A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

A gradient enhanced plasticity-damage microplane model for concrete

NASA Astrophysics Data System (ADS)

Zreid, Imadeddin; Kaliske, Michael

2018-03-01

Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

A Comprehensive Solution of the Problems of Ensuring the Strength of Gas Turbine Engine Compressor at the Design Stage

NASA Astrophysics Data System (ADS)

Vedeneev, V. V.; Kolotnikov, M. E.; Mossakovskii, P. A.; Kostyreva, L. A.; Abdukhakimov, F. A.; Makarov, P. V.; Pyhalov, A. A.; Dudaev, M. A.

2018-01-01

In this paper we present a complex numerical workflow for analysis of blade flutter and high-amplitude resonant oscillations, impenetrability of casing if the blade is broken off, and the rotor reaction to the blade detachment and following misbalance, with the assessment of a safe flight possibility at the auto-rotation regime. All the methods used are carefully verified by numerical convergence study and correlations with experiments. The use of the workflow developed significantly improves the efficiency of the design process of modern jet engine compressors. It ensures a significant reduction of time and cost of the compressor design with the required level of strength and durability.

A numerical performance assessment of a commercial cardiopulmonary by-pass blood heat exchanger.

PubMed

Consolo, Filippo; Fiore, Gianfranco B; Pelosi, Alessandra; Reggiani, Stefano; Redaelli, Alberto

2015-06-01

We developed a numerical model, based on multi-physics computational fluid dynamics (CFD) simulations, to assist the design process of a plastic hollow-fiber bundle blood heat exchanger (BHE) integrated within the INSPIRE(TM), a blood oxygenator (OXY) for cardiopulmonary by-pass procedures, recently released by Sorin Group Italia. In a comparative study, we analyzed five different geometrical design solutions of the BHE module. Quantitative geometrical-dependent parameters providing a comprehensive evaluation of both the hemo- and thermo-dynamics performance of the device were extracted to identify the best-performing prototypical solution. A convenient design configuration was identified, characterized by (i) a uniform blood flow pattern within the fiber bundle, preventing blood flow shunting and the onset of stagnation/recirculation areas and/or high velocity pathways, (ii) an enhanced blood heating efficiency, and (iii) a reduced blood pressure drop. The selected design configuration was then prototyped and tested to experimentally characterize the device performance. Experimental results confirmed numerical predictions, proving the effectiveness of CFD modeling as a reliable tool for in silico identification of suitable working conditions of blood handling medical devices. Notably, the numerical approach limited the need for extensive prototyping, thus reducing the corresponding machinery costs and time-to-market. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

Cost-effective use of minicomputers to solve structural problems

NASA Technical Reports Server (NTRS)

Storaasli, O. O.; Foster, E. P.

1978-01-01

Minicomputers are receiving increased use throughout the aerospace industry. Until recently, their use focused primarily on process control and numerically controlled tooling applications, while their exposure to and the opportunity for structural calculations has been limited. With the increased availability of this computer hardware, the question arises as to the feasibility and practicality of carrying out comprehensive structural analysis on a minicomputer. This paper presents results on the potential for using minicomputers for structural analysis by (1) selecting a comprehensive, finite-element structural analysis system in use on large mainframe computers; (2) implementing the system on a minicomputer; and (3) comparing the performance of the minicomputers with that of a large mainframe computer for the solution to a wide range of finite element structural analysis problems.

The CMC/3DPNS computer program for prediction of three-dimension, subsonic, turbulent aerodynamic juncture region flow. Volume 2: Users' manual

NASA Technical Reports Server (NTRS)

Manhardt, P. D.

1982-01-01

The CMC fluid mechanics program system was developed to transmit the theoretical solution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. Data procedures for the CMC 3 dimensional Parabolic Navier-Stokes (PNS) algorithm are presented. General data procedures a juncture corner flow standard test case data deck is described. A listing of the data deck and an explanation of grid generation methodology are presented. Tabulations of all commands and variables available to the user are described. These are in alphabetical order with cross reference numbers which refer to storage addresses.

A comprehensive one-dimensional numerical model for solute transport in rivers

NASA Astrophysics Data System (ADS)

Barati Moghaddam, Maryam; Mazaheri, Mehdi; MohammadVali Samani, Jamal

2017-01-01

One of the mechanisms that greatly affect the pollutant transport in rivers, especially in mountain streams, is the effect of transient storage zones. The main effect of these zones is to retain pollutants temporarily and then release them gradually. Transient storage zones indirectly influence all phenomena related to mass transport in rivers. This paper presents the TOASTS (third-order accuracy simulation of transient storage) model to simulate 1-D pollutant transport in rivers with irregular cross-sections under unsteady flow and transient storage zones. The proposed model was verified versus some analytical solutions and a 2-D hydrodynamic model. In addition, in order to demonstrate the model applicability, two hypothetical examples were designed and four sets of well-established frequently cited tracer study data were used. These cases cover different processes governing transport, cross-section types and flow regimes. The results of the TOASTS model, in comparison with two common contaminant transport models, shows better accuracy and numerical stability.

Transient Dupuit Interface Flow with partially penetrating features

NASA Astrophysics Data System (ADS)

Bakker, Mark

1998-11-01

A comprehensive potential is presented for Dupuit interface flow in coastal aquifers where both the fresh water and salt water are moving. The resulting potential flow problem may be solved, for incompressible confined aquifers, using analytic functions. The vertical velocity of the interface may then be computed analytically and the change of the position of the interface may be simulated by numerical integration through time, starting with a known (or estimated) initial position. The upconing of the interface below a partially penetrating ditch or well may be studied if Dupuit solutions for such features are available. A new Dupuit solution is derived for a ditch that penetrates the aquifer partially from above; a Dupuit solution for a partially penetrating well may be obtained following a similar derivation. The new Dupuit solution is combined with the interface solution to simulate the upconing of an initially horizontal interface below a series of partially penetrating ditches; the interface converges to the known steady state position.

Towards a comprehensive city emission function (CCEF)

NASA Astrophysics Data System (ADS)

Kocifaj, Miroslav

2018-01-01

The comprehensive city emission function (CCEF) is developed for a heterogeneous light-emitting or blocking urban environments, embracing any combination of input parameters that characterize linear dimensions in the system (size and distances between buildings or luminaires), properties of light-emitting elements (such as luminous building façades and street lighting), ground reflectance and total uplight-fraction, all of these defined for an arbitrarily sized 2D area. The analytical formula obtained is not restricted to a single model class as it can capture any specific light-emission feature for wide range of cities. The CCEF method is numerically fast in contrast to what can be expected of other probabilistic approaches that rely on repeated random sampling. Hence the present solution has great potential in light-pollution modeling and can be included in larger numerical models. Our theoretical findings promise great progress in light-pollution modeling as this is the first time an analytical solution to city emission function (CEF) has been developed that depends on statistical mean size and height of city buildings, inter-building separation, prevailing heights of light fixtures, lighting density, and other factors such as e.g. luminaire light output and light distribution, including the amount of uplight, and representative city size. The model is validated for sensitivity and specificity pertinent to combinations of input parameters in order to test its behavior under various conditions, including those that can occur in complex urban environments. It is demonstrated that the solution model succeeds in reproducing a light emission peak at some elevated zenith angles and is consistent with reduced rather than enhanced emission in directions nearly parallel to the ground.

Electroosmosis over charge-modulated surfaces with finite electrical double layer thicknesses: Asymptotic and numerical investigations

NASA Astrophysics Data System (ADS)

Ghosh, Uddipta; Mandal, Shubhadeep; Chakraborty, Suman

2017-06-01

Here we attempt to solve the fully coupled Poisson-Nernst-Planck-Navier-Stokes equations, to ascertain the influence of finite electric double layer (EDL) thickness on coupled charge and fluid dynamics over patterned charged surfaces. We go beyond the well-studied "weak-field" limit and obtain numerical solutions for a wide range of EDL thicknesses, applied electric field strengths, and the surface potentials. Asymptotic solutions to the coupled system are also derived using a combination of singular and regular perturbation, for thin EDLs and low surface potential, and good agreement between the two solutions is observed. Counterintuitively to common arguments, our analysis reveals that finite EDL thickness may either increase or decrease the "free-stream velocity" (equivalent to net throughput), depending on the strength of the applied electric field. We also unveil a critical EDL thickness for which the effect of finite EDL thickness on the free-stream velocity is the most prominent. Finally, we demonstrate that increasing the surface potential and the applied field tends to influence the overall flow patterns in the contrasting manners. These results may be of profound importance in developing a comprehensive theoretical basis for designing electro-osmotically actuated microfluidic mixtures.

Challenges to Applying a Metamodel for Groundwater Flow Beyond Underlying Numerical Model Boundaries

NASA Astrophysics Data System (ADS)

Reeves, H. W.; Fienen, M. N.; Feinstein, D.

2015-12-01

Metamodels of environmental behavior offer opportunities for decision support, adaptive management, and increased stakeholder engagement through participatory modeling and model exploration. Metamodels are derived from calibrated, computationally demanding, numerical models. They may potentially be applied to non-modeled areas to provide screening or preliminary analysis tools for areas that do not yet have the benefit of more comprehensive study. In this decision-support mode, they may be fulfilling a role often accomplished by application of analytical solutions. The major challenge to transferring a metamodel to a non-modeled area is how to quantify the spatial data in the new area of interest in such a way that it is consistent with the data used to derive the metamodel. Tests based on transferring a metamodel derived from a numerical groundwater-flow model of the Lake Michigan Basin to other glacial settings across the northern U.S. show that the spatial scale of the numerical model must be appropriately scaled to adequately represent different settings. Careful GIS analysis of the numerical model, metamodel, and new area of interest is required for successful transfer of results.

Towards optimization of ACRT schedules applied to the gradient freeze growth of cadmium zinc telluride

NASA Astrophysics Data System (ADS)

Divecha, Mia S.; Derby, Jeffrey J.

2017-12-01

Historically, the melt growth of II-VI crystals has benefitted from the application of the accelerated crucible rotation technique (ACRT). Here, we employ a comprehensive numerical model to assess the impact of two ACRT schedules designed for a cadmium zinc telluride growth system per the classical recommendations of Capper and co-workers. The ;flow maximizing; ACRT schedule, with higher rotation, effectively mixes the solutal field in the melt but does not reduce supercooling adjacent to the growth interface. The ACRT schedule derived for stable Ekman flow, with lower rotation, proves more effective in reducing supercooling and promoting stable growth. These counterintuitive results highlight the need for more comprehensive studies on the optimization of ACRT schedules for specific growth systems and for desired growth outcomes.

Physics and engineering studies on the MITICA accelerator: comparison among possible design solutions

NASA Astrophysics Data System (ADS)

Agostinetti, P.; Antoni, V.; Cavenago, M.; Chitarin, G.; Pilan, N.; Marcuzzi, D.; Serianni, G.; Veltri, P.

2011-09-01

Consorzio RFX in Padova is currently using a comprehensive set of numerical and analytical codes, for the physics and engineering design of the SPIDER (Source for Production of Ion of Deuterium Extracted from RF plasma) and MITICA (Megavolt ITER Injector Concept Advancement) experiments, planned to be built at Consorzio RFX. This paper presents a set of studies on different possible geometries for the MITICA accelerator, with the objective to compare different design concepts and choose the most suitable one (or ones) to be further developed and possibly adopted in the experiment. Different design solutions have been discussed and compared, taking into account their advantages and drawbacks by both the physics and engineering points of view.

Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2002-01-01

The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.

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

Sidler, Rolf, E-mail: rsidler@gmail.com; Carcione, José M.; Holliger, Klaus

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in themore » radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.« less

Numerical shockwave anomalies in presence of hydraulic jumps in the SWE with variable bed elevation.

NASA Astrophysics Data System (ADS)

Navas-Montilla, Adrian; Murillo, Javier

2017-04-01

When solving the shallow water equations appropriate numerical solvers must allow energy-dissipative solutions in presence of steady and unsteady hydraulic jumps. Hydraulic jumps are present in surface flows and may produce significant morphological changes. Unfortunately, it has been documented that some numerical anomalies may appear. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump produced by a non-linearity of the Hugoniot locus connecting the states at both sides of the jump. Therefore, this problem remains unresolved in the context of Godunov's schemes applied to shallow flows. This issue is usually ignored as it does not affect to the solution in steady cases. However, it produces undesirable spurious oscillations in transient cases that can lead to misleading conclusions when moving to realistic scenarios. Using spike-reducing techniques based on the construction of interpolated fluxes, it is possible to define numerical methods including discontinuous topography that reduce the presence of the aforementioned numerical anomalies. References: T. W. Roberts, The behavior of flux difference splitting schemes near slowly moving shock waves, J. Comput. Phys., 90 (1990) 141-160. Y. Stiriba, R. Donat, A numerical study of postshock oscillations in slowly moving shock waves, Comput. Math. with Appl., 46 (2003) 719-739. E. Johnsen, S. K. Lele, Numerical errors generated in simulations of slowly moving shocks, Center for Turbulence Research, Annual Research Briefs, (2008) 1-12. D. W. Zaide, P. L. Roe, Flux functions for reducing numerical shockwave anomalies. ICCFD7, Big Island, Hawaii, (2012) 9-13. D. W. Zaide, Numerical Shockwave Anomalies, PhD thesis, Aerospace Engineering and Scientific Computing, University of Michigan, 2012. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms, J. Comput. Phys. 317 (2016) 108-147. J. Murillo and A. Navas-Montilla, A comprehensive explanation and exercise of the source terms in hyperbolic systems using Roe type solutions. Application to the 1D-2D shallow water equations, Advances in Water Resources {98} (2016) 70-96.

An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone.

PubMed

Liu, Yun-Feng; Fan, Ying-Ying; Dong, Hui-Yue; Zhang, Jian-Xing

2017-12-01

The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

Solution techniques for transient stability-constrained optimal power flow – Part II

DOE PAGES

Geng, Guangchao; Abhyankar, Shrirang; Wang, Xiaoyu; ...

2017-06-28

Transient stability-constrained optimal power flow is an important emerging problem with power systems pushed to the limits for economic benefits, dense and larger interconnected systems, and reduced inertia due to expected proliferation of renewable energy resources. In this study, two more approaches: single machine equivalent and computational intelligence are presented. Also discussed are various application areas, and future directions in this research area. In conclusion, a comprehensive resource for the available literature, publicly available test systems, and relevant numerical libraries is also provided.

Solution techniques for transient stability-constrained optimal power flow – Part II

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

Geng, Guangchao; Abhyankar, Shrirang; Wang, Xiaoyu

Transient stability-constrained optimal power flow is an important emerging problem with power systems pushed to the limits for economic benefits, dense and larger interconnected systems, and reduced inertia due to expected proliferation of renewable energy resources. In this study, two more approaches: single machine equivalent and computational intelligence are presented. Also discussed are various application areas, and future directions in this research area. In conclusion, a comprehensive resource for the available literature, publicly available test systems, and relevant numerical libraries is also provided.

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

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

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Some unsolved problems in discrete mathematics and mathematical cybernetics

NASA Astrophysics Data System (ADS)

Korshunov, Aleksei D.

2009-10-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Towards Optimization of ACRT Schedules Applied to the Gradient Freeze Growth of Cadmium Zinc Telluride

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

Divecha, Mia S.; Derby, Jeffrey J.

Historically, the melt growth of II-VI crystals has benefitted by the application of the accelerated crucible rotation technique (ACRT). Here, we employ a comprehensive numerical model to assess the impact of two ACRT schedules designed for a cadmium zinc telluride growth system per the classical recommendations of Capper and co-workers. The “flow maximizing” ACRT schedule, with higher rotation, effectively mixes the solutal field in the melt but does not reduce supercooling adjacent to the growth interface. The ACRT schedule derived for stable Ekman flow, with lower rotation, proves more effective in reducing supercooling and promoting stable growth. Furthermore, these counterintuitivemore » results highlight the need for more comprehensive studies on the optimization of ACRT schedules for specific growth systems and for desired growth outcomes.« less

Towards Optimization of ACRT Schedules Applied to the Gradient Freeze Growth of Cadmium Zinc Telluride

DOE PAGES

Divecha, Mia S.; Derby, Jeffrey J.

2017-10-03

Historically, the melt growth of II-VI crystals has benefitted by the application of the accelerated crucible rotation technique (ACRT). Here, we employ a comprehensive numerical model to assess the impact of two ACRT schedules designed for a cadmium zinc telluride growth system per the classical recommendations of Capper and co-workers. The “flow maximizing” ACRT schedule, with higher rotation, effectively mixes the solutal field in the melt but does not reduce supercooling adjacent to the growth interface. The ACRT schedule derived for stable Ekman flow, with lower rotation, proves more effective in reducing supercooling and promoting stable growth. Furthermore, these counterintuitivemore » results highlight the need for more comprehensive studies on the optimization of ACRT schedules for specific growth systems and for desired growth outcomes.« less

Space plasma contractor research, 1988

NASA Technical Reports Server (NTRS)

Williams, John D.; Wilbur, Paul J.

1989-01-01

Results of experiments conducted on hollow cathode-based plasma contractors are reported. Specific tests in which attempts were made to vary plasma conditions in the simulated ionospheric plasma are described. Experimental results showing the effects of contractor flowrate and ion collecting surface size on contactor performance and contactor plasma plume geometry are presented. In addition to this work, one-dimensional solutions to spherical and cylindircal space-charge limited double-sheath problems are developed. A technique is proposed that can be used to apply these solutions to the problem of current flow through elongated double-sheaths that separate two cold plasmas. Two conference papers which describe the essential features of the plasma contacting process and present data that should facilitate calibration of comprehensive numerical models of the plasma contacting process are also included.

A comprehensive comparison of turbulence models in the far wake

NASA Technical Reports Server (NTRS)

Cimbala, John M.

1993-01-01

In the present study, the far wake was examined numerically using an implicit, upwind, finite-volume, compressible Navier-Stokes code. The numerical grid started at 500 equivalent circular cylinder diameters in the wave, and extended to 4000 equivalent diameters. By concentrating only on the far wake, the numerical difficulties and fine mesh requirements near the wake-generating body were eliminated. At the time of this writing, results for the K-epsilon and K-omega turbulence models at low Mach number have been completed and show excellent agreement with previous incompressible results and far-wake similarity solutions. The code is presently being used to compare the performance of various other turbulence models, including Reynolds stress models and the new anisotropic two-equation turbulence models being developed at NASA Langley. By increasing our physical understanding of the deficiencies and limits of these models, it is hoped that improvements to the universality of the models can be made. Future plans include examination of two-dimensional momentumless wakes as well.

Presenting numeric information with percentages and descriptive risk labels: A randomized trial

PubMed Central

Sinayev, Aleksandr; Peters, Ellen; Tusler, Martin; Fraenkel, Liana

2015-01-01

Background Previous research demonstrated that providing (vs. not providing) numeric information about medications’ adverse effects (AEs) increased comprehension and willingness to use medication, but left open the question about which numeric format is best. Objective To determine which of four tested formats (percentage, frequency, percentage+risk label, frequency+risk label) maximizes comprehension and willingness to use medication across age and numeracy levels. Design In a cross-sectional internet survey (N=368; American Life Panel, 5/15/08–6/18/08), respondents were presented with a hypothetical prescription medication for high cholesterol. AE likelihoods were described using one of four tested formats. Main outcome measures were risk comprehension (ability to identify AE likelihood from a table) and willingness to use the medication (7-point scale; not likely=0, very likely=6). Results The percentage+risk label format resulted in the highest comprehension and willingness to use the medication compared to the other three formats (mean comprehension in percentage + risk label format=95% vs mean across the other three formats = 81%; mean willingness= 3.3 vs 2.95, respectively). Comprehension differences between percentage and frequency formats were smaller among the less numerate. Willingness to use medication depended less on age and numeracy when labels were used. Limitations Generalizability is limited by use of a sample that was older, more educated, and better off financially than national averages. Conclusions Providing numeric AE-likelihood information in a percentage format with risk labels is likely to increase risk comprehension and willingness to use a medication compared to other numeric formats. PMID:25952743

Presenting Numeric Information with Percentages and Descriptive Risk Labels: A Randomized Trial.

PubMed

Sinayev, Aleksandr; Peters, Ellen; Tusler, Martin; Fraenkel, Liana

2015-11-01

Previous research demonstrated that providing (v. not providing) numeric information about the adverse effects (AEs) of medications increased comprehension and willingness to use medication but left open the question about which numeric format is best. The objective was to determine which of 4 tested formats (percentage, frequency, percentage + risk label, frequency + risk label) maximizes comprehension and willingness to use medication across age and numeracy levels. In a cross-sectional internet survey (N = 368; American Life Panel, 15 May 2008 to 18 June 2008), respondents were presented with a hypothetical prescription medication for high cholesterol. AE likelihoods were described using 1 of 4 tested formats. Main outcome measures were risk comprehension (ability to identify AE likelihood from a table) and willingness to use the medication (7-point scale; not likely = 0, very likely = 6). The percentage + risk label format resulted in the highest comprehension and willingness to use the medication compared with the other 3 formats (mean comprehension in percentage + risk label format = 95% v. mean across the other 3 formats = 81%; mean willingness = 3.3 v. 2.95, respectively). Comprehension differences between percentage and frequency formats were smaller among the less numerate. Willingness to use medication depended less on age and numeracy when labels were used. Generalizability is limited by the use of a sample that was older, more educated, and better off financially than national averages. Providing numeric AE-likelihood information in a percentage format with risk labels is likely to increase risk comprehension and willingness to use a medication compared with other numeric formats. © The Author(s) 2015.

Torque Balances on the Taylor Cylinders in the Geomagnetic Data Assimilation

NASA Technical Reports Server (NTRS)

Kuang, Weijia; Tangborn, Andrew

2004-01-01

In this presentation we report on our continuing effort in geomagnetic data assimilation, aiming at understanding and predicting geomagnetic secular variation on decadal time scales. In particular, we focus on the effect of the torque balances on the cylindrical surfaces in the core co-axial with the Earth's rotation axis (the Taylor cylinders) on the time evolution of assimilated solutions. We use our MoSST core dynamics,model and observed geomagnetic field at the Earth's surface derived via Comprehensive Field Model (CFM) for the geomagnetic data assimilation. In our earlier studies, a model solution is selected randomly from our numerical database. It is then assimilated with the observations such that the poloidal field possesses the same field tomography on the core-mantel boundary (CMB) continued downward from surface observations. This tomography change is assumed to be effective through out the outer core. While this approach allows rapid convergence between model solutions and the observations, it also generates sevee numerical instabilities: the delicate balance between weak fluid inertia and the magnetic torques on the Taylor cylinders are completely altered. Consequently, the assimilated solution diverges quickly (in approximately 10% of the magnetic free-decay time in the core). To improve the assimilation, we propose a partial penetration of the assimilation from the CMB: The full-scale modification at the CMB decreases linearly and vanish at an interior radius r(sub a). We shall examine from our assimilation tests possible relationships between the convergence rate of the model solutions to observations and the cut-off radius r(sub a). A better assimilation shall serve our nudging tests in near future.

Torque Balances on the Taylor Cylinders in the Geomagnetic Data Assimilation

NASA Astrophysics Data System (ADS)

Kuang, W.; Tangborn, A.

2004-05-01

In this presentation we report on our continuing effort in geomagnetic data assimilation, aiming at understanding and predicting geomagnetic secular variation on decadal time scales. In particular, we focus on the effect of the torque balances on the cylindrical surfaces in the core co-axial with the Earth's rotation axis (the Taylor cylinders) on the time evolution of assimilated solutions. We use our MoSST core dynamics model and observed geomagnetic field at the Earth's surface derived via Comprehensive Field Model (CFM) for the geomagnetic data assimilation. In our earlier studies, a model solution is selected randomly from our numerical database. It is then assimilated with the observations such that the poloidal field possesses the same field tomography on the core-mantel boundary (CMB) continued downward from surface observations. This tomography change is assumed to be effective through out the outer core. While this approach allows rapid convergence between model solutions and the observations, it also generates sever numerical instabilities: the delicate balance between weak fluid inertia and the magnetic torques on the Taylor cylinders are completely altered. Consequently, the assimilated solution diverges quickly (in approximately 10% of the magnetic free-decay time in the core). To improve the assimilation, we propose a partial penetration of the assimilation from the CMB: The full-scale modification at the CMB decreases linearly and vanish at an interior radius ra. We shall examine from our assimilation tests possible relationships between the convergence rate of the model solutions to observations and the cut-off radius ra. A better assimilation shall serve our nudging tests in near future.

Revealing Numerical Solutions of a Differential Equation

ERIC Educational Resources Information Center

Glaister, P.

2006-01-01

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…

How to Find a Bug in Ten Thousand Lines Transport Solver? Outline of Experiences from AN Advection-Diffusion Code Verification

NASA Astrophysics Data System (ADS)

Zamani, K.; Bombardelli, F.

2011-12-01

Almost all natural phenomena on Earth are highly nonlinear. Even simplifications to the equations describing nature usually end up being nonlinear partial differential equations. Transport (ADR) equation is a pivotal equation in atmospheric sciences and water quality. This nonlinear equation needs to be solved numerically for practical purposes so academicians and engineers thoroughly rely on the assistance of numerical codes. Thus, numerical codes require verification before they are utilized for multiple applications in science and engineering. Model verification is a mathematical procedure whereby a numerical code is checked to assure the governing equation is properly solved as it is described in the design document. CFD verification is not a straightforward and well-defined course. Only a complete test suite can uncover all the limitations and bugs. Results are needed to be assessed to make a distinction between bug-induced-defect and innate limitation of a numerical scheme. As Roache (2009) said, numerical verification is a state-of-the-art procedure. Sometimes novel tricks work out. This study conveys the synopsis of the experiences we gained during a comprehensive verification process which was done for a transport solver. A test suite was designed including unit tests and algorithmic tests. Tests were layered in complexity in several dimensions from simple to complex. Acceptance criteria defined for the desirable capabilities of the transport code such as order of accuracy, mass conservation, handling stiff source term, spurious oscillation, and initial shape preservation. At the begining, mesh convergence study which is the main craft of the verification is performed. To that end, analytical solution of ADR equation gathered. Also a new solution was derived. In the more general cases, lack of analytical solution could be overcome through Richardson Extrapolation and Manufactured Solution. Then, two bugs which were concealed during the mesh convergence study uncovered with the method of false injection and visualization of the results. Symmetry had dual functionality: there was a bug, which was hidden due to the symmetric nature of a test (it was detected afterward utilizing artificial false injection), on the other hand self-symmetry was used to design a new test, and in a case the analytical solution of the ADR equation was unknown. Assisting subroutines designed to check and post-process conservation of mass and oscillatory behavior. Finally, capability of the solver also checked for stiff reaction source term. The above test suite not only was a decent tool of error detection but also it provided a thorough feedback on the ADR solvers limitations. Such information is the crux of any rigorous numerical modeling for a modeler who deals with surface/subsurface pollution transport.

Numerical Asymptotic Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity.

PubMed

Font, José A

2008-01-01

This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works. Supplementary material is available for this article at 10.12942/lrr-2008-7.

Considerations on the Improved Integration of Medical Guidelines into Routine Clinical Practice – a Review and Concept Proposal

PubMed Central

Beckmann, M. W.; Schlieter, H.; Richter, P.; Wesselmann, S.

2016-01-01

Medical guidelines have become established as the standard for the comprehensive synopsis of all available information (scientific trials, expert opinion) on diagnosis and treatment recommendations. The transfer of guidelines to clinical practice and subsequent monitoring has however proven difficult. In particular the potential interaction between guideline developers and guideline users has not been fully utilised. This review article analyses the status quo and existing methodological and technical information solutions supporting the guideline life cycle. It is shown that there are numerous innovative developments that in isolation do not provide comprehensive support. The vision of the “Living Guidelines 2.0” is therefore presented. This outlines the merging of guideline development and implementation on the basis of clinical pathways and guideline-based quality control, and building on this, the generation of information for guideline development and research. PMID:27134291

"Notice of Violation of IEEE Publication Principles" Multiobjective Reinforcement Learning: A Comprehensive Overview.

PubMed

Liu, Chunming; Xu, Xin; Hu, Dewen

2013-04-29

Reinforcement learning is a powerful mechanism for enabling agents to learn in an unknown environment, and most reinforcement learning algorithms aim to maximize some numerical value, which represents only one long-term objective. However, multiple long-term objectives are exhibited in many real-world decision and control problems; therefore, recently, there has been growing interest in solving multiobjective reinforcement learning (MORL) problems with multiple conflicting objectives. The aim of this paper is to present a comprehensive overview of MORL. In this paper, the basic architecture, research topics, and naive solutions of MORL are introduced at first. Then, several representative MORL approaches and some important directions of recent research are reviewed. The relationships between MORL and other related research are also discussed, which include multiobjective optimization, hierarchical reinforcement learning, and multi-agent reinforcement learning. Finally, research challenges and open problems of MORL techniques are highlighted.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

Does format matter for comprehension of a facial affective scale and a numeric scale for pain by adults with Down syndrome?

PubMed

de Knegt, N C; Evenhuis, H M; Lobbezoo, F; Schuengel, C; Scherder, E J A

2013-10-01

People with intellectual disabilities are at high risk for pain and have communication difficulties. Facial and numeric scales for self-report may aid pain identification. It was examined whether the comprehension of a facial affective scale and a numeric scale for pain in adults with Down syndrome (DS) varies with presentation format. Adults with DS were included (N=106, mild to severe ID, mean age 37 years), both with (N=57) and without (N=49) physical conditions that may cause pain or discomfort. The Facial Affect Scale (FAS) and a numeric rating scale (NRS) were compared. One subgroup of participants (N=50) had to choose the two items within each format to indicate 'least pain' and 'most pain'. The other subgroup of participants (N=56) had to order three faces of the FAS from 'least pain' to 'most pain', and to answer questions about the magnitude of numbers for the NRS. Comprehension percentages were compared between two subgroups. More participants understood the FAS than the NRS, irrespective of the presentation format. The comprehension percentage for the FAS did not differ between the least-most extremities format and the ordering/magnitude format. In contrast, comprehension percentages for the NRS differed significantly between the least-most extremities format (61%) and the ordering/magnitude format (32%). The inclusion of ordering and magnitude in a presentation format is essential to assess thorough comprehension of facial and numeric scales for self-reported pain. The use of this format does not influence the number of adults with DS who pass the comprehension test for the FAS, but reduces the number of adults with DS who pass the comprehension test for the NRS. Copyright © 2013 Elsevier Ltd. All rights reserved.

Stratified flows with variable density: mathematical modelling and numerical challenges.

NASA Astrophysics Data System (ADS)

Murillo, Javier; Navas-Montilla, Adrian

2017-04-01

Stratified flows appear in a wide variety of fundamental problems in hydrological and geophysical sciences. They may involve from hyperconcentrated floods carrying sediment causing collapse, landslides and debris flows, to suspended material in turbidity currents where turbulence is a key process. Also, in stratified flows variable horizontal density is present. Depending on the case, density varies according to the volumetric concentration of different components or species that can represent transported or suspended materials or soluble substances. Multilayer approaches based on the shallow water equations provide suitable models but are not free from difficulties when moving to the numerical resolution of the governing equations. Considering the variety of temporal and spatial scales, transfer of mass and energy among layers may strongly differ from one case to another. As a consequence, in order to provide accurate solutions, very high order methods of proved quality are demanded. Under these complex scenarios it is necessary to observe that the numerical solution provides the expected order of accuracy but also converges to the physically based solution, which is not an easy task. To this purpose, this work will focus in the use of Energy balanced augmented solvers, in particular, the Augmented Roe Flux ADER scheme. References: J. Murillo , P. García-Navarro, Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. J. Comput. Phys. 231 (2012) 1963-2001. J. Murillo B. Latorre, P. García-Navarro. A Riemann solver for unsteady computation of 2D shallow flows with variable density. J. Comput. Phys.231 (2012) 4775-4807. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms, J. Comput. Phys. 317 (2016) 108-147. J. Murillo and A. Navas-Montilla, A comprehensive explanation and exercise of the source terms in hyperbolic systems using Roe type solutions. Application to the 1D-2D shallow water equations, Advances in Water Resources 98 (2016) 70-96.

Analytical three-dimensional neutron transport benchmarks for verification of nuclear engineering codes. Final report

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

Ganapol, B.D.; Kornreich, D.E.

Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) pointmore » source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green`s function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade.« less

Data-driven multi-scale multi-physics models to derive process-structure-property relationships for additive manufacturing

NASA Astrophysics Data System (ADS)

Yan, Wentao; Lin, Stephen; Kafka, Orion L.; Lian, Yanping; Yu, Cheng; Liu, Zeliang; Yan, Jinhui; Wolff, Sarah; Wu, Hao; Ndip-Agbor, Ebot; Mozaffar, Mojtaba; Ehmann, Kornel; Cao, Jian; Wagner, Gregory J.; Liu, Wing Kam

2018-05-01

Additive manufacturing (AM) possesses appealing potential for manipulating material compositions, structures and properties in end-use products with arbitrary shapes without the need for specialized tooling. Since the physical process is difficult to experimentally measure, numerical modeling is a powerful tool to understand the underlying physical mechanisms. This paper presents our latest work in this regard based on comprehensive material modeling of process-structure-property relationships for AM materials. The numerous influencing factors that emerge from the AM process motivate the need for novel rapid design and optimization approaches. For this, we propose data-mining as an effective solution. Such methods—used in the process-structure, structure-properties and the design phase that connects them—would allow for a design loop for AM processing and materials. We hope this article will provide a road map to enable AM fundamental understanding for the monitoring and advanced diagnostics of AM processing.

Bio-Inspired Functional Surfaces Based on Laser-Induced Periodic Surface Structures

PubMed Central

Müller, Frank A.; Kunz, Clemens; Gräf, Stephan

2016-01-01

Nature developed numerous solutions to solve various technical problems related to material surfaces by combining the physico-chemical properties of a material with periodically aligned micro/nanostructures in a sophisticated manner. The utilization of ultra-short pulsed lasers allows mimicking numerous of these features by generating laser-induced periodic surface structures (LIPSS). In this review paper, we describe the physical background of LIPSS generation as well as the physical principles of surface related phenomena like wettability, reflectivity, and friction. Then we introduce several biological examples including e.g., lotus leafs, springtails, dessert beetles, moth eyes, butterfly wings, weevils, sharks, pangolins, and snakes to illustrate how nature solves technical problems, and we give a comprehensive overview of recent achievements related to the utilization of LIPSS to generate superhydrophobic, anti-reflective, colored, and drag resistant surfaces. Finally, we conclude with some future developments and perspectives related to forthcoming applications of LIPSS-based surfaces. PMID:28773596

Analysis of the thermal performance of heat pipe radiators

NASA Technical Reports Server (NTRS)

Boo, J. H.; Hartley, J. G.

1990-01-01

A comprehensive mathematical model and computational methodology are presented to obtain numerical solutions for the transient behavior of a heat pipe radiator in a space environment. The modeling is focused on a typical radiator panel having a long heat pipe at the center and two extended surfaces attached to opposing sides of the heat pipe shell in the condenser section. In the set of governing equations developed for the model, each region of the heat pipe - shell, liquid, and vapor - is thermally lumped to the extent possible, while the fin is lumped only in the direction normal to its surface. Convection is considered to be the only significant heat transfer mode in the vapor, and the evaporation and condensation velocity at the liquid-vapor interface is calculated from kinetic theory. A finite-difference numerical technique is used to predict the transient behavior of the entire radiator in response to changing loads.

Bio-Inspired Functional Surfaces Based on Laser-Induced Periodic Surface Structures.

PubMed

Müller, Frank A; Kunz, Clemens; Gräf, Stephan

2016-06-15

Nature developed numerous solutions to solve various technical problems related to material surfaces by combining the physico-chemical properties of a material with periodically aligned micro/nanostructures in a sophisticated manner. The utilization of ultra-short pulsed lasers allows mimicking numerous of these features by generating laser-induced periodic surface structures (LIPSS). In this review paper, we describe the physical background of LIPSS generation as well as the physical principles of surface related phenomena like wettability, reflectivity, and friction. Then we introduce several biological examples including e.g., lotus leafs, springtails, dessert beetles, moth eyes, butterfly wings, weevils, sharks, pangolins, and snakes to illustrate how nature solves technical problems, and we give a comprehensive overview of recent achievements related to the utilization of LIPSS to generate superhydrophobic, anti-reflective, colored, and drag resistant surfaces. Finally, we conclude with some future developments and perspectives related to forthcoming applications of LIPSS-based surfaces.

Data-driven multi-scale multi-physics models to derive process-structure-property relationships for additive manufacturing

NASA Astrophysics Data System (ADS)

Yan, Wentao; Lin, Stephen; Kafka, Orion L.; Lian, Yanping; Yu, Cheng; Liu, Zeliang; Yan, Jinhui; Wolff, Sarah; Wu, Hao; Ndip-Agbor, Ebot; Mozaffar, Mojtaba; Ehmann, Kornel; Cao, Jian; Wagner, Gregory J.; Liu, Wing Kam

2018-01-01

Additive manufacturing (AM) possesses appealing potential for manipulating material compositions, structures and properties in end-use products with arbitrary shapes without the need for specialized tooling. Since the physical process is difficult to experimentally measure, numerical modeling is a powerful tool to understand the underlying physical mechanisms. This paper presents our latest work in this regard based on comprehensive material modeling of process-structure-property relationships for AM materials. The numerous influencing factors that emerge from the AM process motivate the need for novel rapid design and optimization approaches. For this, we propose data-mining as an effective solution. Such methods—used in the process-structure, structure-properties and the design phase that connects them—would allow for a design loop for AM processing and materials. We hope this article will provide a road map to enable AM fundamental understanding for the monitoring and advanced diagnostics of AM processing.

Building of fuzzy decision trees using ID3 algorithm

NASA Astrophysics Data System (ADS)

Begenova, S. B.; Avdeenko, T. V.

2018-05-01

Decision trees are widely used in the field of machine learning and artificial intelligence. Such popularity is due to the fact that with the help of decision trees graphic models, text rules can be built and they are easily understood by the final user. Because of the inaccuracy of observations, uncertainties, the data, collected in the environment, often take an unclear form. Therefore, fuzzy decision trees becoming popular in the field of machine learning. This article presents a method that includes the features of the two above-mentioned approaches: a graphical representation of the rules system in the form of a tree and a fuzzy representation of the data. The approach uses such advantages as high comprehensibility of decision trees and the ability to cope with inaccurate and uncertain information in fuzzy representation. The received learning method is suitable for classifying problems with both numerical and symbolic features. In the article, solution illustrations and numerical results are given.

Three-dimensional numerical investigation of the separation process in a vortex tube at different operating conditions

NASA Astrophysics Data System (ADS)

Rafiee, Seyed Ehsan; Sadeghiazad, M. M.

2016-06-01

Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process inside a Ranque-Hilsch vortex tube cleaning (cooling) system is investigated to analyze the impact of the operating gas type on the vortex tube performance; the operating gases used are air, nitrogen, oxygen, carbon dioxide and nitrogen dioxide. The computational fluid dynamic model used is equipped with a three-dimensional structure, and the steady-state condition is applied during computations. The standard k-ɛ turbulence model is employed to resolve nonlinear flow equations, and various key parameters, such as hot and cold exhaust thermal drops, and power separation rates, are described numerically. The results show that nitrogen dioxide creates the greatest separation power out of all gases tested, and the numerical results are validated by good agreement with available experimental data. In addition, a comparison is made between the use of two different boundary conditions, the pressure-far-field and the pressure-outlet, when analyzing complex turbulent flows inside the air separators. Results present a comprehensive and practical solution for use in future numerical studies.

Dynamics of elastic nonlinear rotating composite beams with embedded actuators

NASA Astrophysics Data System (ADS)

Ghorashi, Mehrdaad

2009-08-01

A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.

Tailoring risk communication to improve comprehension: Do patient preferences help or hurt?

PubMed

Barnes, Andrew J; Hanoch, Yaniv; Miron-Shatz, Talya; Ozanne, Elissa M

2016-09-01

Risk communication tools can facilitate patients' understanding of risk information. In this novel study, we examine the hypothesis that risk communication methods tailored to individuals' preferences can increase risk comprehension. Preferences for breast cancer risk formats, and risk comprehension data were collected using an online survey from 361 women at high risk for breast cancer. Women's initial preferences were assessed by asking them which of the following risk formats would be the clearest: (a) percentage, (b) frequency, (c) bar graph, (d) pictogram, and (e) comparison to other women. Next, women were presented with 5 different formats for displaying cancer risks and asked to interpret the risk information presented. Finally, they were asked again which risk format they preferred. Initial preferences for risk formats were not associated with risk comprehension scores. However, women with lower risk comprehension scores were more likely to update their risk format preferences after they evaluated risks in different formats. Less numerate women were more likely to prefer graphical rather than numeric risk formats. Importantly, we found that women preferring graphical risk formats had lower risk comprehension in these formats compared to numeric formats. In contrast, women preferring numeric formats performed equally well across formats. Our findings suggest that tailoring risk communication to patient preferences may not improve understanding of medical risks, particularly for less numerate women, and point to the potential perils of tailoring risk communication formats to patient preferences. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

Sedimentary Geothermal Feasibility Study: October 2016

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

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Verification of EPA's " Preliminary remediation goals for radionuclides" (PRG) electronic calculator

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

Stagich, B. H.

The U.S. Environmental Protection Agency (EPA) requested an external, independent verification study of their “Preliminary Remediation Goals for Radionuclides” (PRG) electronic calculator. The calculator provides information on establishing PRGs for radionuclides at Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) sites with radioactive contamination (Verification Study Charge, Background). These risk-based PRGs set concentration limits using carcinogenic toxicity values under specific exposure conditions (PRG User’s Guide, Section 1). The purpose of this verification study is to ascertain that the computer codes has no inherit numerical problems with obtaining solutions as well as to ensure that the equations are programmed correctly.

Innovative solutions in monitoring systems in flood protection

NASA Astrophysics Data System (ADS)

Sekuła, Klaudia; Połeć, Marzena; Borecka, Aleksandra

2018-02-01

The article presents the possibilities of ISMOP - IT System of Levee Monitoring. This system is able to collecting data from the reference and experimental control and measurement network. The experimental levee is build in a 1:1 scale and located in the village of Czernichow, near Cracow. The innovation is the utilization of a series of sensors monitoring the changes in the body of levee. It can be done by comparing the results of numerical simulations with results from installed two groups of sensors: reference sensors and experimental sensors. The reference control and measurement sensors create network based on pore pressure and temperature sensors. Additionally, it contains the fiber-optic technology. The second network include design experimental sensors, constructed for the development of solutions that can be used in existing flood embankments. The results are important to create the comprehensive and inexpensive monitoring system, which could be helpful for state authorities and local governments in flood protection.

A mathematical model for mixed convective flow of chemically reactive Oldroyd-B fluid between isothermal stretching disks

NASA Astrophysics Data System (ADS)

Hashmi, M. S.; Khan, N.; Ullah Khan, Sami; Rashidi, M. M.

In this study, we have constructed a mathematical model to investigate the heat source/sink effects in mixed convection axisymmetric flow of an incompressible, electrically conducting Oldroyd-B fluid between two infinite isothermal stretching disks. The effects of viscous dissipation and Joule heating are also considered in the heat equation. The governing partial differential equations are converted into ordinary differential equations by using appropriate similarity variables. The series solution of these dimensionless equations is constructed by using homotopy analysis method. The convergence of the obtained solution is carefully examined. The effects of various involved parameters on pressure, velocity and temperature profiles are comprehensively studied. A graphical analysis has been presented for various values of problem parameters. The numerical values of wall shear stress and Nusselt number are computed at both upper and lower disks. Moreover, a graphical and tabular explanation for critical values of Frank-Kamenetskii regarding other flow parameters.

methylPipe and compEpiTools: a suite of R packages for the integrative analysis of epigenomics data.

PubMed

Kishore, Kamal; de Pretis, Stefano; Lister, Ryan; Morelli, Marco J; Bianchi, Valerio; Amati, Bruno; Ecker, Joseph R; Pelizzola, Mattia

2015-09-29

Numerous methods are available to profile several epigenetic marks, providing data with different genome coverage and resolution. Large epigenomic datasets are then generated, and often combined with other high-throughput data, including RNA-seq, ChIP-seq for transcription factors (TFs) binding and DNase-seq experiments. Despite the numerous computational tools covering specific steps in the analysis of large-scale epigenomics data, comprehensive software solutions for their integrative analysis are still missing. Multiple tools must be identified and combined to jointly analyze histone marks, TFs binding and other -omics data together with DNA methylation data, complicating the analysis of these data and their integration with publicly available datasets. To overcome the burden of integrating various data types with multiple tools, we developed two companion R/Bioconductor packages. The former, methylPipe, is tailored to the analysis of high- or low-resolution DNA methylomes in several species, accommodating (hydroxy-)methyl-cytosines in both CpG and non-CpG sequence context. The analysis of multiple whole-genome bisulfite sequencing experiments is supported, while maintaining the ability of integrating targeted genomic data. The latter, compEpiTools, seamlessly incorporates the results obtained with methylPipe and supports their integration with other epigenomics data. It provides a number of methods to score these data in regions of interest, leading to the identification of enhancers, lncRNAs, and RNAPII stalling/elongation dynamics. Moreover, it allows a fast and comprehensive annotation of the resulting genomic regions, and the association of the corresponding genes with non-redundant GeneOntology terms. Finally, the package includes a flexible method based on heatmaps for the integration of various data types, combining annotation tracks with continuous or categorical data tracks. methylPipe and compEpiTools provide a comprehensive Bioconductor-compliant solution for the integrative analysis of heterogeneous epigenomics data. These packages are instrumental in providing biologists with minimal R skills a complete toolkit facilitating the analysis of their own data, or in accelerating the analyses performed by more experienced bioinformaticians.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Fluid-solid coupled simulation of the ignition transient of solid rocket motor

NASA Astrophysics Data System (ADS)

Li, Qiang; Liu, Peijin; He, Guoqiang

2015-05-01

The first period of the solid rocket motor operation is the ignition transient, which involves complex processes and, according to chronological sequence, can be divided into several stages, namely, igniter jet injection, propellant heating and ignition, flame spreading, chamber pressurization and solid propellant deformation. The ignition transient should be comprehensively analyzed because it significantly influences the overall performance of the solid rocket motor. A numerical approach is presented in this paper for simulating the fluid-solid interaction problems in the ignition transient of the solid rocket motor. In the proposed procedure, the time-dependent numerical solutions of the governing equations of internal compressible fluid flow are loosely coupled with those of the geometrical nonlinearity problems to determine the propellant mechanical response and deformation. The well-known Zeldovich-Novozhilov model was employed to model propellant ignition and combustion. The fluid-solid coupling interface data interpolation scheme and coupling instance for different computational agents were also reported. Finally, numerical validation was performed, and the proposed approach was applied to the ignition transient of one laboratory-scale solid rocket motor. For the application, the internal ballistics were obtained from the ground hot firing test, and comparisons were made. Results show that the integrated framework allows us to perform coupled simulations of the propellant ignition, strong unsteady internal fluid flow, and propellant mechanical response in SRMs with satisfactory stability and efficiency and presents a reliable and accurate solution to complex multi-physics problems.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations

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

Moridis, G.

1992-03-01

The Laplace Transform Boundary Element (LTBE) method is a recently introduced numerical method, and has been used for the solution of diffusion-type PDEs. It completely eliminates the time dependency of the problem and the need for time discretization, yielding solutions numerical in space and semi-analytical in time. In LTBE solutions are obtained in the Laplace spare, and are then inverted numerically to yield the solution in time. The Stehfest and the DeHoog formulations of LTBE, based on two different inversion algorithms, are investigated. Both formulations produce comparable, extremely accurate solutions.

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2

NASA Technical Reports Server (NTRS)

Ray, Richard D.

1999-01-01

Goddard Ocean Tide model GOT99.2 is a new solution for the amplitudes and phases of the global oceanic tides, based on over six years of sea-surface height measurements by the TOPEX/POSEIDON satellite altimeter. Comparison with deep-ocean tide-gauge measurements show that this new tidal solution is an improvement over previous global models, with accuracies for the main semidiurnal lunar constituent M2 now below 1.5 cm (deep water only). The new solution benefits from use of prior hydrodynamic models, several in shallow and inland seas as well as the global finite-element model FES94.1. This report describes some of the data processing details involved in handling the altimetry, and it provides a comprehensive set of global cotidal charts of the resulting solutions. Various derived tidal charts are also provided, including tidal loading deformation charts, tidal gravimetric charts, and tidal current velocity (or transport) charts. Finally, low-degree spherical harmonic coefficients are computed by numerical quadrature and are tabulated for the major short-period tides; these are useful for a variety of geodetic and geophysical purposes, especially in combination with similar estimates from satellite laser ranging.

Reactive solute transport in an asymmetric aquifer-aquitard system with scale-dependent dispersion

NASA Astrophysics Data System (ADS)

Zhou, R.; Zhan, H.

2017-12-01

Abstract: The understanding of reactive solute transport in an aquifer-aquitard system is important to study transport behavior in the more complex porous media. When transport properties are asymmetric in the upper and lower aquitards, reactive solute transport in such an aquifer-aquitard system becomes a coupled three domain problem that is more complex than the symmetric case in which the upper and lower aquitards have identical transport properties. Meanwhile, the dispersivity of transport in the aquifer is considered as a linear or exponential function of travel distance due to the heterogeneity of aquifer. This study proposed new transport models to describe reactive solute transport in such an asymmetric aquifer-aquitard system with scale-dependent dispersion. Mathematical models were developed for such problems under the first-type and third-type boundary conditions to analyze the spatial-temporal concentration and mass distribution in the aquifer and aquitards with the help of Laplace transform technique and the de Hoog numerical Laplace inversion method. Breakthrough curves (BTCs) and residence time distribution curves (RTDs) obtained from the models with scale-dependent dispersion, constant dispersion and constant effective dispersivity were compared to reflect the lumped scale-dispersion effect in the aquifer-aquitard system. The newly acquired solutions were then tested extensively against previous analytical and numerical solutions and were proven to be robust and accurate. Furthermore, to study the back diffusion of contaminant mass in aquitards, a zero-contaminant mass concentration boundary condition was imposed on the inlet boundary of the system after a certain time, which is also called the process of water flushing. The diffusion loss alone the aquifer/aquitard interfaces and mass stored ratio change in each of three domains (upper aquitard, aquifer, and lower aquitard) after water flushing provided an insightful and comprehensive analysis of transport behavior with asymmetric distribution of transport properties.

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Normal-Gamma-Bernoulli Peak Detection for Analysis of Comprehensive Two-Dimensional Gas Chromatography Mass Spectrometry Data.

PubMed

Kim, Seongho; Jang, Hyejeong; Koo, Imhoi; Lee, Joohyoung; Zhang, Xiang

2017-01-01

Compared to other analytical platforms, comprehensive two-dimensional gas chromatography coupled with mass spectrometry (GC×GC-MS) has much increased separation power for analysis of complex samples and thus is increasingly used in metabolomics for biomarker discovery. However, accurate peak detection remains a bottleneck for wide applications of GC×GC-MS. Therefore, the normal-exponential-Bernoulli (NEB) model is generalized by gamma distribution and a new peak detection algorithm using the normal-gamma-Bernoulli (NGB) model is developed. Unlike the NEB model, the NGB model has no closed-form analytical solution, hampering its practical use in peak detection. To circumvent this difficulty, three numerical approaches, which are fast Fourier transform (FFT), the first-order and the second-order delta methods (D1 and D2), are introduced. The applications to simulated data and two real GC×GC-MS data sets show that the NGB-D1 method performs the best in terms of both computational expense and peak detection performance.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

Numerical Algorithm for Delta of Asian Option

PubMed Central

Zhang, Boxiang; Yu, Yang; Wang, Weiguo

2015-01-01

We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options. PMID:26266271

Numerical simulation of KdV equation by finite difference method

NASA Astrophysics Data System (ADS)

Yokus, A.; Bulut, H.

2018-05-01

In this study, the numerical solutions to the KdV equation with dual power nonlinearity by using the finite difference method are obtained. Discretize equation is presented in the form of finite difference operators. The numerical solutions are secured via the analytical solution to the KdV equation with dual power nonlinearity which is present in the literature. Through the Fourier-Von Neumann technique and linear stable, we have seen that the FDM is stable. Accuracy of the method is analyzed via the L2 and L_{∞} norm errors. The numerical, exact approximations and absolute error are presented in tables. We compare the numerical solutions with the exact solutions and this comparison is supported with the graphic plots. Under the choice of suitable values of parameters, the 2D and 3D surfaces for the used analytical solution are plotted.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

A stability analysis on forced convection boundary layer stagnation-point slip flow in Darcy-Forchheimer porous medium towards a shrinking sheet

NASA Astrophysics Data System (ADS)

Bakar, Shahirah Abu; Arifin, Norihan Md; Ali, Fadzilah Md; Bachok, Norfifah; Nazar, Roslinda

2017-08-01

The stagnation-point flow over a shrinking sheet in Darcy-Forchheimer porous medium is numerically studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, and then solved numerically by using shooting technique method with Maple implementation. Dual solutions are observed in a certain range of the shrinking parameter. Regarding on numerical solutions, we prepared stability analysis to identify which solution is stable between non-unique solutions by bvp4c solver in Matlab. Further we obtain numerical results or each solution, which enable us to discuss the features of the respective solutions.

A comprehensive dairy valorization model.

PubMed

Banaszewska, A; Cruijssen, F; van der Vorst, J G A J; Claassen, G D H; Kampman, J L

2013-02-01

Dairy processors face numerous challenges resulting from both unsteady dairy markets and some specific characteristics of dairy supply chains. To maintain a competitive position on the market, companies must look beyond standard solutions currently used in practice. This paper presents a comprehensive dairy valorization model that serves as a decision support tool for mid-term allocation of raw milk to end products and production planning. The developed model was used to identify the optimal product portfolio composition. The model allocates raw milk to the most profitable dairy products while accounting for important constraints (i.e., recipes, composition variations, dairy production interdependencies, seasonality, demand, supply, capacities, and transportation flows). The inclusion of all relevant constraints and the ease of understanding dairy production dynamics make the model comprehensive. The developed model was tested at the international dairy processor FrieslandCampina (Amersfoort, the Netherlands). The structure of the model and its output were discussed in multiple sessions with and approved by relevant FrieslandCampina employees. The elements included in the model were considered necessary to optimally valorize raw milk. To illustrate the comprehensiveness and functionality of the model, we analyzed the effect of seasonality on milk valorization. A large difference in profit and a shift in the allocation of milk showed that seasonality has a considerable impact on the valorization of raw milk. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Thermodynamically self-consistent theory for the Blume-Capel model.

PubMed

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

TOUGHREACT: a new code of the TOUGH Family for Non-Isothermal multiphase reactive geochemical transport in variably saturated geologic media

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

Xu, Tianfu; Sonnenthal, Eric; Spycher, Nicolas

Coupled modeling of subsurface multiphase fluid and heat flow, solute transport and chemical reactions can be used for the assessment of acid mine drainage remediation, waste disposal sites, hydrothermal convection, contaminant transport, and groundwater quality. We have developed a comprehensive numerical simulator, TOUGHREACT, which considers non-isothermal multi-component chemical transport in both liquid and gas phases. A wide range of subsurface thermo-physical-chemical processes is considered under various thermohydrological and geochemical conditions of pressure, temperature, water saturation, and ionic strength. The code can be applied to one-, two- or three-dimensional porous and fractured media with physical and chemical heterogeneity.

A Theory for Self-consistent Acceleration of Energetic Charged Particles by Dynamic Small-scale Flux Ropes

NASA Astrophysics Data System (ADS)

le Roux, J. A.; Zank, G. P.; Khabarova, O.; Webb, G. M.

2016-12-01

Simulations of charged particle acceleration in turbulent plasma regions with numerous small-scale contracting and merging (reconnecting) magnetic islands/flux ropes emphasize the key role of temporary particle trapping in these structures for efficient acceleration that can result in power-law spectra. In response, a comprehensive kinetic transport theory framework was developed by Zank et al. and le Roux et al. to capture the essential physics of energetic particle acceleration in solar wind regions containing numerous dynamic small-scale flux ropes. Examples of test particle solutions exhibiting hard power-law spectra for energetic particles were presented in recent publications by both Zank et al. and le Roux et al.. However, the considerable pressure in the accelerated particles suggests the need for expanding the kinetic transport theory to enable a self-consistent description of energy exchange between energetic particles and small-scale flux ropes. We plan to present the equations of an expanded kinetic transport theory framework that will enable such a self-consistent description.

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

A numerical method for solving systems of linear ordinary differential equations with rapidly oscillating solutions

NASA Technical Reports Server (NTRS)

Bernstein, Ira B.; Brookshaw, Leigh; Fox, Peter A.

1992-01-01

The present numerical method for accurate and efficient solution of systems of linear equations proceeds by numerically developing a set of basis solutions characterized by slowly varying dependent variables. The solutions thus obtained are shown to have a computational overhead largely independent of the small size of the scale length which characterizes the solutions; in many cases, the technique obviates series solutions near singular points, and its known sources of error can be easily controlled without a substantial increase in computational time.

Treating stimuli as a random factor in social psychology: a new and comprehensive solution to a pervasive but largely ignored problem.

PubMed

Judd, Charles M; Westfall, Jacob; Kenny, David A

2012-07-01

Throughout social and cognitive psychology, participants are routinely asked to respond in some way to experimental stimuli that are thought to represent categories of theoretical interest. For instance, in measures of implicit attitudes, participants are primed with pictures of specific African American and White stimulus persons sampled in some way from possible stimuli that might have been used. Yet seldom is the sampling of stimuli taken into account in the analysis of the resulting data, in spite of numerous warnings about the perils of ignoring stimulus variation (Clark, 1973; Kenny, 1985; Wells & Windschitl, 1999). Part of this failure to attend to stimulus variation is due to the demands imposed by traditional analysis of variance procedures for the analysis of data when both participants and stimuli are treated as random factors. In this article, we present a comprehensive solution using mixed models for the analysis of data with crossed random factors (e.g., participants and stimuli). We show the substantial biases inherent in analyses that ignore one or the other of the random factors, and we illustrate the substantial advantages of the mixed models approach with both hypothetical and actual, well-known data sets in social psychology (Bem, 2011; Blair, Chapleau, & Judd, 2005; Correll, Park, Judd, & Wittenbrink, 2002). PsycINFO Database Record (c) 2012 APA, all rights reserved

Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

NASA Astrophysics Data System (ADS)

Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

2017-01-01

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

A Systematic Review of the Research on Vocabulary Instruction That Impacts Text Comprehension

ERIC Educational Resources Information Center

Wright, Tanya S.; Cervetti, Gina N.

2017-01-01

Although numerous studies have identified a correlational relationship between vocabulary and comprehension, we know less about vocabulary interventions that impact reading comprehension. Therefore, this study is a systematic review of vocabulary interventions with comprehension outcomes. Analyses of 36 studies that met criteria are organized…

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

NASA Astrophysics Data System (ADS)

Sewerin, Fabian; Rigopoulos, Stelios

2017-10-01

Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicates the computational efficiency of the numerical solution scheme.

Theory of precipitation effects on dead cylindrical fuels

Treesearch

Michael A. Fosberg

1972-01-01

Numerical and analytical solutions of the Fickian diffusion equation were used to determine the effects of precipitation on dead cylindrical forest fuels. The analytical solution provided a physical framework. The numerical solutions were then used to refine the analytical solution through a similarity argument. The theoretical solutions predicted realistic rates of...

Computational physical oceanography -- A comprehensive approach based on generalized CFD/grid techniques for planetary scale simulations of oceanic flows. Final report, September 1, 1995--August 31, 1996

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

Beddhu, M.; Jiang, M.Y.; Whitfield, D.L.

The original intention for this work was to impart the technology that was developed in the field of computational aeronautics to the field of computational physical oceanography. This technology transfer involved grid generation techniques and solution procedures to solve the governing equations over the grids thus generated. Specifically, boundary fitting non-orthogonal grids would be generated over a sphere taking into account the topography of the ocean floor and the topography of the continents. The solution methodology to be employed involved the application of an upwind, finite volume discretization procedure that uses higher order numerical fluxes at the cell faces tomore » discretize the governing equations and an implicit Newton relaxation technique to solve the discretized equations. This report summarizes the efforts put forth during the past three years to achieve these goals and indicates the future direction of this work as it is still an ongoing effort.« less

Quantitative phase-field lattice-Boltzmann study of lamellar eutectic growth under natural convection

NASA Astrophysics Data System (ADS)

Zhang, A.; Guo, Z.; Xiong, S.-M.

2018-05-01

The influence of natural convection on lamellar eutectic growth was determined by a comprehensive phase-field lattice-Boltzmann study for Al-Cu and CB r4-C2C l6 eutectic alloys. The mass differences resulting from concentration differences led to the fluid flow and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency. By means of carefully designed "numerical experiments", the eutectic growth under natural convection was explored and a simple analytical model was proposed to predict the adjustment of the lamellar spacing. Furthermore, by alternating the solute expansion coefficient, initial lamellar spacing, and undercooling, the microstructure evolution was presented and compared with the classical eutectic growth theory. Results showed that both interfacial solute distribution and average curvature were affected by the natural convection, the effect of which could be further quantified by adding a constant into the growth rule proposed by Jackson and Hunt [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)].

Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

NASA Astrophysics Data System (ADS)

Duan, Xueyang

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with or without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational efficiency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.

Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

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

Ashyralyev, Allaberen; Okur, Ulker

In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

The Biopsychosocial-Digital Approach to Health and Disease: Call for a Paradigm Expansion

PubMed Central

2018-01-01

Digital health is an advancing phenomenon in modern health care systems. Currently, numerous stakeholders in various countries are evaluating the potential benefits of digital health solutions at the individual, population, and/or organizational levels. Additionally, driving factors are being created from the customer-side of the health care systems to push health care providers, policymakers, or researchers to embrace digital health solutions. However, health care providers may differ in their approach to adopt these solutions. Health care providers are not assumed to be appropriately trained to address the requirements of integrating digital health solutions into daily everyday practices and procedures. To adapt to the changing demands of health care systems, it is necessary to expand relevant paradigms and to train human resources as required. In this article, a more comprehensive paradigm will be proposed, based on the ‘biopsychosocial model’ of assessing health and disease, originally introduced by George L Engel. The “biopsychosocial model” must be leveraged to include a “digital” component, thus suggesting a ‘biopsychosocial-digital’ approach to health and disease. Modifications to the “biopsychosocial” model and transition to the “biopsychosocial-digital” model are explained. Furthermore, the emerging implications of understanding health and disease are clarified pertaining to their relevance in training human resources for health care provision and research. PMID:29776900

A numerical study of transient heat and mass transfer in crystal growth

NASA Technical Reports Server (NTRS)

Han, Samuel Bang-Moo

1987-01-01

A numerical analysis of transient heat and solute transport across a rectangular cavity is performed. Five nonlinear partial differential equations which govern the conservation of mass, momentum, energy and solute concentration related to crystal growth in solution, are simultaneously integrated by a numerical method based on the SIMPLE algorithm. Numerical results showed that the flow, temperature and solute fields are dependent on thermal and solutal Grashoff number, Prandtl number, Schmidt number and aspect ratio. The average Nusselt and Sherwood numbers evaluated at the center of the cavity decrease markedly when the solutal buoyancy force acts in the opposite direction to the thermal buoyancy force. When the solutal and thermal buoyancy forces act in the same direction, however, Sherwood number increases significantly and yet Nusselt number decreases. Overall effects of convection on the crystal growth are seen to be an enhancement of growth rate as expected but with highly nonuniform spatial growth variations.

Numbers matter to informed patient choices: A randomized design across age and numeracy levels

PubMed Central

Peters, Ellen; Hart, P. Sol; Tusler, Martin; Fraenkel, Liana

2013-01-01

Background How drug adverse events (AEs) are communicated in the United States may mislead consumers and result in low adherence. Requiring written information to include numeric AE-likelihood information might lessen these effects, but providing numbers may disadvantage less skilled populations. Objective To determine risk comprehension and willingness to use a medication when presented with numeric or non-numeric AE-likelihood information across age, numeracy, and cholesterol-lowering-drug-usage groups. Design In a cross-sectional internet survey (N=905; American Life Panel, 5/15/08–6/18/08), respondents were presented with a hypothetical prescription medication for high cholesterol. AE likelihoods were described using one of six formats (non-numeric: Consumer-Medication-Information (CMI)-like list, risk labels; numeric: percentage, frequency, risk-labels-plus-percentage, risk-labels-plus-frequency). Main outcome measures were risk comprehension (recoded to indicate presence/absence of risk overestimation and underestimation), willingness to use the medication (7-point scale; not likely=0, very likely=6), and main reason for willingness (chosen from eight predefined reasons). Results Individuals given non-numeric information were more likely to overestimate risk, less willing to take the medication, and gave different reasons than those provided numeric information across numeracy and age groups (e.g., among less numerate: 69% and 18% overestimated risks in non-numeric and numeric formats, respectively; among more numerate: these same proportions were 66% and 6%). Less numerate middle-aged and older adults, however, showed less influence of numeric format on willingness to take the medication. Limitations It is unclear whether differences are clinically meaningful although some differences are large. Conclusions Providing numeric AE-likelihood information (compared to non-numeric) is likely to increase risk comprehension across numeracy and age levels. Its effects on uptake and adherence of prescribed drugs should be similar across the population, except perhaps in older, less numerate individuals. PMID:24246563

Comprehensive study of numerical anisotropy and dispersion in 3-D TLM meshes

NASA Astrophysics Data System (ADS)

Berini, Pierre; Wu, Ke

1995-05-01

This paper presents a comprehensive analysis of the numerical anisotropy and dispersion of 3-D TLM meshes constructed using several generalized symmetrical condensed TLM nodes. The dispersion analysis is performed in isotropic lossless, isotropic lossy and anisotropic lossless media and yields a comparison of the simulation accuracy for the different TLM nodes. The effect of mesh grading on the numerical dispersion is also determined. The results compare meshes constructed with Johns' symmetrical condensed node (SCN), two hybrid symmetrical condensed nodes (HSCN) and two frequency domain symmetrical condensed nodes (FDSCN). It has been found that under certain circumstances, the time domain nodes may introduce numerical anisotropy when modelling isotropic media.

Late-time behaviour of the tilted Bianchi type VIh models

NASA Astrophysics Data System (ADS)

Hervik, S.; van den Hoogen, R. J.; Lim, W. C.; Coley, A. A.

2007-08-01

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Langer, S.

2016-01-01

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

Desorption of 1,3,5-Trichlorobenzene from Multi-Walled Carbon Nanotubes: Impact of Solution Chemistry and Surface Chemistry

PubMed Central

Ma, Xingmao; Uddin, Sheikh

2013-01-01

The strong affinity of carbon nanotubes (CNTs) to environmental contaminants has raised serious concern that CNTs may function as a carrier of environmental pollutants and lead to contamination in places where the environmental pollutants are not expected. However, this concern will not be realized until the contaminants are desorbed from CNTs. It is well recognized that the desorption of environmental pollutants from pre-laden CNTs varies with the environmental conditions, such as the solution pH and ionic strength. However, comprehensive investigation on the influence of solution chemistry on the desorption process has not been carried out, even though numerous investigations have been conducted to investigate the impact of solution chemistry on the adsorption of environmental pollutants on CNTs. The main objective of this study was to determine the influence of solution chemistry (e.g., pH, ionic strength) and surface functionalization on the desorption of preloaded 1,3,5-trichlorobenzene (1,3,5-TCB) from multi-walled carbon nanotubes (MWNTs). The results suggested that higher pH, ionic strength and natural organic matter in solution generally led to higher desorption of 1,3,5-TCB from MWNTs. However, the extent of change varied at different values of the tested parameters (e.g., pH < 7 vs. pH > 7). In addition, the impact of these parameters varied with MWNTs possessing different surface functional groups, suggesting that surface functionalization could considerably alter the environmental behaviors and impact of MWNTs. PMID:28348336

Development of Comprehensive Reduced Kinetic Models for Supersonic Reacting Shear Layer Simulations

NASA Technical Reports Server (NTRS)

Zambon, A. C.; Chelliah, H. K.; Drummond, J. P.

2006-01-01

Large-scale simulations of multi-dimensional unsteady turbulent reacting flows with detailed chemistry and transport can be computationally extremely intensive even on distributed computing architectures. With the development of suitable reduced chemical kinetic models, the number of scalar variables to be integrated can be decreased, leading to a significant reduction in the computational time required for the simulation with limited loss of accuracy in the results. A general MATLAB-based automated mechanism reduction procedure is presented to reduce any complex starting mechanism (detailed or skeletal) with minimal human intervention. Based on the application of the quasi steady-state (QSS) approximation for certain chemical species and on the elimination of the fast reaction rates in the mechanism, several comprehensive reduced models, capable of handling different fuels such as C2H4, CH4 and H2, have been developed and thoroughly tested for several combustion problems (ignition, propagation and extinction) and physical conditions (reactant compositions, temperatures, and pressures). A key feature of the present reduction procedure is the explicit solution of the concentrations of the QSS species, needed for the evaluation of the elementary reaction rates. In contrast, previous approaches relied on an implicit solution due to the strong coupling between QSS species, requiring computationally expensive inner iterations. A novel algorithm, based on the definition of a QSS species coupling matrix, is presented to (i) introduce appropriate truncations to the QSS algebraic relations and (ii) identify the optimal sequence for the explicit solution of the concentration of the QSS species. With the automatic generation of the relevant source code, the resulting reduced models can be readily implemented into numerical codes.

Factor structure of the Hooper Visual Organization Test: a cross-cultural replication and extension.

PubMed

Merten, Thomas

2005-01-01

To investigate construct validity of the Hooper Visual Organization Test (VOT), a principal-axis analysis was performed on the neuropsychological test results of 200 German-speaking neurological patients who received a comprehensive battery, encompassing tests of visuospatial functions, memory, attention, executive functions, naming ability, and vocabulary. A four-factor solution was obtained with substantial loadings of the VOT only on the first factor, interpreted as a global dimension of non-verbal cognitive functions. This factor loaded significantly on numerous measures of visuospatial processing and attention (with particularly high loadings on WAIS-R Block Design, Trails A and B, and Raven's Standard Progressive Matrices). The remaining three factors were interpreted as memory, verbal abilities (vocabulary), and a separate factor of naming abilities.

Automatic welding systems for large ship hulls

NASA Astrophysics Data System (ADS)

Arregi, B.; Granados, S.; Hascoet, JY.; Hamilton, K.; Alonso, M.; Ares, E.

2012-04-01

Welding processes represents about 40% of the total production time in shipbuilding. Although most of the indoor welding work is automated, outdoor operations still require the involvement of numerous operators. To automate hull welding operations is a priority in large shipyards. The objective of the present work is to develop a comprehensive welding system capable of working with several welding layers in an automated way. There are several difficulties for the seam tracking automation of the welding process. The proposed solution is the development of a welding machine capable of moving autonomously along the welding seam, controlling both the position of the torch and the welding parameters to adjust the thickness of the weld bead to the actual gap between the hull plates.

Qualitative simulation for process modeling and control

NASA Technical Reports Server (NTRS)

Dalle Molle, D. T.; Edgar, T. F.

1989-01-01

A qualitative model is developed for a first-order system with a proportional-integral controller without precise knowledge of the process or controller parameters. Simulation of the qualitative model yields all of the solutions to the system equations. In developing the qualitative model, a necessary condition for the occurrence of oscillatory behavior is identified. Initializations that cannot exhibit oscillatory behavior produce a finite set of behaviors. When the phase-space behavior of the oscillatory behavior is properly constrained, these initializations produce an infinite but comprehensible set of asymptotically stable behaviors. While the predictions include all possible behaviors of the real system, a class of spurious behaviors has been identified. When limited numerical information is included in the model, the number of predictions is significantly reduced.

A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

NASA Astrophysics Data System (ADS)

Zabihi, F.; Saffarian, M.

2016-07-01

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Modeling flow and solute transport in irrigation furrows

USDA-ARS?s Scientific Manuscript database

This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...

Numerical Capacities as Domain-Specific Predictors beyond Early Mathematics Learning: A Longitudinal Study

PubMed Central

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3rd and 4th grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively “start-up” tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school. PMID:24255710

Numerical capacities as domain-specific predictors beyond early mathematics learning: a longitudinal study.

PubMed

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3(rd) and 4(th) grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively "start-up" tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school.

Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh-Taylor instability

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

Reckinger, Scott James; Livescu, Daniel; Vasilyev, Oleg V.

A comprehensive numerical methodology has been developed that handles the challenges introduced by considering the compressive nature of Rayleigh-Taylor instability (RTI) systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification-dependent vorticity production. The computational framework is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.

Long range forecasts of the Northern Hemisphere anomalies with antecedent sea surface temperature patterns

NASA Technical Reports Server (NTRS)

Kung, Ernest C.

1994-01-01

The contract research has been conducted in the following three major areas: analysis of numerical simulations and parallel observations of atmospheric blocking, diagnosis of the lower boundary heating and the response of the atmospheric circulation, and comprehensive assessment of long-range forecasting with numerical and regression methods. The essential scientific and developmental purpose of this contract research is to extend our capability of numerical weather forecasting by the comprehensive general circulation model. The systematic work as listed above is thus geared to developing a technological basis for future NASA long-range forecasting.

Metal Complexation in Xylem Fluid 1

PubMed Central

White, Michael C.; Decker, A. Morris; Chaney, Rufus L.

1981-01-01

Xylem fluid was analyzed for numerous solutes to characterize chemically the sap as a medium for forming and transporting metal complexes. The stem exudate was collected hourly for 8 hours from topped 31-day-old soybean (Glycine max L. Merr.) and 46-day-old tomato (Lycopersicon esculentum Mill.) plants grown in normal (0.5 micromolar) and Za-phytotoxic nutrient solutions. Soybean plants were grown in the normal and high-Zn solutions for 24 days; tomato plants were grown for 32 days. The exudate was analyzed for seven organic acids, 22 amino acids, eight inorganic solutes, apparent ionic strength, and pH. Significant changes in many solutes occurred over the 8-hour sampling period. These fluctuations depended on plant species, individual solute, and Zn treatment, and demonstrated that extrapolation of xylem-fluid analyses to whole-plant xylem sap is valid only for sap samples collected shortly after topping a plant. Exudate pH decreased over the 8-hour period for both species; exudate ionic strength increased for tomato and decreased for soybean. At the normal-Zn treatment (0 to 1 hour), the highest acid micromolar concentrations in soybean exudate were: asparagine, 2,583; citric, 1,706; malic, 890; and malonic, 264. Under the same conditions, the highest acid micromolar concentrations in tomato exudate were: maleic, 1,206; malic, 628; glutamine, 522; citric, 301; and asparagine, 242. Cysteine and methionine were above detection limits only in soybean exudate. Zinc phytotoxicity caused significant changes in many solutes. The analyses reported here provide a comprehensive data base for further studies on metal-complex equilibria in xylem fluid. PMID:16661664

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

A mathematical approach to HIV infection dynamics

NASA Astrophysics Data System (ADS)

Ida, A.; Oharu, S.; Oharu, Y.

2007-07-01

In order to obtain a comprehensive form of mathematical models describing nonlinear phenomena such as HIV infection process and AIDS disease progression, it is efficient to introduce a general class of time-dependent evolution equations in such a way that the associated nonlinear operator is decomposed into the sum of a differential operator and a perturbation which is nonlinear in general and also satisfies no global continuity condition. An attempt is then made to combine the implicit approach (usually adapted for convective diffusion operators) and explicit approach (more suited to treat continuous-type operators representing various physiological interactions), resulting in a semi-implicit product formula. Decomposing the operators in this way and considering their individual properties, it is seen that approximation-solvability of the original model is verified under suitable conditions. Once appropriate terms are formulated to describe treatment by antiretroviral therapy, the time-dependence of the reaction terms appears, and such product formula is useful for generating approximate numerical solutions to the governing equations. With this knowledge, a continuous model for HIV disease progression is formulated and physiological interpretations are provided. The abstract theory is then applied to show existence of unique solutions to the continuous model describing the behavior of the HIV virus in the human body and its reaction to treatment by antiretroviral therapy. The product formula suggests appropriate discrete models describing the dynamics of host pathogen interactions with HIV1 and is applied to perform numerical simulations based on the model of the HIV infection process and disease progression. Finally, the results of our numerical simulations are visualized and it is observed that our results agree with medical and physiological aspects.

Spectral methods in general relativity and large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; \\\\; Yaghoobpour-Tari, Shima

2013-06-01

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS5-CFT4 solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

On recent advances and future research directions for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Soliman, M. O.; Manhardt, P. D.

1986-01-01

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

Multiresolution representation and numerical algorithms: A brief review

NASA Technical Reports Server (NTRS)

Harten, Amiram

1994-01-01

In this paper we review recent developments in techniques to represent data in terms of its local scale components. These techniques enable us to obtain data compression by eliminating scale-coefficients which are sufficiently small. This capability for data compression can be used to reduce the cost of many numerical solution algorithms by either applying it to the numerical solution operator in order to get an approximate sparse representation, or by applying it to the numerical solution itself in order to reduce the number of quantities that need to be computed.

Constructing exact symmetric informationally complete measurements from numerical solutions

NASA Astrophysics Data System (ADS)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

A GENERAL MASS-CONSERVATIVE NUMERICAL SOLUTION FOR THE UNSATURATED FLOW EQUATION

EPA Science Inventory

Numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems. Numerical solution based on the standard h-based form of Richards equation generally yields poor results, ch...

Flow and Heat Transfer Analysis of an Eyring-Powell Fluid in a Pipe

NASA Astrophysics Data System (ADS)

Ali, N.; Nazeer, F.; Nazeer, Mubbashar

2018-02-01

The steady non-isothermal flow of an Eyring-Powell fluid in a pipe is investigated using both perturbation and numerical methods. The results are presented for two viscosity models, namely the Reynolds model and the Vogel model. The shooting method is employed to compute the numerical solution. Criteria for validity of perturbation solution are developed. When these criteria are met, it is shown that the perturbation solution is in good agreement with the numerical solution. The influence of various emerging parameters on the velocity and temperature field is also shown.

A 1D radiative transfer benchmark with polarization via doubling and adding

NASA Astrophysics Data System (ADS)

Ganapol, B. D.

2017-11-01

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to seven places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

NASA Astrophysics Data System (ADS)

Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

2015-10-01

We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

A Review of Natural Joint Systems and Numerical Investigation of Bio-Inspired GFRP-to-Steel Joints

PubMed Central

Avgoulas, Evangelos I.; Sutcliffe, Michael P. F.

2016-01-01

There are a great variety of joint types used in nature which can inspire engineering joints. In order to design such biomimetic joints, it is at first important to understand how biological joints work. A comprehensive literature review, considering natural joints from a mechanical point of view, was undertaken. This was used to develop a taxonomy based on the different methods/functions that nature successfully uses to attach dissimilar tissues. One of the key methods that nature uses to join dissimilar materials is a transitional zone of stiffness at the insertion site. This method was used to propose bio-inspired solutions with a transitional zone of stiffness at the joint site for several glass fibre reinforced plastic (GFRP) to steel adhesively bonded joint configurations. The transition zone was used to reduce the material stiffness mismatch of the joint parts. A numerical finite element model was used to identify the optimum variation in material stiffness that minimises potential failure of the joint. The best bio-inspired joints showed a 118% increase of joint strength compared to the standard joints. PMID:28773688

Evaluation of physics-based numerical modelling for diverse design architecture of perovskite solar cells

NASA Astrophysics Data System (ADS)

Mishra, A. K.; Catalan, Jorge; Camacho, Diana; Martinez, Miguel; Hodges, D.

2017-08-01

Solution processed organic-inorganic metal halide perovskite based solar cells are emerging as a new cost effective photovoltaic technology. In the context of increasing the power conversion efficiency (PCE) and sustainability of perovskite solar cells (PSC) devices, we comprehensively analyzed a physics-based numerical modelling for doped and un-doped PSC devices. Our analytics emphasized the role of different charge carrier layers from the view point of interfacial adhesion and its influence on charge extraction rate and charge recombination mechanism. Morphological and charge transport properties of perovskite thin film as a function of device architecture are also considered to investigate the photovoltaic properties of PSC. We observed that photocurrent is dominantly influenced by interfacial recombination process and photovoltage has functional relationship with defect density of perovskite absorption layer. A novel contour mapping method to understand the characteristics of current density-voltage (J-V) curves for each device as a function of perovskite layer thickness provide an important insight about the distribution spectrum of photovoltaic properties. Functional relationship of device efficiency and fill factor with absorption layer thickness are also discussed.

A Review of Natural Joint Systems and Numerical Investigation of Bio-Inspired GFRP-to-Steel Joints.

PubMed

Avgoulas, Evangelos I; Sutcliffe, Michael P F

2016-07-12

There are a great variety of joint types used in nature which can inspire engineering joints. In order to design such biomimetic joints, it is at first important to understand how biological joints work. A comprehensive literature review, considering natural joints from a mechanical point of view, was undertaken. This was used to develop a taxonomy based on the different methods/functions that nature successfully uses to attach dissimilar tissues. One of the key methods that nature uses to join dissimilar materials is a transitional zone of stiffness at the insertion site. This method was used to propose bio-inspired solutions with a transitional zone of stiffness at the joint site for several glass fibre reinforced plastic (GFRP) to steel adhesively bonded joint configurations. The transition zone was used to reduce the material stiffness mismatch of the joint parts. A numerical finite element model was used to identify the optimum variation in material stiffness that minimises potential failure of the joint. The best bio-inspired joints showed a 118% increase of joint strength compared to the standard joints.

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-07-01

The study of the electrodynamics of static, axisymmetric, and force-free Kerr magnetospheres relies vastly on solutions of the so-called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give a detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established set-ups (split-monopole, paraboloidal, BH disc, uniform).

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: Numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-04-01

The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, paraboloidal, BH-disk, uniform).

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

NASA Astrophysics Data System (ADS)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Laboratory longitudinal diffusion tests: 1. Dimensionless formulations and validity of simplified solutions

NASA Astrophysics Data System (ADS)

Takeda, M.; Nakajima, H.; Zhang, M.; Hiratsuka, T.

2008-04-01

To obtain reliable diffusion parameters for diffusion testing, multiple experiments should not only be cross-checked but the internal consistency of each experiment should also be verified. In the through- and in-diffusion tests with solution reservoirs, test interpretation of different phases often makes use of simplified analytical solutions. This study explores the feasibility of steady, quasi-steady, equilibrium and transient-state analyses using simplified analytical solutions with respect to (i) valid conditions for each analytical solution, (ii) potential error, and (iii) experimental time. For increased generality, a series of numerical analyses are performed using unified dimensionless parameters and the results are all related to dimensionless reservoir volume (DRV) which includes only the sorptive parameter as an unknown. This means the above factors can be investigated on the basis of the sorption properties of the testing material and/or tracer. The main findings are that steady, quasi-steady and equilibrium-state analyses are applicable when the tracer is not highly sorptive. However, quasi-steady and equilibrium-state analyses become inefficient or impractical compared to steady state analysis when the tracer is non-sorbing and material porosity is significantly low. Systematic and comprehensive reformulation of analytical models enables the comparison of experimental times between different test methods. The applicability and potential error of each test interpretation can also be studied. These can be applied in designing, performing, and interpreting diffusion experiments by deducing DRV from the available information for the target material and tracer, combined with the results of this study.

Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

NASA Astrophysics Data System (ADS)

Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

2015-12-01

Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

NASA Astrophysics Data System (ADS)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration.

PubMed

Budak, Vladimir P; Kaloshin, Gennady A; Shagalov, Oleg V; Zheltov, Victor S

2015-07-27

In this paper we propose the fast, but the accurate algorithm for numerical modeling of light fields in the turbid media slab. For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. The solution regular part is determined numerically. A good choice of the method of the solution anisotropic part elimination determines the high convergence of the algorithm in the mean square metric. The method of synthetic iterations can be used to improve the convergence in the uniform metric. A significant increase in the solution accuracy with the use of synthetic iterations allows applying the two-stream approximation for the regular part determination. This approach permits to generalize the proposed method in the case of an arbitrary 3D geometry of the medium.

Listening Comprehension Strategies: A Review of the Literature

ERIC Educational Resources Information Center

Berne, Jane E.

2004-01-01

Numerous studies related to listening comprehension strategies have been published in the past two decades. The present study seeks to build upon two previous reviews of listening comprehension strategies research. Of particular interest in this review are studies dealing with the types of cues used by listeners, the sequence of listening,…

An improved conjugate gradient scheme to the solution of least squares SVM.

PubMed

Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya

2005-03-01

The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

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

Woods, Mark Christopher; Holmes, Mark; Sailor, William C

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Designing an algorithm to preserve privacy for medical record linkage with error-prone data.

PubMed

Pal, Doyel; Chen, Tingting; Zhong, Sheng; Khethavath, Praveen

2014-01-20

Linking medical records across different medical service providers is important to the enhancement of health care quality and public health surveillance. In records linkage, protecting the patients' privacy is a primary requirement. In real-world health care databases, records may well contain errors due to various reasons such as typos. Linking the error-prone data and preserving data privacy at the same time are very difficult. Existing privacy preserving solutions for this problem are only restricted to textual data. To enable different medical service providers to link their error-prone data in a private way, our aim was to provide a holistic solution by designing and developing a medical record linkage system for medical service providers. To initiate a record linkage, one provider selects one of its collaborators in the Connection Management Module, chooses some attributes of the database to be matched, and establishes the connection with the collaborator after the negotiation. In the Data Matching Module, for error-free data, our solution offered two different choices for cryptographic schemes. For error-prone numerical data, we proposed a newly designed privacy preserving linking algorithm named the Error-Tolerant Linking Algorithm, that allows the error-prone data to be correctly matched if the distance between the two records is below a threshold. We designed and developed a comprehensive and user-friendly software system that provides privacy preserving record linkage functions for medical service providers, which meets the regulation of Health Insurance Portability and Accountability Act. It does not require a third party and it is secure in that neither entity can learn the records in the other's database. Moreover, our novel Error-Tolerant Linking Algorithm implemented in this software can work well with error-prone numerical data. We theoretically proved the correctness and security of our Error-Tolerant Linking Algorithm. We have also fully implemented the software. The experimental results showed that it is reliable and efficient. The design of our software is open so that the existing textual matching methods can be easily integrated into the system. Designing algorithms to enable medical records linkage for error-prone numerical data and protect data privacy at the same time is difficult. Our proposed solution does not need a trusted third party and is secure in that in the linking process, neither entity can learn the records in the other's database.

Numbers matter to informed patient choices: a randomized design across age and numeracy levels.

PubMed

Peters, Ellen; Hart, P Sol; Tusler, Martin; Fraenkel, Liana

2014-05-01

How drug adverse events (AEs) are communicated in the United States may mislead consumers and result in low adherence. Requiring written information to include numeric AE-likelihood information might lessen these effects, but providing numbers may disadvantage less skilled populations. The objective was to determine risk comprehension and willingness to use a medication when presented with numeric or nonnumeric AE-likelihood information across age, numeracy, and cholesterol-lowering drug-use groups. In a cross-sectional Internet survey (N = 905; American Life Panel, 15 May 2008 to 18 June 2008), respondents were presented with a hypothetical prescription medication for high cholesterol. AE likelihoods were described using 1 of 6 formats (nonnumeric: consumer medication information (CMI)-like list, risk labels; numeric: percentage, frequency, risk labels + percentage, risk labels + frequency). Main outcome measures were risk comprehension (recoded to indicate presence/absence of risk overestimation and underestimation), willingness to use the medication (7-point scale; not likely = 0, very likely = 6), and main reason for willingness (chosen from 8 predefined reasons). Individuals given nonnumeric information were more likely to overestimate risk, were less willing to take the medication, and gave different reasons than those provided numeric information across numeracy and age groups (e.g., among the less numerate, 69% and 18% overestimated risks in nonnumeric and numeric formats, respectively; among the more numerate, these same proportions were 66% and 6%). Less numerate middle-aged and older adults, however, showed less influence of numeric format on willingness to take the medication. It is unclear whether differences are clinically meaningful, although some differences are large. Providing numeric AE-likelihood information (compared with nonnumeric) is likely to increase risk comprehension across numeracy and age levels. Its effects on uptake and adherence of prescribed drugs should be similar across the population, except perhaps in older, less numerate individuals.

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy (Editor); Deconinck, Herman (Editor)

1999-01-01

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

PubMed Central

Zhao, Lei; Yue, Xingye; Waxman, David

2013-01-01

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size. PMID:23749318

Determination of Mechanical Properties of Spatially Heterogeneous Breast Tissue Specimens Using Contact Mode Atomic Force Microscopy (AFM)

PubMed Central

Roy, Rajarshi; Desai, Jaydev P.

2016-01-01

This paper outlines a comprehensive parametric approach for quantifying mechanical properties of spatially heterogeneous thin biological specimens such as human breast tissue using contact-mode Atomic Force Microscopy. Using inverse finite element (FE) analysis of spherical nanoindentation, the force response from hyperelastic material models is compared with the predicted force response from existing analytical contact models, and a sensitivity study is carried out to assess uniqueness of the inverse FE solution. Furthermore, an automation strategy is proposed to analyze AFM force curves with varying levels of material nonlinearity with minimal user intervention. Implementation of our approach on an elastic map acquired from raster AFM indentation of breast tissue specimens indicates that a judicious combination of analytical and numerical techniques allow more accurate interpretation of AFM indentation data compared to relying on purely analytical contact models, while keeping the computational cost associated an inverse FE solution with reasonable limits. The results reported in this study have several implications in performing unsupervised data analysis on AFM indentation measurements on a wide variety of heterogeneous biomaterials. PMID:25015130

A brief overview of computational structures technology related activities at NASA Lewis Research Center

NASA Technical Reports Server (NTRS)

Hopkins, Dale A.

1992-01-01

The presentation gives a partial overview of research and development underway in the Structures Division of LeRC, which collectively is referred to as the Computational Structures Technology Program. The activities in the program are diverse and encompass four major categories: (1) composite materials and structures; (2) probabilistic analysis and reliability; (3) design optimization and expert systems; and (4) computational methods and simulation. The approach of the program is comprehensive and entails exploration of fundamental theories of structural mechanics to accurately represent the complex physics governing engine structural performance, formulation, and implementation of computational techniques and integrated simulation strategies to provide accurate and efficient solutions of the governing theoretical models by exploiting the emerging advances in computer technology, and validation and verification through numerical and experimental tests to establish confidence and define the qualities and limitations of the resulting theoretical models and computational solutions. The program comprises both in-house and sponsored research activities. The remainder of the presentation provides a sample of activities to illustrate the breadth and depth of the program and to demonstrate the accomplishments and benefits that have resulted.

Documentation for the MODFLOW 6 framework

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; Banta, Edward R.

2017-08-10

MODFLOW is a popular open-source groundwater flow model distributed by the U.S. Geological Survey. Growing interest in surface and groundwater interactions, local refinement with nested and unstructured grids, karst groundwater flow, solute transport, and saltwater intrusion, has led to the development of numerous MODFLOW versions. Often times, there are incompatibilities between these different MODFLOW versions. The report describes a new MODFLOW framework called MODFLOW 6 that is designed to support multiple models and multiple types of models. The framework is written in Fortran using a modular object-oriented design. The primary framework components include the simulation (or main program), Timing Module, Solutions, Models, Exchanges, and Utilities. The first version of the framework focuses on numerical solutions, numerical models, and numerical exchanges. This focus on numerical models allows multiple numerical models to be tightly coupled at the matrix level.

Numerical Study of Periodic Traveling Wave Solutions for the Predator-Prey Model with Landscape Features

NASA Astrophysics Data System (ADS)

Yun, Ana; Shin, Jaemin; Li, Yibao; Lee, Seunggyu; Kim, Junseok

We numerically investigate periodic traveling wave solutions for a diffusive predator-prey system with landscape features. The landscape features are modeled through the homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle domain. To effectively treat the Dirichlet boundary condition, we employ a robust and accurate numerical technique by using a boundary control function. We also propose a robust algorithm for calculating the numerical periodicity of the traveling wave solution. In numerical experiments, we show that periodic traveling waves which move out and away from the obstacle are effectively generated. We explain the formation of the traveling waves by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail for various obstacles. Furthermore, we apply our numerical technique to the complicated real landscape features.

Application of symbolic/numeric matrix solution techniques to the NASTRAN program

NASA Technical Reports Server (NTRS)

Buturla, E. M.; Burroughs, S. H.

1977-01-01

The matrix solving algorithm of any finite element algorithm is extremely important since solution of the matrix equations requires a large amount of elapse time due to null calculations and excessive input/output operations. An alternate method of solving the matrix equations is presented. A symbolic processing step followed by numeric solution yields the solution very rapidly and is especially useful for nonlinear problems.

The scaling of oblique plasma double layers

NASA Technical Reports Server (NTRS)

Borovsky, J. E.

1983-01-01

Strong oblique plasma double layers are investigated using three methods, i.e., electrostatic particle-in-cell simulations, numerical solutions to the Poisson-Vlasov equations, and analytical approximations to the Poisson-Vlasov equations. The solutions to the Poisson-Vlasov equations and numerical simulations show that strong oblique double layers scale in terms of Debye lengths. For very large potential jumps, theory and numerical solutions indicate that all effects of the magnetic field vanish and the oblique double layers follow the same scaling relation as the field-aligned double layers.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

A modified dynamical model of drying process of polymer blend solution coated on a flat substrate

NASA Astrophysics Data System (ADS)

Kagami, Hiroyuki

2008-05-01

We have proposed and modified a model of drying process of polymer solution coated on a flat substrate for flat polymer film fabrication. And for example numerical simulation of the model reproduces a typical thickness profile of the polymer film formed after drying. Then we have clarified dependence of distribution of polymer molecules on a flat substrate on a various parameters based on analysis of numerical simulations. Then we drove nonlinear equations of drying process from the dynamical model and the fruits were reported. The subject of above studies was limited to solution having one kind of solute though the model could essentially deal with solution having some kinds of solutes. But nowadays discussion of drying process of a solution having some kinds of solutes is needed because drying process of solution having some kinds of solutes appears in many industrial scenes. Polymer blend solution is one instance. And typical resist consists of a few kinds of polymers. Then we introduced a dynamical model of drying process of polymer blend solution coated on a flat substrate and results of numerical simulations of the dynamical model. But above model was the simplest one. In this study, we modify above dynamical model of drying process of polymer blend solution adding effects that some parameters change with time as functions of some variables to it. Then we consider essence of drying process of polymer blend solution through comparison between results of numerical simulations of the modified model and those of the former model.

Patterns of linguistic and numerical performance in aphasia.

PubMed

Rath, Dajana; Domahs, Frank; Dressel, Katharina; Claros-Salinas, Dolores; Klein, Elise; Willmes, Klaus; Krinzinger, Helga

2015-02-04

Empirical research on the relationship between linguistic and numerical processing revealed inconsistent results for different levels of cognitive processing (e.g., lexical, semantic) as well as different stimulus materials (e.g., Arabic digits, number words, letters, non-number words). Information of dissociation patterns in aphasic patients was used in order to investigate the dissociability of linguistic and numerical processes. The aim of the present prospective study was a comprehensive, specific, and systematic investigation of relationships between linguistic and numerical processing, considering the impact of asemantic vs. semantic processing and the type of material employed (numbers compared to letters vs. words). A sample of aphasic patients (n = 60) was assessed with a battery of linguistic and numerical tasks directly comparable for their cognitive processing levels (e.g., perceptual, morpho-lexical, semantic). Mean performance differences and frequencies of (complementary) dissociations in individual patients revealed the most prominent numerical advantage for asemantic tasks when comparing the processing of numbers vs. letters, whereas the least numerical advantage was found for semantic tasks when comparing the processing of numbers vs. words. Different patient subgroups showing differential dissociation patterns were further analysed and discussed. A comprehensive model of linguistic and numerical processing should take these findings into account.

Quasi-generalized variables

NASA Technical Reports Server (NTRS)

Baumgarten, J.; Ostermeyer, G. P.

1986-01-01

The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics.

Numerical analysis of the transient response of an axisymmetric ablative char layer considering internal flow effects

NASA Technical Reports Server (NTRS)

Pittman, C. M.; Howser, L. M.

1972-01-01

The differential equations governing the transient response of the char layer of an ablating axisymmetric body, internal pyrolysis gas flow effects being considered, have been derived. These equations have been expanded into finite difference form and programed for numerical solution on a digital computer. Numerical results compare favorably with simplified exact solutions. The complete numerical analysis was used to obtain solutions for two representative body shapes subjected to a typical entry heating environment. Pronounced effects of the lateral flow of pyrolysis gases on the mass flow field within the char layer and the associated surface and pyrolysis interface recession rates are shown.

Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Sarıaydın, Selin; Yıldırım, Ahmet

2010-05-01

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt -uxx-uyy-(u2)xx-uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt -6ux 2 +6uuxx -uxxxx -uyy -uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

Finite element solutions of free convective Casson fluid flow past a vertically inclined plate submitted in magnetic field in presence of heat and mass transfer

NASA Astrophysics Data System (ADS)

Raju, R. Srinivasa; Reddy, B. Mahesh; Reddy, G. Jithender

2017-09-01

The aim of this research work is to study the influence of thermal radiation on steady magnetohydrodynamic-free convective Casson fluid flow of an optically thick fluid over an inclined vertical plate with heat and mass transfer. Combined phenomenon of heat and mass transfer is considered. Numerical solutions in general form are obtained by using the finite element method. The sum of thermal and mechanical parts is expressed as velocity of fluid. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained numerical solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Numerical results for the controlling flow parameters are drawn graphically and discussed in detail. In some special cases, the obtained numerical results are compared and found to be in good agreement with the previously published results which are available in literature. Applications of this study includes laminar magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics, etc.

Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Dynamic Beam Solutions for Real-Time Simulation and Control Development of Flexible Rockets

NASA Technical Reports Server (NTRS)

Su, Weihua; King, Cecilia K.; Clark, Scott R.; Griffin, Edwin D.; Suhey, Jeffrey D.; Wolf, Michael G.

2016-01-01

In this study, flexible rockets are structurally represented by linear beams. Both direct and indirect solutions of beam dynamic equations are sought to facilitate real-time simulation and control development for flexible rockets. The direct solution is completed by numerically integrate the beam structural dynamic equation using an explicit Newmark-based scheme, which allows for stable and fast transient solutions to the dynamics of flexile rockets. Furthermore, in the real-time operation, the bending strain of the beam is measured by fiber optical sensors (FOS) at intermittent locations along the span, while both angular velocity and translational acceleration are measured at a single point by the inertial measurement unit (IMU). Another study in this paper is to find the analytical and numerical solutions of the beam dynamics based on the limited measurement data to facilitate the real-time control development. Numerical studies demonstrate the accuracy of these real-time solutions to the beam dynamics. Such analytical and numerical solutions, when integrated with data processing and control algorithms and mechanisms, have the potential to increase launch availability by processing flight data into the flexible launch vehicle's control system.

Modeling of Compressible Flow with Friction and Heat Transfer Using the Generalized Fluid System Simulation Program (GFSSP)

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Alak; Majumdar, Alok

2007-01-01

The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

NASA Astrophysics Data System (ADS)

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

Advanced numerical methods for three dimensional two-phase flow calculations

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

Toumi, I.; Caruge, D.

1997-07-01

This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses anmore » extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.« less

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

Calculating corner singularities by boundary integral equations.

PubMed

Shi, Hualiang; Lu, Ya Yan; Du, Qiang

2017-06-01

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions. Our integral equations are formulated for rescaled unknown functions to avoid unbounded field components, and are discretized with a graded mesh and properly chosen quadrature schemes. The numerically found singularity exponents agree well with the exact values in all the test cases presented here, indicating that the numerical solutions are accurate.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

A numerical solution of Duffing's equations including the prediction of jump phenomena

NASA Technical Reports Server (NTRS)

Moyer, E. T., Jr.; Ghasghai-Abdi, E.

1987-01-01

Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

PubMed

Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

2016-05-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

PubMed Central

Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

2015-01-01

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

A New Control Paradigm for Stochastic Differential Equations

NASA Astrophysics Data System (ADS)

Schmid, Matthias J. A.

This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension to scalar systems subject to state-dependent noise and to systems of higher order. The suggested control paradigm is further advanced when a sequential application of MLD control is considered. This technique yields a nominal path corresponding to the minimum total deviation probability on the entire time domain. It is demonstrated that this sequential optimization concept can be unified in a single objective function which is revealed to be the Jacobi field performance index on the entire domain subject to an endpoint deviation. The emerging closed-form term replaces the previously required nested optimization and, thus, results in a highly efficient application-ready control design. This effectively substantiates Minimum Path Deviation (MPD) control. The proposed control paradigm allows the specific problem of stochastic cost control to be addressed as a special case. This new technique is employed within this study for the stochastic cost problem giving rise to Cost Constrained MPD (CCMPD) as well as to Minimum Quadratic Cost Deviation (MQCD) control. An exemplary treatment of a generic scalar nonlinear system subject to quadratic costs is performed for MQCD control to demonstrate the elementary expandability of the new control paradigm. This work concludes with a numerical evaluation of both MPD and CCMPD control for three exemplary benchmark problems. Numerical issues associated with the simulation of SDEs are briefly discussed and illustrated. The numerical examples furnish proof of the successful design. This study is complemented by a thorough review of statistical control methods, stochastic processes, Large Deviations techniques and the Freidlin-Wentzell theory, providing a comprehensive, self-contained account. The presentation of the mathematical tools and concepts is of a unique character, specifically addressing an engineering audience.

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

NASA Technical Reports Server (NTRS)

Goodrich, John W.

2017-01-01

This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].

The Contribution of Text-Highlighting to Comprehension: A Comparison of Print and Digital Reading

ERIC Educational Resources Information Center

Ben-Yehudah, Gal; Eshet-Alkalai, Yoram

2018-01-01

The use of digital materials in educational settings is common, despite evidence indicating that comprehension of digital text is inferior to comprehension of printed text. A potential solution to this problem is to use learning strategies for deeper text processing. Text-highlighting is a strategy known to improve comprehension of printed text;…

On the limits of numerical astronomical solutions used in paleoclimate studies

NASA Astrophysics Data System (ADS)

Zeebe, Richard E.

2017-04-01

Numerical solutions of the equations of the Solar System estimate Earth's orbital parameters in the past and represent the backbone of cyclostratigraphy and astrochronology, now widely applied in geology and paleoclimatology. Given one numerical realization of a Solar System model (i.e., obtained using one code or integrator package), various parameters determine the properties of the solution and usually limit its validity to a certain time period. Such limitations are denoted here as "internal" and include limitations due to (i) the underlying physics/physical model and (ii) numerics. The physics include initial coordinates and velocities of Solar System bodies, treatment of the Moon and asteroids, the Sun's quadrupole moment, and the intrinsic dynamics of the Solar System itself, i.e., its chaotic nature. Numerical issues include solver algorithm, numerical accuracy (e.g., time step), and round-off errors. At present, internal limitations seem to restrict the validity of astronomical solutions to perhaps the past 50 or 60 myr. However, little is currently known about "external" limitations, that is, how do different numerical realizations compare, say, between different investigators using different codes and integrators? Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 myr (Laskar and coworkers and Varadi et al. 2003). In this contribution, I will present results from new Solar System integrations for Earth's eccentricity obtained using the integrator package HNBody (Rauch and Hamilton 2002). I will discuss the various internal limitations listed above within the framework of the present simulations. I will also compare the results to the existing solutions, the details of which are still being sorted out as several simulations are still running at the time of writing.

Partial differential equations of 3D boundary layer and their numerical solutions in turbomachinery

NASA Astrophysics Data System (ADS)

Zhang, Guoqing; Hua, Yaonan; Wu, Chung-Hua

1991-08-01

This paper studies the 3D boundary layer equations (3DBLE) and their numerical solutions in turbomachinery: (1) the general form of 3DBLE in turbomachines with rotational and curvature effects are derived under the semiorthogonal coordinate system, in which the normal pressure gradient is not equal to zero; (2) the method of solution of the 3DBLE is discussed; (3) the 3D boundary layers on the rotating blade surface, IGV endwall, rotor endwall (with a relatively moving boundary) are numerically solved, and the predicted data correlates well with the measured data; and (4) the comparison is made between the numerical results of 3DBLE with and without normal pressure gradient.

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

NASA Technical Reports Server (NTRS)

Black, Carrie; Germaschewski, Kai; Bhattacharjee, Amitava; Ng, C. S.

2013-01-01

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y

Fast and robust estimation of spectro-temporal receptive fields using stochastic approximations.

PubMed

Meyer, Arne F; Diepenbrock, Jan-Philipp; Ohl, Frank W; Anemüller, Jörn

2015-05-15

The receptive field (RF) represents the signal preferences of sensory neurons and is the primary analysis method for understanding sensory coding. While it is essential to estimate a neuron's RF, finding numerical solutions to increasingly complex RF models can become computationally intensive, in particular for high-dimensional stimuli or when many neurons are involved. Here we propose an optimization scheme based on stochastic approximations that facilitate this task. The basic idea is to derive solutions on a random subset rather than computing the full solution on the available data set. To test this, we applied different optimization schemes based on stochastic gradient descent (SGD) to both the generalized linear model (GLM) and a recently developed classification-based RF estimation approach. Using simulated and recorded responses, we demonstrate that RF parameter optimization based on state-of-the-art SGD algorithms produces robust estimates of the spectro-temporal receptive field (STRF). Results on recordings from the auditory midbrain demonstrate that stochastic approximations preserve both predictive power and tuning properties of STRFs. A correlation of 0.93 with the STRF derived from the full solution may be obtained in less than 10% of the full solution's estimation time. We also present an on-line algorithm that allows simultaneous monitoring of STRF properties of more than 30 neurons on a single computer. The proposed approach may not only prove helpful for large-scale recordings but also provides a more comprehensive characterization of neural tuning in experiments than standard tuning curves. Copyright © 2015 Elsevier B.V. All rights reserved.

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

NASA Technical Reports Server (NTRS)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Measuring the Lense-Thirring precession using a second Lageos satellite

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Ciufolini, I.

1989-01-01

A complete numerical simulation and error analysis was performed for the proposed experiment with the objective of establishing an accurate assessment of the feasibility and the potential accuracy of the measurement of the Lense-Thirring precession. Consideration was given to identifying the error sources which limit the accuracy of the experiment and proposing procedures for eliminating or reducing the effect of these errors. Analytic investigations were conducted to study the effects of major error sources with the objective of providing error bounds on the experiment. The analysis of realistic simulated data is used to demonstrate that satellite laser ranging of two Lageos satellites, orbiting with supplemental inclinations, collected for a period of 3 years or more, can be used to verify the Lense-Thirring precession. A comprehensive covariance analysis for the solution was also developed.

Development of a Vorticity-Velocity Navier-Stokes Formulation for the Study of Compressibility Effects on Dynamic Stall

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Ghia, U.

1996-01-01

The first major area of this study was to develop a vorticity-velocity formulation and numerical solution algorithms suitable for the analyses of incompressible as well as low-to- moderate-speed compressible flows. Research performed towards contributing to the determination of the appropriate vorticity and dilation creation boundary conditions suggested to temporarily set aside this approach and use a primitive-variable approach other than the pseudo-compressibility approach used. The second major area of study was initiated to comprehensively examine the INS-2D and INS-3D programs from the point of view of boundary conditions. The research carried out was documented in the form of two technical papers which are included in Appendices A and B; the boundary-condition related issues for INS-3D are briefly mentioned.

Pattern formation in superdiffusion Oregonator model

NASA Astrophysics Data System (ADS)

Feng, Fan; Yan, Jia; Liu, Fu-Cheng; He, Ya-Feng

2016-10-01

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.

Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.

PubMed

Li, Ben; Stenstrom, M K

2014-01-01

One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

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

Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

2016-08-10

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

An iterative transformation procedure for numerical solution of flutter and similar characteristics-value problems

NASA Technical Reports Server (NTRS)

Gossard, Myron L

1952-01-01

An iterative transformation procedure suggested by H. Wielandt for numerical solution of flutter and similar characteristic-value problems is presented. Application of this procedure to ordinary natural-vibration problems and to flutter problems is shown by numerical examples. Comparisons of computed results with experimental values and with results obtained by other methods of analysis are made.

A Dominance Analysis Approach to Determining Predictor Importance in Third, Seventh, and Tenth Grade Reading Comprehension Skills

PubMed Central

Tighe, Elizabeth; Schatschneider, Christopher

2015-01-01

The purpose of the present study was to investigate and rank order by importance the contributions of various cognitive predictors to reading comprehension in third, seventh, and tenth graders. An exploratory factor analysis revealed that for third grade, the best fit was a four-factor solution including Fluency, Verbal Reasoning, Nonverbal Reasoning, and Working Memory factors. For seventh and tenth grade, three-factor solutions with Fluency, Reasoning, and Working Memory factors were the best fit. The three and four-factor models were used in separate dominance analyses for each grade to rank order the factors by predictive importance to reading comprehension. Results indicated that Fluency and Verbal Reasoning were the most important predictors of third grade reading comprehension. For seventh grade, Fluency and Reasoning were the most important predictors. By tenth grade, Reasoning was the most important predictor of reading comprehension. Working Memory was the least predictive of reading comprehension across all grade levels. These results suggest that inferential reasoning skills become an important contributor to reading comprehension at increasing grade levels. PMID:26346315

Analytical and numerical solutions of the equation for the beam propagation in a photovoltaic-photorefractive media

NASA Astrophysics Data System (ADS)

Lin, Ji; Wang, Hou

2013-07-01

We use the classical Lie-group method to study the evolution equation describing a photovoltaic-photorefractive media with the effects of diffusion process and the external electric field. We reduce it to some similarity equations firstly, and then obtain some analytically exact solutions including the soliton solution, the exponential solution and the oscillatory solution. We also obtain the numeric solitons from these similarity equations. Moreover, We show theoretically that these solutions have two types of trajectories. One type is a straight line. The other is a parabolic curve, which indicates these solitons have self-deflection.

Chimpanzee Problem-Solving: A Test for Comprehension.

ERIC Educational Resources Information Center

Premack, David; Woodruff, Guy

1978-01-01

Investigates a chimpanzee's capacity to recognize representations of problems and solutions, as well as its ability to perceive the relationship between each type of problem and its appropriate solutions using televised programs and photographic solutions. (HM)

The Biopsychosocial-Digital Approach to Health and Disease: Call for a Paradigm Expansion.

PubMed

Ahmadvand, Alireza; Gatchel, Robert; Brownstein, John; Nissen, Lisa

2018-05-18

Digital health is an advancing phenomenon in modern health care systems. Currently, numerous stakeholders in various countries are evaluating the potential benefits of digital health solutions at the individual, population, and/or organizational levels. Additionally, driving factors are being created from the customer-side of the health care systems to push health care providers, policymakers, or researchers to embrace digital health solutions. However, health care providers may differ in their approach to adopt these solutions. Health care providers are not assumed to be appropriately trained to address the requirements of integrating digital health solutions into daily everyday practices and procedures. To adapt to the changing demands of health care systems, it is necessary to expand relevant paradigms and to train human resources as required. In this article, a more comprehensive paradigm will be proposed, based on the 'biopsychosocial model' of assessing health and disease, originally introduced by George L Engel. The "biopsychosocial model" must be leveraged to include a "digital" component, thus suggesting a 'biopsychosocial-digital' approach to health and disease. Modifications to the "biopsychosocial" model and transition to the "biopsychosocial-digital" model are explained. Furthermore, the emerging implications of understanding health and disease are clarified pertaining to their relevance in training human resources for health care provision and research. ©Alireza Ahmadvand, Robert Gatchel, John Brownstein, Lisa Nissen. Originally published in the Journal of Medical Internet Research (http://www.jmir.org), 18.05.2018.

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

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

Xia, Yidong, E-mail: yidong.xia@inl.gov; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the Hydra-TH code. -- Highlights: •We performed a comprehensive study to verify and validate the turbulence models in Hydra-TH. •Hydra-TH delivers 2nd-order grid convergence for the incompressible Navier–Stokes equations. •Hydra-TH can accurately simulate the laminar boundary layers. •Hydra-TH can accurately simulate the turbulent boundary layers with RANS turbulence models. •Hydra-TH delivers high-fidelity LES capability for simulating turbulent flows in confined space.« less

Singular boundary method for global gravity field modelling

NASA Astrophysics Data System (ADS)

Cunderlik, Robert

2014-05-01

The singular boundary method (SBM) and method of fundamental solutions (MFS) are meshless boundary collocation techniques that use the fundamental solution of a governing partial differential equation (e.g. the Laplace equation) as their basis functions. They have been developed to avoid singular numerical integration as well as mesh generation in the traditional boundary element method (BEM). SBM have been proposed to overcome a main drawback of MFS - its controversial fictitious boundary outside the domain. The key idea of SBM is to introduce a concept of the origin intensity factors that isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques. Consequently, the source points can be placed directly on the real boundary and coincide with the collocation nodes. In this study we deal with SBM applied for high-resolution global gravity field modelling. The first numerical experiment presents a numerical solution to the fixed gravimetric boundary value problem. The achieved results are compared with the numerical solutions obtained by MFS or the direct BEM indicating efficiency of all methods. In the second numerical experiments, SBM is used to derive the geopotential and its first derivatives from the Tzz components of the gravity disturbing tensor observed by the GOCE satellite mission. A determination of the origin intensity factors allows to evaluate the disturbing potential and gravity disturbances directly on the Earth's surface where the source points are located. To achieve high-resolution numerical solutions, the large-scale parallel computations are performed on the cluster with 1TB of the distributed memory and an iterative elimination of far zones' contributions is applied.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-07-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+-up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Spinning solutions in general relativity with infinite central density

NASA Astrophysics Data System (ADS)

Flammer, P. D.

2018-05-01

This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.

Flow through three-dimensional arrangements of cylinders with alternating streamwise planar tilt

NASA Astrophysics Data System (ADS)

Sahraoui, M.; Marshall, H.; Kaviany, M.

1993-09-01

In this report, fluid flow through a three-dimensional model for the fibrous filters is examined. In this model, the three-dimensional Stokes equation with the appropriate periodic boundary conditions is solved using the finite volume method. In addition to the numerical solution, we attempt to model this flow analytically by using the two-dimensional extended analytic solution in each of the unit cells of the three-dimensional structure. Particle trajectories computed using the superimposed analytic solution of the flow field are closed to those computed using the numerical solution of the flow field. The numerical results show that the pressure drop is not affected significantly by the relative angle of rotation of the cylinders for the high porosity used in this study (epsilon = 0.8 and epsilon = 0.95). The numerical solution and the superimposed analytic solution are also compared in terms of the particle capture efficiency. The results show that the efficiency predictions using the two methods are within 10% for St = 0.01 and 5% for St = 100. As the the porosity decreases, the three-dimensional effect becomes more significant and a difference of 35% is obtained for epsilon = 0.8.

Numerical Simulations of STOVL Hot Gas Ingestion in Ground Proximity Using a Multigrid Solution Procedure

NASA Technical Reports Server (NTRS)

Wang, Gang

2003-01-01

A multi grid solution procedure for the numerical simulation of turbulent flows in complex geometries has been developed. A Full Multigrid-Full Approximation Scheme (FMG-FAS) is incorporated into the continuity and momentum equations, while the scalars are decoupled from the multi grid V-cycle. A standard kappa-Epsilon turbulence model with wall functions has been used to close the governing equations. The numerical solution is accomplished by solving for the Cartesian velocity components either with a traditional grid staggering arrangement or with a multiple velocity grid staggering arrangement. The two solution methodologies are evaluated for relative computational efficiency. The solution procedure with traditional staggering arrangement is subsequently applied to calculate the flow and temperature fields around a model Short Take-off and Vertical Landing (STOVL) aircraft hovering in ground proximity.

Flow to a well in a water-table aquifer: An improved laplace transform solution

USGS Publications Warehouse

Moench, A.F.

1996-01-01

An alternative Laplace transform solution for the problem, originally solved by Neuman, of constant discharge from a partially penetrating well in a water-table aquifer was obtained. The solution differs from existing solutions in that it is simpler in form and can be numerically inverted without the need for time-consuming numerical integration. The derivation invloves the use of the Laplace transform and a finite Fourier cosine series and avoids the Hankel transform used in prior derivations. The solution allows for water in the overlying unsaturated zone to be released either instantaneously in response to a declining water table as assumed by Neuman, or gradually as approximated by Boulton's convolution integral. Numerical evaluation yields results identical with results obtained by previously published methods with the advantage, under most well-aquifer configurations, of much reduced computation time.

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.

Automating FEA programming

NASA Technical Reports Server (NTRS)

Sharma, Naveen

1992-01-01

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer.

Exact Closed-form Solutions for Lamb's Problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-04-01

In this article, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem, for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's (1974) integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson (1974), which strongly confirms the correctness of our explicit formulas. It is hoped that in due time, these formulas may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Exact closed-form solutions for Lamb's problem

NASA Astrophysics Data System (ADS)

Feng, Xi; Zhang, Haiming

2018-07-01

In this paper, we report on an exact closed-form solution for the displacement at the surface of an elastic half-space elicited by a buried point source that acts at some point underneath that surface. This is commonly referred to as the 3-D Lamb's problem for which previous solutions were restricted to sources and receivers placed at the free surface. By means of the reciprocity theorem, our solution should also be valid as a means to obtain the displacements at interior points when the source is placed at the free surface. We manage to obtain explicit results by expressing the solution in terms of elementary algebraic expression as well as elliptic integrals. We anchor our developments on Poisson's ratio 0.25 starting from Johnson's integral solutions which must be computed numerically. In the end, our closed-form results agree perfectly with the numerical results of Johnson, which strongly confirms the correctness of our explicit formulae. It is hoped that in due time, these formulae may constitute a valuable canonical solution that will serve as a yardstick against which other numerical solutions can be compared and measured.

Behavior of Industrial Steel Rack Connections

NASA Astrophysics Data System (ADS)

Shah, S. N. R.; Ramli Sulong, N. H.; Khan, R.; Jumaat, M. Z.; Shariati, M.

2016-03-01

Beam-to-column connections (BCCs) used in steel pallet racks (SPRs) play a significant role to maintain the stability of rack structures in the down-aisle direction. The variety in the geometry of commercially available beam end connectors hampers the development of a generalized analytic design approach for SPR BCCs. The experimental prediction of flexibility in SPR BCCs is prohibitively expensive and difficult for all types of commercially available beam end connectors. A suitable solution to derive a particular uniform M-θ relationship for each connection type in terms of geometric parameters may be achieved through finite element (FE) modeling. This study first presents a comprehensive description of the experimental investigations that were performed and used as the calibration bases for the numerical study that constituted its main contribution. A three dimensioned (3D) non-linear finite element (FE) model was developed and calibrated against the experimental results. The FE model took into account material nonlinearities, geometrical properties and large displacements. Comparisons between numerical and experimental data for observed failure modes and M-θ relationship showed close agreement. The validated FE model was further extended to perform parametric analysis to identify the effects of various parameters which may affect the overall performance of the connection.

Effect of Melt Convection and Solid Transport on Macrosegregation and Grain Structure in Equiaxed Al-Cu Alloys

NASA Technical Reports Server (NTRS)

Rerko, Rodney S.; deGroh, Henry C., III; Beckermann, Christoph; Gray, Hugh R. (Technical Monitor)

2002-01-01

Macrosegregation in metal casting can be caused by thermal and solutal melt convection, and the transport of unattached solid crystals. These free grains can be a result of, for example, nucleation in the bulk liquid or dendrite fragmentation. In an effort to develop a comprehensive numerical model for the casting of alloys, an experimental study has been conducted to generate benchmark data with which such a solidification model could be tested. The specific goal of the experiments was to examine equiaxed solidification in situations where sinking of grains is (and is not) expected. The objectives were: 1) experimentally study the effects of solid transport and thermosolutal convection on macrosegregation and grain size distribution patterns; and 2) provide a complete set of controlled thermal boundary conditions, temperature data, segregation data, and grain size data, to validate numerical codes. The alloys used were Al-1 wt. pct. Cu, and Al-10 wt. pct. Cu with various amounts of the grain refiner TiB2 added. Cylindrical samples were either cooled from the top, or the bottom. Several trends in the data stand out. In attempting to model these experiments, concentrating on experiments that show clear trends or differences is recommended.

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.

Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

PubMed Central

Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

2013-01-01

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

Recent advances in two-phase flow numerics

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

Mahaffy, J.H.; Macian, R.

1997-07-01

The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.

Hydraulic performance improvement of the bidirectional pit pump installation based on CFD

NASA Astrophysics Data System (ADS)

Chen, H. X.; Zhou, D. Q.

2013-12-01

At present, the efficiency of bidirectional pit pump installation with lift under 2m is still low because of lack of research on it in the past. In the paper, the CFD numerical method and experimental test were applied to study flow characteristic of bidirectional pit pump installation under positive and reverse condition. Through changing airfoil type and position of blade and stay vane, the comprehensive performance of improved model were obtained by calculating many different models. The results showed that when improved model is obtained with type A runner with 4 blades that is 0.7D away from pit exit and unsymmetrical guide vane 0.25dh which away from the impeller outlet, and the flow pattern of the improved solution is steady with high efficiency. Compared with the original scheme, the efficiency of positive and reverse design condition reach to 67.23% and 58.32% respectively, which is increased 6% more than original model on the design condition and 5% on the optimum operating condition, and it achieved the purpose of improvement. According to the runner blade angle of the optimization solution, model synthetic characteristic curve was drawn and internal flow field characteristics was analyzed under optimal positive and reverse conditions. The numerical calculation shows that owing to the lack of stay vane to recycle the energy in outlet runner chamber, the water flow regime is not steady enough in the outlet passage, and that is the main reason for lower efficiency at reverse condition than that at positive condition.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

On the Minimal Accuracy Required for Simulating Self-gravitating Systems by Means of Direct N-body Methods

NASA Astrophysics Data System (ADS)

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-01

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-body interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.

Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

2017-06-01

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate. M.S. Thesis

NASA Technical Reports Server (NTRS)

Dow, J. W.

1972-01-01

A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.

The numerical calculation of laminar boundary-layer separation

NASA Technical Reports Server (NTRS)

Klineberg, J. M.; Steger, J. L.

1974-01-01

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

Comprehensive Solutions for Urban Reform

ERIC Educational Resources Information Center

Kilgore, Sally

2005-01-01

The comprehensive school reform (CSR) models build consistency throughout a district while addressing the needs of individual schools. The high-quality CSR programs offer a most effective option for urban education reform.

An efficient technique for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2008-08-01

Computing the numerical solution of the bidomain equations is widely accepted to be a significant computational challenge. In this study we extend a previously published semi-implicit numerical scheme with good stability properties that has been used to solve the bidomain equations (Whiteley, J.P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006). A new, efficient numerical scheme is developed which utilizes the observation that the only component of the ionic current that must be calculated on a fine spatial mesh and updated frequently is the fast sodium current. Other components of the ionic current may be calculated on a coarser mesh and updated less frequently, and then interpolated onto the finer mesh. Use of this technique to calculate the transmembrane potential and extracellular potential induces very little error in the solution. For the simulations presented in this study an increase in computational efficiency of over two orders of magnitude over standard numerical techniques is obtained.

Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

NASA Astrophysics Data System (ADS)

Fasondini, Marco; Fornberg, Bengt; Weideman, J. A. C.

2017-09-01

We extend the numerical pole field solver (Fornberg and Weideman (2011) [12]) to enable the computation of the multivalued Painlevé transcendents, which are the solutions to the third, fifth and sixth Painlevé equations, on their Riemann surfaces. We display, for the first time, solutions to these equations on multiple Riemann sheets. We also provide numerical evidence for the existence of solutions to the sixth Painlevé equation that have pole-free sectors, known as tronquée solutions.

Solutions of conformal Israel-Stewart relativistic viscous fluid dynamics

NASA Astrophysics Data System (ADS)

Marrochio, Hugo; Noronha, Jorge; Denicol, Gabriel S.; Luzum, Matthew; Jeon, Sangyong; Gale, Charles

2015-01-01

We use symmetry arguments developed by Gubser to construct the first radially expanding explicit solutions of the Israel-Stewart formulation of hydrodynamics. Along with a general semi-analytical solution, an exact analytical solution is given which is valid in the cold plasma limit where viscous effects from shear viscosity and the relaxation time coefficient are important. The radially expanding solutions presented in this paper can be used as nontrivial checks of numerical algorithms employed in hydrodynamic simulations of the quark-gluon plasma formed in ultrarelativistic heavy ion collisions. We show this explicitly by comparing such analytic and semi-analytic solutions with the corresponding numerical solutions obtained using the music viscous hydrodynamics simulation code.

A comparison of numerical methods for the prediction of two-dimensional heat transfer in an electrothermal deicer pad. M.S. Thesis. Final Contractor Report

NASA Technical Reports Server (NTRS)

Wright, William B.

1988-01-01

Transient, numerical simulations of the deicing of composite aircraft components by electrothermal heating have been performed in a 2-D rectangular geometry. Seven numerical schemes and four solution methods were used to find the most efficient numerical procedure for this problem. The phase change in the ice was simulated using the Enthalpy method along with the Method for Assumed States. Numerical solutions illustrating deicer performance for various conditions are presented. Comparisons are made with previous numerical models and with experimental data. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

A Numerical Simulation of Scattering from One-Dimensional Inhomogeneous Dielectric Random Surfaces

NASA Technical Reports Server (NTRS)

Sarabandi, Kamal; Oh, Yisok; Ulaby, Fawwaz T.

1996-01-01

In this paper, an efficient numerical solution for the scattering problem of inhomogeneous dielectric rough surfaces is presented. The inhomogeneous dielectric random surface represents a bare soil surface and is considered to be comprised of a large number of randomly positioned dielectric humps of different sizes, shapes, and dielectric constants above an impedance surface. Clods with nonuniform moisture content and rocks are modeled by inhomogeneous dielectric humps and the underlying smooth wet soil surface is modeled by an impedance surface. In this technique, an efficient numerical solution for the constituent dielectric humps over an impedance surface is obtained using Green's function derived by the exact image theory in conjunction with the method of moments. The scattered field from a sample of the rough surface is obtained by summing the scattered fields from all the individual humps of the surface coherently ignoring the effect of multiple scattering between the humps. The statistical behavior of the scattering coefficient sigma(sup 0) is obtained from the calculation of scattered fields of many different realizations of the surface. Numerical results are presented for several different roughnesses and dielectric constants of the random surfaces. The numerical technique is verified by comparing the numerical solution with the solution based on the small perturbation method and the physical optics model for homogeneous rough surfaces. This technique can be used to study the behavior of scattering coefficient and phase difference statistics of rough soil surfaces for which no analytical solution exists.

Nonlinear Mechanisms for the Generation of Nearshore Wave Phenomena.

DTIC Science & Technology

1988-04-01

Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is negative; otherwise...leads to a forced Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is

A Semi-Analytical Solution to Time Dependent Groundwater Flow Equation Incorporating Stream-Wetland-Aquifer Interactions

NASA Astrophysics Data System (ADS)

Boyraz, Uǧur; Melek Kazezyılmaz-Alhan, Cevza

2017-04-01

Groundwater is a vital element of hydrologic cycle and the analytical & numerical solutions of different forms of groundwater flow equations play an important role in understanding the hydrological behavior of subsurface water. The interaction between groundwater and surface water bodies can be determined using these solutions. In this study, new hypothetical approaches are implemented to groundwater flow system in order to contribute to the studies on surface water/groundwater interactions. A time dependent problem is considered in a 2-dimensional stream-wetland-aquifer system. The sloped stream boundary is used to represent the interaction between stream and aquifer. The rest of the aquifer boundaries are assumed as no-flux boundary. In addition, a wetland is considered as a surface water body which lies over the whole aquifer. The effect of the interaction between the wetland and the aquifer is taken into account with a source/sink term in the groundwater flow equation and the interaction flow is calculated by using Darcy's approach. A semi-analytical solution is developed for the 2-dimensional groundwater flow equation in 5 steps. First, Laplace and Fourier cosine transforms are employed to obtain the general solution in Fourier and Laplace domain. Then, the initial and boundary conditions are applied to obtain the particular solution. Finally, inverse Fourier transform is carried out analytically and inverse Laplace transform is carried out numerically to obtain the final solution in space and time domain, respectively. In order to verify the semi-analytical solution, an explicit finite difference algorithm is developed and analytical and numerical solutions are compared for synthetic examples. The comparison of the analytical and numerical solutions shows that the analytical solution gives accurate results.

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

DOE PAGES

Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

2015-07-10

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.« less

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Supersonic flow of chemically reacting gas-particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A numerical solution for chemically reacting supersonic gas-particle flows in rocket nozzles and exhaust plumes was described. The gas-particle flow solution is fully coupled in that the effects of particle drag and heat transfer between the gas and particle phases are treated. Gas and particles exchange momentum via the drag exerted on the gas by the particles. Energy is exchanged between the phases via heat transfer (convection and/or radiation). Thermochemistry calculations (chemical equilibrium, frozen or chemical kinetics) were shown to be uncoupled from the flow solution and, as such, can be solved separately. The solution to the set of governing equations is obtained by utilizing the method of characteristics. The equations cast in characteristic form are shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The particle distribution is represented in the numerical solution by a finite distribution of particle sizes.

Arbitrary Steady-State Solutions with the K-epsilon Model

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Pettersson Reif, B. A.; Gatski, Thomas B.

2006-01-01

Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

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

Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Designing an Algorithm to Preserve Privacy for Medical Record Linkage With Error-Prone Data

PubMed Central

Pal, Doyel; Chen, Tingting; Khethavath, Praveen

2014-01-01

Background Linking medical records across different medical service providers is important to the enhancement of health care quality and public health surveillance. In records linkage, protecting the patients’ privacy is a primary requirement. In real-world health care databases, records may well contain errors due to various reasons such as typos. Linking the error-prone data and preserving data privacy at the same time are very difficult. Existing privacy preserving solutions for this problem are only restricted to textual data. Objective To enable different medical service providers to link their error-prone data in a private way, our aim was to provide a holistic solution by designing and developing a medical record linkage system for medical service providers. Methods To initiate a record linkage, one provider selects one of its collaborators in the Connection Management Module, chooses some attributes of the database to be matched, and establishes the connection with the collaborator after the negotiation. In the Data Matching Module, for error-free data, our solution offered two different choices for cryptographic schemes. For error-prone numerical data, we proposed a newly designed privacy preserving linking algorithm named the Error-Tolerant Linking Algorithm, that allows the error-prone data to be correctly matched if the distance between the two records is below a threshold. Results We designed and developed a comprehensive and user-friendly software system that provides privacy preserving record linkage functions for medical service providers, which meets the regulation of Health Insurance Portability and Accountability Act. It does not require a third party and it is secure in that neither entity can learn the records in the other’s database. Moreover, our novel Error-Tolerant Linking Algorithm implemented in this software can work well with error-prone numerical data. We theoretically proved the correctness and security of our Error-Tolerant Linking Algorithm. We have also fully implemented the software. The experimental results showed that it is reliable and efficient. The design of our software is open so that the existing textual matching methods can be easily integrated into the system. Conclusions Designing algorithms to enable medical records linkage for error-prone numerical data and protect data privacy at the same time is difficult. Our proposed solution does not need a trusted third party and is secure in that in the linking process, neither entity can learn the records in the other’s database. PMID:25600786

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Numerical simulation of the hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor

NASA Astrophysics Data System (ADS)

Fortova, S. V.; Shepelev, V. V.; Troshkin, O. V.; Kozlov, S. A.

2017-09-01

The paper presents the results of numerical simulation of the development of hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor encountered in experiments [1-3]. For the numerical solution used the TPS software package (Turbulence Problem Solver) that implements a generalized approach to constructing computer programs for a wide range of problems of hydrodynamics, described by the system of equations of hyperbolic type. As numerical methods are used the method of large particles and ENO-scheme of the second order with Roe solver for the approximate solution of the Riemann problem.

Intelligent Space Tube Optimization for speeding ground water remedial design.

PubMed

Kalwij, Ineke M; Peralta, Richard C

2008-01-01

An innovative Intelligent Space Tube Optimization (ISTO) two-stage approach facilitates solving complex nonlinear flow and contaminant transport management problems. It reduces computational effort of designing optimal ground water remediation systems and strategies for an assumed set of wells. ISTO's stage 1 defines an adaptive mobile space tube that lengthens toward the optimal solution. The space tube has overlapping multidimensional subspaces. Stage 1 generates several strategies within the space tube, trains neural surrogate simulators (NSS) using the limited space tube data, and optimizes using an advanced genetic algorithm (AGA) with NSS. Stage 1 speeds evaluating assumed well locations and combinations. For a large complex plume of solvents and explosives, ISTO stage 1 reaches within 10% of the optimal solution 25% faster than an efficient AGA coupled with comprehensive tabu search (AGCT) does by itself. ISTO input parameters include space tube radius and number of strategies used to train NSS per cycle. Larger radii can speed convergence to optimality for optimizations that achieve it but might increase the number of optimizations reaching it. ISTO stage 2 automatically refines the NSS-AGA stage 1 optimal strategy using heuristic optimization (we used AGCT), without using NSS surrogates. Stage 2 explores the entire solution space. ISTO is applicable for many heuristic optimization settings in which the numerical simulator is computationally intensive, and one would like to reduce that burden.

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

NASA Technical Reports Server (NTRS)

Compton, William B., III; Thomas, James L.; Abeyounis, William K.; Mason, Mary L.

1989-01-01

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations.

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

NASA Astrophysics Data System (ADS)

Dudley Ward, N. F.; Lähivaara, T.; Eveson, S.

2017-12-01

In this paper, we consider a high-order discontinuous Galerkin (DG) method for modelling wave propagation in coupled poroelastic-elastic media. The upwind numerical flux is derived as an exact solution for the Riemann problem including the poroelastic-elastic interface. Attenuation mechanisms in both Biot's low- and high-frequency regimes are considered. The current implementation supports non-uniform basis orders which can be used to control the numerical accuracy element by element. In the numerical examples, we study the convergence properties of the proposed DG scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions.

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE PAGES

Grout, Ray; Kolla, Hemanth; Minion, Michael; ...

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. Here, we demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

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

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Projection scheme for a reflected stochastic heat equation with additive noise

NASA Astrophysics Data System (ADS)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1982-01-01

Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.

A mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Does Guiding Toward Task-Relevant Information Help Improve Graph Processing and Graph Comprehension of Individuals with Low or High Numeracy? An Eye-Tracker Experiment.

PubMed

Keller, Carmen; Junghans, Alex

2017-11-01

Individuals with low numeracy have difficulties with understanding complex graphs. Combining the information-processing approach to numeracy with graph comprehension and information-reduction theories, we examined whether high numerates' better comprehension might be explained by their closer attention to task-relevant graphical elements, from which they would expect numerical information to understand the graph. Furthermore, we investigated whether participants could be trained in improving their attention to task-relevant information and graph comprehension. In an eye-tracker experiment ( N = 110) involving a sample from the general population, we presented participants with 2 hypothetical scenarios (stomach cancer, leukemia) showing survival curves for 2 treatments. In the training condition, participants received written instructions on how to read the graph. In the control condition, participants received another text. We tracked participants' eye movements while they answered 9 knowledge questions. The sum constituted graph comprehension. We analyzed visual attention to task-relevant graphical elements by using relative fixation durations and relative fixation counts. The mediation analysis revealed a significant ( P < 0.05) indirect effect of numeracy on graph comprehension through visual attention to task-relevant information, which did not differ between the 2 conditions. Training had a significant main effect on visual attention ( P < 0.05) but not on graph comprehension ( P < 0.07). Individuals with high numeracy have better graph comprehension due to their greater attention to task-relevant graphical elements than individuals with low numeracy. With appropriate instructions, both groups can be trained to improve their graph-processing efficiency. Future research should examine (e.g., motivational) mediators between visual attention and graph comprehension to develop appropriate instructions that also result in higher graph comprehension.

Spurious Behavior of Shock-Capturing Methods: Problems Containing Stiff Source Terms and Discontinuities

NASA Technical Reports Server (NTRS)

Yee, Helen M. C.; Kotov, D. V.; Wang, Wei; Shu, Chi-Wang

2013-01-01

The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise evaluation of the source term, previous studies indicated that the phenomenon of wrong propagation speed of discontinuities is connected with the smearing of the discontinuity caused by the discretization of the advection term. The smearing introduces a nonequilibrium state into the calculation. Thus as soon as a nonequilibrium value is introduced in this manner, the source term turns on and immediately restores equilibrium, while at the same time shifting the discontinuity to a cell boundary. The present study is to show that the degree of wrong propagation speed of discontinuities is highly dependent on the accuracy of the numerical method. The manner in which the smearing of discontinuities is contained by the numerical method and the overall amount of numerical dissipation being employed play major roles. Moreover, employing finite time steps and grid spacings that are below the standard Courant-Friedrich-Levy (CFL) limit on shockcapturing methods for compressible Euler and Navier-Stokes equations containing stiff reacting source terms and discontinuities reveals surprising counter-intuitive results. Unlike non-reacting flows, for stiff reactions with discontinuities, employing a time step and grid spacing that are below the CFL limit (based on the homogeneous part or non-reacting part of the governing equations) does not guarantee a correct solution of the chosen governing equations. Instead, depending on the numerical method, time step and grid spacing, the numerical simulation may lead to (a) the correct solution (within the truncation error of the scheme), (b) a divergent solution, (c) a wrong propagation speed of discontinuities solution or (d) other spurious solutions that are solutions of the discretized counterparts but are not solutions of the governing equations. The present investigation for three very different stiff system cases confirms some of the findings of Lafon & Yee (1996) and LeVeque & Yee (1990) for a model scalar PDE. The findings might shed some light on the reported difficulties in numerical combustion and problems with stiff nonlinear (homogeneous) source terms and discontinuities in general.

Comment on “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition” by A. Aziz, Comm. Nonlinear Sci. Numer. Simul. 2009;14:1064-8

NASA Astrophysics Data System (ADS)

Magyari, Eugen

2011-01-01

In a recent paper published in this Journal the title problem has been investigated numerically. In the present paper the exact solution for the temperature boundary layer is given in terms of the solution of the flow problem (the Blasius problem) in a compact integral form.

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Triangular dislocation: an analytical, artefact-free solution

NASA Astrophysics Data System (ADS)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

The stagnation-point flow towards a shrinking sheet with homogeneous - heterogeneous reactions effects: A stability analysis

NASA Astrophysics Data System (ADS)

Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah

2017-01-01

A numerical study is performed to evaluate the problem of stagnation - point flow towards a shrinking sheet with homogeneous - heterogeneous reaction effects. By using non-similar transformation, the governing equations be able to reduced to an ordinary differential equation. Then, results of the equations can be obtained numerically by shooting method with maple implementation. Based on the numerical results obtained, the velocity ratio parameter λ< 0, the dual solutions do exist. Then, the stability analysis is carried out to determine which solution is more stable between both of the solutions by bvp4c solver in Matlab.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

Refined numerical solution of the transonic flow past a wedge

NASA Technical Reports Server (NTRS)

Liang, S.-M.; Fung, K.-Y.

1985-01-01

A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

Some remarks on the numerical solution of parabolic partial differential equations

NASA Astrophysics Data System (ADS)

Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

2017-11-01

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

Constrained and Unconstrained Variational Finite Element Formulation of Solutions to a Stress Wave Problem - a Numerical Comparison.

DTIC Science & Technology

1982-10-01

Element Unconstrained Variational Formulations," Innovativ’e Numerical Analysis For the Applied Engineering Science, R. P. Shaw, et at, Fitor...Initial Boundary Value of Gun Dynamics Solved by Finite Element Unconstrained Variational Formulations," Innovative Numerical Analysis For the Applied ... Engineering Science, R. P. Shaw, et al, Editors, University Press of Virginia, Charlottesville, pp. 733-741, 1980. 2 J. J. Wu, "Solutions to Initial

Designing and defining dynamic protein cage nanoassemblies in solution

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

Lai, Y. -T.; Hura, G. L.; Dyer, K. N.

Central challenges in the design of large and dynamic macromolecular assemblies for synthetic biology lie in developing effective methods for testing design strategies and their outcomes, including comprehensive assessments of solution behavior. Here, we created and validated an advanced design of a 600-kDa protein homododecamer that self-assembles into a symmetric tetrahedral cage. The monomeric unit is composed of a trimerizing apex-forming domain genetically linked to an edge-forming dimerizing domain. Enhancing the crystallographic results, high-throughput small-angle x-ray scattering (SAXS) comprehensively contrasted our modifications under diverse solution conditions. To generate a phase diagram associating structure and assembly, we developed force plots thatmore » measure dissimilarity among multiple SAXS data sets. These new tools, which provided effective feedback on experimental constructs relative to design, have general applicability in analyzing the solution behavior of heterogeneous nanosystems and have been made available as a web-based application. Specifically, our results probed the influence of solution conditions and symmetry on stability and structural adaptability, identifying the dimeric interface as the weak point in the assembly. Force plots comparing SAXS data sets further reveal more complex and controllable behavior in solution than captured by our crystal structures. Lastly, these methods for objectively and comprehensively comparing SAXS profiles for systems critically affected by solvent conditions and structural heterogeneity provide an enabling technology for advancing the design and bioengineering of nanoscale biological materials.« less

Designing and defining dynamic protein cage nanoassemblies in solution

DOE PAGES

Lai, Y. -T.; Hura, G. L.; Dyer, K. N.; ...

2016-12-14

Central challenges in the design of large and dynamic macromolecular assemblies for synthetic biology lie in developing effective methods for testing design strategies and their outcomes, including comprehensive assessments of solution behavior. Here, we created and validated an advanced design of a 600-kDa protein homododecamer that self-assembles into a symmetric tetrahedral cage. The monomeric unit is composed of a trimerizing apex-forming domain genetically linked to an edge-forming dimerizing domain. Enhancing the crystallographic results, high-throughput small-angle x-ray scattering (SAXS) comprehensively contrasted our modifications under diverse solution conditions. To generate a phase diagram associating structure and assembly, we developed force plots thatmore » measure dissimilarity among multiple SAXS data sets. These new tools, which provided effective feedback on experimental constructs relative to design, have general applicability in analyzing the solution behavior of heterogeneous nanosystems and have been made available as a web-based application. Specifically, our results probed the influence of solution conditions and symmetry on stability and structural adaptability, identifying the dimeric interface as the weak point in the assembly. Force plots comparing SAXS data sets further reveal more complex and controllable behavior in solution than captured by our crystal structures. Lastly, these methods for objectively and comprehensively comparing SAXS profiles for systems critically affected by solvent conditions and structural heterogeneity provide an enabling technology for advancing the design and bioengineering of nanoscale biological materials.« less

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters

EPA Science Inventory

Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Thermal, size and surface effects on the nonlinear pull-in of small-scale piezoelectric actuators

NASA Astrophysics Data System (ADS)

SoltanRezaee, Masoud; Ghazavi, Mohammad-Reza

2017-09-01

Electrostatically actuated miniature wires/tubes have many operational applications in the high-tech industries. In this research, the nonlinear pull-in instability of piezoelectric thermal small-scale switches subjected to Coulomb and dissipative forces is analyzed using strain gradient and modified couple stress theories. The discretized governing equation is solved numerically by means of the step-by-step linearization method. The correctness of the formulated model and solution procedure is validated through comparison with experimental and several theoretical results. Herein, the length-scale, surface energy, van der Waals attraction and nonlinear curvature are considered in the present comprehensive model and the thermo-electro-mechanical behavior of cantilever piezo-beams are discussed in detail. It is found that the piezoelectric actuation can be used as a design parameter to control the pull-in phenomenon. The obtained results are applicable in stability analysis, practical design and control of actuated miniature intelligent devices.

Dispersion and viscous attenuation of capillary waves with finite amplitude

NASA Astrophysics Data System (ADS)

Denner, Fabian; Paré, Gounséti; Zaleski, Stéphane

2017-04-01

We present a comprehensive study of the dispersion of capillary waves with finite amplitude, based on direct numerical simulations. The presented results show an increase of viscous attenuation and, consequently, a smaller frequency of capillary waves with increasing initial wave amplitude. Interestingly, however, the critical wavenumber as well as the wavenumber at which the maximum frequency is observed remain the same for a given two-phase system, irrespective of the wave amplitude. By devising an empirical correlation that describes the effect of the wave amplitude on the viscous attenuation, the dispersion of capillary waves with finite initial amplitude is shown to be, in very good approximation, self-similar throughout the entire underdamped regime and independent of the fluid properties. The results also shown that analytical solutions for capillary waves with infinitesimal amplitude are applicable with reasonable accuracy for capillary waves with moderate amplitude.

Obesity epidemic in Brazil and Argentina: a public health concern.

PubMed

Arbex, Alberto K; Rocha, Denise R T W; Aizenberg, Marisa; Ciruzzi, Maria S

2014-06-01

The obesity epidemic is rapidly advancing in South America, leading to inevitable health consequences. Argentinian and Brazilian health policies try to become adapted to the new economic and social framework that follows from this epidemic. It is in incipient and ineffective control so far since the prevalence of obesity was not restrained. The Argentine national legislation is more advanced, through the so-called "Ley de Obesidad." In Brazil, there are numerous local initiatives but still not a comprehensive law. National policies relating to decisions regarding obesity are discussed in this paper. Trends in decisions issued in higher courts of Argentina (Supreme Court of Justice of the Nation--CSJN) and Brazil (Supreme Court of Justice--STF), in the last 15 years, seek to clarify the approach of each country and court's resolutions. Marked differences were found in their positions. Finally, legal and health solutions to this obesity epidemic are proposed.

The GALAXIE all-optical FEL project

NASA Astrophysics Data System (ADS)

Rosenzweig, J. B.; Arab, E.; Andonian, G.; Cahill, A.; Fitzmorris, K.; Fukusawa, A.; Hoang, P.; Jovanovic, I.; Marcus, G.; Marinelli, A.; Murokh, A.; Musumeci, P.; Naranjo, B.; O'Shea, B.; O'Shea, F.; Ovodenko, A.; Pogorelsky, I.; Putterman, S.; Roberts, K.; Shumail, M.; Tantawi, S.; Valloni, A.; Yakimenko, V.; Xu, G.

2012-12-01

We describe a comprehensive project, funded under the DARPA AXiS program, to develop an all-optical table-top X-ray FEL based on dielectric acceleration and electromagnetic undulators, yielding a compact source of coherent X-rays for medical and related applications. The compactness of this source demands that high field (>GV/m) acceleration and undulation-inducing fields be employed, thus giving rise to the project's acronym: GV/m AcceLerator And X-ray Integrated Experiment (GALAXIE). There are numerous physics and technical hurdles to surmount in this ambitious scenario, and the integrated solutions include: a biharmonic photonic TW structure, 200 micron wavelength electromagnetic undulators, 5 μm laser development, ultra-high brighness magnetized/asymmetric emittance electron beam generation, and SASE FEL operation. We describe the overall design philosophy of the project, the innovative approaches to addressing the challenges presented by the design, and the significant progress towards realization of these approaches in the nine months since project initialization.

Obesity Epidemic in Brazil and Argentina: A Public Health Concern

PubMed Central

Rocha, Denise R.T.W.; Aizenberg, Marisa; Ciruzzi, Maria S.

2014-01-01

ABSTRACT The obesity epidemic is rapidly advancing in South America, leading to inevitable health consequences. Argentinian and Brazilian health policies try to become adapted to the new economic and social framework that follows from this epidemic. It is in incipient and ineffective control so far since the prevalence of obesity was not restrained. The Argentine national legislation is more advanced, through the so-called “Ley de Obesidad.” In Brazil, there are numerous local initiatives but still not a comprehensive law. National policies relating to decisions regarding obesity are discussed in this paper. Trends in decisions issued in higher courts of Argentina (Supreme Court of Justice of the Nation—CSJN) and Brazil (Supreme Court of Justice—STF), in the last 15 years, seek to clarify the approach of each country and court's resolutions. Marked differences were found in their positions. Finally, legal and health solutions to this obesity epidemic are proposed. PMID:25076669

A tutorial on the CARE III approach to reliability modeling. [of fault tolerant avionics and control systems

NASA Technical Reports Server (NTRS)

Trivedi, K. S.; Geist, R. M.

1981-01-01

The CARE 3 reliability model for aircraft avionics and control systems is described by utilizing a number of examples which frequently use state-of-the-art mathematical modeling techniques as a basis for their exposition. Behavioral decomposition followed by aggregration were used in an attempt to deal with reliability models with a large number of states. A comprehensive set of models of the fault-handling processes in a typical fault-tolerant system was used. These models were semi-Markov in nature, thus removing the usual restrictions of exponential holding times within the coverage model. The aggregate model is a non-homogeneous Markov chain, thus allowing the times to failure to posses Weibull-like distributions. Because of the departures from traditional models, the solution method employed is that of Kolmogorov integral equations, which are evaluated numerically.

Can the world afford to ignore biotechnology solutions that address food insecurity?

PubMed

Berman, Judit; Zhu, Changfu; Pérez-Massot, Eduard; Arjó, Gemma; Zorrilla-López, Uxue; Masip, Gemma; Banakar, Raviraj; Sanahuja, Georgina; Farré, Gemma; Miralpeix, Bruna; Bai, Chao; Vamvaka, Evangelia; Sabalza, Maite; Twyman, Richard M; Bassié, Ludovic; Capell, Teresa; Christou, Paul

2013-09-01

Genetically engineered (GE) crops can be used as part of a combined strategy to address food insecurity, which is defined as a lack of sustainable access to safe and nutritious food. In this article, we discuss the causes and consequences of food insecurity in the developing world, and the indirect economic impact on industrialized countries. We dissect the healthcare costs and lost productivity caused by food insecurity, and evaluate the relative merits of different intervention programs including supplementation, fortification and the deployment of GE crops with higher yields and enhanced nutritional properties. We provide clear evidence for the numerous potential benefits of GE crops, particularly for small-scale and subsistence farmers. GE crops with enhanced yields and nutritional properties constitute a vital component of any comprehensive strategy to tackle poverty, hunger and malnutrition in developing countries and thus reduce the global negative economic effects of food insecurity.

Propagation of Cosmic Rays and Diffuse Galactic Gamma Rays

NASA Technical Reports Server (NTRS)

Moskalenko, Igor V.

2004-01-01

This paper presents an introduction to the astrophysics of cosmic rays and diffuse gamma-rays and discusses some of the puzzles that have emerged recently due to more precise data and improved propagation models: the excesses in Galactic diffuse gamma-ray emission, secondary antiprotons and positrons, and the flatter than expected gradient of cosmic rays in the Galaxy. These also involve the dark matter, a challenge to modern physics, through its indirect searches in cosmic rays. Though the final solutions are yet to be found, I discuss some ideas and results obtained mostly with the numerical propagation model GALPROP. A fleet of spacecraft and balloon experiments targeting these specific issues is set to lift off in a few years, imparting a feeling of optimism that a new era of exciting discoveries is just around the corner. A complete and comprehensive discussion of all the recent results is not attempted here due to the space limitations.

Qualitative Description of Spatial Quality in Inclusive Architecture.

PubMed

Ryhl, Camilla; Kajita, Masashi; Sørensen, René

2016-01-01

Universal design (UD) has gained global significance and is in the process of institutionalisation in the Nordic Region. This is despite an urgent necessity for developing the theoretical basis and practical applicability of UD. Reflecting this need for furthering the comprehensive understanding of spatial implication of UD, this paper aims to contribute for articulating a means to assess the quality of UD in architecture. Drawing upon numerous cases from research conducted at the Danish Building Research Institute, the paper focuses on sensory aspects of spatial quality, and discusses as well as reflects an applied method for producing the qualitative description of selected buildings that embody UD through creative solutions. The qualitative description of collected examples appears to be effective in delineating sensory aspects of spatial experience; however the systematic development of assessment criteria is essential in order to support students and designers to make responsible decisions in shaping built environments that are accessible and inclusive but also enjoyable.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

A viscous flow study of shock-boundary layer interaction, radial transport, and wake development in a transonic compressor

NASA Technical Reports Server (NTRS)

Hah, Chunill; Reid, Lonnie

1991-01-01

A numerical study based on the 3D Reynolds-averaged Navier-Stokes equation has been conducted to investigate the detailed flow physics inside a transonic compressor. 3D shock structure, shock-boundary layer interaction, flow separation, radial mixing, and wake development are all investigated at design and off-design conditions. Experimental data based on laser anemometer measurements are used to assess the overall quality of the numerical solution. An additional experimental study to investigate end-wall flow with a hot-film was conducted, and these results are compared with the numerical results. Detailed comparison with experimental data indicates that the overall features of the 3D shock structure, the shock-boundary layer interaction, and the wake development are all calculated very well in the numerical solution. The numerical results are further analyzed to examine the radial mixing phenomena in the transonic compressor. A thin sheet of particles is injected in the numerical solution upstream of the compressor. The movement of particles is traced with a 3D plotting package. This numerical survey of tracer concentration reveals the fundamental mechanisms of radial transport in this transonic compressor.

ON THE MINIMAL ACCURACY REQUIRED FOR SIMULATING SELF-GRAVITATING SYSTEMS BY MEANS OF DIRECT N-BODY METHODS

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

Portegies Zwart, Simon; Boekholt, Tjarda

2014-04-10

The conservation of energy, linear momentum, and angular momentum are important drivers of our physical understanding of the evolution of the universe. These quantities are also conserved in Newton's laws of motion under gravity. Numerical integration of the associated equations of motion is extremely challenging, in particular due to the steady growth of numerical errors (by round-off and discrete time-stepping and the exponential divergence between two nearby solutions. As a result, numerical solutions to the general N-body problem are intrinsically questionable. Using brute force integrations to arbitrary numerical precision we demonstrate empirically that ensembles of different realizations of resonant three-bodymore » interactions produce statistically indistinguishable results. Although individual solutions using common integration methods are notoriously unreliable, we conjecture that an ensemble of approximate three-body solutions accurately represents an ensemble of true solutions, so long as the energy during integration is conserved to better than 1/10. We therefore provide an independent confirmation that previous work on self-gravitating systems can actually be trusted, irrespective of the intrinsically chaotic nature of the N-body problem.« less

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1990-01-01

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Numerical Boundary Condition Procedures

NASA Technical Reports Server (NTRS)

1981-01-01

Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.

Comprehensive survey of deep learning in remote sensing: theories, tools, and challenges for the community

NASA Astrophysics Data System (ADS)

Ball, John E.; Anderson, Derek T.; Chan, Chee Seng

2017-10-01

In recent years, deep learning (DL), a rebranding of neural networks (NNs), has risen to the top in numerous areas, namely computer vision (CV), speech recognition, and natural language processing. Whereas remote sensing (RS) possesses a number of unique challenges, primarily related to sensors and applications, inevitably RS draws from many of the same theories as CV, e.g., statistics, fusion, and machine learning, to name a few. This means that the RS community should not only be aware of advancements such as DL, but also be leading researchers in this area. Herein, we provide the most comprehensive survey of state-of-the-art RS DL research. We also review recent new developments in the DL field that can be used in DL for RS. Namely, we focus on theories, tools, and challenges for the RS community. Specifically, we focus on unsolved challenges and opportunities as they relate to (i) inadequate data sets, (ii) human-understandable solutions for modeling physical phenomena, (iii) big data, (iv) nontraditional heterogeneous data sources, (v) DL architectures and learning algorithms for spectral, spatial, and temporal data, (vi) transfer learning, (vii) an improved theoretical understanding of DL systems, (viii) high barriers to entry, and (ix) training and optimizing the DL.

NONLINEAR AND FIBER OPTICS: Self-similar solution obtained by self-focusing of annular laser beams

NASA Astrophysics Data System (ADS)

Azimov, B. S.; Platonenko, Viktor T.; Sagatov, M. M.

1991-03-01

A numerical modeling is reported of steady-state self-focusing of an annular beam with thin "walls." An approximate similar solution is found to describe well the relationships observed in the numerical experiment for a special selection of the input parameters of the beam. This solution is used to estimate the focal length. Such self-similar self-focusing is shown to affect the whole power of the beam.

Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution

ERIC Educational Resources Information Center

Subramanian, Venkat R.

2006-01-01

High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

EPA Science Inventory

Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

Improvements to embedded shock wave calculations for transonic flow-applications to wave drag and pressure rise predictions

NASA Technical Reports Server (NTRS)

Seebass, A. R.

1974-01-01

The numerical solution of a single, mixed, nonlinear equation with prescribed boundary data is discussed. A second order numerical procedure for solving the nonlinear equation and a shock fitting scheme was developed to treat the discontinuities that appear in the solution.

NUMERICAL TECHNIQUES TO SOLVE CONDENSATIONAL AND DISSOLUTIONAL GROWTH EQUATIONS WHEN GROWTH IS COUPLED TO REVERSIBLE REACTIONS (R823186)

EPA Science Inventory

Noniterative, unconditionally stable numerical techniques for solving condensational and
dissolutional growth equations are given. Growth solutions are compared to Gear-code solutions for
three cases when growth is coupled to reversible equilibrium chemistry. In all cases, ...

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

NASA Technical Reports Server (NTRS)

Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

2002-01-01

We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

NASA Technical Reports Server (NTRS)

Reynolds, W. C. (Editor); Maccormack, R. W.

1981-01-01

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Ezz-Eldien, S. S.; Van Gorder, Robert A.

2014-12-01

The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Liu, Hailiang; Wang, Zhongming

2017-01-01

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

A numerical and experimental study of three-dimensional liquid sloshing in a rotating spherical container

NASA Technical Reports Server (NTRS)

Chen, Kuo-Huey; Kelecy, Franklyn J.; Pletcher, Richard H.

1992-01-01

A numerical and experimental study of three dimensional liquid sloshing inside a partially-filled spherical container undergoing an orbital rotating motion is described. Solutions of the unsteady, three-dimensional Navier-Stokes equations for the case of a gradual spin-up from rest are compared with experimental data obtained using a rotating test rig fitted with two liquid-filled spherical tanks. Data gathered from several experiments are reduced in terms of a dimensionless free surface height for comparison with transient results from the numerical simulations. The numerical solutions are found to compare favorably with the experimental data.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Vezewski, D. J.

1980-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1979-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

NASA Astrophysics Data System (ADS)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow condition but discrete-continuum models provide more accurate results. Parameters sensitivities analysis indicates that conduit diameter and friction factor, matrix hydraulic conductivity and porosity are important parameters that significantly affect variable-density flow and solute transport simulation. The pros and cons of model assumptions, conceptual simplifications and numerical techniques in VDFST-CFP are discussed. In general, the development of VDFST-CFP model is an innovation in numerical modeling methodology and could be applied to quantitatively evaluate the seawater/freshwater interaction in coastal karst aquifers. Keywords: Discrete-continuum numerical model; Variable density flow and transport; Coastal karst aquifer; Non-laminar flow

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

A Comprehensive Analytical Solution of the Nonlinear Pendulum

ERIC Educational Resources Information Center

Ochs, Karlheinz

2011-01-01

In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…

Verbal versus Numerical Probabilities: Does Format Presentation of Probabilistic Information regarding Breast Cancer Screening Affect Women's Comprehension?

ERIC Educational Resources Information Center

Vahabi, Mandana

2010-01-01

Objective: To test whether the format in which women receive probabilistic information about breast cancer and mammography affects their comprehension. Methods: A convenience sample of 180 women received pre-assembled randomized packages containing a breast health information brochure, with probabilities presented in either verbal or numeric…

Implementing Comprehensive School Physical Activity Programs: A Wayne State University Case Study

ERIC Educational Resources Information Center

Centeio, Erin E.; McCaughtry, Nate

2017-01-01

Comprehensive school physical activity programs (CSPAPs) have been highlighted by numerous public health and education agencies for their potential to improve the health and academic achievement of American youth. A CSPAP integrates physical activity throughout the school environment before, during and after school by engaging educators, children,…

Simulating the phase partitioning of NH3, HNO3, and HCl with size-resolved particles over northern Colorado in winter

EPA Science Inventory

Numerical modeling of inorganic aerosol processes is useful in air quality management, but comprehensive evaluation of modeled aerosol processes is rarely possible due to the lack of comprehensive datasets. During the Nitrogen, Aerosol Composition, and Halogens on a Tall Tower (N...

An e-Learning System for Extracting Text Comprehension and Learning Style Characteristics

ERIC Educational Resources Information Center

Samarakou, Maria; Tsaganou, Grammatiki; Papadakis, Andreas

2018-01-01

Technology-mediated learning is very actively and widely researched, with numerous e-learning environments designed for different educational purposes developed during the past few decades. Still, their organization and texts are not structured according to any theory of educational comprehension. Modern education is even more flexible and, thus,…

Numerical uncertainty in computational engineering and physics

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

Hemez, Francois M

2009-01-01

Obtaining a solution that approximates ordinary or partial differential equations on a computational mesh or grid does not necessarily mean that the solution is accurate or even 'correct'. Unfortunately assessing the quality of discrete solutions by questioning the role played by spatial and temporal discretizations generally comes as a distant third to test-analysis comparison and model calibration. This publication is contributed to raise awareness of the fact that discrete solutions introduce numerical uncertainty. This uncertainty may, in some cases, overwhelm in complexity and magnitude other sources of uncertainty that include experimental variability, parametric uncertainty and modeling assumptions. The concepts ofmore » consistency, convergence and truncation error are overviewed to explain the articulation between the exact solution of continuous equations, the solution of modified equations and discrete solutions computed by a code. The current state-of-the-practice of code and solution verification activities is discussed. An example in the discipline of hydro-dynamics illustrates the significant effect that meshing can have on the quality of code predictions. A simple method is proposed to derive bounds of solution uncertainty in cases where the exact solution of the continuous equations, or its modified equations, is unknown. It is argued that numerical uncertainty originating from mesh discretization should always be quantified and accounted for in the overall uncertainty 'budget' that supports decision-making for applications in computational physics and engineering.« less

Analytical guidance law development for aerocapture at Mars

NASA Technical Reports Server (NTRS)

Calise, A. J.

1992-01-01

During the first part of this reporting period research has concentrated on performing a detailed evaluation, to zero order, of the guidance algorithm developed in the first period taking the numerical approach developed in the third period. A zero order matched asymptotic expansion (MAE) solution that closely satisfies a set of 6 implicit equations in 6 unknowns to an accuracy of 10(exp -10), was evaluated. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the MAE problem to obtain the feedback controls. A zero order guided solution was evaluated and compared with optimal solution that was obtained by numerical methods. Numerical experience shows that the zero order guided solution is close to optimal solution, and that the zero order MAE outer solution plays a critical role in accounting for the variations in Loh's term near the exit phase of the maneuver. However, the deficiency that remains in several of the critical variables indicates the need for a first order correction. During the second part of this period, methods for computing a first order correction were explored.

Essentially nonoscillatory postprocessing filtering methods

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1992-01-01

High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

A real success in numerical modeling of dynamics of the Earth can be achieved only by multidisciplinary research teams of experts in geodynamics, applied and pure mathematics, and computer science. The success in numerical modeling is based on the following basic, but simple, rules. (i) People need simplicity most, but they understand intricacies best (B. Pasternak, writer). Start from a simple numerical model, which describes basic physical laws by a set of mathematical equations, and move then to a complex model. Never start from a complex model, because you cannot understand the contribution of each term of the equations to the modeled geophysical phenomenon. (ii) Study the numerical methods behind your computer code. Otherwise it becomes difficult to distinguish true and erroneous solutions to the geodynamic problem, especially when your problem is complex enough. (iii) Test your model versus analytical and asymptotic solutions, simple 2D and 3D model examples. Develop benchmark analysis of different numerical codes and compare numerical results with laboratory experiments. Remember that the numerical tool you employ is not perfect, and there are small bugs in every computer code. Therefore the testing is the most important part of your numerical modeling. (iv) Prove (if possible) or learn relevant statements concerning the existence, uniqueness and stability of the solution to the mathematical and discrete problems. Otherwise you can solve an improperly-posed problem, and the results of the modeling will be far from the true solution of your model problem. (v) Try to analyze numerical models of a geological phenomenon using as less as possible tuning model variables. Already two tuning variables give enough possibilities to constrain your model well enough with respect to observations. The data fitting sometimes is quite attractive and can take you far from a principal aim of your numerical modeling: to understand geophysical phenomena. (vi) If the number of tuning model variables are greater than two, test carefully the effect of each of the variables on the modeled phenomenon. Remember: With four exponents I can fit an elephant (E. Fermi, physicist). (vii) Make your numerical model as accurate as possible, but never put the aim to reach a great accuracy: Undue precision of computations is the first symptom of mathematical illiteracy (N. Krylov, mathematician). How complex should be a numerical model? A model which images any detail of the reality is as useful as a map of scale 1:1 (J. Robinson, economist). This message is quite important for geoscientists, who study numerical models of complex geodynamical processes. I believe that geoscientists will never create a model of the real Earth dynamics, but we should try to model the dynamics such a way to simulate basic geophysical processes and phenomena. Does a particular model have a predictive power? Each numerical model has a predictive power, otherwise the model is useless. The predictability of the model varies with its complexity. Remember that a solution to the numerical model is an approximate solution to the equations, which have been chosen in believe that they describe dynamic processes of the Earth. Hence a numerical model predicts dynamics of the Earth as well as the mathematical equations describe this dynamics. What methodological advances are still needed for testable geodynamic modeling? Inverse (time-reverse) numerical modeling and data assimilation are new methodologies in geodynamics. The inverse modeling can allow to test geodynamic models forward in time using restored (from present-day observations) initial conditions instead of unknown conditions.

A collocation-shooting method for solving fractional boundary value problems

NASA Astrophysics Data System (ADS)

Al-Mdallal, Qasem M.; Syam, Muhammed I.; Anwar, M. N.

2010-12-01

In this paper, we discuss the numerical solution of special class of fractional boundary value problems of order 2. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proven. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

NASA Astrophysics Data System (ADS)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

NASA Astrophysics Data System (ADS)

Beléndez, Augusto; Francés, Jorge; Beléndez, Tarsicio; Bleda, Sergio; Pascual, Carolina; Arribas, Enrique

2015-05-01

A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.

Exact analytic solution for the spin-up maneuver of an axially symmetric spacecraft

NASA Astrophysics Data System (ADS)

Ventura, Jacopo; Romano, Marcello

2014-11-01

The problem of spinning-up an axially symmetric spacecraft subjected to an external torque constant in magnitude and parallel to the symmetry axis is considered. The existing exact analytic solution for an axially symmetric body is applied for the first time to this problem. The proposed solution is valid for any initial conditions of attitude and angular velocity and for any length of time and rotation amplitude. Furthermore, the proposed solution can be numerically evaluated up to any desired level of accuracy. Numerical experiments and comparison with an existing approximated solution and with the integration of the equations of motion are reported in the paper. Finally, a new approximated solution obtained from the exact one is introduced in this paper.

Fast sweeping method for the factored eikonal equation

NASA Astrophysics Data System (ADS)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

Using 4th order Runge-Kutta method for solving a twisted Skyrme string equation

NASA Astrophysics Data System (ADS)

Hadi, Miftachul; Anderson, Malcolm; Husein, Andri

2016-03-01

We study numerical solution, especially using 4th order Runge-Kutta method, for solving a twisted Skyrme string equation. We find numerically that the value of minimum energy per unit length of vortex solution for a twisted Skyrmion string is 20.37 × 1060 eV/m.

Difference-Equation/Flow-Graph Circuit Analysis

NASA Technical Reports Server (NTRS)

Mcvey, I. M.

1988-01-01

Numerical technique enables rapid, approximate analyses of electronic circuits containing linear and nonlinear elements. Practiced in variety of computer languages on large and small computers; for circuits simple enough, programmable hand calculators used. Although some combinations of circuit elements make numerical solutions diverge, enables quick identification of divergence and correction of circuit models to make solutions converge.

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

NASA Astrophysics Data System (ADS)

Al-Marouf, M.; Samtaney, R.

2017-05-01

We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

On the Unreasonable Effectiveness of post-Newtonian Theory in Gravitational-Wave Physics

ScienceCinema

Will, Clifford M.

2017-12-22

The first indirect detection of gravitational waves involved a binary system of neutron stars.  In the future, the first direct detection may also involve binary systems -- inspiralling and merging binary neutron stars or black holes. This means that it is essential to understand in full detail the two-body system in general relativity, a notoriously difficult problem with a long history. Post-Newtonian approximation methods are thought to work only under slow motion and weak field conditions, while numerical solutions of Einstein's equations are thought to be limited to the final merger phase.  Recent results have shown that post-Newtonian approximations seem to remain unreasonably valid well into the relativistic regime, while advances in numerical relativity now permit solutions for numerous orbits before merger.  It is now possible to envision linking post-Newtonian theory and numerical relativity to obtain a complete "solution" of the general relativistic two-body problem.  These solutions will play a central role in detecting and understanding gravitational wave signals received by interferometric observatories on Earth and in space.

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

NASA Astrophysics Data System (ADS)

Trinkle, Dallas R.

2017-10-01

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

Numerical method for the solution of large systems of differential equations of the boundary layer type

NASA Technical Reports Server (NTRS)

Green, M. J.; Nachtsheim, P. R.

1972-01-01

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

NASA Astrophysics Data System (ADS)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

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

Starodumov, Ilya; Kropotin, Nikolai

2016-08-10

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phasemore » Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.« less

Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

NASA Astrophysics Data System (ADS)

Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

2017-11-01

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

Numerical methods for axisymmetric and 3D nonlinear beams

NASA Astrophysics Data System (ADS)

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

NASA Astrophysics Data System (ADS)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

A numerical solution for thermoacoustic convection of fluids in low gravity

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Bourgeois, S. V., Jr.; Fan, C.; Grodzka, P. G.

1973-01-01

A finite difference numerical technique for solving the differential equations which describe thermal convection of compressible fluids in low gravity are reported. Results of one-dimensional calculations are presented, and comparisons are made to previous solutions. The primary result presented is a one-dimensional radial model of the Apollo 14 heat flow and convection demonstration flight experiment. The numerical calculations show that thermally induced convective motion in a confined fluid can have significant effects on heat transfer in a low gravity environment.

Introduction to Numerical Methods

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

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Data-Centric Situational Awareness and Management in Intelligent Power Systems

NASA Astrophysics Data System (ADS)

Dai, Xiaoxiao

The rapid development of technology and society has made the current power system a much more complicated system than ever. The request for big data based situation awareness and management becomes urgent today. In this dissertation, to respond to the grand challenge, two data-centric power system situation awareness and management approaches are proposed to address the security problems in the transmission/distribution grids and social benefits augmentation problem at the distribution-customer lever, respectively. To address the security problem in the transmission/distribution grids utilizing big data, the first approach provides a fault analysis solution based on characterization and analytics of the synchrophasor measurements. Specically, the optimal synchrophasor measurement devices selection algorithm (OSMDSA) and matching pursuit decomposition (MPD) based spatial-temporal synchrophasor data characterization method was developed to reduce data volume while preserving comprehensive information for the big data analyses. And the weighted Granger causality (WGC) method was investigated to conduct fault impact causal analysis during system disturbance for fault localization. Numerical results and comparison with other methods demonstrate the effectiveness and robustness of this analytic approach. As more social effects are becoming important considerations in power system management, the goal of situation awareness should be expanded to also include achievements in social benefits. The second approach investigates the concept and application of social energy upon the University of Denver campus grid to provide management improvement solutions for optimizing social cost. Social element--human working productivity cost, and economic element--electricity consumption cost, are both considered in the evaluation of overall social cost. Moreover, power system simulation, numerical experiments for smart building modeling, distribution level real-time pricing and social response to the pricing signals are studied for implementing the interactive artificial-physical management scheme.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Computations of ideal and real gas high altitude plume flows

NASA Technical Reports Server (NTRS)

Feiereisen, William J.; Venkatapathy, Ethiraj

1988-01-01

In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

NASA Technical Reports Server (NTRS)

Nixon, D. D.

2001-01-01

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Contribution of the Recent AUSM Schemes to the Overflow Code: Implementation and Validation

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Buning, Pieter G.

2000-01-01

We shall present results of a recent collaborative effort between the authors attempting to implement the numerical flux scheme, AUSM+ and its new developments, into a widely used NASA code, OVERFLOW. This paper is intended to give a thorough and systematic documentation about the solutions of default test cases using the AUSNI+ scheme. Hence we will address various aspects of numerical solutions, such as accuracy, convergence rate, and effects of turbulence models, over a variety of geometries, speed regimes. We will briefly describe the numerical schemes employed in the calculations, including the capability of solving for low-speed flows and multiphase flows by employing the concept of numerical speed of sound. As a bonus, this low Mach number formulations also enhances convergence to steady solutions for flows even at transonic speed. Calculations for complex 3D turbulent flows were performed with several turbulence models and the results display excellent agreements with measured data.

Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

NASA Astrophysics Data System (ADS)

Kakhktsyan, V. M.; Khachatryan, A. Kh.

2013-07-01

A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy.

PubMed

Bergues Pupo, Ana E; Reyes, Juan Bory; Bergues Cabrales, Luis E; Bergues Cabrales, Jesús M

2011-09-24

Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

NASA Astrophysics Data System (ADS)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

2016-04-01

The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1991-01-01

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Transport of a decay chain in homogenous porous media: analytical solutions.

PubMed

Bauer, P; Attinger, S; Kinzelbach, W

2001-06-01

With the aid of integral transforms, analytical solutions for the transport of a decay chain in homogenous porous media are derived. Unidirectional steady-state flow and radial steady-state flow in single and multiple porosity media are considered. At least in Laplace domain, all solutions can be written in closed analytical formulae. Partly, the solutions can also be inverted analytically. If not, analytical calculation of the steady-state concentration distributions, evaluation of temporal moments and numerical inversion are still possible. Formulae for several simple boundary conditions are given and visualized in this paper. The derived novel solutions are widely applicable and are very useful for the validation of numerical transport codes.

Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

NASA Astrophysics Data System (ADS)

d'Aquino, M.; Capuano, F.; Coppola, G.; Serpico, C.; Mayergoyz, I. D.

2018-05-01

Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

Numerical algorithms based on Galerkin methods for the modeling of reactive interfaces in photoelectrochemical (PEC) solar cells

NASA Astrophysics Data System (ADS)

Harmon, Michael; Gamba, Irene M.; Ren, Kui

2016-12-01

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical (PEC) solar cells with reactive semiconductor and electrolyte interfaces. We present three numerical algorithms, mainly based on a mixed finite element and a local discontinuous Galerkin method for spatial discretization, with carefully chosen numerical fluxes, and implicit-explicit time stepping techniques, for solving the time-dependent nonlinear systems of partial differential equations. We perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model.

On the Possibilities of Predicting Geomagnetic Secular Variation with Geodynamo Modeling

NASA Technical Reports Server (NTRS)

Kuang, Wei-Jia; Tangborn, Andrew; Sabaka, Terrance

2004-01-01

We use our MoSST core dynamics model and geomagnetic field at the core-mantle boundary (CMB) continued downward from surface observations to investigate possibilities of geomagnetic data assimilation, so that model results and current geomagnetic observations can be used to predict geomagnetic secular variation in future. As the first attempt, we apply data insertion technique to examine evolution of the model solution that is modified by geomagnetic input. Our study demonstrate that, with a single data insertion, large-scale poloidal magnetic field obtained from subsequent numerical simulation evolves similarly to the observed geomagnetic variation, regardless of the initial choice of the model solution (so long it is a well developed numerical solution). The model solution diverges on the time scales on the order of 60 years, similar to the time scales of the torsional oscillations in the Earth's core. Our numerical test shows that geomagnetic data assimilation is promising with our MoSST model.

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

NASA Astrophysics Data System (ADS)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Numerical Tests and Properties of Waves in Radiating Fluids

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

Johnson, B M; Klein, R I

2009-09-03

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare themore » solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.« less

Numerical solution of the full potential equation using a chimera grid approach

NASA Technical Reports Server (NTRS)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Numerical Simulations of Laminar Air-Water Flow of a Non-linear Progressive Wave at Low Wind Speed

NASA Astrophysics Data System (ADS)

Wen, X.; Mobbs, S.

2014-03-01

A numerical simulation for two-dimensional laminar air-water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, , (the maximum orbital velocity of a water wave), and (the wave phase speed), are important in distinguishing different features of the flow patterns.

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective Lagrangian step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-Lagrangian-Collocation scheme resolves all mentioned numerical problems due to its adaptive nature and ability to control numerical errors in space and time. Proposed method solves advection in Lagrangian way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in Lagrangian methods. Finally, numerical tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.

Stochasticity in numerical solutions of the nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Shen, Mei-Mei; Nicholson, D. R.

1987-01-01

The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

Preliminary numerical analysis of improved gas chromatograph model

NASA Technical Reports Server (NTRS)

Woodrow, P. T.

1973-01-01

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

NASA Astrophysics Data System (ADS)

Antunes, Pedro R. S.; Ferreira, Rui A. C.

2017-07-01

In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented -RBF method. Several examples illustrate the good performance of the numerical method.

Calculation of double-lunar swingby trajectories: Part 2: Numerical solutions in the restricted problem of three bodies

NASA Technical Reports Server (NTRS)

Stalos, S.

1990-01-01

The double-lunar swingby trajectory is a method for maintaining alignment of an Earth satellite's line of apsides with the Sun-Earth line. From a Keplerian point of view, successive close encounters with the Moon cause discrete, instantaneous changes in the satellite's eccentricity and semimajor axis. Numerical solutions to the planar, restricted problem of three bodies as double-lunar swingby trajectories are identified. The method of solution is described and the results compared to the Keplerian formulation.

Real gas flow fields about three dimensional configurations

NASA Technical Reports Server (NTRS)

Balakrishnan, A.; Lombard, C. K.; Davy, W. C.

1983-01-01

Real gas, inviscid supersonic flow fields over a three-dimensional configuration are determined using a factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are presented for both real and ideal gases at three different Mach numbers and at two different altitudes. Selected results are illustrated by contour plots and are also tabulated for future reference. Results obtained compare well with existing tabulated numerical solutions and hence validate the solution technique.

Numerical analysis of soliton solutions of the modified Korteweg-de Vries-sine-Gordon equation

NASA Astrophysics Data System (ADS)

Popov, S. P.

2015-03-01

Multisoliton solutions of the modified Korteweg-de Vries-sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge-Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied.

Effects of Melt Convection and Solid Transport on Macrosegregation and Grain Structure in Equiaxed Al-Cu Alloys

NASA Technical Reports Server (NTRS)

Rerko, Rodney S.; deGroh, Henry C., III; Beckermann, Christoph

2000-01-01

Macrosegregation in metal casting can be caused by thermal and solutal melt convection, and the transport of unattached solid crystals resulting from nucleation in the bulk liquid or dendrite fragmentation. To develop a comprehensive numerical model for the casting of alloys, an experimental study has been conducted to generate benchmark data with which such a solidification model could be tested. The objectives were: (1) experimentally study the effects of solid transport and thermosolutal convection on macrosegregation and grain size; and (2) provide a complete set of boundary conditions temperature data, segregation data, and grain size data - to validate numerical models. Through the control of end cooling and side wall heating, radial temperature gradients in the sample and furnace were minimized. Thus the vertical crucible wall was adiabatic. Samples at room temperature were 24 cc and 95 mm long. The alloys used were Al-1 wt. pct. Cu, and Al- 10 wt. pct. Cu; the starting point for solidification was isothermal at 710 and 685 C respectively. To induce an equiaxed structure various amounts of the grain refiner TiB2 were added. Samples were either cooled from the top, or the bottom. Several trends in the data stand out. In attempting to model these experiments, concentrating on these trends or differences may be beneficial.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Hathwar, Raghuraj; Saraniti, Marco; Goodnick, Stephen M.

2016-07-01

We report on a new numerical approach for multi-band drift within the context of full band Monte Carlo (FBMC) simulation and apply this to Si and InAs nanowires. The approach is based on the solution of the Krieger and Iafrate (KI) equations [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)], which gives the probability of carriers undergoing interband transitions subject to an applied electric field. The KI equations are based on the solution of the time-dependent Schrödinger equation, and previous solutions of these equations have used Runge-Kutta (RK) methods to numerically solve the KI equations. This approach made the solution of the KI equations numerically expensive and was therefore only applied to a small part of the Brillouin zone (BZ). Here we discuss an alternate approach to the solution of the KI equations using the Magnus expansion (also known as "exponential perturbation theory"). This method is more accurate than the RK method as the solution lies on the exponential map and shares important qualitative properties with the exact solution such as the preservation of the unitary character of the time evolution operator. The solution of the KI equations is then incorporated through a modified FBMC free-flight drift routine and applied throughout the nanowire BZ. The importance of the multi-band drift model is then demonstrated for the case of Si and InAs nanowires by simulating a uniform field FBMC and analyzing the average carrier energies and carrier populations under high electric fields. Numerical simulations show that the average energy of the carriers under high electric field is significantly higher when multi-band drift is taken into consideration, due to the interband transitions allowing carriers to achieve higher energies.

Enviroplan—a summary methodology for comprehensive environmental planning and design

Treesearch

Robert Allen Jr.; George Nez; Fred Nicholson; Larry Sutphin

1979-01-01

This paper will discuss a comprehensive environmental assessment methodology that includes a numerical method for visual management and analysis. This methodology employs resource and human activity units as a means to produce a visual form unit which is the fundamental unit of the perceptual environment. The resource unit is based on the ecosystem as the fundamental...

Making Green Cleaning Easy for Local School Boards

ERIC Educational Resources Information Center

Ashkin, Stephen

2012-01-01

Ten or even five years ago, it would have been a major undertaking for a school district to convert to a comprehensive green cleaning program. At that time there was little precedence and no "roadmaps" for doing so. Thus schools faced numerous challenges that included: (1) what defined a green cleaning product; (2) should a comprehensive program…

Writing for Learning to Improve Students' Comprehension at the College Level

ERIC Educational Resources Information Center

Alharbi, Fahad

2015-01-01

This literature review will illustrate how writing could improve students' comprehension. Writing is one of the most important skills that students need to master for college level work. Therefore, students should be prepared with these skills before moving to the college level because they are required to write numerous papers that tend to be…

The Differential Relations between Verbal, Numerical and Spatial Working Memory Abilities and Children's Reading Comprehension

ERIC Educational Resources Information Center

Oakhill, Jane; Yuill, Nicola; Garnham, Alan

2011-01-01

Working memory predicts children's reading comprehension but it is not clear whether this relation is due to a modality-specific or general working memory. This study, which investigated the relations between children's reading skills and working memory (WM) abilities in 3 modalities, extends previous work by including measures of both reading…

Storybook Read-Alouds to Enhance Students' Comprehension Skills in ESL Classrooms: A Case Study

ERIC Educational Resources Information Center

Omar, Ainon; Saufi, Maizatulliza Mohd.

2015-01-01

The effectiveness of using storybooks during read-alouds to develop children's comprehension skills as well as in understanding the story has been widely studied. The reading aloud strategy has also been proven through numerous researches to be the most highly recommended activity for encouraging language and literacy. The study identified the…

The Effects of Think-Aloud in a Collaborative Environment to Improve Comprehension of L2 Texts

ERIC Educational Resources Information Center

Seng, Goh Hock

2007-01-01

Numerous studies have shown that thinking aloud while reading can be an effective instructional technique in helping students improve their reading comprehension. However, most of the studies that examined the effects of think-aloud involve subjects reading individually and carried out in isolation away from the classroom context. Recently,…

On singularities of capillary surfaces in the absence of gravity

DOE PAGES

Roytburd, V.

1983-01-01

We smore » tudy numerical solutions to the equation of capillary surfaces in trapezoidal domains in the absence of gravity when the boundary contact angle declines from 90 ° to some critical value. We also discuss a result on the behavior of solutions in more general domains that confirms numerical calculations.« less

Numerical Simulations of Multidimensional Flows in Presence of either Strong Shocks or Strong Gravitational Fields

NASA Astrophysics Data System (ADS)

Font, J. A.; Ibanez, J. M.; Marti, J. M.

1993-04-01

Some numerical solutions via local characteristic approach have been obtained describing multidimensional flows. These solutions have been used as tests of a two- dimensional code which extends some high-resolution shock-captunng methods, designed recently to solve nonlinear hyperbolic systems of conservation laws. K words: HYDRODYNAMICS - BLACK HOLE - RELATIVITY - SHOCK WAVES

Numerical Problems and Agent-Based Models for a Mass Transfer Course

ERIC Educational Resources Information Center

Murthi, Manohar; Shea, Lonnie D.; Snurr, Randall Q.

2009-01-01

Problems requiring numerical solutions of differential equations or the use of agent-based modeling are presented for use in a course on mass transfer. These problems were solved using the popular technical computing language MATLABTM. Students were introduced to MATLAB via a problem with an analytical solution. A more complex problem to which no…

Numerical modelling of the Black Sea eigen-oscillations on a curvilinear boundary fitted coordinate system

NASA Astrophysics Data System (ADS)

Koychev Demirov, Encho

1994-12-01

The paper presents a numerical solution of barotropic and two-layer eigen-oscillation problems for the Black Sea on a boundary fitted coordinate system. This solution is compared with model and empirical data obtained by other workers. Frequencies of the eigen-oscillations found by the numerical solution of spectral problem are compared with the data obtained by spectral analysis of the sea-level oscillations measured near the town of Achtopol and Cape Irakli in stormy sea on 17-21 February 1979. Extreme oscillations of the sea-level result from resonant amplifications of three eigenmodes of the Black Sea of 68.3 -1, 36.6 -1 and 27.3 -1 cycles h -1 frequency.

An analytically iterative method for solving problems of cosmic-ray modulation

NASA Astrophysics Data System (ADS)

Kolesnyk, Yuriy L.; Bobik, Pavol; Shakhov, Boris A.; Putis, Marian

2017-09-01

The development of an analytically iterative method for solving steady-state as well as unsteady-state problems of cosmic-ray (CR) modulation is proposed. Iterations for obtaining the solutions are constructed for the spherically symmetric form of the CR propagation equation. The main solution of the considered problem consists of the zero-order solution that is obtained during the initial iteration and amendments that may be obtained by subsequent iterations. The finding of the zero-order solution is based on the CR isotropy during propagation in the space, whereas the anisotropy is taken into account when finding the next amendments. To begin with, the method is applied to solve the problem of CR modulation where the diffusion coefficient κ and the solar wind speed u are constants with an Local Interstellar Spectra (LIS) spectrum. The solution obtained with two iterations was compared with an analytical solution and with numerical solutions. Finally, solutions that have only one iteration for two problems of CR modulation with u = constant and the same form of LIS spectrum were obtained and tested against numerical solutions. For the first problem, κ is proportional to the momentum of the particle p, so it has the form κ = k0η, where η =p/m_0c. For the second problem, the diffusion coefficient is given in the form κ = k0βη, where β =v/c is the particle speed relative to the speed of light. There was a good matching of the obtained solutions with the numerical solutions as well as with the analytical solution for the problem where κ = constant.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2002-01-01

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.

2005-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

An interative solution of an integral equation for radiative transfer by using variational technique

NASA Technical Reports Server (NTRS)

Yoshikawa, K. K.

1973-01-01

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone.

PubMed

Peng, Jie; He, Xiang; Ye, Hanming

2015-01-01

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution.

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.

Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone

PubMed Central

Peng, Jie; He, Xiang; Ye, Hanming

2015-01-01

The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD) is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution. PMID:26447973

IMC/RMC Network Professional Film Collection.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Special Education Instructional Materials Center.

The compilation is a comprehensive listing of films available from the centers in the Instructional Materials Centers/Regional Media Centers (IMC/RMC) Network. Each IMC/RMC location is given a numerical code in a preliminary listing. These numerical codes are used within the film listing, which is arranged alphabetically according to film titles,…

Cognitive correlates of performance in advanced mathematics.

PubMed

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

Time-periodic solutions of the Benjamin-Ono equation

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

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less

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

Spatiotemporal Airy Ince-Gaussian wave packets in strongly nonlocal nonlinear media.

PubMed

Peng, Xi; Zhuang, Jingli; Peng, Yulian; Li, DongDong; Zhang, Liping; Chen, Xingyu; Zhao, Fang; Deng, Dongmei

2018-03-08

The self-accelerating Airy Ince-Gaussian (AiIG) and Airy helical Ince-Gaussian (AihIG) wave packets in strongly nonlocal nonlinear media (SNNM) are obtained by solving the strongly nonlocal nonlinear Schrödinger equation. For the first time, the propagation properties of three dimensional localized AiIG and AihIG breathers and solitons in the SNNM are demonstrated, these spatiotemporal wave packets maintain the self-accelerating and approximately non-dispersion properties in temporal dimension, periodically oscillating (breather state) or steady (soliton state) in spatial dimension. In particular, their numerical experiments of spatial intensity distribution, numerical simulations of spatiotemporal distribution, as well as the transverse energy flow and the angular momentum in SNNM are presented. Typical examples of the obtained solutions are based on the ratio between the input power and the critical power, the ellipticity and the strong nonlocality parameter. The comparisons of analytical solutions with numerical simulations and numerical experiments of the AiIG and AihIG optical solitons show that the numerical results agree well with the analytical solutions in the case of strong nonlocality.

Methods in the study of discrete upper hybrid waves

NASA Astrophysics Data System (ADS)

Yoon, P. H.; Ye, S.; Labelle, J.; Weatherwax, A. T.; Menietti, J. D.

2007-11-01

Naturally occurring plasma waves characterized by fine frequency structure or discrete spectrum, detected by satellite, rocket-borne instruments, or ground-based receivers, can be interpreted as eigenmodes excited and trapped in field-aligned density structures. This paper overviews various theoretical methods to study such phenomena for a one-dimensional (1-D) density structure. Among the various methods are parabolic approximation, eikonal matching, eigenfunction matching, and full numerical solution based upon shooting method. Various approaches are compared against the full numerical solution. Among the analytic methods it is found that the eigenfunction matching technique best approximates the actual numerical solution. The analysis is further extended to 2-D geometry. A detailed comparative analysis between the eigenfunction matching and fully numerical methods is carried out for the 2-D case. Although in general the two methods compare favorably, significant differences are also found such that for application to actual observations it is prudent to employ the fully numerical method. Application of the methods developed in the present paper to actual geophysical problems will be given in a companion paper.

Numerical simulations of the flow with the prescribed displacement of the airfoil and comparison with experiment

NASA Astrophysics Data System (ADS)

Řidký, V.; Šidlof, P.; Vlček, V.

2013-04-01

The work is devoted to comparing measured data with the results of numerical simulations. As mathematical model was used mathematical model whitout turbulence for incompressible flow In the experiment was observed the behavior of designed NACA0015 airfoil in airflow. For the numerical solution was used OpenFOAM computational package, this is open-source software based on finite volume method. In the numerical solution is prescribed displacement of the airfoil, which corresponds to the experiment. The velocity at a point close to the airfoil surface is compared with the experimental data obtained from interferographic measurements of the velocity field. Numerical solution is computed on a 3D mesh composed of about 1 million ortogonal hexahedron elements. The time step is limited by the Courant number. Parallel computations are run on supercomputers of the CIV at Technical University in Prague (HAL and FOX) and on a computer cluster of the Faculty of Mechatronics of Liberec (HYDRA). Run time is fixed at five periods, the results from the fifth periods and average value for all periods are then be compared with experiment.

Efficient uncertainty quantification in fully-integrated surface and subsurface hydrologic simulations

NASA Astrophysics Data System (ADS)

Miller, K. L.; Berg, S. J.; Davison, J. H.; Sudicky, E. A.; Forsyth, P. A.

2018-01-01

Although high performance computers and advanced numerical methods have made the application of fully-integrated surface and subsurface flow and transport models such as HydroGeoSphere common place, run times for large complex basin models can still be on the order of days to weeks, thus, limiting the usefulness of traditional workhorse algorithms for uncertainty quantification (UQ) such as Latin Hypercube simulation (LHS) or Monte Carlo simulation (MCS), which generally require thousands of simulations to achieve an acceptable level of accuracy. In this paper we investigate non-intrusive polynomial chaos for uncertainty quantification, which in contrast to random sampling methods (e.g., LHS and MCS), represents a model response of interest as a weighted sum of polynomials over the random inputs. Once a chaos expansion has been constructed, approximating the mean, covariance, probability density function, cumulative distribution function, and other common statistics as well as local and global sensitivity measures is straightforward and computationally inexpensive, thus making PCE an attractive UQ method for hydrologic models with long run times. Our polynomial chaos implementation was validated through comparison with analytical solutions as well as solutions obtained via LHS for simple numerical problems. It was then used to quantify parametric uncertainty in a series of numerical problems with increasing complexity, including a two-dimensional fully-saturated, steady flow and transient transport problem with six uncertain parameters and one quantity of interest; a one-dimensional variably-saturated column test involving transient flow and transport, four uncertain parameters, and two quantities of interest at 101 spatial locations and five different times each (1010 total); and a three-dimensional fully-integrated surface and subsurface flow and transport problem for a small test catchment involving seven uncertain parameters and three quantities of interest at 241 different times each. Numerical experiments show that polynomial chaos is an effective and robust method for quantifying uncertainty in fully-integrated hydrologic simulations, which provides a rich set of features and is computationally efficient. Our approach has the potential for significant speedup over existing sampling based methods when the number of uncertain model parameters is modest ( ≤ 20). To our knowledge, this is the first implementation of the algorithm in a comprehensive, fully-integrated, physically-based three-dimensional hydrosystem model.

Comprehensive Numerical Simulation of Filling and Solidification of Steel Ingots

PubMed Central

Pola, Annalisa; Gelfi, Marcello; La Vecchia, Giovina Marina

2016-01-01

In this paper, a complete three-dimensional numerical model of mold filling and solidification of steel ingots is presented. The risk of powder entrapment and defects formation during filling is analyzed in detail, demonstrating the importance of using a comprehensive geometry, with trumpet and runner, compared to conventional simplified models. By using a case study, it was shown that the simplified model significantly underestimates the defects sources, reducing the utility of simulations in supporting mold and process design. An experimental test was also performed on an instrumented mold and the measurements were compared to the calculation results. The good agreement between calculation and trial allowed validating the simulation. PMID:28773890

The Use of a Multidimensional Measure of Dialysis Adequacy—Moving beyond Small Solute Kinetics

PubMed Central

Perl, Jeffrey; Dember, Laura M.; Bargman, Joanne M.; Browne, Teri; Charytan, David M.; Flythe, Jennifer E.; Hickson, LaTonya J.; Hung, Adriana M.; Jadoul, Michel; Lee, Timmy Chang; Meyer, Klemens B.; Moradi, Hamid; Shafi, Tariq; Teitelbaum, Isaac; Wong, Leslie P.

2017-01-01

Urea removal has become a key measure of the intensity of dialysis treatment for kidney failure. Small solute removal, exemplified by Kt/Vurea, has been broadly applied as a means to quantify the dose of thrice weekly hemodialysis. Yet, the reliance on small solute clearances alone as a measure of dialysis adequacy fails fully to quantify the intended clinical effects of dialysis therapy. This review aims to (1) understand the strengths and limitations of small solute kinetics as a surrogate marker of dialysis dose, and (2) present the prospect of a more comprehensive construct for dialysis dose, one that considers more broadly the goals of ESRD care to maximize both quality of life and survival. On behalf of the American Society of Nephrology Dialysis Advisory Group, we propose the need to ascertain the validity and utility of a multidimensional measure that moves beyond small solute kinetics alone to quantify optimal dialysis derived from both patient-reported and comprehensive clinical and dialysis-related measures. PMID:28314806

A Framework for Considering Comprehensibility in Modeling

PubMed Central

Gleicher, Michael

2016-01-01

Abstract Comprehensibility in modeling is the ability of stakeholders to understand relevant aspects of the modeling process. In this article, we provide a framework to help guide exploration of the space of comprehensibility challenges. We consider facets organized around key questions: Who is comprehending? Why are they trying to comprehend? Where in the process are they trying to comprehend? How can we help them comprehend? How do we measure their comprehension? With each facet we consider the broad range of options. We discuss why taking a broad view of comprehensibility in modeling is useful in identifying challenges and opportunities for solutions. PMID:27441712

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

Localized solutions of Lugiato-Lefever equations with focused pump.

PubMed

Cardoso, Wesley B; Salasnich, Luca; Malomed, Boris A

2017-12-04

Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too-in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump and loss. Then, a family of exact analytical solutions for spatially confined modes is produced for the pump focused in the form of a delta-function, with a nonlinear loss (two-photon absorption) added to the LL model. Numerical findings demonstrate that these exact solutions are stable, both dynamically and structurally (the latter means that stable numerical solutions close to the exact ones are found when a specific condition, necessary for the existence of the analytical solution, does not hold). In 2D, vast families of stable confined modes are produced by means of a variational approximation and full numerical simulations.

Transport of reacting solutes subject to a moving dissolution boundary: Numerical methods and solutions

USGS Publications Warehouse

Willis, Catherine; Rubin, Jacob

1987-01-01

A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters. Although the water flow rate does not explicitly appear in the equation for the velocity of the moving boundary, the speed of the boundary depends more on the flux rate than on the dispersion coefficient. The discontinuity in the gradient of the solute concentration profile at the boundary increases with convection and with the initial concentration of the mineral. Our implicit method is extended to allow participation of the solutes in complexation reactions as well as the precipitation-dissolution reaction. This extension is easily made and does not change the basic method.

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

You Don't Need Richards'... A New General 1-D Vadose Zone Solution Method that is Reliable

NASA Astrophysics Data System (ADS)

Ogden, F. L.; Lai, W.; Zhu, J.; Steinke, R. C.; Talbot, C. A.

2015-12-01

Hydrologic modelers and mathematicians have strived to improve 1-D Richards' equation (RE) solution reliability for predicting vadose zone fluxes. Despite advances in computing power and the numerical solution of partial differential equations since Richards first published the RE in 1931, the solution remains unreliable. That is to say that there is no guarantee that for a particular set of soil constitutive relations, moisture profile conditions, or forcing input that a numerical RE solver will converge to an answer. This risk of non-convergence renders prohibitive the use of RE solvers in hydrological models that need perhaps millions of infiltration solutions. In lieu of using unreliable numerical RE solutions, researchers have developed a wide array of approximate solutions that more-or-less mimic the behavior of the RE, with some notable deficiencies such as parameter insensitivity or divergence over time. The improved Talbot-Ogden (T-O) finite water-content scheme was shown by Ogden et al. (2015) to be an extremely good approximation of the 1-D RE solution, with a difference in cumulative infiltration of only 0.2 percent over an 8 month simulation comparing the improved T-O scheme with a RE numerical solver. The reason is that the newly-derived fundamental flow equation that underpins the improved T-O method is equivalent to the RE minus a term that is equal to the diffusive flux divided by the slope of the wetting front. Because the diffusive flux has zero mean, this term is not important in calculating the mean flux. The wetting front slope is near infinite (sharp) in coarser soils that produce more significant hydrological interactions between surface and ground waters, which also makes this missing term 1) disappear in the limit, and, 2) create stability challenges for the numerical solution of RE. The improved T-O method is a replacement for the 1-D RE in soils that can be simulated as homogeneous layers, where the user is willing to neglect the effects of soil water diffusivity. This presentation emphasizes the transformative nature of the improved T-O finite water-content solution, and highlights the benefits of the methods' reliability in high-resolution large watershed simulations in the high performance computing environment, and discusses coupling of the soil matrix and non-Darcian macropores.

Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields

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

Xu, Zhijie; Meakin, Paul

2013-10-01

An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5]more » for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.« less

Multicultural Environmental Education: Theory and Practice.

ERIC Educational Resources Information Center

Marouli, Christina

2002-01-01

Explains the importance of cross-cultural communication and gains special significance in the comprehension of environmental degradation and the identification of environmental solutions. Questions multicultural environmental education as a solution to the problems. (Contains 23 references.) (Author/YDS)

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Numerical simulation of the transonic flow past the blunted wedge in the diverging channel

NASA Astrophysics Data System (ADS)

Ryabinin, Anatoly

2018-05-01

Positions of shock waves in the 2D channel with a blunted wedge are studied numerically. Solutions of the Euler equations are obtained with finite-volume solver SU2 for 15 variants of channel geometry. Numerical simulations reveal a considerable hysteresis in the shock wave position versus the supersonic Mach number given at the inlet. In the certain range of inlet Mach number, there are asymmetrical solutions of the equations. Small change in the geometry of the channel leads to shift of boundaries of the hysteresis range.

Salt-water-freshwater transient upconing - An implicit boundary-element solution

USGS Publications Warehouse

Kemblowski, M.

1985-01-01

The boundary-element method is used to solve the set of partial differential equations describing the flow of salt water and fresh water separated by a sharp interface in the vertical plane. In order to improve the accuracy and stability of the numerical solution, a new implicit scheme was developed for calculating the motion of the interface. The performance of this scheme was tested by means of numerical simulation. The numerical results are compared to experimental results for a salt-water upconing under a drain problem. ?? 1985.

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution. [rocket nozzle and orbital plume flow fields

NASA Technical Reports Server (NTRS)

Smith, S. D.

1984-01-01

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

A multistage time-stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1985-01-01

A class of explicit multistage time-stepping schemes is used to construct an algorithm for solving the compressible Navier-Stokes equations. Flexibility in treating arbitrary geometries is obtained with a finite-volume formulation. Numerical efficiency is achieved by employing techniques for accelerating convergence to steady state. Computer processing is enhanced through vectorization of the algorithm. The scheme is evaluated by solving laminar and turbulent flows over a flat plate and an NACA 0012 airfoil. Numerical results are compared with theoretical solutions or other numerical solutions and/or experimental data.

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

USGS Publications Warehouse

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

Numerical Modelling of Foundation Slabs with use of Schur Complement Method

NASA Astrophysics Data System (ADS)

Koktan, Jiří; Brožovský, Jiří

2017-10-01

The paper discusses numerical modelling of foundation slabs with use of advanced numerical approaches, which are suitable for parallel processing. The solution is based on the Finite Element Method with the slab-type elements. The subsoil is modelled with use of Winklertype contact model (as an alternative a multi-parameter model can be used). The proposed modelling approach uses the Schur Complement method to speed-up the computations of the problem. The method is based on a special division of the analyzed model to several substructures. It adds some complexity to the numerical procedures, especially when subsoil models are used inside the finite element method solution. In other hand, this method makes possible a fast solution of large models but it introduces further problems to the process. Thus, the main aim of this paper is to verify that such method can be successfully used for this type of problem. The most suitable finite elements will be discussed, there will be also discussion related to finite element mesh and limitations of its construction for such problem. The core approaches of the implementation of the Schur Complement Method for this type of the problem will be also presented. The proposed approach was implemented in the form of a computer program, which will be also briefly introduced. There will be also presented results of example computations, which prove the speed-up of the solution - there will be shown important speed-up of solution even in the case of on-parallel processing and the ability of bypass size limitations of numerical models with use of the discussed approach.

Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

NASA Astrophysics Data System (ADS)

Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang

2018-03-01

This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

NASA Astrophysics Data System (ADS)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

New solutions for steady bubbles in a Hele-Shaw cell

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

Tanveer, S.

1987-03-01

Exact solutions are presented for steadily moving bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area, both the speed of the bubble and the distance of its centroid from the channel centerline remain arbitrary when surface tension is ignored. However, numerical evidence suggests that this twofold arbitrariness is removed by the effect of surface tension, i.e., for given bubble area and surface tension, solutions exist only when the bubble velocity and the centroid distance from the channel centerline attain one or more isolated values. From a limitedmore » numerical search, no nonsymmetric solutions could be found; however, a branch of symmetric bubble solutions that was not found in earlier work was found. This branch corresponds to one of the Romero-Vanden-Broeck branch of finger solutions when the bubble size is large. A new procedure for numerical calculations of bubble solutions in the presence of surface tension is presented and is found to work very well for reasonably large bubbles, unlike the previous method of Tanveer (Phys. Fluids 29, 3537 (1986)). The precise power law dependence of bubble velocity on surface tension for small surface tension is explored for bubbles of different area. Agreement is noted with recent analytical results for a finger.« less

Self-similar solutions to isothermal shock problems

NASA Astrophysics Data System (ADS)

Deschner, Stephan C.; Illenseer, Tobias F.; Duschl, Wolfgang J.

We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary differential equations. We test the numerical solutions against the analytical expressions to verify the correctness of all numerical algorithms. We use similarity methods to derive a system of ordinary differential equations (ODE) yielding exact solutions for power law density distributions as initial conditions. Further, the system of ODEs accounts for implosion problems (IP) as well as explosion problems (EP) by changing the initial or boundary conditions, respectively. Taking genuinely isothermal approximations into account leads to additional insights of EPs in contrast to earlier models. We neglect a constant initial energy contribution but introduce a parameter to adjust the initial mass distribution of the system. Moreover, we show that due to this parameter a constant initial density is not allowed for isothermal EPs. Reasonable restrictions for this parameter are given. Both, the (genuinely) isothermal implosion as well as the explosion problem are solved for the first time.

Numerical modeling of an alloy droplet deposition with non-equilibrium solidification

NASA Astrophysics Data System (ADS)

Ramanuj, Vimal

Droplet deposition is a process of extensive relevance to the microfabrication industry. Various bonding and film deposition methods utilize single or multiple droplet impingements on a substrate with subsequent splat formation through simultaneous spreading and solidification. Splat morphology and solidification characteristics play vital roles in determining the final outcome. Experimental methods have limited reach in studying such phenomena owing to the extremely small time and length scales involved. Fundamental understanding of the governing principles of fluid flow, heat transfer and phase change provide effective means of studying such processes through computational techniques. The present study aims at numerically modeling and analyzing the phenomenon of splat formation and phase change in an alloy droplet deposition process. Phase change in alloys occurs non-isothermally and its formulation poses mathematical challenges. A highly non-linear flow field in conjunction with multiple interfaces and convection-diffusion governed phase transition are some of the highlighting features involved in the numerical formulation. Moreover, the non-equilibrium solidification behavior in eutectic systems is of prime concern. The peculiar phenomenon requires special treatments in terms of modeling solid phase species diffusion, liquid phase enrichment during solute partitioning and isothermal eutectic transformation. The flow field is solved using a two-step projection algorithm coupled with enhanced interface modeling schemes. The free surface tracking and reconstruction is achieved through two approaches: VOF-PLIC and CLSVOF to achieve optimum interface accuracy with minimal computational resources. The energy equation is written in terms of enthalpy with an additional source term to account for the phase change. The solidification phenomenon is modeled using a coupled temperature-solute scheme that reflects the microscopic effects arising due to dendritic growth taking place in rapidly solidifying domains. Solid phase diffusion theories proposed in the literature are incorporated in the solute conservation equation through a back diffusion parameter till the eutectic composition; beyond which a special treatment is proposed. A simplified homogeneous mushy region model has also been outline. Both models are employed to reproduce analytical results under limiting conditions and also experimentally verified. The primary objective of the present work is to examine the splat morphology, solidification behavior and microstructural characteristics under varying operational parameters. A simplified homogeneous mushy region model is first applied to study the role of convection in an SS304 droplet deposition with substrate remelting. The results are compared with experimental findings reported in the literature and a good agreement is observed. Furthermore, a hypoeutectic Sn-Pb alloy droplet deposition is studied using a comprehensive coupled temperature solute model that accounts for the non-equilibrium solidification occurring in eutectic type of alloys. Particular focus is laid on the limitations of a homogeneous mushy region assumption, role of species composition in governing solidification, estimation of the microstructural properties and eutectic formation.

The Bean model in suprconductivity: Variational formulation and numerical solution

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

Prigozhin, L.

The Bean critical-state model describes the penetration of magnetic field into type-II superconductors. Mathematically, this is a free boundary problem and its solution is of interest in applied superconductivity. We derive a variational formulation for the Bean model and use it to solve two-dimensional and axially symmetric critical-state problems numerically. 25 refs., 9 figs., 1 tab.

Numerical prediction of three-dimensional juncture region flow using the parabolic Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.; Orzechowski, J. A.

1979-01-01

A numerical solution algorithm is established for prediction of subsonic turbulent three-dimensional flows in aerodynamic configuration juncture regions. A turbulence closure model is established using the complete Reynolds stress. Pressure coupling is accomplished using the concepts of complementary and particular solutions to a Poisson equation. Specifications for data input juncture geometry modification are presented.

Does the Acquisition of Mathematical Knowledge Make Students Better Problem Solvers? An Examination of Third Graders' Solutions of Division-with-Remainder (DWR) Problems.

ERIC Educational Resources Information Center

Guerrero, Lourdes; Rivera, Antonio

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 1. Formulation and Validation

NASA Astrophysics Data System (ADS)

Daniele, Vito G.; Lombardi, Guido; Zich, Rodolfo S.

2017-12-01

Complex scattering problems are often made by composite structures where wedges and penetrable substrates may interact at near field. In this paper (Part 1) together with its companion paper (Part 2) we study the canonical problem constituted of a Perfectly Electrically Conducting (PEC) wedge lying on a grounded dielectric slab with a comprehensive mathematical model based on the application of the Generalized Wiener-Hopf Technique (GWHT) with the help of equivalent circuital representations for linear homogenous regions (angular and layered regions). The proposed procedure is valid for the general case, and the papers focus on E-polarization. The solution is obtained using analytical and semianalytical approaches that reduce the Wiener-Hopf factorization to integral equations. Several numerical test cases validate the proposed method. The scope of Part 1 is to present the method and its validation applied to the problem. The companion paper Part 2 focuses on the properties of the solution, and it presents physical and engineering insights as Geometrical Theory of Diffraction (GTD)/Uniform Theory of Diffraction(UTD) coefficients, total far fields, modal fields, and excitation of surface and leaky waves for different kinds of source. The structure is of interest in antenna technologies and electromagnetic compatibility (tip on a substrate with guiding and antenna properties).

A 2D model of axial symmetry for proximal tubule of an average human nephron: indicative results of diffusion, convection and absorption processes

NASA Astrophysics Data System (ADS)

Insfrán, J. F.; Ubal, S.; Di Paolo, y. J.

2016-04-01

A simplified model of a proximal convoluted tubule of an average human nephron is presented. The model considers the 2D axisymmetric flow of the luminal solution exchanging matter with the tubule walls and the peritubular fluid by means of 0D models for the epithelial cells. The tubule radius is considered to vary along the conduit due to the trans-epithelial pressure difference. The fate of more than ten typical solutes is tracked down by the model. The Navier-Stokes and Reaction-Diffusion-Advection equations (considering the electro-neutrality principle) are solved in the lumen, giving a detailed picture of the velocity, pressure and concentration fields, along with trans-membrane fluxes and tubule deformation, via coupling with the 0D model for the tubule wall. The calculations are carried out numerically by means of the finite element method. The results obtained show good agreement with those published by other authors using models that ignore the diffusive transport and disregard a detailed calculation of velocity, pressure and concentrations. This work should be seen as a first approach towards the development of a more comprehensive model of the filtration process taking place in the kidneys, which ultimately helps in devising a device that can mimic/complement the renal function.

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

Numerical schemes for anomalous diffusion of single-phase fluids in porous media

NASA Astrophysics Data System (ADS)

Awotunde, Abeeb A.; Ghanam, Ryad A.; Al-Homidan, Suliman S.; Tatar, Nasser-eddine

2016-10-01

Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

Numerical considerations for Lagrangian stochastic dispersion models: Eliminating rogue trajectories, and the importance of numerical accuracy

USDA-ARS?s Scientific Manuscript database

When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...

Analytical and numerical solutions of the potential and electric field generated by different electrode arrays in a tumor tissue under electrotherapy

PubMed Central

2011-01-01

Background Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Methods Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Results Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. Conclusion The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections. PMID:21943385

Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A.

2014-03-01

A Jacobi-Gauss-Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge-Kutta method of fourth order, is proposed as a numerical algorithm for the approximation of solutions to nonlinear Schrödinger equations (NLSE) with initial-boundary data in 1+1 dimensions. Our procedure is implemented in two successive steps. In the first one, the J-GL-C is employed for approximating the functional dependence on the spatial variable, using (N-1) nodes of the Jacobi-Gauss-Lobatto interpolation which depends upon two general Jacobi parameters. The resulting equations together with the two-point boundary conditions induce a system of 2(N-1) first-order ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve this temporal system. The proposed J-GL-C method, used in combination with the implicit Runge-Kutta method of fourth order, is employed to obtain highly accurate numerical approximations to four types of NLSE, including the attractive and repulsive NLSE and a Gross-Pitaevskii equation with space-periodic potential. The numerical results obtained by this algorithm have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively few nodes used, the absolute error in our numerical solutions is sufficiently small.

Use of Green's functions in the numerical solution of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

Improved word comprehension in Global aphasia using a modified semantic feature analysis treatment.

PubMed

Munro, Philippa; Siyambalapitiya, Samantha

2017-01-01

Limited research has investigated treatment of single word comprehension in people with aphasia, despite numerous studies examining treatment of naming deficits. This study employed a single case experimental design to examine efficacy of a modified semantic feature analysis (SFA) therapy in improving word comprehension in an individual with Global aphasia, who presented with a semantically based comprehension impairment. Ten treatment sessions were conducted over a period of two weeks. Following therapy, the participant demonstrated improved comprehension of treatment items and generalisation to control items, measured by performance on a spoken word picture matching task. Improvements were also observed on other language assessments (e.g. subtests of WAB-R; PALPA subtest 47) and were largely maintained over a period of 12 weeks without further therapy. This study provides support for the efficacy of a modified SFA therapy in remediating single word comprehension in individuals with aphasia with a semantically based comprehension deficit.

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

NASA Astrophysics Data System (ADS)

Nguyen, S. T.; Vu, M.-H.; Vu, M. N.; Tang, A. M.

2017-05-01

The present work aims to modeling the thermal conductivity of fractured materials using homogenization-based analytical and pattern-based numerical methods. These materials are considered as a network of cracks distributed inside a solid matrix. Heat flow through such media is perturbed by the crack system. The problem of heat flow across a single crack is firstly investigated. The classical Eshelby's solution, extended to the thermal conduction problem of an ellipsoidal inclusion embedding in an infinite homogeneous matrix, gives an analytical solution of temperature discontinuity across a non-conducting penny-shaped crack. This solution is then validated by the numerical simulation based on the finite elements method. The numerical simulation allows analyzing the effect of crack conductivity. The problem of a single crack is then extended to a medium containing multiple cracks. Analytical estimations for effective thermal conductivity, that take into account the interaction between cracks and their spatial distribution, are developed for the case of non-conducting cracks. Pattern-based numerical method is then employed for both cases non-conducting and conducting cracks. In the case of non-conducting cracks, numerical and analytical methods, both account for the spatial distribution of the cracks, fit perfectly. In the case of conducting cracks, the numerical analyzing of crack conductivity effect shows that highly conducting cracks weakly affect heat flow and the effective thermal conductivity of fractured media.

The origin of spurious solutions in computational electromagnetics

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Wu, Jie; Povinelli, L. A.

1995-01-01

The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

A Study on Water Surface Profiles of Rivers with Constriction

NASA Astrophysics Data System (ADS)

Qian, Chaochao; Yamada, Tadashi

2013-04-01

Water surface profile of rivers with constrictions is precious in both classic hydraulics and river management practice. This study was conducted to clarify the essences of the water surface profiles. 3 cases of experiments and 1D numerical calculations with different discharges were made in the study and analysis solutions of the non-linear basic equation of surface profile in varied flow without considering friction were derived. The manning's number was kept in the same in each case by using crosspiece roughness. We found a new type of water surface profile of varied flow from the results of 1D numerical calculation and that of experiments and named it as Mc curve because of its mild condition with constriction segment. This kind of curves appears as a nature phenomenon ubiquitously. The process of water surface forming is dynamic and bore occurs at the upper side of constriction during increasing discharge before the surface profile formed. As a theoretical work, 3 analysis solutions were derived included 2 physical-meaning solutions in the study by using Man-Machine system. One of the derived physical-meaning solutions was confirmed that it is validity by comparing to the results of 1D numerical calculation and that of experiments. The solution represents a flow profile from under critical condition at the upper side to super critical condition at the down side of constriction segment. The other derived physical-meaning solution represents a flow profile from super critical condition at the upper side to under critical condition at the down side of constriction segment. These two kinds of flow profiles exist in the nature but no theoretical solution can express the phenomenon. We find the depth distribution only concerned with unit width discharge distribution and critical depth under a constant discharge from the derived solutions. Therefor, the profile can be gained simply and precisely by using the theoretical solutions instead of numerical calculation even in practice.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

PubMed

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

NASA Astrophysics Data System (ADS)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Computer simulation of solutions of polyharmonic equations in plane domain

NASA Astrophysics Data System (ADS)

Kazakova, A. O.

2018-05-01

A systematic study of plane problems of the theory of polyharmonic functions is presented. A method of reducing boundary problems for polyharmonic functions to the system of integral equations on the boundary of the domain is given and a numerical algorithm for simulation of solutions of this system is suggested. Particular attention is paid to the numerical solution of the main tasks when the values of the function and its derivatives are given. Test examples are considered that confirm the effectiveness and accuracy of the suggested algorithm.

Stability of sequences generated by nonlinear differential systems. [for analysis of glider jet aircraft motion

NASA Technical Reports Server (NTRS)

Brown, R. L.

1979-01-01

A local stability analysis is presented for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. It is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and the one-leg k-step numerical solution can be approximated. Attention is given to the example of the two-dimensional problem involving the stability of the longitudinal equations of motion of a gliding jet aircraft.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

On the road to a stronger public health workforce: visual tools to address complex challenges.

PubMed

Drehobl, Patricia; Stover, Beth H; Koo, Denise

2014-11-01

The public health workforce is vital to protecting the health and safety of the public, yet for years, state and local governmental public health agencies have reported substantial workforce losses and other challenges to the workforce that threaten the public's health. These challenges are complex, often involve multiple influencing or related causal factors, and demand comprehensive solutions. However, proposed solutions often focus on selected factors and might be fragmented rather than comprehensive. This paper describes approaches to characterizing the situation more comprehensively and includes two visual tools: (1) a fishbone, or Ishikawa, diagram that depicts multiple factors affecting the public health workforce; and (2) a roadmap that displays key elements-goals and strategies-to strengthen the public health workforce, thus moving from the problems depicted in the fishbone toward solutions. The visual tools aid thinking about ways to strengthen the public health workforce through collective solutions and to help leverage resources and build on each other's work. The strategic roadmap is intended to serve as a dynamic tool for partnership, prioritization, and gap assessment. These tools reflect and support CDC's commitment to working with partners on the highest priorities for strengthening the workforce to improve the public's health. Published by Elsevier Inc.

Photon and neutron interrogation techniques for chemical explosives detection in air cargo: A critical review

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

Runkle, Robert C.; White, Timothy A.; Miller, Erin A.

Scanning cargo transported via aircraft ("air cargo") for explosive threats is a problem that, at present, lacks a comprehensive technical solution. While explosives detection in the baggage-scanning domain has a rich history that sheds light on potential solutions for air cargo, baggage scanning differs in several ways and thus one cannot look to the present array of technologies. Some contemporary solutions, like trace analysis, are not readily applied to cargo due to sampling challenges while the larger geometry of air cargo makes others less effective. This review article examines an array of interrogation techniques using photons and neutrons as incidentmore » particles. We first present a summary of the signatures and observables explosives provide and review how they have been exploited in baggage scanning. Following this is a description of the challenges posed by the air cargo application space. After considering interrogation sources, methods focused on transmission imaging, sub-surface examination and elemental characterization are described. It is our goal to shed light on the technical promise of each method while largely deferring questions that revolve around footprint, safety and conduct of operations. Our overarching intent is that a comprehensive understanding of potential techniques will foster development of a comprehensive solution.« less

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

Khan, Masood; Malik, Rabia, E-mail: rabiamalik.qau@gmail.com; Department of Mathematics and Statistics, International Islamic University Islamabad 44000

In the present paper, we endeavor to perform a numerical analysis in connection with the nonlinear radiative stagnation-point flow and heat transfer to Sisko fluid past a stretching cylinder in the presence of convective boundary conditions. The influence of thermal radiation using nonlinear Rosseland approximation is explored. The numerical solutions of transformed governing equations are calculated through forth order Runge-Kutta method using shooting technique. With the help of graphs and tables, the influence of non-dimensional parameters on velocity and temperature along with the local skin friction and Nusselt number is discussed. The results reveal that the temperature increases however, heatmore » transfer from the surface of cylinder decreases with the increasing values of thermal radiation and temperature ratio parameters. Moreover, the authenticity of numerical solutions is validated by finding their good agreement with the HAM solutions.« less

Sensitivity of inelastic response to numerical integration of strain energy. [for cantilever beam

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1976-01-01

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

NASA Astrophysics Data System (ADS)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

RELAP-7 Software Verification and Validation Plan: Requirements Traceability Matrix (RTM) Part 1 – Physics and numerical methods

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

Choi, Yong Joon; Yoo, Jun Soo; Smith, Curtis Lee

2015-09-01

This INL plan comprehensively describes the Requirements Traceability Matrix (RTM) on main physics and numerical method of the RELAP-7. The plan also describes the testing-based software verification and validation (SV&V) process—a set of specially designed software models used to test RELAP-7.

Cognitive Skills Used to Solve Mathematical Word Problems and Numerical Operations: A Study of 6- to 7-Year-Old Children

ERIC Educational Resources Information Center

Bjork, Isabel Maria; Bowyer-Crane, Claudine

2013-01-01

This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

A comparison of solute-transport solution techniques based on inverse modelling results

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2000-01-01

Five common numerical techniques (finite difference, predictor-corrector, total-variation-diminishing, method-of-characteristics, and modified-method-of-characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using randomly distributed homogeneous blocks of five sand types. This experimental model provides an outstanding opportunity to compare the solution techniques because of the heterogeneous hydraulic conductivity distribution of known structure, and the availability of detailed measurements with which to compare simulated concentrations. The present work uses this opportunity to investigate how three common types of results-simulated breakthrough curves, sensitivity analysis, and calibrated parameter values-change in this heterogeneous situation, given the different methods of simulating solute transport. The results show that simulated peak concentrations, even at very fine grid spacings, varied because of different amounts of numerical dispersion. Sensitivity analysis results were robust in that they were independent of the solution technique. They revealed extreme correlation between hydraulic conductivity and porosity, and that the breakthrough curve data did not provide enough information about the dispersivities to estimate individual values for the five sands. However, estimated hydraulic conductivity values are significantly influenced by both the large possible variations in model dispersion and the amount of numerical dispersion present in the solution technique.Five common numerical techniques (finite difference, predictor-corrector, total-variation-diminishing, method-of-characteristics, and modified-method-of-characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using randomly distributed homogeneous blocks of five sand types. This experimental model provides an outstanding opportunity to compare the solution techniques because of the heterogeneous hydraulic conductivity distribution of known structure, and the availability of detailed measurements with which to compare simulated concentrations. The present work uses this opportunity to investigate how three common types of results - simulated breakthrough curves, sensitivity analysis, and calibrated parameter values - change in this heterogeneous situation, given the different methods of simulating solute transport. The results show that simulated peak concentrations, even at very fine grid spacings, varied because of different amounts of numerical dispersion. Sensitivity analysis results were robust in that they were independent of the solution technique. They revealed extreme correlation between hydraulic conductivity and porosity, and that the breakthrough curve data did not provide enough information about the dispersivities to estimate individual values for the five sands. However, estimated hydraulic conductivity values are significantly influenced by both the large possible variations in model dispersion and the amount of numerical dispersion present in the solution technique.

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage.

PubMed

Stuebner, Michael; Haider, Mansoor A

2010-06-18

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Tidally induced residual current over the Malin Sea continental slope

NASA Astrophysics Data System (ADS)

Stashchuk, Nataliya; Vlasenko, Vasiliy; Hosegood, Phil; Nimmo-Smith, W. Alex M.

2017-05-01

Tidally induced residual currents generated over shelf-slope topography are investigated analytically and numerically using the Massachusetts Institute of Technology general circulation model. Observational support for the presence of such a slope current was recorded over the Malin Sea continental slope during the 88-th cruise of the RRS ;James Cook; in July 2013. A simple analytical formula developed here in the framework of time-averaged shallow water equations has been validated against a fully nonlinear nonhydrostatic numerical solution. A good agreement between analytical and numerical solutions is found for a wide range of input parameters of the tidal flow and bottom topography. In application to the Malin Shelf area both the numerical model and analytical solution predicted a northward moving current confined to the slope with its core located above the 400 m isobath and with vertically averaged maximum velocities up to 8 cm s-1, which is consistent with the in-situ data recorded at three moorings and along cross-slope transects.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.

PubMed

Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S

2014-09-01

A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

A Comprehensive Investigation of Copper Pitting Corrosion in a Drinking Water Distribution System

EPA Science Inventory

Copper pipe pitting is a complicated corrosion process for which exact causes and solutions are uncertain. This paper presents the findings of a comprehensive investigation of a cold water copper pitting corrosion problem in a drinking water distribution system, including a refi...

Classroom Disruption in English Comprehensive Schools.

ERIC Educational Resources Information Center

Dierenfield, Richard B.

A comparative study was made of disruptive behavior in British comprehensive schools and American high schools. A survey was conducted in 41 British schools to obtain the opinions of teachers and administrators on severe discipline problems, causes of disruptive behavior, and possible solutions. There was general agreement that classroom…

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

NASA Astrophysics Data System (ADS)

Xu, Shigang; Liu, Yang

2018-03-01

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

Numerical solution of fractured horizontal wells in shale gas reservoirs considering multiple transport mechanisms

NASA Astrophysics Data System (ADS)

Zhao, Yu-long; Tang, Xu-chuan; Zhang, Lie-hui; Tang, Hong-ming; Tao, Zheng-Wu

2018-06-01

The multiscale pore size and specific gas storage mechanism in organic-rich shale gas reservoirs make gas transport in such reservoirs complicated. Therefore, a model that fully incorporates all transport mechanisms and employs an accurate numerical method is urgently needed to simulate the gas production process. In this paper, a unified model of apparent permeability was first developed, which took into account multiple influential factors including slip flow, Knudsen diffusion (KD), surface diffusion, effects of the adsorbed layer, permeability stress sensitivity, and ad-/desorption phenomena. Subsequently, a comprehensive mathematical model, which included the model of apparent permeability, was derived to describe gas production behaviors. Thereafter, on the basis of unstructured perpendicular bisection grids and finite volume method, a fully implicit numerical simulator was developed using Matlab software. The validation and application of the new model were confirmed using a field case reported in the literature. Finally, the impacts of related influencing factors on gas production were analyzed. The results showed that KD resulted in a negligible impact on gas production in the proposed model. The smaller the pore size was, the more obvious the effects of the adsorbed layer on the well production rate would be. Permeability stress sensitivity had a slight effect on well cumulative production in shale gas reservoirs. Adsorbed gas made a major contribution to the later flow period of the well; the greater the adsorbed gas content, the greater the well production rate would be. This paper can improve the understanding of gas production in shale gas reservoirs for petroleum engineers.

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

Rupture dynamics along bimaterial interfaces: a parametric study of the coupling between interfacial sliding and normal traction perturbation

NASA Astrophysics Data System (ADS)

Scala, Antonio; Festa, Gaetano; Vilotte, Jean-Pierre

2017-04-01

Earthquake ruptures often develop along faults separating materials with dissimilar elastic properties. Due to the broken symmetry, the propagation of the rupture along the bimaterial interface is driven by the coupling between interfacial sliding and normal traction perturbations. We numerically investigate in-plane rupture growth along a planar interface, under slip weakening friction, separating two dissimilar isotropic linearly elastic half-spaces. We perform a parametric study of the classical Prakash-Clifton regularisation for different material contrasts. In particular mesh-dependence and regularisation-dependence of the numerical solutions are analysed in this parameter space. When regularisation involves a slip-rate dependent relaxation time, a characteristic sliding distance is identified below which numerical solutions no longer depend on the regularisation parameter, i.e. they are consistent solutions of the same physical problem. Such regularisation provides an adaptive high-frequency filter of the slip-induced normal traction perturbations, following the dynamic shrinking of the dissipation zone during the acceleration phase. In contrast, regularisation involving a constant relaxation time leads to numerical solutions that always depend on the regularisation parameter since it fails adapting to the shrinking of the process zone. Dynamic regularisation is further investigated using a non-local regularisation based on a relaxation time that depends on the dynamic length of the dissipation zone. Such reformulation is shown to provide similar results as the dynamic time scale regularisation proposed by Prakash-Clifton when slip rate is replaced by the maximum slip rate along the sliding interface. This leads to the identification of a dissipative length scale associated with the coupling between interfacial sliding and normal traction perturbations, together with a scaling law between the maximum slip rate and the dynamic size of the process zone during the rupture propagation. Dynamic time scale regularisation is show to provide mesh-independent and physically well-posed numerical solutions during the acceleration phase toward an asymptotic speed. When generalised Rayleigh wave does not exist, numerical solutions are shown to tend toward an asymptotic velocity higher than the slowest shear wave speed. When generalised Rayleigh wave speed exists, as numerical solutions tend toward this velocity, increasing spurious oscillations develop and solutions become unstable. In this regime regularisation dependent and unstable finite-size pulses may be generated. This instability is associated with the singular behaviour of the slip-induced normal traction perturbations, and of the slip rate at the rupture front, in relation with complete shrinking of the dissipation zone. This phase requires to be modelled either by more complex interface constitutive laws involving velocity-strengthening effects that may stabilize short wavelength interfacial propagating modes or by considering non-ideal interfaces that introduce a new length scale in the problem that may promote selection and stabilization of the slip pulses.

Global Properties of Fully Convective Accretion Disks from Local Simulations

NASA Astrophysics Data System (ADS)

Bodo, G.; Cattaneo, F.; Mignone, A.; Ponzo, F.; Rossi, P.

2015-08-01

We present an approach to deriving global properties of accretion disks from the knowledge of local solutions derived from numerical simulations based on the shearing box approximation. The approach consists of a two-step procedure. First, a local solution valid for all values of the disk height is constructed by piecing together an interior solution obtained numerically with an analytical exterior radiative solution. The matching is obtained by assuming hydrostatic balance and radiative equilibrium. Although in principle the procedure can be carried out in general, it simplifies considerably when the interior solution is fully convective. In these cases, the construction is analogous to the derivation of the Hayashi tracks for protostars. The second step consists of piecing together the local solutions at different radii to obtain a global solution. Here we use the symmetry of the solutions with respect to the defining dimensionless numbers—in a way similar to the use of homology relations in stellar structure theory—to obtain the scaling properties of the various disk quantities with radius.

An analytical-numerical approach for parameter determination of a five-parameter single-diode model of photovoltaic cells and modules

NASA Astrophysics Data System (ADS)

Hejri, Mohammad; Mokhtari, Hossein; Azizian, Mohammad Reza; Söder, Lennart

2016-04-01

Parameter extraction of the five-parameter single-diode model of solar cells and modules from experimental data is a challenging problem. These parameters are evaluated from a set of nonlinear equations that cannot be solved analytically. On the other hand, a numerical solution of such equations needs a suitable initial guess to converge to a solution. This paper presents a new set of approximate analytical solutions for the parameters of a five-parameter single-diode model of photovoltaic (PV) cells and modules. The proposed solutions provide a good initial point which guarantees numerical analysis convergence. The proposed technique needs only a few data from the PV current-voltage characteristics, i.e. open circuit voltage Voc, short circuit current Isc and maximum power point current and voltage Im; Vm making it a fast and low cost parameter determination technique. The accuracy of the presented theoretical I-V curves is verified by experimental data.

A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations

NASA Astrophysics Data System (ADS)

Marras, Simone; Kopera, Michal A.; Constantinescu, Emil M.; Suckale, Jenny; Giraldo, Francis X.

2018-04-01

The high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. When applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme which, however, we do not address in this paper.

Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner

NASA Technical Reports Server (NTRS)

Carter, J. E.

1972-01-01

Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

A numerical study of the steady scalar convective diffusion equation for small viscosity

NASA Technical Reports Server (NTRS)

Giles, M. B.; Rose, M. E.

1983-01-01

A time-independent convection diffusion equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

A new theoretical basis for numerical simulations of nonlinear acoustic fields

NASA Astrophysics Data System (ADS)

Wójcik, Janusz

2000-07-01

Nonlinear acoustic equations can be considerably simplified. The presented model retains the accuracy of a more complex description of nonlinearity and a uniform description of near and far fields (in contrast to the KZK equation). A method has been presented for obtaining solutions of Kuznetsov's equation from the solutions of the model under consideration. Results of numerical calculations, including comparative ones, are presented.

A PLUG-AND-PLAY ARCHITECTURE FOR PROBABILISTIC PROGRAMMING

DTIC Science & Technology

2017-04-01

programs that use discrete numerical distributions, but even then, the space of possible outcomes may be uncountable (as a solution can be infinite...also identify conditions guaranteeing that all possible outcomes are finite (and then the probability space is discrete ). 2.2.2 The PlogiQL...and not determined at runtime. Nevertheless, the PRAiSE team plans to extend their solution to support numerical (continuous or discrete

Some Boussinesq Equations with Saturation

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

Christou, M. A.

2010-11-25

We investigate numerically some Boussinesq type equations with square or cubic and saturated nonlinearity. We examine the propagation, interaction and overtake interaction of soliton solutions. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the square or cubic nonlinearity without saturation. We calculate numerically the phase shift experienced by the solitons upon collision and conclude the impact of saturation.

Entropy-Based Approach To Nonlinear Stability

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1991-01-01

NASA technical memorandum suggests schemes for numerical solution of differential equations of flow made more accurate and robust by invoking second law of thermodynamics. Proposes instead of using artificial viscosity to suppress such unphysical solutions as spurious numerical oscillations and nonlinear instabilities, one should formulate equations so that rate of production of entropy within each cell of computational grid be nonnegative, as required by second law.

Application of artificial intelligence to impulsive orbital transfers

NASA Technical Reports Server (NTRS)

Burns, Rowland E.

1987-01-01

A generalized technique for the numerical solution of any given class of problems is presented. The technique requires the analytic (or numerical) solution of every applicable equation for all variables that appear in the problem. Conditional blocks are employed to rapidly expand the set of known variables from a minimum of input. The method is illustrated via the use of the Hohmann transfer problem from orbital mechanics.

An approach of traffic signal control based on NLRSQP algorithm

NASA Astrophysics Data System (ADS)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

Solidification of a binary alloy: Finite-element, single-domain simulation and new benchmark solutions

NASA Astrophysics Data System (ADS)

Le Bars, Michael; Worster, M. Grae

2006-07-01

A finite-element simulation of binary alloy solidification based on a single-domain formulation is presented and tested. Resolution of phase change is first checked by comparison with the analytical results of Worster [M.G. Worster, Solidification of an alloy from a cooled boundary, J. Fluid Mech. 167 (1986) 481-501] for purely diffusive solidification. Fluid dynamical processes without phase change are then tested by comparison with previous numerical studies of thermal convection in a pure fluid [G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer. Meth. Fluids 3 (1983) 249-264; D.A. Mayne, A.S. Usmani, M. Crapper, h-adaptive finite element solution of high Rayleigh number thermally driven cavity problem, Int. J. Numer. Meth. Heat Fluid Flow 10 (2000) 598-615; D.C. Wan, B.S.V. Patnaik, G.W. Wei, A new benchmark quality solution for the buoyancy driven cavity by discrete singular convolution, Numer. Heat Transf. 40 (2001) 199-228], in a porous medium with a constant porosity [G. Lauriat, V. Prasad, Non-darcian effects on natural convection in a vertical porous enclosure, Int. J. Heat Mass Transf. 32 (1989) 2135-2148; P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in an enclosure filled with fluid saturated variable porosity medium, Int. J. Heat Mass Transf. 40 (1997) 3955-3967] and in a mixed liquid-porous medium with a spatially variable porosity [P. Nithiarasu, K.N. Seetharamu, T. Sundararajan, Natural convective heat transfer in an enclosure filled with fluid saturated variable porosity medium, Int. J. Heat Mass Transf. 40 (1997) 3955-3967; N. Zabaras, D. Samanta, A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes, Int. J. Numer. Meth. Eng. 60 (2004) 1103-1138]. Finally, new benchmark solutions for simultaneous flow through both fluid and porous domains and for convective solidification processes are presented, based on the similarity solutions in corner-flow geometries recently obtained by Le Bars and Worster [M. Le Bars, M.G. Worster, Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification, J. Fluid Mech. (in press)]. Good agreement is found for all tests, hence validating our physical and numerical methods. More generally, the computations presented here could now be considered as standard and reliable analytical benchmarks for numerical simulations, specifically and independently testing the different processes underlying binary alloy solidification.

Numerical methods in heat transfer

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

Lewis, R.W.

1985-01-01

This third volume in the series in Numerical Methods in Engineering presents expanded versions of selected papers given at the Conference on Numerical Methods in Thermal Problems held in Venice in July 1981. In this reference work, contributors offer the current state of knowledge on the numerical solution of convective heat transfer problems and conduction heat transfer problems.

Development of Comprehensive State Dissemination Plans: An Overview of Present Status.

ERIC Educational Resources Information Center

Haenn, Joseph F.

Established by NIE in June 1975, the State Dissemination Grants Program provides resources to state education agencies to develop comprehensive and generalized dissemination capacity, which is defined as the leadership and service capability to provide information and technical assistance in the solution of problems identified by the dissemination…

A Comprehensive General Chemistry Demonstration

ERIC Educational Resources Information Center

Sweeder, Ryan D.; Jeffery, Kathleen A.

2013-01-01

This article describes the use of a comprehensive demonstration suitable for a high school or first-year undergraduate introductory chemistry class. The demonstration involves placing a burning candle in a container adjacent to a beaker containing a basic solution with indicator. After adding a lid, the candle will extinguish and the produced…

Linguistic Features of Middle School Environmental Education Texts.

ERIC Educational Resources Information Center

Chenhansa, Suporn; Schleppegrell, Mary

1998-01-01

The language used in environmental education texts has linguistic features that affect students' comprehension of concepts and their ability to envision solutions to environmental problems. Findings indicate that features of texts such as abstract nouns and lack of explicit agents impede students' full comprehension of complex issues and obscure…

The Function of Frame in the Comprehension of Scientific Text.

ERIC Educational Resources Information Center

Rossi, Jean Pierre

1990-01-01

One hundred French children in grade five participated in an experiment to determine how the problem frame facilitates comprehension of a problem solution text. Results demonstrate the positive role of frames in macrostructure construction and support the model of T. A. van Dijk and W. Kintsch (1983). (SLD)

A modal approach based on perfectly matched layers for the forced response of elastic open waveguides

NASA Astrophysics Data System (ADS)

Gallezot, M.; Treyssède, F.; Laguerre, L.

2018-03-01

This paper investigates the computation of the forced response of elastic open waveguides with a numerical modal approach based on perfectly matched layers (PML). With a PML of infinite thickness, the solution can theoretically be expanded as a discrete sum of trapped modes, a discrete sum of leaky modes and a continuous sum of radiation modes related to the PML branch cuts. Yet with numerical methods (e.g. finite elements), the waveguide cross-section is discretized and the PML must be truncated to a finite thickness. This truncation transforms the continuous sum into a discrete set of PML modes. To guarantee the uniqueness of the numerical solution of the forced response problem, an orthogonality relationship is proposed. This relationship is applicable to any type of modes (trapped, leaky and PML modes) and hence allows the numerical solution to be expanded on a discrete sum in a convenient manner. This also leads to an expression for the modal excitability valid for leaky modes. The physical relevance of each type of mode for the solution is clarified through two numerical test cases, a homogeneous medium and a circular bar waveguide example, excited by a point source. The former is favourably compared to a transient analytical solution, showing that PML modes reassemble the bulk wave contribution in a homogeneous medium. The latter shows that the PML mode contribution yields the long-term diffraction phenomenon whereas the leaky mode contribution prevails closer to the source. The leaky mode contribution is shown to remain accurate even with a relatively small PML thickness, hence reducing the computational cost. This is of particular interest for solving three-dimensional waveguide problems, involving two-dimensional cross-sections of arbitrary shapes. Such a problem is handled in a third numerical example by considering a buried square bar.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

New vibro-acoustic paradigms in biological tissues with application to diagnosis of pulmonary disorders

NASA Astrophysics Data System (ADS)

Zhang, Xiangling

The fundamental objective of the present study is to improve our understanding of audible sound propagation in the pulmonary system and torso. A related applied objective is to assess the feasibility of using audible acoustics for diagnosis of specific pulmonary conditions, such as pneumothorax (PTX). To accomplish these objectives, this study includes theoretical, computational and experimental developments aimed at: (1) better identifying the mechanical dynamic properties of soft biological tissues found in the torso region, (2) investigating the mechanisms of sound attenuation that occur when a PTX is present using greatly simplified theoretical and computational models, and (3) exploring the feasibility and utility of more comprehensive and precise computational finite element models of audible sound propagation in the pulmonary system and torso that would aid in related diagnostic developments. Mechanical material properties of soft biological tissue are studied for the low audible frequency range. The sensitivity to shear viscoelastic material constants of theoretical solutions for radiation impedance and surface wave motion are compared. Theoretical solutions are also compared to experimental measurements and numerical results from finite element analysis. It is found that, while prior theoretical solutions for radiation impedance are accurate, use of such measurements to estimate shear viscoelastic constants is not as precise as the use of surface wave measurements. The feasibility of using audible sound for diagnosis of pneumothorax is studied. Simplified one- and two-dimensional theoretical and numerical models of sound transmission through the pulmonary system and chest region to the chest wall surface are developed to more clearly understand the mechanism of energy loss when a pneumothorax is present, relative to a baseline case. A canine study on which these models are based predicts significant decreases in acoustic transmission strength when a pneumothorax is presented, in qualitative agreement with experimental measurements in dogs. Finally, the feasibility of building three-dimensional computational models is studied based on CT images of human subject or combination of the Horsfield airway model with geometry of other parts approximate from medical illustration. Preliminary results from these models show the same trend of acoustic energy loss when a PTX is present.

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Numerical Algorithms Based on Biorthogonal Wavelets

NASA Technical Reports Server (NTRS)

Ponenti, Pj.; Liandrat, J.

1996-01-01

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Purely numerical approach for analyzing flow to a well intercepting a vertical fracture

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

Narasimhan, T.N.; Palen, W.A.

1979-03-01

A numerical method, based on an Integral Finite Difference approach, is presented to investigate wells intercepting fractures in general and vertical fractures in particular. Such features as finite conductivity, wellbore storage, damage, and fracture deformability and its influence as permeability are easily handled. The advantage of the numerical approach is that it is based on fewer assumptions than analytic solutions and hence has greater generality. Illustrative examples are given to validate the method against known solutions. New results are presenteed to demonstrate the applicability of the method to problems not apparently considered in the literature so far.

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Fundamental solution of the problem of linear programming and method of its determination

NASA Technical Reports Server (NTRS)

Petrunin, S. V.

1978-01-01

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

NASA Astrophysics Data System (ADS)

Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

2018-01-01

Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

An efficient and guaranteed stable numerical method for continuous modeling of infiltration and redistribution with a shallow dynamic water table

NASA Astrophysics Data System (ADS)

Lai, Wencong; Ogden, Fred L.; Steinke, Robert C.; Talbot, Cary A.

2015-03-01

We have developed a one-dimensional numerical method to simulate infiltration and redistribution in the presence of a shallow dynamic water table. This method builds upon the Green-Ampt infiltration with Redistribution (GAR) model and incorporates features from the Talbot-Ogden (T-O) infiltration and redistribution method in a discretized moisture content domain. The redistribution scheme is more physically meaningful than the capillary weighted redistribution scheme in the T-O method. Groundwater dynamics are considered in this new method instead of hydrostatic groundwater front. It is also computationally more efficient than the T-O method. Motion of water in the vadose zone due to infiltration, redistribution, and interactions with capillary groundwater are described by ordinary differential equations. Numerical solutions to these equations are computationally less expensive than solutions of the highly nonlinear Richards' (1931) partial differential equation. We present results from numerical tests on 11 soil types using multiple rain pulses with different boundary conditions, with and without a shallow water table and compare against the numerical solution of Richards' equation (RE). Results from the new method are in satisfactory agreement with RE solutions in term of ponding time, deponding time, infiltration rate, and cumulative infiltrated depth. The new method, which we call "GARTO" can be used as an alternative to the RE for 1-D coupled surface and groundwater models in general situations with homogeneous soils with dynamic water table. The GARTO method represents a significant advance in simulating groundwater surface water interactions because it very closely matches the RE solution while being computationally efficient, with guaranteed mass conservation, and no stability limitations that can affect RE solvers in the case of a near-surface water table.

The Law of Higher Education: A Comprehensive Guide to Legal Implications of Administrative Decision Making. Third Edition. Jossey-Bass Higher and Adult Education Series.

ERIC Educational Resources Information Center

Kaplin, William A.; Lee, Barbara A.

This volume is the third edition of a comprehensive treatment of higher education law and is current through approximately August 1994. The nine chapters are divided into numerous sections and subsections. Chapter 1 provides a framework for understanding and integrating what is presented in subsequent chapters and a perspective for future…

Davidenko’s Method for the Solution of Nonlinear Operator Equations.

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), OPERATORS(MATHEMATICS), BANACH SPACE , MAPPING (TRANSFORMATIONS), NUMERICAL METHODS AND PROCEDURES, INTEGRALS, SET THEORY, CONVERGENCE, MATRICES(MATHEMATICS)

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics

NASA Astrophysics Data System (ADS)

Xie, Dexuan

2014-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.

Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method

NASA Astrophysics Data System (ADS)

Zhang, Hong; Zegeling, Paul Andries

2017-09-01

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow in porous media incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behavior. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

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

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

Modeling process-structure-property relationships for additive manufacturing

NASA Astrophysics Data System (ADS)

Yan, Wentao; Lin, Stephen; Kafka, Orion L.; Yu, Cheng; Liu, Zeliang; Lian, Yanping; Wolff, Sarah; Cao, Jian; Wagner, Gregory J.; Liu, Wing Kam

2018-02-01

This paper presents our latest work on comprehensive modeling of process-structure-property relationships for additive manufacturing (AM) materials, including using data-mining techniques to close the cycle of design-predict-optimize. To illustrate the processstructure relationship, the multi-scale multi-physics process modeling starts from the micro-scale to establish a mechanistic heat source model, to the meso-scale models of individual powder particle evolution, and finally to the macro-scale model to simulate the fabrication process of a complex product. To link structure and properties, a highefficiency mechanistic model, self-consistent clustering analyses, is developed to capture a variety of material response. The model incorporates factors such as voids, phase composition, inclusions, and grain structures, which are the differentiating features of AM metals. Furthermore, we propose data-mining as an effective solution for novel rapid design and optimization, which is motivated by the numerous influencing factors in the AM process. We believe this paper will provide a roadmap to advance AM fundamental understanding and guide the monitoring and advanced diagnostics of AM processing.

The GALAXIE all-optical FEL project

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

Rosenzweig, J. B.; Arab, E.; Andonian, G.

2012-12-21

We describe a comprehensive project, funded under the DARPA AXiS program, to develop an all-optical table-top X-ray FEL based on dielectric acceleration and electromagnetic undulators, yielding a compact source of coherent X-rays for medical and related applications. The compactness of this source demands that high field (>GV/m) acceleration and undulation-inducing fields be employed, thus giving rise to the project's acronym: GV/m AcceLerator And X-ray Integrated Experiment (GALAXIE). There are numerous physics and technical hurdles to surmount in this ambitious scenario, and the integrated solutions include: a biharmonic photonic TW structure, 200 micron wavelength electromagnetic undulators, 5 {mu}m laser development, ultra-highmore » brightness magnetized/asymmetric emittance electron beam generation, and SASE FEL operation. We describe the overall design philosophy of the project, the innovative approaches to addressing the challenges presented by the design, and the significant progress towards realization of these approaches in the nine months since project initialization.« less

Directing lateral growth of lithium dendrites in micro-compartmented anode arrays for safe lithium metal batteries.

PubMed

Zou, Peichao; Wang, Yang; Chiang, Sum-Wai; Wang, Xuanyu; Kang, Feiyu; Yang, Cheng

2018-01-31

Uncontrolled growth of lithium dendrites during cycling has remained a challenging issue for lithium metal batteries. Thus far, various approaches have been proposed to delay or suppress dendrite growth, yet little attention has been paid to the solutions that can make batteries keep working when lithium dendrites are already extensively present. Here we develop an industry-adoptable technology to laterally direct the growth of lithium dendrites, where all dendrites are retained inside the compartmented copper current collector in a given limited cycling capacity. This featured electrode layout renders superior cycling stability (e.g., smoothly running for over 150 cycles at 0.5 mA cm -2 ). Numerical simulations indicate that reduced dendritic stress and damage to the separator are achieved when the battery is abusively running over the ceiling capacity to generate protrusions. This study may contribute to a deeper comprehension of metal dendrites and provide a significant step towards ultimate safe batteries.

Verification of EPA's ''Preliminary Remediation Goals for radionuclides'' (PRG) electronic calculator

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

Jannik, Tim; Stagich, Brooke

The U.S. Environmental Protection Agency (EPA) requested an external, independent verification study of their updated “Preliminary Remediation Goals for Radionuclides” (PRG) electronic calculator. The calculator provides PRGs for radionuclides that are used as a screening tool at Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) and Resource Conservation and Recovery Act (RCRA) sites. These risk-based PRGs establish concentration limits under specific exposure scenarios. The purpose of this verification study is to determine that the calculator has no inherit numerical problems with obtaining solutions as well as to ensure that the equations are programmed correctly. There are 167 equations used inmore » the calculator. To verify the calculator, all equations for each of seven receptor types (resident, construction worker, outdoor and indoor worker, recreator, farmer, and composite worker) were hand calculated using the default parameters. The same four radionuclides (Am-241, Co-60, H-3, and Pu-238) were used for each calculation for consistency throughout.« less

The CMC/3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 3: Programmers' manual

NASA Technical Reports Server (NTRS)

Orzechowski, J. A.

1982-01-01

The CMC fluid mechanics program system was developed to transmit the theoretical evolution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. A detailed view of the code from the standpoint of a computer programmer's use is presented. A system macroflow chart and detailed flow charts of several routines necessary to interact with a theoretican/user to modify the operation of this program are presented. All subroutines and details of usage, primarily for input and output routines are described. Integer and real scalars and a cross reference list denoting subroutine usage for these scalars are outlined. Entry points in dynamic storage vector IZ; the lengths of each vector accompanying the scalar definitions are described. A listing of the routines peculiar to the standard test case and a listing of the input deck and printout for this case are included.

Helicopter Rotor Blade Computation in Unsteady Flows Using Moving Overset Grids

NASA Technical Reports Server (NTRS)

Ahmad, Jasim; Duque, Earl P. N.

1996-01-01

An overset grid thin-layer Navier-Stokes code has been extended to include dynamic motion of helicopter rotor blades through relative grid motion. The unsteady flowfield and airloads on an AH-IG rotor in forward flight were computed to verify the methodology and to demonstrate the method's potential usefulness towards comprehensive helicopter codes. In addition, the method uses the blade's first harmonics measured in the flight test to prescribe the blade motion. The solution was impulsively started and became periodic in less than three rotor revolutions. Detailed unsteady numerical flow visualization techniques were applied to the entire unsteady data set of five rotor revolutions and exhibited flowfield features such as blade vortex interaction and wake roll-up. The unsteady blade loads and surface pressures compare well against those from flight measurements. Details of the method, a discussion of the resulting predicted flowfield, and requirements for future work are presented. Overall, given the proper blade dynamics, this method can compute the unsteady flowfield of a general helicopter rotor in forward flight.

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.

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

NASA Astrophysics Data System (ADS)

Lin, Chao-Chih; Chang, Ya-Chi; Yeh, Hund-Der

2018-04-01

Understanding the head distribution in aquifers is crucial for the evaluation of groundwater resources. This article develops a model for describing flow induced by pumping in an L-shaped fluvial aquifer bounded by impermeable bedrocks and two nearly fully penetrating streams. A similar scenario for numerical studies was reported in Kihm et al. (2007). The water level of the streams is assumed to be linearly varying with distance. The aquifer is divided into two subregions and the continuity conditions of the hydraulic head and flux are imposed at the interface of the subregions. The steady-state solution describing the head distribution for the model without pumping is first developed by the method of separation of variables. The transient solution for the head distribution induced by pumping is then derived based on the steady-state solution as initial condition and the methods of finite Fourier transform and Laplace transform. Moreover, the solution for stream depletion rate (SDR) from each of the two streams is also developed based on the head solution and Darcy's law. Both head and SDR solutions in the real time domain are obtained by a numerical inversion scheme called the Stehfest algorithm. The software MODFLOW is chosen to compare with the proposed head solution for the L-shaped aquifer. The steady-state and transient head distributions within the L-shaped aquifer predicted by the present solution are compared with the numerical simulations and measurement data presented in Kihm et al. (2007).

Lexical decision as an endophenotype for reading comprehension: An exploration of an association

PubMed Central

NAPLES, ADAM; KATZ, LEN; GRIGORENKO, ELENA L.

2012-01-01

Based on numerous suggestions in the literature, we evaluated lexical decision (LD) as a putative endophenotype for reading comprehension by investigating heritability estimates and segregation analyses parameter estimates for both of these phenotypes. Specifically, in a segregation analysis of a large sample of families, we established that there is little to no overlap between genes contributing to LD and reading comprehension and that the genetic mechanism behind LD derived from this analysis appears to be more complex than that for reading comprehension. We conclude that in our sample, LD is not a good candidate as an endophenotype for reading comprehension, despite previous suggestions from the literature. Based on this conclusion, we discuss the role and benefit of the endophenotype approach in studies of complex human cognitive functions. PMID:23062302

Reactions and Surface Transformations of a Bone-Bioactive Material in a Simulated Microgravity Environment

NASA Technical Reports Server (NTRS)

Radin, S.; Ducheyne, P.; Ayyaswamy, P. S.

1999-01-01

A comprehensive program to investigate the expeditious in vitro formation of three-dimensional bone-like tissue is currently underway at the University of Pennsylvania. The study reported here forms a part of that program. Three-dimensional bone-like tissue structures may be grown under the simulated microgravity conditions of NASA designed Rotating Wall Bioreactor Vessels (RWV's). Such tissue growth will have wide clinical applications. In addition, an understanding of the fundamental changes that occur to bone cells under simulated microgravity would yield important information that will help in preventing or minimizing astronaut bone loss, a major health issue with travel or stay in space over long periods of time. The growth of three-dimensional bone-like tissue structures in RWV's is facilitated by the use of microcarriers which provide structural support. If the microcarrier material additionally promotes bone cell growth, then it is particularly advantageous to employ such microcarriers. We have found that reactive, bone-bioactive glass (BBG) is an attractive candidate for use as microcarrier material. Specifically, it has been found that BBG containing Ca- and P- oxides upregulates osteoprogenitor cells to osteoblasts. This effect on cells is preceded by BBG reactions in solution which result in the formation of a Ca-P surface layer. This surface further transforms to a bone-like mineral (i.e., carbonated crystalline hydroxyapatite (c-HA)). At normal gravity, time-dependent, immersion-induced BBG reactions and transformations are greatly affected both by variations in the composition of the milieu in which the glass is immersed and on the immersion conditions. However, the nature of BBG reactions and phase transformations under the simulated microgravity conditions of RWV's are unknown, and must be understood in order to successfully use BBG as microcarrier material in RWV'S. In this paper, we report some of our recent findings in this regard using experimental and numerical methods. BBG composition 45S5, the most reactive among known bone-bioactive glasses, was chosen for the study. BBG 45S5 behavior in physiological solutions was tested in simulated microgravity and compared with that at normal gravity. On the basis of our numerical study, we have chosen the BBG granule size to be in the range 40-70 microns, and a RWV rotational speed of 10 rpm. Our numerical study has shown that these parameters enable the microcarrier to remain suspended in the medium without experiencing collisions with the wall of the vessel. Immersion-induced changes in the solution composition and the material surface were analyzed after immersion.

Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

NASA Technical Reports Server (NTRS)

Balakrishnan, A.

1987-01-01

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Advanced Secure Optical Image Processing for Communications

NASA Astrophysics Data System (ADS)

Al Falou, Ayman

2018-04-01

New image processing tools and data-processing network systems have considerably increased the volume of transmitted information such as 2D and 3D images with high resolution. Thus, more complex networks and long processing times become necessary, and high image quality and transmission speeds are requested for an increasing number of applications. To satisfy these two requests, several either numerical or optical solutions were offered separately. This book explores both alternatives and describes research works that are converging towards optical/numerical hybrid solutions for high volume signal and image processing and transmission. Without being limited to hybrid approaches, the latter are particularly investigated in this book in the purpose of combining the advantages of both techniques. Additionally, pure numerical or optical solutions are also considered since they emphasize the advantages of one of the two approaches separately.