ag gas-diffusion cathodes is investigated by a combination of experimental studies and preliminary mathematical modeling of the polarization curve. We investigate the effects of four variables: cathode side metallic mesh fluid distributor, separator type (Nafion 112® vs. Viledon®), cathode catalyst (MnO2 vs. Ag), and the hydrophilic pore volume fraction of the gas-diffusion cathode. Using a two-phase feed of alkaline borohydride solution (1 M NaBH4 - 2 M NaOH) and O2 gas in an SR-MRFC equipped with Pt/C 3D anode, MnO2 gas diffusion cathode, Viledon® porous diaphragm, expanded mesh cathode-side fluid distributor, the maximum superficial power density is 2230 W m-2 at 323 K and 105 kPa(abs). The latter superficial power density is almost 3.5 times higher than our previously reported superficial power density for the same catalyst combinations. Furthermore, with a Pt anode and Ag cathode catalyst combination, a superficial power density of 2500 W m-2 is achieved with superior performance durability compared to the MnO2 cathode. The fuel cell results are substantiated by impedance spectroscopy analysis and preliminary mathematical model predictions based on mixed potential theory.

Investigating the influence of lithologic heterogeneity on gas hydrate formation and methane recycling at the base of the gas hydrate stability zone in channelized systems

NASA Astrophysics Data System (ADS)

Daigle, H.; Nole, M.; Cook, A.; Malinverno, A.

2017-12-01

In marine environments, gas hydrate preferentially accumulates in coarse-grained sediments. At the meso- to micro-scale, however, hydrate distribution in these coarse-grained units is often heterogeneous. We employ a methane hydrate reservoir simulator coupling heat and mass transfer as well as capillary effects to investigate how capillary controls on methane solubility affect gas and hydrate accumulations in reservoirs characterized by graded bedding and alternating sequences of coarse-grained sands and fine-grained silt and clay. Simulations bury a channelized reservoir unit encased in homogeneous, fine-grained material characterized by small pores (150 nm) and low permeability ( 1 md in the absence of hydrate). Pore sizes within each reservoir bed between vary between coarse sand and fine silt. Sands have a median pore size of 35 microns and a lognormal pore size distribution. We also investigate how the amount of labile organic carbon (LOC) affects hydrate growth due to microbial methanogenesis within the sediments. In a diffusion-dominated system, methane movies into reservoir layers along spatial gradients in dissolved methane concentration. Hydrate grows in such a way as to minimize these concentration gradients by accumulating slower in finer-grained reservoir layers and faster in coarser-grained layers. Channelized, fining-upwards sediment bodies accumulate hydrate first along their outer surfaces and thence inward from top to bottom. If LOC is present in thin beds within the channel, higher saturations of hydrate will be distributed more homogeneously throughout the unit. When buried beneath the GHSZ, gas recycling can occur only if enough hydrate is present to form a connected gas phase upon dissociation. Simulations indicate that this is difficult to achieve for diffusion-dominated systems, especially those with thick GHSZs and/or small amounts of LOC. However, capillary-driven fracturing behavior may be more prevalent in settings with thick GHSZs.

Investigating the influence of lithologic heterogeneity on gas hydrate formation and methane recycling at the base of the gas hydrate stability zone in channelized systems

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

Daigle, Hugh; Nole, Michael; Cook, Ann

In marine environments, gas hydrate preferentially accumulates in coarse-grained sediments. At the meso- to micro-scale, however, hydrate distribution in these coarse-grained units is often heterogeneous. We employ a methane hydrate reservoir simulator coupling heat and mass transfer as well as capillary effects to investigate how capillary controls on methane solubility affect gas and hydrate accumulations in reservoirs characterized by graded bedding and alternating sequences of coarse-grained sands and fine-grained silt and clay. Simulations bury a channelized reservoir unit encased in homogeneous, fine-grained material characterized by small pores (150 nm) and low permeability (~1 md in the absence of hydrate). Poremore » sizes within each reservoir bed between vary between coarse sand and fine silt. Sands have a median pore size of 35 microns and a lognormal pore size distribution. We also investigate how the amount of labile organic carbon (LOC) affects hydrate growth due to microbial methanogenesis within the sediments. In a diffusion-dominated system, methane movies into reservoir layers along spatial gradients in dissolved methane concentration. Hydrate grows in such a way as to minimize these concentration gradients by accumulating slower in finer-grained reservoir layers and faster in coarser-grained layers. Channelized, fining-upwards sediment bodies accumulate hydrate first along their outer surfaces and thence inward from top to bottom. If LOC is present in thin beds within the channel, higher saturations of hydrate will be distributed more homogeneously throughout the unit. When buried beneath the GHSZ, gas recycling can occur only if enough hydrate is present to form a connected gas phase upon dissociation. Simulations indicate that this is difficult to achieve for diffusion-dominated systems, especially those with thick GHSZs and/or small amounts of LOC. However, capillary-driven fracturing behavior may be more prevalent in settings with thick GHSZs.« less

Oscillating-grid experiments in water and superfluid helium

NASA Astrophysics Data System (ADS)

Honey, Rose E.; Hershberger, Robert; Donnelly, Russell J.; Bolster, Diogo

2014-05-01

Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., d ˜√t ) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order 30000. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about 43000. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary H on tube diameter D and find that H =cD with c ˜2. We suggest this may be explained by saturation of the energy-containing length scale ℓe. We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid 4He in the light of the present results.

Operator induced multigrid algorithms using semirefinement

NASA Technical Reports Server (NTRS)

Decker, Naomi; Vanrosendale, John

1989-01-01

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.

Challenges of Representing Sub-Grid Physics in an Adaptive Mesh Refinement Atmospheric Model

NASA Astrophysics Data System (ADS)

O'Brien, T. A.; Johansen, H.; Johnson, J. N.; Rosa, D.; Benedict, J. J.; Keen, N. D.; Collins, W.; Goodfriend, E.

2015-12-01

Some of the greatest potential impacts from future climate change are tied to extreme atmospheric phenomena that are inherently multiscale, including tropical cyclones and atmospheric rivers. Extremes are challenging to simulate in conventional climate models due to existing models' coarse resolutions relative to the native length-scales of these phenomena. Studying the weather systems of interest requires an atmospheric model with sufficient local resolution, and sufficient performance for long-duration climate-change simulations. To this end, we have developed a new global climate code with adaptive spatial and temporal resolution. The dynamics are formulated using a block-structured conservative finite volume approach suitable for moist non-hydrostatic atmospheric dynamics. By using both space- and time-adaptive mesh refinement, the solver focuses computational resources only where greater accuracy is needed to resolve critical phenomena. We explore different methods for parameterizing sub-grid physics, such as microphysics, macrophysics, turbulence, and radiative transfer. In particular, we contrast the simplified physics representation of Reed and Jablonowski (2012) with the more complex physics representation used in the System for Atmospheric Modeling of Khairoutdinov and Randall (2003). We also explore the use of a novel macrophysics parameterization that is designed to be explicitly scale-aware.

Multiscale geometric modeling of macromolecules II: Lagrangian representation

PubMed Central

Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

2013-01-01

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599

Adaptive mesh refinement for characteristic grids

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan

2011-05-01

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius and Lehner (J Comp Phys 198:10, 2004), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in two-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null slices. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both second and fourth order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response

PubMed Central

Jiang, Shuyong; Zhou, Tao; Tu, Jian; Shi, Laixin; Chen, Qiang; Yang, Mingbo

2017-01-01

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process. PMID:29027925

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response.

PubMed

Hu, Li; Jiang, Shuyong; Zhou, Tao; Tu, Jian; Shi, Laixin; Chen, Qiang; Yang, Mingbo

2017-10-13

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process.

An Examination of Parameters Affecting Large Eddy Simulations of Flow Past a Square Cylinder

NASA Technical Reports Server (NTRS)

Mankbadi, M. R.; Georgiadis, N. J.

2014-01-01

Separated flow over a bluff body is analyzed via large eddy simulations. The turbulent flow around a square cylinder features a variety of complex flow phenomena such as highly unsteady vortical structures, reverse flow in the near wall region, and wake turbulence. The formation of spanwise vortices is often times artificially suppressed in computations by either insufficient depth or a coarse spanwise resolution. As the resolution is refined and the domain extended, the artificial turbulent energy exchange between spanwise and streamwise turbulence is eliminated within the wake region. A parametric study is performed highlighting the effects of spanwise vortices where the spanwise computational domain's resolution and depth are varied. For Re=22,000, the mean and turbulent statistics computed from the numerical large eddy simulations (NLES) are in good agreement with experimental data. Von-Karman shedding is observed in the wake of the cylinder. Mesh independence is illustrated by comparing a mesh resolution of 2 million to 16 million. Sensitivities to time stepping were minimized and sampling frequency sensitivities were nonpresent. While increasing the spanwise depth and resolution can be costly, this practice was found to be necessary to eliminating the artificial turbulent energy exchange.

Summary of the Fourth AIAA CFD Drag Prediction Workshop

NASA Technical Reports Server (NTRS)

Vassberg, John C.; Tinoco, Edward N.; Mani, Mori; Rider, Ben; Zickuhr, Tom; Levy, David W.; Brodersen, Olaf P.; Eisfeld, Bernhard; Crippa, Simone; Wahls, Richard A.;

Gas diffusivity and permeability through the firn column at Summit, Greenland: measurements and comparison to microstructural properties

NASA Astrophysics Data System (ADS)

Adolph, A. C.; Albert, M. R.

2014-02-01

The physical structure of polar firn plays a key role in the mechanisms by which glaciers and ice sheets preserve a natural archive of past atmospheric composition. This study presents the first measurements of gas diffusivity and permeability along with microstructural information measured from the near-surface firn through the firn column to pore close-off. Both fine- and coarse-grained firn from Summit, Greenland are included in this study to investigate the variability in firn caused by seasonal and storm-event layering. Our measurements reveal that the porosity of firn (derived from density) is insufficient to describe the full profiles of diffusivity and permeability, particularly at porosity values above 0.5. Thus, even a model that could perfectly predict the density profile would be insufficient for application to issues involving gas transport. The measured diffusivity profile presented here is compared to two diffusivity profiles modeled from firn air measurements from Summit. Because of differences in scale and in firn processes between the true field situation, firn modeling, and laboratory measurements, the results follow a similar overall pattern but do not align; our results constitute a lower bound on diffusive transport. In comparing our measurements of both diffusivity and permeability to previous parameterizations from numerical 3-D lattice-Boltzmann modeling, it is evident that the previous relationships to porosity are likely site-specific. We present parameterizations relating diffusivity and permeability to porosity as a possible tool, though use of direct measurements would be far more accurate when feasible. The relationships between gas transport properties and microstructural properties are characterized and compared to existing relationships for general porous media, specifically the Katz-Thompson (KT), Kozeny-Carman (KC), and Archie's law approximations. While those approximations can capture the general trend of gas transport relationships, they result in high errors for individual samples and fail to fully describe firn variability, particularly the differences between coarse- and fine-grained firn. We present a direct power law relationship between permeability and gas diffusivity based on our co-located measurements; further research will indicate if this type of relationship is site-specific. This set of measurements and relationships contributes a unique starting point for future investigations in developing more physically based models of firn gas transport.

3-D Modeling of a Nearshore Dye Release

NASA Astrophysics Data System (ADS)

Maxwell, A. R.; Hibler, L. F.; Miller, L. M.

2006-12-01

The usage of computer modeling software in predicting the behavior of a plume discharged into deep water is well established. Nearfield plume spreading in coastal areas with complex bathymetry is less commonly studied; in addition to geometry, some of the difficulties of this environment include: tidal exchange, temperature, and salinity gradients. Although some researchers have applied complex hydrodynamic models to this problem, nearfield regions are typically modeled by calibration of an empirical or expert system model. In the present study, the 3D hydrodynamic model Delft3D-FLOW was used to predict the advective transport from a point release in Sequim Bay, Washington. A nested model approach was used, wherein a coarse model using a mesh extending to nearby tide gages (cell sizes up to 1 km) was run over several tidal cycles in order to provide boundary conditions to a smaller area. The nested mesh (cell sizes up to 30 m) was forced on two open boundaries using the water surface elevation derived from the coarse model. Initial experiments with the uncalibrated model were conducted in order to predict plume propagation based on the best available field data. Field experiments were subsequently carried out by releasing rhodamine dye into the bay at near-peak flood tidal current and near high slack tidal conditions. Surface and submerged releases were carried out from an anchored vessel. Concurrently collected data from the experiment include temperature, salinity, dye concentration, and hyperspectral imagery, collected from boats and aircraft. A REMUS autonomous underwater vehicle was used to measure current velocity and dye concentration at varying depths, as well as to acquire additional bathymetric information. Preliminary results indicate that the 3D hydrodynamic model offers a reasonable prediction of plume propagation speed and shape. A sensitivity analysis is underway to determine the significant factors in effectively using the model as a predictive tool for plume tracking in data-limited environments. The Delft-PART stochastic particle transport model is also being examined to determine its utility for the present study.

Automated optimization of water-water interaction parameters for a coarse-grained model.

PubMed

Fogarty, Joseph C; Chiu, See-Wing; Kirby, Peter; Jakobsson, Eric; Pandit, Sagar A

2014-02-13

We have developed an automated parameter optimization software framework (ParOpt) that implements the Nelder-Mead simplex algorithm and applied it to a coarse-grained polarizable water model. The model employs a tabulated, modified Morse potential with decoupled short- and long-range interactions incorporating four water molecules per interaction site. Polarizability is introduced by the addition of a harmonic angle term defined among three charged points within each bead. The target function for parameter optimization was based on the experimental density, surface tension, electric field permittivity, and diffusion coefficient. The model was validated by comparison of statistical quantities with experimental observation. We found very good performance of the optimization procedure and good agreement of the model with experiment.

Texture evolution during thermomechanical processing in rare earth free magnesium alloys

NASA Astrophysics Data System (ADS)

Miller, Victoria Mayne

The use of wrought magnesium alloys is highly desirable for a wide range of applications where low component weight is desirable due to the high specific strength and stiffness the alloys can achieve. However, the implementation of wrought magnesium has been hindered by the limited room temperature formability which typically results from deformation processing. This work identifies opportunities for texture modification during thermomechanical processing of conventional (rare earth free) magnesium alloys via a combination of experimental investigation and polycrystal plasticity simulations. During deformation, it is observed that a homogeneous distribution of coarse intermetallic particles efficiently weakens deformation texture at all strain levels, while a highly inhomogeneous particle distribution is only effective at high strains. The particle deformation effects are complemented by the addition of alkaline earth solute, which modifies the relative deformation mode activity. During recrystallization, grains with basal orientations recrystallize more readily than off-basal grains, despite similar levels of internal misorientation. Dislocation substructure investigations revealed that this is a result of enhanced nucleation in the basal grains due to the dominance of prismatic slip. This dissertation identifies avenues to enhance the potential formability of magnesium alloys during thermomechanical processing by minimizing the evolved texture strength. The following are the identified key aspects of microstructural control: -Maintaining a fine grain size, likely via Zener pinning, to favorably modify deformation mode activity and homogenize deformation. -Developing a coarse, homogeneously distributed population of coarse intermetallic particles to promote a diffuse deformation texture. -Minimizing the activity of prismatic slip to retard the recrystallization of grains with basal orientations, allowing the development of a more diffuse recrystallization texture.

Structure and Relaxation in Solutions of Monoclonal Antibodies.

PubMed

Wang, Gang; Varga, Zsigmond; Hofmann, Jennifer; Zarraga, Isidro E; Swan, James W

2018-03-22

Reversible self-association of therapeutic antibodies is a key factor in high protein solution viscosities. In the present work, a coarse-grained computational model accounting for electrostatic, dispersion, and long-ranged hydrodynamic interactions of two model monoclonal antibodies is applied to understand the nature of self-association, predicting the solution microstructure and resulting transport properties of the solution. For the proteins investigated, the structure factor across a range of solution conditions shows quantitative agreement with neutron-scattering experiments. We observe a homogeneous, dynamical association of the antibodies with no evidence of phase separation. Calculations of self-diffusivity and viscosity from coarse-grained dynamic simulations show the appropriate trends with concentration but, respectively, over- and under-predict the experimentally measured values. By adding constraints to the self-associated clusters that rigidify them under flow, prediction of the transport properties is significantly improved with respect to experimental measurements. We hypothesize that these rigidity constraints are associated with missing degrees of freedom in the coarse-grained model resulting from patchy and heterogeneous interactions among coarse-grained domains. These results demonstrate how structural anisotropy and anisotropy of interactions generated by features at the 2-5 nm length scale in antibodies are sufficient to recover the dynamics and rheological properties of these important macromolecular solutions.

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.

Hyper-Resolution Groundwater Modeling using MODFLOW 6

NASA Astrophysics Data System (ADS)

Hughes, J. D.; Langevin, C.

2017-12-01

MODFLOW 6 is the latest version of the U.S. Geological Survey's modular hydrologic model. MODFLOW 6 was developed to synthesize many of the recent versions of MODFLOW into a single program, improve the way different process models are coupled, and to provide an object-oriented framework for adding new types of models and packages. The object-oriented framework and underlying numerical solver make it possible to tightly couple any number of hyper-resolution models within coarser regional models. The hyper-resolution models can be used to evaluate local-scale groundwater issues that may be affected by regional-scale forcings. In MODFLOW 6, hyper-resolution meshes can be maintained as separate model datasets, similar to MODFLOW-LGR, which simplifies the development of a coarse regional model with imbedded hyper-resolution models from a coarse regional model. For example, the South Atlantic Coastal Plain regional water availability model was converted from a MODFLOW-2000 model to a MODFLOW 6 model. The horizontal discretization of the original model is approximately 3,218 m x 3,218 m. Hyper-resolution models of the Aiken and Sumter County water budget areas in South Carolina with a horizontal discretization of approximately 322 m x 322 m were developed and were tightly coupled to a modified version of the original coarse regional model that excluded these areas. Hydraulic property and aquifer geometry data from the coarse model were mapped to the hyper-resolution models. The discretization of the hyper-resolution models is fine enough to make detailed analyses of the effect that changes in groundwater withdrawals in the production aquifers have on the water table and surface-water/groundwater interactions. The approach used in this analysis could be applied to other regional water availability models that have been developed by the U.S. Geological Survey to evaluate local scale groundwater issues.

Local diffusion and diffusion-T2 distribution measurements in porous media

NASA Astrophysics Data System (ADS)

Vashaee, S.; Newling, B.; MacMillan, B.; Marica, F.; Li, M.; Balcom, B. J.

2017-05-01

Slice-selective pulsed field gradient (PFG) and PFG-T2 measurements are developed to measure spatially-resolved molecular diffusion and diffusion-T2 distributions. A spatially selective adiabatic inversion pulse was employed for slice-selection. The slice-selective pulse is able to select a coarse slice, on the order of 1 cm, at an arbitrary position in the sample. The new method can be employed to characterize oil-water mixtures in porous media. The new technique has an inherent sensitivity advantage over phase encoding imaging based methods due to signal being localized from a thick slice. The method will be advantageous for magnetic resonance of porous media at low field where sensitivity is problematic. Experimental CPMG data, following PFG diffusion measurement, were compromised by a transient ΔB0(t) field offset. The off resonance effects of ΔB0(t) were examined by simulation. The ΔB0 offset artifact in D-T2 distribution measurements may be avoided by employing real data, instead of magnitude data.

Molecular and Subcellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice

PubMed Central

Kekenes-Huskey, Peter M.; Liao, Tao; Gillette, Andrew K.; Hake, Johan E.; Zhang, Yongjie; Michailova, Anushka P.; McCulloch, Andrew D.; McCammon, J. Andrew

2013-01-01

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions. PMID:24209858

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric J.; Duraisamy, Karthik

2017-01-01

This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from nonequilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered, and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of subgrid models is considered which represent nonlocal behavior via a finite memory approximation [Stinis, arXiv:1211.4285 (2012)], the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase space is accurately predicted for cases where the coarse graining is moderate. Large eddy simulations (LESs) of homogeneous isotropic turbulence and the Taylor-Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the subgrid contribution to energy transfer. Last, LESs of fully developed channel flow demonstrate the applicability of M-Z-based models to nondecaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse graining, highlighting the potential of M-Z-based techniques to define LES closures.

A new class of accurate, mesh-free hydrodynamic simulation methods

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2015-06-01

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.

Drag Prediction for the DLR-F6 Wing/Body and DPW Wing using CFL3D and OVERFLOW Overset Mesh

NASA Technical Reports Server (NTRS)

Sclanfani, Anthony J.; Vassberg, John C.; Harrison, Neal A.; DeHaan, Mark A.; Rumsey, Christopher L.; Rivers, S. Melissa; Morrison, Joseph H.

2007-01-01

A series of overset grids was generated in response to the 3rd AIAA CFD Drag Prediction Workshop (DPW-III) which preceded the 25th Applied Aerodynamics Conference in June 2006. DPW-III focused on accurate drag prediction for wing/body and wing-alone configurations. The grid series built for each configuration consists of a coarse, medium, fine, and extra-fine mesh. The medium mesh is first constructed using the current state of best practices for overset grid generation. The medium mesh is then coarsened and enhanced by applying a factor of 1.5 to each (I,J,K) dimension. The resulting set of parametrically equivalent grids increase in size by a factor of roughly 3.5 from one level to the next denser level. CFD simulations were performed on the overset grids using two different RANS flow solvers: CFL3D and OVERFLOW. The results were post-processed using Richardson extrapolation to approximate grid converged values of lift, drag, pitching moment, and angle-of-attack at the design condition. This technique appears to work well if the solution does not contain large regions of separated flow (similar to that seen n the DLR-F6 results) and appropriate grid densities are selected. The extra-fine grid data helped to establish asymptotic grid convergence for both the OVERFLOW FX2B wing/body results and the OVERFLOW DPW-W1/W2 wing-alone results. More CFL3D data is needed to establish grid convergence trends. The medium grid was utilized beyond the grid convergence study by running each configuration at several angles-of-attack so drag polars and lift/pitching moment curves could be evaluated. The alpha sweep results are used to compare data across configurations as well as across flow solvers. With the exception of the wing/body drag polar, the two codes compare well qualitatively showing consistent incremental trends and similar wing pressure comparisons.

Leaching assessment of concrete made of recycled coarse aggregate: physical and environmental characterisation of aggregates and hardened concrete.

PubMed

Galvín, A P; Agrela, F; Ayuso, J; Beltrán, M G; Barbudo, A

2014-09-01

Each year, millions of tonnes of waste are generated worldwide, partially through the construction and demolition of buildings. Recycling the resulting waste could reduce the amount of materials that need to be manufactured. Accordingly, the present work has analysed the potential reuse of construction waste in concrete manufacturing by replacing the natural aggregate with recycled concrete coarse aggregate. However, incorporating alternative materials in concrete manufacturing may increase the pollutant potential of the product, presenting an environmental risk via ground water contamination. The present work has tested two types of concrete batches that were manufactured with different replacement percentages. The experimental procedure analyses not only the effect of the portion of recycled aggregate on the physical properties of concrete but also on the leaching behaviour as indicative of the contamination degree. Thus, parameters such as slump, density, porosity and absorption of hardened concrete, were studied. Leaching behaviour was evaluated based on the availability test performed to three aggregates (raw materials of the concrete batches) and on the diffusion test performed to all concrete. From an environmental point of view, the question of whether the cumulative amount of heavy metals that are released by diffusion reaches the availability threshold was answered. The analysis of concentration levels allowed the establishment of different groups of metals according to the observed behaviour, the analysis of the role of pH and the identification of the main release mechanisms. Finally, through a statistical analysis, physical parameters and diffusion data were interrelated. It allowed estimating the relevance of porosity, density and absorption of hardened concrete on diffusion release of the metals in study. Copyright © 2014 Elsevier Ltd. All rights reserved.

Interstitial and Interlayer Ion Diffusion Geometry Extraction in Graphitic Nanosphere Battery Materials.

PubMed

Gyulassy, Attila; Knoll, Aaron; Lau, Kah Chun; Wang, Bei; Bremer, Peer-Timo; Papka, Michael E; Curtiss, Larry A; Pascucci, Valerio

2016-01-01

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermally annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.

Interstitial and Interlayer Ion Diffusion Geometry Extraction in Graphitic Nanosphere Battery Materials

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

Gyulassy, Attila; Knoll, Aaron; Lau, Kah Chun

2016-01-01

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermallymore » annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.« less

Interstitial and interlayer ion diffusion geometry extraction in graphitic nanosphere battery materials

DOE PAGES

Gyulassy, Attila; Knoll, Aaron; Lau, Kah Chun; ...

2016-01-31

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermallymore » annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Lastly, our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.« less

The Canadian Hydrological Model (CHM): A multi-scale, variable-complexity hydrological model for cold regions

NASA Astrophysics Data System (ADS)

Marsh, C.; Pomeroy, J. W.; Wheater, H. S.

2016-12-01

There is a need for hydrological land surface schemes that can link to atmospheric models, provide hydrological prediction at multiple scales and guide the development of multiple objective water predictive systems. Distributed raster-based models suffer from an overrepresentation of topography, leading to wasted computational effort that increases uncertainty due to greater numbers of parameters and initial conditions. The Canadian Hydrological Model (CHM) is a modular, multiphysics, spatially distributed modelling framework designed for representing hydrological processes, including those that operate in cold-regions. Unstructured meshes permit variable spatial resolution, allowing coarse resolutions at low spatial variability and fine resolutions as required. Model uncertainty is reduced by lessening the necessary computational elements relative to high-resolution rasters. CHM uses a novel multi-objective approach for unstructured triangular mesh generation that fulfills hydrologically important constraints (e.g., basin boundaries, water bodies, soil classification, land cover, elevation, and slope/aspect). This provides an efficient spatial representation of parameters and initial conditions, as well as well-formed and well-graded triangles that are suitable for numerical discretization. CHM uses high-quality open source libraries and high performance computing paradigms to provide a framework that allows for integrating current state-of-the-art process algorithms. The impact of changes to model structure, including individual algorithms, parameters, initial conditions, driving meteorology, and spatial/temporal discretization can be easily tested. Initial testing of CHM compared spatial scales and model complexity for a spring melt period at a sub-arctic mountain basin. The meshing algorithm reduced the total number of computational elements and preserved the spatial heterogeneity of predictions.

Open abdomen with vacuum-assisted wound closure and mesh-mediated fascial traction in patients with complicated diffuse secondary peritonitis: A single-center 8-year experience.

PubMed

Tolonen, Matti; Mentula, Panu; Sallinen, Ville; Rasilainen, Suvi; Bäcklund, Minna; Leppäniemi, Ari

2017-06-01

Open abdomen (OA) treatment in patients with peritonitis is increasing worldwide. Various temporary abdominal closure devices are being used. This study included patients with complicated diffuse secondary peritonitis, OA, and vacuum-assisted wound closure and mesh-mediated fascial traction (VAWCM). The aim of this study was to describe mortality and major morbidity in terms of delayed primary fascial closure and enteroatmospheric fistula rates. This was a single-academic-center retrospective study of consecutive patients with diffuse peritonitis, OA, and VAWCM between years 2008 and 2016. Descriptive and univariate analyses were performed. Forty-one patients were identified and analyzed. Median age was 59 years, preoperative septic shock was diagnosed in 54% (n = 22), and 59% (n = 24) had a postoperative peritonitis. Mortality was 29% (n = 12), and 76% (n = 31) of patients were admitted in the intensive care unit. The median duration of OA was 7 days with a median of two dressing changes. Delayed primary fascial closure rate among survivors was 92% (n = 33), and enteroatmospheric fistulas developed in 7% (n = 3). In a subgroup analysis, patients with OA in the primary laparotomy for peritonitis (n = 27) were compared with patients with OA in the subsequent laparotomies (n = 14). There were no significant differences between groups. The VAWCM technique in patients with complicated secondary diffuse peritonitis and OA yields excellent results in terms of delayed primary fascial closure rate and a low number of enteroatmospheric fistulas. It seems to be safe to close the abdomen at the index laparotomy, if possible, even if there is a risk of a need of OA later. Therapeutic/care management study, level IV.

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

Model comparisons of the reactive burn model SURF in three ASC codes

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

Whitley, Von Howard; Stalsberg, Krista Lynn; Reichelt, Benjamin Lee

A study of the SURF reactive burn model was performed in FLAG, PAGOSA and XRAGE. In this study, three different shock-to-detonation transition experiments were modeled in each code. All three codes produced similar model results for all the experiments modeled and at all resolutions. Buildup-to-detonation time, particle velocities and resolution dependence of the models was notably similar between the codes. Given the current PBX 9502 equations of state and SURF calibrations, each code is equally capable of predicting the correct detonation time and distance when impacted by a 1D impactor at pressures ranging from 10-16 GPa, as long as themore » resolution of the mesh is not too coarse.« less

Comparison of Several Dissipation Algorithms for Central Difference Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.; Turkel, E.

1997-01-01

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

Francis-99 turbine numerical flow simulation of steady state operation using RANS and RANS/LES turbulence model

NASA Astrophysics Data System (ADS)

Minakov, A.; Platonov, D.; Sentyabov, A.; Gavrilov, A.

2017-01-01

We performed numerical simulation of flow in a laboratory model of a Francis hydroturbine at three regimes, using two eddy-viscosity- (EVM) and a Reynolds stress (RSM) RANS models (realizable k-ɛ, k-ω SST, LRR) and detached-eddy-simulations (DES), as well as large-eddy simulations (LES). Comparison of calculation results with the experimental data was carried out. Unlike the linear EVMs, the RSM, DES, and LES reproduced well the mean velocity components, and pressure pulsations in the diffusor draft tube. Despite relatively coarse meshes and insufficient resolution of the near-wall region, LES, DES also reproduced well the intrinsic flow unsteadiness and the dominant flow structures and the associated pressure pulsations in the draft tube.

MC21 analysis of the MIT PWR benchmark: Hot zero power results

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

Kelly Iii, D. J.; Aviles, B. N.; Herman, B. R.

2013-07-01

MC21 Monte Carlo results have been compared with hot zero power measurements from an operating pressurized water reactor (PWR), as specified in a new full core PWR performance benchmark from the MIT Computational Reactor Physics Group. Included in the comparisons are axially integrated full core detector measurements, axial detector profiles, control rod bank worths, and temperature coefficients. Power depressions from grid spacers are seen clearly in the MC21 results. Application of Coarse Mesh Finite Difference (CMFD) acceleration within MC21 has been accomplished, resulting in a significant reduction of inactive batches necessary to converge the fission source. CMFD acceleration has alsomore » been shown to work seamlessly with the Uniform Fission Site (UFS) variance reduction method. (authors)« less

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

Schnack, D.D.; Lottati, I.; Mikic, Z.

The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

On the dynamics of some grid adaption schemes

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, Helen C.

1994-01-01

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Igneous fractionation and subsolidus equilibration of diogenite meteorites

NASA Technical Reports Server (NTRS)

Mittlefehldt, David W.

1993-01-01

Diogenites are coarse-grained orthopyroxenite breccias of remarkably uniform major element composition. Most diogenites contain homogeneous pyroxene fragments up to 5 cm across of Wo2En74Fs24 composition. Common minor constituents are chromite, olivine, trolite and metal, while silica, plagioclase, merrillite and diopside are trace phases. Diogenites are generally believed to be cumulates from the eucrite parent body, although their relationship with eucrites remains obscure. It has been suggested that some diogenites are residues after partial melting. I have performed EMPA and INAA for major, minor and trace elements on most diogenites, concentrating on coarse-grained mineral and lithic clasts in order to elucidate their igneous formation and subsequent metamorphic history. Major element compositions of diogenites are decoupled from minor and trace element compositions; the latter record an igneous fractionation sequence that is not preserved in the former. Low equilibration temperatures indicate that major element diffusion continued long after crystallization. Diffusion coefficients for trivalent and tetravalent elements in pyroxene are lower than those of divalent elements. Therefore, major element compositions of diogenites may represent means of unknown portions of a cumulate homogenized by diffusion, while minor and trace elements still yield information on their igneous history. The scale of major element equilibration is unknown, but is likely to be on the order of a few cm. Therefore, the diogenite precursors may have consisted largely of cm-sized, igneously zoned orthopyroxene grains, which were subsequently annealed during slow cooling, obliterating major element zoning but preserving minor and trace incompatible element zoning.

Permeation-Enhancing Effects and Mechanisms of Borneol and Menthol on Ligustrazine: A Multiscale Study using In Vitro and Coarse-Grained Molecular Dynamics Simulation Methods.

PubMed

Dai, Xingxing; Wang, Ran; Wu, Zhimin; Guo, Shujuan; Yang, Chang; Ma, Lina; Chen, Liping; Shi, Xinyuan; Qiao, Yanjiang

2018-06-20

Borneol (BO) and menthol (MEN) are two widely used natural permeation enhancers in the transdermal drug delivery system. In previous studies, their permeation enhancement effects and mechanisms of action on the hydrophobic drug osthole (logP=3.8) and hydrophilic drug 5-fluorouracil (logP=-0.9) have been studied. In this study, ligustrazine (LTZ), whose logP is 1.3, was used as a model drug to provide a comprehensive understanding of the influence of its logP on the permeation-enhancing effects of BO and MEN. Both BO and MEN enhanced the permeation of LTZ through the skin stratum corneum, as determined using the modified Franz diffusion cell experiment. The enhancement mechanisms were illustrated by coarse-grained molecular dynamics simulations as follows: at low concentrations, the enhancing ratio of MEN was higher than that of BO because of the stronger perturbation effects of MEN on the lipid bilayer, making it looser and facilitating LTZ diffusion. However, at high concentrations, in addition to the diffusion mechanism, BO induced the formation of water channels to improve the permeation of LTZ; however, MEN had no significant effects through this mechanism. Their results were different from those found with osthole and 5-fluorouracil and have been discussed in this paper. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

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

De Corato, M., E-mail: marco.decorato@unina.it; Slot, J.J.M., E-mail: j.j.m.slot@tue.nl; Hütter, M., E-mail: m.huetter@tue.nl

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered withinmore » the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.« less

Zero dimensional model of atmospheric SMD discharge and afterglow in humid air

NASA Astrophysics Data System (ADS)

Smith, Ryan; Kemaneci, Efe; Offerhaus, Bjoern; Stapelmann, Katharina; Peter Brinkmann, Ralph

2016-09-01

A novel mesh-like Surface Micro Discharge (SMD) device designed for surface wound treatment is simulated by multiple time-scaled zero-dimensional models. The chemical dynamics of the discharge are resolved in time at atmospheric pressure in humid conditions. Simulated are the particle densities of electrons, 26 ionic species, and 26 reactive neutral species including: O3, NO, and HNO3. The total of 53 described species are constrained by 624 reactions within the simulated plasma discharge volume. The neutral species are allowed to diffuse into a diffusive gas regime which is of primary interest. Two interdependent zero-dimensional models separated by nine orders of magnitude in temporal resolution are used to accomplish this; thereby reducing the computational load. Through variation of control parameters such as: ignition frequency, deposited power density, duty cycle, humidity level, and N2 content, the ideal operation conditions for the SMD device can be predicted. The described model has been verified by matching simulation parameters and comparing results to that of previous works. Current operating conditions of the experimental mesh-like SMD were matched and results are compared to the simulations. Work supported by SFB TR 87.

Realistic mass ratio magnetic reconnection simulations with the Multi Level Multi Domain method

NASA Astrophysics Data System (ADS)

Innocenti, Maria Elena; Beck, Arnaud; Lapenta, Giovanni; Markidis, Stefano

2014-05-01

Space physics simulations with the ambition of realistically representing both ion and electron dynamics have to be able to cope with the huge scale separation between the electron and ion parameters while respecting the stability constraints of the numerical method of choice. Explicit Particle In Cell (PIC) simulations with realistic mass ratio are limited in the size of the problems they can tackle by the restrictive stability constraints of the explicit method (Birdsall and Langdon, 2004). Many alternatives are available to reduce such computation costs. Reduced mass ratios can be used, with the caveats highlighted in Bret and Dieckmann (2010). Fully implicit (Chen et al., 2011a; Markidis and Lapenta, 2011) or semi implicit (Vu and Brackbill, 1992; Lapenta et al., 2006; Cohen et al., 1989) methods can bypass the strict stability constraints of explicit PIC codes. Adaptive Mesh Refinement (AMR) techniques (Vay et al., 2004; Fujimoto and Sydora, 2008) can be employed to change locally the simulation resolution. We focus here on the Multi Level Multi Domain (MLMD) method introduced in Innocenti et al. (2013) and Beck et al. (2013). The method combines the advantages of implicit algorithms and adaptivity. Two levels are fully simulated with fields and particles. The so called "refined level" simulates a fraction of the "coarse level" with a resolution RF times bigger than the coarse level resolution, where RF is the Refinement Factor between the levels. This method is particularly suitable for magnetic reconnection simulations (Biskamp, 2005), where the characteristic Ion and Electron Diffusion Regions (IDR and EDR) develop at the ion and electron scales respectively (Daughton et al., 2006). In Innocenti et al. (2013) we showed that basic wave and instability processes are correctly reproduced by MLMD simulations. In Beck et al. (2013) we applied the technique to plasma expansion and magnetic reconnection problems. We showed that notable computational time savings can be achieved. More importantly, we were able to correctly reproduce EDR features, such as the inversion layer of the electric field observed in Chen et al. (2011b), with a MLMD simulation at a significantly lower cost. Here, we present recent results on EDR dynamics achieved with the MLMD method and a realistic mass ratio.

Coarse-Graining of Polymer Dynamics via Energy Renormalization

NASA Astrophysics Data System (ADS)

Xia, Wenjie; Song, Jake; Phelan, Frederick; Douglas, Jack; Keten, Sinan

The computational prediction of the properties of polymeric materials to serve the needs of materials design and prediction of their performance is a grand challenge due to the prohibitive computational times of all-atomistic (AA) simulations. Coarse-grained (CG) modeling is an essential strategy for making progress on this problem. While there has been intense activity in this area, effective methods of coarse-graining have been slow to develop. Our approach to this fundamental problem starts from the observation that integrating out degrees of freedom of the AA model leads to a strong modification of the configurational entropy and cohesive interaction. Based on this observation, we propose a temperature-dependent systematic renormalization of the cohesive interaction in the CG modeling to recover the thermodynamic modifications in the system and the dynamics of the AA model. Here, we show that this energy renormalization approach to CG can faithfully estimate the diffusive, segmental and glassy dynamics of the AA model over a large temperature range spanning from the Arrhenius melt to the non-equilibrium glassy states. Our proposed CG strategy offers a promising strategy for developing thermodynamically consistent CG models with temperature transferability.

Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation.

PubMed

Erban, Radek; Kevrekidis, Ioannis G; Adalsteinsson, David; Elston, Timothy C

2006-02-28

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Phi and of a state-dependent effective diffusion coefficient D that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

Development and Application of Agglomerated Multigrid Methods for Complex Geometries

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.

2010-01-01

We report progress in the development of agglomerated multigrid techniques for fully un- structured grids in three dimensions, building upon two previous studies focused on efficiently solving a model diffusion equation. We demonstrate a robust fully-coarsened agglomerated multigrid technique for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A signi cant speed-up in computer time is demonstrated for a model diffusion problem, the Euler equations, and the Reynolds-averaged Navier-Stokes equations for 3D realistic complex geometries.

Application of the Hilbert space average method on heat conduction models.

PubMed

Michel, Mathias; Gemmer, Jochen; Mahler, Günter

2006-01-01

We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy diffusion with respect to a coarse-grained description for almost all initial states. Close to the respective equilibrium, we investigate this behavior in terms of heat transport and derive the heat conduction coefficient. Thus, we are able to show that both heat (energy) diffusive behavior as well as Fourier's law follows from and is compatible with a reversible Schrödinger dynamics on the complete level of description.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Ion Thruster Discharge Performance Per Magnetic Field Topography

NASA Technical Reports Server (NTRS)

Wirz, Richard E.; Goebel, Dan

2006-01-01

DC-ION is a detailed computational model for predicting the plasma characteristics of rain-cusp ion thrusters. The advanced magnetic field meshing algorithm used by DC-ION allows precise treatment of the secondary electron flow. This capability allows self-consistent estimates of plasma potential that improves the overall consistency of the results of the discharge model described in Reference [refJPC05mod1]. Plasma potential estimates allow the model to predict the onset of plasma instabilities, and important shortcoming of the previous model for optimizing the design of discharge chambers. A magnetic field mesh simplifies the plasma flow calculations, for both the ions and the secondary electrons, and significantly reduces numerical diffusion that can occur with meshes not aligned with the magnetic field. Comparing the results of this model to experimental data shows that the behavior of the primary electrons, and the precise manner of their confinement, dictates the fundamental efficiency of ring-cusp. This correlation is evident in simulations of the conventionally sized NSTAR thruster (30 cm diameter) and the miniature MiXI thruster (3 cm diameter).

Finite element modeling of mass transport in high-Péclet cardiovascular flows

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Fluorescence correlation spectroscopy diffusion laws to probe the submicron cell membrane organization.

PubMed

Wawrezinieck, Laure; Rigneault, Hervé; Marguet, Didier; Lenne, Pierre-François

2005-12-01

To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.

Adaptive unified continuum FEM modeling of a 3D FSI benchmark problem.

PubMed

Jansson, Johan; Degirmenci, Niyazi Cem; Hoffman, Johan

2017-09-01

In this paper, we address a 3D fluid-structure interaction benchmark problem that represents important characteristics of biomedical modeling. We present a goal-oriented adaptive finite element methodology for incompressible fluid-structure interaction based on a streamline diffusion-type stabilization of the balance equations for mass and momentum for the entire continuum in the domain, which is implemented in the Unicorn/FEniCS software framework. A phase marker function and its corresponding transport equation are introduced to select the constitutive law, where the mesh tracks the discontinuous fluid-structure interface. This results in a unified simulation method for fluids and structures. We present detailed results for the benchmark problem compared with experiments, together with a mesh convergence study. Copyright © 2016 John Wiley & Sons, Ltd.

An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl Lawrence

1993-01-01

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

A Finite Difference Method for Modeling Migration of Impurities in Multilayer Systems

NASA Astrophysics Data System (ADS)

Tosa, V.; Kovacs, Katalin; Mercea, P.; Piringer, O.

2008-09-01

A finite difference method to solve the one-dimensional diffusion of impurities in a multilayer system was developed for the special case in which a partition coefficient K impose a ratio of the concentrations at the interface between two adiacent layers. The fictitious point method was applied to derive the algebraic equations for the mesh points at the interface, while for the non-uniform mesh points within the layers a combined method was used. The method was tested and then applied to calculate migration of impurities from multilayer systems into liquids or solids samples, in migration experiments performed for quality testing purposes. An application was developed in the field of impurities migrations from multilayer plastic packagings into food, a problem of increasing importance in food industry.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

NASA Astrophysics Data System (ADS)

Sadeghi, Mohsen; Weikl, Thomas R.; Noé, Frank

2018-01-01

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Nonlinear Computational Aeroelasticity: Formulations and Solution Algorithms

DTIC Science & Technology

2003-03-01

problem is proposed. Fluid-structure coupling algorithms are then discussed with some emphasis on distributed computing strategies. Numerical results...the structure and the exchange of structure motion to the fluid. The computational fluid dynamics code PFES is our finite element code for the numerical ...unstructured meshes). It was numerically demonstrated [1-3] that EBS can be less diffusive than SUPG [4-6] and the standard Finite Volume schemes

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

PubMed

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at an early stage of development. In this paper we demonstrate, in a series of examples with high relevance to the molecular systems biology community, that the proposed software framework is a useful tool for both practitioners and developers of spatial stochastic simulation algorithms. Through the combined efforts of algorithm development and improved modeling accuracy, increasingly complex biological models become feasible to study through computational methods. URDME is freely available at http://www.urdme.org.

On a turbulent wall model to predict hemolysis numerically in medical devices

NASA Astrophysics Data System (ADS)

Lee, Seunghun; Chang, Minwook; Kang, Seongwon; Hur, Nahmkeon; Kim, Wonjung

2017-11-01

Analyzing degradation of red blood cells is very important for medical devices with blood flows. The blood shear stress has been recognized as the most dominant factor for hemolysis in medical devices. Compared to laminar flows, turbulent flows have higher shear stress values in the regions near the wall. In case of predicting hemolysis numerically, this phenomenon can require a very fine mesh and large computational resources. In order to resolve this issue, the purpose of this study is to develop a turbulent wall model to predict the hemolysis more efficiently. In order to decrease the numerical error of hemolysis prediction in a coarse grid resolution, we divided the computational domain into two regions and applied different approaches to each region. In the near-wall region with a steep velocity gradient, an analytic approach using modeled velocity profile is applied to reduce a numerical error to allow a coarse grid resolution. We adopt the Van Driest law as a model for the mean velocity profile. In a region far from the wall, a regular numerical discretization is applied. The proposed turbulent wall model is evaluated for a few turbulent flows inside a cannula and centrifugal pumps. The results present that the proposed turbulent wall model for hemolysis improves the computational efficiency significantly for engineering applications. Corresponding author.

Mesoscale Fracture Analysis of Multiphase Cementitious Composites Using Peridynamics

PubMed Central

Yaghoobi, Amin; Chorzepa, Mi G.; Kim, S. Sonny; Durham, Stephan A.

2017-01-01

Concrete is a complex heterogeneous material, and thus, it is important to develop numerical modeling methods to enhance the prediction accuracy of the fracture mechanism. In this study, a two-dimensional mesoscale model is developed using a non-ordinary state-based peridynamic (NOSBPD) method. Fracture in a concrete cube specimen subjected to pure tension is studied. The presence of heterogeneous materials consisting of coarse aggregates, interfacial transition zones, air voids and cementitious matrix is characterized as particle points in a two-dimensional mesoscale model. Coarse aggregates and voids are generated using uniform probability distributions, while a statistical study is provided to comprise the effect of random distributions of constituent materials. In obtaining the steady-state response, an incremental and iterative solver is adopted for the dynamic relaxation method. Load-displacement curves and damage patterns are compared with available experimental and finite element analysis (FEA) results. Although the proposed model uses much simpler material damage models and discretization schemes, the load-displacement curves show no difference from the FEA results. Furthermore, no mesh refinement is necessary, as fracture is inherently characterized by bond breakages. Finally, a sensitivity study is conducted to understand the effect of aggregate volume fraction and porosity on the load capacity of the proposed mesoscale model. PMID:28772518

A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

NASA Astrophysics Data System (ADS)

Stolk, Christiaan C.

2016-06-01

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system

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

Zhang, Jie; Ni, Ming-Jiu, E-mail: mjni@ucas.ac.cn

2014-01-01

The numerical simulation of Magnetohydrodynamics (MHD) flows with complex boundaries has been a topic of great interest in the development of a fusion reactor blanket for the difficulty to accurately simulate the Hartmann layers and side layers along arbitrary geometries. An adaptive version of a consistent and conservative scheme has been developed for simulating the MHD flows. Besides, the present study forms the first attempt to apply the cut-cell approach for irregular wall-bounded MHD flows, which is more flexible and conveniently implemented under adaptive mesh refinement (AMR) technique. It employs a Volume-of-Fluid (VOF) approach to represent the fluid–conducting wall interfacemore » that makes it possible to solve the fluid–solid coupling magnetic problems, emphasizing at how electric field solver is implemented when conductivity is discontinuous in cut-cell. For the irregular cut-cells, the conservative interpolation technique is applied to calculate the Lorentz force at cell-center. On the other hand, it will be shown how consistent and conservative scheme is implemented on fine/coarse mesh boundaries when using AMR technique. Then, the applied numerical schemes are validated by five test simulations and excellent agreement was obtained for all the cases considered, simultaneously showed good consistency and conservative properties.« less

Simultaneous multiple view high resolution surface geometry acquisition using structured light and mirrors.

PubMed

Basevi, Hector R A; Guggenheim, James A; Dehghani, Hamid; Styles, Iain B

2013-03-25

Knowledge of the surface geometry of an imaging subject is important in many applications. This information can be obtained via a number of different techniques, including time of flight imaging, photogrammetry, and fringe projection profilometry. Existing systems may have restrictions on instrument geometry, require expensive optics, or require moving parts in order to image the full surface of the subject. An inexpensive generalised fringe projection profilometry system is proposed that can account for arbitrarily placed components and use mirrors to expand the field of view. It simultaneously acquires multiple views of an imaging subject, producing a cloud of points that lie on its surface, which can then be processed to form a three dimensional model. A prototype of this system was integrated into an existing Diffuse Optical Tomography and Bioluminescence Tomography small animal imaging system and used to image objects including a mouse-shaped plastic phantom, a mouse cadaver, and a coin. A surface mesh generated from surface capture data of the mouse-shaped plastic phantom was compared with ideal surface points provided by the phantom manufacturer, and 50% of points were found to lie within 0.1mm of the surface mesh, 82% of points were found to lie within 0.2mm of the surface mesh, and 96% of points were found to lie within 0.4mm of the surface mesh.

Fabrication, pore structure and compressive behavior of anisotropic porous titanium for human trabecular bone implant applications.

PubMed

Li, Fuping; Li, Jinshan; Xu, Guangsheng; Liu, Gejun; Kou, Hongchao; Zhou, Lian

2015-06-01

Porous titanium with average pore size of 100-650 μm and porosity of 30-70% was fabricated by diffusion bonding of titanium meshes. Pore structure was characterized by Micro-CT scan and SEM. Compressive behavior of porous titanium in the out-of-plane direction was studied. The effect of porosity and pore size on the compressive properties was also discussed based on the deformation mode. The results reveal that the fabrication process can control the porosity precisely. The average pore size of porous titanium can be tailored by adjusting the pore size of titanium meshes. The fabricated porous titanium possesses an anisotropic structure with square pores in the in-plane direction and elongated pores in the out-of-plane direction. The compressive Young's modulus and yield stress are in the range of 1-7.5 GPa and 10-110 MPa, respectively. The dominant compressive deformation mode is buckling of mesh wires, but some uncoordinated buckling is present in porous titanium with lower porosity. Relationship between compressive properties and porosity conforms well to the Gibson-Ashby model. The effect of pore size on compressive properties is fundamentally ascribed to the aspect ratio of titanium meshes. Porous titanium with 60-70% porosity has potential for trabecular bone implant applications. Copyright © 2015 Elsevier Ltd. All rights reserved.

Dynamic subfilter-scale stress model for large-eddy simulations

NASA Astrophysics Data System (ADS)

Rouhi, A.; Piomelli, U.; Geurts, B. J.

2016-08-01

We present a modification of the integral length-scale approximation (ILSA) model originally proposed by Piomelli et al. [Piomelli et al., J. Fluid Mech. 766, 499 (2015), 10.1017/jfm.2015.29] and apply it to plane channel flow and a backward-facing step. In the ILSA models the length scale is expressed in terms of the integral length scale of turbulence and is determined by the flow characteristics, decoupled from the simulation grid. In the original formulation the model coefficient was constant, determined by requiring a desired global contribution of the unresolved subfilter scales (SFSs) to the dissipation rate, known as SFS activity; its value was found by a set of coarse-grid calculations. Here we develop two modifications. We de-fine a measure of SFS activity (based on turbulent stresses), which adds to the robustness of the model, particularly at high Reynolds numbers, and removes the need for the prior coarse-grid calculations: The model coefficient can be computed dynamically and adapt to large-scale unsteadiness. Furthermore, the desired level of SFS activity is now enforced locally (and not integrated over the entire volume, as in the original model), providing better control over model activity and also improving the near-wall behavior of the model. Application of the local ILSA to channel flow and a backward-facing step and comparison with the original ILSA and with the dynamic model of Germano et al. [Germano et al., Phys. Fluids A 3, 1760 (1991), 10.1063/1.857955] show better control over the model contribution in the local ILSA, while the positive properties of the original formulation (including its higher accuracy compared to the dynamic model on coarse grids) are maintained. The backward-facing step also highlights the advantage of the decoupling of the model length scale from the mesh.

A network of discrete events for the representation and analysis of diffusion dynamics.

PubMed

Pintus, Alberto M; Pazzona, Federico G; Demontis, Pierfranco; Suffritti, Giuseppe B

2015-11-14

We developed a coarse-grained description of the phenomenology of diffusive processes, in terms of a space of discrete events and its representation as a network. Once a proper classification of the discrete events underlying the diffusive process is carried out, their transition matrix is calculated on the basis of molecular dynamics data. This matrix can be represented as a directed, weighted network where nodes represent discrete events, and the weight of edges is given by the probability that one follows the other. The structure of this network reflects dynamical properties of the process of interest in such features as its modularity and the entropy rate of nodes. As an example of the applicability of this conceptual framework, we discuss here the physics of diffusion of small non-polar molecules in a microporous material, in terms of the structure of the corresponding network of events, and explain on this basis the diffusivity trends observed. A quantitative account of these trends is obtained by considering the contribution of the various events to the displacement autocorrelation function.

Statistical Mechanical Theory of Penetrant Diffusion in Polymer Melts and Glasses

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth

We generalize our force-level, self-consistent nonlinear Langevin equation theory of activated diffusion of a dilute spherical penetrant in hard sphere fluids to predict the long-time diffusivity of molecular penetrants in supercooled polymer liquids and non-aging glasses. Chemical complexity is treated using an a priori mapping to a temperature-dependent hard sphere mixture model where polymers are disconnected into effective spheres based on the Kuhn length as the relevant coarse graining scale. A key parameter for mobility is the penetrant to polymer segment diameter ratio, R. Our calculations agree well with experimental measurements for a wide range of temperatures, penetrant sizes (from gas molecules with R ~0.3 to aromatic molecules with R ~1) and diverse amorphous polymers, over 10 decades variation of penetrant diffusivity. Structural parameter transferability is good. We have also formulated a theory at finite penetrant loading for the coupled penetrant-polymer dynamics in chemically (nearly) matched mixtures (e.g., toluene-polystyrene) which captures well the increase of penetrant diffusivity and decrease of polymer matrix vitrification temperature with increasing loading.

Characterization of fly ash from low-sulfur and high-sulfur coal sources: Partitioning of carbon and trace elements with particle size

USGS Publications Warehouse

Hower, J.C.; Trimble, A.S.; Eble, C.F.; Palmer, C.A.; Kolker, A.

1999-01-01

Fly ash samples were collected in November and December of 1994, from generating units at a Kentucky power station using high- and low-sulfur feed coals. The samples are part of a two-year study of the coal and coal combustion byproducts from the power station. The ashes were wet screened at 100, 200, 325, and 500 mesh (150, 75, 42, and 25 ??m, respectively). The size fractions were then dried, weighed, split for petrographic and chemical analysis, and analyzed for ash yield and carbon content. The low-sulfur "heavy side" and "light side" ashes each have a similar size distribution in the November samples. In contrast, the December fly ashes showed the trend observed in later months, the light-side ash being finer (over 20 % more ash in the -500 mesh [-25 ??m] fraction) than the heavy-side ash. Carbon tended to be concentrated in the coarse fractions in the December samples. The dominance of the -325 mesh (-42 ??m) fractions in the overall size analysis implies, though, that carbon in the fine sizes may be an important consideration in the utilization of the fly ash. Element partitioning follows several patterns. Volatile elements, such as Zn and As, are enriched in the finer sizes, particularly in fly ashes collected at cooler, light-side electrostatic precipitator (ESP) temperatures. The latter trend is a function of precipitation at the cooler-ESP temperatures and of increasing concentration with the increased surface area of the finest fraction. Mercury concentrations are higher in high-carbon fly ashes, suggesting Hg adsorption on the fly ash carbon. Ni and Cr are associated, in part, with the spinel minerals in the fly ash. Copyright ?? 1999 Taylor & Francis.

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

NASA Technical Reports Server (NTRS)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

The Osher scheme for non-equilibrium reacting flows

NASA Technical Reports Server (NTRS)

Suresh, Ambady; Liou, Meng-Sing

1992-01-01

An extension of the Osher upwind scheme to nonequilibrium reacting flows is presented. Owing to the presence of source terms, the Riemann problem is no longer self-similar and therefore its approximate solution becomes tedious. With simplicity in mind, a linearized approach which avoids an iterative solution is used to define the intermediate states and sonic points. The source terms are treated explicitly. Numerical computations are presented to demonstrate the feasibility, efficiency and accuracy of the proposed method. The test problems include a ZND (Zeldovich-Neumann-Doring) detonation problem for which spurious numerical solutions which propagate at mesh speed have been observed on coarse grids. With the present method, a change of limiter causes the solution to change from the physically correct CJ detonation solution to the spurious weak detonation solution.

Analysis and improvements of Adaptive Particle Refinement (APR) through CPU time, accuracy and robustness considerations

NASA Astrophysics Data System (ADS)

Chiron, L.; Oger, G.; de Leffe, M.; Le Touzé, D.

2018-02-01

While smoothed-particle hydrodynamics (SPH) simulations are usually performed using uniform particle distributions, local particle refinement techniques have been developed to concentrate fine spatial resolutions in identified areas of interest. Although the formalism of this method is relatively easy to implement, its robustness at coarse/fine interfaces can be problematic. Analysis performed in [16] shows that the radius of refined particles should be greater than half the radius of unrefined particles to ensure robustness. In this article, the basics of an Adaptive Particle Refinement (APR) technique, inspired by AMR in mesh-based methods, are presented. This approach ensures robustness with alleviated constraints. Simulations applying the new formalism proposed achieve accuracy comparable to fully refined spatial resolutions, together with robustness, low CPU times and maintained parallel efficiency.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

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

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

Duranty, Edward R.; Baschnagel, Jörg; Dadmun, Mark

Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this paper, coarse-grained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary themore » connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. Finally, the results of this work indicate that PS-r-PMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer’s local volume.« less

One-dimensional pore pressure diffusion of different grain-fluid mixtures

NASA Astrophysics Data System (ADS)

von der Thannen, Magdalena; Kaitna, Roland

2015-04-01

During the release and the flow of fully saturated debris, non-hydrostatic fluid pressure can build up and probably dissipate during the event. This excess fluid pressure has a strong influence on the flow and deposition behaviour of debris flows. Therefore, we investigate the influence of mixture composition on the dissipation of non-hydrostatic fluid pressures. For this we use a cylindrical pipe of acrylic glass with installed pore water pressure sensors in different heights and measure the evolution of the pore water pressure over time. Several mixtures with variable content of fine sediment (silt and clay) and variable content of coarse sediment (with fixed relative fractions of grains between 2 and 32 mm) are tested. For the fines two types of clay (smectite and kaolinite) and loam (Stoober Lehm) are used. The analysis is based on the one-dimensional consolidation theory which uses a diffusion coefficient D to model the decay of excess fluid pressure over time. Starting from artificially induced super-hydrostatic fluid pressures, we find dissipation coefficients ranging from 10-5 m²/s for liquid mixtures to 10-8 m²/s for viscous mixtures. The results for kaolinite and smectite are quite similar. For our limited number of mixtures the effect of fines content is more pronounced than the effect of different amounts of coarse particles.

PSO-Assisted Development of New Transferable Coarse-Grained Water Models.

PubMed

Bejagam, Karteek K; Singh, Samrendra; An, Yaxin; Berry, Carter; Deshmukh, Sanket A

2018-02-15

We have employed two-to-one mapping scheme to develop three coarse-grained (CG) water models, namely, 1-, 2-, and 3-site CG models. Here, for the first time, particle swarm optimization (PSO) and gradient descent methods were coupled to optimize the force-field parameters of the CG models to reproduce the density, self-diffusion coefficient, and dielectric constant of real water at 300 K. The CG MD simulations of these new models conducted with various timesteps, for different system sizes, and at a range of different temperatures are able to predict the density, self-diffusion coefficient, dielectric constant, surface tension, heat of vaporization, hydration free energy, and isothermal compressibility of real water with excellent accuracy. The 1-site model is ∼3 and ∼4.5 times computationally more efficient than 2- and 3-site models, respectively. To utilize the speed of 1-site model and electrostatic interactions offered by 2- and 3-site models, CG MD simulations of 1:1 combination of 1- and 2-/3-site models were performed at 300 K. These mixture simulations could also predict the properties of real water with good accuracy. Two new CG models of benzene, consisting of beads with and without partial charges, were developed. All three water models showed good capacity to solvate these benzene models.

DNS/LES Simulations of Separated Flows at High Reynolds Numbers

NASA Technical Reports Server (NTRS)

Balakumar, P.

2015-01-01

Direct numerical simulations (DNS) and large-eddy simulations (LES) simulations of flow through a periodic channel with a constriction are performed using the dynamic Smagorinsky model at two Reynolds numbers of 2800 and 10595. The LES equations are solved using higher order compact schemes. DNS are performed for the lower Reynolds number case using a fine grid and the data are used to validate the LES results obtained with a coarse and a medium size grid. LES simulations are also performed for the higher Reynolds number case using a coarse and a medium size grid. The results are compared with an existing reference data set. The DNS and LES results agreed well with the reference data. Reynolds stresses, sub-grid eddy viscosity, and the budgets for the turbulent kinetic energy are also presented. It is found that the turbulent fluctuations in the normal and spanwise directions have the same magnitude. The turbulent kinetic energy budget shows that the production peaks near the separation point region and the production to dissipation ratio is very high on the order of five in this region. It is also observed that the production is balanced by the advection, diffusion, and dissipation in the shear layer region. The dominant term is the turbulent diffusion that is about two times the molecular dissipation.

Coarse-grained Brownian dynamics simulations of protein translocation through nanopores

NASA Astrophysics Data System (ADS)

Lee, Po-Hsien; Helms, Volkhard; Geyer, Tihamér

2012-10-01

A crucial process in biological cells is the translocation of newly synthesized proteins across cell membranes via integral membrane protein pores termed translocons. Recent improved techniques now allow producing artificial membranes with pores of similar dimensions of a few nm as the translocon system. For the translocon system, the protein has to be unfolded, whereas the artificial pores are wide enough so that small proteins can pass through even when folded. To study how proteins permeate through such membrane pores, we used coarse-grained Brownian dynamics simulations where the proteins were modeled as single beads or bead-spring polymers for both folded and unfolded states. The pores were modeled as cylindrical holes through the membrane with various radii and lengths. Diffusion was driven by a concentration gradient created across the porous membrane. Our results for both folded and unfolded configurations show the expected reciprocal relation between the flow rate and the pore length in agreement with an analytical solution derived by Brunn et al. [Q. J. Mech. Appl. Math. 37, 311 (1984)], 10.1093/qjmam/37.2.311. Furthermore, we find that the geometric constriction by the narrow pore leads to an accumulation of proteins at the pore entrance, which in turn compensates for the reduced diffusivity of the proteins inside the pore.

Multiscale approach to the determination of the photoactive yellow protein signaling state ensemble.

PubMed

A Rohrdanz, Mary; Zheng, Wenwei; Lambeth, Bradley; Vreede, Jocelyne; Clementi, Cecilia

2014-10-01

The nature of the optical cycle of photoactive yellow protein (PYP) makes its elucidation challenging for both experiment and theory. The long transition times render conventional simulation methods ineffective, and yet the short signaling-state lifetime makes experimental data difficult to obtain and interpret. Here, through an innovative combination of computational methods, a prediction and analysis of the biological signaling state of PYP is presented. Coarse-grained modeling and locally scaled diffusion map are first used to obtain a rough bird's-eye view of the free energy landscape of photo-activated PYP. Then all-atom reconstruction, followed by an enhanced sampling scheme; diffusion map-directed-molecular dynamics are used to focus in on the signaling-state region of configuration space and obtain an ensemble of signaling state structures. To the best of our knowledge, this is the first time an all-atom reconstruction from a coarse grained model has been performed in a relatively unexplored region of molecular configuration space. We compare our signaling state prediction with previous computational and more recent experimental results, and the comparison is favorable, which validates the method presented. This approach provides additional insight to understand the PYP photo cycle, and can be applied to other systems for which more direct methods are impractical.

Accurate, meshless methods for magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.; Raives, Matthias J.

2016-01-01

Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

NASA Technical Reports Server (NTRS)

Maliassov, Serguei

1996-01-01

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Integration of experimental and computational methods for identifying geometric, thermal and diffusive properties of biomaterials

NASA Astrophysics Data System (ADS)

Weres, Jerzy; Kujawa, Sebastian; Olek, Wiesław; Czajkowski, Łukasz

2016-04-01

Knowledge of physical properties of biomaterials is important in understanding and designing agri-food and wood processing industries. In the study presented in this paper computational methods were developed and combined with experiments to enhance identification of agri-food and forest product properties, and to predict heat and water transport in such products. They were based on the finite element model of heat and water transport and supplemented with experimental data. Algorithms were proposed for image processing, geometry meshing, and inverse/direct finite element modelling. The resulting software system was composed of integrated subsystems for 3D geometry data acquisition and mesh generation, for 3D geometry modelling and visualization, and for inverse/direct problem computations for the heat and water transport processes. Auxiliary packages were developed to assess performance, accuracy and unification of data access. The software was validated by identifying selected properties and using the estimated values to predict the examined processes, and then comparing predictions to experimental data. The geometry, thermal conductivity, specific heat, coefficient of water diffusion, equilibrium water content and convective heat and water transfer coefficients in the boundary layer were analysed. The estimated values, used as an input for simulation of the examined processes, enabled reduction in the uncertainty associated with predictions.

Radiosity diffusion model in 3D

NASA Astrophysics Data System (ADS)

Riley, Jason D.; Arridge, Simon R.; Chrysanthou, Yiorgos; Dehghani, Hamid; Hillman, Elizabeth M. C.; Schweiger, Martin

2001-11-01

We present the Radiosity-Diffusion model in three dimensions(3D), as an extension to previous work in 2D. It is a method for handling non-scattering spaces in optically participating media. We present the extension of the model to 3D including an extension to the model to cope with increased complexity of the 3D domain. We show that in 3D more careful consideration must be given to the issues of meshing and visibility to model the transport of light within reasonable computational bounds. We demonstrate the model to be comparable to Monte-Carlo simulations for selected geometries, and show preliminary results of comparisons to measured time-resolved data acquired on resin phantoms.

Mechanism of Facilitated Diffusion during a DNA Search in Crowded Environments.

PubMed

Krepel, Dana; Gomez, David; Klumpp, Stefan; Levy, Yaakov

2016-11-03

The key feature explaining the rapid recognition of a DNA target site by its protein lies in the combination of one- and three-dimensional (1D and 3D) diffusion, which allows efficient scanning of the many alternative sites. This facilitated diffusion mechanism is expected to be affected by cellular conditions, particularly crowding, given that up to 40% of the total cellular volume may by occupied by macromolecules. Using coarse-grained molecular dynamics and Monte Carlo simulations, we show that the crowding particles can enhance facilitated diffusion and accelerate search kinetics. This effect originates from a trade-off between 3D and 1D diffusion. The 3D diffusion coefficient is lower under crowded conditions, but it has little influence because the excluded volume effect of molecular crowding restricts its use. Largely prevented from using 3D diffusion, the searching protein dramatically increases its use of the hopping search mode, which results in a higher linear diffusion coefficient. The coefficient of linear diffusion also increases under crowded conditions as a result of increased collisions between the crowding particles and the searching protein. Overall, less 3D diffusion coupled with an increase in the use of the hopping and speed of 1D diffusion results in faster search kinetics under crowded conditions. Our study shows that the search kinetics and mechanism are modulated not only by the crowding occupancy but also by the properties of the crowding particles and the salt concentration.

Space-time VMS computation of wind-turbine rotor and tower aerodynamics

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; McIntyre, Spenser; Kostov, Nikolay; Kolesar, Ryan; Habluetzel, Casey

2014-01-01

We present the space-time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

Space-Time VMS Computation of Wind-Turbine Rotor and Tower Aerodynamics

NASA Astrophysics Data System (ADS)

McIntyre, Spenser W.

This thesis is on the space{time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent ows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called "DSD/SST-VMST" method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of ows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this "ST/NURBS Mesh Update Method (STNMUM)." The STNMUM increases computational efficiency in terms of computer time and storage, and computational exibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys

NASA Astrophysics Data System (ADS)

Balakrishna, Ananya Renuka; Carter, W. Craig

2018-04-01

Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.

Diffusion of copolymers composed of monomers with drastically different friction factors in copolymer/homopolymer blends

DOE PAGES

Duranty, Edward R.; Baschnagel, Jörg; Dadmun, Mark

2017-02-07

Copolymers are commonly used as interface modifiers that allow for the compatibilization of polymer components in a blend. For copolymers to function as a compatibilizer, they must diffuse through the matrix of the blend to the interface between the two blend components. The diffusivity of a copolymer in a blend matrix therefore becomes important in determining good candidates for use as compatibilizers. In this paper, coarse-grained Monte Carlo simulations using the bond fluctuation model modified with an overlap penalty have been developed to study the diffusive behavior of PS/PMMA random copolymers in a PMMA homopolymer blend. The simulations vary themore » connectivity between different monomers, the thermodynamic interactions between the monomers which manifest within a chain, and between copolymer and homopolymer matrix and define the monomer friction coefficient of each component independently, allowing for the determination of the combined effect of these parameters on copolymer chain diffusion. Finally, the results of this work indicate that PS-r-PMMA copolymer diffusion is not linearly dependent on the copolymer composition on a logarithmic scale, but its diffusion is a balance of the kinetics governed by the dominant motion of the faster styrene monomers and thermodynamics, which are governed by the concentration of styrene monomer within a given monomer’s local volume.« less

Forwarding techniques for IP fragmented packets in a real 6LoWPAN network.

PubMed

Ludovici, Alessandro; Calveras, Anna; Casademont, Jordi

2011-01-01

Wireless Sensor Networks (WSNs) are attracting more and more interest since they offer a low-cost solution to the problem of providing a means to deploy large sensor networks in a number of application domains. We believe that a crucial aspect to facilitate WSN diffusion is to make them interoperable with external IP networks. This can be achieved by using the 6LoWPAN protocol stack. 6LoWPAN enables the transmission of IPv6 packets over WSNs based on the IEEE 802.15.4 standard. IPv6 packet size is considerably larger than that of IEEE 802.15.4 data frame. To overcome this problem, 6LoWPAN introduces an adaptation layer between the network and data link layers, allowing IPv6 packets to be adapted to the lower layer constraints. This adaptation layer provides fragmentation and header compression of IP packets. Furthermore, it also can be involved in routing decisions. Depending on which layer is responsible for routing decisions, 6LoWPAN divides routing in two categories: mesh under if the layer concerned is the adaptation layer and route over if it is the network layer. In this paper we analyze different routing solutions (route over, mesh under and enhanced route over) focusing on how they forward fragments. We evaluate their performance in terms of latency and energy consumption when transmitting IP fragmented packets. All the tests have been performed in a real 6LoWPAN implementation. After consideration of the main problems in forwarding of mesh frames in WSN, we propose and analyze a new alternative scheme based on mesh under, which we call controlled mesh under.

Forwarding Techniques for IP Fragmented Packets in a Real 6LoWPAN Network

PubMed Central

Ludovici, Alessandro; Calveras, Anna; Casademont, Jordi

2011-01-01

Wireless Sensor Networks (WSNs) are attracting more and more interest since they offer a low-cost solution to the problem of providing a means to deploy large sensor networks in a number of application domains. We believe that a crucial aspect to facilitate WSN diffusion is to make them interoperable with external IP networks. This can be achieved by using the 6LoWPAN protocol stack. 6LoWPAN enables the transmission of IPv6 packets over WSNs based on the IEEE 802.15.4 standard. IPv6 packet size is considerably larger than that of IEEE 802.15.4 data frame. To overcome this problem, 6LoWPAN introduces an adaptation layer between the network and data link layers, allowing IPv6 packets to be adapted to the lower layer constraints. This adaptation layer provides fragmentation and header compression of IP packets. Furthermore, it also can be involved in routing decisions. Depending on which layer is responsible for routing decisions, 6LoWPAN divides routing in two categories: mesh under if the layer concerned is the adaptation layer and route over if it is the network layer. In this paper we analyze different routing solutions (route over, mesh under and enhanced route over) focusing on how they forward fragments. We evaluate their performance in terms of latency and energy consumption when transmitting IP fragmented packets. All the tests have been performed in a real 6LoWPAN implementation. After consideration of the main problems in forwarding of mesh frames in WSN, we propose and analyze a new alternative scheme based on mesh under, which we call controlled mesh under. PMID:22346615

Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy.

PubMed

Chaimovich, Aviel; Shell, M Scott

2009-03-28

Recent efforts have attempted to understand many of liquid water's anomalous properties in terms of effective spherically-symmetric pairwise molecular interactions entailing two characteristic length scales (so-called "core-softened" potentials). In this work, we examine the extent to which such simple descriptions of water are representative of the true underlying interactions by extracting coarse-grained potential functions that are optimized to reproduce the behavior of an all-atom model. To perform this optimization, we use a novel procedure based upon minimizing the relative entropy, a quantity that measures the extent to which a coarse-grained configurational ensemble overlaps with a reference all-atom one. We show that the optimized spherically-symmetric water models exhibit notable variations with the state conditions at which they were optimized, reflecting in particular the shifting accessibility of networked hydrogen bonding interactions. Moreover, we find that water's density and diffusivity anomalies are only reproduced when the effective coarse-grained potentials are allowed to vary with state. Our results therefore suggest that no state-independent spherically-symmetric potential can fully capture the interactions responsible for water's unique behavior; rather, the particular way in which the effective interactions vary with temperature and density contributes significantly to anomalous properties.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne

2011-11-01

We present a coarse-grid projection (CGP) algorithm for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. Here, we investigate a particular CGP method for the vorticity-stream function formulation that uses the full weighting operation for mapping from fine to coarse grids, the third-order Runge-Kutta method for time stepping, and finite differences for the spatial discretization. After solving the Poisson equation on a coarsened grid, bilinear interpolation is used to obtain the fine data for consequent time stepping on the full grid. We compute several benchmark flows: the Taylor-Green vortex, a vortex pair merging, a double shear layer, decaying turbulence and the Taylor-Green vortex on a distorted grid. In all cases we use either FFT-based or V-cycle multigrid linear-cost Poisson solvers. Reducing the number of degrees of freedom of the Poisson solver by powers of two accelerates these computations while, for the first level of coarsening, retaining the same level of accuracy in the fine resolution vorticity field.

Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane

PubMed Central

Fujiwara, Takahiro K.; Iwasawa, Kokoro; Kalay, Ziya; Tsunoyama, Taka A.; Watanabe, Yusuke; Umemura, Yasuhiro M.; Murakoshi, Hideji; Suzuki, Kenichi G. N.; Nemoto, Yuri L.; Morone, Nobuhiro; Kusumi, Akihiro

2016-01-01

The mechanisms by which the diffusion rate in the plasma membrane (PM) is regulated remain unresolved, despite their importance in spatially regulating the reaction rates in the PM. Proposed models include entrapment in nanoscale noncontiguous domains found in PtK2 cells, slow diffusion due to crowding, and actin-induced compartmentalization. Here, by applying single-particle tracking at high time resolutions, mainly to the PtK2-cell PM, we found confined diffusion plus hop movements (termed “hop diffusion”) for both a nonraft phospholipid and a transmembrane protein, transferrin receptor, and equal compartment sizes for these two molecules in all five of the cell lines used here (actual sizes were cell dependent), even after treatment with actin-modulating drugs. The cross-section size and the cytoplasmic domain size both affected the hop frequency. Electron tomography identified the actin-based membrane skeleton (MSK) located within 8.8 nm from the PM cytoplasmic surface of PtK2 cells and demonstrated that the MSK mesh size was the same as the compartment size for PM molecular diffusion. The extracellular matrix and extracellular domains of membrane proteins were not involved in hop diffusion. These results support a model of anchored TM-protein pickets lining actin-based MSK as a major mechanism for regulating diffusion. PMID:26864625

Nitriding of AISI 4140 steel by a low energy broad ion source

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

Ochoa, E. A.; Figueroa, C. A.; Alvarez, F.

2006-11-15

A comprehensive study of the thermochemical nitriding process of steel AISI 4140 by low energy ion implantation (Kaufmann cell) is reported. Different times of implantation were employed and the studied samples were characterized by x-ray diffraction, in situ photoemission electron spectroscopy, scanning electron microscopy, and hardness (nanoindentation) measurements. The linear relationship between nitrogen content and hardness was verified. The structure of the nitrided layer was characterized yielding that the compound layer is formed by coarse precipitates, around small grains, constituted principally by {epsilon}-Fe{sub 2-3}N and {gamma}-Fe{sub 4}N phases and the diffusion zone is formed by fine precipitates, around big grainsmore » of the original martensitic phase, constituted principally by {gamma}-Fe{sub 4}N phase. Finally, a diffusion model for multiphase systems was applied to determine effective diffusion coefficients of nitrogen in the different phases.« less

Solute-defect interactions in Al-Mg alloys from diffusive variational Gaussian calculations

NASA Astrophysics Data System (ADS)

Dontsova, E.; Rottler, J.; Sinclair, C. W.

2014-11-01

Resolving atomic-scale defect topologies and energetics with accurate atomistic interaction models provides access to the nonlinear phenomena inherent at atomic length and time scales. Coarse graining the dynamics of such simulations to look at the migration of, e.g., solute atoms, while retaining the rich atomic-scale detail required to properly describe defects, is a particular challenge. In this paper, we present an adaptation of the recently developed "diffusive molecular dynamics" model to describe the energetics and kinetics of binary alloys on diffusive time scales. The potential of the technique is illustrated by applying it to the classic problems of solute segregation to a planar boundary (stacking fault) and edge dislocation in the Al-Mg system. Our approach provides fully dynamical solutions in situations with an evolving energy landscape in a computationally efficient way, where atomistic kinetic Monte Carlo simulations are difficult or impractical to perform.

Social relevance: toward understanding the impact of the individual in an information cascade

NASA Astrophysics Data System (ADS)

Hall, Robert T.; White, Joshua S.; Fields, Jeremy

2016-05-01

Information Cascades (IC) through a social network occur due to the decision of users to disseminate content. We define this decision process as User Diffusion (UD). IC models typically describe an information cascade by treating a user as a node within a social graph, where a node's reception of an idea is represented by some activation state. The probability of activation then becomes a function of a node's connectedness to other activated nodes as well as, potentially, the history of activation attempts. We enrich this Coarse-Grained User Diffusion (CGUD) model by applying actor type logics to the nodes of the graph. The resulting Fine-Grained User Diffusion (FGUD) model utilizes prior research in actor typing to generate a predictive model regarding the future influence a user will have on an Information Cascade. Furthermore, we introduce a measure of Information Resonance that is used to aid in predictions regarding user behavior.

Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows

NASA Astrophysics Data System (ADS)

Lenarda, Pietro; Paggi, Marco; Ruiz Baier, Ricardo

2017-09-01

We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-diffusion-reaction systems and incompressible, viscous flow. The space discretisation of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction, advection, and diffusion processes, considering the global system as a number of sequentially linked sets of partial differential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

The influence of ionic strength on DNA diffusion in gel networks

NASA Astrophysics Data System (ADS)

Fu, Yuanxi; Jee, Ah-Young; Kim, Hyeong-Ju; Granick, Steve

Cations are known to reduce the rigidity of the DNA molecules by screening the negative charge along the sugar phosphate backbone. This was established by optical tweezer pulling experiment of immobilized DNA strands. However, little is known regarding the influence of ions on the motion of DNA molecules as they thread through network meshes. We imaged in real time the Brownian diffusion of fluorescent labeled lambda-DNA in an agarose gel network in the presence of salt with monovalent or multivalent cations. Each movie was analyzed using home-written program to yield a trajectory of center of the mass and the accompanying history of the shape fluctuations. One preliminary finding is that ionic strength has a profound influence on the slope of the trace of mean square displacement (MSD) versus time. The influence of ionic strength on DNA diffusion in gel networks.

A projection hybrid high order finite volume/finite element method for incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.

2018-01-01

In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.

A cellular automaton - finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

NASA Astrophysics Data System (ADS)

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

2017-11-01

A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid-liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid-liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton-Glicksman-Kurz model for the steady growth of a dendrite tip and the Jackson-Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

IFCPT S-Duct Grid-Adapted FUN3D Computations for the Third Propulsion Aerodynamics Works

NASA Technical Reports Server (NTRS)

Davis, Zach S.; Park, M. A.

2017-01-01

Contributions of the unstructured Reynolds-averaged Navier-Stokes code, FUN3D, to the 3rd AIAA Propulsion Aerodynamics Workshop are described for the diffusing IFCPT S-Duct. Using workshop-supplied grids, results for the baseline S-Duct, baseline S-Duct with Aerodynamic Interface Plane (AIP) rake hardware, and baseline S-Duct with flow control devices are compared with experimental data and results computed with output-based, off-body grid adaptation in FUN3D. Due to the absence of influential geometry components, total pressure recovery is overpredicted on the baseline S-Duct and S-Duct with flow control vanes when compared to experimental values. An estimate for the exact value of total pressure recovery is derived for these cases given an infinitely refined mesh. When results from output-based mesh adaptation are compared with those computed on workshop-supplied grids, a considerable improvement in predicting total pressure recovery is observed. By including more representative geometry, output-based mesh adaptation compares very favorably with experimental data in terms of predicting the total pressure recovery cost-function; whereas, results computed using the workshop-supplied grids are underpredicted.

Non-ideal magnetohydrodynamics on a moving mesh

NASA Astrophysics Data System (ADS)

Marinacci, Federico; Vogelsberger, Mark; Kannan, Rahul; Mocz, Philip; Pakmor, Rüdiger; Springel, Volker

2018-05-01

In certain astrophysical systems, the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfvén waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.

Simulation of Deep Convective Clouds with the Dynamic Reconstruction Turbulence Closure

NASA Astrophysics Data System (ADS)

Shi, X.; Chow, F. K.; Street, R. L.; Bryan, G. H.

2017-12-01

The terra incognita (TI), or gray zone, in simulations is a range of grid spacing comparable to the most energetic eddy diameter. Spacing in mesoscale and simulations is much larger than the eddies, and turbulence is parameterized with one-dimensional vertical-mixing. Large eddy simulations (LES) have grid spacing much smaller than the energetic eddies, and use three-dimensional models of turbulence. Studies of convective weather use convection-permitting resolutions, which are in the TI. Neither mesoscale-turbulence nor LES models are designed for the TI, so TI turbulence parameterization needs to be discussed. Here, the effects of sub-filter scale (SFS) closure schemes on the simulation of deep tropical convection are evaluated by comparing three closures, i.e. Smagorinsky model, Deardorff-type TKE model and the dynamic reconstruction model (DRM), which partitions SFS turbulence into resolvable sub-filter scales (RSFS) and unresolved sub-grid scales (SGS). The RSFS are reconstructed, and the SGS are modeled with a dynamic eddy viscosity/diffusivity model. The RSFS stresses/fluxes allow backscatter of energy/variance via counter-gradient stresses/fluxes. In high-resolution (100m) simulations of tropical convection use of these turbulence models did not lead to significant differences in cloud water/ice distribution, precipitation flux, or vertical fluxes of momentum and heat. When model resolutions are coarsened, the Smagorinsky and TKE models overestimate cloud ice and produces large-amplitude downward heat flux in the middle troposphere (not found in the high-resolution simulations). This error is a result of unrealistically large eddy diffusivities, i.e., the eddy diffusivity of the DRM is on the order of 1 for the coarse resolution simulations, the eddy diffusivity of the Smagorinsky and TKE model is on the order of 100. Splitting the eddy viscosity/diffusivity scalars into vertical and horizontal components by using different length scales and strain rate components helps to reduce the errors, but does not completely remedy the problem. In contrast, the coarse resolution simulations using the DRM produce results that are more consistent with the high-resolution results, suggesting that the DRM is a more appropriate turbulence model for simulating convection in the TI.

Modelling Near-Surface Metallic Clutter Without the Excruciating Pain

NASA Astrophysics Data System (ADS)

Downs, C. M.; Weiss, C. J.; Bach, J.; Williams, J. T.

2016-12-01

An ongoing problem in modeling electromagnetic (EM) interactions with the near-surface and related anthropogenic metal clutter is the large difference in length scale between the clutter dimensions and their resulting EM response. For example, observational evidence shows that cables, pipes and rail lines can have a strong influence far from where they are located, even in situations where these artefacts are volumetrically insignificant over the scale of the model. This poses a significant modeling problem for understanding geohazards in urban environments, for example, because of the very fine numerical discretization required for accurate representation of an artefact embedded in a larger computational domain. We adopt a sub-grid approximation and impose a boundary condition along grid edges to capture the vanishing fields of a perfect conductor. We work in a Cartesian system where the EM fields are solved via finite volumes in the frequency domain in terms of the Lorenz gauged magnetic vector (A) and electric scalar (Phi) potentials. The electric fied is given simply by A-grad(Phi), and set identically to zero along edges of the mesh that coincide with the center of long, slender metallic conductors. A simple extension to bulky artefacts like blocks or slabs involves endowing all such edges in their interior with the same "internal" boundary condition. In essence, we apply the "perfect electric conductor" boundary condition to select edges interior to the modeling domain. We note a few minor numerical consequences of this approach, namely: the zero-E field internal boundary condition destroys the symmetry of the finite volume coefficient matrix; and, the accuracy of the representation of the conducting artefact is restricted by the relatively coarse discretization mesh. The former is overcome with the use of preconditioned bi-conjugate gradient methods instead of the quasi-minimal-residual method. Both are matrix-free iterative solvers - thus avoiding unnecessary storage- and both exhibit generally good convergence for well-posed problems. The latter is more difficult to overcome without either modifying the mesh (potentially degrading the condition number of the coefficient matrix) or with novel mesh sub-gridding. Initial results show qualitative agreement with the expected physics.

Effects of debris flow composition on runout, depositional mechanisms, and deposit morphology in laboratory experiments

NASA Astrophysics Data System (ADS)

Haas, Tjalling; Braat, Lisanne; Leuven, Jasper R. F. W.; Lokhorst, Ivar R.; Kleinhans, Maarten G.

2015-09-01

Predicting debris flow runout is of major importance for hazard mitigation. Apart from topography and volume, runout distance and area depends on debris flow composition and rheology, but how is poorly understood. We experimentally investigated effects of composition on debris flow runout, depositional mechanisms, and deposit geometry. The small-scale experimental debris flows were largely similar to natural debris flows in terms of flow behavior, deposit morphology, grain size sorting, channel width-depth ratio, and runout. Deposit geometry (lobe thickness and width) in our experimental debris flows is largely determined by composition, while the effects of initial conditions of topography (i.e., outflow plain slope and channel slope and width) and volume are negligible. We find a clear optimum in the relations of runout with coarse-material fraction and clay fraction. Increasing coarse-material concentration leads to larger runout. However, excess coarse material results in a large accumulation of coarse debris at the flow front and enhances diffusivity, increasing frontal friction and decreasing runout. Increasing clay content initially enhances runout, but too much clay leads to very viscous flows, reducing runout. Runout increases with channel slope and width, outflow plain slope, debris flow volume, and water fraction. These results imply that debris flow runout depends at least as much on composition as on topography. This study improves understanding of the effects of debris flow composition on runout and may aid future debris flow hazard assessments.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution.

PubMed

Lu, Benzhuo; Zhou, Y C; Huber, Gary A; Bond, Stephen D; Holst, Michael J; McCammon, J Andrew

2007-10-07

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

Diffusion of GPI-anchored proteins is influenced by the activity of dynamic cortical actin

PubMed Central

Saha, Suvrajit; Lee, Il-Hyung; Polley, Anirban; Groves, Jay T.; Rao, Madan; Mayor, Satyajit

2015-01-01

Molecular diffusion at the surface of living cells is believed to be predominantly driven by thermal kicks. However, there is growing evidence that certain cell surface molecules are driven by the fluctuating dynamics of cortical cytoskeleton. Using fluorescence correlation spectroscopy, we measure the diffusion coefficient of a variety of cell surface molecules over a temperature range of 24–37°C. Exogenously incorporated fluorescent lipids with short acyl chains exhibit the expected increase of diffusion coefficient over this temperature range. In contrast, we find that GPI-anchored proteins exhibit temperature-independent diffusion over this range and revert to temperature-dependent diffusion on cell membrane blebs, in cells depleted of cholesterol, and upon acute perturbation of actin dynamics and myosin activity. A model transmembrane protein with a cytosolic actin-binding domain also exhibits the temperature-independent behavior, directly implicating the role of cortical actin. We show that diffusion of GPI-anchored proteins also becomes temperature dependent when the filamentous dynamic actin nucleator formin is inhibited. However, changes in cortical actin mesh size or perturbation of branched actin nucleator Arp2/3 do not affect this behavior. Thus cell surface diffusion of GPI-anchored proteins and transmembrane proteins that associate with actin is driven by active fluctuations of dynamic cortical actin filaments in addition to thermal fluctuations, consistent with expectations from an “active actin-membrane composite” cell surface. PMID:26378258

Towards retrievable vascularized bioartificial pancreas: induction and long-lasting stability of polymeric mesh implant vascularized with the help of acidic and basic fibroblast growth factors and hydrogel coating.

PubMed

Prokop, A; Kozlov, E; Nun Non, S; Dikov, M M; Sephel, G C; Whitsitt, J S; Davidson, J M

2001-01-01

We seek to improve existing methodologies for allogenic grafting of pancreatic islets. The lack of success of encapsulated transplanted islets inside the peritoneal cavity is presently attributed to poor vascularization of the implant. A thick, fibrotic capsule often surrounds the graft, limiting survival. We have tested the hypothesis that neovascularization of the graft material can be induced by the addition of proper angiogenic factors embedded within a polymeric coat. Biocompatible and nonresorbable meshes coated with hydrophilic polymers were implanted in rats and harvested after 1-, 6-, and 12-week intervals. The implant response was assessed by histological observations on the degree of vascularity, fibrosis, and inflammation. Macrostructural geometry of meshes was conducive to tissue ingrowth into the interstitial space between the mesh filaments. Hydrogel coating with incorporated acidic or basic FGF in an electrostatic complex with polyelectrolytes and/or with heparin provided a sustained slow release of the angiogenic growth factor. Anti-factor VIII and anti-collagen type IV antibodies and a GSL I-B4 lectin were used to measure the extent of vascularization. Vigorous and persistent vascularization radiated several hundred microns from the implant. The level of vascularization should provide a sufficient diffusion of nutrients and oxygen to implanted islets. Based on our observations, stable vascularization may require a sustained angiogenic signal to allow for the development of a permanent implant structure.

Surfactant effects on alpha-factors in aeration systems.

PubMed

Rosso, Diego; Stenstrom, Michael K

2006-04-01

Aeration in wastewater treatment processes accounts for the largest fraction of plant energy costs. Aeration systems function by shearing the surface (surface aerators) or releasing bubbles at the bottom of the tank (coarse- or fine-bubble aerators). Surfactant accumulation on gas-liquid interfaces reduces mass transfer rates, and this reduction in general is larger for fine-bubble aerators. This study evaluates mass transfer effects on the characterization and specification of aeration systems in clean and process water conditions. Tests at different interfacial turbulence regimes show higher gas transfer depression for lower turbulence regimes. Contamination effects can be offset at the expense of operating efficiency, which is characteristic of surface aerators and coarse-bubble diffusers. Results describe the variability of alpha-factors measured at small scale, due to uncontrolled energy density. Results are also reported in dimensionless empirical correlations describing mass transfer as a function of physiochemical and geometrical characteristics of the aeration process.

Modelling Detailed-Chemistry Effects on Turbulent Diffusion Flames using a Parallel Solution-Adaptive Scheme

NASA Astrophysics Data System (ADS)

Jha, Pradeep Kumar

Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow. Comparisons are made between the predicted results of the present FPI scheme and Steady Laminar Flamelet Model (SLFM) approach for diffusion flames. The effects of grid resolution on the predicted overall flame solutions are also assessed. Other non-reacting flows have also been considered to further validate other aspects of the numerical scheme. The present schemes predict results which are in good agreement with published experimental results and reduces the computational cost involved in modelling turbulent diffusion flames significantly, both in terms of storage and processing time.

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

Collins, Benjamin S.; Hamilton, Steven P.; Stimpson, Shane

The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solvesmore » the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.« less

Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

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

Liu, Ju, E-mail: jliu@ices.utexas.edu; Gomez, Hector; Evans, John A.

2013-09-01

We propose a new methodology for the numerical solution of the isothermal Navier–Stokes–Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionallymore » stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws.« less

Pathloss Calculation Using the Transmission Line Matrix and Finite Difference Time Domain Methods With Coarse Grids

DOE PAGES

Nutaro, James; Kuruganti, Teja

2017-02-24

Numerical simulations of the wave equation that are intended to provide accurate time domain solutions require a computational mesh with grid points separated by a distance less than the wavelength of the source term and initial data. However, calculations of radio signal pathloss generally do not require accurate time domain solutions. This paper describes an approach for calculating pathloss by using the finite difference time domain and transmission line matrix models of wave propagation on a grid with points separated by distances much greater than the signal wavelength. The calculated pathloss can be kept close to the true value formore » freespace propagation with an appropriate selection of initial conditions. This method can also simulate diffraction with an error governed by the ratio of the signal wavelength to the grid spacing.« less

Subsonic Analysis of 0.04-Scale F-16XL Models Using an Unstructured Euler Code

NASA Technical Reports Server (NTRS)

Lessard, Wendy B.

1996-01-01

The subsonic flow field about an F-16XL airplane model configuration was investigated with an inviscid unstructured grid technique. The computed surface pressures were compared to wind-tunnel test results at Mach 0.148 for a range of angles of attack from 0 deg to 20 deg. To evaluate the effect of grid dependency on the solution, a grid study was performed in which fine, medium, and coarse grid meshes were generated. The off-surface vortical flow field was locally adapted and showed improved correlation to the wind-tunnel data when compared to the nonadapted flow field. Computational results are also compared to experimental five-hole pressure probe data. A detailed analysis of the off-body computed pressure contours, velocity vectors, and particle traces are presented and discussed.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Rule-based spatial modeling with diffusing, geometrically constrained molecules.

PubMed

Gruenert, Gerd; Ibrahim, Bashar; Lenser, Thorsten; Lohel, Maiko; Hinze, Thomas; Dittrich, Peter

2010-06-07

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

PubMed Central

2010-01-01

Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly. PMID:20529264

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

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

Prokopenko, Andrey; Tuminaro, Raymond S.

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

PubMed

Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J

2009-11-28

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

DOE PAGES

Prokopenko, Andrey; Tuminaro, Raymond S.

2016-07-01

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

Capturing Multiscale Phenomena via Adaptive Mesh Refinement (AMR) in 2D and 3D Atmospheric Flows

NASA Astrophysics Data System (ADS)

Ferguson, J. O.; Jablonowski, C.; Johansen, H.; McCorquodale, P.; Ullrich, P. A.; Langhans, W.; Collins, W. D.

2017-12-01

Extreme atmospheric events such as tropical cyclones are inherently complex multiscale phenomena. Such phenomena are a challenge to simulate in conventional atmosphere models, which typically use rather coarse uniform-grid resolutions. To enable study of these systems, Adaptive Mesh Refinement (AMR) can provide sufficient local resolution by dynamically placing high-resolution grid patches selectively over user-defined features of interest, such as a developing cyclone, while limiting the total computational burden of requiring such high-resolution globally. This work explores the use of AMR with a high-order, non-hydrostatic, finite-volume dynamical core, which uses the Chombo AMR library to implement refinement in both space and time on a cubed-sphere grid. The characteristics of the AMR approach are demonstrated via a series of idealized 2D and 3D test cases designed to mimic atmospheric dynamics and multiscale flows. In particular, new shallow-water test cases with forcing mechanisms are introduced to mimic the strengthening of tropical cyclone-like vortices and to include simplified moisture and convection processes. The forced shallow-water experiments quantify the improvements gained from AMR grids, assess how well transient features are preserved across grid boundaries, and determine effective refinement criteria. In addition, results from idealized 3D test cases are shown to characterize the accuracy and stability of the non-hydrostatic 3D AMR dynamical core.

Segmentation of brain volume based on 3D region growing by integrating intensity and edge for image-guided surgery

NASA Astrophysics Data System (ADS)

Tsagaan, Baigalmaa; Abe, Keiichi; Goto, Masahiro; Yamamoto, Seiji; Terakawa, Susumu

2006-03-01

This paper presents a segmentation method of brain tissues from MR images, invented for our image-guided neurosurgery system under development. Our goal is to segment brain tissues for creating biomechanical model. The proposed segmentation method is based on 3-D region growing and outperforms conventional approaches by stepwise usage of intensity similarities between voxels in conjunction with edge information. Since the intensity and the edge information are complementary to each other in the region-based segmentation, we use them twice by performing a coarse-to-fine extraction. First, the edge information in an appropriate neighborhood of the voxel being considered is examined to constrain the region growing. The expanded region of the first extraction result is then used as the domain for the next processing. The intensity and the edge information of the current voxel only are utilized in the final extraction. Before segmentation, the intensity parameters of the brain tissues as well as partial volume effect are estimated by using expectation-maximization (EM) algorithm in order to provide an accurate data interpretation into the extraction. We tested the proposed method on T1-weighted MR images of brain and evaluated the segmentation effectiveness comparing the results with ground truths. Also, the generated meshes from the segmented brain volume by using mesh generating software are shown in this paper.

A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs

NASA Astrophysics Data System (ADS)

Dana, Saumik; Ganis, Benjamin; Wheeler, Mary F.

2018-01-01

In coupled flow and poromechanics phenomena representing hydrocarbon production or CO2 sequestration in deep subsurface reservoirs, the spatial domain in which fluid flow occurs is usually much smaller than the spatial domain over which significant deformation occurs. The typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a coupled problem domain or to model flow on a huge domain with zero permeability cells to mimic the no flow boundary condition on the interface of the reservoir and the surrounding rock. The former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs. In order to address these challenges, we augment the fixed-stress split iterative scheme with upscaling and downscaling operators to enable modeling flow and mechanics on overlapping nonmatching hexahedral grids. Flow is solved on a finer mesh using a multipoint flux mixed finite element method and mechanics is solved on a coarse mesh using a conforming Galerkin method. The multiscale operators are constructed using a procedure that involves singular value decompositions, a surface intersections algorithm and Delaunay triangulations. We numerically demonstrate the convergence of the augmented scheme using the classical Mandel's problem solution.

Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing.

PubMed

Hou, Tingbo; Qin, Hong

2013-01-01

As signal processing tools, diffusion wavelets and biorthogonal diffusion wavelets have been propelled by recent research in mathematics. They employ diffusion as a smoothing and scaling process to empower multiscale analysis. However, their applications in graphics and visualization are overshadowed by nonadmissible wavelets and their expensive computation. In this paper, our motivation is to broaden the application scope to space-frequency processing of shape geometry and scalar fields. We propose the admissible diffusion wavelets (ADW) on meshed surfaces and point clouds. The ADW are constructed in a bottom-up manner that starts from a local operator in a high frequency, and dilates by its dyadic powers to low frequencies. By relieving the orthogonality and enforcing normalization, the wavelets are locally supported and admissible, hence facilitating data analysis and geometry processing. We define the novel rapid reconstruction, which recovers the signal from multiple bands of high frequencies and a low-frequency base in full resolution. It enables operations localized in both space and frequency by manipulating wavelet coefficients through space-frequency filters. This paper aims to build a common theoretic foundation for a host of applications, including saliency visualization, multiscale feature extraction, spectral geometry processing, etc.

Influence of pore size of porous titanium fabricated by vacuum diffusion bonding of titanium meshes on cell penetration and bone ingrowth.

PubMed

Chang, Bei; Song, Wen; Han, Tianxiao; Yan, Jun; Li, Fuping; Zhao, Lingzhou; Kou, Hongchao; Zhang, Yumei

2016-03-01

The present work assesses the potential of three-dimensional (3D) porous titanium (pore size of 188-390 μm and porosity of 70%) fabricated by vacuum diffusion bonding of titanium meshes for applications in bone engineering. Rat bone marrow mesenchymal stem cells were used to investigate the proliferation and differentiation of cells on titanium scaffolds with different pore sizes at day 7, day 14 and day 21 based on DNA contents, alkaline phosphatase (ALP) activity, collagen (COL) secretion and osteogenic gene expressions including ALP, COL-1, bone morphogenetic protein-2 (BMP-2), osteopontin (OPN), runt-related transcription factor 2 (RUNX2), using smooth solid titanium plate as reference material. The rabbit models with distal femoral condyles defect were used to investigate the bone ingrowth into the porous titanium. All samples were subjected to Micro-CT and histological analysis after 4 and 12 weeks of healing. A one-way ANOVA followed by Tukey post hoc tests was used to analyze the data. It was found that the differentiation stage of cells on the porous titanium delayed compared with the smooth solid titanium plate and Ti 188 was more inclined to promote cell differentiation at the initial stage (day 14) while cell proliferation (day 1, 4, 7, 10, 14 and 21) and bone ingrowth (4 and 12 weeks) were biased to Ti 313 and Ti 390. The study indicates that the hybrid porous implant design which combines the advantages of different pore sizes may be meaningful and promising for bone defect restoration. One of the significant challenges in bone defect restoration is the integration of biomaterials and surrounding bone tissue. Porous titanium may be a promising choice for bone ingrowth and mineralization with appropriate mechanical and biological properties. In this study, based on porous titanium fabricated by vacuum diffusion bonding of titanium meshes, we have evaluated the influence of various pore sizes on rat bone marrow mesenchymal stem cells (rBMMSCs) penetration in vitro and bone ingrowth in vivo. It was interesting that we found the proliferation and differentiation abilities of rBMMSCs, as well as bone ingrowth were related to different pore sizes of such porous scaffolds. The results may provide guidance for porous titanium design for bone defect restoration. Copyright © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Markov-state model for CO2 binding with carbonic anhydrase under confinement

NASA Astrophysics Data System (ADS)

Chen, Gong; Xu, Weina; Lu, Diannan; Wu, Jianzhong; Liu, Zheng

2018-01-01

Enzyme immobilization with a nanostructure material can enhance its stability and facilitate reusability. However, the apparent activity is often compromised due to additional diffusion barriers and complex interactions with the substrates and solvent molecules. The present study elucidates the effects of the surface hydrophobicity of nano-confinement on CO2 diffusion to the active site of human carbonic anhydrase II (CA), an enzyme that is able to catalyze CO2 hydration at extremely high turnover rates. Using the Markov-state model in combination with coarse-grained molecular dynamics simulations, we demonstrate that a hydrophobic cage increases CO2 local density but hinders its diffusion towards the active site of CA under confinement. By contrast, a hydrophilic cage hinders CO2 adsorption but promotes its binding with CA. An optimal surface hydrophobicity can be identified to maximize both the CO2 occupation probability and the diffusion rate. The simulation results offer insight into understanding enzyme performance under nano-confinement and help us to advance broader applications of CA for CO2 absorption and recovery.

Localization and diffusion of tracer particles in viscoelastic media with active force dipoles

NASA Astrophysics Data System (ADS)

Yasuda, Kento; Okamoto, Ryuichi; Komura, Shigeyuki; Mikhailov, Alexander S.

2017-02-01

Optical tracking in vivo experiments reveal that diffusion of particles in biological cells is strongly enhanced in the presence of ATP and the experimental data for animal cells could previously be reproduced within a phenomenological model of a gel with myosin motors acting within it (Fodor É. et al., EPL, 110 (2015) 48005). Here, the two-fluid model of a gel is considered where active macromolecules, described as force dipoles, cyclically operate both in the elastic and the fluid components. Through coarse-graining, effective equations of motions for idealized tracer particles displaying local deformations and local fluid flows are derived. The equation for deformation tracers coincides with the earlier phenomenological model and thus confirms it. For flow tracers, diffusion enhancement caused by active force dipoles in the fluid component, and thus due to metabolic activity, is found. The latter effect may explain why ATP-dependent diffusion enhancement could also be observed in bacteria that lack molecular motors in their skeleton or when the activity of myosin motors was chemically inhibited in eukaryotic cells.

Effect of diffusion annealing regimes on the structure of Nb3Sn layers in ITER-type bronze-processed wires

NASA Astrophysics Data System (ADS)

Valova-Zaharevskaya, E. G.; Popova, E. N.; Deryagina, I. L.; Abdyukhanov, I. M.; Tsapleva, A. S.

2018-03-01

The goal of the present study is to characterize the growth kinetics and structural parameters of the Nb3Sn layers formed under various regimes of the diffusion annealing of bronze-processed Nb/Cu-Sn composites. The structure of the superconducting layers is characterized by their thickness, average size of equiaxed grains and by the ratio of fractions of columnar and equiaxed grains. It was found that at higher diffusion annealing temperatures (above 650°C) thicker superconducting layers are obtained, but the average sizes of equiaxed Nb3Sn grains even under short exposures (10 h) are much larger than after the long low-temperature annealing. At the low-temperature (575 °C) annealing the relative fraction of columnar grains increases with increasing annealing time. Based on the data obtained, optimal regimes of the diffusion annealing can be chosen, which would on the one hand ensure complete transformation of Nb into Nb3Sn of close to the stoichiometric composition, and on the other hand prevent the formation of coarse and columnar grains.

CARS Temperature Measurements in Sooting, Laminar Diffusion Flames.

DTIC Science & Technology

1984-07-30

the flame. In preliminary calculations with coarse axial and radial grids, the flames all reached their respective AFT’s, and flame lengths were just...welded to the outside of the tube. Such rugenerative heat feedback is not part of the K? model. Calculated flame length is seen on Figure 11 to increase...heights in the measurements, Figure 6, and the calculated flame lengths , Figure 11, is seen to be reduced substantially with increasing dilution. When

Fiber Orientation Estimation Guided by a Deep Network.

PubMed

Ye, Chuyang; Prince, Jerry L

2017-09-01

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs. However, accurate estimation of complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent diffusion signals. To estimate the mixture fractions of the dictionary atoms, a deep network is designed to solve the sparse reconstruction problem. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding a dense basis of FOs is used and a weighted ℓ 1 -norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and typical clinical dMRI data. The results demonstrate the benefit of using a deep network for FO estimation.

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Measuring and modeling diffuse scattering in protein X-ray crystallography

PubMed Central

Van Benschoten, Andrew H.; Liu, Lin; Gonzalez, Ana; Brewster, Aaron S.; Sauter, Nicholas K.; Wall, Michael E.

2016-01-01

X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practices for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation–libration–screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. These results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering. PMID:27035972

Measuring and modeling diffuse scattering in protein X-ray crystallography

DOE PAGES

Van Benschoten, Andrew H.; Liu, Lin; Gonzalez, Ana; ...

2016-03-28

X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practicesmore » for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation–libration–screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. In conclusion, these results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering.« less

Effects of debris-flow composition on runout and erosion

NASA Astrophysics Data System (ADS)

Haas, T. D.; Kleinhans, M. G.

2016-12-01

Predicting debris-flow runout is of major importance for hazard mitigation. Apart from topography and volume, runout depends on debris-flow composition (i.e., particle-size distribution and water content), but how is poorly understood. Moreover, debris flows can grow greatly in size by entrainment of bed material, enhancing their volume and thereby runout and hazardous impact. Debris-flow erosion rates also depend on debris-flow composition, but the relation between the two is largely unexplored. Composition thus strongly affects the dynamics of debris flows. We experimentally investigate the effects of composition on debris-flow runout and erosion. We find a clear optimum in the relations of runout with coarse-material fraction and clay fraction. Increasing coarse material concentration leads to larger runout. However, excess coarse material results in a large accumulation of coarse debris at the flow front and enhances diffusivity, increasing frontal friction and decreasing runout. Increasing clay content initially enhances runout, but too much clay leads to very viscous flows, reducing runout. We further find that debris-flow runout depends at least as much on composition as on topography. In general, erosion depth increases with basal shear stress in our experiments, while there is no correlation with grain collisional stress. There are substantial differences in the scour caused by different types of debris flows. Mean and maximum erosion depths generally become larger with increasing water fraction and grain size and decrease with increasing clay content. However, the erodibility of the very coarse-grained experimental debris flows is unrelated to basal shear stress. This relates to the relatively large influence of grain-collisional stress to the total bed stress in these flows (30-50%). The relative effect of grain-collisional stress is low in the other experimental debris flows (<5%) causing erosion to be largely controlled by basal shear stress. These results show that the erosive behaviour of debris flows may change from basal-shear stress dominated to grain-collisional stress dominated in increasingly coarse-grained debris flows. In short, this study improves our understanding of the effects of debris-flow composition on runout and erosion.

Direct construction of mesoscopic models from microscopic simulations

NASA Astrophysics Data System (ADS)

Lei, Huan; Caswell, Bruce; Karniadakis, George Em

2010-02-01

Starting from microscopic molecular-dynamics (MD) simulations of constrained Lennard-Jones (LJ) clusters (with constant radius of gyration Rg ), we construct two mesoscopic models [Langevin dynamics and dissipative particle dynamics (DPD)] by coarse graining the LJ clusters into single particles. Both static and dynamic properties of the coarse-grained models are investigated and compared with the MD results. The effective mean force field is computed as a function of the intercluster distance, and the corresponding potential scales linearly with the number of particles per cluster and the temperature. We verify that the mean force field can reproduce the equation of state of the atomistic systems within a wide density range but the radial distribution function only within the dilute and the semidilute regime. The friction force coefficients for both models are computed directly from the time-correlation function of the random force field of the microscopic system. For high density or a large cluster size the friction force is overestimated and the diffusivity underestimated due to the omission of many-body effects as a result of the assumed pairwise form of the coarse-grained force field. When the many-body effect is not as pronounced (e.g., smaller Rg or semidilute system), the DPD model can reproduce the dynamic properties of the MD system.

Transport and dielectric properties of water and the influence of coarse-graining: Comparing BMW, SPC/E, and TIP3P models

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

Braun, Daniel; Boresch, Stefan; Steinhauser, Othmar

Long-term molecular dynamics simulations are used to compare the single particle dipole reorientation time, the diffusion constant, the viscosity, and the frequency-dependent dielectric constant of the coarse-grained big multipole water (BMW) model to two common atomistic three-point water models, SPC/E and TIP3P. In particular, the agreement between the calculated viscosity of BMW and the experimental viscosity of water is satisfactory. We also discuss contradictory values for the static dielectric properties reported in the literature. Employing molecular hydrodynamics, we show that the viscosity can be computed from single particle dynamics, circumventing the slow convergence of the standard approaches. Furthermore, our datamore » indicate that the Kivelson relation connecting single particle and collective reorientation time holds true for all systems investigated. Since simulations with coarse-grained force fields often employ extremely large time steps, we also investigate the influence of time step on dynamical properties. We observe a systematic acceleration of system dynamics when increasing the time step. Carefully monitoring energy/temperature conservation is found to be a sufficient criterion for the reliable calculation of dynamical properties. By contrast, recommended criteria based on the ratio of fluctuations of total vs. kinetic energy are not sensitive enough.« less

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

PubMed

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Mineralogical and microscopic evaluation of coarse taconite tailings from Minnesota taconite operations.

PubMed

Zanko, Lawrence M; Niles, Harlan B; Oreskovich, Julie A

2008-10-01

Eighteen coarse taconite tailings samples were collected in 2000-2001 from five western Mesabi Range taconite (iron ore) operations located in northern Minnesota, i.e., EVTAC, Hibbing Taconite (Hibtac), USX Minntac, Ispat Inland (Minorca), and National Steel Pellet Company (NSPC), to test their physical, geological, chemical, and mineralogical properties [Zanko, L.M., Niles, H.B., Oreskovich, J.A., 2003. Properties and aggregate potential of coarse taconite tailings from five Minnesota taconite operations, Minnesota Department of Transportation, Local Road Research Board, St. Paul, MN, Report No. 2004-06 (also as Natural Resources Research Institute technical report, NRRI/TR-2003/44)]. The goal was to assemble a body of technical data that could be used to better assess the potential of using a crushed taconite mining byproduct like coarse tailings for more widespread construction aggregate purposes, primarily in roads and highways. An important part of the mineralogical assessment included X-ray diffraction (XRD) analyses and microscopic (polarized light microscopy, scanning electron microscopy, and transmission electron microscopy, i.e., PLM, SEM, and TEM, respectively) evaluation of the size and shape (morphological) characteristics of potentially respirable microscopic mineral particles and fragments. Quantitative mineralogy, based on XRD analyses, showed that the dominant mineral in all samples was quartz (55-60%), followed by much smaller amounts of iron oxides, carbonates, and silicates. Specialized microscopic analyses and testing performed by the RJ Lee Group, Monroeville, PA, on both pulverized (-200 mesh, or 0.075mm) and as-is sample composites showed that no regulated asbestos minerals or amphibole minerals were detected in the western Mesabi Range samples. A small number (26) of non-asbestos and non-amphibole mineral cleavage fragments/mineral fibers were detected by SEM out of 1000 fields analyzed, but most were identified as minnesotaite and talc, silicate minerals common to the Biwabik Iron Formation. Amphibole minerals, absent in coarse tailings samples from the five western Mesabi Range taconite operations, were present in a single eastern Biwabik Iron Formation sample collected in 2003 for Lake County from the Cliffs Northshore operation in Silver Bay, MN. Importantly, the Superfund Method for the Determination of Releasable Asbestos in Soils and Bulk Materials [United States Environmental Protection Agency (USEPA), 1997. Superfund method for the determination of releasable asbestos in soils and bulk materials, EPA 540-R-97-028, U.S. Environmental Protection Agency, Washington], as modified by Berman and Kolk [Berman, D.W., Kolk, A.J., 2000. Modified elutriator method for the determination of asbestos in soils and bulk materials, Revision 1: Submitted to the U.S. Environmental Protection Agency, Region 8, May 23, 2000] failed to generate any protocol fibers, i.e., fibers longer than 5mum and thinner than 0.5mum, from either the western coarse tailings samples or the single eastern Biwabik Iron Formation sample. The combined findings suggest coarse tailings and other taconite mining byproducts should be treated with the same common sense safety and industrial hygiene approach practiced for all mineral-based materials that have the potential to generate respirable dust.

Multi-Material ALE with AMR for Modeling Hot Plasmas and Cold Fragmenting Materials

NASA Astrophysics Data System (ADS)

Alice, Koniges; Nathan, Masters; Aaron, Fisher; David, Eder; Wangyi, Liu; Robert, Anderson; David, Benson; Andrea, Bertozzi

2015-02-01

We have developed a new 3D multi-physics multi-material code, ALE-AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR) to connect the continuum to the microstructural regimes. The code is unique in its ability to model hot radiating plasmas and cold fragmenting solids. New numerical techniques were developed for many of the physics packages to work efficiently on a dynamically moving and adapting mesh. We use interface reconstruction based on volume fractions of the material components within mixed zones and reconstruct interfaces as needed. This interface reconstruction model is also used for void coalescence and fragmentation. A flexible strength/failure framework allows for pluggable material models, which may require material history arrays to determine the level of accumulated damage or the evolving yield stress in J2 plasticity models. For some applications laser rays are propagating through a virtual composite mesh consisting of the finest resolution representation of the modeled space. A new 2nd order accurate diffusion solver has been implemented for the thermal conduction and radiation transport packages. One application area is the modeling of laser/target effects including debris/shrapnel generation. Other application areas include warm dense matter, EUV lithography, and material wall interactions for fusion devices.

Macroporous mesh of nanoporous gold in electrochemical monitoring of superoxide release from skeletal muscle cells.

PubMed

Banan Sadeghian, Ramin; Han, Jiuhui; Ostrovidov, Serge; Salehi, Sahar; Bahraminejad, Behzad; Ahadian, Samad; Chen, Mingwei; Khademhosseini, Ali

2017-02-15

Real-time monitoring of metabolically relevant biochemicals released in minuscule amounts is of utmost diagnostic importance. Superoxide anion as a primary member of reactive oxygen species, has physiological and pathological effects that depend on its concentration and release rate. Here we present fabrication and successfully testing of a highly sensitive electrochemical biosensor featuring a three-dimensional macroporous mesh of nanoporous gold tailored to measure the dynamics of extracellular superoxide concentration. Wide and accessible surface of the mesh combined with high porosity of the thin nanoporous gold coating enables capturing the analyte in pico- to nano-molar ranges. The mesh is functionalized with cytochrome-c (cyt-c) and incorporated as a working electrode to measure the release rate of drug-induced superoxides from C2C12 cells through a porous membrane. The device displays a considerably improved superoxide sensitivity of 7.29nAnM - 1 cm - 2 and a low level of detection of 70pM. Such sensitivity is orders of magnitude higher than any similar enzyme-based electrochemical superoxide sensor and is attributed to the facile diffusion of the analyte through the well-spread nanofeatured gold skin. Superoxide generation rates captured from monolayer myoblast cultures containing about 4×10 4 cells, varied from 1.0 to 9.0nMmin - 1 in a quasi-linear fashion as a function of drug concentration. This work provides a platform for the development of highly sensitive molecular electrochemical biosensors. Copyright © 2016 Elsevier B.V. All rights reserved.

Modelling highly deformable metal extrusion using SPH

NASA Astrophysics Data System (ADS)

Prakash, Mahesh; Cleary, Paul W.

2015-05-01

Computational modelling is often used to reduce trial extrusions through accurate defect prediction. Traditionally, metal extrusion is modelled using mesh based finite element methods. However, large plastic deformations can lead to heavy re-meshing and numerical diffusion. Here we use the mesh-less smoothed particle hydrodynamics method since it allows simulation of large deformations without re-meshing and the tracking of history dependent properties such as plastic strain making it suitable for defect prediction. The variation in plastic strain and deformation for aluminium alloy in a cylindrical 3D geometry with extrusion ratio and die angle is evaluated. The extrusion process is found to have three distinct phases consisting of an initial sharp rise in extrusion force, a steady phase requiring constant force and terminating in a sharp decline in force as metal is completely extruded. Deformation and plastic strain increased significantly with extrusion ratio but only moderately with die angle. Extrusion force increased by 150 % as the extrusion ratio increased from 2:1 to 4:1 but had only a marginal change with die angle. A low strain zone in the centre of the extruded product was found to be a function of extrusion ratio but was persistent and did not vary with die angle. Simulation of a complex 3D building industry component showed large variations in plastic strain along the length of the product at two scales. These were due to change in metal behaviour as extrusion progressed from phase 1 to phase 2. A stagnation zone at the back of the die was predicted that could lead to the "funnel" or "pipe" defect.

Mesoscopic Modeling of Blood Clotting: Coagulation Cascade and Platelets Adhesion

NASA Astrophysics Data System (ADS)

Yazdani, Alireza; Li, Zhen; Karniadakis, George

2015-11-01

The process of clot formation and growth at a site on a blood vessel wall involve a number of multi-scale simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and flow. To model these processes we have incorporated advection-diffusion-reaction (ADR) of multiple species into an extended version of Dissipative Particle Dynamics (DPD) method which is considered as a coarse-grained Molecular Dynamics method. At the continuum level this is equivalent to the Navier-Stokes equation plus one advection-diffusion equation for each specie. The chemistry of clot formation is now understood to be determined by mechanisms involving reactions among many species in dilute solution, where reaction rate constants and species diffusion coefficients in plasma are known. The role of blood particulates, i.e. red cells and platelets, in the clotting process is studied by including them separately and together in the simulations. An agonist-induced platelet activation mechanism is presented, while platelets adhesive dynamics based on a stochastic bond formation/dissociation process is included in the model.

Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

Flux front penetration in disordered superconductors.

PubMed

Zapperi, S; Moreira, A A; Andrade, J S

2001-04-16

We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.

Hierarchical Boltzmann simulations and model error estimation

NASA Astrophysics Data System (ADS)

Torrilhon, Manuel; Sarna, Neeraj

2017-08-01

A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains. The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

Membrane tension controls the assembly of curvature-generating proteins

PubMed Central

Simunovic, Mijo; Voth, Gregory A.

2015-01-01

Proteins containing a Bin/Amphiphysin/Rvs (BAR) domain regulate membrane curvature in the cell. Recent simulations have revealed that BAR proteins assemble into linear aggregates, strongly affecting membrane curvature and its in-plane stress profile. Here, we explore the opposite question: do mechanical properties of the membrane impact protein association? By using coarse-grained molecular dynamics simulations, we show that increased surface tension significantly impacts the dynamics of protein assembly. While tensionless membranes promote a rapid formation of long-living linear aggregates of N-BAR proteins, increase in tension alters the geometry of protein association. At high tension, protein interactions are strongly inhibited. Increasing surface density of proteins leads to a wider range of protein association geometries, promoting the formation of meshes, which can be broken apart with membrane tension. Our work indicates that surface tension may play a key role in recruiting proteins to membrane-remodelling sites in the cell. PMID:26008710

Continuous Data Assimilation for a 2D Bénard Convection System Through Horizontal Velocity Measurements Alone

NASA Astrophysics Data System (ADS)

Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S.

2017-06-01

In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-dimensional Bénard convection problem. Specifically we consider the two-dimensional Boussinesq system of a layer of incompressible fluid between two solid horizontal walls, with no-normal flow and stress-free boundary conditions on the walls, and the fluid is heated from the bottom and cooled from the top. In this algorithm, we incorporate the observables as a feedback (nudging) term in the evolution equation of the horizontal velocity. We show that under an appropriate choice of the nudging parameter and the size of the spatial coarse mesh observables, and under the assumption that the observed data are error free, the solution of the proposed algorithm converges at an exponential rate, asymptotically in time, to the unique exact unknown reference solution of the original system, associated with the observed data on the horizontal component of the velocity.

Do initial conditions matter? A comparison of model climatologies generated from different initial states

NASA Technical Reports Server (NTRS)

Spar, J.; Cohen, C.; Wu, P.

1981-01-01

A coarse mesh (8 by 10) 7 layer global climate model was used to compute 15 months of meteorological history in two perpetual January experiments on a water planet (without continents) with a zonally symmetric climatological January sea surface temperature field. In the first of the two water planet experiments the initial atmospheric state was a set of zonal mean values of specific humidity, temperature, and wind at each latitude. In the second experiment the model was initialized with globally uniform mean values of specific humidity and temperature on each sigma level surface, constant surface pressure (1010 mb), and zero wind everywhere. A comparison was made of the mean January climatic states generated by the two water planet experiments. The first two months of each 15 January run were discarded, and 13 month averages were computed from months 3 through 15.

Prediction of the diffuse-field transmission loss of interior natural-ventilation openings and silencers.

PubMed

Bibby, Chris; Hodgson, Murray

2017-01-01

The work reported here, part of a study on the performance and optimal design of interior natural-ventilation openings and silencers ("ventilators"), discusses the prediction of the acoustical performance of such ventilators, and the factors that affect it. A wave-based numerical approach-the finite-element method (FEM)-is applied. The development of a FEM technique for the prediction of ventilator diffuse-field transmission loss is presented. Model convergence is studied with respect to mesh, frequency-sampling and diffuse-field convergence. The modeling technique is validated by way of predictions and the comparison of them to analytical and experimental results. The transmission-loss performance of crosstalk silencers of four shapes, and the factors that affect it, are predicted and discussed. Performance increases with flow-path length for all silencer types. Adding elbows significantly increases high-frequency transmission loss, but does not increase overall silencer performance which is controlled by low-to-mid-frequency transmission loss.

Information loss and reconstruction in diffuse fluorescence tomography

PubMed Central

Bonfert-Taylor, Petra; Leblond, Frederic; Holt, Robert W.; Tichauer, Kenneth; Pogue, Brian W.; Taylor, Edward C.

2012-01-01

This paper is a theoretical exploration of spatial resolution in diffuse fluorescence tomography. It is demonstrated that, given a fixed imaging geometry, one cannot—relative to standard techniques such as Tikhonov regularization and truncated singular value decomposition—improve the spatial resolution of the optical reconstructions via increasing the node density of the mesh considered for modeling light transport. Using techniques from linear algebra, it is shown that, as one increases the number of nodes beyond the number of measurements, information is lost by the forward model. It is demonstrated that this information cannot be recovered using various common reconstruction techniques. Evidence is provided showing that this phenomenon is related to the smoothing properties of the elliptic forward model that is used in the diffusion approximation to light transport in tissue. This argues for reconstruction techniques that are sensitive to boundaries, such as L1-reconstruction and the use of priors, as well as the natural approach of building a measurement geometry that reflects the desired image resolution. PMID:22472763

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.

Biocompatible Capsules and Methods of Making

NASA Technical Reports Server (NTRS)

Loftus, David J. (Inventor)

2017-01-01

Embodiments of the invention include capsules for containing medical implants and delivery systems for release of active biological substances into a host body. Delivery systems comprise a capsule comprising an interior enclosed by walls, and a source of active biological substances enclosed within the capsule interior, wherein the active biological substances are free to diffuse across the capsule walls. The capsule walls comprise a continuous mesh of biocompatible fibers and a seal region where two capsule walls overlap. The interior of the capsule is substantially isolated from the medium surrounding the capsule, except for diffusion of at least one species of molecule between the capsule interior and the ambient medium, and prevents cell migration into or out of the capsule. Methods for preparing and using the capsules and delivery systems are provided.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

A study of the radiative transfer equation using a spherical harmonics-nodal collocation method

NASA Astrophysics Data System (ADS)

Capilla, M. T.; Talavera, C. F.; Ginestar, D.; Verdú, G.

2017-03-01

Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.

[Tracheobronchoplasty for Severe Diffuse Tracheomalacia].

PubMed

Hoffmann, H; Gompelmann, D; Heußel, C P; Dienemann, H; Eberhardt, R

2016-09-01

Patients with diffuse airway instability due to tracheobronchomalacia or excessive dynamic airway collapse are typically highly symptomatic, with marked dyspnoea, recurrent bronchopulmonary infections and excruciating intractable cough. Silicone stents achieve immediate symptom control, but are - due to the typical complications associated with stent treatment - usually not an option for long-term treatment. The aim of surgical intervention is definitive stabilisation of the trachea and of both main bronchi by posterior splinting of the Paries membranaceus with a polypropylene mesh. This operation is an appropriate treatment option for patients with documented severe tracheobronchomalacia or excessive dynamic airway collapse and is ultimately the only therapy that can achieve permanent symptom control. The success of the operation, however, depends on many factors and requires close interdisciplinary collaboration. Georg Thieme Verlag KG Stuttgart · New York.

Porous coatings from wire mesh for bone implants

DOEpatents

Sump, Kenneth R.

1986-01-01

A method of coating areas of bone implant elements and the resulting implant having a porous coating are described. Preselected surface areas are covered by a preform made from continuous woven lengths of wire. The preform is compressed and heated to assure that diffusion bonding occurs between the wire surfaces and between the surface boundaries of the implant element and the wire surfaces in contact with it. Porosity is achieved by control of the resulting voids between the bonded wire portions.

Diffuser/ejector system for a very high vacuum environment

NASA Technical Reports Server (NTRS)

Riggs, K. E.; Wojciechowski, C. J. (Inventor)

1984-01-01

Turbo jet engines are used to furnish the necessary high temperature, high volume, medium pressure gas to provide a high vacuum test environment at comparatively low cost for space engines at sea level. Moreover, the invention provides a unique way by use of the variable area ratio ejectors with a pair of meshing cones are used. The outer cone is arranged to translate fore and aft, and the inner cone is interchangeable with other cones having varying angles of taper.

Posterior Mesh Tracheoplasty for Cervical Tracheomalacia: A Novel Trachea-Preserving Technique.

PubMed

Wilson, Jennifer L; Folch, Erik; Kent, Michael S; Majid, Adnan; Gangadharan, Sidhu P

2016-01-01

Tracheal resection or placement of airway prostheses (stents, tracheostomy tubes, or T tubes) are techniques currently used to treat severe cervical tracheomalacia. We have developed a new technique to secure a polypropylene splint to the posterior membrane of the cervical trachea in a patient with diffuse, acquired tracheobronchomalacia. This novel posterior tracheoplasty avoids anastomotic and intraluminal adverse events that may occur with existing techniques. Copyright © 2016 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

Characteristic of root decomposition in a tropical rainforest in Sarawak, Malaysi

NASA Astrophysics Data System (ADS)

Ohashi, Mizue; Makita, Naoki; Katayam, Ayumi; Kume, Tomonori; Matsumoto, Kazuho; Khoon Kho, L.

2016-04-01

Woody roots play a significant role in forest carbon cycling, as up to 60 percent of tree photosynthetic production can be allocated to belowground. Root decay is one of the main processes of soil C dynamics and potentially relates to soil C sequestration. However, much less attention has been paid for root litter decomposition compared to the studies of leaf litter because roots are hidden from view. Previous studies have revealed that physico-chemical quality of roots, climate, and soil organisms affect root decomposition significantly. However, patterns and mechanisms of root decomposition are still poorly understood because of the high variability of root properties, field environment and potential decomposers. For example, root size would be a factor controlling decomposition rates, but general understanding of the difference between coarse and fine root decompositions is still lacking. Also, it is known that root decomposition is performed by soil animals, fungi and bacteria, but their relative importance is poorly understood. In this study, therefore, we aimed to characterize the root decomposition in a tropical rainforest in Sarawak, Malaysia, and clarify the impact of soil living organisms and root sizes on root litter decomposition. We buried soil cores with fine and coarse root litter bags in soil in Lambir Hills National Park. Three different types of soil cores that are covered by 1.5 cm plastic mesh, root-impermeable sheet (50um) and fungi-impermeable sheet (1um) were prepared. The soil cores were buried in February 2013 and collected 4 times, 134 days, 226 days, 786 days and 1151 days after the installation. We found that nearly 80 percent of the coarse root litter was decomposed after two years, whereas only 60 percent of the fine root litter was decomposed. Our results also showed significantly different ratio of decomposition between different cores, suggesting the different contribution of soil living organisms to decomposition process.