
Numerical Recipes in C++: The Art of Scientific Computing (2nd edn). Numerical Recipes Example Book (C++) (2nd edn). Numerical Recipes MultiLanguage Code CD ROM with LINUX or UNIX SingleScreen License Revised Version
International Nuclear Information System (INIS)
Borcherds, P
20030101
The two Numerical Recipes books are marvellous. The principal book, The Art of Scientific Computing, contains program listings for almost every conceivable requirement, and it also contains a well written discussion of the algorithms and the numerical methods involved. The Example Book provides a complete driving program, with helpful notes, for nearly all the routines in the principal book. The first edition of Numerical Recipes: The Art of Scientific Computing was published in 1986 in two versions, one with programs in Fortran, the other with programs in Pascal. There were subsequent versions with programs in BASIC and in C. The second, enlarged edition was published in 1992, again in two versions, one with programs in Fortran (NR(F)), the other with programs in C (NR(C)). In 1996 the authors produced Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing as a supplement, called Volume 2, with the original (Fortran) version referred to as Volume 1. Numerical Recipes in C++ (NR(C++)) is another version of the 1992 edition. The numerical recipes are also available on a CD ROM: if you want to use any of the recipes, I would strongly advise you to buy the CD ROM. The CD ROM contains the programs in all the languages. When the first edition was published I bought it, and have also bought copies of the other editions as they have appeared. Anyone involved in scientific computing ought to have a copy of at least one version of Numerical Recipes, and there also ought to be copies in every library. If you already have NR(F), should you buy the NR(C++) and, if not, which version should you buy? In the preface to Volume 2 of NR(F), the authors say 'C and C++ programmers have not been far from our minds as we have written this volume, and we think that you will find that time spent in absorbing its principal lessons will be amply repaid in the future as C and C++ eventually develop standard parallel extensions'. In the preface and introduction to NR

Numerical
Directory of Open Access Journals (Sweden)
M. Boumaza
20150701
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.

Building Models in the Classroom: Taking Advantage of Sophisticated Geomorphic Numerical Tools Using a Simple Graphical User Interface
Science.gov (United States)
Roy, S. G.; Koons, P. O.; Gerbi, C. C.; Capps, D. K.; Tucker, G. E.; Rogers, Z. A.
20141201
Sophisticated numerical tools exist for modeling geomorphic processes and linking them to tectonic and climatic systems, but they are often seen as inaccessible for users with an exploratory level of interest. We have improved the accessibility of landscape evolution models by producing a simple graphics user interface (GUI) that takes advantage of the ChannelHillslope Integrated Landscape Development (CHILD) model. Model access is flexible: the user can edit values for basic geomorphic, tectonic, and climate parameters, or obtain greater control by defining the spatiotemporal distributions of those parameters. Users can make educated predictions by choosing their own parametric values for the governing equations and interpreting the results immediately through model graphics. This method of modeling allows users to iteratively build their understanding through experimentation. Use of this GUI is intended for inquiry and discoverybased learning activities. We discuss a number of examples of how the GUI can be used at the upper high school, introductory university, and advanced university level. Effective teaching modules initially focus on an inquirybased example guided by the instructor. As students become familiar with the GUI and the CHILD model, the class can shift to more studentcentered exploration and experimentation. To make model interpretations more robust, digital elevation models can be imported and direct comparisons can be made between CHILD model results and natural topography. The GUI is available online through the University of Maine's Earth and Climate Sciences website, through the Community Surface Dynamics Modeling System (CSDMS) model repository, or by contacting the corresponding author.

Introducing Geoscience Students to Numerical Modeling of Volcanic Hazards: The example of Tephra2 on VHub.org
Directory of Open Access Journals (Sweden)
Leah M. Courtland
20120701
Full Text Available The Tephra2 numerical model for tephra fallout from explosive volcanic eruptions is specifically designed to enable students to probe ideas in model literacy, including code validation and verification, the role of simplifying assumptions, and the concepts of uncertainty and forecasting. This numerical model is implemented on the VHub.org website, a venture in cyberinfrastructure that brings together volcanological models and educational materials. The VHub.org resource provides students with the ability to explore and execute sophisticated numerical models like Tephra2. We present a strategy for using this model to introduce university students to key concepts in the use and evaluation of Tephra2 for probabilistic forecasting of volcanic hazards. Through this critical examination students are encouraged to develop a deeper understanding of the applicability and limitations of hazard models. Although the model and applications are intended for use in both introductory and advanced geoscience courses, they could easily be adapted to work in other disciplines, such as astronomy, physics, computational methods, data analysis, or computer science.

The Fundamentals of Economic Dynamics and Policy Analyses : Learning through Numerical Examples. Part Ⅳ. Overlapping Generations Model
OpenAIRE
Futamura, Hiroshi
20150101
An overlapping generations model is an applied dynamic general equilibrium model for which the lifecycle models are employed as main analytical tools. At any point in time, there are overlapping generations consisting of individuals born this year, individuals born last year, individuals born two years ago, and so on. As we saw in the analysis of lifecycle models, each individual makes an optimal consumptionsaving plan to maximize lifetime utility over her/his lifecycle. For example, an indi...

Success of Using Technology and Manipulatives To Introduce Numerical Problem Solving Skills in Monolingual/Bilingual Early Childhood Classrooms.
Science.gov (United States)
Ainsa, Trisha
19990101
Pilots and evaluates a math activity initially utilizing M&Ms as manipulatives, then progressing to computer software math activities, in five early childhood classrooms. Concludes that there were no significant differences between learning tasks, monolingual students vs. bilingual students, and manipulative (handsoff) activities vs. computer…

Arts Integration: A Classroom Example.
Science.gov (United States)
Merrion, Margaret Dee; Boothby, Paula R.
19860101
To integrate the arts and basic curriculum, teachers used advertising as a theme. Viewing it as a form of communication, they developed an integrated reading/language arts and music unit to strengthen both right and left brain modes of knowing. (LHW)

Numerical and statistical based damage analysis by the example of kiln elements; Numerisch und statistisch gestuetzte Schadensanalyse am Beispiel von Brennofenelementen
Energy Technology Data Exchange (ETDEWEB)
Reinert, U. [DEKRAETS Europaeische Gesellschaft fuer Technische Sicherheit mbH, Saarbruecken (Germany); Klaer, P. [SaarHartmetall und Werkzeuge GmbH, Voelklingen (Germany)
19990201
The nonoxidic ceramics (for example SiC), used as a supporting structure in kilns, are subject to instantaneous damage, which as a rule is accompanied by high costs. Of interest in this context is the question whether a satisfactory statement can be made about the increase of damage frequency as a function of the firing temperature, the firing time, the geometry of the component, the material properties and the loading. Knowledge of these correlations provides the user with the possibility of minimizing the costs of damage by means of suitable selection of material and timely replacement of the components. The procedure presented in the following is based on the combination of numerical studies with statistically evaluated experiments. (orig.)

What can a numerical landscape evolution model tell us about the evolution of a real landscape? Two examples of modeling a real landscape without recreating it
Science.gov (United States)
Gasparini, N. M.; Whipple, K. X.; Willenbring, J.; Crosby, B. T.; Brocard, G. Y.
20131201
Numerical landscape evolution models (LEMs) offer us the unique opportunity to watch a landscape evolve under any set of environmental forcings that we can quantify. The possibilities for using LEMs are infinite, but complications arise when trying to model a real landscape. Specifically, numerical models cannot recreate every aspect of a real landscape because exact initial conditions are unknown, there will always be gaps in the known tectonic and climatic history, and the geomorphic transport laws that govern redistribution of mass due to surface processes will always be a simplified representation of the actual process. Yet, even with these constraints, numerical models remain the only tool that offers us the potential to explore a limitless range of evolutionary scenarios, allowing us to, at the very least, identify possible drivers responsible for the morphology of the current landscape, and just as importantly, rule out others. Here we highlight two examples in which we use a numerical model to explore the signature of different forcings on landscape morphology and erosion patterns. In the first landscape, the Northern Bolivian Andes, the relative imprint of rock uplift and precipitation patterns on landscape morphology is widely contested. We use the CHILD LEM to systematically vary climate and tectonics and quantify their fingerprints on channel profiles across a steep mountain front. We find that rock uplift and precipitation patterns in this landscape and others can be teased out by examining channel profiles of variably sized catchments that drain different parts of the topography. In the second landscape, the South Fork Eel River (SFER), northern California, USA, the tectonic history is relatively well known; a wave of rock uplift swept through the watershed from headwaters to outlet, perturbing the landscape and sending a wave of bedrock incision upstream. Nine millennialscale erosion rates from along the mainstem of the river illustrate a pattern of

A Finite Difference, Semiimplicit, EquationofState Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples
KAUST Repository
Saavedra, Sebastian
20120701
The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)Volumebalance (VB), twophase, equationofstate, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and compositiondependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PREOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phasesplitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phasevolumetricflux estimation eases the calculation of phase velocities by naturally fitting to phaseupstreamupwinding. And contributes to a faster computation and an efficient programming development.

A Comparison of the CHILD and Landlab Computational Landscape Evolution Models and Examples of Best Practices in Numerical Modeling of Surface Processes
Science.gov (United States)
Gasparini, N. M.; Hobley, D. E. J.; Tucker, G. E.; Istanbulluoglu, E.; Adams, J. M.; Nudurupati, S. S.; Hutton, E. W. H.
20141201
Computational models are important tools that can be used to quantitatively understand the evolution of real landscapes. Commonalities exist among most landscape evolution models, although they are also idiosyncratic, in that they are coded in different languages, require different input values, and are designed to tackle a unique set of questions. These differences can make applying a landscape evolution model challenging, especially for novice programmers. In this study, we compare and contrast two landscape evolution models that are designed to tackle similar questions, but the actual model designs are quite different. The first model, CHILD, is over a decadeold and is relatively welltested, welldeveloped and wellused. It is coded in C++, operates on an irregular grid and was designed more with function rather than userexperience in mind. In contrast, the second model, Landlab, is relatively new and was designed to be accessible to a wide range of scientists, including those who have not previously used or developed a numerical model. Landlab is coded in Python, a relatively easy language for the nonproficient programmer, and has the ability to model landscapes described on both regular and irregular grids. We present landscape simulations from both modeling platforms. Our goal is to illustrate best practices for implementing a new process module in a landscape evolution model, and therefore the simulations are applicable regardless of the modeling platform. We contrast differences and highlight similarities between the use of the two models, including settingup the model and input file for different evolutionary scenarios, computational time, and model output. Whenever possible, we compare model output with analytical solutions and illustrate the effects, or lack thereof, of a uniform vs. nonuniform grid. Our simulations focus on implementing a single process, including detachmentlimited or transportlimited fluvial bedrock incision and linear or non

The use of Webbased GIS data technologies in the construction of geoscience instructional materials: examples from the MARGINS Data in the Classroom project
Science.gov (United States)
Ryan, J. G.; McIlrath, J. A.
20081201
Webaccessible geospatial information system (GIS) technologies have advanced in concert with an expansion of data resources that can be accessed and used by researchers, educators and students. These resources facilitate the development of datarich instructional resources and activities that can be used to transition seamlessly into undergraduate research projects. MARGINS Data in the Classroom (http://serc.carleton.edu/ margins/index.html) seeks to engage MARGINS researchers and educators in using the images, datasets, and visualizations produced by NSFMARGINS Programfunded research and related efforts to create Webdeliverable instructional materials for use in undergraduatelevel geoscience courses (MARGINS MiniLessons). MARGINS science data is managed by the Marine Geosciences Data System (MGDS), and these and all other MGDShosted data can be accessed, manipulated and visualized using GeoMapApp (www.geomapapp.org; Carbotte et al, 2004), a freely available geographic information system focused on the marine environment. Both "packaged" MGDS datasets (i.e., global earthquake foci, volcanoes, bathymetry) and "raw" data (seismic surveys, magnetics, gravity) are accessible via GeoMapApp, with WFS linkages to other resources (geodesy from UNAVCO; seismic profiles from IRIS; geochemical and drillsite data from EarthChem, IODP, and others), permitting the comprehensive characterization of many regions of the ocean basins. Geospatially controlled datasets can be imported into GeoMapApp visualizations, and these visualizations can be exported into Google Earth as .kmz image files. Many of the MARGINS MiniLessons thus far produced use (or have studentss use the varied capabilities of GeoMapApp (i.e., constructing topographic profiles, overlaying varied geophysical and bathymetric datasets, characterizing geochemical data). These materials are available for use and testing from the project webpage (http://serc.carleton.edu/margins/). Classroom testing and assessment

Numerická simulace v biomechanice – forenzní příklad Numerical simulation in biomechanics – a forensic example
Directory of Open Access Journals (Sweden)
Norbert Praxl
20060201
áním odpovídají zcela pasivnímu lidskému tělu. The paper presents an example of a forensic application of biomechanical methods including numerical simulation with human body models. By means of a case study of an unwitnessed lethal fall the course of the biomechanical forensic reconstruction is demonstrated. The traces available at the place of finding and the injuries of the victim are the facts that the analysis is based on. The ultimate expected result of the biomechanical analysis is the assignment of all available traces and the explanation of the event. The injuries observed in the described case were partly typical fall injuries, but there were also some injuries that could not be prima vista assigned. The police investigation at the place of finding also brought to light some facts that could not be satisfactorily explained at first. By using numerical simulation, additional information was obtained that enabled us to explain many aspects of the case that could not have been analysed otherwise. Numerical simulation offers objective and quantitative data enabling a far more exact analysis of the studied event – the kinematical as well as dynamical parameters of the human body and its interaction with the surroundings structures can be studied and even the human body’s internal forces can be analysed enabling thus an accurate injury prediction. All the important unknown parameters (initial conditions of the simulated event, i. e. body position, body orientation, initial velocity etc. can be easily varied so that all the possibilities can be taken into account. Another very important asset of this method is its powerful visualisation capability that enhances the understanding of the studied events even for persons without extensive biomechanical knowledge. The major limitation of numerical simulation at the moment is the lack of muscle activity; the models represent only a totally passive human body so far.

Development of a Generalized Version of the PoissonNernstPlanck Equations Using the Hybrid Mixture Theory: Presentation of 2D Numerical Examples
DEFF Research Database (Denmark)
Johannesson, Björn
20100101
A numerical scheme for the transient solution of generalized version of the PoissonNernstPlanck equations is presented. The finite element method is used to establish the coupled nonlinear matrix system of equations capable of solving the present problem iteratively. The Poisson......scale and that it includes the volume fractions of phases in its structure. The background to the PoissonNernstPlanck equations can by the HMT approach be described by using the postulates of mass conservation of constituents together with the Gauss’ law used together with consistent constitutive laws. The HMT theory......NernstPlanck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The NernstPlanck equations describing the diffusion of the ionic species and the Gauss’ law in used are...

Faults architecture and growth in claylimestone alternation. Examples in the SE Basin alternations (France) and numerical modeling
International Nuclear Information System (INIS)
Roche, Vincent
20110101
The following work has been carried out in the framework of the studies conducted by IRSN in support of its safety evaluation of the geological disposal programme of high and intermediate level, longlived radioactive waste. Such a disposal is planned to be hosted by the CallovianOxfordian indurate clay formation between two limestone formations in eastern Paris basin, France. Hypothetical faults may crosscut this layered section, decreasing the clay containment ability by creating preferential pathways for radioactive solute towards limestones. This study aims at characterising the fault architecture and the normal fault growth in clay/limestone layered sections. Structural analysis and displacement profiles have been carried out in normal faults crossing several decimetres to metre thick sedimentary alternations in the SouthEastern Basin (France) and petrophysical properties have been determined for each layer. The studied faults are simple fault planes or complex fault zones showing are significantly controlled by the layering. The analysis of the fault characteristics and the results obtained on numerical models enlighten several processes such as fault nucleation, fault restriction, and fault growth through layered section. Some studied faults nucleated in the limestone layers, without using preexisting fractures such as joints, and according to our numerical analysis, a strong stiffness, a low strength contrast between the limestone and the clay layer, and/or s a greater thickness of the clay layer are conditions which favour nucleation of faults in limestone. The range of mechanical properties leading to the fault nucleation in one layer type or another was investigated using a 3D modelling approach. After its nucleation, the fault propagates within a homogeneous medium with a constant displacement gradient until its vertical propagation is stopped by a restrictor. The evidenced restrictors are limestoneclay interfaces or faults in clays, sub

Evaluation of a landscape evolution model to simulate stream piracies: Insights from multivariable numerical tests using the example of the Meuse basin, France
Science.gov (United States)
Benaïchouche, Abed; Stab, Olivier; Tessier, Bruno; Cojan, Isabelle
20160101
In landscapes dominated by fluvial erosion, the landscape morphology is closely related to the hydrographic network system. In this paper, we investigate the hydrographic network reorganization caused by a headward piracy mechanism between two drainage basins in France, the Meuse and the Moselle. Several piracies occurred in the Meuse basin during the past one million years, and the basin's current characteristics are favorable to new piracies by the Moselle river network. This study evaluates the consequences over the next several million years of a relative lowering of the Moselle River (and thus of its basin) with respect to the Meuse River. The problem is addressed with a numerical modeling approach (landscape evolution model, hereafter LEM) that requires empirical determinations of parameters and threshold values. Classically, fitting of the parameters is based on analysis of the relationship between the slope and the drainage area and is conducted under the hypothesis of equilibrium. Application of this conventional approach to the capture issue yields incomplete results that have been consolidated by a parametric sensitivity analysis. The LEM equations give a sixdimensional parameter space that was explored with over 15,000 simulations using the landscape evolution model GOLEM. The results demonstrate that stream piracies occur in only four locations in the studied reach near the city of Toul. The locations are mainly controlled by the local topography and are modelindependent. Nevertheless, the chronology of the captures depends on two parameters: the river concavity (given by the fluvial advection equation) and the hillslope erosion factor. Thus, the simulations lead to three different scenarios that are explained by a phenomenon of exclusion or a string of events.

Numerical analysis
CERN Document Server
Rao, G Shanker
20060101
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of workedout examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...

The Flipped Classroom in Counselor Education
Science.gov (United States)
Moran, Kristen; Milsom, Amy
20150101
The flipped classroom is proposed as an effective instructional approach in counselor education. An overview of the flippedclassroom approach, including advantages and disadvantages, is provided. A case example illustrates how the flipped classroom can be applied in counselor education. Recommendations for implementing or researching flipped…

Example book
International Nuclear Information System (INIS)
Donnat, Ph.; Treimany, C.; Gouedard, C.; Morice, O.
19980601
This document presents some examples which were used for debugging the code. It seemed useful to write these examples onto a book to be sure the code would not regret; to give warranties for the code's functionality; to propose some examples to illustrate the possibilities and the limits of Miro. (author)

Learning Algebra from Worked Examples
Science.gov (United States)
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
20140101
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student selfexplanation. "Selfexplanation" is the…