A Comparative Analysis of a Generalized Lanchester Equation Model and a Stochastic Computer Simulation Model.

DTIC Science & Technology

1987-03-01

model is one in which words or numerical descriptions are used to represent an entity or process. An example of a symbolic model is a mathematical ...are the third type of model used in modeling combat attrition. Analytical models are symbolic models which use mathematical symbols and equations to...simplicity and the ease of tracing through the mathematical computations. In this section I will discuss some of the shortcoming which have been

Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

NASA Astrophysics Data System (ADS)

Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

2014-11-01

Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

Using models to manage systems subject to sustainability indicators

USGS Publications Warehouse

Hill, M.C.

2006-01-01

Mathematical and numerical models can provide insight into sustainability indicators using relevant simulated quantities, which are referred to here as predictions. To be useful, many concerns need to be considered. Four are discussed here: (a) mathematical and numerical accuracy of the model; (b) the accuracy of the data used in model development, (c) the information observations provide to aspects of the model important to predictions of interest as measured using sensitivity analysis; and (d) the existence of plausible alternative models for a given system. The four issues are illustrated using examples from conservative and transport modelling, and using conceptual arguments. Results suggest that ignoring these issues can produce misleading conclusions.

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

CFD analysis of the plate heat exchanger - Mathematical modelling of mass and heat transfer in serial connection with tubular heat exchanger

NASA Astrophysics Data System (ADS)

Bojko, Marian; Kocich, Radim

2016-06-01

Application of numerical simulations based on the CFD calculation when the mass and heat transfer between the fluid flows is essential component of thermal calculation. In this article the mathematical model of the heat exchanger is defined, which is subsequently applied to the plate heat exchanger, which is connected in series with the other heat exchanger (tubular heat exchanger). The present contribution deals with the possibility to use the waste heat of the flue gas produced by small micro turbine. Inlet boundary conditions to the mathematical model of the plate heat exchanger are obtained from the results of numerical simulation of the tubular heat exchanger. Required parameters such for example inlet temperature was evaluated from temperature field, which was subsequently imported to the inlet boundary condition to the simulation of plate heat exchanger. From the results of 3D numerical simulations are evaluated basic flow variables including the evaluation of dimensionless parameters such as Colburn j-factor and friction ft factor. Numerical simulation is realized by software ANSYS Fluent15.0.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

The Mathematics of the Return from Home Ownership.

ERIC Educational Resources Information Center

Vest, Floyd; Griffith, Reynolds

1991-01-01

A mathematical model or project analysis that calculates the financial return from home ownership is described. This analysis illustrates topics such as compound interest, annuities, amortization schedules, internal rate of return, and other elements of school and college mathematics up through numerical analysis. (KR)

3-D Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

DTIC Science & Technology

2014-01-01

resistant mutants [?]. Inspired by experimental findings, researchers have come up with some mathematical models to study biofilm formation and function...develop a full 3D mathematical model to study how quorum sensing regulates biofilm formation and development as well as the pros and cons of quorum...have given an overview of current advances in mathematical modeling of biofilms. Concerning coupling biofilm growth with quorum sensing features

Application of differential transformation method for solving dengue transmission mathematical model

NASA Astrophysics Data System (ADS)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

Variational data assimilation system "INM RAS - Black Sea"

NASA Astrophysics Data System (ADS)

Parmuzin, Eugene; Agoshkov, Valery; Assovskiy, Maksim; Giniatulin, Sergey; Zakharova, Natalia; Kuimov, Grigory; Fomin, Vladimir

2013-04-01

Development of Informational-Computational Systems (ICS) for Data Assimilation Procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The problems discussed above are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for Personal Computers (PC). Special problems and questions arise while effective ICS versions for PC are being developed. These problems and questions can be solved with applying modern methods of numerical mathematics and by solving "parallelism problem" using OpenMP technology and special linear algebra packages. In this work the results on the ICS development for PC-ICS "INM RAS - Black Sea" are presented. In the work the following problems and questions are discussed: practical problems that can be studied by ICS; parallelism problems and their solutions with applying of OpenMP technology and the linear algebra packages used in ICS "INM - Black Sea"; Interface of ICS. The results of ICS "INM RAS - Black Sea" testing are presented. Efficiency of technologies and methods applied are discussed. The work was supported by RFBR, grants No. 13-01-00753, 13-05-00715 and by The Ministry of education and science of Russian Federation, project 8291, project 11.519.11.1005 References: [1] V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 5-31 [2] E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 69-94 [3] V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, 95-111 [4] V.I. Agoshkov, S.V. Giniatulin, G.V. Kuimov. OpenMP technology and linear algebra packages in the variation data assimilation systems. - Abstracts of the 1-st China-Russia Conference on Numerical Algebra with Applications in Radiactive Hydrodynamics, Beijing, China, October 16-18, 2012. [5] Zakharova N.B., Agoshkov V.I., Parmuzin E.I., The new method of ARGO buoys system observation data interpolation. Russian Journal of Numerical Analysis and Mathematical Modelling. Vol. 28, Issue 1, 2013.

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.

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1997-01-01

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Mathematical and Computational Aspects of Multiscale Materials Modeling, Mathematics-Numerical analysis, Section II.A.a.3.4, Conference and symposia organization II.A.2.a

DTIC Science & Technology

2015-02-04

dislocation dynamics models ( DDD ), continuum representations). Coupling of these models is difficult. Coupling of atomistics and DDD models has been...explored to some extent, but the coupling between DDD and continuum models of the evolution of large populations of dislocations is essentially unexplored

Vistas in applied mathematics: Numerical analysis, atmospheric sciences, immunology

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

Balakrishnan, A.V.; Dorodnitsyn, A.A.; Lions, J.L.

1986-01-01

Advances in the theory and application of numerical modeling techniques are discussed in papers contributed, primarily by Soviet scientists, on the occasion of the 60th birthday of Gurii I. Marchuk. Topics examined include splitting techniques for computations of industrial flows, the mathematical foundations of the k-epsilon turbulence model, splitting methods for the solution of the incompressible Navier-Stokes equations, the approximation of inhomogeneous hyperbolic boundary-value problems, multigrid methods, and the finite-element approximation of minimal surfaces. Consideration is given to dynamic modeling of moist atmospheres, satellite observations of the earth radiation budget and the problem of energy-active ocean regions, a numerical modelmore » of the biosphere for use with GCMs, and large-scale modeling of ocean circulation. Also included are several papers on modeling problems in immunology.« less

The Evolvement of Numeracy and Mathematical Literacy Curricula and the Construction of Hierarchies of Numerate or Mathematically Literate Subjects

ERIC Educational Resources Information Center

Jablonka, Eva

2015-01-01

This contribution briefly sketches the evolvement of numeracy or mathematical literacy as models for mathematics curricula, which will be described as driven by a weakening of the insulation between discourses, that is, as a process of "declassification". The question then arises as to whether and how coherence of new forms of initially…

Mathematical modeling and numerical simulation of the mitotic spindle orientation system.

PubMed

Ibrahim, Bashar

2018-05-21

The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division. Copyright © 2018. Published by Elsevier Inc.

Optimization of a new mathematical model for bacterial growth

USDA-ARS?s Scientific Manuscript database

The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...

Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine.

PubMed

Erdem, Mustafa; Safan, Muntaser; Castillo-Chavez, Carlos

2017-07-01

The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

PubMed Central

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

Basic mathematical rules are encoded by primate prefrontal cortex neurons

PubMed Central

Bongard, Sylvia; Nieder, Andreas

2010-01-01

Mathematics is based on highly abstract principles, or rules, of how to structure, process, and evaluate numerical information. If and how mathematical rules can be represented by single neurons, however, has remained elusive. We therefore recorded the activity of individual prefrontal cortex (PFC) neurons in rhesus monkeys required to switch flexibly between “greater than” and “less than” rules. The monkeys performed this task with different numerical quantities and generalized to set sizes that had not been presented previously, indicating that they had learned an abstract mathematical principle. The most prevalent activity recorded from randomly selected PFC neurons reflected the mathematical rules; purely sensory- and memory-related activity was almost absent. These data show that single PFC neurons have the capacity to represent flexible operations on most abstract numerical quantities. Our findings support PFC network models implementing specific “rule-coding” units that control the flow of information between segregated input, memory, and output layers. We speculate that these neuronal circuits in the monkey lateral PFC could readily have been adopted in the course of primate evolution for syntactic processing of numbers in formalized mathematical systems. PMID:20133872

Identification of Student- and Teacher-Level Variables in Modeling Variation of Mathematics Achievement Data

ERIC Educational Resources Information Center

Tarr, James E.; Ross, Daniel J.; McNaught, Melissa D.; Chavez, Oscar; Grouws, Douglas A.; Reys, Robert E.; Sears, Ruthmae; Taylan, R. Didem

2010-01-01

The Comparing Options in Secondary Mathematics: Investigating Curriculum (COSMIC) project is a longitudinal study of student learning from two types of mathematics curricula: integrated and subject-specific. Previous large-scale research studies such as the National Assessment of Educational Progress (NAEP) indicate that numerous variables are…

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

NASA Astrophysics Data System (ADS)

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies.

PubMed

Liu, Cheng-Lin; Sun, Ze; Lu, Gui-Min; Yu, Jian-Guo

2018-05-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

PubMed Central

Lu, Gui-Min; Yu, Jian-Guo

2018-01-01

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study. PMID:29892347

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

Modelling of Factors Influencing Gender Difference in Mathematics Achievement Using TIMSS 2011 Data for Singaporean Eighth Grade Students

ERIC Educational Resources Information Center

Yoo, Yang Seok

2018-01-01

Numerous studies have attributed gender difference in mathematics achievement to various sociocultural influences. Singapore is a country of higher gender equality as represented in the Global Gender Gap Index and Singaporean girls perform as well or higher than boys in international mathematics assessments. This study develops a conceptual model…

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Intentional and automatic numerical processing as predictors of mathematical abilities in primary school children

PubMed Central

Pina, Violeta; Castillo, Alejandro; Cohen Kadosh, Roi; Fuentes, Luis J.

2015-01-01

Previous studies have suggested that numerical processing relates to mathematical performance, but it seems that such relationship is more evident for intentional than for automatic numerical processing. In the present study we assessed the relationship between the two types of numerical processing and specific mathematical abilities in a sample of 109 children in grades 1–6. Participants were tested in an ample range of mathematical tests and also performed both a numerical and a size comparison task. The results showed that numerical processing related to mathematical performance only when inhibitory control was involved in the comparison tasks. Concretely, we found that intentional numerical processing, as indexed by the numerical distance effect in the numerical comparison task, was related to mathematical reasoning skills only when the task-irrelevant dimension (the physical size) was incongruent; whereas automatic numerical processing, indexed by the congruency effect in the size comparison task, was related to mathematical calculation skills only when digits were separated by small distance. The observed double dissociation highlights the relevance of both intentional and automatic numerical processing in mathematical skills, but when inhibitory control is also involved. PMID:25873909

Developing group investigation-based book on numerical analysis to increase critical thinking student’s ability

NASA Astrophysics Data System (ADS)

Maharani, S.; Suprapto, E.

2018-03-01

Critical thinking is very important in Mathematics; it can make student more understanding mathematics concept. Critical thinking is also needed in numerical analysis. The Numerical analysis's book is not yet including critical thinking in them. This research aims to develop group investigation-based book on numerical analysis to increase critical thinking student’s ability, to know the quality of the group investigation-based book on numerical analysis is valid, practical, and effective. The research method is Research and Development (R&D) with the subject are 30 student college department of Mathematics education at Universitas PGRI Madiun. The development model used is 4-D modified to 3-D until the stage development. The type of data used is descriptive qualitative data. Instruments used are sheets of validation, test, and questionnaire. Development results indicate that group investigation-based book on numerical analysis in the category of valid a value 84.25%. Students response to the books very positive, so group investigation-based book on numerical analysis category practical, i.e., 86.00%. The use of group investigation-based book on numerical analysis has been meeting the completeness criteria classical learning that is 84.32 %. Based on research result of this study concluded that group investigation-based book on numerical analysis is feasible because it meets the criteria valid, practical, and effective. So, the book can be used by every mathematics academician. The next research can be observed that book based group investigation in other subjects.

Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?

PubMed

Ledzewicz, Urszula; Schättler, Heinz

2017-08-10

Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens. Copyright © 2017 Elsevier B.V. All rights reserved.

CSP - The 19th European Conference on Mathematics for Industry (ECMI 2016)

DTIC Science & Technology

2017-03-02

Quality physics in game cinematics. Conclusions Most significant advance reported The ECMI 2016 exceeded by far the expectations of the Organizing... games . 15. SUBJECT TERMS Industrial mathematics; numerical simulation ; optimization; modelling; innovation. 16. SECURITY CLASSIFICATION OF: 17

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

NASA Astrophysics Data System (ADS)

Muntean, S.; Ciocan, T.; Susan-Resiga, R. F.; Cervantes, M.; Nilsson, H.

2012-11-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Biological system interactions.

PubMed Central

Adomian, G; Adomian, G E; Bellman, R E

1984-01-01

Mathematical modeling of cellular population growth, interconnected subsystems of the body, blood flow, and numerous other complex biological systems problems involves nonlinearities and generally randomness as well. Such problems have been dealt with by mathematical methods often changing the actual model to make it tractable. The method presented in this paper (and referenced works) allows much more physically realistic solutions. PMID:6585837

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…

Coastal Modeling System: Mathematical Formulations and Numerical Methods

DTIC Science & Technology

2014-03-01

sediment transport , and morphology change. The CMS was designed and developed for coastal inlets and navigation applications, including channel...numerical methods of hydrodynamic, salinity and sediment transport , and morphology change model CMS-Flow. The CMS- Flow uses the Finite Volume...and the influence of coastal structures. The implicit hydrodynamic model is coupled to a nonequilibrium transport model of multiple-sized total

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

Mathematical Basis and Test Cases for Colloid-Facilitated Radionuclide Transport Modeling in GDSA-PFLOTRAN

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

Reimus, Paul William

This report provides documentation of the mathematical basis for a colloid-facilitated radionuclide transport modeling capability that can be incorporated into GDSA-PFLOTRAN. It also provides numerous test cases against which the modeling capability can be benchmarked once the model is implemented numerically in GDSA-PFLOTRAN. The test cases were run using a 1-D numerical model developed by the author, and the inputs and outputs from the 1-D model are provided in an electronic spreadsheet supplement to this report so that all cases can be reproduced in GDSA-PFLOTRAN, and the outputs can be directly compared with the 1-D model. The cases include examplesmore » of all potential scenarios in which colloid-facilitated transport could result in the accelerated transport of a radionuclide relative to its transport in the absence of colloids. Although it cannot be claimed that all the model features that are described in the mathematical basis were rigorously exercised in the test cases, the goal was to test the features that matter the most for colloid-facilitated transport; i.e., slow desorption of radionuclides from colloids, slow filtration of colloids, and equilibrium radionuclide partitioning to colloids that is strongly favored over partitioning to immobile surfaces, resulting in a substantial fraction of radionuclide mass being associated with mobile colloids.« less

Configuration of the Hemoglobin Oxygen Dissociation Curve Demystified: A Basic Mathematical Proof for Medical and Biological Sciences Undergraduates

ERIC Educational Resources Information Center

Leow, Melvin Khee-Shing

2007-01-01

The oxygen dissociation curve (ODC) of hemoglobin (Hb) has been widely studied and mathematically described for nearly a century. Numerous mathematical models have been designed to predict with ever-increasing accuracy the behavior of oxygen transport by Hb in differing conditions of pH, carbon dioxide, temperature, Hb levels, and…

The effect of mathematics anxiety on the processing of numerical magnitude.

PubMed

Maloney, Erin A; Ansari, Daniel; Fugelsang, Jonathan A

2011-01-01

In an effort to understand the origins of mathematics anxiety, we investigated the processing of symbolic magnitude by high mathematics-anxious (HMA) and low mathematics-anxious (LMA) individuals by examining their performance on two variants of the symbolic numerical comparison task. In two experiments, a numerical distance by mathematics anxiety (MA) interaction was obtained, demonstrating that the effect of numerical distance on response times was larger for HMA than for LMA individuals. These data support the claim that HMA individuals have less precise representations of numerical magnitude than their LMA peers, suggesting that MA is associated with low-level numerical deficits that compromise the development of higher level mathematical skills.

Manual of phosphoric acid fuel cell stack three-dimensional model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

A detailed distributed mathematical model of phosphoric acid fuel cell stack have been developed, with the FORTRAN computer program, for analyzing the temperature distribution in the stack and the associated current density distribution on the cell plates. Energy, mass, and electrochemical analyses in the stack were combined to develop the model. Several reasonable assumptions were made to solve this mathematical model by means of the finite differences numerical method.

Formulation of a General Technique for Predicting Pneumatic Attenuation Errors in Airborne Pressure Sensing Devices

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.

1988-01-01

Presented is a mathematical model derived from the Navier-Stokes equations of momentum and continuity, which may be accurately used to predict the behavior of conventionally mounted pneumatic sensing systems subject to arbitrary pressure inputs. Numerical techniques for solving the general model are developed. Both step and frequency response lab tests were performed. These data are compared with solutions of the mathematical model and show excellent agreement. The procedures used to obtain the lab data are described. In-flight step and frequency response data were obtained. Comparisons with numerical solutions of the math model show good agreement. Procedures used to obtain the flight data are described. Difficulties encountered with obtaining the flight data are discussed.

A mathematical model for CTL effect on a latently infected cell inclusive HIV dynamics and treatment

NASA Astrophysics Data System (ADS)

Tarfulea, N. E.

2017-10-01

This paper investigates theoretically and numerically the effect of immune effectors, such as the cytotoxic lymphocyte (CTL), in modeling HIV pathogenesis (via a newly developed mathematical model); our results suggest the significant impact of the immune response on the control of the virus during primary infection. Qualitative aspects (including positivity, boundedness, stability, uncertainty, and sensitivity analysis) are addressed. Additionally, by introducing drug therapy, we analyze numerically the model to assess the effect of treatment consisting of a combination of several antiretroviral drugs. Our results show that the inclusion of the CTL compartment produces a higher rebound for an individual's healthy helper T-cell compartment than drug therapy alone. Furthermore, we quantitatively characterize successful drugs or drug combination scenarios.

The human body metabolism process mathematical simulation based on Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur

2017-08-01

The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.

Optimal Repair And Replacement Policy For A System With Multiple Components

DTIC Science & Technology

2016-06-17

Numerical Demonstration To implement the linear program, we use the Python Programming Language (PSF 2016) with the Pyomo optimization modeling language...opre.1040.0133. Hart, W.E., C. Laird, J. Watson, D.L. Woodruff. 2012. Pyomo–optimization modeling in python , vol. 67. Springer Science & Business...Media. Hart, W.E., J. Watson, D.L. Woodruff. 2011. Pyomo: modeling and solving mathematical programs in python . Mathematical Programming Computation 3(3

Mathematical modeling of the heat transfer for determining the depth of thawing basin buildings with long service life

NASA Astrophysics Data System (ADS)

Sirditov, Ivan; Stepanov, Sergei

2017-11-01

In this paper, a numerical study of the problem of determining a thawing basin in the permafrost soil for buildings with a long service life is carried out using two methods, with the formulas of set of rules 25.13330.2012 "Soil bases and foundations on permafrost soils" and using a mathematical model.

Asset surveillance system: apparatus and method

NASA Technical Reports Server (NTRS)

Bickford, Randall L. (Inventor)

2007-01-01

System and method for providing surveillance of an asset comprised of numerically fitting at least one mathematical model to obtained residual data correlative to asset operation; storing at least one mathematical model in a memory; obtaining a current set of signal data from the asset; retrieving at least one mathematical model from the memory, using the retrieved mathematical model in a sequential hypothesis test for determining if the current set of signal data is indicative of a fault condition; determining an asset fault cause correlative to a determined indication of a fault condition; providing an indication correlative to a determined fault cause, and an action when warranted. The residual data can be mode partitioned, a current mode of operation can be determined from the asset, and at least one mathematical model can be retrieved from the memory as a function of the determined mode of operation.

A Gompertzian model with random effects to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni; Rosli, Norhayati

2015-05-15

In this paper, a Gompertzian model with random effects is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via maximum likehood estimation. We apply 4-stage Runge-Kutta (SRK4) for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of the cervical cancer growth. Low values of root mean-square error (RMSE) of Gompertzian model with random effect indicate good fits.

Gompertzian stochastic model with delay effect to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

A mathematical model for simulating noise suppression of lined ejectors

NASA Technical Reports Server (NTRS)

Watson, Willie R.

1994-01-01

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

A numerical solution of the problem of crown forest fire initiation and spread

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. The study takes in to account the mutual interaction of the forest fires and three-dimensional atmosphere flows. The research is done by means of mathematical modeling of physical processes. It is based on numerical solution of Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. It is assumed that the forest during a forest fire can be modeled as a two-temperature multiphase non-deformable porous reactive medium. A discrete analog for the system of equations was obtained by means of the control volume method. The developed model of forest fire initiation and spreading would make it possible to obtain a detailed picture of the variation in the velocity, temperature and chemical species concentration fields with time. Mathematical model and the result of the calculation give an opportunity to evaluate critical conditions of the forest fire initiation and spread which allows applying the given model for of means for preventing fires.

Mathematical modelling and numerical simulation of forces in milling process

NASA Astrophysics Data System (ADS)

Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

2018-04-01

Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

Numerical Validation of Chemical Compositional Model for Wettability Alteration Processes

NASA Astrophysics Data System (ADS)

Bekbauov, Bakhbergen; Berdyshev, Abdumauvlen; Baishemirov, Zharasbek; Bau, Domenico

2017-12-01

Chemical compositional simulation of enhanced oil recovery and surfactant enhanced aquifer remediation processes is a complex task that involves solving dozens of equations for all grid blocks representing a reservoir. In the present work, we perform a numerical validation of the newly developed mathematical formulation which satisfies the conservation laws of mass and energy and allows applying a sequential solution approach to solve the governing equations separately and implicitly. Through its application to the numerical experiment using a wettability alteration model and comparisons with existing chemical compositional model's numerical results, the new model has proven to be practical, reliable and stable.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

PubMed Central

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

PubMed

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

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.

Equations to assess the impact resistance of fiber composites

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Hanson, M. P.; Serafini, T. T.

1972-01-01

Numerical analysis of impact resistance of composite materials containing fibers is discussed. Mathematical model of longitudinal impact resistance is presented. Potential impact resistance of various fiber composites as obtained by numerical analysis is presented as plotted curve.

Methodology and Results of Mathematical Modelling of Complex Technological Processes

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

A Mathematical Model of Economic Population Dynamics in a Country That Has Optimal Zakat Management

NASA Astrophysics Data System (ADS)

Subhan, M.

2018-04-01

Zakat is the main tools against two issues in Islamic economy: economic justice and helping the poor. However, no government of Islamic countries can solve the economic disparity today. A mathematical model could give some understanding about this phenomenon. The goal of this research is to obtain a mathematical model that can describe the dynamic of economic group population. The research is theoretical based on relevance references. From the analytical and numerical simulation, we conclude that well-manage zakat and full comitment of the wealthy can achieve wealth equilibrium that represents minimum poverty.

An epidemiological model with vaccination strategies

NASA Astrophysics Data System (ADS)

Prates, Dérek B.; Silva, Jaqueline M.; Gomes, Jessica L.; Kritz, Maurício V.

2016-06-01

Mathematical models can be widely found in the literature describing epidemics. The epidemical models that use differential equations to represent mathematically such description are especially sensible to parameters. This work analyze a variation of the SIR model when applied to a epidemic scenario including several aspects, as constant vaccination, pulse vaccination, seasonality, cross-immunity factor, birth and dead rate. The analysis and results are performed through numerical solutions of the model and a special attention is given to the discussion generated by the paramenters variation.

A mathematical model for the Andean Tiwanaku civilization collapse: climate variations.

PubMed

Flores, J C; Bologna, Mauro; Urzagasti, Deterlino

2011-12-21

We propose a mathematical nonlinear model for the Tiwanaku civilization collapse based on the assumption, supported by archeological data, that a drought caused a lack of the main resource, water. We evaluate the parameter of our model using archaeological data. According to our numerical simulation the population core should have decreased from 45,000 to 2000 inhabitants due to lake surface contraction. Copyright © 2011 Elsevier Ltd. All rights reserved.

OPTIMIZATION OF COUNTERCURRENT STAGED PROCESSES.

DTIC Science & Technology

CHEMICAL ENGINEERING , OPTIMIZATION), (*DISTILLATION, OPTIMIZATION), INDUSTRIAL PRODUCTION, INDUSTRIAL EQUIPMENT, MATHEMATICAL MODELS, DIFFERENCE EQUATIONS, NONLINEAR PROGRAMMING, BOUNDARY VALUE PROBLEMS, NUMERICAL INTEGRATION

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.

The effect of numerical methods on the simulation of mid-ocean ridge hydrothermal models

NASA Astrophysics Data System (ADS)

Carpio, J.; Braack, M.

2012-01-01

This work considers the effect of the numerical method on the simulation of a 2D model of hydrothermal systems located in the high-permeability axial plane of mid-ocean ridges. The behavior of hot plumes, formed in a porous medium between volcanic lava and the ocean floor, is very irregular due to convective instabilities. Therefore, we discuss and compare two different numerical methods for solving the mathematical model of this system. In concrete, we consider two ways to treat the temperature equation of the model: a semi-Lagrangian formulation of the advective terms in combination with a Galerkin finite element method for the parabolic part of the equations and a stabilized finite element scheme. Both methods are very robust and accurate. However, due to physical instabilities in the system at high Rayleigh number, the effect of the numerical method is significant with regard to the temperature distribution at a certain time instant. The good news is that relevant statistical quantities remain relatively stable and coincide for the two numerical schemes. The agreement is larger in the case of a mathematical model with constant water properties. In the case of a model with nonlinear dependence of the water properties on the temperature and pressure, the agreement in the statistics is clearly less pronounced. Hence, the presented work accentuates the need for a strengthened validation of the compatibility between numerical scheme (accuracy/resolution) and complex (realistic/nonlinear) models.

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

ERIC Educational Resources Information Center

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings.

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development. This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Method and system to perform energy-extraction based active noise control

NASA Technical Reports Server (NTRS)

Kelkar, Atul (Inventor); Joshi, Suresh M. (Inventor)

2009-01-01

A method to provide active noise control to reduce noise and vibration in reverberant acoustic enclosures such as aircraft, vehicles, appliances, instruments, industrial equipment and the like is presented. A continuous-time multi-input multi-output (MIMO) state space mathematical model of the plant is obtained via analytical modeling and system identification. Compensation is designed to render the mathematical model passive in the sense of mathematical system theory. The compensated system is checked to ensure robustness of the passive property of the plant. The check ensures that the passivity is preserved if the mathematical model parameters are perturbed from nominal values. A passivity-based controller is designed and verified using numerical simulations and then tested. The controller is designed so that the resulting closed-loop response shows the desired noise reduction.

Numerical study of propagation of forest fires in the presence of fire breaks using an averaged setting

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

The forest fires spread in the pine forests have been numerically simulated using a three-dimensional mathematical model. The model was integrated with respect to the vertical coordinate because horizontal sizes of forest are much greater than the heights of trees. In this paper, the assignment and theoretical investigations of the problems of crown forest fires spread pass the firebreaks were carried out. In this context, a study ( mathematical modeling) of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with these fire breaks.

Extension of transonic flow computational concepts in the analysis of cavitated bearings

NASA Technical Reports Server (NTRS)

Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

1990-01-01

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries

NASA Astrophysics Data System (ADS)

Morales Escalante, José A.; Gamba, Irene M.

2018-06-01

We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann-Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k →). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.

An Innovative Learning Model for Computation in First Year Mathematics

ERIC Educational Resources Information Center

Tonkes, E. J.; Loch, B. I.; Stace, A. W.

2005-01-01

MATLAB is a sophisticated software tool for numerical analysis and visualization. The University of Queensland has adopted Matlab as its official teaching package across large first year mathematics courses. In the past, the package has met severe resistance from students who have not appreciated their computational experience. Several main…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

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.

A Mathematical Model of the Thermo-Anemometric Flowmeter

PubMed Central

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-01-01

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed. PMID:26378535

A Mathematical Model of the Thermo-Anemometric Flowmeter.

PubMed

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-09-11

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

A mathematical model of the passage of an asteroid-comet body through the Earth’s atmosphere

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

Shaydurov, V., E-mail: shaidurov04@mail.ru; Siberian Federal University, 79 Svobodny pr., 660041 Krasnoyarsk; Shchepanovskaya, G.

In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth’s atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) andmore » the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.« less

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Mathematical modeling of radiative-conductive heat transfer in semitransparent medium with phase change

NASA Astrophysics Data System (ADS)

Savvinova, Nadezhda A.; Sleptsov, Semen D.; Rubtsov, Nikolai A.

2017-11-01

A mathematical phase change model is a formulation of the Stefan problem. Various formulations of the Stefan problem modeling of radiative-conductive heat transfer during melting or solidification of a semitransparent material are presented. Analysis of numerical results show that the radiative heat transfer has a significant effect on temperature distributions during melting (solidification) of the semitransparent material. In this paper conditions for application of various statements of the Stefan problem are analyzed.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952

Mathematical manipulative models: in defense of "beanbag biology".

PubMed

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

The study of thermal processes in control systems of heat consumption of buildings

NASA Astrophysics Data System (ADS)

Tsynaeva, E.; A, Tsynaeva

2017-11-01

The article discusses the main thermal processes in the automated control systems for heat consumption (ACSHC) of buildings, schematic diagrams of these systems, mathematical models used for description of thermal processes in ACSHC. Conducted verification represented by mathematical models. It was found that the efficiency of the operation of ACSHC depend from the external and internal factors. Numerical study of dynamic modes of operation of ACSHC.

A simple mathematical model of society collapse applied to Easter Island

NASA Astrophysics Data System (ADS)

Bologna, M.; Flores, J. C.

2008-02-01

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.

A three-dimensional, time-dependent model of Mobile Bay

NASA Technical Reports Server (NTRS)

Pitts, F. H.; Farmer, R. C.

1976-01-01

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Development and Application of Numerical Models for Reactive Flows

DTIC Science & Technology

1990-08-15

Shear Layers: Ill. Effect of Convective Mach number Raafat H. Guirguis Abstract Model This paper addresses some of the fundamental We have made the...OTIC FILE COPY / 0 00 DTIC N~l 9 ELECTE D CbBA9-OI Development and Application of Numerical Models for Reactive Flows Berkeley Research Associates...Laboratory for Computa- tional Physics (LCP), hav focused on developing mathematical and computational models which accurately and efficiently describe the

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

PubMed

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-09-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Simulation of a class of hazardous situations in the ICS «INM RAS - Baltic Sea»

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Aseev, Nikita; Parmuzin, Eugene; Sheloput, Tateana; Shutyaev, Victor

2017-04-01

Development of Informational Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in mathematical modeling, theory of adjoint equations and optimal control, inverse problems, numerical methods theory, numerical algebra, scientific computing and processing of satellite data. In this work the results on the ICS development for PC-ICS "INM RAS - Baltic Sea" are presented. We discuss practical problems studied by ICS. The System includes numerical model of the Baltic Sea thermodynamics, the new oil spill model describing the propagation of a slick at the Sea surface (Agoshkov, Aseev et al., 2014) and the optimal ship route calculating block (Agoshkov, Zayachkovsky et al., 2014). The ICS is based on the INMOM numerical model of the Baltic Sea thermodynamics (Zalesny et al., 2013). It is possible to calculate main hydrodynamic parameters (temperature, salinity, velocities, sea level) using user-friendly interface of the ICS. The System includes data assimilation procedures (Agoshkov, 2003, Parmuzin, Agoshkov, 2012) and one can use the block of variational assimilation of the sea surface temperature in order to obtain main hydrodynamic parameters. Main possibilities of the ICS and several numerical experiments are presented in the work. By the problem of risk control is meant a problem of determination of optimal resources quantity which are necessary for decreasing the risk to some acceptable value. Mass of oil slick is chosen as a function of control. For the realization of the random variable the quadratic "functional of cost" is introduced. It comprises cleaning costs and deviation of damage of oil pollution from its acceptable value. The problem of minimization of this functional is solved based on the methods of optimal control and the theory of adjoint equations. The solution of this problem is explicitly found. The study was supported by the Russian Foundation for Basic Research (project 16-31-00510) and by the Russian Science Foundation (project №14-11-00609). V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling 28 (2013), No. 1, 85-100. V.I. Agoshkov, A.O. Zayachkovskiy, R. Aps, P. Kujala, and J. Rytkönen. Risk theory based solution to the problem of optimal vessel route // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 69-78. Agoshkov, V., Aseev, N., Aps, R., Kujala, P., Rytkönen, J., Zalesny, V. The problem of control of oil pollution risk in the Baltic Sea // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 93-105. E. I. Parmuzin and V. I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 69-94. Olof Liungman and Johan Mattsson. Scientic Documentation of Seatrack Web; physical processes, algorithms and references, 2011.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

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

Allen, Christopher K.

2017-07-01

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms ofmore » a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.« less

An analytical approach to top predator interference on the dynamics of a food chain model

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Vijayalakshmi, T.

2018-04-01

In this paper, a nonlinear mathematical model is proposed and analyzed to study of top predator interference on the dynamics of a food chain model. The mathematical model is formulated using the system of non-linear ordinary differential equations. In this model, there are three state dimensionless variables, viz, size of prey population x, size of intermediate predator y and size of top predator population z. The analytical results are compared with the numerical simulation using MATLAB software and satisfactory results are noticed.

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.

Study on the Effect of water Injection Momentum on the Cooling Effect of Rocket Engine Exhaust Plume

NASA Astrophysics Data System (ADS)

Yang, Kan; Qiang, Yanhui; Zhong, Chenghang; Yu, Shaozhen

2017-10-01

For the study of water injection momentum factors impact on flow field of the rocket engine tail flame, the numerical computation model of gas-liquid two phase flow in the coupling of high temperature and high speed gas flow and low temperature liquid water is established. The accuracy and reliability of the numerical model are verified by experiments. Based on the numerical model, the relationship between the flow rate and the cooling effect is analyzed by changing the water injection momentum of the water spray pipes. And the effective mathematical expression is obtained. What’s more, by changing the number of the water spray and using small flow water injection, the cooling effect is analyzed to check the application range of the mathematical expressions. The results show that: the impact and erosion of the gas flow field could be reduced greatly by water injection, and there are two parts in the gas flow field, which are the slow cooling area and the fast cooling area. In the fast cooling area, the influence of the water flow momentum and nozzle quantity on the cooling effect can be expressed by mathematical functions without causing bifurcation flow for the mainstream gas. The conclusion provides a theoretical reference for the engineering application.

Mathematical model of compact type evaporator

NASA Astrophysics Data System (ADS)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

Numerical simulation of injection process of warm carbon dioxide into layer saturated with methane and its hydrate

NASA Astrophysics Data System (ADS)

Khasanov, M. K.; Stolpovsky, M. V.; Gimaltdinov, I. K.

2018-05-01

In this article, in a flat-one-dimensional approximation, a mathematical model is presented for injecting warm carbon dioxide into a methane hydrate formation of finite length. It is established that the model of formation of hydrate of carbon dioxide in the absence of an area saturated with methane and water, under certain parameters, leads to thermodynamic contradiction. The mathematical model of carbon dioxide injection with formation of the region saturated with methane and water is constructed.

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

Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

The new version of the Institute of Numerical Mathematics Sigma Ocean Model (INMSOM) for simulation of Global Ocean circulation and its variability

NASA Astrophysics Data System (ADS)

Gusev, Anatoly; Fomin, Vladimir; Diansky, Nikolay; Korshenko, Evgeniya

2017-04-01

In this paper, we present the improved version of the ocean general circulation sigma-model developed in the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The previous version referred to as INMOM (Institute of Numerical Mathematics Ocean Model) is used as the oceanic component of the IPCC climate system model INMCM (Institute of Numerical Mathematics Climate Model (Volodin et al 2010,2013). Besides, INMOM as the only sigma-model was used for simulations according to CORE-II scenario (Danabasoglu et al. 2014,2016; Downes et al. 2015; Farneti et al. 2015). In general, INMOM results are comparable to ones of other OGCMs and were used for investigation of climatic variations in the North Atlantic (Gusev and Diansky 2014). However, detailed analysis of some CORE-II INMOM results revealed some disadvantages of the INMOM leading to considerable errors in reproducing some ocean characteristics. So, the mass transport in the Antarctic Circumpolar Current (ACC) was overestimated. As well, there were noticeable errors in reproducing thermohaline structure of the ocean. After analysing the previous results, the new version of the OGCM was developed. It was decided to entitle is INMSOM (Institute of Numerical Mathematics Sigma Ocean Model). The new title allows one to distingwish the new model, first, from its older version, and second, from another z-model developed in the INM RAS and referred to as INMIO (Institute of Numerical Mathematics and Institute of Oceanology ocean model) (Ushakov et al. 2016). There were numerous modifications in the model, some of them are as follows. 1) Formulation of the ocean circulation problem in terms of full free surface with taking into account water amount variation. 2) Using tensor form of lateral viscosity operator invariant to rotation. 3) Using isopycnal diffusion including Gent-McWilliams mixing. 4) Using atmospheric forcing computation according to NCAR methodology (Large and Yeager 2009). 5) Improvement river runoff algorithm accounting the total amount of discharged water. 6) Using explicit leapfrog time scheme for all lateral operators and implicit Euler scheme for vertical diffusion and viscosity. The INMSOM is tested by reproducing World Ocean circulation and thermohaline characteristics using the well-proved CORE dataset. The presentation is devoted to the analysis of new INMSOM simulation results, estimation of their quality and comparison to the ones previously obtained with the INMOM. The main aim of the INMSOM development is using it as the oceanic component of the next version of INMCM. The work was supported by the Russian Foundation for Basic Research (grants № 16-05-00534 and № 15-05-07539) References 1. Danabasoglu, G., Yeager S.G., Bailey D., et al., 2014: North Atlantic simulations in Coordinated Ocean-ice Reference Experiments phase II (CORE-II). Part I: Mean states. Ocean Modelling, 73, 76-107. 2. Danabasoglu, G., Yeager S.G., Kim W.M. et al., 2016: North Atlantic simulations in Coordinated Ocean-ice Reference Experiments phase II (CORE-II). Part II: Inter-annual to decadal variability. Ocean Modelling, 97, 65-90. 3. Downes S.M., Farneti R., Uotila P. et al. An assessment of Southern Ocean water masses and sea ice during 1988-2007 in a suite of interannual CORE-II simulations. Ocean Modelling (2015), 94, 67-94. 4. Farneti R., Downes S.M., Griffies S.M. et al. An assessment of Antarctic Circumpolar Current and Southern Ocean Meridional Overturning Circulation during 1958-2007 in a suite of interannual CORE-II simulations, Ocean Modelling (2015), 93, 84-120. 5. Gusev A.V. and Diansky N.A. Numerical simulation of the World ocean circulation and its climatic variability for 1948-2007 using the INMOM. Izvestiya, Atmospheric and Oceanic Physics, 2014, V. 50, N. 1, P. 1-12 6. Large, W., Yeager, S., 2009. The global climatology of an interannually varying air-sea flux data set. Clim Dyn, V. 33, P. 341-364. 7. Ushakov K.V., Grankina T.B., Ibraev R.A. Modeling the water circulation in the North Atlantic in the scope of the CORE-II experiment. Izvestiya, Atmospheric and Oceanic Physics. 2016. V. 52, № 4, P. 365-375

Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method

NASA Astrophysics Data System (ADS)

Eremin, Yu. A.; Sveshnikov, A. G.

2018-04-01

The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

Using Computational and Mechanical Models to Study Animal Locomotion

PubMed Central

Miller, Laura A.; Goldman, Daniel I.; Hedrick, Tyson L.; Tytell, Eric D.; Wang, Z. Jane; Yen, Jeannette; Alben, Silas

2012-01-01

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.” PMID:22988026

Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

NASA Astrophysics Data System (ADS)

Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.

2017-10-01

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.

EVALUATION OF UNSATURATED/VADOSE ZONE MODELS FOR SUPERFUND SITES

EPA Science Inventory

Mathematical models of water and chemical movement in soils are being used as decision aids for defining groundwater protection practices for Superfund sites. Numerous transport models exist for predicting movementand degradation of hazardous chemicals through soils. Many of thes...

Relations of different types of numerical magnitude representations to each other and to mathematics achievement.

PubMed

Fazio, Lisa K; Bailey, Drew H; Thompson, Clarissa A; Siegler, Robert S

2014-07-01

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both magnitude comparison and number line estimation tasks. After controlling for non-mathematical cognitive proficiency, both symbolic and non-symbolic numerical magnitude understandings were uniquely related to mathematics achievement, but the relation was much stronger for symbolic numbers. A meta-analysis of 19 published studies indicated that relations between non-symbolic numerical magnitude knowledge and mathematics achievement are present but tend to be weak, especially beyond 6 years of age. Copyright © 2014 Elsevier Inc. All rights reserved.

Theoretical and experimental researches of the liquid evaporation during thermal vacuum influences

NASA Astrophysics Data System (ADS)

Trushlyakov, V.; Panichkin, A.; Prusova, O.; Zharikov, K.; Dron, M.

2018-01-01

The mathematical model of the evaporation process of model liquid with the free surface boundary conditions of the "mirror" type under thermal vacuum influence and the numerical estimates of the evaporation process parameters are developed. An experimental stand, comprising a vacuum chamber, an experimental model tank with a heating element is designed; the experimental data are obtained. A comparative analysis of numerical and experimental results showed their close match.

Numerical Simulation of Rheological, Chemical and Hydromechanical Processes of Thrombolysis

NASA Astrophysics Data System (ADS)

Khramchenkov, E.; Khramchenkov, M.

2015-04-01

Mathematical model of clot lysis in blood vessels is developed on the basis of equations of convection-diffusion. Fibrin of the clot is considered stationary solid phase, and plasminogen, plasmin and plasminogen-activators - as dissolved fluid phases. As a result of numerical solution of the model predictions of lysis process are gained. Important influence of clot swelling on the process of lysis is revealed.

Numerical Simulation Of Silicon-Ribbon Growth

NASA Technical Reports Server (NTRS)

Woda, Ben K.; Kuo, Chin-Po; Utku, Senol; Ray, Sujit Kumar

1987-01-01

Mathematical model includes nonlinear effects. In development simulates growth of silicon ribbon from melt. Takes account of entire temperature and stress history of ribbon. Numerical simulations performed with new model helps in search for temperature distribution, pulling speed, and other conditions favoring growth of wide, flat, relatively defect-free silicon ribbons for solar photovoltaic cells at economically attractive, high production rates. Also applicable to materials other than silicon.

A mathematical model for ethanol fermentation from oil palm trunk sap using Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Sultana, S.; Jamil, Norazaliza Mohd; Saleh, E. A. M.; Yousuf, A.; Faizal, Che Ku M.

2017-09-01

This paper presents a mathematical model and solution strategy of ethanol fermentation for oil palm trunk (OPT) sap by considering the effect of substrate limitation, substrate inhibition product inhibition and cell death. To investigate the effect of cell death rate on the fermentation process we extended and improved the current mathematical model. The kinetic parameters of the model were determined by nonlinear regression using maximum likelihood function. The temporal profiles of sugar, cell and ethanol concentrations were modelled by a set of ordinary differential equations, which were solved numerically by the 4th order Runge-Kutta method. The model was validated by the experimental data and the agreement between the model and experimental results demonstrates that the model is reasonable for prediction of the dynamic behaviour of the fermentation process.

Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

PubMed Central

Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.

2015-01-01

Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372

Mathematical model of the glucose-insulin regulatory system: From the bursting electrical activity in pancreatic β-cells to the glucose dynamics in the whole body

NASA Astrophysics Data System (ADS)

Han, Kyungreem; Kang, Hyuk; Choi, M. Y.; Kim, Jinwoong; Lee, Myung-Shik

2012-10-01

A theoretical approach to the glucose-insulin regulatory system is presented. By means of integrated mathematical modeling and extensive numerical simulations, we probe the cell-level dynamics of the membrane potential, intracellular Ca2+ concentration, and insulin secretion in pancreatic β-cells, together with the whole-body level glucose-insulin dynamics in the liver, brain, muscle, and adipose tissues. In particular, the three oscillatory modes of insulin secretion are reproduced successfully. Such comprehensive mathematical modeling may provide a theoretical basis for the simultaneous assessment of the β-cell function and insulin resistance in clinical examination.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Modeling and numerical simulations of the influenced Sznajd model

NASA Astrophysics Data System (ADS)

Karan, Farshad Salimi Naneh; Srinivasan, Aravinda Ramakrishnan; Chakraborty, Subhadeep

2017-08-01

This paper investigates the effects of independent nonconformists or influencers on the behavioral dynamic of a population of agents interacting with each other based on the Sznajd model. The system is modeled on a complete graph using the master equation. The acquired equation has been numerically solved. Accuracy of the mathematical model and its corresponding assumptions have been validated by numerical simulations. Regions of initial magnetization have been found from where the system converges to one of two unique steady-state PDFs, depending on the distribution of influencers. The scaling property and entropy of the stationary system in presence of varying level of influence have been presented and discussed.

Modeling and numerical simulations of the influenced Sznajd model.

PubMed

Karan, Farshad Salimi Naneh; Srinivasan, Aravinda Ramakrishnan; Chakraborty, Subhadeep

2017-08-01

This paper investigates the effects of independent nonconformists or influencers on the behavioral dynamic of a population of agents interacting with each other based on the Sznajd model. The system is modeled on a complete graph using the master equation. The acquired equation has been numerically solved. Accuracy of the mathematical model and its corresponding assumptions have been validated by numerical simulations. Regions of initial magnetization have been found from where the system converges to one of two unique steady-state PDFs, depending on the distribution of influencers. The scaling property and entropy of the stationary system in presence of varying level of influence have been presented and discussed.

Numerical simulations of a reduced model for blood coagulation

NASA Astrophysics Data System (ADS)

Pavlova, Jevgenija; Fasano, Antonio; Sequeira, Adélia

2016-04-01

In this work, the three-dimensional numerical resolution of a complex mathematical model for the blood coagulation process is presented. The model was illustrated in Fasano et al. (Clin Hemorheol Microcirc 51:1-14, 2012), Pavlova et al. (Theor Biol 380:367-379, 2015). It incorporates the action of the biochemical and cellular components of blood as well as the effects of the flow. The model is characterized by a reduction in the biochemical network and considers the impact of the blood slip at the vessel wall. Numerical results showing the capacity of the model to predict different perturbations in the hemostatic system are discussed.

The Transition from Informal to Formal Mathematical Knowledge: Mediation by Numeral Knowledge

ERIC Educational Resources Information Center

Purpura, David J.; Baroody, Arthur J.; Lonigan, Christopher J.

2013-01-01

The purpose of the present study was to determine if numeral knowledge--the ability to identify Arabic numerals and connect Arabic numerals to their respective quantities--mediates the relation between informal and formal mathematical knowledge. A total of 206 3- to 5-year-old preschool children were assessed on 6 informal mathematics tasks and 2…

Effects of Finger Counting on Numerical Development – The Opposing Views of Neurocognition and Mathematics Education

PubMed Central

Moeller, Korbinian; Martignon, Laura; Wessolowski, Silvia; Engel, Joachim; Nuerk, Hans-Christoph

2011-01-01

Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis, or “finger sense,” enhances mathematical skills. Therefore neurocognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development. However, research in mathematics education recommends fostering mentally based numerical representations so as to induce children to abandon finger counting. More precisely, mathematics education recommends first using finger counting, then concrete structured representations and, finally, mental representations of numbers to perform numerical operations. Taken together, these results reveal an important debate between neurocognitive and mathematics education research concerning the benefits and detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be discussed. PMID:22144969

In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue.

PubMed

Antonopoulos, Markos; Stamatakos, Georgios

2015-01-01

Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

2003-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

Role of mathematical models in assessment of risk and in attempts to define management strategy.

PubMed

Flamm, W G; Winbush, J S

1984-06-01

Risk assessment of food-borne carcinogens is becoming a common practice at FDA. Actual risk is not being estimated, only the upper limit of risk. The risk assessment process involves a large number of steps and assumptions, many of which affect the numerical value estimated. The mathematical model which is to be applied is only one of the factors which affect these numerical values. To fulfill the policy objective of using the "worst plausible case" in estimating the upper limit of risk, recognition needs to be given to a proper balancing of assumptions and decisions. Interaction between risk assessors and risk managers should avoid making or giving the appearance of making specific technical decisions such as the choice of the mathematical model. The importance of this emerging field is too great to jeopardize it by inappropriately mixing scientific judgments with policy judgments. The risk manager should understand fully the points and range of uncertainty involved in arriving at the estimates of risk which must necessarily affect the choice of the policy or regulatory options available.

Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions.

PubMed

Schmithorst, Vincent J; Brown, Rhonda Douglas

2004-07-01

The suitability of a previously hypothesized triple-code model of numerical processing, involving analog magnitude, auditory verbal, and visual Arabic codes of representation, was investigated for the complex mathematical task of the mental addition and subtraction of fractions. Functional magnetic resonance imaging (fMRI) data from 15 normal adult subjects were processed using exploratory group Independent Component Analysis (ICA). Separate task-related components were found with activation in bilateral inferior parietal, left perisylvian, and ventral occipitotemporal areas. These results support the hypothesized triple-code model corresponding to the activated regions found in the individual components and indicate that the triple-code model may be a suitable framework for analyzing the neuropsychological bases of the performance of complex mathematical tasks. Copyright 2004 Elsevier Inc.

A Mathematical Model for the Exhaust Gas Temperature Profile of a Diesel Engine

NASA Astrophysics Data System (ADS)

Brito, C. H. G.; Maia, C. B.; Sodré, J. R.

2015-09-01

This work presents a heat transfer model for the exhaust gas of a diesel power generator to determine the gas temperature profile in the exhaust pipe. The numerical methodology to solve the mathematical model was developed using a finite difference method approach for energy equation resolution and determination of temperature profiles considering turbulent fluid flow and variable fluid properties. The simulation was carried out for engine operation under loads from 0 kW to 40 kW. The model was compared with results obtained using the multidimensional Ansys CFX software, which was applied to solve the governor equations of turbulent fluid flow. The results for the temperature profiles in the exhaust pipe show a good proximity between the mathematical model developed and the multidimensional software.

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

2017-12-01

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.

Parametric diagnosis of the adaptive gas path in the automatic control system of the aircraft engine

NASA Astrophysics Data System (ADS)

Kuznetsova, T. A.

2017-01-01

The paper dwells on the adaptive multimode mathematical model of the gas-turbine aircraft engine (GTE) embedded in the automatic control system (ACS). The mathematical model is based on the throttle performances, and is characterized by high accuracy of engine parameters identification in stationary and dynamic modes. The proposed on-board engine model is the state space linearized low-level simulation. The engine health is identified by the influence of the coefficient matrix. The influence coefficient is determined by the GTE high-level mathematical model based on measurements of gas-dynamic parameters. In the automatic control algorithm, the sum of squares of the deviation between the parameters of the mathematical model and real GTE is minimized. The proposed mathematical model is effectively used for gas path defects detecting in on-line GTE health monitoring. The accuracy of the on-board mathematical model embedded in ACS determines the quality of adaptive control and reliability of the engine. To improve the accuracy of identification solutions and sustainability provision, the numerical method of Monte Carlo was used. The parametric diagnostic algorithm based on the LPτ - sequence was developed and tested. Analysis of the results suggests that the application of the developed algorithms allows achieving higher identification accuracy and reliability than similar models used in practice.

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

A Novel Numerical Method for Fuzzy Boundary Value Problems

NASA Astrophysics Data System (ADS)

Can, E.; Bayrak, M. A.; Hicdurmaz

2016-05-01

In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

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.

Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

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

Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.

1975-11-01

A mathematical model and a numerical solution scheme for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)

On mathematical modelling of flameless combustion

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

Mancini, Marco; Schwoeppe, Patrick; Weber, Roman

2007-07-15

A further analysis of the IFRF semi-industrial-scale experiments on flameless (mild) combustion of natural gas is carried out. The experimental burner features a strong oxidizer jet and two weak natural gas jets. Numerous publications have shown the inability of various RANS-based mathematical models to predict the structure of the weak jet. We have proven that the failure is in error predictions of the entrainment and therefore is not related to any chemistry submodels, as has been postulated. (author)

The Influence of Pre-University Students' Mathematics Test Anxiety and Numerical Anxiety on Mathematics Achievement

ERIC Educational Resources Information Center

Seng, Ernest Lim Kok

2015-01-01

This study examines the relationship between mathematics test anxiety and numerical anxiety on students' mathematics achievement. 140 pre-university students who studied at one of the institutes of higher learning were being investigated. Gender issue pertaining to mathematics anxieties was being addressed besides investigating the magnitude of…

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.

Computational method for analysis of polyethylene biodegradation

NASA Astrophysics Data System (ADS)

Watanabe, Masaji; Kawai, Fusako; Shibata, Masaru; Yokoyama, Shigeo; Sudate, Yasuhiro

2003-12-01

In a previous study concerning the biodegradation of polyethylene, we proposed a mathematical model based on two primary factors: the direct consumption or absorption of small molecules and the successive weight loss of large molecules due to β-oxidation. Our model is an initial value problem consisting of a differential equation whose independent variable is time. Its unknown variable represents the total weight of all the polyethylene molecules that belong to a molecular-weight class specified by a parameter. In this paper, we describe a numerical technique to introduce experimental results into analysis of our model. We first establish its mathematical foundation in order to guarantee its validity, by showing that the initial value problem associated with the differential equation has a unique solution. Our computational technique is based on a linear system of differential equations derived from the original problem. We introduce some numerical results to illustrate our technique as a practical application of the linear approximation. In particular, we show how to solve the inverse problem to determine the consumption rate and the β-oxidation rate numerically, and illustrate our numerical technique by analyzing the GPC patterns of polyethylene wax obtained before and after 5 weeks cultivation of a fungus, Aspergillus sp. AK-3. A numerical simulation based on these degradation rates confirms that the primary factors of the polyethylene biodegradation posed in modeling are indeed appropriate.

Dynamic behavior of a rolling housing

NASA Astrophysics Data System (ADS)

Gentile, A.; Messina, A. M.; Trentadue, Bartolo

1994-09-01

One of the major objectives of industry is to curtail costs. An element, among others, that enables to achieve such goal is the efficiency of the production cycle machines. Such efficiency lies in the reliability of the upkeeping operations. Among maintenance procedures, measuring and analyzing vibrations is a way to detect structure modifications over the machine's lifespan. Further, the availability of a mathematical model describing the influence of each individual part of the machine on the total dynamic behavior of the whole machine may help localizing breakdowns during diagnosis operations. The paper hereof illustrates an analytical-numerical model which can simulate the behavior of a rolling housing. The aforesaid mathematical model has been obtained by FEM techniques, the dynamic response by mode superposition and the synthesis of the vibration time sequence in the frequency versus by FFT numerical techniques.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school.

PubMed

Cerda, Gamal; Pérez, Carlos; Navarro, José I; Aguilar, Manuel; Casas, José A; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students' level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics

NASA Technical Reports Server (NTRS)

Zhu, J. Z.; He, Guowei; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

Numerical simulation has now become an integral part of engineering design process. Critical design decisions are routinely made based on the simulation results and conclusions. Verification and validation of the reliability of the numerical simulation is therefore vitally important in the engineering design processes. We propose to develop theories and methodologies that can automatically provide quantitative information about the reliability of the numerical simulation by estimating numerical approximation error, computational model induced errors and the uncertainties contained in the mathematical models so that the reliability of the numerical simulation can be verified and validated. We also propose to develop and implement methodologies and techniques that can control the error and uncertainty during the numerical simulation so that the reliability of the numerical simulation can be improved.

Numerical analysis and experimental research of the rubber boot of the joint drive vehicle

NASA Astrophysics Data System (ADS)

Ziobro, Jan

2016-04-01

The article presents many numerical studies and experimental research of the drive rubber boot of the joint drive vehicle. Performance requirements have been discussed and the required coefficients of the mathematical model for numerical simulation have been determined. The behavior of living in MSC.MARC environment was examined. In the analysis the following have been used: hyperplastic two-parameter model of the Mooney-Rivlin material, large displacements procedure, safe contact condition, friction on the sides of the boots. 3D numerical model of the joint bootwas analyzed under influence of the forces: tensile, compressive, centrifugal and angular. Numerous results of studies have been presented. An appropriate test stand was built and comparison of the results of the numerical analysis and the results of experimental studies was made. Numerous requests and recommendations for utilitarian character have been presented.

An attempt at the computer-aided management of HIV infection

NASA Astrophysics Data System (ADS)

Ida, A.; Oharu, Y.; Sankey, O.

2007-07-01

The immune system is a complex and diverse system in the human body and HIV virus disrupts and destroys it through extremely complicated but surprisingly logical process. The purpose of this paper is to make an attempt to present a method for the computer-aided management of HIV infection process by means of a mathematical model describing the dynamics of the host pathogen interaction with HIV-1. Treatments for the AIDS disease must be changed to more efficient ones in accordance with the disease progression and the status of the immune system. The level of progression and the status are represented by parameters which are governed by our mathematical model. It is then exhibited that our model is numerically stable and uniquely solvable. With this knowledge, our mathematical model for HIV disease progression is formulated and physiological interpretations are provided. The results of our numerical simulations are visualized, and it is seen that our results agree with medical aspects from the point of view of antiretroviral therapy. It is then expected that our approach will take to address practical clinical issues and will be applied to the computer-aided management of antiretroviral therapies.

Foxes and Rabbits - and a Spreadsheet.

ERIC Educational Resources Information Center

Carson, S. R.

1996-01-01

Presents a numerical simulation of a simple food chain together with a set of mathematical rules generalizing the model to a food web of any complexity. Discusses some of the model's interesting features and its use by students. (Author/JRH)

Numerical simulation of dynamics of brushless dc motors for aerospace and other applications. Volume 1: Model development and applications, part A

NASA Technical Reports Server (NTRS)

Demerdash, N. A. O.; Nehl, T. W.

1979-01-01

The development, fabrication and evaluation of a prototype electromechanical actuator (EMA) is discussed. Application of the EMA as a motor for control surfaces in aerospace flight is examined. A mathematical model of the EMA is developed for design optimization. Nonlinearities which complicate the mathematical model are discussed. The dynamics of the EMA from the underlying physical principles are determined and a discussion of similating the control logic by means of equivalent boolean expressions is presented.

Numerical modeling of heat transfer in the fuel oil storage tank at thermal power plant

NASA Astrophysics Data System (ADS)

Kuznetsova, Svetlana A.

2015-01-01

Presents results of mathematical modeling of convection of a viscous incompressible fluid in a rectangular cavity with conducting walls of finite thickness in the presence of a local source of heat in the bottom of the field in terms of convective heat exchange with the environment. A mathematical model is formulated in terms of dimensionless variables "stream function - vorticity vector speed - temperature" in the Cartesian coordinate system. As the results show the distributions of hydrodynamic parameters and temperatures using different boundary conditions on the local heat source.

Mathematical model describing the thyroids-pituitary axis with distributed time delays in hormone transportation

NASA Astrophysics Data System (ADS)

Neamţu, Mihaela; Stoian, Dana; Navolan, Dan Bogdan

2014-12-01

In the present paper we provide a mathematical model that describe the hypothalamus-pituitary-thyroid axis in autoimmune (Hashimoto's) thyroiditis. Since there is a spatial separation between thyroid and pituitary gland in the body, time is needed for transportation of thyrotropin and thyroxine between the glands. Thus, the distributed time delays are considered as both weak and Dirac kernels. The delayed model is analyzed regarding the stability and bifurcation behavior. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.

Chancroid transmission dynamics: a mathematical modeling approach.

PubMed

Bhunu, C P; Mushayabasa, S

2011-12-01

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.

The mathematical modeling of rapid solidification processing. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Gutierrez-Miravete, E.

1986-01-01

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

A study of the dynamics of rotating space stations with elastically connected counterweight and attached flexible appendages. Volume 1: Theory

NASA Technical Reports Server (NTRS)

Austin, F.; Markowitz, J.; Goldenberg, S.; Zetkov, G. A.

1973-01-01

The formulation of a mathematical model for predicting the dynamic behavior of rotating flexible space station configurations was conducted. The overall objectives of the study were: (1) to develop the theoretical techniques for determining the behavior of a realistically modeled rotating space station, (2) to provide a versatile computer program for the numerical analysis, and (3) to present practical concepts for experimental verification of the analytical results. The mathematical model and its associated computer program are described.

ON SOME MATHEMATICAL PROBLEMS SUGGESTED BY BIOLOGICAL SCHEMES

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

Luehr, C.

1958-08-01

A simplified model of a population which reproduces asexually and is subject to random mututions implying improvement in chances of survival and procreation is treated by a numerical calculation. The behavior of such a system is then summarized by an analytical formula. The paper is intended as the first one of a series devoted to mathematical studies of simplified genetic situations. (auth)

Numerical approaches to model perturbation fire in turing pattern formations

NASA Astrophysics Data System (ADS)

Campagna, R.; Brancaccio, M.; Cuomo, S.; Mazzoleni, S.; Russo, L.; Siettos, K.; Giannino, F.

2017-11-01

Turing patterns were observed in chemical, physical and biological systems described by coupled reaction-diffusion equations. Several models have been formulated proposing the water as the causal mechanism of vegetation pattern formation, but this isn't an exhaustive hypothesis in some natural environments. An alternative explanation has been related to the plant-soil negative feedback. In Marasco et al. [1] the authors explored the hypothesis that both mechanisms contribute in the formation of regular and irregular vegetation patterns. The mathematical model consists in three partial differential equations (PDEs) that take into account for a dynamic balance between biomass, water and toxic compounds. A numerical approach is mandatory also to investigate on the predictions of this kind of models. In this paper we start from the mathematical model described in [1], set the model parameters such that the biomass reaches a stable spatial pattern (spots) and present preliminary studies about the occurrence of perturbing events, such as wildfire, that can affect the regularity of the biomass configuration.

The MATH--Open Source Application for Easier Learning of Numerical Mathematics

ERIC Educational Resources Information Center

Glaser-Opitz, Henrich; Budajová, Kristina

2016-01-01

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Numerical Ordering Ability Mediates the Relation between Number-Sense and Arithmetic Competence

ERIC Educational Resources Information Center

Lyons, Ian M.; Beilock, Sian L.

2011-01-01

What predicts human mathematical competence? While detailed models of number representation in the brain have been developed, it remains to be seen exactly how basic number representations link to higher math abilities. We propose that representation of ordinal associations between numerical symbols is one important factor that underpins this…

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.

Computational ecology as an emerging science

PubMed Central

Petrovskii, Sergei; Petrovskaya, Natalia

2012-01-01

It has long been recognized that numerical modelling and computer simulations can be used as a powerful research tool to understand, and sometimes to predict, the tendencies and peculiarities in the dynamics of populations and ecosystems. It has been, however, much less appreciated that the context of modelling and simulations in ecology is essentially different from those that normally exist in other natural sciences. In our paper, we review the computational challenges arising in modern ecology in the spirit of computational mathematics, i.e. with our main focus on the choice and use of adequate numerical methods. Somewhat paradoxically, the complexity of ecological problems does not always require the use of complex computational methods. This paradox, however, can be easily resolved if we recall that application of sophisticated computational methods usually requires clear and unambiguous mathematical problem statement as well as clearly defined benchmark information for model validation. At the same time, many ecological problems still do not have mathematically accurate and unambiguous description, and available field data are often very noisy, and hence it can be hard to understand how the results of computations should be interpreted from the ecological viewpoint. In this scientific context, computational ecology has to deal with a new paradigm: conventional issues of numerical modelling such as convergence and stability become less important than the qualitative analysis that can be provided with the help of computational techniques. We discuss this paradigm by considering computational challenges arising in several specific ecological applications. PMID:23565336

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

Jablonská, Jana, E-mail: jana.jablonska@vsb.cz; Kozubková, Milada, E-mail: milada.kozubkova@vsb.cz

Cavitation today is a very important problem that is solved by means of experimental and mathematical methods. The article deals with the generation of cavitation in convergent divergent nozzle of rectangular cross section. Measurement of pressure, flow rate, temperature, amount of dissolved air in the liquid and visualization of cavitation area using high-speed camera was performed for different flow rates. The measurement results were generalized by dimensionless analysis, which allows easy detection of cavitation in the nozzle. For numerical simulation the multiphase mathematical model of cavitation consisting of water and vapor was created. During verification the disagreement with the measurementsmore » for higher flow rates was proved, therefore the model was extended to multiphase mathematical model (water, vapor and air), due to release of dissolved air. For the mathematical modeling the multiphase turbulence RNG k-ε model for low Reynolds number flow with vapor and air cavitation was used. Subsequently the sizes of the cavitation area were verified. In article the inlet pressure and loss coefficient depending on the amount of air added to the mathematical model are evaluated. On the basis of the approach it may be create a methodology to estimate the amount of released air added at the inlet to the modeled area.« less

Determination of thermophysical characteristics of vulcanizable rubber products by the mathematical modeling method

NASA Astrophysics Data System (ADS)

Tikhomirov, S. G.; Pyatakov, Y. V.; Karmanova, O. V.; Maslov, A. A.

2018-03-01

The studies of the vulcanization kinetics of elastomers were carried out using a Truck tyre tread rubber compound. The formal kinetic scheme of vulcanization of rubbers sulfur-accelerator curing system was used which generalizes the set of reactions occurring in the curing process. A mathematical model is developed for determining the thermal parameters vulcanizable mixture comprising algorithms for solving direct and inverse problems for system of equations of heat conduction and kinetics of the curing process. The performance of the model is confirmed by the results of numerical experiments on model examples.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Nature and origins of mathematics difficulties in very preterm children: a different etiology than developmental dyscalculia.

PubMed

Simms, Victoria; Gilmore, Camilla; Cragg, Lucy; Clayton, Sarah; Marlow, Neil; Johnson, Samantha

2015-02-01

Children born very preterm (<32 wk) are at high risk for mathematics learning difficulties that are out of proportion to other academic and cognitive deficits. However, the etiology of mathematics difficulties in very preterm children is unknown. We sought to identify the nature and origins of preterm children's mathematics difficulties. One hundred and fifteen very preterm children aged 8-10 y were assessed in school with a control group of 77 term-born classmates. Achievement in mathematics, working memory, visuospatial processing, inhibition, and processing speed were assessed using standardized tests. Numerical representations and specific mathematics skills were assessed using experimental tests. Very preterm children had significantly poorer mathematics achievement, working memory, and visuospatial skills than term-born controls. Although preterm children had poorer performance in specific mathematics skills, there was no evidence of imprecise numerical representations. Difficulties in mathematics were associated with deficits in visuospatial processing and working memory. Mathematics difficulties in very preterm children are associated with deficits in working memory and visuospatial processing not numerical representations. Thus, very preterm children's mathematics difficulties are different in nature from those of children with developmental dyscalculia. Interventions targeting general cognitive problems, rather than numerical representations, may improve very preterm children's mathematics achievement.

Development Of Maneuvering Autopilot For Flight Tests

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Walker, R. A.

1992-01-01

Report describes recent efforts to develop automatic control system operating under supervision of pilot and making airplane follow prescribed trajectories during flight tests. Report represents additional progress on this project. Gives background information on technology of control of test-flight trajectories; presents mathematical models of airframe, engine and command-augmentation system; focuses on mathematical modeling of maneuvers; addresses design of autopilots for maneuvers; discusses numerical simulation and evaluation of results of simulation of eight maneuvers under control of simulated autopilot; and presents summary and discussion of future work.

Scilab software as an alternative low-cost computing in solving the linear equations problem

NASA Astrophysics Data System (ADS)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

Stochastic growth logistic model with aftereffect for batch fermentation process

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

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Mathematical Modelling of Bacterial Populations in Bio-remediation Processes

NASA Astrophysics Data System (ADS)

Vasiliadou, Ioanna A.; Vayenas, Dimitris V.; Chrysikopoulos, Constantinos V.

2011-09-01

An understanding of bacterial behaviour concerns many field applications, such as the enhancement of water, wastewater and subsurface bio-remediation, the prevention of environmental pollution and the protection of human health. Numerous microorganisms have been identified to be able to degrade chemical pollutants, thus, a variety of bacteria are known that can be used in bio-remediation processes. In this study the development of mathematical models capable of describing bacterial behaviour considered in bio-augmentation plans, such as bacterial growth, consumption of nutrients, removal of pollutants, bacterial transport and attachment in porous media, is presented. The mathematical models may be used as a guide in designing and assessing the conditions under which areas contaminated with pollutants can be better remediated.

Time-Series INSAR: An Integer Least-Squares Approach For Distributed Scatterers

NASA Astrophysics Data System (ADS)

Samiei-Esfahany, Sami; Hanssen, Ramon F.

2012-01-01

The objective of this research is to extend the geode- tic mathematical model which was developed for persistent scatterers to a model which can exploit distributed scatterers (DS). The main focus is on the integer least- squares framework, and the main challenge is to include the decorrelation effect in the mathematical model. In order to adapt the integer least-squares mathematical model for DS we altered the model from a single master to a multi-master configuration and introduced the decorrelation effect stochastically. This effect is described in our model by a full covariance matrix. We propose to de- rive this covariance matrix by numerical integration of the (joint) probability distribution function (PDF) of interferometric phases. This PDF is a function of coherence values and can be directly computed from radar data. We show that the use of this model can improve the performance of temporal phase unwrapping of distributed scatterers.

A study of direct moxibustion using mathematical methods.

PubMed

Liu, Miao; Kauh, Sang Ken; Lim, Sabina

2012-01-01

Direct moxibustion is an important and widely used treatment method in traditional medical science. The use of a mathematical method to analyse direct moxibustion treatment is necessary and helpful in exploring the new direct moxibustion instruments and their standardisation. Thus, this paper aims to use a mathematical method to study direct moxibustion in skin to demonstrate a direct relationship between direct moxibustion and skin stimuli. In this paper, the transient thermal response of skin layers is analysed to study direct moxibustion using the data got from standardised method to measure the temperature of a burning moxa cone. Numerical simulations based on an appropriate finite element model are developed to predict the heat transfer, thermal damage and thermal stress distribution of barley moxa cones and jujube moxa cones in the skin tissue. The results are verified by the ancient literatures of traditional Chinese medicine and clinical application, and showed that mathematical method can be a good interface between moxa cone and skin tissue providing the numerical value basis for moxibustion.

A Long-Term Mathematical Model for Mining Industries

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Giraud, Pierre-Noel; Lasry, Jean-Michel

A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In somemore » cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.« less

Numerical Magnitude Representation in Children With Mathematical Difficulties With or Without Reading Difficulties.

PubMed

Tobia, Valentina; Fasola, Anna; Lupieri, Alice; Marzocchi, Gian Marco

2016-01-01

This study aimed to explore the spatial numerical association of response codes (SNARC), the flanker, and the numerical distance effects in children with mathematical difficulties. From a sample of 720 third, fourth, and fifth graders, 60 children were selected and divided into the following three groups: typically developing children (TD; n = 29), children with mathematical difficulties only (MD only; n = 21), and children with mathematical and reading difficulties (MD+RD; n = 10). Children were tested with a numerical Eriksen task that was built to assess SNARC, numerical distance, and flanker (first and second order congruency) effects. Children with MD only showed stronger SNARC and second order congruency effects than did TD children, whereas the numerical distance effects were similar across the three groups. Finally, the first order congruency effect was associated with reading difficulties. These results showed that children with mathematical difficulties with or without reading difficulties were globally more impaired when spatial incompatibilities were presented. © Hammill Institute on Disabilities 2014.

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.

Mathematical Modeling of Multiphase Filtration in Porous Media with a Chemically Active Skeleton

NASA Astrophysics Data System (ADS)

Khramchenkov, M. G.; Khramchenkov, É. M.

2018-01-01

The authors propose a mathematical model of two-phase filtration that occurs under the conditions of dissolution of a porous medium. The model can be used for joint description of complex chemical-hydrogeomechanical processes that are of frequent occurrence in the oil-and-gas producing and nature conservation practice. As an example, consideration is given to the acidizing of the bottom zone of the injection well of an oil reservoir. Enclosing rocks are represented by carbonates. The phases of the process are an aqueous solution of hydrochloric acid and oil. A software product for computational experiments is developed. For the numerical experiments, use is made of the data on the wells of an actual oil field. Good agreement is obtained between the field data and the calculated data. Numerical experiments with different configurations of the permeability of an oil stratum are conducted.

Mathematical model for path selection by ants between nest and food source.

PubMed

Bodnar, Marek; Okińczyc, Natalia; Vela-Pérez, M

2017-03-01

Several models have been proposed to describe the behavior of ants when moving from nest to food sources. Most of these studies where based on numerical simulations with no mathematical justification. In this paper, we propose a mechanism for the formation of paths of minimal length between two points by a collection of individuals undergoing reinforced random walks taking into account not only the lengths of the paths but also the angles (connected to the preference of ants to move along straight lines). Our model involves reinforcement (pheromone accumulation), persistence (tendency to preferably follow straight directions in absence of any external effect) and takes into account the bifurcation angles of each edge (represented by a probability of willingness of choosing the path with the smallest angle). We describe analytically the results for 2 ants and different path lengths and numerical simulations for several ants. Copyright © 2016 Elsevier Inc. All rights reserved.

Traffic Flow Density Distribution Based on FEM

NASA Astrophysics Data System (ADS)

Ma, Jing; Cui, Jianming

In analysis of normal traffic flow, it usually uses the static or dynamic model to numerical analyze based on fluid mechanics. However, in such handling process, the problem of massive modeling and data handling exist, and the accuracy is not high. Finite Element Method (FEM) is a production which is developed from the combination of a modern mathematics, mathematics and computer technology, and it has been widely applied in various domain such as engineering. Based on existing theory of traffic flow, ITS and the development of FEM, a simulation theory of the FEM that solves the problems existing in traffic flow is put forward. Based on this theory, using the existing Finite Element Analysis (FEA) software, the traffic flow is simulated analyzed with fluid mechanics and the dynamics. Massive data processing problem of manually modeling and numerical analysis is solved, and the authenticity of simulation is enhanced.

Heat and Mass Transfer with Condensation in Capillary Porous Bodies

PubMed Central

2014-01-01

The purpose of this present work is related to wetting process analysis caused by condensation phenomena in capillary porous material by using a numerical simulation. Special emphasis is given to the study of the mechanism involved and the evaluation of classical theoretical models used as a predictive tool. A further discussion will be given for the distribution of the liquid phase for both its pendular and its funicular state and its consequence on diffusion coefficients of the mathematical model used. Beyond the complexity of the interaction effects between vaporisation-condensation processes on the gas-liquid interfaces, the comparison between experimental and numerical simulations permits to identify the specific contribution and the relative part of mass and energy transport parameters. This analysis allows us to understand the contribution of each part of the mathematical model used and to simplify the study. PMID:24688366

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Stability of Nonlinear Swarms on Flat and Curved Surfaces

DTIC Science & Technology

numerical experiments have shown that the system either converges to a rotating circular limit cycle with a fixed center of mass, or the agents clump ...Swarming is a near-universal phenomenon in nature. Many mathematical models of swarms exist , both to model natural processes and to control robotic...agents. We study a swarm of agents with spring-like at-traction and nonlinear self-propulsion. Swarms of this type have been studied numerically, but

Mathematical modeling analysis of intratumoral disposition of anticancer agents and drug delivery systems.

PubMed

Popilski, Hen; Stepensky, David

2015-05-01

Solid tumors are characterized by complex morphology. Numerous factors relating to the composition of the cells and tumor stroma, vascularization and drainage of fluids affect the local microenvironment within a specific location inside the tumor. As a result, the intratumoral drug/drug delivery system (DDS) disposition following systemic or local administration is non-homogeneous and its complexity reflects the differences in the local microenvironment. Mathematical models can be used to analyze the intratumoral drug/DDS disposition and pharmacological effects and to assist in choice of optimal anticancer treatment strategies. The mathematical models that have been applied by different research groups to describe the intratumoral disposition of anticancer drugs/DDSs are summarized in this article. The properties of these models and of their suitability for prediction of the drug/DDS intratumoral disposition and pharmacological effects are reviewed. Currently available mathematical models appear to neglect some of the major factors that govern the drug/DDS intratumoral disposition, and apparently possess limited prediction capabilities. More sophisticated and detailed mathematical models and their extensive validation are needed for reliable prediction of different treatment scenarios and for optimization of drug treatment in the individual cancer patients.

A numerical study of steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Jalics, Miklos Kalman

Electronics based on semiconductors creates an enormous demand for high quality semiconductor single crystals. The vertical Bridgman device is commonly used for growing single crystals for a variety of materials such as GaAs, InP and HgCdTe. A mathematical model is presented for steady crystal growth under conditions where crystal growth is determined strictly by heat transfer. The ends of the ampoule are chosen far away from the insulation zone to allow for steady growth. A numerical solution is sought for this mathematical model. The equations are transformed into a rectangular geometry and appropriate finite difference techniques are applied on the transformed equations. Newton's method solves the nonlinear problem. To improve efficiency GMRES with preconditioning is used to compute the Newton iterates. The numerical results are used to compare with two current asymptotic theories that assume small Biot numbers. Results indicate that one of the asymptotic theories is accurate for even moderate Biot numbers.

Mathematical model for self-propelled droplets driven by interfacial tension

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

Nagai, Ken H.; Tachibana, Kunihito; Tobe, Yuta

2016-03-21

We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically.

Stability analysis for a delay differential equations model of a hydraulic turbine speed governor

NASA Astrophysics Data System (ADS)

Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.

2017-01-01

The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.

Comparing functional responses in predator-infected eco-epidemics models.

PubMed

Haque, Mainul; Rahman, Md Sabiar; Venturino, Ezio

2013-11-01

The current paper deals with the mathematical models of predator-prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator-prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

ESTIMATION OF INFILTRATION RATE IN THE VADOSE ZONE: COMPILATION OF SIMPLE MATHEMATICAL MODELS - VOLUME I

EPA Science Inventory

The unsaturated or vadose zone provides a complex system for the simulation of water movement and contaminant transport and fate. Numerous models are available for performing simulations related to the movement of water. There exists extensive documentation of these models. Ho...

SIMULATING RADIONUCLIDE FATE AND TRANSPORT IN THE UNSATURATED ZONE: EVALUATION AND SENSITIVITY ANALYSES OF SELECT COMPUTER MODELS

EPA Science Inventory

Numerical, mathematical models of water and chemical movement in soils are used as decision aids for determining soil screening levels (SSLs) of radionuclides in the unsaturated zone. Many models require extensive input parameters which include uncertainty due to soil variabil...

Numerical approaches to combustion modeling. Progress in Astronautics and Aeronautics. Vol. 135

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

Oran, E.S.; Boris, J.P.

1991-01-01

Various papers on numerical approaches to combustion modeling are presented. The topics addressed include; ab initio quantum chemistry for combustion; rate coefficient calculations for combustion modeling; numerical modeling of combustion of complex hydrocarbons; combustion kinetics and sensitivity analysis computations; reduction of chemical reaction models; length scales in laminar and turbulent flames; numerical modeling of laminar diffusion flames; laminar flames in premixed gases; spectral simulations of turbulent reacting flows; vortex simulation of reacting shear flow; combustion modeling using PDF methods. Also considered are: supersonic reacting internal flow fields; studies of detonation initiation, propagation, and quenching; numerical modeling of heterogeneous detonations, deflagration-to-detonationmore » transition to reactive granular materials; toward a microscopic theory of detonations in energetic crystals; overview of spray modeling; liquid drop behavior in dense and dilute clusters; spray combustion in idealized configurations: parallel drop streams; comparisons of deterministic and stochastic computations of drop collisions in dense sprays; ignition and flame spread across solid fuels; numerical study of pulse combustor dynamics; mathematical modeling of enclosure fires; nuclear systems.« less

Active Problem Solving and Applied Research Methods in a Graduate Course on Numerical Methods

ERIC Educational Resources Information Center

Maase, Eric L.; High, Karen A.

2008-01-01

"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

Neurocognitive Approaches to Developmental Disorders of Numerical and Mathematical Cognition: The Perils of Neglecting the Role of Development

ERIC Educational Resources Information Center

Ansari, Daniel

2010-01-01

The present paper provides a critical overview of how adult neuropsychological models have been applied to the study of the atypical development of numerical cognition. Specifically, the following three assumptions are challenged: 1. Profiles of strength and weaknesses do not change over developmental time. 2. Similar neuronal structures are…

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school

PubMed Central

Cerda, Gamal; Pérez, Carlos; Navarro, José I.; Aguilar, Manuel; Casas, José A.; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students’ performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain. PMID:26441739

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

NASA Astrophysics Data System (ADS)

La Rocca, Michele; Adduce, Claudia; Sciortino, Giampiero; Pinzon, Allen Bateman

2008-10-01

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe's approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.

Hydrodynamic water impact. [Apollo spacecraft waterlanding

NASA Technical Reports Server (NTRS)

Kettleborough, C. F.

1972-01-01

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Refining the quantitative pathway of the Pathways to Mathematics model.

PubMed

Sowinski, Carla; LeFevre, Jo-Anne; Skwarchuk, Sheri-Lynn; Kamawar, Deepthi; Bisanz, Jeffrey; Smith-Chant, Brenda

2015-03-01

In the current study, we adopted the Pathways to Mathematics model of LeFevre et al. (2010). In this model, there are three cognitive domains--labeled as the quantitative, linguistic, and working memory pathways--that make unique contributions to children's mathematical development. We attempted to refine the quantitative pathway by combining children's (N=141 in Grades 2 and 3) subitizing, counting, and symbolic magnitude comparison skills using principal components analysis. The quantitative pathway was examined in relation to dependent numerical measures (backward counting, arithmetic fluency, calculation, and number system knowledge) and a dependent reading measure, while simultaneously accounting for linguistic and working memory skills. Analyses controlled for processing speed, parental education, and gender. We hypothesized that the quantitative, linguistic, and working memory pathways would account for unique variance in the numerical outcomes; this was the case for backward counting and arithmetic fluency. However, only the quantitative and linguistic pathways (not working memory) accounted for unique variance in calculation and number system knowledge. Not surprisingly, only the linguistic pathway accounted for unique variance in the reading measure. These findings suggest that the relative contributions of quantitative, linguistic, and working memory skills vary depending on the specific cognitive task. Copyright © 2014 Elsevier Inc. All rights reserved.

Special data base of Informational - Computational System 'INM RAS - Black Sea' for solving inverse and data assimilation problems

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Piskovatsky, Nicolay; Gusev, Anatoly

2014-05-01

Development of Informational-Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in: mathematical modeling; theory of adjoint equations and optimal control; inverse problems; numerical methods theory; numerical algebra and scientific computing. The above problems are studied in the Institute of Numerical Mathematics of the Russian Academy of Science (INM RAS) in ICS for personal computers. In this work the results on the Special data base development for ICS "INM RAS - Black Sea" are presented. In the presentation the input information for ICS is discussed, some special data processing procedures are described. In this work the results of forecast using ICS "INM RAS - Black Sea" with operational observation data assimilation are presented. This study was supported by the Russian Foundation for Basic Research (project No 13-01-00753) and by Presidium Program of Russian Academy of Sciences (project P-23 "Black sea as an imitational ocean model"). References 1. V.I. Agoshkov, M.V. Assovskii, S.A. Lebedev, Numerical simulation of Black Sea hydrothermodynamics taking into account tide-forming forces. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 5-31. 2. E.I. Parmuzin, V.I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 69-94. 3. V.B. Zalesny, N.A. Diansky, V.V. Fomin, S.N. Moshonkin, S.G. Demyshev, Numerical model of the circulation of Black Sea and Sea of Azov. Russ. J. Numer. Anal. Math. Modelling (2012) 27, No.1, pp. 95-111. 4. Agoshkov V.I.,Assovsky M.B., Giniatulin S. V., Zakharova N.B., Kuimov G.V., Parmuzin E.I., Fomin V.V. Informational Computational system of variational assimilation of observation data "INM RAS - Black sea"// Ecological safety of coastal and shelf zones and complex use of shelf resources: Collection of scientific works. Issue 26, Volume 2. - National Academy of Sciences of Ukraine, Marine Hydrophysical Institute, Sebastopol, 2012. Pages 352-360. (In russian)

Integrating spatial and numerical structure in mathematical patterning

NASA Astrophysics Data System (ADS)

Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.

2018-03-01

This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.

On continuous and discontinuous approaches for modeling groundwater flow in heterogeneous media using the Numerical Manifold Method: Model development and comparison

NASA Astrophysics Data System (ADS)

Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny

2015-06-01

One major challenge in modeling groundwater flow within heterogeneous geological media is that of modeling arbitrarily oriented or intersected boundaries and inner material interfaces. The Numerical Manifold Method (NMM) has recently emerged as a promising method for such modeling, in its ability to handle boundaries, its flexibility in constructing physical cover functions (continuous or with gradient jump), its meshing efficiency with a fixed mathematical mesh (covers), its convenience for enhancing approximation precision, and its integration precision, achieved by simplex integration. In this paper, we report on developing and comparing two new approaches for boundary constraints using the NMM, namely a continuous approach with jump functions and a discontinuous approach with Lagrange multipliers. In the discontinuous Lagrange multiplier method (LMM), the material interfaces are regarded as discontinuities which divide mathematical covers into different physical covers. We define and derive stringent forms of Lagrange multipliers to link the divided physical covers, thus satisfying the continuity requirement of the refraction law. In the continuous Jump Function Method (JFM), the material interfaces are regarded as inner interfaces contained within physical covers. We briefly define jump terms to represent the discontinuity of the head gradient across an interface to satisfy the refraction law. We then make a theoretical comparison between the two approaches in terms of global degrees of freedom, treatment of multiple material interfaces, treatment of small area, treatment of moving interfaces, the feasibility of coupling with mechanical analysis and applicability to other numerical methods. The newly derived boundary-constraint approaches are coded into a NMM model for groundwater flow analysis, and tested for precision and efficiency on different simulation examples. We first test the LMM for a Dirichlet boundary and then test both LMM and JFM for an idealized heterogeneous model, comparing the numerical results with analytical solutions. Then we test both approaches for a heterogeneous model and compare the results of hydraulic head and specific discharge. We show that both approaches are suitable for modeling material boundaries, considering high accuracy for the boundary constraints, the capability to deal with arbitrarily oriented or complexly intersected boundaries, and their efficiency using a fixed mathematical mesh.

Defective Number Module or Impaired Access? Numerical Magnitude Processing in First Graders with Mathematical Difficulties

ERIC Educational Resources Information Center

De Smedt, Bert; Gilmore, Camilla K.

2011-01-01

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical…

University Students' Problem Posing Abilities and Attitudes towards Mathematics.

ERIC Educational Resources Information Center

Grundmeier, Todd A.

2002-01-01

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

Pest control through viral disease: mathematical modeling and analysis.

PubMed

Bhattacharyya, S; Bhattacharya, D K

2006-01-07

This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'kappa' viruses per host, kappain(1,infinity), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value kappa(0) beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing kappa values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented.

Numerical model updating technique for structures using firefly algorithm

NASA Astrophysics Data System (ADS)

Sai Kubair, K.; Mohan, S. C.

2018-03-01

Numerical model updating is a technique used for updating the existing experimental models for any structures related to civil, mechanical, automobiles, marine, aerospace engineering, etc. The basic concept behind this technique is updating the numerical models to closely match with experimental data obtained from real or prototype test structures. The present work involves the development of numerical model using MATLAB as a computational tool and with mathematical equations that define the experimental model. Firefly algorithm is used as an optimization tool in this study. In this updating process a response parameter of the structure has to be chosen, which helps to correlate the numerical model developed with the experimental results obtained. The variables for the updating can be either material or geometrical properties of the model or both. In this study, to verify the proposed technique, a cantilever beam is analyzed for its tip deflection and a space frame has been analyzed for its natural frequencies. Both the models are updated with their respective response values obtained from experimental results. The numerical results after updating show that there is a close relationship that can be brought between the experimental and the numerical models.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent advances in the analytical and numerical treatment of physical and engineering problems are discussed in reviews and reports. Topics addressed include fluid mechanics, numerical methods for differential equations, FEM approaches, and boundary-element methods. Consideration is given to optimization, decision theory, stochastics, actuarial mathematics, applied mathematics and mathematical physics, and numerical analysis.

Wind laws for shockless initialization. [numerical forecasting model

NASA Technical Reports Server (NTRS)

Ghil, M.; Shkoller, B.

1976-01-01

A system of diagnostic equations for the velocity field, or wind laws, was derived for each of a number of models of large-scale atmospheric flow. The derivation in each case is mathematically exact and does not involve any physical assumptions not already present in the prognostic equations, such as nondivergence or vanishing of derivatives of the divergence. Therefore, initial states computed by solving these diagnostic equations should be compatible with the type of motion described by the prognostic equations of the model and should not generate initialization shocks when inserted into the model. Numerical solutions of the diagnostic system corresponding to a barotropic model are exhibited. Some problems concerning the possibility of implementing such a system in operational numerical weather prediction are discussed.

Simulating the evolution of non-point source pollutants in a shallow water environment.

PubMed

Yan, Min; Kahawita, Rene

2007-03-01

Non-point source pollution originating from surface applied chemicals in either liquid or solid form as part of agricultural activities, appears in the surface runoff caused by rainfall. The infiltration and transport of these pollutants has a significant impact on subsurface and riverine water quality. The present paper describes the development of a unified 2-D mathematical model incorporating individual models for infiltration, adsorption, solubility rate, advection and diffusion, which significantly improve the current practice on mathematical modeling of pollutant evolution in shallow water. The governing equations have been solved numerically using cubic spline integration. Experiments were conducted at the Hydrodynamics Laboratory of the Ecole Polytechnique de Montreal to validate the mathematical model. Good correspondence between the computed results and experimental data has been obtained. The model may be used to predict the ultimate fate of surface applied chemicals by evaluating the proportions that are dissolved, infiltrated into the subsurface or are washed off.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

Using numeric simulation in an online e-learning environment to teach functional physiological contexts.

PubMed

Christ, Andreas; Thews, Oliver

2016-04-01

Mathematical models are suitable to simulate complex biological processes by a set of non-linear differential equations. These simulation models can be used as an e-learning tool in medical education. However, in many cases these mathematical systems have to be treated numerically which is computationally intensive. The aim of the study was to develop a system for numerical simulation to be used in an online e-learning environment. In the software system the simulation is located on the server as a CGI application. The user (student) selects the boundary conditions for the simulation (e.g., properties of a simulated patient) on the browser. With these parameters the simulation on the server is started and the simulation result is re-transferred to the browser. With this system two examples of e-learning units were realized. The first one uses a multi-compartment model of the glucose-insulin control loop for the simulation of the plasma glucose level after a simulated meal or during diabetes (including treatment by subcutaneous insulin application). The second one simulates the ion transport leading to the resting and action potential in nerves. The student can vary parameters systematically to explore the biological behavior of the system. The described system is able to simulate complex biological processes and offers the possibility to use these models in an online e-learning environment. As far as the underlying principles can be described mathematically, this type of system can be applied to a broad spectrum of biomedical or natural scientific topics. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Numerical simulation of the alloying process during impulse induction heating of the metal substrate

NASA Astrophysics Data System (ADS)

Popov, V. N.

2017-10-01

2D numerical modeling of the processes during the alloying of the substrate surface metal layer is carried out. Heating, phase transition, heat and mass transfer in the molten metal, solidification of the melt are considered with the aid the proposed mathematical model. Under study is the applicability of the high-frequency electromagnetic field impulse for metal heating and melting. The distribution of the electromagnetic energy in the metal is described by empirical formulas. According to the results of numerical experiments, the flow structure in the melt and distribution of the alloying substances is evaluated.

Handling qualities of large flexible control-configured aircraft

NASA Technical Reports Server (NTRS)

Swaim, R. L.

1980-01-01

The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task.

A coupled chemo-thermo-hygro-mechanical model of concrete at high temperature and failure analysis

NASA Astrophysics Data System (ADS)

Li, Xikui; Li, Rongtao; Schrefler, B. A.

2006-06-01

A hierarchical mathematical model for analyses of coupled chemo-thermo-hygro-mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible-miscible levels. The thermo-induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo-thermo-hygro-mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non-self-adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo-thermo-hygro-mechanical behaviour in concretes subjected to fire and thermal radiation.

Physically based modeling in catchment hydrology at 50: Survey and outlook

NASA Astrophysics Data System (ADS)

Paniconi, Claudio; Putti, Mario

2015-09-01

Integrated, process-based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection-dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science.

Proceedings of the Annual Conference of the International Group for the Psychology of Mathematics Education (13th, Paris, France, July 9-13, 1989), Volume 3.

ERIC Educational Resources Information Center

Vergnaud, Gerard, Ed.; Rogalski, Janine, Ed.; Artique, Michele, Ed.

This proceedings of the annual conference of the International Group for the Psychology of Mathematics Education (PME) includes the following research papers: "A Model of Understanding Two-Digit Numeration and Computation" (H. Murray & A. Olivier); "The Computer Produces a Special Graphic Situation of Learning the Change of Coordinate System" (S.…

The numerical model of multi-layer insulation with a defined wrapping pattern immersed in superfluid helium

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Lubryka, Eliza

2017-11-01

The numerical model of thin layers, characterized by a defined wrapping pattern can be a crucial element of many computational problems related to engineering and science. A motivating example is found in multilayer electrical insulation, which is an important component of superconducting magnets and other cryogenic installations. The wrapping pattern of the insulation can significantly affect heat transport and the performance of the considered instruments. The major objective of this study is to develop the numerical boundary conditions (BC) needed to model the wrapping pattern of thin insulation. An example of the practical application of the proposed BC includes the heat transfer of Rutherford NbTi cables immersed in super-fluid helium (He II) across thin layers of electrical insulation. The proposed BC and a mathematical model of heat transfer in He II are implemented in the open source CFD toolbox OpenFOAM. The implemented mathematical model and the BC are compared in the experiments. The study confirms that the thermal resistance of electrical insulation can be lowered by implementing the proper wrapping pattern. The proposed BC can be useful in the study of new patterns for wrapping schemes. The work has been supported by statutory funds from Polish Ministry for Science and Higher Education for the year of 2017.

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities

PubMed Central

Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin

2013-01-01

Previous research has found a relationship between individual differences in children’s precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the present study we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of two years. Additionally, at the last time point, we tested children’s informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3; Ginsburg & Baroody, 2003). We found that children’s numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned, non-symbolic system of quantity representation and the system of mathematical reasoning that children come to master through instruction. PMID:24076381

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

PubMed

Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

2013-12-01

Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

The electromagnetic pendulum in quickly changing magnetic field of constant intensity

NASA Astrophysics Data System (ADS)

Rodyukov, F. F.; Shepeljavyi, A. I.

2018-05-01

The Lagrange-Maxwell equations for the pendulum in the form of a conductive frame, which is suspended in a uniform sinusoidal electromagnetic field of constant intensity, are obtained. The procedure for obtaining simplified mathematical models by a traditional method of separating fast and slow motions with subsiquent averaging a fast time is used. It is shown that this traditional approach may lead to inappropriate mathematical models. Suggested ways on how this can be avoided for the case are considered. The main statements by numerical experiments are illustrated.

Numerical simulation of the coaxial magneto-plasma accelerator and non-axisymmetric radio frequency discharge

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.; Frolko, P. A.

2017-05-01

The paper presents the results of mathematical modeling of physical processes in electronic devices such as helicon discharge and coaxial pulsed plasma thruster. A mathematical model of coaxial magneto-plasma accelerator (with a preionization helicon discharge), which allows estimating the transformation of one form of energy to another, as well as to evaluate the level of the contribution of different types of energy, the increase in mass of the accelerated plasmoid in the process of changing the speed. Main plasma parameters with experimental data were compared.

Developing Teaching Material Software Assisted for Numerical Methods

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study*

PubMed Central

Huang, Jian; Du, Feng-lei; Yao, Yuan; Wan, Qun; Wang, Xiao-song; Chen, Fei-yan

2015-01-01

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation. PMID:26238541

Pulsatile blood flow in elastic artery with model aneurysm

NASA Astrophysics Data System (ADS)

Nikolov, N.; Radev, St.; Tabakova, S.

2017-11-01

The mathematical modeling and numerical simulations are expected to play an important role to predict the genesis of different cardiovascular diseases, such as the formation and rupture of aneurysms. In the present work, the numerical solutions of the oscillatory blood flow are constructed for an elastic artery with a model aneurysm by use of the software ANSYS. It is observed that the artery elastic strain behaves in a different way: stably or unstably depending on the different combinations between the flow parameter (outlet pressure) and the elastic modulus of the artery wall.

Finger-Based Numerical Skills Link Fine Motor Skills to Numerical Development in Preschoolers.

PubMed

Suggate, Sebastian; Stoeger, Heidrun; Fischer, Ursula

2017-12-01

Previous studies investigating the association between fine-motor skills (FMS) and mathematical skills have lacked specificity. In this study, we test whether an FMS link to numerical skills is due to the involvement of finger representations in early mathematics. We gave 81 pre-schoolers (mean age of 4 years, 9 months) a set of FMS measures and numerical tasks with and without a specific finger focus. Additionally, we used receptive vocabulary and chronological age as control measures. FMS linked more closely to finger-based than to nonfinger-based numerical skills even after accounting for the control variables. Moreover, the relationship between FMS and numerical skill was entirely mediated by finger-based numerical skills. We concluded that FMS are closely related to early numerical skill development through finger-based numerical counting that aids the acquisition of mathematical mental representations.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children.

PubMed

Lourenco, Stella F; Bonny, Justin W

2017-07-01

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude. © 2016 John Wiley & Sons Ltd.

Foundations of children's numerical and mathematical skills: the roles of symbolic and nonsymbolic representations of numerical magnitude.

PubMed

Lyons, Ian M; Ansari, Daniel

2015-01-01

Numerical and mathematical skills are critical predictors of academic success. The last three decades have seen a substantial growth in our understanding of how the human mind and brain represent and process numbers. In particular, research has shown that we share with animals the ability to represent numerical magnitude (the total number of items in a set) and that preverbal infants can process numerical magnitude. Further research has shown that similar processing signatures characterize numerical magnitude processing across species and developmental time. These findings suggest that an approximate system for nonsymbolic (e.g., dot arrays) numerical magnitude representation serves as the basis for the acquisition of cultural, symbolic (e.g., Arabic numerals) representations of numerical magnitude. This chapter explores this hypothesis by reviewing studies that have examined the relation between individual differences in nonsymbolic numerical magnitude processing and symbolic math abilities (e.g., arithmetic). Furthermore, we examine the extent to which the available literature provides strong evidence for a link between symbolic and nonsymbolic representations of numerical magnitude at the behavioral and neural levels of analysis. We conclude that claims that symbolic number abilities are grounded in the approximate system for the nonsymbolic representation of numerical magnitude are not strongly supported by the available evidence. Alternative models and future research directions are discussed. © 2015 Elsevier Inc. All rights reserved.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

USSR Space Life Sciences Digest, issue 20

NASA Technical Reports Server (NTRS)

Hooke, Lydia Razran (Editor); Donaldson, P. Lynn (Editor); Teeter, Ronald (Editor); Garshnek, Victoria (Editor); Rowe, Joseph (Editor)

1988-01-01

Abstracts of research in the areas of biological rhythms, body fluids, botany, endrocrinology, enzymology, exobiology, genetics, human performance, immunology, life support systems, mathematical modeling, and numerous other topics related to space and life sciences are given.

Determination of effective thoracic mass.

DOT National Transportation Integrated Search

1996-02-01

Effective thoracic mass is a critical parameter in specifying mathematical and mechanical models (such as crash dummies) of humans exposed to impact conditions. A method is developed using a numerical optimizer to determine effective thoracic mass (a...

Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens.

PubMed

Urs, Raksha; Ho, Arthur; Manns, Fabrice; Parel, Jean-Marie

2010-06-01

To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205 microm. The age-dependent equations provide a reliable lens model for ages 20-60 years. The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Preface.

PubMed

Friedman, Avner; Lachowicz, Mirosław; Ledzewicz, Urszula; Piotrowska, Monika Joanna; Szymanska, Zuzanna

2017-02-01

This volume was inspired by the topics presented at the international conference "Micro and Macro Systems in Life Sciences" which was held on Jun 8-12, 2015 in Będlewo, Poland. System biology is an approach which tries to understand how micro systems, at the molecular and cellular levels, affect macro systems such as organs, tissue and populations. Thus it is not surprising that a major theme of this volume evolves around cancer and its treatment. Articles on this topic include models for tumor induced angiogenesis, without and with delays, metastatic niche of the bone marrow, drug resistance and metronomic chemotherapy, and virotherapy of glioma. Methods range from dynamical systems to optimal control. Another well represented topic of this volume is mathematical modeling in epidemiology. Mathematical approaches to modeling and control of more specific diseases like malaria, Ebola or human papillomavirus are discussed as well as a more general approaches to the SEIR, and even more general class of models in epidemiology, by using the tools of optimal control and optimization. The volume also brings up challenges in mathematical modeling of other diseases such as tuberculosis. Partial differential equations combined with numerical approaches are becoming important tools in modeling not only tumor growth and treatment, but also other diseases, such as fibrosis of the liver, and atherosclerosis and its associated blood flow dynamics, and our volume presents a state of the art approach on these topics. Understanding mathematics behind the cell motion, appearance of the special patterns in various cell populations, and age structured mutations are among topics addressed inour volume. A spatio-temporal models of synthetic genetic oscillators brings the analysis to the gene level which is the focus of much of current biological research. Mathematics can help biologists to explain the collective behavior of bacterial, a topic that is also presented here. Finally some more across the discipline topics are being addresses, which can appear as a challenge in studying problems in systems biology on all, macro, meso and micro levels. They include numerical approaches to stochastic wave equation arising in modeling Brownian motion, discrete velocity models, many particle approximations as well as very important aspect on the connection between discrete measurement and the construction of the models for various phenomena, particularly the one involving delays. With the variety of biological topics and their mathematical approaches we very much hope that the reader of the Mathematical Biosciences and Engineering will find this volume interesting and inspirational for their own research.

Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

NASA Astrophysics Data System (ADS)

Budi Darmayasa, Jero; Wahyudin; Mulyana, Tatang; Subali Noto, Muchamad

2018-04-01

Ethnomathematicsis considered as a new study in mathematic education. As a study, numerous regions in this world starts to explore through ethnomathematics, including Indonesia. As the intersection between mathematics and mathematical modelling and culture, ethnomathematics exists in various society’s cultural elements, including in the Balinese Hindus’ festivities. To find the mathematical concept used in determining the festivity days, the researcher(s) conducted ethnographic research in Bali Mula society in Kintamani District, Bali. Participation observation, in-depth interview, and literature and documentation were used in collecting the data. As the result, the researcher(s) revealed that the mathematical concept used is integer operations, least common multiple, mixed fraction, and number sequences. Since it contains mathematical concept used in junior high, thus ethnomathematics of “4-hindu’s festivities” may be used as context in mathematics learning. By using ethnomathematics as the context, the researcher(s) expect that it will help teachers in motivation their students to learn mathematics.

Computational fluid dynamics combustion analysis evaluation

NASA Technical Reports Server (NTRS)

Kim, Y. M.; Shang, H. M.; Chen, C. P.; Ziebarth, J. P.

1992-01-01

This study involves the development of numerical modelling in spray combustion. These modelling efforts are mainly motivated to improve the computational efficiency in the stochastic particle tracking method as well as to incorporate the physical submodels of turbulence, combustion, vaporization, and dense spray effects. The present mathematical formulation and numerical methodologies can be casted in any time-marching pressure correction methodologies (PCM) such as FDNS code and MAST code. A sequence of validation cases involving steady burning sprays and transient evaporating sprays will be included.

Faraday waves in a Hele-Shaw cell

NASA Astrophysics Data System (ADS)

Li, Jing; Li, Xiaochen; Chen, Kaijie; Xie, Bin; Liao, Shijun

2018-04-01

We investigate Faraday waves in a Hele-Shaw cell via experimental, numerical, and theoretical studies. Inspired by the Kelvin-Helmholtz-Darcy theory, we develop the gap-averaged Navier-Stokes equations and end up with the stable standing waves with half frequency of the external forced vibration. To overcome the dependency of a numerical model on the experimental parameter of wave length, we take two-phase flow into consideration and a novel dispersion relation is derived. The numerical results compare well with our experimental data, which effectively validates our proposed mathematical model. Therefore, this model can produce robust solutions of Faraday wave patterns and resolve related physical phenomena, which demonstrates the practical importance of the present study.

Numerical Analysis of a Class of THM Coupled Model for Porous Materials

NASA Astrophysics Data System (ADS)

Liu, Tangwei; Zhou, Jingying; Lu, Hongzhi

2018-01-01

We consider the coupled models of the Thermo-hydro-mechanical (THM) problem for porous materials which arises in many engineering applications. Firstly, mathematical models of the THM coupled problem for porous materials were discussed. Secondly, for different cases, some numerical difference schemes of coupled model were constructed, respectively. Finally, aassuming that the original water vapour effect is neglectable and that the volume fraction of liquid phase and the solid phase are constants, the nonlinear equations can be reduced to linear equations. The discrete equations corresponding to the linear equations were solved by the Arnodli method.

Modeling the effects of inflammation in bone fracture healing

NASA Astrophysics Data System (ADS)

Kojouharov, H. V.; Trejo, I.; Chen-Charpentier, B. M.

2017-10-01

A new mathematical model is presented to study the early inflammatory effects in bone healing. It consists of a system of nonlinear ordinary differential equations that represents the interactions among macrophages, mesenchymal stem cells, and osteoblasts. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. A set of numerical simulations is performed to support the theoretical results. The model is also used to numerically monitor the evolution of a broken bone for different types of fractures and to explore possible treatments to accelerate bone healing by administrating anti-inflammatory drugs.

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.

Numerical modeling and preliminary validation of drag-based vertical axis wind turbine

NASA Astrophysics Data System (ADS)

Krysiński, Tomasz; Buliński, Zbigniew; Nowak, Andrzej J.

2015-03-01

The main purpose of this article is to verify and validate the mathematical description of the airflow around a wind turbine with vertical axis of rotation, which could be considered as representative for this type of devices. Mathematical modeling of the airflow around wind turbines in particular those with the vertical axis is a problematic matter due to the complex nature of this highly swirled flow. Moreover, it is turbulent flow accompanied by a rotation of the rotor and the dynamic boundary layer separation. In such conditions, the key aspects of the mathematical model are accurate turbulence description, definition of circular motion as well as accompanying effects like centrifugal force or the Coriolis force and parameters of spatial and temporal discretization. The paper presents the impact of the different simulation parameters on the obtained results of the wind turbine simulation. Analysed models have been validated against experimental data published in the literature.

Prediction of inspiratory flow shapes during sleep with a mathematic model of upper airway forces.

PubMed

Aittokallio, Tero; Gyllenberg, Mats; Saaresranta, Tarja; Polo, Olli

2003-11-01

To predict the airflow dynamics during sleep using a mathematic model that incorporates a number of static and dynamic upper airway forces, and to compare the numerical results to clinical flow data recorded from patients with sleep-disordered breathing on and off various treatment options. Upper airway performance was modeled in virtual subjects characterized by parameter settings that describe common combinations of risk factors predisposing to upper airway collapse during sleep. The treatments effect were induced by relevant changes of the initial parameter values. Computer simulations at our website (http://www.utu.fi/ml/sovmat/bio/). Risk factors considered in the simulation settings were sex, obesity, pharyngeal collapsibility, and decreased phasic activity of pharyngeal muscles. The effects of weight loss, pharyngeal surgery, nasal continuous positive airway pressure, and respiratory stimulation on the inspiratory flow characteristics were tested with the model. Numerical predictions were investigated by means of 3 measurable inspiratory airflow characteristics: initial slope, total volume, and flow shape. The model was able to reproduce the inspiratory flow shape characteristics that have previously been described in the literature. Simulation results also supported the observations that a multitude of factors underlie the pharyngeal collapse and, therefore, certain medical therapies that are effective in some conditions may prove ineffective in others. A mathematic model integrating the current knowledge of upper airway physiology is able to predict individual treatment responses. The model provides a framework for designing novel and potentially feasible treatment alternatives for sleep-disordered breathing.

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)

Variable thickness transient ground-water flow model. Volume 1. Formulation

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

Reisenauer, A.E.

1979-12-01

Mathematical formulation for the variable thickness transient (VTT) model of an aquifer system is presented. The basic assumptions are described. Specific data requirements for the physical parameters are discussed. The boundary definitions and solution techniques of the numerical formulation of the system of equations are presented.

Design of numerical model for thermoacoustic devices using OpenFOAM

NASA Astrophysics Data System (ADS)

Tisovsky, Tomas; Vit, Tomas

2017-09-01

Thermoacoustic devices are increasingly popular especially because of their construction simplicity and the ability to easily convert waste heat into the form of usable energy. Aim of this paper is to introduce some of the effective procedures for creating a complex mathematical model of thermoacoustic devices in OpenFOAM.

THE ABCS OF SNOWMELT: A TOPOGRAPHICALLY FACTORIZED ENERGY COMPONENT SNOWMELT MODEL. (R824784)

EPA Science Inventory

Because of the crucial role snowmelt plays in many watersheds around the world, it is important to understand and accurately quantify the melt process. As such, numerous mathematical models attempting to describe and predict snowmelt have arisen. There are two main categories of ...

Effects of soil moisture on the diurnal pattern of pesticide emission: Numerical simulation and sensitivity analysis

USDA-ARS?s Scientific Manuscript database

Accurate prediction of pesticide volatilization is important for the protection of human and environmental health. Due to the complexity of the volatilization process, sophisticated predictive models are needed, especially for dry soil conditions. A mathematical model was developed to allow simulati...

Mathematical model for gyroscope effects

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2015-05-01

Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).

Homeostatic and Circadian Modulation of Cognition: Integrating Mathematical and Computational Modeling Approaches

DTIC Science & Technology

2012-08-20

Leonid V. Kalachev, Ph.D. (University of Montana, not supported on grant) Daniel J. Mollicone, Ph.D. ( Pulsar Informatics, Inc., not supported on grant...project to Pulsar Informatics, Inc., who are providing an implementation suitable for integration with crew rostering to the U.S. Navy (key...individuals involved: Daniel Mollicone, Ph.D. and Mike Stubna, Ph.D. of Pulsar Informatics, Inc.).  We transitioned a numerical library for the mathematical

The Modulus of Rupture from a Mathematical Point of View

NASA Astrophysics Data System (ADS)

Quintela, P.; Sánchez, M. T.

2007-04-01

The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

Effects of Extreme Prematurity on Numerical Skills and Executive Function in Kindergarten Children: An Application of Partially Ordered Classification Modeling

PubMed Central

Tatsuoka, Curtis; McGowan, Bridget; Yamada, Tomoko; Espy, Kimberly Andrews; Minich, Nori; Taylor, H. Gerry

2016-01-01

Although mathematics disabilities (MD) are common in extremely preterm/extremely low birth weight (EPT/ELBW) children, little is known about the nature of these problems. In this study partially ordered set (POSET) models were applied to classify 140 EPT/ELBW kindergarten children (gestational age <28 weeks and/or birth weight <1000 g) and 110 normal birth weight (NBW) controls into profiles of numerical and cognitive skills. Models based on five numerical skills and five executive function and processing speed skills provided a good fit to performance data. The EPT/ELBW group had poorer skills in all areas than NBW controls but the models also revealed substantial individual variability in skill profiles. Weaknesses in executive function were associated with poorer mastery of numerical skills. The findings illustrate the applicability of POSET models to research on MD and suggest distinct types of early numerical deficits in EPT/ELBW children that are related to their impairments in executive function. PMID:27818602

Effects of Extreme Prematurity on Numerical Skills and Executive Function in Kindergarten Children: An Application of Partially Ordered Classification Modeling.

PubMed

Tatsuoka, Curtis; McGowan, Bridget; Yamada, Tomoko; Espy, Kimberly Andrews; Minich, Nori; Taylor, H Gerry

2016-07-01

Although mathematics disabilities (MD) are common in extremely preterm/extremely low birth weight (EPT/ELBW) children, little is known about the nature of these problems. In this study partially ordered set (POSET) models were applied to classify 140 EPT/ELBW kindergarten children (gestational age <28 weeks and/or birth weight <1000 g) and 110 normal birth weight (NBW) controls into profiles of numerical and cognitive skills. Models based on five numerical skills and five executive function and processing speed skills provided a good fit to performance data. The EPT/ELBW group had poorer skills in all areas than NBW controls but the models also revealed substantial individual variability in skill profiles. Weaknesses in executive function were associated with poorer mastery of numerical skills. The findings illustrate the applicability of POSET models to research on MD and suggest distinct types of early numerical deficits in EPT/ELBW children that are related to their impairments in executive function.

Sources of Individual Differences in Emerging Competence With Numeration Understanding Versus Multidigit Calculation Skill

PubMed Central

Fuchs, Lynn S.; Geary, David C.; Fuchs, Douglas; Compton, Donald L.; Hamlett, Carol L.

2014-01-01

This study investigated contributions of general cognitive abilities and foundational mathematical competencies to numeration understanding (i.e., base-10 structure) versus multidigit calculation skill. Children (n = 394, M = 6.5 years) were assessed on general cognitive abilities and foundational numerical competencies at start of 1st grade; on the same numerical competencies, multidigit calculation skill, and numeration understanding at end of 2nd grade; and on multidigit calculation skill and numeration understanding at end of 3rd grade. Path-analytic mediation analysis revealed that general cognitive predictors exerted more direct and more substantial effects on numeration understanding than on multidigit calculations. Foundational mathematics competencies contributed to both outcomes, but largely via 2nd-grade mathematics achievement, and results suggest a mutually supportive role between numeration understanding and multidigit calculations. PMID:25284885

Research in progress in applied mathematics, numerical analysis, and computer science

NASA Technical Reports Server (NTRS)

1990-01-01

Research conducted at the Institute in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized. The Institute conducts unclassified basic research in applied mathematics in order to extend and improve problem solving capabilities in science and engineering, particularly in aeronautics and space.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

PubMed

Flegg, Jennifer A; Menon, Shakti N; Maini, Philip K; McElwain, D L Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

PubMed Central

Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695

Numerical tension adjustment of x-ray membrane to represent goat skin kompang

NASA Astrophysics Data System (ADS)

Siswanto, Waluyo Adi; Abdullah, Muhammad Syiddiq Bin

2017-04-01

This paper presents a numerical membrane model of traditional musical instrument kompang that will be used to find the parameter of membrane tension of x-ray membrane representing the classical goat-skin membrane of kompang. In this study, the experiment towards the kompang is first conducted in an acoustical anechoic enclosure and in parallel a mathematical model of the kompang membrane is developed to simulate the vibration of the kompang membrane in polar coordinate by implementing Fourier-Bessel wave function. The wave equation in polar direction in mode 0,1 is applied to provide the corresponding natural frequencies of the circular membrane. The value of initial and boundary conditions in the function is determined from experiment to allow the correct development of numerical equation. The numerical mathematical model is coded in SMath for the accurate numerical analysis as well as the plotting tool. Two kompang membrane cases with different membrane materials, i.e. goat skin and x-ray film membranes with fixed radius of 0.1 m are used in the experiment. An alternative of kompang's membrane made of x-ray film with the appropriate tension setting can be used to represent the sound of traditional goat-skin kompang. The tension setting of the membrane to resemble the goat-skin is 24N. An effective numerical tool has been develop to help kompang maker to set the tension of x-ray membrane. In the future application, any tradional kompang with different size can be replaced by another membrane material if the tension is set to the correct tension value. The developed numerical tool is useful and handy to calculate the tension of the alternative membrane material.

Numerical Tension Adjustment of X-Ray Membrane to Represent Goat Skin Kompang

NASA Astrophysics Data System (ADS)

Syiddiq, M.; Siswanto, W. A.

2017-01-01

This paper presents a numerical membrane model of traditional musical instrument kompang that will be used to find the parameter of membrane tension of x-ray membrane representing the classical goat-skin membrane of kompang. In this study, the experiment towards the kompang is first conducted in an acoustical anechoic enclosure and in parallel a mathematical model of the kompang membrane is developed to simulate the vibration of the kompang membrane in polar coordinate by implementing Fourier-Bessel wave function. The wave equation in polar direction in mode 0,1 is applied to provide the corresponding natural frequencies of the circular membrane. The value of initial and boundary conditions in the function is determined from experiment to allow the correct development of numerical equation. The numerical mathematical model is coded in SMath for the accurate numerical analysis as well as the plotting tool. Two kompang membrane cases with different membrane materials, i.e. goat skin and x-ray film membranes with fixed radius of 0.1 m are used in the experiment. An alternative of kompang’s membrane made of x-ray film with the appropriate tension setting can be used to represent the sound of traditional goat-skin kompang. The tension setting of the membrane to resemble the goat-skin is 24N. An effective numerical tool has been used to help kompang maker to set the tension of x-ray membrane. In the future application, any traditional kompang with different size can be replaced by another membrane material if the tension is set to the correct tension value. The numerical tool used is useful and handy to calculate the tension of the alternative membrane material.

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

NASA Astrophysics Data System (ADS)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

Influence of bed material entrainment and non-Newtonian rheology on turbulent geophysical flows dynamics. Numerical study

NASA Astrophysics Data System (ADS)

Eglit, M. E.; Yakubenko, A. E.; Yakubenko, T. A.

2017-10-01

This paper deals with the mathematical and numerical modeling of the propagation stage of geophysical gravity-driven flows, such as snow avalanches, mudflows, and rapid landslides. New mathematical models are presented which are based on full, not-depth-averaged equations of mechanics of continuous media. The models account for three important issues: non-Newtonian rheology of the moving material, entrainment of the bed material by the flow, and turbulence. The main objective is to investigate the effect of these three factors on the flow dynamics and on the value of the entrainment rate. To exclude the influence of many other factors, e.g., the complicated slope topography, only the motion down a long uniform slope with a constant inclination angle is studied numerically. Moreover, the entire flow from the front to the rear area was not modeled, but only its middle part where the flow is approximately uniform in length. One of the qualitative results is that in motion along homogeneous slope the mass entrainment increases the flow velocity and depth while the entrainment rate at large time tends to become constant which depends on the physical properties of the flow and the underlying material but not on the current values of the flow velocity and depth.

Using special functions to model the propagation of airborne diseases

NASA Astrophysics Data System (ADS)

Bolaños, Daniela

2014-06-01

Some special functions of the mathematical physics are using to obtain a mathematical model of the propagation of airborne diseases. In particular we study the propagation of tuberculosis in closed rooms and we model the propagation using the error function and the Bessel function. In the model, infected individual emit pathogens to the environment and this infect others individuals who absorb it. The evolution in time of the concentration of pathogens in the environment is computed in terms of error functions. The evolution in time of the number of susceptible individuals is expressed by a differential equation that contains the error function and it is solved numerically for different parametric simulations. The evolution in time of the number of infected individuals is plotted for each numerical simulation. On the other hand, the spatial distribution of the pathogen around the source of infection is represented by the Bessel function K0. The spatial and temporal distribution of the number of infected individuals is computed and plotted for some numerical simulations. All computations were made using software Computer algebra, specifically Maple. It is expected that the analytical results that we obtained allow the design of treatment rooms and ventilation systems that reduce the risk of spread of tuberculosis.

Representations of Numerical and Non-Numerical Magnitude Both Contribute to Mathematical Competence in Children

ERIC Educational Resources Information Center

Lourenco, Stella F.; Bonny, Justin W.

2017-01-01

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises…

Hydrodynamic characteristics of viscous fluid flow in screw channels formed by two ribs

NASA Astrophysics Data System (ADS)

Kadyirov, A. I.; Abaydullin, B. R.; Vachagina, E. K.

2018-03-01

The mathematical model of laminar viscous flows in screw channels, formed by two ribs, is developed using the helical coordinates. The numerical results of the flow with helical symmetry are presented.

NAPL: SIMULATOR DOCUMENTATION

EPA Science Inventory

A mathematical and numerical model is developed to simulate the transport and fate of NAPLs (Non-Aqueous Phase Liquids) in near-surface granular soils. The resulting three-dimensional, three phase simulator is called NAPL. The simulator accommodates three mobile phases: water, NA...

Mathematical Simulation of Perturbations of Attack Angle of Asymmetric Nanosatellite Passing through Resonance

NASA Astrophysics Data System (ADS)

Lyubimov, V. V.; Kurkina, E. V.

2018-05-01

The authors consider the problem of a dynamic system passing through a low-order resonance, describing an uncontrolled atmospheric descent of an asymmetric nanosatellite in the Earth's atmosphere. The authors perform mathematical and numerical modeling of the motion of the nanosatellite with a small mass-aerodynamic asymmetry relative to the center of mass. The aim of the study is to obtain new reliable approximate analytical estimates of perturbations of the angle of attack of a nanosatellite passing through resonance at angles of attack of not more than 0.5π. By using the stationary phase method, the authors were able to investigate a discontinuous perturbation in the angle of attack of a nanosatellite passing through a resonance with two different nanosatellite designs. Comparison of the results of the numerical modeling and new approximate analytical estimates of the perturbation of the angle of attack confirms the reliability of the said estimates.

Volcano Modelling and Simulation gateway (VMSg): A new web-based framework for collaborative research in physical modelling and simulation of volcanic phenomena

NASA Astrophysics Data System (ADS)

Esposti Ongaro, T.; Barsotti, S.; de'Michieli Vitturi, M.; Favalli, M.; Longo, A.; Nannipieri, L.; Neri, A.; Papale, P.; Saccorotti, G.

2009-12-01

Physical and numerical modelling is becoming of increasing importance in volcanology and volcanic hazard assessment. However, new interdisciplinary problems arise when dealing with complex mathematical formulations, numerical algorithms and their implementations on modern computer architectures. Therefore new frameworks are needed for sharing knowledge, software codes, and datasets among scientists. Here we present the Volcano Modelling and Simulation gateway (VMSg, accessible at http://vmsg.pi.ingv.it), a new electronic infrastructure for promoting knowledge growth and transfer in the field of volcanological modelling and numerical simulation. The new web portal, developed in the framework of former and ongoing national and European projects, is based on a dynamic Content Manager System (CMS) and was developed to host and present numerical models of the main volcanic processes and relationships including magma properties, magma chamber dynamics, conduit flow, plume dynamics, pyroclastic flows, lava flows, etc. Model applications, numerical code documentation, simulation datasets as well as model validation and calibration test-cases are also part of the gateway material.

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

PubMed

Wong, Terry Tin-Yau

2017-12-01

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

Vaccination Strategies: a comparative study in an epidemic scenario

NASA Astrophysics Data System (ADS)

Prates, D. B.; Jardim, C. L. T. F.; Ferreira, L. A. F.; da Silva, J. M.; Kritz, M. V.

2016-08-01

Epidemics are an extremely important matter of study within the Mathematical Modeling area and can be widely found in the literature. Some epidemiological models use differential equations, which are very sensible to parameters, to represent and describe the diseases mathematically. For this work, a variation of the SIR model is discussed and applied to a certain epidemic scenario, wherein vaccination is introduced through two different strategies: constant vaccination and vaccination in pulses. Other epidemiological and population aspects are also considered, such as mortality/natality and infection rates. The analysis and results are performed through numerical solutions of the model and a special attention is given to the discussion generated by the paramenters variation.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

PubMed

Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

2017-08-01

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

A Density Perturbation Method to Study the Eigenstructure of Two-Phase Flow Equation Systems

NASA Astrophysics Data System (ADS)

Cortes, J.; Debussche, A.; Toumi, I.

1998-12-01

Many interesting and challenging physical mechanisms are concerned with the mathematical notion of eigenstructure. In two-fluid models, complex phasic interactions yield a complex eigenstructure which may raise numerous problems in numerical simulations. In this paper, we develop a perturbation method to examine the eigenvalues and eigenvectors of two-fluid models. This original method, based on the stiffness of the density ratio, provides a convenient tool to study the relevance of pressure momentum interactions and allows us to get precise approximations of the whole flow eigendecomposition for minor requirements. Roe scheme is successfully implemented and some numerical tests are presented.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

ERIC Educational Resources Information Center

Cowan, Richard; Powell, Daisy

2014-01-01

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…

On dynamics of integrate-and-fire neural networks with conductance based synapses.

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IF models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

Splitting algorithm for numerical simulation of Li-ion battery electrochemical processes

NASA Astrophysics Data System (ADS)

Iliev, Oleg; Nikiforova, Marina A.; Semenov, Yuri V.; Zakharov, Petr E.

2017-11-01

In this paper we present a splitting algorithm for a numerical simulation of Li-ion battery electrochemical processes. Liion battery consists of three domains: anode, cathode and electrolyte. Mathematical model of electrochemical processes is described on a microscopic scale, and contains nonlinear equations for concentration and potential in each domain. On the interface of electrodes and electrolyte there are the Lithium ions intercalation and deintercalation processes, which are described by Butler-Volmer nonlinear equation. To approximate in spatial coordinates we use finite element methods with discontinues Galerkin elements. To simplify numerical simulations we develop the splitting algorithm, which split the original problem into three independent subproblems. We investigate the numerical convergence of the algorithm on 2D model problem.

Mathematical modeling of flow in the working part of an acousto-convective drying system

NASA Astrophysics Data System (ADS)

Kravchenko, A. S.; Zhilin, A. A.; Fedorova, N. N.

2018-03-01

The objective of this study was to numerically simulate the nonstationary processes occurring in the acoustic-convective dryer (ACD) channel. In the present work, the problem was solved numerically in a three-dimensional formulation taking into account all features of the ACD duct in real geometry. The processes occurring in the ACD duct were simulated using the ANSYS Fluent 18.0 software. The numerical experiments provided an aggregate picture of the working gas flow in the ACD duct with the features near the subsonic nozzle and the cavity. The results of the numerical calculations were compared with experimental data. The best agreement with the experimental data was obtained for the viscosity model neglecting turbulent effects.

Numerical implementation of the S-matrix algorithm for modeling of relief diffraction gratings

NASA Astrophysics Data System (ADS)

Yaremchuk, Iryna; Tamulevičius, Tomas; Fitio, Volodymyr; Gražulevičiūte, Ieva; Bobitski, Yaroslav; Tamulevičius, Sigitas

2013-11-01

A new numerical implementation is developed to calculate the diffraction efficiency of relief diffraction gratings. In the new formulation, vectors containing the expansion coefficients of electric and magnetic fields on boundaries of the grating layer are expressed by additional constants. An S-matrix algorithm has been systematically described in detail and adapted to a simple matrix form. This implementation is suitable for the study of optical characteristics of periodic structures by using modern object-oriented programming languages and different standard mathematical software. The modeling program has been developed on the basis of this numerical implementation and tested by comparison with other commercially available programs and experimental data. Numerical examples are given to show the usefulness of the new implementation.

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.

Simulation of a manual electric-arc welding in a working gas pipeline. 1. Formulation of the problem

NASA Astrophysics Data System (ADS)

Baikov, V. I.; Gishkelyuk, I. A.; Rus', A. M.; Sidorovich, T. V.; Tonkonogov, B. A.

2010-11-01

Problems of mathematical simulation of the temperature stresses arising in the wall of a pipe of a cross-country gas pipeline in the process of electric-arc welding of defects in it have been considered. Mathematical models of formation of temperatures, deformations, and stresses in a gas pipe subjected to phase transformations have been developed. These models were numerically realized in the form of algorithms representing a part of an application-program package. Results of verification of the computational complex and calculation results obtained with it are presented.

Continuum mathematical modelling of pathological growth of blood vessels

NASA Astrophysics Data System (ADS)

Stadnik, N. E.; Dats, E. P.

2018-04-01

The present study is devoted to the mathematical modelling of a human blood vessel pathological growth. The vessels are simulated as the thin-walled circular tube. The boundary value problem of the surface growth of an elastic thin-walled cylinder is solved. The analytical solution is obtained in terms of velocities of stress strain state parameters. The condition of thinness allows us to study finite displacements of cylinder surfaces by means of infinitesimal deformations. The stress-strain state characteristics, which depend on the mechanical parameters of the biological processes, are numerically computed and graphically analysed.

Reevaluating the two-representation model of numerical magnitude processing.

PubMed

Jiang, Ting; Zhang, Wenfeng; Wen, Wen; Zhu, Haiting; Du, Han; Zhu, Xiangru; Gao, Xuefei; Zhang, Hongchuan; Dong, Qi; Chen, Chuansheng

2016-01-01

One debate in mathematical cognition centers on the single-representation model versus the two-representation model. Using an improved number Stroop paradigm (i.e., systematically manipulating physical size distance), in the present study we tested the predictions of the two models for number magnitude processing. The results supported the single-representation model and, more importantly, explained how a design problem (failure to manipulate physical size distance) and an analytical problem (failure to consider the interaction between congruity and task-irrelevant numerical distance) might have contributed to the evidence used to support the two-representation model. This study, therefore, can help settle the debate between the single-representation and two-representation models.

Dimensionless Analysis and Numerical Modeling of Rebalancing Phenomena During Levitation

NASA Astrophysics Data System (ADS)

Gao, Lei; Shi, Zhe; Li, Donghui; McLean, Alexander; Chattopadhyay, Kinnor

2016-06-01

Electromagnetic levitation (EML) has proved to be a powerful tool for research activities in areas pertaining to materials physics and engineering. The customized EML setups in various fields, ranging from solidification to nanomaterial manufacturing, require the designing of stable levitation systems. Since the elevated droplet is opaque, the most effective way to research on EML is mathematical modeling. In the present study, a 3D model was built to investigate the rebalancing phenomenon causing instabilities during droplet melting. A mathematical model modified based on Hooke's law (spring) was proposed to describe the levitation system. This was combined with dimensionless analysis to investigate the generation of levitation forces as it will significantly affect the behavior of the spring model.

The role of mathematical models in understanding pattern formation in developmental biology.

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

MI-Sim: A MATLAB package for the numerical analysis of microbial ecological interactions.

PubMed

Wade, Matthew J; Oakley, Jordan; Harbisher, Sophie; Parker, Nicholas G; Dolfing, Jan

2017-01-01

Food-webs and other classes of ecological network motifs, are a means of describing feeding relationships between consumers and producers in an ecosystem. They have application across scales where they differ only in the underlying characteristics of the organisms and substrates describing the system. Mathematical modelling, using mechanistic approaches to describe the dynamic behaviour and properties of the system through sets of ordinary differential equations, has been used extensively in ecology. Models allow simulation of the dynamics of the various motifs and their numerical analysis provides a greater understanding of the interplay between the system components and their intrinsic properties. We have developed the MI-Sim software for use with MATLAB to allow a rigorous and rapid numerical analysis of several common ecological motifs. MI-Sim contains a series of the most commonly used motifs such as cooperation, competition and predation. It does not require detailed knowledge of mathematical analytical techniques and is offered as a single graphical user interface containing all input and output options. The tools available in the current version of MI-Sim include model simulation, steady-state existence and stability analysis, and basin of attraction analysis. The software includes seven ecological interaction motifs and seven growth function models. Unlike other system analysis tools, MI-Sim is designed as a simple and user-friendly tool specific to ecological population type models, allowing for rapid assessment of their dynamical and behavioural properties.

Relations of Different Types of Numerical Magnitude Representations to Each Other and to Mathematics Achievement

ERIC Educational Resources Information Center

Fazio, Lisa K.; Bailey, Drew H.; Thompson, Clarissa A.; Siegler, Robert S.

2014-01-01

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both…

The Source of the Symbolic Numerical Distance and Size Effects

PubMed Central

Krajcsi, Attila; Lengyel, Gábor; Kojouharova, Petia

2016-01-01

Human number understanding is thought to rely on the analog number system (ANS), working according to Weber’s law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects. Second, we demonstrate that the DSS model can give quantitatively as appropriate a description of the effects as the ANS model. Finally, we show that symbolic numerical size effect is mainly influenced by the frequency of the symbols, and not by the ratios of their values. This last result suggests that numerical distance and size effects cannot be caused by the ANS, while the DSS model might be the alternative approach that can explain the frequency-based size effect. PMID:27917139

Electrophoretic separator for purifying biologicals, part 1

NASA Technical Reports Server (NTRS)

Mccreight, L. R.

1978-01-01

A program to develop an engineering model of an electrophoretic separator for purifying biologicals is summarized. An extensive mathematical modeling study and numerous ground based tests were included. Focus was placed on developing an actual electrophoretic separator of the continuous flow type, configured and suitable for flight testing as a space processing applications rocket payload.

Numerical modelling of river morphodynamics: Latest developments and remaining challenges

NASA Astrophysics Data System (ADS)

Siviglia, Annunziato; Crosato, Alessandra

2016-07-01

Numerical morphodynamic models provide scientific frameworks for advancing our understanding of river systems. The research on involved topics is an important and socially relevant undertaking regarding our environment. Nowadays numerical models are used for different purposes, from answering questions about basic morphodynamic research to managing complex river engineering problems. Due to increasing computer power and the development of advanced numerical techniques, morphodynamic models are now more and more used to predict the bed patterns evolution to a broad spectrum of spatial and temporal scales. The development and the success of application of such models are based upon a wide range of disciplines from applied mathematics for the numerical solution of the equations to geomorphology for the physical interpretation of the results. In this light we organized this special issue (SI) soliciting multidisciplinary contributions which encompass any aspect needed for the development and applications of such models. Most of the papers in the SI stem from contributions to session HS9.5/GM7.11 on numerical modelling and experiments in river morphodynamics at the European Geosciences Union (EGU) General Assembly held in Vienna, April 27th to May 2nd 2014.

Mathematical model of the heat transfer process taking into account the consequences of nonlocality in structurally sensitive materials

NASA Astrophysics Data System (ADS)

Kuvyrkin, G. N.; Savelyeva, I. Y.; Kuvshynnikova, D. A.

2018-04-01

Creation of new materials based on nanotechnology is an important direction of modern materials science development. Materials obtained using nanotechnology can possess unique physical-mechanical and thermophysical properties, allowing their effective use in structures exposed to high-intensity thermomechanical effects. An important step in creation and use of new materials is the construction of mathematical models to describe the behavior of these materials in a wide range of changes under external effects. The model of heat conduction of structural-sensitive materials is considered with regard to the medium nonlocality effects. The relations of the mathematical model include an integral term describing the spatial nonlocality of the medium. A difference scheme, which makes it possible to obtain a numerical solution of the problem of nonstationary heat conduction with regard to the influence of the medium nonlocality on space, has been developed. The influence of the model parameters on the temperature distributions is analyzed.

Number sense in infancy predicts mathematical abilities in childhood.

PubMed

Starr, Ariel; Libertus, Melissa E; Brannon, Elizabeth M

2013-11-05

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

Number sense in infancy predicts mathematical abilities in childhood

PubMed Central

Starr, Ariel; Libertus, Melissa E.; Brannon, Elizabeth M.

2013-01-01

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language. PMID:24145427

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Multiphysics Simulation of Welding-Arc and Nozzle-Arc System: Mathematical-Model, Solution-Methodology and Validation

NASA Astrophysics Data System (ADS)

Pawar, Sumedh; Sharma, Atul

2018-01-01

This work presents mathematical model and solution methodology for a multiphysics engineering problem on arc formation during welding and inside a nozzle. A general-purpose commercial CFD solver ANSYS FLUENT 13.0.0 is used in this work. Arc formation involves strongly coupled gas dynamics and electro-dynamics, simulated by solution of coupled Navier-Stoke equations, Maxwell's equations and radiation heat-transfer equation. Validation of the present numerical methodology is demonstrated with an excellent agreement with the published results. The developed mathematical model and the user defined functions (UDFs) are independent of the geometry and are applicable to any system that involves arc-formation, in 2D axisymmetric coordinates system. The high-pressure flow of SF6 gas in the nozzle-arc system resembles arc chamber of SF6 gas circuit breaker; thus, this methodology can be extended to simulate arcing phenomenon during current interruption.

Modeling of transient heat pipe operation

NASA Technical Reports Server (NTRS)

Colwell, G. T.; Hartley, J. G.

1986-01-01

Mathematical models and associated solution procedures which can be used to design heat pipe cooled structures for use on hypersonic vehicles are being developed. The models should also have the capability to predict off-design performance for a variety of operating conditions. It is expected that the resulting models can be used to predict startup behavior of liquid metal heat pipes to be used in reentry vehicles, hypersonic aircraft, and space nuclear reactors. Work to date related to numerical solutions of governing differential equations for the outer shell and the combination capillary structure and working fluid is summarized. Finite element numerical equations using both implicit, explicit, and combination methods were examined.

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Numerical investigation of cryogen re-gasification in a plate heat exchanger

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Płuszka, Paweł; Brenk, Arkadiusz

2017-12-01

The efficient re-gasification of cryogen is a crucial process in many cryogenic installations. It is especially important in the case of LNG evaporators used in stationary and mobile applications (e.g. marine and land transport). Other gases, like nitrogen or argon can be obtained at highest purity after re-gasification from their liquid states. Plate heat exchangers (PHE) are characterized by a high efficiency. Application of PHE for liquid gas vaporization processes can be beneficial. PHE design and optimization can be significantly supported by numerical modelling. Such calculations are very challenging due to very high computational demands and complexity related to phase change modelling. In the present work, a simplified mathematical model of a two phase flow with phase change was introduced. To ensure fast calculations a simplified two-dimensional (2D) numerical model of a real PHE was developed. It was validated with experimental measurements and finally used for LNG re-gasification modelling. The proposed numerical model showed to be orders of magnitude faster than its full 3D original.

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…

Numerical study of combustion processes in afterburners

NASA Technical Reports Server (NTRS)

Zhou, Xiaoqing; Zhang, Xiaochun

1986-01-01

Mathematical models and numerical methods are presented for computer modeling of aeroengine afterburners. A computer code GEMCHIP is described briefly. The algorithms SIMPLER, for gas flow predictions, and DROPLET, for droplet flow calculations, are incorporated in this code. The block correction technique is adopted to facilitate convergence. The method of handling irregular shapes of combustors and flameholders is described. The predicted results for a low-bypass-ratio turbofan afterburner in the cases of gaseous combustion and multiphase spray combustion are provided and analyzed, and engineering guides for afterburner optimization are presented.

Efficient solution methodology for calibrating the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

PubMed

Zambri, Brian; Djellouli, Rabia; Laleg-Kirati, Taous-Meriem

2015-08-01

Our aim is to propose a numerical strategy for retrieving accurately and efficiently the biophysiological parameters as well as the external stimulus characteristics corresponding to the hemodynamic mathematical model that describes changes in blood flow and blood oxygenation during brain activation. The proposed method employs the TNM-CKF method developed in [1], but in a prediction/correction framework. We present numerical results using both real and synthetic functional Magnetic Resonance Imaging (fMRI) measurements to highlight the performance characteristics of this computational methodology.

Iontophoretic transdermal drug delivery: a multi-layered approach.

PubMed

Pontrelli, Giuseppe; Lauricella, Marco; Ferreira, José A; Pena, Gonçalo

2017-12-11

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions. © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

On the Concept of Random Orientation in Far-Field Electromagnetic Scattering by Nonspherical Particles

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2017-01-01

Although the model of randomly oriented nonspherical particles has been used in a great variety of applications of far-field electromagnetic scattering, it has never been defined in strict mathematical terms. In this Letter we use the formalism of Euler rigid-body rotations to clarify the concept of statistically random particle orientations and derive its immediate corollaries in the form of most general mathematical properties of the orientation-averaged extinction and scattering matrices. Our results serve to provide a rigorous mathematical foundation for numerous publications in which the notion of randomly oriented particles and its light-scattering implications have been considered intuitively obvious.

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming.

PubMed

Ashkenazi, Sarit

2018-02-05

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.

Associations of Non-Symbolic and Symbolic Numerical Magnitude Processing with Mathematical Competence: A Meta-Analysis

ERIC Educational Resources Information Center

Schneider, Michael; Beeres, Kassandra; Coban, Leyla; Merz, Simon; Schmidt, S. Susan; Stricker, Johannes; De Smedt, Bert

2017-01-01

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent…

Development of the mathematical model for design and verification of acoustic modal analysis methods

NASA Astrophysics Data System (ADS)

Siner, Alexander; Startseva, Maria

2016-10-01

To reduce the turbofan noise it is necessary to develop methods for the analysis of the sound field generated by the blade machinery called modal analysis. Because modal analysis methods are very difficult and their testing on the full scale measurements are very expensive and tedious it is necessary to construct some mathematical models allowing to test modal analysis algorithms fast and cheap. At this work the model allowing to set single modes at the channel and to analyze generated sound field is presented. Modal analysis of the sound generated by the ring array of point sound sources is made. Comparison of experimental and numerical modal analysis results is presented at this work.

Modeling of MOEMS electromagnetic scanning grating mirror for NIR micro-spectrometer

NASA Astrophysics Data System (ADS)

Zhou, Ying; Wen, Quan; Wen, Zhiyu; Yang, Tingyan

2016-02-01

In this paper, the mathematical model is developed for researching the detailed electromagnetic mechanism of MOEMS scanning mirror. We present the relationship between spectral range and optical scanning angle. Furthermore, the variation tendencies of resonant frequency and maximal torsional angle are studied in detail under different aspect ratios of MOEMS scanning mirror and varied dimensions of torsional bar. The numerical results and Finite Element Analysis simulations both indicate that the thickness of torsional bar is the most important factor. The maximal torsional angle appears when the aspect ratio equals to 1. This mathematical model is an effective way for designing the MOEMS electromagnetic scanning grating mirror in actual fabrication.

Curve fitting methods for solar radiation data modeling

NASA Astrophysics Data System (ADS)

Karim, Samsul Ariffin Abdul; Singh, Balbir Singh Mahinder

2014-10-01

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R2. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both with two terms) gives better results as compare with the other fitting methods.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Curve fitting methods for solar radiation data modeling

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

Karim, Samsul Ariffin Abdul, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my; Singh, Balbir Singh Mahinder, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my

2014-10-24

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R{sup 2}. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both withmore » two terms) gives better results as compare with the other fitting methods.« less

Efficient Numerical Methods for Nonlinear-Facilitated Transport and Exchange in a Blood-Tissue Exchange Unit

PubMed Central

Poulain, Christophe A.; Finlayson, Bruce A.; Bassingthwaighte, James B.

2010-01-01

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data. PMID:9146808

Invariant characteristics of self-organization modes in Belousov reaction modeling

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Goryunov, V. E.; Kolesov, A. Yu

2018-01-01

We consider the problem of mathematical modeling of oxidation-reduction oscillatory chemical reactions based on the mechanism of Belousov reaction. The process of the main components interaction in such reaction can be interpreted by a phenomenologically similar to it “predator-prey” model. Thereby, we consider a parabolic boundary value problem consisting of three Volterra-type equations, which is a mathematical model of this reaction. We carry out a local study of the neighborhood of the system’s non-trivial equilibrium state and construct the normal form of the considering system. Finally, we do a numerical analysis of the coexisting chaotic oscillatory modes of the boundary value problem in a flat area, which have different nature and occur as the diffusion coefficient decreases.

Equilibrium paths analysis of materials with rheological properties by using the chaos theory

NASA Astrophysics Data System (ADS)

Bednarek, Paweł; Rządkowski, Jan

2018-01-01

The numerical equilibrium path analysis of the material with random rheological properties by using standard procedures and specialist computer programs was not successful. The proper solution for the analysed heuristic model of the material was obtained on the base of chaos theory elements and neural networks. The paper deals with mathematical reasons of used computer programs and also are elaborated the properties of the attractor used in analysis. There are presented results of conducted numerical analysis both in a numerical and in graphical form for the used procedures.

Approximate numerical abilities and mathematics: Insight from correlational and experimental training studies.

PubMed

Hyde, D C; Berteletti, I; Mou, Y

2016-01-01

Humans have the ability to nonverbally represent the approximate numerosity of sets of objects. The cognitive system that supports this ability, often referred to as the approximate number system (ANS), is present in early infancy and continues to develop in precision over the life span. It has been proposed that the ANS forms a foundation for uniquely human symbolic number and mathematics learning. Recent work has brought two types of evidence to bear on the relationship between the ANS and human mathematics: correlational studies showing individual differences in approximate numerical abilities correlate with individual differences in mathematics achievement and experimental studies showing enhancing effects of nonsymbolic approximate numerical training on exact, symbolic mathematical abilities. From this work, at least two accounts can be derived from these empirical data. It may be the case that the ANS and mathematics are related because the cognitive and brain processes responsible for representing numerical quantity in each format overlap, the Representational Overlap Hypothesis, or because of commonalities in the cognitive operations involved in mentally manipulating the representations of each format, the Operational Overlap hypothesis. The two hypotheses make distinct predictions for future work to test. © 2016 Elsevier B.V. All rights reserved.

Transcoding abilities in typical and atypical mathematics achievers: the role of working memory and procedural and lexical competencies.

PubMed

Moura, Ricardo; Wood, Guilherme; Pinheiro-Chagas, Pedro; Lonnemann, Jan; Krinzinger, Helga; Willmes, Klaus; Haase, Vitor Geraldi

2013-11-01

Transcoding between numerical systems is one of the most basic abilities acquired by children during their early school years. One important topic that requires further exploration is how mathematics proficiency can affect number transcoding. The aim of the current study was to investigate transcoding abilities (i.e., reading Arabic numerals and writing dictation) in Brazilian children with and without mathematics difficulties, focusing on different school grades. We observed that children with learning difficulties in mathematics demonstrated lower achievement in number transcoding in both early and middle elementary school. In early elementary school, difficulties were observed in both the basic numerical lexicon and the management of numerical syntax. In middle elementary school, difficulties appeared mainly in the transcoding of more complex numbers. An error analysis revealed that the children with mathematics difficulties struggled mainly with the acquisition of transcoding rules. Although we confirmed the previous evidence on the impact of working memory capacity on number transcoding, we found that it did not fully account for the observed group differences. The results are discussed in the context of a maturational lag in number transcoding ability in children with mathematics difficulties. Copyright © 2013 Elsevier Inc. All rights reserved.

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Conditions for duality between fluxes and concentrations in biochemical networks

PubMed Central

Fleming, Ronan M.T.; Vlassis, Nikos; Thiele, Ines; Saunders, Michael A.

2016-01-01

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality. The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes. PMID:27345817

Conditions for duality between fluxes and concentrations in biochemical networks

DOE PAGES

Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines; ...

2016-06-23

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We alsomore » provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes« less

Conditions for duality between fluxes and concentrations in biochemical networks

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

Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We alsomore » provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes« less

Influence of the vertical mixing parameterization on the modeling results of the Arctic Ocean hydrology

NASA Astrophysics Data System (ADS)

Iakshina, D. F.; Golubeva, E. N.

2017-11-01

The vertical distribution of the hydrological characteristics in the upper ocean layer is mostly formed under the influence of turbulent and convective mixing, which are not resolved in the system of equations for large-scale ocean. Therefore it is necessary to include additional parameterizations of these processes into the numerical models. In this paper we carry out a comparative analysis of the different vertical mixing parameterizations in simulations of climatic variability of the Arctic water and sea ice circulation. The 3D regional numerical model for the Arctic and North Atlantic developed in the ICMMG SB RAS (Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Science) and package GOTM (General Ocean Turbulence Model1,2, http://www.gotm.net/) were used as the numerical instruments . NCEP/NCAR reanalysis data were used for determination of the surface fluxes related to ice and ocean. The next turbulence closure schemes were used for the vertical mixing parameterizations: 1) Integration scheme based on the Richardson criteria (RI); 2) Second-order scheme TKE with coefficients Canuto-A3 (CANUTO); 3) First-order scheme TKE with coefficients Schumann and Gerz4 (TKE-1); 4) Scheme KPP5 (KPP). In addition we investigated some important characteristics of the Arctic Ocean state including the intensity of Atlantic water inflow, ice cover state and fresh water content in Beaufort Sea.

A mathematical model for the stressed state analysis of cylindrical laminated-composite pressure vessels

NASA Astrophysics Data System (ADS)

Bak, Roman; Matyja, Tomasz

An algorithm and a computer program have been developed for calculating the strength of pressure vessels made of laminated composites. Numerical results for pressure vessels of Kevlar 49 laminates are compared with experimental data in the literature.

Launch window analysis of satellites in high eccentricity or large circular orbits

NASA Technical Reports Server (NTRS)

Renard, M. L.; Bhate, S. K.; Sridharan, R.

1973-01-01

Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions.

NAPL: SIMULATOR DOCUMENTATION (EPA/600/SR-97/102)

EPA Science Inventory

A mathematical and numerical model is developed to simulate the transport and fate of NAPLs (Non-Aqueous Phase Liquids) in near-surface granular soils. The resulting three-dimensional, three phase simulator is called NAPL. The simulator accommodates three mobile phases: water, NA...

Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814

Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity

NASA Astrophysics Data System (ADS)

Aziz, Asim; Jamshed, Wasim; Aziz, Taha

2018-04-01

In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The non-Newtonian Maxwell nanofluid model is utilized for the working fluid along with slip and convective boundary conditions and comprehensive analysis of entropy generation in the system is also observed. The effect of thermal radiation and variable thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for Cu-water and TiO2-water nanofluids. Results are presented for the velocity, temperature and entropy generation profiles, skin friction coefficient and Nusselt number. The discussion is concluded on the effect of various governing parameters on the motion, temperature variation, entropy generation, velocity gradient and the rate of heat transfer at the boundary.

Numerical simulation of dynamics of brushless dc motors for aerospace and other applications. Volume 1: Model development and applications, part B

NASA Technical Reports Server (NTRS)

Demerdash, N. A. O.; Nehl, T. W.

1979-01-01

A mathematical model was developed and computerized simulations were obtained for a brushless dc motor. Experimentally obtained oscillograms of the machine phase currents are presented and the corresponding current and voltage waveforms for various modes of operation of the motor are presented and discussed.

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

Optimal control of HIV/AIDS dynamic: Education and treatment

NASA Astrophysics Data System (ADS)

Sule, Amiru; Abdullah, Farah Aini

2014-07-01

A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.

Prediction of blood pressure and blood flow in stenosed renal arteries using CFD

NASA Astrophysics Data System (ADS)

Jhunjhunwala, Pooja; Padole, P. M.; Thombre, S. B.; Sane, Atul

2018-04-01

In the present work an attempt is made to develop a diagnostive tool for renal artery stenosis (RAS) which is inexpensive and in-vitro. To analyse the effects of increase in the degree of severity of stenosis on hypertension and blood flow, haemodynamic parameters are studied by performing numerical simulations. A total of 16 stenosed models with varying degree of stenosis severity from 0-97.11% are assessed numerically. Blood is modelled as a shear-thinning, non-Newtonian fluid using the Carreau model. Computational Fluid Dynamics (CFD) analysis is carried out to compute the values of flow parameters like maximum velocity and maximum pressure attained by blood due to stenosis under pulsatile flow. These values are further used to compute the increase in blood pressure and decrease in available blood flow to kidney. The computed available blood flow and secondary hypertension for varying extent of stenosis are mapped by curve fitting technique using MATLAB and a mathematical model is developed. Based on these mathematical models, a quantification tool is developed for tentative prediction of probable availability of blood flow to the kidney and severity of stenosis if secondary hypertension is known.

Mathematical models for principles of gyroscope theory

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2017-01-01

Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.

Effect of Multiple Delays in an Eco-Epidemiological Model with Strong Allee Effect

NASA Astrophysics Data System (ADS)

Ghosh, Kakali; Biswas, Santanu; Samanta, Sudip; Tiwari, Pankaj Kumar; Alshomrani, Ali Saleh; Chattopadhyay, Joydev

In the present article, we make an attempt to investigate the effect of two time delays, logistic delay and gestation delay, on an eco-epidemiological model. In the proposed model, strong Allee effect is considered in the growth term of the prey population. We incorporate two time lags and inspect elementary mathematical characteristic of the proposed model such as boundedness, uniform persistence, stability and Hopf-bifurcation for all possible combinations of both delays at the interior equilibrium point of the system. We observe that increase in gestation delay leads to chaotic solutions through the limit cycle. We also observe that the Allee effect play a major role in controlling the chaos. We execute several numerical simulations to illustrate the proposed mathematical model and our analytical findings.

Problem-Based Instructional Strategy and Numerical Ability as Determinants of Senior Secondary Achievement in Mathematics

ERIC Educational Resources Information Center

Badru, Ademola K.

2016-01-01

The study investigated Problem-based Instructional Strategy and Numerical ability as determinants of Senior Secondary Achievement in Mathematics. This study used 4 x 2 x 2 non-randomised control group Pretest-Posttest Quasi-experimental Factorial design. It consisted of two independent variables (treatment and Numerical ability) and one moderating…

Numerical Magnitude Representation in Children with Mathematical Difficulties with or without Reading Difficulties

ERIC Educational Resources Information Center

Tobia, Valentina; Fasola, Anna; Lupieri, Alice; Marzocchi, Gian Marco

2016-01-01

This study aimed to explore the spatial numerical association of response codes (SNARC), the flanker, and the numerical distance effects in children with mathematical difficulties. From a sample of 720 third, fourth, and fifth graders, 60 children were selected and divided into the following three groups: typically developing children (TD; n =…

Differences in the acuity of the Approximate Number System in adults: the effect of mathematical ability.

PubMed

Guillaume, Mathieu; Nys, Julie; Mussolin, Christophe; Content, Alain

2013-11-01

It is largely admitted that processing numerosity relies on an innate Approximate Number System (ANS), and recent research consistently observed a relationship between ANS acuity and mathematical ability in childhood. However, studies assessing this relationship in adults led to contradictory results. In this study, adults with different levels of mathematical expertise performed two tasks on the same pairs of dot collections, based either on numerosity comparison or on cumulative area comparison. Number of dots and cumulative area were congruent in half of the stimuli, and incongruent in the other half. The results showed that adults with higher mathematical ability obtained lower Weber fractions in the numerical condition than participants with lower mathematical ability. Further, adults with lower mathematical ability were more affected by the interference of the continuous dimension in the numerical comparison task, whereas conversely higher-expertise adults showed stronger interference of the numerical dimension in the continuous comparison task. Finally, ANS acuity correlated with arithmetic performance. Taken together, the data suggest that individual differences in ANS acuity subsist in adulthood, and that they are related to mathematical ability. © 2013.

Experimental determination of surface heat transfer coefficient in a dry ice-ethanol cooling bath using a numerical approach.

PubMed

Santos, M V; Sansinena, M; Zaritzky, N; Chirife, J

BACKGROUND: Dry ice-ethanol bath (-78 degree C) have been widely used in low temperature biological research to attain rapid cooling of samples below freezing temperature. The prediction of cooling rates of biological samples immersed in dry ice-ethanol bath is of practical interest in cryopreservation. The cooling rate can be obtained using mathematical models representing the heat conduction equation in transient state. Additionally, at the solid cryogenic-fluid interface, the knowledge of the surface heat transfer coefficient (h) is necessary for the convective boundary condition in order to correctly establish the mathematical problem. The study was to apply numerical modeling to obtain the surface heat transfer coefficient of a dry ice-ethanol bath. A numerical finite element solution of heat conduction equation was used to obtain surface heat transfer coefficients from measured temperatures at the center of polytetrafluoroethylene and polymethylmetacrylate cylinders immersed in a dry ice-ethanol cooling bath. The numerical model considered the temperature dependence of thermophysical properties of plastic materials used. A negative linear relationship is observed between cylinder diameter and heat transfer coefficient in the liquid bath, the calculated h values were 308, 135 and 62.5 W/(m 2 K) for PMMA 1.3, PTFE 2.59 and 3.14 cm in diameter, respectively. The calculated heat transfer coefficients were consistent among several replicates; h in dry ice-ethanol showed an inverse relationship with cylinder diameter.

From virtual clustering analysis to self-consistent clustering analysis: a mathematical study

NASA Astrophysics Data System (ADS)

Tang, Shaoqiang; Zhang, Lei; Liu, Wing Kam

2018-03-01

In this paper, we propose a new homogenization algorithm, virtual clustering analysis (VCA), as well as provide a mathematical framework for the recently proposed self-consistent clustering analysis (SCA) (Liu et al. in Comput Methods Appl Mech Eng 306:319-341, 2016). In the mathematical theory, we clarify the key assumptions and ideas of VCA and SCA, and derive the continuous and discrete Lippmann-Schwinger equations. Based on a key postulation of "once response similarly, always response similarly", clustering is performed in an offline stage by machine learning techniques (k-means and SOM), and facilitates substantial reduction of computational complexity in an online predictive stage. The clear mathematical setup allows for the first time a convergence study of clustering refinement in one space dimension. Convergence is proved rigorously, and found to be of second order from numerical investigations. Furthermore, we propose to suitably enlarge the domain in VCA, such that the boundary terms may be neglected in the Lippmann-Schwinger equation, by virtue of the Saint-Venant's principle. In contrast, they were not obtained in the original SCA paper, and we discover these terms may well be responsible for the numerical dependency on the choice of reference material property. Since VCA enhances the accuracy by overcoming the modeling error, and reduce the numerical cost by avoiding an outer loop iteration for attaining the material property consistency in SCA, its efficiency is expected even higher than the recently proposed SCA algorithm.

Mathematical model of information process of protection of the social sector

NASA Astrophysics Data System (ADS)

Novikov, D. A.; Tsarkova, E. G.; Dubrovin, A. S.; Soloviev, A. S.

2018-03-01

In work the mathematical model of information protection of society against distribution of extremist moods by means of impact on mass consciousness of information placed in media is investigated. Internal and external channels on which there is a dissemination of information are designated. The problem of optimization consisting in search of the optimum strategy allowing to use most effectively media for dissemination of antiterrorist information with the minimum financial expenses is solved. The algorithm of a numerical method of the solution of a problem of optimization is constructed and also the analysis of results of a computing experiment is carried out.

Stability analysis of host dynamics for hiv

NASA Astrophysics Data System (ADS)

Geetha, V.; Balamuralitharan, S.

2018-04-01

The phenomenon of disease modeling can be easily accomplished through mathematical framework. In this paper the transmission of disease in human is represented mathematically as a nonlinear system. We think about the components of the Human Immunodeficiency Virus (HIV) among the beginning periods of illness. Throughout this paper we have determined those logical representation of a three-compartmental HIV demonstrate for their stability evaluation. We tend to likewise explore the stimulating behavior of the model and acquire those Steady states for the disease-free and the endemic agreement. The framework can be evaluated by reproduction number R0. We additionally clarify the numerical recreation and their outcomes.

Mathematical model for the assessment of fracture risk associated with osteoporosis

NASA Astrophysics Data System (ADS)

Dinis, Jairson; Pereira, Ana I.; Fonseca, Elza M.

2012-09-01

Osteoporosis is a skeletal disease characterized by low bone mass. It is considered a worldwide public health problem that affects a large number of people, in particularly for women with more than 50 years old. The occurrence pattern of osteoporosis in a population may be related to several factors, including socio-economic factors such as income, educational attainment, and factors related to lifestyle such as diet and physical activity. These and other aspects have increasingly been identified as determining the occurrence of various diseases, including osteoporosis. This work proposes a mathematical model that provides the level of osteoporosis in the patient. Preliminary numerical results are presented.

Analysis and Management of Animal Populations: Modeling, Estimation and Decision Making

USGS Publications Warehouse

Williams, B.K.; Nichols, J.D.; Conroy, M.J.

2002-01-01

This book deals with the processes involved in making informed decisions about the management of animal populations. It covers the modeling of population responses to management actions, the estimation of quantities needed in the modeling effort, and the application of these estimates and models to the development of sound management decisions. The book synthesizes and integrates in a single volume the methods associated with these themes, as they apply to ecological assessment and conservation of animal populations. KEY FEATURES * Integrates population modeling, parameter estimation and * decision-theoretic approaches to management in a single, cohesive framework * Provides authoritative, state-of-the-art descriptions of quantitative * approaches to modeling, estimation and decision-making * Emphasizes the role of mathematical modeling in the conduct of science * and management * Utilizes a unifying biological context, consistent mathematical notation, * and numerous biological examples

Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

NASA Astrophysics Data System (ADS)

Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T. M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.

2018-05-01

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

Numerical modeling of heat and mass transport processes in an evaporative thermal protection system

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

Bobrov, I.N.; Kuryachii, A.P.

1992-08-01

We propose a mathematical model of heat and mass transport processes in a moist, porous material subject to capillary action. The material is in contact with a heated surface, and the processes take place while the liquid is evaporating in a cavity with a drainage hole. A sample calculation based on the model is presented. 45 refs., 4 figs.

Spray combustion model improvement study, 1

NASA Technical Reports Server (NTRS)

Chen, C. P.; Kim, Y. M.; Shang, H. M.

1993-01-01

This study involves the development of numerical and physical modeling in spray combustion. These modeling efforts are mainly motivated to improve the physical submodels of turbulence, combustion, atomization, dense spray effects, and group vaporization. The present mathematical formulation can be easily implemented in any time-marching multiple pressure correction methodologies such as MAST code. A sequence of validation cases includes the nonevaporating, evaporating and_burnin dense_sprays.

Brain stimulation, mathematical, and numerical training: Contribution of core and noncore skills.

PubMed

Looi, C Y; Cohen Kadosh, R

2016-01-01

Mathematical abilities that are correlated with various life outcomes vary across individuals. One approach to improve mathematical abilities is by understanding the underlying cognitive functions. Theoretical and experimental evidence suggest that mathematical abilities are subserved by "core" and "noncore" skills. Core skills are commonly regarded as the "innate" capacity to attend to and process numerical information, while noncore skills are those that are important for mathematical cognition, but are not exclusive to the mathematical domain such as executive functions, spatial skills, and attention. In recent years, mathematical training has been combined with the application of noninvasive brain stimulation to further enhance training outcomes. However, the development of more strategic training paradigms is hindered by the lack of understanding on the contributory nature of core and noncore skills and their neural underpinnings. In the current review, we will examine the effects of brain stimulation with focus on transcranial electrical stimulation on core and noncore skills, and its impact on mathematical and numerical training. We will conclude with a discussion on the theoretical and experimental implications of these studies and directions for further research. © 2016 Elsevier B.V. All rights reserved.

On numerical model of time-dependent processes in three-dimensional porous heat-releasing objects

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2016-10-01

The gas flows in the gravity field through porous objects with heat-releasing sources are investigated when the self-regulation of the flow rate of the gas passing through the porous object takes place. Such objects can appear after various natural or man-made disasters (like the exploded unit of the Chernobyl NPP). The mathematical model and the original numerical method, based on a combination of explicit and implicit finite difference schemes, are developed for investigating the time-dependent processes in 3D porous energy-releasing objects. The advantage of the numerical model is its ability to describe unsteady processes under both natural convection and forced filtration. The gas cooling of 3D porous objects with different distribution of heat sources is studied using computational experiment.

Triggering effect of mining at different horizons in the rock mass with excavations. Mathematical modeling

NASA Astrophysics Data System (ADS)

Eremin, M. O.; Makarov, P. V.

2017-12-01

On the basis of a quite simple structural model of rock mass, containing coal seams on two horizons, coal mining is numerically modeled. A finite difference numerical technique is applied. At first, mining starts at the upper horizon and then moves to the lower horizon. It is shown that a mining process at the lower horizon has a significant triggering influence on the growth of damage zones in the roof and floor at the upper horizon. The features of spatiotemporal migration of deformation activity are studied numerically. Foci of large-scale fracture are located at the boundary of the seismic silence zone and the zone where the deformation activity migrates. This boundary has an additional characteristic: the maximum gradient of rock pressure is observed in this zone.

Las Matematicas: Lenguaje Universal. Nivel 1: Numeros y Numeracion (Mathematics: A Universal Language. Level 1: Numbers and Numeration).

ERIC Educational Resources Information Center

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include graphing on a number line, place value, using exponents, flow charts, and Roman numerals. (MK)

A nonlinear SIR with stability

NASA Astrophysics Data System (ADS)

Trisilowati, Darti, I.; Fitri, S.

2014-02-01

The aim of this work is to develop a mathematical model of a nonlinear susceptible-infectious-removed (SIR) epidemic model with vaccination. We analyze the stability of the model by linearizing the model around the equilibrium point. Then, diphtheria data from East Java province is fitted to the model. From these estimated parameters, we investigate which parameters that play important role in the epidemic model. Some numerical simulations are given to illustrate the analytical results and the behavior of the model.

Discrete-time model reduction in limited frequency ranges

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

On numerical model of one-dimensional time-dependent gas flows through bed of encapsulated phase change material

NASA Astrophysics Data System (ADS)

Lutsenko, N. A.; Fetsov, S. S.

2017-10-01

Mathematical model and numerical method are proposed for investigating the one-dimensional time-dependent gas flows through a packed bed of encapsulated Phase Change Material (PCM). The model is based on the assumption of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for PCM and gas. The advantage of the method is that it does not require predicting the location of phase transition zone and can define it automatically as in a usual shock-capturing method. One of the applications of the developed numerical model is the simulation of novel Adiabatic Compressed Air Energy Storage system (A-CAES) with Thermal Energy Storage subsystem (TES) based on using the encapsulated PCM in packed bed. Preliminary test calculations give hope that the method can be effectively applied in the future for modelling the charge and discharge processes in such TES with PCM.

Complex Dynamics of Wetland Ecosystem with Nonlinear Harvesting: Application to Chilika Lake in Odisha, India

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Tiwari, S. K.; Roy, Parimita

2015-06-01

In this paper, an attempt has been made to study the spatial and temporal dynamical interactions among the species of wetland ecosystem through a mathematical model. The model represents the population dynamics of phytoplankton, zooplankton and fish species found in Chilika lake, Odisha, India. Nonlinear stability analysis of both the temporal and spatial models has been carried out. Maximum sustainable yield and optimal harvesting policy have been studied for a nonspatial model system. Numerical simulation has been performed to figure out the parameters responsible for the complex dynamics of the wetland system. Significant outcomes of our numerical findings and their interpretations from an ecological point of view are provided in this paper. Numerical simulation of spatial model exhibits some interesting and beautiful patterns. We have also pointed out the parameters that are responsible for the good health of wetland ecosystem.

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

Predicting debris-flow initiation and run-out with a depth-averaged two-phase model and adaptive numerical methods

NASA Astrophysics Data System (ADS)

George, D. L.; Iverson, R. M.

2012-12-01

Numerically simulating debris-flow motion presents many challenges due to the complicated physics of flowing granular-fluid mixtures, the diversity of spatial scales (ranging from a characteristic particle size to the extent of the debris flow deposit), and the unpredictability of the flow domain prior to a simulation. Accurately predicting debris-flows requires models that are complex enough to represent the dominant effects of granular-fluid interaction, while remaining mathematically and computationally tractable. We have developed a two-phase depth-averaged mathematical model for debris-flow initiation and subsequent motion. Additionally, we have developed software that numerically solves the model equations efficiently on large domains. A unique feature of the mathematical model is that it includes the feedback between pore-fluid pressure and the evolution of the solid grain volume fraction, a process that regulates flow resistance. This feature endows the model with the ability to represent the transition from a stationary mass to a dynamic flow. With traditional approaches, slope stability analysis and flow simulation are treated separately, and the latter models are often initialized with force balances that are unrealistically far from equilibrium. Additionally, our new model relies on relatively few dimensionless parameters that are functions of well-known material properties constrained by physical data (eg. hydraulic permeability, pore-fluid viscosity, debris compressibility, Coulomb friction coefficient, etc.). We have developed numerical methods and software for accurately solving the model equations. By employing adaptive mesh refinement (AMR), the software can efficiently resolve an evolving debris flow as it advances through irregular topography, without needing terrain-fit computational meshes. The AMR algorithms utilize multiple levels of grid resolutions, so that computationally inexpensive coarse grids can be used where the flow is absent, and much higher resolution grids evolve with the flow. The reduction in computational cost, due to AMR, makes very large-scale problems tractable on personal computers. Model accuracy can be tested by comparison of numerical predictions and empirical data. These comparisons utilize controlled experiments conducted at the USGS debris-flow flume, which provide detailed data about flow mobilization and dynamics. Additionally, we have simulated historical large-scale debris flows, such as the (≈50 million m^3) debris flow that originated on Mt. Meager, British Columbia in 2010. This flow took a very complex route through highly variable topography and provides a valuable benchmark for testing. Maps of the debris flow deposit and data from seismic stations provide evidence regarding flow initiation, transit times and deposition. Our simulations reproduce many of the complex patterns of the event, such as run-out geometry and extent, and the large-scale nature of the flow and the complex topographical features demonstrate the utility of AMR in flow simulations.

New method of contour image processing based on the formalism of spiral light beams

NASA Astrophysics Data System (ADS)

Volostnikov, Vladimir G.; Kishkin, S. A.; Kotova, S. P.

2013-07-01

The possibility of applying the mathematical formalism of spiral light beams to the problems of contour image recognition is theoretically studied. The advantages and disadvantages of the proposed approach are evaluated; the results of numerical modelling are presented.

Computing Surface Coordinates Of Face-Milled Spiral-Bevel Gear Teeth

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.; Litvin, Faydor L.

1995-01-01

Surface coordinates of face-milled spiral-bevel gear teeth computed by method involving numerical solution of governing equations. Needed to generate mathematical models of tooth surfaces for use in finite-element analyses of stresses, strains, and vibrations in meshing spiral-bevel gears.

A MATHEMATICAL MODEL FOR CALCULATING ELECTRICAL CONDITIONS IN WIRE-DUCT ELECTROSTATIC PRECIPITATION DEVICES

EPA Science Inventory

The article reports the development of a new method of calculating electrical conditions in wire-duct electrostatic precipitation devices. The method, based on a numerical solution to the governing differential equations under a suitable choice of boundary conditions, accounts fo...

The role of carbon dioxide in ammonia emission from manure

USDA-ARS?s Scientific Manuscript database

Ammonia emission from manure is a significant loss of fixed N from agricultural systems, and contributes to air pollution and ecosystem degradation. Despite the development of numerous mathematical models for predicting ammonia emission, the interactions between carbon dioxide emission, manure pH, a...

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

Optimizing romanian maritime coastline using mathematical model Litpack

NASA Astrophysics Data System (ADS)

Anton, I. A.; Panaitescu, M.; Panaitescu, F. V.

2017-08-01

There are many methods and tools to study shoreline change in coastal engineering. LITPACK is a numerical model included in MIKE software developed by DHI (Danish Hydraulic Institute). With this matehematical model we can simulate coastline evolution and profile along beach. Research and methodology: the paper contents location of the study area, the current status of Midia-Mangalia shoreline, protection objectives, the changes of shoreline after having protected constructions. In this paper are presented numerical and graphycal results obtained with this model for studying the romanian maritime coastline in area MIDIA-MANGALIA: non-cohesive sediment transport, long-shore current and littoral drift, coastline evolution, crossshore profile evolution, the development of the coastline position in time.

Towards a category theory approach to analogy: Analyzing re-representation and acquisition of numerical knowledge.

PubMed

Navarrete, Jairo A; Dartnell, Pablo

2017-08-01

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called "flexibility" whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena.

MODELING THE ENDOCRINE CONTROL OF VITELLOGENIN PRODUCTION IN FEMALE RAINBOW TROUT

PubMed Central

Sundling, Kaitlin; Craciun, Gheorghe; Schultz, Irvin; Hook, Sharon; Nagler, James; Cavileer, Tim; Verducci, Joseph; Liu, Yushi; Kim, Jonghan; Hayton, William

2015-01-01

The rainbow trout endocrine system is sensitive to changes in annual day length, which is likely the principal environmental cue controlling its reproductive cycle. This study focuses on the endocrine regulation of vitellogenin (Vg) protein synthesis, which is the major egg yolk precursor in this fish species. We present a model of Vg production in female rainbow trout which incorporates a biological pathway beginning with sex steroid estradiol-17β levels in the plasma and concluding with Vg secretion by the liver and sequestration in the oocytes. Numerical simulation results based on this model are compared with experimental data for estrogen receptor mRNA, Vg mRNA, and Vg in the plasma from female rainbow trout over a normal annual reproductive cycle. We also analyze the response of the model to parameter changes. The model is subsequently tested against experimental data from female trout under a compressed photoperiod regime. Comparison of numerical and experimental results suggests the possibility of a time-dependent change in oocyte Vg uptake rate. This model is part of a larger effort that is developing a mathematical description of the endocrine control of reproduction in female rainbow trout. We anticipate that these mathematical and computational models will play an important role in future regulatory toxicity assessments and in the prediction of ecological risk. PMID:24506554

Towards a category theory approach to analogy: Analyzing re-representation and acquisition of numerical knowledge

PubMed Central

2017-01-01

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called “flexibility” whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena. PMID:28841643

Do Different Types of School Mathematics Development Depend on Different Constellations of Numerical versus General Cognitive Abilities?

ERIC Educational Resources Information Center

Fuchs, Lynn S.; Geary, David C.; Compton, Donald L.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Bryant, Joan D.; Schatschneider, Christopher

2010-01-01

The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations, and word…

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

NASA Technical Reports Server (NTRS)

1994-01-01

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Modeling the Performance of Water-Zeolite 13X Adsorption Heat Pump

NASA Astrophysics Data System (ADS)

Kowalska, Kinga; Ambrożek, Bogdan

2017-12-01

The dynamic performance of cylindrical double-tube adsorption heat pump is numerically analysed using a non-equilibrium model, which takes into account both heat and mass transfer processes. The model includes conservation equations for: heat transfer in heating/cooling fluids, heat transfer in the metal tube, and heat and mass transfer in the adsorbent. The mathematical model is numerically solved using the method of lines. Numerical simulations are performed for the system water-zeolite 13X, chosen as the working pair. The effect of the evaporator and condenser temperatures on the adsorption and desorption kinetics is examined. The results of the numerical investigation show that both of these parameters have a significant effect on the adsorption heat pump performance. Based on computer simulation results, the values of the coefficients of performance for heating and cooling are calculated. The results show that adsorption heat pumps have relatively low efficiency compared to other heat pumps. The value of the coefficient of performance for heating is higher than for cooling

Numerical simulation of the structure of the high-latitude ionospheric F region during meridional HF propagation

NASA Astrophysics Data System (ADS)

Andreev, M. Yu.; Mingaleva, G. I.; Mingalev, V. S.

2007-08-01

A previously developed model of the high-latitude ionosphere is used to calculate the distribution of the ionospheric parameters in the polar region. A specific method for specifying input parameters of the mathematical model, using the experimental data obtained by the method of satellite radio tomography, is used in this case. The spatial distributions of the ionospheric parameters characterized by a complex inhomogeneous structure in the high-latitude region, calculated with the help of the mathematical model, are used to simulate the HF propagation along the meridionally oriented radio paths extending from middle to high latitudes. The method for improving the HF communication between a midlatitude transmitter and a polar-cap receiver is proposed.

Numerical Solution of a 3-D Advection-Dispersion Model for Dissolved Oxygen Distribution in Facultative Ponds

NASA Astrophysics Data System (ADS)

Sunarsih; Sasongko, Dwi P.; Sutrisno

2018-02-01

This paper describes a mathematical model for the dissolved oxygen distribution in the plane of a facultative pond with a certain depth. The purpose of this paper is to determine the variation of dissolved oxygen concentration in facultative ponds. The 3-dimensional advection-diffusion equation is solved using the finite difference method Forward Time Central Space (FTCS). Numerical results show that the aerator greatly affects the occurrence of oxygen concentration variations in the facultative pond in the certain depth. The concentration of dissolved oxygen decreases as the depth of the pond increases.

Dispersive models describing mosquitoes’ population dynamics

NASA Astrophysics Data System (ADS)

Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.

2016-08-01

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

NASA Technical Reports Server (NTRS)

Jang, Jong Hoon; Faghri, Amir; Chang, Won Soon; Mahefkey, Edward T.

1989-01-01

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

NASA Technical Reports Server (NTRS)

Jang, J. H.; Faghri, A.; Chang, W. S.; Mahefkey, E. T.

1990-01-01

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Modeling crustal deformation near active faults and volcanic centers: a catalog of deformation models and modeling approaches

USGS Publications Warehouse

Battaglia, Maurizio; ,; Peter, F.; Murray, Jessica R.

2013-01-01

This manual provides the physical and mathematical concepts for selected models used to interpret deformation measurements near active faults and volcanic centers. The emphasis is on analytical models of deformation that can be compared with data from the Global Positioning System (GPS) receivers, Interferometric synthetic aperture radar (InSAR), leveling surveys, tiltmeters and strainmeters. Source models include pressurized spherical, ellipsoidal, and horizontal penny-shaped geometries in an elastic, homogeneous, flat half-space. Vertical dikes and faults are described following the mathematical notation for rectangular dislocations in an elastic, homogeneous, flat half-space. All the analytical expressions were verified against numerical models developed by use of COMSOL Multyphics, a Finite Element Analysis software (http://www.comsol.com). In this way, typographical errors present were identified and corrected. Matlab scripts are also provided to facilitate the application of these models.

Analytic uncertainty and sensitivity analysis of models with input correlations

NASA Astrophysics Data System (ADS)

Zhu, Yueying; Wang, Qiuping A.; Li, Wei; Cai, Xu

2018-03-01

Probabilistic uncertainty analysis is a common means of evaluating mathematical models. In mathematical modeling, the uncertainty in input variables is specified through distribution laws. Its contribution to the uncertainty in model response is usually analyzed by assuming that input variables are independent of each other. However, correlated parameters are often happened in practical applications. In the present paper, an analytic method is built for the uncertainty and sensitivity analysis of models in the presence of input correlations. With the method, it is straightforward to identify the importance of the independence and correlations of input variables in determining the model response. This allows one to decide whether or not the input correlations should be considered in practice. Numerical examples suggest the effectiveness and validation of our analytic method in the analysis of general models. A practical application of the method is also proposed to the uncertainty and sensitivity analysis of a deterministic HIV model.

Seasonal thermal energy storage in aquifers: Mathematical modeling studies in 1979

NASA Technical Reports Server (NTRS)

Tsang, C. F.

1980-01-01

A numerical model of water and heat flow in geologic media was developed, verified, and tested. The hydraulic parameters (transmittivity and storativity) and the location of a linear hydrologic barrier were simulated and compared with results from field experiments involving two injection-storage-recovery cycles. For both cycles, the initial simulated and observed temperatures agree (55c).

Mathematical Models of Gas Turbine Engines and Their Components (Les Modeles Mathematiques des Turbomoteurs et de leurs organes)

DTIC Science & Technology

1994-12-01

measurements of heat-transfer rate to a gas turbine rotor blade. J.Engng Power . V. 104. No.3. 1982. pp. 542-551. 19. Venediktov V.D., Granovsky A.V...Preprint CIAM, No 11, 1993 (in Russian). 28. Granovsky AV., Danilkin A.V., Rogkov S.G., Rudenko S.V. Numerical and experimental investigation of

Evaluation of massless-spring modeling of suspension-line elasticity during the parachute unfurling process

NASA Technical Reports Server (NTRS)

Poole, L. R.; Huckins, E. K., III

1972-01-01

A general theory on mathematical modeling of elastic parachute suspension lines during the unfurling process was developed. Massless-spring modeling of suspension-line elasticity was evaluated in detail. For this simple model, equations which govern the motion were developed and numerically integrated. The results were compared with flight test data. In most regions, agreement was satisfactory. However, poor agreement was obtained during periods of rapid fluctuations in line tension.

Modelling water hammer in viscoelastic pipelines: short brief

NASA Astrophysics Data System (ADS)

Urbanowicz, K.; Firkowski, M.; Zarzycki, Z.

2016-10-01

The model of water hammer in viscoelastic pipelines is analyzed. An appropriate mathematical model of water hammer in polymer pipelines is presented. An additional term has been added to continuity equation to describe the retarded deformation of the pipe wall. The mechanical behavior of viscoelastic material is described by generalized Kelvin-Voigt model. The comparison of numerical simulation and experimental data from well known papers is presented. Short discussion about obtained results are given.

A simulation model of the oxygen alveolo-capillary exchange in normal and pathological conditions.

PubMed

Brighenti, Chiara; Gnudi, Gianni; Avanzolini, Guido

2003-05-01

This paper presents a mathematical model of the oxygen alveolo-capillary exchange to provide the capillary oxygen partial pressure profile in normal and pathological conditions. In fact, a thickening of the blood-gas barrier, heavy exercise or a low oxygen partial pressure (PO2) in the alveolar space can reduce the O2 alveolo-capillary exchange. Since the reversible binding between haemoglobin and oxygen makes it impossible to determine the closed form for the mathematical description of the PO2 profile along the pulmonary capillaries, an approximate analytical solution of the capillary PO2 profile is proposed. Simulation results are compared with the capillary PO2 profile obtained by numerical integration and by a piecewise linear interpolation of the oxyhaemoglobin dissociation curve. Finally, the proposed model is evaluated in a large range of physiopathological diffusive conditions. The good fit to numerical solutions in all experimental conditions seems to represent a substantial improvement with respect to the approach based on a linear approximation of the oxyhaemoglobin dissociation curve, and makes this model a candidate to be incorporated into the integrated descriptions of the entire respiratory system, where the datum of primary interest is the value of end capillary PO2.

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

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

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

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

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Mathematical Modeling of Dual Layer Shell Type Recuperation System for Biogas Dehumidification

NASA Astrophysics Data System (ADS)

Gendelis, S.; Timuhins, A.; Laizans, A.; Bandeniece, L.

2015-12-01

The main aim of the current paper is to create a mathematical model for dual layer shell type recuperation system, which allows reducing the heat losses from the biomass digester and water amount in the biogas without any additional mechanical or chemical components. The idea of this system is to reduce the temperature of the outflowing gas by creating two-layered counter-flow heat exchanger around the walls of biogas digester, thus increasing a thermal resistance and the gas temperature, resulting in a condensation on a colder surface. Complex mathematical model, including surface condensation, is developed for this type of biogas dehumidifier and the parameter study is carried out for a wide range of parameters. The model is reduced to 1D case to make numerical calculations faster. It is shown that latent heat of condensation is very important for the total heat balance and the condensation rate is highly dependent on insulation between layers and outside temperature. Modelling results allow finding optimal geometrical parameters for the known gas flow and predicting the condensation rate for different system setups and seasons.

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

NASA Technical Reports Server (NTRS)

1987-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April, 1986 through September 30, 1986 is summarized.

Mathematical Storage-Battery Models

NASA Technical Reports Server (NTRS)

Chapman, C. P.; Aston, M.

1985-01-01

Empirical formula represents performance of electrical storage batteries. Formula covers many battery types and includes numerous coefficients adjusted to fit peculiarities of each type. Battery and load parameters taken into account include power density in battery, discharge time, and electrolyte temperature. Applications include electric-vehicle "fuel" gages and powerline load leveling.

Optimization of the Bridgman crystal growth process

NASA Astrophysics Data System (ADS)

Margulies, M.; Witomski, P.; Duffar, T.

2004-05-01

A numerical optimization method of the vertical Bridgman growth configuration is presented and developed. It permits to optimize the furnace temperature field and the pulling rate versus time in order to decrease the radial thermal gradients in the sample. Some constraints are also included in order to insure physically realistic results. The model includes the two classical non-linearities associated to crystal growth processes, the radiative thermal exchange and the release of latent heat at the solid-liquid interface. The mathematical analysis and development of the problem is shortly described. On some examples, it is shown that the method works in a satisfactory way; however the results are dependent on the numerical parameters. Improvements of the optimization model, on the physical and numerical point of view, are suggested.

Mr.CAS-A minimalistic (pure) Ruby CAS for fast prototyping and code generation

NASA Astrophysics Data System (ADS)

Ragni, Matteo

There are Computer Algebra System (CAS) systems on the market with complete solutions for manipulation of analytical models. But exporting a model that implements specific algorithms on specific platforms, for target languages or for particular numerical library, is often a rigid procedure that requires manual post-processing. This work presents a Ruby library that exposes core CAS capabilities, i.e. simplification, substitution, evaluation, etc. The library aims at programmers that need to rapidly prototype and generate numerical code for different target languages, while keeping separated mathematical expression from the code generation rules, where best practices for numerical conditioning are implemented. The library is written in pure Ruby language and is compatible with most Ruby interpreters.

Stability analysis and application of a mathematical cholera model.

PubMed

Liao, Shu; Wang, Jin

2011-07-01

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

USAF/SCEEE Summer Faculty Research Program (1982). Management Report.

DTIC Science & Technology

1982-10-01

Patrick J. Sweeney, Ph.D., P.E. Mary Doddy, M.S. ABSTRACT This dynamic simulation computer model demonstrates the affects of C-forces upon the eyeball...Assistant Professor Specialty: Numerical Modeling and University of Lowell Computer Simulation of Mathematics Department Geophysical Problems Lowell...Problems And Promises 25 Modeling And Tracking Saccadic Dr. John D. Enderle Eye Movements 26 Dynamic Response Of Doubly Curved Dr. Fernando E. Fagundo

Mathematical Fluid Dynamic Modeling of Plasma Stall-Spin Departure Control

DTIC Science & Technology

2007-04-01

filter (4), is appropriate for further CSN modeling of the vortical flow. The CNS solver reproduces symmetric and asymmetric vortex fields (Figure 11...calculations conducted for laminar flow showed that the CNS solver reproduces symmetric and asymmetric vortex fields and can be used for estimation of the...Galilean-invariant leeward vortex filter. The modified k-F EASM model was incorporated into our CSN solver. Parametric calculations showed that numerical

Study on seepage characteristics of inclined wall dam after heavy drought

NASA Astrophysics Data System (ADS)

Wei, YE; Fuheng, MA

2018-05-01

For seepage of the dam slope with cracks after drought, there are two methods to study including the physical model test and numerical calculation. However, the physical model test can not visualize the seepage field in the dam body intuitively, and the mathematical model is not accurate because of the precision of the parameter. So in this paper, combined physical model with mathematical model, the surface crack development on the dam slope and the changes of pore water pressure were studied through the physical model test, and then numerical calculation was carried out to analyze the internal seepage of the dam body. The results showed that cracks were more likely to develop at middle of the upstream dam slope and dam heel, and cracks for different degrees appeared at different parts of the dam slope after drought. The development of cracks provided a preferential permeable channel which caused that the area near the crack was easily to become saturated. The saturated zone kept expanding leading the infiltration line to be close to the transition layer and the infiltration line was no longer a smooth curve. There were seepage damages and landslide hazards existing with such seepage characteristics, which would threaten the safety of the dam.

Indicators of Arctic Sea Ice Bistability in Climate Model Simulations and Observations

DTIC Science & Technology

2014-09-30

ultimately developed a novel mathematical method to solve the system of equations involving the addition of a numerical “ ghost ” layer, as described in the...balance models ( EBMs ) and (ii) seasonally-varying single-column models (SCMs). As described in Approach item #1, we developed an idealized model that...includes both latitudinal and seasonal variations (Fig. 1). The model reduces to a standard EBM or SCM as limiting cases in the parameter space, thus

compuGUT: An in silico platform for simulating intestinal fermentation

NASA Astrophysics Data System (ADS)

Moorthy, Arun S.; Eberl, Hermann J.

The microbiota inhabiting the colon and its effect on health is a topic of significant interest. In this paper, we describe the compuGUT - a simulation tool developed to assist in exploring interactions between intestinal microbiota and their environment. The primary numerical machinery is implemented in C, and the accessory scripts for loading and visualization are prepared in bash (LINUX) and R. SUNDIALS libraries are employed for numerical integration, and googleVis API for interactive visualization. Supplementary material includes a concise description of the underlying mathematical model, and detailed characterization of numerical errors and computing times associated with implementation parameters.

Correlation between multispectral photography and near-surface turbidities

NASA Technical Reports Server (NTRS)

Wertz, D. L.; Mealor, W. T.; Steele, M. L.; Pinson, J. W.

1976-01-01

Four-band multispectral photography obtained from an aerial platform at an altitude of about 10,000 feet has been utilized to measure near-surface turbidity at numerous sampling sites in the Ross Barnett Reservoir, Mississippi. Correlation of the photographs with turbidity measurements has been accomplished via an empirical mathematical model which depends upon visual color recognition when the composited photographs are examined on either an I squared S model 600 or a Spectral Data model 65 color-additive viewer. The mathematical model was developed utilizing least-squares, iterative, and standard statistical methods and includes a time-dependent term related to sun angle. This model is consistent with information obtained from two overflights of the target area - July 30, 1973 and October 30, 1973 - and now is being evaluated with regard to information obtained from a third overflight on November 8, 1974.

Fluid Flow and Solidification Under Combined Action of Magnetic Fields and Microgravity

NASA Technical Reports Server (NTRS)

Li, B. Q.; Shu, Y.; Li, K.; deGroh, H. C.

2002-01-01

Mathematical models, both 2-D and 3-D, are developed to represent g-jitter induced fluid flows and their effects on solidification under combined action of magnetic fields and microgravity. The numerical model development is based on the finite element solution of governing equations describing the transient g-jitter driven fluid flows, heat transfer and solutal transport during crystal growth with and without an applied magnetic field in space vehicles. To validate the model predictions, a ground-based g-jitter simulator is developed using the oscillating wall temperatures where timely oscillating fluid flows are measured using a laser PIV system. The measurements are compared well with numerical results obtained from the numerical models. Results show that a combined action derived from magnetic damping and microgravity can be an effective means to control the melt flow and solutal transport in space single crystal growth systems.

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling.

PubMed

O'Dea, R D; King, J R

2013-06-01

Juxtacrine signalling mechanisms are known to be crucial in tissue and organ development, leading to spatial patterns in gene expression. We investigate the patterning behaviour of a discrete model of juxtacrine cell signalling due to Owen & Sherratt (1998, Mathematical modelling of juxtacrine cell signalling. Math. Biosci., 153, 125-150) in which ligand molecules, unoccupied receptors and bound ligand-receptor complexes are modelled. Feedback between the ligand and receptor production and the level of bound receptors is incorporated. By isolating two parameters associated with the feedback strength and employing numerical simulation, linear stability and bifurcation analysis, the pattern-forming behaviour of the model is analysed under regimes corresponding to lateral inhibition and induction. Linear analysis of this model fails to capture the patterning behaviour exhibited in numerical simulations. Via bifurcation analysis, we show that since the majority of periodic patterns fold subcritically from the homogeneous steady state, a wide variety of stable patterns exists at a given parameter set, providing an explanation for this failure. The dominant pattern is isolated via numerical simulation. Additionally, by sampling patterns of non-integer wavelength on a discrete mesh, we highlight a disparity between the continuous and discrete representations of signalling mechanisms: in the continuous case, patterns of arbitrary wavelength are possible, while sampling such patterns on a discrete mesh leads to longer wavelength harmonics being selected where the wavelength is rational; in the irrational case, the resulting aperiodic patterns exhibit 'local periodicity', being constructed from distorted stable shorter wavelength patterns. This feature is consistent with experimentally observed patterns, which typically display approximate short-range periodicity with defects.

Basic research for the geodynamics program

NASA Technical Reports Server (NTRS)

1991-01-01

The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.

The Sizing and Optimization Language, (SOL): Computer language for design problems

NASA Technical Reports Server (NTRS)

Lucas, Stephen H.; Scotti, Stephen J.

1988-01-01

The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

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

PubMed

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

2017-10-07

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

Research in applied mathematics, numerical analysis, and computer science

NASA Technical Reports Server (NTRS)

1984-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

NASA Technical Reports Server (NTRS)

1988-01-01

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988.

Summary of research in applied mathematics, numerical analysis and computer science at the Institute for Computer Applications in Science and Engineering

NASA Technical Reports Server (NTRS)

1984-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period October 1, 1983 through March 31, 1984 is summarized.

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

NASA Technical Reports Server (NTRS)

1987-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1986 through March 31, 1987 is summarized.

The normative structure of mathematization in systematic biology.

PubMed

Sterner, Beckett; Lidgard, Scott

2014-06-01

We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. Copyright © 2014. Published by Elsevier Ltd.

Handwritten mathematical symbols dataset.

PubMed

Chajri, Yassine; Bouikhalene, Belaid

2016-06-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc.

Numerical modeling for the retrofit of the hydraulic cooling subsystems in operating power plant

NASA Astrophysics Data System (ADS)

AlSaqoor, S.; Alahmer, A.; Al Quran, F.; Andruszkiewicz, A.; Kubas, K.; Regucki, P.; Wędrychowicz, W.

2017-08-01

This paper presents the possibility of using the numerical methods to analyze the work of hydraulic systems on the example of a cooling system of a power boiler auxiliary devices. The variety of conditions at which hydraulic system that operated in specific engineering subsystems requires an individualized approach to the model solutions that have been developed for these systems modernizing. A mathematical model of a series-parallel propagation for the cooling water was derived and iterative methods were used to solve the system of nonlinear equations. The results of numerical calculations made it possible to analyze different variants of a modernization of the studied system and to indicate its critical elements. An economic analysis of different options allows an investor to choose an optimal variant of a reconstruction of the installation.

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

NASA Technical Reports Server (NTRS)

Engquist, B. E. (Editor); Osher, S. (Editor); Somerville, R. C. J. (Editor)

1985-01-01

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

On the botanic model of plant growth with intermediate vegetative-reproductive stage.

PubMed

Ioslovich, Ilya; Gutman, Per-Olof

2005-11-01

The application of dynamic optimization to mathematical models of ontogenic biological growth has been the subject of much research [see e.g. . J. Theor. Biol. 33, 299-307]. Kozłowsky and Ziółko [1988. Thor. Popul. Biol. 34, 118-129] and Ziółko and Kozłowski [1995. IEEE Trans. Automat. Contr. 40(10), 1779-1783] presented a model with gradual transition from vegetative to reproductive growth. The central point of their model is a mixed state-control constraint on the rate of reproductive growth, which leads to a mixed vegetative-reproductive growth period. Their model is modified here in order to take into account the difference of photosynthesis use efficiency when energy is accumulated in the vegetative and in the reproductive organs of a plant, respectively. The simple assumption on correlation between photosynthesis and temperature permits us to modify the model in a form that is useful for changing climate. Unfortunately, the mathematical solution of the optimal control problem in Kozłowsky and Ziółko (1988) and Ziółko and Kozłowski (1995) is incorrect. The strict mathematical solution is presented here, the numerical example from is solved, and the results are compared. The influence of the length of the season and the relative photosynthesis use efficiency, as well as of the potential sink demand of the reproductive organs, on the location and duration of the mixed vegetative-reproduction period of growth is investigated numerically. The results show that the mixed growth period is increased and shifted toward the end of the season when the lengths of the season is increased. Additional details of the sensitivity analysis are also presented.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Objective biofidelity rating of a numerical human occupant model in frontal to lateral impact.

PubMed

de Lange, Ronald; van Rooij, Lex; Mooi, Herman; Wismans, Jac

2005-11-01

Both hardware crash dummies and mathematical human models have been developed largely using the same biomechanical data. For both, biofidelity is a main requirement. Since numerical modeling is not bound to hardware crash dummy design constraints, it allows more detailed modeling of the human and offering biofidelity for multiple directions. In this study the multi-directional biofidelity of the MADYMO human occupant model is assessed, to potentially protect occupants under various impact conditions. To evaluate the model's biofidelity, generally accepted requirements were used for frontal and lateral impact: tests proposed by EEVC and NHTSA and tests specified by ISO TR9790, respectively. A subset of the specified experiments was simulated with the human model. For lateral impact, the results were objectively rated according to the ISO protocol. Since no rating protocol was available for frontal impact, the ISO rating scheme for lateral was used for frontal, as far as possible. As a result, two scores show the overall model biofidelity for frontal and lateral impact, while individual ratings provide insight in the quality on body segment level. The results were compared with the results published for the THOR and WorldSID dummies, showing that the mathematical model exhibits a high level of multi-directional biofidelity. In addition, the performance of the human model in the NBDL 11G oblique test indicates a valid behavior of the model in intermediate directions as well. A new aspect of this study is the objective assessment of the multi-directional biofidelity of the mathematical human model according to accepted requirements. Although hardware dummies may always be used in regulations, it is expected that virtual testing with human models will serve in extrapolating outside the hardware test environment. This study was a first step towards simulating a wider range of impact conditions, such as angled impact and rollover.

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

ERIC Educational Resources Information Center

Powell, Sarah R.; Nelson, Gena

2017-01-01

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

On Theoretical Limits of Dynamic Model Updating Using a Sensitivity-Based Approach

NASA Astrophysics Data System (ADS)

GOLA, M. M.; SOMÀ, A.; BOTTO, D.

2001-07-01

The present work deals with the determination of the newly discovered conditions necessary for model updating with the eigensensitivity approach. The treatment concerns the maximum number of identifiable parameters regarding the structure of the eigenvectors derivatives. A mathematical demonstration is based on the evaluation of the rank of the least-squares matrix and produces the algebraic limiting conditions. Numerical application to a lumped parameter structure is employed to validate the mathematical limits taking into account different subsets of mode shapes. The demonstration is extended to the calculation of the eigenvector derivatives with both the Fox and Kapoor, and Nelson methods. III conditioning of the least-squares sensitivity matrix is revealed through the covariance jump.

Assessing the effect of extrinsic incubation period (EIP) prolongation in controlling dengue transmission with wolbachia-infected mosquito intervention

NASA Astrophysics Data System (ADS)

Putri, Y. E.; Rozi, S.; Tasman, H.; Aldila, D.

2017-03-01

A mathematical model of dengue disease transmission with involving Extrinsic Incubation Period (EIP) effect as a consequence of wolbachia introduction into mossquito population will be discussed in this article. Mathematical model analysis to find equilibrium points, basic reproductive ratio (ℛ0), and criteria of endemic occurrence which depend on some parameters were performed. From analytical result, we find that ℛ0 hold an important role to determine the existence and local stability of equilibrium points. From sensitivity analysis of ℛ0 and numerical simulation, we conclude that prolongation of EIP with wolbachia intervention succeed to reduce number of infected human and mosquito significantly.

Basic number processing in children with specific learning disorders: Comorbidity of reading and mathematics disorders.

PubMed

Moll, Kristina; Göbel, Silke M; Snowling, Margaret J

2015-01-01

As well as being the hallmark of mathematics disorders, deficits in number processing have also been reported for individuals with reading disorders. The aim of the present study was to investigate separately the components of numerical processing affected in reading and mathematical disorders within the framework of the Triple Code Model. Children with reading disorders (RD), mathematics disorders (MD), comorbid deficits (RD + MD), and typically developing children (TD) were tested on verbal, visual-verbal, and nonverbal number tasks. As expected, children with MD were impaired across a broad range of numerical tasks. In contrast, children with RD were impaired in (visual-)verbal number tasks but showed age-appropriate performance in nonverbal number skills, suggesting their impairments were domain specific and related to their reading difficulties. The comorbid group showed an additive profile of the impairments of the two single-deficit groups. Performance in speeded verbal number tasks was related to rapid automatized naming, a measure of visual-verbal access in the RD but not in the MD group. The results indicate that deficits in number skills are due to different underlying cognitive deficits in children with RD compared to children with MD: a phonological deficit in RD and a deficit in processing numerosities in MD.

Compression of magnetized target in the magneto-inertial fusion

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.

2017-12-01

This paper presents a mathematical model, numerical method and results of the computer analysis of the compression process and the energy transfer in the target plasma, used in magneto-inertial fusion. The computer simulation of the compression process of magnetized cylindrical target by high-power laser pulse is presented.

Cultural Horizons for Mathematics

ERIC Educational Resources Information Center

Owens, Kay; Paraides, Patricia; Nutti, Ylva Jannok; Johansson, Gunilla; Bennet, Maria; Doolan, Pat; Peckham, Ray; Hill, John; Doolan, Frank; O'Sullivan, Dominic; Murray, Libbey; Logan, Patricia; McNair, Melissa; Sunnari, Vappu; Murray, Beatrice; Miller, Alissa; Nolan, John; Simpson, Alca; Ohrin, Christine; Doolan, Terry; Doolan, Michelle; Taylor, Paul

2011-01-01

As a result of a number of government reports, there have been numerous systemic changes in Indigenous education in Australia revolving around the importance of partnerships with the community. A forum with our local Dubbo community established the importance of working together and developed a model which placed the child in an ecological…

Rotor-to-stator Partial Rubbing and Its Effects on Rotor Dynamic Response

NASA Technical Reports Server (NTRS)

Muszynska, Agnes; Franklin, Wesley D.; Hayashida, Robert D.

1991-01-01

Results from experimental and analytical studies on rotor to stationary element partial rubbings at several locations and their effects on rotor dynamic responses are presented. The mathematical model of a rubbing rotor is given. The computer program provides numerical results which agree with experimentally obtained rotor responses.

Simulation of aerosol flow interaction with a solid body on molecular level

NASA Astrophysics Data System (ADS)

Amelyushkin, Ivan A.; Stasenko, Albert L.

2018-05-01

Physico-mathematical models and numerical algorithm of two-phase flow interaction with a solid body are developed. Results of droplet motion and its impingement upon a rough surface in real gas boundary layer simulation on the molecular level obtained via molecular dynamics technique are presented.

Effect of section shape on frequencies of natural oscillations of tubular springs

NASA Astrophysics Data System (ADS)

Pirogov, S. P.; Chuba, A. Yu; Cherentsov, D. A.

2018-05-01

The necessity of determining the frequencies of natural oscillations of manometric tubular springs is substantiated. Based on the mathematical model and computer program, numerical experiments were performed that allowed us to reveal the effect of geometric parameters on the frequencies of free oscillations of manometric tubular springs.

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

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.

Numeracy and Communication with Patients: They Are Counting on Us

PubMed Central

Paasche-Orlow, Michael K.; Remillard, Janine T.; Bennett, Ian M.; Ben-Joseph, Elana Pearl; Batista, Rosanna M.; Hyde, James; Rudd, Rima E.

2008-01-01

Patient-centered interactive communication between physicians and patients is recommended to improve the quality of medical care. Numerical concepts are important components of such exchanges and include arithmetic and use of percentages, as well as higher level tasks like estimation, probability, problem-solving, and risk assessment - the basis of preventive medicine. Difficulty with numerical concepts may impede communication. The current evidence on prevalence, measurement, and outcomes related to numeracy is presented, along with a summary of best practices for communication of numerical information. This information is integrated into a hierarchical model of mathematical concepts and skills, which can guide clinicians toward numerical communication that is easier to use with patients. PMID:18830764

Modeling and simulation of different and representative engineering problems using Network Simulation Method

PubMed Central

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model. PMID:29518121

Numerical algebraic geometry for model selection and its application to the life sciences

PubMed Central

Gross, Elizabeth; Davis, Brent; Ho, Kenneth L.; Bates, Daniel J.

2016-01-01

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology. PMID:27733697

Modeling and simulation of different and representative engineering problems using Network Simulation Method.

PubMed

Sánchez-Pérez, J F; Marín, F; Morales, J L; Cánovas, M; Alhama, F

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model.

Summary of research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

NASA Technical Reports Server (NTRS)

1989-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1988 through March 31, 1989 is summarized.

Uncertainties in Engineering Design. Mathematical Theory and Numerical Experience.

DTIC Science & Technology

1985-08-01

Theoretical Mannual, Noetic Technologies Corpora- tion, St. Louis, Missouri, 1985. F :.5,. "V. .. " ,9.., 25 . - 5* 5 .° . . . . .. ,koA ’FIGURES...international center of study and research for foreign students in numerical mathematics who are supported by foreign govern- ments or exchange agencies

Reading Visual Representations

ERIC Educational Resources Information Center

Rubenstein, Rheta N.; Thompson, Denisse R.

2012-01-01

Mathematics is rich in visual representations. Such visual representations are the means by which mathematical patterns "are recorded and analyzed." With respect to "vocabulary" and "symbols," numerous educators have focused on issues inherent in the language of mathematics that influence students' success with mathematics communication.…

A Fractional PDE Approach to Turbulent Mixing; Part II: Numerical Simulation

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen

2016-11-01

We propose a generalizing fractional order transport model of advection-diffusion kind with fractional time- and space-derivatives, governing the evolution of passive scalar turbulence. This approach allows one to incorporate the nonlocal and memory effects in the underlying anomalous diffusion i.e., sub-to-standard diffusion to model the trapping of particles inside the eddied, and super-diffusion associated with the sudden jumps of particles from one coherent region to another. For this nonlocal model, we develop a high order numerical (spectral) method in addition to a fast solver, examined in the context of some canonical problems. PhD student, Department of Mechanical Engineering, & Department Computational Mathematics, Science, and Engineering.

Numerical Simulations of Plasma Based Flow Control Applications

NASA Technical Reports Server (NTRS)

Suzen, Y. B.; Huang, P. G.; Jacob, J. D.; Ashpis, D. E.

2005-01-01

A mathematical model was developed to simulate flow control applications using plasma actuators. The effects of the plasma actuators on the external flow are incorporated into Navier Stokes computations as a body force vector. In order to compute this body force vector, the model solves two additional equations: one for the electric field due to the applied AC voltage at the electrodes and the other for the charge density representing the ionized air. The model is calibrated against an experiment having plasma-driven flow in a quiescent environment and is then applied to simulate a low pressure turbine flow with large flow separation. The effects of the plasma actuator on control of flow separation are demonstrated numerically.

[Characteristics of Waves Generated Beneath the Solar Convection Zone by Penetrative Overshoot

NASA Technical Reports Server (NTRS)

Julien, Keith

2000-01-01

The goal of this project was to theoretically and numerically characterize the waves generated beneath the solar convection zone by penetrative overshoot. Three dimensional model simulations were designed to isolate the effects of rotation and shear. In order to overcome the numerically imposed limitations of finite Reynolds numbers (Re) below solar values, series of simulations were designed to elucidate the Reynolds-number dependence (hoped to exhibit mathematically simple scaling on Re) so that one could cautiously extrapolate to solar values.

Numerical Analysis of the Heat Transfer Characteristics within an Evaporating Meniscus

NASA Astrophysics Data System (ADS)

Ball, Gregory

A numerical analysis was performed as to investigate the heat transfer characteristics of an evaporating thin-film meniscus. A mathematical model was used in the formulation of a third order ordinary differential equation. This equation governs the evaporating thin-film through use of continuity, momentum, energy equations and the Kelvin-Clapeyron model. This governing equation was treated as an initial value problem and was solved numerically using a Runge-Kutta technique. The numerical model uses varying thermophysical properties and boundary conditions such as channel width, applied superheat, accommodation coefficient and working fluid which can be tailored by the user. This work focused mainly on the effects of altering accommodation coefficient and applied superheat. A unified solution is also presented which models the meniscus to half channel width. The model was validated through comparison to literature values. In varying input values the following was determined; increasing superheat was found to shorten the film thickness and greatly increase the interfacial curvature overshoot values. The effect of decreasing accommodation coefficient lengthened the thin-film and retarded the evaporative effects.

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

Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM.

PubMed

Agrillo, Christian; Piffer, Laura; Adriano, Andrea

2013-07-01

A significant debate surrounds the nature of the cognitive mechanisms involved in non-symbolic number estimation. Several studies have suggested the existence of the same cognitive system for estimation of time, space, and number, called "a theory of magnitude" (ATOM). In addition, researchers have proposed the theory that non-symbolic number abilities might support our mathematical skills. Despite the large number of studies carried out, no firm conclusions can be drawn on either topic. In the present study, we correlated the performance of adults on non-symbolic magnitude estimations and symbolic numerical tasks. Non-symbolic magnitude abilities were assessed by asking participants to estimate which auditory tone lasted longer (time), which line was longer (space), and which group of dots was more numerous (number). To assess symbolic numerical abilities, participants were required to perform mental calculations and mathematical reasoning. We found a positive correlation between non-symbolic and symbolic numerical abilities. On the other hand, no correlation was found among non-symbolic estimations of time, space, and number. Our study supports the idea that mathematical abilities rely on rudimentary numerical skills that predate verbal language. By contrast, the lack of correlation among non-symbolic estimations of time, space, and number is incompatible with the idea that these magnitudes are entirely processed by the same cognitive system.

Numerical study on turbulence modulation in gas-particle flows

NASA Astrophysics Data System (ADS)

Yan, F.; Lightstone, M. F.; Wood, P. E.

2007-01-01

A mathematical model is proposed based on the Eulerian/Lagrangian approach to account for both the particle crossing trajectory effect and the extra turbulence production due to particle wake effects. The resulting model, together with existing models from the literature, is applied to two different particle-laden flow configurations, namely a vertical pipe flow and axisymmetric downward jet flow. The results show that the proposed model is able to provide improved predictions of the experimental results.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

PubMed

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

PubMed Central

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

Physical and numerical modeling of hydrophysical proceses on the site of underwater pipelines

NASA Astrophysics Data System (ADS)

Garmakova, M. E.; Degtyarev, V. V.; Fedorova, N. N.; Shlychkov, V. A.

2018-03-01

The paper outlines issues related to ensuring the exploitation safety of underwater pipelines that are at risk of accidents. The performed research is based on physical and mathematical modeling of local bottom erosion in the area of pipeline location. The experimental studies were performed on the basis of the Hydraulics Laboratory of the Department of Hydraulic Engineering Construction, Safety and Ecology of NSUACE (Sibstrin). In the course of physical experiments it was revealed that the intensity of the bottom soil reforming depends on the deepening of the pipeline. The ANSYS software has been used for numerical modeling. The process of erosion of the sandy bottom was modeled under the pipeline. Comparison of computational results at various mass flow rates was made.

Hybrid reduced order modeling for assembly calculations

DOE PAGES

Bang, Youngsuk; Abdel-Khalik, Hany S.; Jessee, Matthew A.; ...

2015-08-14

While the accuracy of assembly calculations has greatly improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the usemore » of the reduced order modeling for a single physics code, such as a radiation transport calculation. This paper extends those works to coupled code systems as currently employed in assembly calculations. Finally, numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system.« less

Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution

NASA Astrophysics Data System (ADS)

Ahmadian, A.; Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.

2017-12-01

The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed.

Modeling of carbonate reservoir variable secondary pore space based on CT images

NASA Astrophysics Data System (ADS)

Nie, X.; Nie, S.; Zhang, J.; Zhang, C.; Zhang, Z.

2017-12-01

Digital core technology has brought convenience to us, and X-ray CT scanning is one of the most common way to obtain 3D digital cores. However, it can only provide the original information of the only samples being scanned, and we can't modify the porosity of the scanned cores. For numerical rock physical simulations, a series of cores with variable porosities are needed to determine the relationship between the physical properties and porosity. In carbonate rocks, the secondary pore space including dissolution pores, caves and natural fractures is the key reservoir space, which makes the study of carbonate secondary porosity very important. To achieve the variation of porosities in one rock sample, based on CT scanned digital cores, according to the physical and chemical properties of carbonate rocks, several mathematical methods are chosen to simulate the variation of secondary pore space. We use the erosion and dilation operations of mathematical morphology method to simulate the pore space changes of dissolution pores and caves. We also use the Fractional Brownian Motion model to generate natural fractures with different widths and angles in digital cores to simulate fractured carbonate rocks. The morphological opening-and-closing operations in mathematical morphology method are used to simulate distribution of fluid in the pore space. The established 3D digital core models with different secondary porosities and water saturation status can be used in the study of the physical property numerical simulations of carbonate reservoir rocks.

Preface to the special volume on the second Sandia Fracture Challenge

DOE PAGES

Kramer, Sharlotte Lorraine Bolyard; Boyce, Brad

2016-01-01

In this study, ductile failure of structural metals is a pervasive issue for applications such as automotive manufacturing, transportation infrastructures, munitions and armor, and energy generation. Experimental investigation of all relevant failure scenarios is intractable, requiring reliance on computation models. Our confidence in model predictions rests on unbiased assessments of the entire predictive capability, including the mathematical formulation, numerical implementation, calibration, and execution.

An Explicit Algorithm for the Simulation of Fluid Flow through Porous Media

NASA Astrophysics Data System (ADS)

Trapeznikova, Marina; Churbanova, Natalia; Lyupa, Anastasiya

2018-02-01

The work deals with the development of an original mathematical model of porous medium flow constructed by analogy with the quasigasdynamic system of equations and allowing implementation via explicit numerical methods. The model is generalized to the case of multiphase multicomponent fluid and takes into account possible heat sources. The proposed approach is verified by a number of test predictions.

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

Handwritten mathematical symbols dataset

PubMed Central

Chajri, Yassine; Bouikhalene, Belaid

2016-01-01

Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975

Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno's mathematical model

NASA Astrophysics Data System (ADS)

Wakif, Abderrahim; Boulahia, Zoubair; Mishra, S. R.; Mehdi Rashidi, Mohammad; Sehaqui, Rachid

2018-05-01

The onset of nanofluid convection in the presence of an externally applied magnetic field is investigated numerically based on the non-homogeneous Buongiorno's mathematical model. In this study, we use the latest experimental correlations and powerful analytical models for expressing the thermo-physical properties of some electrically conducting nanofluids, such as copper-water, sliver-water and gold-water nanofluids, in which the Brownian motion and thermophoresis effects on slip flow in nanofluids are taken into account in this model ( i.e., two-phase transport model). In this paper, we assume that the nanofluid has Newtonian behavior, confined horizontally between two infinite impermeable boundaries and heated from below, in such a way that the nanoparticles tend to concentrate near the upper wall. Considering the basic state of the nanofluidic system, the linear stability theory has been successfully applied to obtain the principal stability equations, which are solved numerically for an imposed volumetric fraction of nanoparticles and no-slip impermeable conditions at the isothermal walls bounding the nanofluid layer. The linear boundary-value problem obtained in this investigation is converted into a pure initial-value problem, so that we can solve it numerically by the fourth-fifth-order Runge-Kutta-Fehlberg method. The generalized Buongiorno's mathematical model proposed in this study allows performing a highly accurate computational analysis. In addition, the obtained results show that the stability of the studied nanofluidic system depends on several parameters, namely, the magnetic Chandrasekhar number Q , the reference value for the volumetric fraction of nanoparticles φ_0 and the size of nanoparticles d_p . In this analysis, the thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical thermal Rayleigh number R_{ac} , which characterizes the onset of convection cells, whose size is L_c=2π/a_c . Furthermore, the effects of various pertinent parameters on the critical stability parameters R_{ac} and a_c are discussed in more detail through graphical and tabular illustrations, for three types of nanofluids including copper-water, sliver-water, and gold-water.

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

NASA Technical Reports Server (NTRS)

Young, Gerald W.; Clemons, Curtis B.

2004-01-01

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

CFD Modelling Applied to the Co-Combustion of Paper Sludge and Coal in a 130 t/h CFB Boiler

NASA Astrophysics Data System (ADS)

Yu, Z. S.; Ma, X. Q.; Lai, Z. Y.; Xiao, H. M.

Three-dimensional mathematical model has been developed as a tool for co-combustion of paper sludge and coal in a 130 tJh Circulating Fluidized Bed (CFB) boiler. Mathematical methods had been used based on a commercial software FLUENT for combustion. The predicted results of CFB furnace show that the co-combustion of paper sludge/coal is initially intensively at the bottom of bed; the temperature reaches its maximum in the dense-phase zone, around l400K. It indicates that paper sludge spout into furnace from the recycle inlet can increase the furnace maximum temperature (l396.3K), area-weighted average temperature (l109.6K) and the furnace gas outlet area-weighted average temperature(996.8K).The mathematical modeling also predicts that 15 mass% paper sludge co-combustion is the highest temperature at the flue gas outlet, it is 1000.8K. Moreover, it is proved that mathematical models can serve as a tool for detailed analysis of co-combustion of paper sludge and coal processes in a circulating fluidized bed furnace when in view of its convenience. The results gained from numerical simulation show that paper sludge enter into furnace from the recycle inlet excelled than mixing with coal and at the underside of phase interface.

EOQ model for perishable products with price-dependent demand, pre and post discounted selling price

NASA Astrophysics Data System (ADS)

Santhi, G.; Karthikeyan, K.

2017-11-01

In this article we introduce an economic order quantity model for perishable products like vegetables, fruits, milk, flowers, meat, etc.,with price-dependent demand, pre and post discounted selling price. Here we consider the demand is depending on selling price and deterioration rate is constant. Here we developed mathematical model to determine optimal discounton the unit selling price to maximize total profit. Numerical examples are given for illustrated.

Error enhancement in geomagnetic models derived from scalar data

NASA Technical Reports Server (NTRS)

Stern, D. P.; Bredekamp, J. H.

1975-01-01

An investigation conducted by Backus (1970) regarding the possible existence of two harmonic functions of certain characteristics in three-dimensional space is considered. The derivation of a model of the main geomagnetic field from scalar data is discussed along with a numerical simulation study. It is found that experimental discrepancies between vector field observations and the predictions of the model may have a mathematical origin, related to the work of Backus.

Design of a Field Test for Probability of Hit by Antiaircraft Guns

DTIC Science & Technology

1973-02-01

not available. • The cost of conducting the numerous field test trials that would be needed to establish the loss rates of aircraft to antiaircraft...mathematical models provide a readily available and relatively inexpensive way to obtain estimates of aircraft losses to antiaircraft guns. Because these...aircraft losses to antiaircraft guns, the use of the models can contribute greatly to better decisions. But if the models produce invalid estimates

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

Bastian, Mark; Trigueros, Jose V.

Phoenix is a Java Virtual Machine (JVM) based library for performing mathematical and astrodynamics calculations. It consists of two primary sub-modules, phoenix-math and phoenix-astrodynamics. The mathematics package has a variety of mathematical classes for performing 3D transformations, geometric reasoning, and numerical analysis. The astrodynamics package has various classes and methods for computing locations, attitudes, accesses, and other values useful for general satellite modeling and simulation. Methods for computing celestial locations, such as the location of the Sun and Moon, are also included. Phoenix is meant to be used as a library within the context of a larger application. For example,more » it could be used for a web service, desktop client, or to compute simple values in a scripting environment.« less

A numerical study of the effects of bell pulsation dynamics and oral arms on the exchange currents generated by the upside-down jellyfish Cassiopea xamachana.

PubMed

Hamlet, Christina; Santhanakrishnan, Arvind; Miller, Laura A

2011-06-01

Mathematical and experimental studies of the flows generated by jellyfish have focused primarily on mechanisms of swimming. More recent work has also considered the fluid dynamics of feeding from currents generated during swimming. Here we capitalize on the benthic lifestyle of the upside-down jellyfish (Cassiopea xamachana) to explore the fluid dynamics of feeding uncoupled from swimming. A two-dimensional mathematical model is developed to capture the fundamental characteristics of the motion of the unique concave bell shape. Given the prominence of the oral arms, this structure is included and modeled as a porous layer that perturbs the flow generated by bell contractions. The immersed boundary method is used to solve the fluid-structure interaction problem. Velocity fields obtained from live organisms using digital particle image velocimetry were used to validate the numerical simulations. Parameter sweeps were used to numerically explore the effects of changes in pulse dynamics and the properties of the oral arms independently. Numerical experiments allow the opportunity to examine physical effects and limits within and beyond the biologically relevant range to develop a better understanding of the system. The presence of the prominent oral arm structures in the field of flow increased the flux of new fluid from along the substrate to the bell. The numerical simulations also showed that the presence of pauses between bell expansion and the next contraction alters the flow of the fluid over the bell and through the oral arms.

Intergenerational Associations in Numerical Approximation and Mathematical Abilities

ERIC Educational Resources Information Center

Braham, Emily J.; Libertus, Melissa E.

2017-01-01

Although growing evidence suggests a link between children's math skills and their ability to estimate numerical quantities using the approximate number system (ANS), little is known about the sources underlying individual differences in ANS acuity and their relation with specific mathematical skills. To examine the role of intergenerational…

Current research activities: Applied and numerical mathematics, fluid mechanics, experiments in transition and turbulence and aerodynamics, and computer science

NASA Technical Reports Server (NTRS)

1992-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, fluid mechanics including fluid dynamics, acoustics, and combustion, aerodynamics, and computer science during the period 1 Apr. 1992 - 30 Sep. 1992 is summarized.

A hybrid model for traffic flow and crowd dynamics with random individual properties.

PubMed

Schleper, Veronika

2015-04-01

Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.

Mathematical modeling of the Stirling engine in terms of applying the composition of the power complex containing non-conventional and renewable energy

NASA Astrophysics Data System (ADS)

Gaponenko, A. M.; Kagramanova, A. A.

2017-11-01

The opportunity of application of Stirling engine with non-conventional and renewable sources of energy. The advantage of such use. The resulting expression for the thermal efficiency of the Stirling engine. It is shown that the work per cycle is proportional to the quantity of matter, and hence the pressure of the working fluid, the temperature difference and, to a lesser extent, depends on the expansion coefficient; efficiency of ideal Stirling cycle coincides with the efficiency of an ideal engine working on the Carnot cycle, which distinguishes a Stirling cycle from the cycles of Otto and Diesel underlying engine. It has been established that the four input parameters, the only parameter which can be easily changed during operation, and which effectively affects the operation of the engine is the phase difference. Dependence of work per cycle of the phase difference, called the phase characteristic, visually illustrates mode of operation of Stirling engine. The mathematical model of the cycle of Schmidt and the analysis of operation of Stirling engine in the approach of Schmidt with the aid of numerical analysis. To conduct numerical experiments designed program feature in the language MathLab. The results of numerical experiments are illustrated by graphical charts.

Nonlinear analysis of a model of vascular tumour growth and treatment

NASA Astrophysics Data System (ADS)

Tao, Youshan; Yoshida, Norio; Guo, Qian

2004-05-01

We consider a mathematical model describing the evolution of a vascular tumour in response to traditional chemotherapy. The model is a free boundary problem for a system of partial differential equations governing intratumoural drug concentration, cancer cell density and blood vessel density. Tumour cells consist of two types of competitive cells that have different proliferation rates and different sensitivities to drugs. The balance between cell proliferation and death generates a velocity field that drives tumour cell movement. The tumour surface is a moving boundary. The purpose of this paper is to establish a rigorous mathematical analysis of the model for studying the dynamics of intratumoural blood vessels and to explore drug dosage for the successful treatment of a tumour. We also study numerically the competitive effects of the two cell types on tumour growth.

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

PubMed

Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

2011-08-01

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

Incorporating neurophysiological concepts in mathematical thermoregulation models

NASA Astrophysics Data System (ADS)

Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.

2014-01-01

Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.

Data mining techniques for scientific computing: Application to asymptotic paraxial approximations to model ultrarelativistic particles

NASA Astrophysics Data System (ADS)

Assous, Franck; Chaskalovic, Joël

2011-06-01

We propose a new approach that consists in using data mining techniques for scientific computing. Indeed, data mining has proved to be efficient in other contexts which deal with huge data like in biology, medicine, marketing, advertising and communications. Our aim, here, is to deal with the important problem of the exploitation of the results produced by any numerical method. Indeed, more and more data are created today by numerical simulations. Thus, it seems necessary to look at efficient tools to analyze them. In this work, we focus our presentation to a test case dedicated to an asymptotic paraxial approximation to model ultrarelativistic particles. Our method directly deals with numerical results of simulations and try to understand what each order of the asymptotic expansion brings to the simulation results over what could be obtained by other lower-order or less accurate means. This new heuristic approach offers new potential applications to treat numerical solutions to mathematical models.

Numerical simulation of the baking of porous anode carbon in a vertical flue ring furnace

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

Jacobsen, M.; Melaaen, M.C.

The interaction of pitch pyrolysis in porous anode carbon during heating and volatiles combustion in the flue gas channel has been analyzed to gain insight in the anode baking process. A two-dimensional geometry of a flue gas channel adjacent to a porous flue gas wall, packing coke, and an anode was used for studying the effect of heating rate on temperature gradients and internal gas pressure in the anodes. The mathematical model included porous heat and mass transfer, pitch pyrolysis, combustion of volatiles, radiation, and turbulent channel flow. The mathematical model was developed through source code modification of the computationalmore » fluid dynamics code FLUENT. The model was useful for studying the effects of heating rate, geometry, and anode properties.« less

Supporting Clear and Concise Mathematics Language: Say This, Not That

ERIC Educational Resources Information Center

Hughes, Elizabeth M.; Powell, Sarah R.; Stevens, Elizabeth A.

2016-01-01

One influence contributing to this trend may be the imprecise use of mathematics language. Educators may not interpret mathematics as a second (or third) language for children, when, in fact, all children are mathematical-language learners (Barrow, 2014). The numerals, symbols, and terms that explain mathematics concepts and procedures are…

Pathway Model of the Kinetics of the TGFbeta Antagonist Smad7 and Cross-Talk with the ATM and WNT Pathways

NASA Technical Reports Server (NTRS)

Carra, Claudio; Wang, Minli; Huff, Janice L.; Hada, Megumi; ONeill, Peter; Cucinotta, Francis A.

2010-01-01

Signal transduction controls cellular and tissue responses to radiation. Transforming growth factor beta (TGFbeta) is an important regulator of cell growth and differentiation and tissue homeostasis, and is often dis-regulated in tumor formation. Mathematical models of signal transduction pathways can be used to elucidate how signal transduction varies with radiation quality, and dose and dose-rate. Furthermore, modeling of tissue specific responses can be considered through mechanistic based modeling. We developed a mathematical model of the negative feedback regulation by Smad7 in TGFbeta-Smad signaling and are exploring possible connections to the WNT/beta -catenin, and ATM/ATF2 signaling pathways. A pathway model of TGFbeta-Smad signaling that includes Smad7 kinetics based on data in the scientific literature is described. Kinetic terms included are TGFbeta/Smad transcriptional regulation of Smad7 through the Smad3-Smad4 complex, Smad7-Smurf1 translocation from nucleus to cytoplasm, and Smad7 negative feedback regulation of the TGFO receptor through direct binding to the TGFO receptor complex. The negative feedback controls operating in this pathway suggests non-linear responses in signal transduction, which are described mathematically. We then explored possibilities for cross-talk mediated by Smad7 between DNA damage responses mediated by ATM, and with the WNT pathway and consider the design of experiments to test model driven hypothesis. Numerical comparisons of the mathematical model to experiments and representative predictions are described.

Numerical simulation of the actuation system for the ALDF's propulsion control valve. [Aircraft Landing Dynamics Facility

NASA Technical Reports Server (NTRS)

Korte, John J.

1990-01-01

A numerical simulation of the actuation system for the propulsion control valve (PCV) of the NASA Langley Aircraft Landing Dynamics Facility was developed during the preliminary design of the PCV and used throughout the entire project. The simulation is based on a predictive model of the PCV which is used to evaluate and design the actuation system. The PCV controls a 1.7 million-pound thrust water jet used in propelling a 108,000-pound test carriage. The PCV can open and close in 0.300 second and deliver over 9,000 gallons of water per sec at pressures up to 3150 psi. The numerical simulation results are used to predict transient performance and valve opening characteristics, specify the hydraulic control system, define transient loadings on components, and evaluate failure modes. The mathematical model used for numerically simulating the mechanical fluid power system is described, and numerical results are demonstrated for a typical opening and closing cycle of the PCV. A summary is then given on how the model is used in the design process.

Cellular automata-based modelling and simulation of biofilm structure on multi-core computers.

PubMed

Skoneczny, Szymon

2015-01-01

The article presents a mathematical model of biofilm growth for aerobic biodegradation of a toxic carbonaceous substrate. Modelling of biofilm growth has fundamental significance in numerous processes of biotechnology and mathematical modelling of bioreactors. The process following double-substrate kinetics with substrate inhibition proceeding in a biofilm has not been modelled so far by means of cellular automata. Each process in the model proposed, i.e. diffusion of substrates, uptake of substrates, growth and decay of microorganisms and biofilm detachment, is simulated in a discrete manner. It was shown that for flat biofilm of constant thickness, the results of the presented model agree with those of a continuous model. The primary outcome of the study was to propose a mathematical model of biofilm growth; however a considerable amount of focus was also placed on the development of efficient algorithms for its solution. Two parallel algorithms were created, differing in the way computations are distributed. Computer programs were created using OpenMP Application Programming Interface for C++ programming language. Simulations of biofilm growth were performed on three high-performance computers. Speed-up coefficients of computer programs were compared. Both algorithms enabled a significant reduction of computation time. It is important, inter alia, in modelling and simulation of bioreactor dynamics.

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970–2010

PubMed Central

Reiner, Robert C.; Perkins, T. Alex; Barker, Christopher M.; Niu, Tianchan; Chaves, Luis Fernando; Ellis, Alicia M.; George, Dylan B.; Le Menach, Arnaud; Pulliam, Juliet R. C.; Bisanzio, Donal; Buckee, Caroline; Chiyaka, Christinah; Cummings, Derek A. T.; Garcia, Andres J.; Gatton, Michelle L.; Gething, Peter W.; Hartley, David M.; Johnston, Geoffrey; Klein, Eili Y.; Michael, Edwin; Lindsay, Steven W.; Lloyd, Alun L.; Pigott, David M.; Reisen, William K.; Ruktanonchai, Nick; Singh, Brajendra K.; Tatem, Andrew J.; Kitron, Uriel; Hay, Simon I.; Scott, Thomas W.; Smith, David L.

2013-01-01

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process. PMID:23407571

System equivalent model mixing

NASA Astrophysics Data System (ADS)

Klaassen, Steven W. B.; van der Seijs, Maarten V.; de Klerk, Dennis

2018-05-01

This paper introduces SEMM: a method based on Frequency Based Substructuring (FBS) techniques that enables the construction of hybrid dynamic models. With System Equivalent Model Mixing (SEMM) frequency based models, either of numerical or experimental nature, can be mixed to form a hybrid model. This model follows the dynamic behaviour of a predefined weighted master model. A large variety of applications can be thought of, such as the DoF-space expansion of relatively small experimental models using numerical models, or the blending of different models in the frequency spectrum. SEMM is outlined, both mathematically and conceptually, based on a notation commonly used in FBS. A critical physical interpretation of the theory is provided next, along with a comparison to similar techniques; namely DoF expansion techniques. SEMM's concept is further illustrated by means of a numerical example. It will become apparent that the basic method of SEMM has some shortcomings which warrant a few extensions to the method. One of the main applications is tested in a practical case, performed on a validated benchmark structure; it will emphasize the practicality of the method.

Detonation onset following shock wave focusing

NASA Astrophysics Data System (ADS)

Smirnov, N. N.; Penyazkov, O. G.; Sevrouk, K. L.; Nikitin, V. F.; Stamov, L. I.; Tyurenkova, V. V.

2017-06-01

The aim of the present paper is to study detonation initiation due to focusing of a shock wave reflected inside a cone. Both numerical and experimental investigations were conducted. Comparison of results made it possible to validate the developed 3-d transient mathematical model of chemically reacting gas mixture flows incorporating hydrogen - air mixtures. The results of theoretical and numerical experiments made it possible improving kinetic schemes and turbulence models. Several different flow scenarios were detected in reflection of shock waves all being dependent on incident shock wave intensity: reflecting of shock wave with lagging behind combustion zone, formation of detonation wave in reflection and focusing, and intermediate transient regimes.

Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

NASA Astrophysics Data System (ADS)

Pikulin, S. V.

2018-02-01

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.

Numerical simulation of fluid flow through simplified blade cascade with prescribed harmonic motion using discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Vimmr, Jan; Bublík, Ondřej; Prausová, Helena; Hála, Jindřich; Pešek, Luděk

2018-06-01

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Mathematical modeling of a multi-product EMQ model with an enhanced end items issuing policy and failures in rework.

PubMed

Chiu, Yuan-Shyi Peter; Sung, Peng-Cheng; Chiu, Singa Wang; Chou, Chung-Li

2015-01-01

This study uses mathematical modeling to examine a multi-product economic manufacturing quantity (EMQ) model with an enhanced end items issuing policy and rework failures. We assume that a multi-product EMQ model randomly generates nonconforming items. All of the defective are reworked, but a certain portion fails and becomes scraps. When rework process ends and the entire lot of each product is quality assured, a cost reduction n + 1 end items issuing policy is used to transport finished items of each product. As a result, a closed-form optimal production cycle time is obtained. A numerical example demonstrates the practical usage of our result and confirms a significant savings in stock holding and overall production costs as compared to that of a prior work (Chiu et al. in J Sci Ind Res India, 72:435-440 2013) in the literature.

Mathematical modeling of the integrated process of mercury bioremediation in the industrial bioreactor.

PubMed

Głuszcz, Paweł; Petera, Jerzy; Ledakowicz, Stanisław

2011-03-01

The mathematical model of the integrated process of mercury contaminated wastewater bioremediation in a fixed-bed industrial bioreactor is presented. An activated carbon packing in the bioreactor plays the role of an adsorbent for ionic mercury and at the same time of a carrier material for immobilization of mercury-reducing bacteria. The model includes three basic stages of the bioremediation process: mass transfer in the liquid phase, adsorption of mercury onto activated carbon and ionic mercury bioreduction to Hg(0) by immobilized microorganisms. Model calculations were verified using experimental data obtained during the process of industrial wastewater bioremediation in the bioreactor of 1 m³ volume. It was found that the presented model reflects the properties of the real system quite well. Numerical simulation of the bioremediation process confirmed the experimentally observed positive effect of the integration of ionic mercury adsorption and bioreduction in one apparatus.

Analysis of geologic terrain models for determination of optimum SAR sensor configuration and optimum information extraction for exploration of global non-renewable resources. Pilot study: Arkansas Remote Sensing Laboratory, part 1, part 2, and part 3

NASA Technical Reports Server (NTRS)

Kaupp, V. H.; Macdonald, H. C.; Waite, W. P.; Stiles, J. A.; Frost, F. S.; Shanmugam, K. S.; Smith, S. A.; Narayanan, V.; Holtzman, J. C. (Principal Investigator)

1982-01-01

Computer-generated radar simulations and mathematical geologic terrain models were used to establish the optimum radar sensor operating parameters for geologic research. An initial set of mathematical geologic terrain models was created for three basic landforms and families of simulated radar images were prepared from these models for numerous interacting sensor, platform, and terrain variables. The tradeoffs between the various sensor parameters and the quantity and quality of the extractable geologic data were investigated as well as the development of automated techniques of digital SAR image analysis. Initial work on a texture analysis of SEASAT SAR imagery is reported. Computer-generated radar simulations are shown for combinations of two geologic models and three SAR angles of incidence.

Impulsive control of a continuous-culture and flocculation harvest chemostat model

NASA Astrophysics Data System (ADS)

Zhang, Tongqian; Ma, Wanbiao; Meng, Xinzhu

2017-12-01

In this paper, a new mathematical model describing the process of continuous culture and harvest of microalgaes is proposed. By inputting medium and flocculant at two different fixed moments periodically, continuous culture and harvest of microalgaes is implemented. The mathematical analysis is conducted and the whole dynamics of model is investigated by using theory of impulsive differential equations. We find that the model has a microalgaes-extinction periodic solution and it is globally asymptotically stable when some certain threshold value is less than the unit. And the model is permanent when some certain threshold value is larger than the unit. Then, according to the threshold, the control strategies of continuous culture and harvest of microalgaes are discussed. The results show that continuous culture and harvest of microalgaes can be archived by adjusting suitable input time, input amount of medium or flocculant. Finally, some numerical simulations are carried out to verify the control strategy.

The measurement of enhancement in mathematical abilities as a result of joint cognitive trainings in numerical and visual- spatial skills: A preliminary study

NASA Astrophysics Data System (ADS)

Agus, M.; Mascia, M. L.; Fastame, M. C.; Melis, V.; Pilloni, M. C.; Penna, M. P.

2015-02-01

A body of literature shows the significant role of visual-spatial skills played in the improvement of mathematical skills in the primary school. The main goal of the current study was to investigate the impact of a combined visuo-spatial and mathematical training on the improvement of mathematical skills in 146 second graders of several schools located in Italy. Participants were presented single pencil-and-paper visuo-spatial or mathematical trainings, computerised version of the above mentioned treatments, as well as a combined version of computer-assisted and pencil-and-paper visuo-spatial and mathematical trainings, respectively. Experimental groups were presented with training for 3 months, once a week. All children were treated collectively both in computer-assisted or pencil-and-paper modalities. At pre and post-test all our participants were presented with a battery of objective tests assessing numerical and visuo-spatial abilities. Our results suggest the positive effect of different types of training for the empowerment of visuo-spatial and numerical abilities. Specifically, the combination of computerised and pencil-and-paper versions of visuo-spatial and mathematical trainings are more effective than the single execution of the software or of the pencil-and-paper treatment.

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2018-03-01

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.

Simulation of friction stir drilling process

NASA Astrophysics Data System (ADS)

Vijayabaskar, P.; Hynes, N. Rajesh Jesudoss

2018-05-01

The project is the study of the thermal drilling process. The process is a hole forming process in the sheet metals using the heat generated by means of friction. The main advantage of the process over the conventional drilling process is that the holes formed using this process does not need any backing arrangements such as weld nuts, rivet nuts etc. Because the extruded bush itself acts as a supporting structure for the fasteners. This eliminates the need for the access to the backside of the work material for fastening operations. The major factors contributing the thermal drilling operation are the spindle speed and the thrust force required for forming a hole. The process of finding out the suitable thrust force and the speed for drilling a particular material with particular thickness is a tedious process. The process can be simplified by forming a mathematical model by combining the empirical formulae from the literature. These formulae were derived in the literature from the experimental trials by following certain assumptions. In this paper a suitable mathematical model is formed by replicating the experiments and tried to be validated by the results from numerical analysis. The numerical analysis of the model is done using the ANSYS software.

Spatial transformation abilities and their relation to later mathematics performance.

PubMed

Frick, Andrea

2018-04-10

Using a longitudinal approach, this study investigated the relational structure of different spatial transformation skills at kindergarten age, and how these spatial skills relate to children's later mathematics performance. Children were tested at three time points, in kindergarten, first grade, and second grade (N = 119). Exploratory factor analyses revealed two subcomponents of spatial transformation skills: one representing egocentric transformations (mental rotation and spatial scaling), and one representing allocentric transformations (e.g., cross-sectioning, perspective taking). Structural equation modeling suggested that egocentric transformation skills showed their strongest relation to the part of the mathematics test tapping arithmetic operations, whereas allocentric transformations were strongly related to Numeric-Logical and Spatial Functions as well as geometry. The present findings point to a tight connection between early mental transformation skills, particularly the ones requiring a high level of spatial flexibility and a strong sense for spatial magnitudes, and children's mathematics performance at the beginning of their school career.

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

PubMed Central

Käser, Tanja; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; Richtmann, Verena; Grond, Ursina; Gross, Markus; von Aster, Michael

2013-01-01

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child's individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities. PMID:23935586

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

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

M. A. Wasiolek

The purpose of this report is to document the biosphere model, the Environmental Radiation Model for Yucca Mountain, Nevada (ERMYN), which describes radionuclide transport processes in the biosphere and associated human exposure that may arise as the result of radionuclide release from the geologic repository at Yucca Mountain. The biosphere model is one of the process models that support the Yucca Mountain Project (YMP) Total System Performance Assessment (TSPA) for the license application (LA), the TSPA-LA. The ERMYN model provides the capability of performing human radiation dose assessments. This report documents the biosphere model, which includes: (1) Describing the referencemore » biosphere, human receptor, exposure scenarios, and primary radionuclides for each exposure scenario (Section 6.1); (2) Developing a biosphere conceptual model using site-specific features, events, and processes (FEPs), the reference biosphere, the human receptor, and assumptions (Section 6.2 and Section 6.3); (3) Building a mathematical model using the biosphere conceptual model and published biosphere models (Sections 6.4 and 6.5); (4) Summarizing input parameters for the mathematical model, including the uncertainty associated with input values (Section 6.6); (5) Identifying improvements in the ERMYN model compared with the model used in previous biosphere modeling (Section 6.7); (6) Constructing an ERMYN implementation tool (model) based on the biosphere mathematical model using GoldSim stochastic simulation software (Sections 6.8 and 6.9); (7) Verifying the ERMYN model by comparing output from the software with hand calculations to ensure that the GoldSim implementation is correct (Section 6.10); and (8) Validating the ERMYN model by corroborating it with published biosphere models; comparing conceptual models, mathematical models, and numerical results (Section 7).« less

A mathematical model of physiological processes and its application to the study of aging

NASA Technical Reports Server (NTRS)

Hibbs, A. R.; Walford, R. L.

1989-01-01

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Comparison of using different bridge prosthetic designs for partial defect restoration through mathematical modeling.

PubMed

Styranivska, Oksana; Kliuchkovska, Nataliia; Mykyyevych, Nataliya

2017-01-01

To analyze the stress-strain states of bone and abutment teeth during the use of different prosthetic designs of fixed partial dentures with the use of relevant mathematical modeling principles. The use of Comsol Multiphysics 3.5 (Comsol AB, Sweden) software during the mathematical modeling of stress-strain states provided numerical data for analytical interpretation in three different clinical scenarios with fixed dentures and different abutment teeth and demountable prosthetic denture with the saddle-shaped intermediate part. Microsoft Excel Software (Microsoft Office 2017) helped to evaluate absolute mistakes of stress and strain parameters of each abutment tooth during three modeled scenarios and normal condition and to summarize data into the forms of tables. In comparison with the fixed prosthetic denture supported by the canine, first premolar, and third molar, stresses at the same abutment teeth with the use of demountable denture with the saddle-shaped intermediate part decreased: at the mesial abutment tooth by 2.8 times, at distal crown by 6.1 times, and at the intermediate part by 11.1 times, respectively, the deformation level decreased by 3.1, 1.9, and 1.4 times at each area. The methods of mathematical modeling proved that complications during the use of fixed partial dentures based on the overload effect of the abutment teeth and caused by the deformation process inside the intermediate section of prosthetic construction.

Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface

NASA Astrophysics Data System (ADS)

Bibi, Madiha; Khalil-Ur-Rehman; Malik, M. Y.; Tahir, M.

2018-04-01

In the present article, unsteady flow field characteristics of the Williamson fluid model are explored. The nanosized particles are suspended in the flow regime having the interaction of a magnetic field. The fluid flow is induced due to a stretching permeable surface. The flow model is controlled through coupled partial differential equations to the used shooting method for a numerical solution. The obtained partial differential equations are converted into ordinary differential equations as an initial value problem. The shooting method is used to find a numerical solution. The mathematical modeling yields physical parameters, namely the Weissenberg number, the Prandtl number, the unsteadiness parameter, the magnetic parameter, the mass transfer parameter, the Lewis number, the thermophoresis parameter and Brownian parameters. It is found that the Williamson fluid velocity, temperature and nanoparticles concentration are a decreasing function of the unsteadiness parameter.